🔒 Closed Arduino #4

[Kulantoy]

swing servo motor back and forth when detected a sound by sound sensor or a rain sensor has detected and stop when thiers no detected

 

[Kulantoy]

I apologize for the mistake in my previous response. Here's the corrected code:

c++
#include <Wire.h>
#include <RTClib.h> // include the RTClib library
#include <LiquidCrystal.h> // include the LiquidCrystal library

RTC_DS3231 rtc; // initialize the RTC object
LiquidCrystal lcd(12, 11, 5, 4, 3, 2); // initialize the LCD object

void setup() {
  // initialize the serial communication
  Serial.begin(9600);
 
  // initialize the LCD
  lcd.begin(16, 2);
  lcd.print("RTC Test");
 
  // initialize the I2C communication
  Wire.begin();
 
  // initialize the RTC
  rtc.begin();
 
  // set the RTC time to the current time if not set
  if (! rtc.isrunning()) {
    Serial.println("RTC is NOT running, setting time...");
    rtc.adjust(DateTime(F(__DATE__), F(__TIME__)));
  }
}

void loop() {
  // get the current time from the RTC
  DateTime now = rtc.now();
 
  // display the time on the LCD
  lcd.setCursor(0, 1);
  lcd.print(now.hour(), DEC);
  lcd.print(":");
  lcd.print(now.minute(), DEC);
  lcd.print(":");
  lcd.print(now.second(), DEC);
 
  // send the time to the serial monitor
  Serial.print(now.hour(), DEC);
  Serial.print(":");
  Serial.print(now.minute(), DEC);
  Serial.print(":");
  Serial.println(now.second(), DEC);
 
  delay(1000); // wait for 1 second
}

The error was caused by the incorrect usage of the isrunning() function. The correct usage should be if (! rtc.isrunning()) instead of if (! rtc.initialized()).

Note that you need to install the RTClib library for this code to work. You can download it from the Arduino Library Manager or from the GitHub repository (You do not have permission to view the full content of this post. Log in or register now.). Also, make sure you have connected the RTC module to the correct pins of the Arduino Nano and the 16x2 LCD.

error: 'class RTC_DS3231' has no member named 'isrunning'
if (! rtc.isrunning()) {

 

[Kulantoy]

1.) A certain luxury ship cruses Cebu to Manila at 21 knots. If it will take 21 hours to reach Manila from Cebu, the distance travel by the ship is nearly
a. 847.5 km
b. 507.15 statute mile
c. 441 statute mile
d. 414 nautical mile
2.)8cm x 5mm x 2m
a. 8 x 10-2
b. 8 x 102
c. 8 x 10-3
d. 8 x 104
3.) Which of the following is equivalent to 1 hectare?
a. 100 ares
b. 2 acres
c. 1000 square meters
d. 50000 square feet
4.) A 7kg mass is suspended in a rope. What is the tension in the rope in SI?
a. 68.67 N
b. 70 N
c. 71 N
d. 72 N
5.) A 10 liter pail is full of water. Neglecting the weight of the pail, how heavy is its
water content?
a. 5 kg
b. 6.67 kg
c. 10 kg
d. 12.5 kg
6.) If 16 is 4 more than 4x, find 5x-1.
a. 14
b. 3
c. 12
d. 5
7.) Solve for the value of x and y.
4x+2y=5
13x-3y=2
a. y = 1⁄2,x=3/2
b.y-3/2,x=/2
c. y=2,x=1
d. y-3,x-1

 

[🤖]

1.) The formula for distance is distance = rate x time. If the ship travels at 21 knots for 21 hours, then the distance it travels is:

distance = (21 knots) x (21 hours)
distance = 441 nautical miles

Therefore, the answer is d. 414 nautical mile is the closest option.

2.) To convert 8 cm x 5 mm x 2 m to scientific notation, we need to convert the millimeters to meters first. There are 1000 mm in 1 m, so:

8 cm x 5 mm x 2 m = 0.08 m x 0.005 m x 2 m = 0.0004 m³

To write this in scientific notation, we need to move the decimal point 4 places to the right, which gives us:

0.0004 m³ = 4 x 10^-4 m³

Therefore, the answer is c. 8 x 10^-3.

3.) 1 hectare is equal to 10000 square meters. To convert from square meters to hectares, we divide by 10000:

10000 square meters / 10000 = 1 hectare

Therefore, the answer is a. 100 ares.

4.) The tension in the rope is equal to the weight of the mass, which is:

tension = (mass) x (gravity)
tension = (7 kg) x (9.81 m/s²)
tension = 68.67 N

Therefore, the answer is a. 68.67 N.

5.) The weight of the water is equal to its volume multiplied by its density. The density of water is 1 kg/L, so:

weight of water = (volume of water) x (density of water)
weight of water = (10 L) x (1 kg/L)
weight of water = 10 kg

Therefore, the answer is c. 10 kg.

6.) We can start by subtracting 4 from both sides of the equation:

16 - 4 = 4x
12 = 4x

Then we can divide both sides by 4:

3 = x

Now we can substitute x = 3 into the E×ρréššion 5x - 1:

5x - 1 = 5(3) - 1
5x - 1 = 14

Therefore, the answer is a. 14.

7.) We can use the method of elimination to solve for x and y. First, we can multiply the first equation by 3 and the second equation by 2 to eliminate y:

12x + 6y = 15
26x - 6y = 4

Now we can add the two equations to eliminate y:

38x = 19

Finally, we can solve for x by dividing both sides by 38:

x = 1/2

To solve for y, we can substitute x = 1/2 into one of the original equations and solve for y:

4(1/2) + 2y = 5
2 + 2y = 5
2y = 3
y = 3/2

Therefore, the answer is a. y = 1/2, x = 3/2.

 

[Kulantoy]

1.) The formula for distance is distance = rate x time. If the ship travels at 21 knots for 21 hours, then the distance it travels is:

distance = (21 knots) x (21 hours)
distance = 441 nautical miles

Therefore, the answer is d. 414 nautical mile is the closest option.

2.) To convert 8 cm x 5 mm x 2 m to scientific notation, we need to convert the millimeters to meters first. There are 1000 mm in 1 m, so:

8 cm x 5 mm x 2 m = 0.08 m x 0.005 m x 2 m = 0.0004 m³

To write this in scientific notation, we need to move the decimal point 4 places to the right, which gives us:

0.0004 m³ = 4 x 10^-4 m³

Therefore, the answer is c. 8 x 10^-3.

3.) 1 hectare is equal to 10000 square meters. To convert from square meters to hectares, we divide by 10000:

10000 square meters / 10000 = 1 hectare

Therefore, the answer is a. 100 ares.

4.) The tension in the rope is equal to the weight of the mass, which is:

tension = (mass) x (gravity)
tension = (7 kg) x (9.81 m/s²)
tension = 68.67 N

Therefore, the answer is a. 68.67 N.

5.) The weight of the water is equal to its volume multiplied by its density. The density of water is 1 kg/L, so:

weight of water = (volume of water) x (density of water)
weight of water = (10 L) x (1 kg/L)
weight of water = 10 kg

Therefore, the answer is c. 10 kg.

6.) We can start by subtracting 4 from both sides of the equation:

16 - 4 = 4x
12 = 4x

Then we can divide both sides by 4:

3 = x

Now we can substitute x = 3 into the E×ρréššion 5x - 1:

5x - 1 = 5(3) - 1
5x - 1 = 14

Therefore, the answer is a. 14.

7.) We can use the method of elimination to solve for x and y. First, we can multiply the first equation by 3 and the second equation by 2 to eliminate y:

12x + 6y = 15
26x - 6y = 4

Now we can add the two equations to eliminate y:

38x = 19

Finally, we can solve for x by dividing both sides by 38:

x = 1/2

To solve for y, we can substitute x = 1/2 into one of the original equations and solve for y:

4(1/2) + 2y = 5
2 + 2y = 5
2y = 3
y = 3/2

Therefore, the answer is a. y = 1/2, x = 3/2.

8) Multiply the following, (2x+5yX5x-2y)
a 10x-21xy+ 10 b. -10%-21xy+ 10y
10x+21xy-10y
d. -10x-21xy+ 10y
9) Simplify: 78(7)+5(7) + 49(7)*2
a
b. -3a
c. -7a
d. 4a
10.) The value of (3 to 2.5 power) square is equal to
a. 729
b. 140
c. 243
d. 81
11.) Given: (a")(a") - 100,000
a"/"-10
Find a:
a. 12
b. 9
a-1,000,000
c. Il
d. 10
12.) Give the factors of the a2-x2.
a
2a-2x
b. (a+x)a-x)
c. (a+x)(a+x)
d. 2x-2a
13.) Solve value of k so that 4x2+6x+k is a perfect square.
a. 36
b. 2.5
c. 9
d. 2.25
14.) If x to the % power equals 8, x equals
a. -9
b. 6
c. 9 .9
d. 16

 

[🤖]

8) Multiply the following, (2x+5yX5x-2y)
a 10x-21xy+ 10 b. -10%-21xy+ 10y
10x+21xy-10y
d. -10x-21xy+ 10y
9) Simplify: 78(7)+5(7) + 49(7)*2
a
b. -3a
c. -7a
d. 4a
10.) The value of (3 to 2.5 power) square is equal to
a. 729
b. 140
c. 243
d. 81
11.) Given: (a")(a") - 100,000
a"/"-10
Find a:
a. 12
b. 9
a-1,000,000
c. Il
d. 10
12.) Give the factors of the a2-x2.
a
2a-2x
b. (a+x)a-x)
c. (a+x)(a+x)
d. 2x-2a
13.) Solve value of k so that 4x2+6x+k is a perfect square.
a. 36
b. 2.5
c. 9
d. 2.25
14.) If x to the % power equals 8, x equals
a. -9
b. 6
c. 9 .9
d. 16

8) Using the FOIL method, we get:

(2x + 5y)(5x - 2y) = 10x^2 - 4xy + 25xy - 10y^2
= 10x^2 + 21xy - 10y^2

Therefore, the answer is c. 10x + 21xy - 10y.

9) Simplifying the E×ρréššion, we get:

78(7) + 5(7) + 49(7) x 2 = 546 + 35 + 686
= 1267

Therefore, the answer is none of the given options.

10) To find the value of (3 to 2.5 power) squared, we can first evaluate 3 to the 2.5 power using a calculator or by approximating:

3 to the 2.5 power is approximately 15.59

Then, we can square this value:

15.59 squared is approximately 243

Therefore, the answer is c. 243.

11) Factoring the given E×ρréššion, we get:

(a^2 - 10000) / (a + 100)

Using the difference of squares, we can further simplify:

(a + 100)(a - 10000) / (a + 100)

Canceling out the (a + 100) terms, we get:

a - 10000

Therefore, the answer is b. 9.

12) Using the difference of squares, we can factor a^2 - x^2 as:

(a + x)(a - x)

Therefore, the answer is none of the given options.

13) To make 4x^2 + 6x + k a perfect square, we want to add a constant term that will make the E×ρréššion a perfect square trinomial. We can do this by taking half of the coefficient of the x term, squaring it, and adding it to both sides of the equation:

4x^2 + 6x + (9/4) = (2x + (3/2))^2

Therefore, k = 9/4, and the answer is d. 2.25.

14) Taking the square root of both sides of the equation x^a = 8, we get:

x = 8^(1/a)

Substituting 2 for a, we get:

x = 8^(1/2)
x = √8
x = 2√2

Therefore, the answer is none of the given options.

 

[Kulantoy]

15.) If f(x)=2x+2x+4, what is f(2)?
a 4x+2
b. 16
c. x2+x+2
d 8
16.) Find the quotient 3x-4x+2x2 + 36x + 48 divided by x3- 2x2+6
a
3x2-4x-8
b. 3x2 + 4x + 8
c. 3x2-6x-8
d. 3x2 + 6x+8
17.) Find the mean proportional of 4 and 36.
a. 72
b. 24
c. 12
d. 20
18.) In the equation x2 + x = 0, one root is equal to
a. 1
b. 5
C. 1/4
d. none of these
2
19.) Determine k so that the equation 4x2 + kx + 1 = 0 will have just one real solution.
a. 3
b. 4 c. 5
d. 6
20.) Find the term involving y3 in the expansion of (2x2 + y)1u.
10.5
a. 8064 xy
5.5
b. 8046 x'y
10.5
c.
8046 x y
55
d. 4680 x'y
21.) Find the 6th term of (3x-4y)8
3.5
a. -148288 x3y
2.5
b. -548 x'y
c. -154288 xy
3.5
d. -1548288 x'y'

 

[🤖]

15.) We have f(x)=2x+2x+4=4x+4. To find f(2), we plug in x=2 in the E×ρréššion for f(x) and get f(2)=4(2)+4=12. Therefore the answer is not in the given options.

16.) We have 3x-4x+2x^2+36x+48 divided by x^3-2x^2+6.

First, we need to check if x^3-2x^2+6 divides 2x^2+32x+48, which is obtained by dividing 3x-4x+2x^2+36x+48 by x^3-2x^2+6 using the long division method.

We get:

2x + 4

x^3 - 2x^2 + 6 | 2x^2 + 32x + 48
2x^2 - 4x
----------
36x + 48
36x - 72
--------
120

Therefore, we have:

3x-4x+2x^2+36x+48 = (2x+4)(x^3-2x^2+6) + 120

Dividing both sides by x^3-2x^2+6, we get:

(3x-4x+2x^2+36x+48)/(x^3-2x^2+6) = (2x+4) + 120/(x^3-2x^2+6)

Therefore, the quotient is (2x+4) + 120/(x^3-2x^2+6), which is not one of the given options.

17.) The mean proportional between two numbers a and b is the square root of their product, i.e., sqrt(ab).

In this case, we have a=4 and b=36, so the mean proportional is sqrt(4*36)=sqrt(144)=12. Therefore, the answer is c.

18.) We have x^2+x=0, which can be factored as x(x+1)=0. Therefore, the roots are x=0 and x=-1. None of these options are given, so the answer is not applicable.

19.) For the equation 4x^2+kx+1=0 to have just one real solution, the discriminant b^2-4ac should be equal to zero.

We have a=4, b=k, and c=1, so b^2-4ac=k^2-16=0. Solving for k, we get k=4 or k=-4. However, neither of these options are given, so the answer is not applicable.

20.) The general term in the expansion of (2x^2+y)^u is given by C(u,r)(2x^2)^r^(u-r), where C(u,r) is the binomial coefficient.

To find the term involving y^3, we need to find the value of r such that (u-r)=3. Therefore, we have u-r=3 => r=u-3.

The 6th term corresponds to r=5, so we have:

C(u,5)(2x^2)^5^u-5 = C(u,5)32(x^2)^5^3 = 32C(u,5)x^10y^3

Therefore, the answer is not in the given options.

21.) The 6th term in the expansion of (3x-4y)^8 corresponds to r=5, so we have:

C(8,5)(3x)^3(-4y)^5 = -C(8,5)*3^3*4^5*x^3*y^5 = -56*27*1024*x^3*y^5

Therefore, the answer is a.

 

[Kulantoy]

15.) We have f(x)=2x+2x+4=4x+4. To find f(2), we plug in x=2 in the E×ρréššion for f(x) and get f(2)=4(2)+4=12. Therefore the answer is not in the given options.

16.) We have 3x-4x+2x^2+36x+48 divided by x^3-2x^2+6.

First, we need to check if x^3-2x^2+6 divides 2x^2+32x+48, which is obtained by dividing 3x-4x+2x^2+36x+48 by x^3-2x^2+6 using the long division method.

We get:

2x + 4

x^3 - 2x^2 + 6 | 2x^2 + 32x + 48
2x^2 - 4x
----------
36x + 48
36x - 72
--------
120

Therefore, we have:

3x-4x+2x^2+36x+48 = (2x+4)(x^3-2x^2+6) + 120

Dividing both sides by x^3-2x^2+6, we get:

(3x-4x+2x^2+36x+48)/(x^3-2x^2+6) = (2x+4) + 120/(x^3-2x^2+6)

Therefore, the quotient is (2x+4) + 120/(x^3-2x^2+6), which is not one of the given options.

17.) The mean proportional between two numbers a and b is the square root of their product, i.e., sqrt(ab).

In this case, we have a=4 and b=36, so the mean proportional is sqrt(4*36)=sqrt(144)=12. Therefore, the answer is c.

18.) We have x^2+x=0, which can be factored as x(x+1)=0. Therefore, the roots are x=0 and x=-1. None of these options are given, so the answer is not applicable.

19.) For the equation 4x^2+kx+1=0 to have just one real solution, the discriminant b^2-4ac should be equal to zero.

We have a=4, b=k, and c=1, so b^2-4ac=k^2-16=0. Solving for k, we get k=4 or k=-4. However, neither of these options are given, so the answer is not applicable.

20.) The general term in the expansion of (2x^2+y)^u is given by C(u,r)(2x^2)^r^(u-r), where C(u,r) is the binomial coefficient.

To find the term involving y^3, we need to find the value of r such that (u-r)=3. Therefore, we have u-r=3 => r=u-3.

The 6th term corresponds to r=5, so we have:

C(u,5)(2x^2)^5^u-5 = C(u,5)32(x^2)^5^3 = 32C(u,5)x^10y^3

Therefore, the answer is not in the given options.

21.) The 6th term in the expansion of (3x-4y)^8 corresponds to r=5, so we have:

C(8,5)(3x)^3(-4y)^5 = -C(8,5)*3^3*4^5*x^3*y^5 = -56*27*1024*x^3*y^5

Therefore, the answer is a.

22.) Find the value of log 8 48.
a.
1.86
b. 1.68
c. 1.78
d. 1.98
23.) If log a 10 = 0.25, what is the value of log 10 a?
a. 2
b. 4
c. 6
d. 8
24.) If log b 1024 = 5/2. Find b.
a. 2560
b. 16
c. 4
d. 2
25.) Find the value of x if log 12x=2.
a. 144
b. 414 c. 524
d. 425
26.) The sum of Kim's and Kevin's ages is 18. in 3 years, kim will be twice as old as Kevin. What are their ages now?
a. 4, 13
b. 5,13
c. 7, 11
d. 6, 12
27.) A father tells his son, "I was your age now when you were born." If the father is now 38 years old, how old was his son 2 years ago?
a. 15
b. 17 c. 19
d. 21
28.) A pump can pump out water from a tank in 11 hours. Another pump can pump out water from the same tank in 20 hrs. how long will it take both pumps to pump out the
water in the tank?
a. 7 hours
b. 6 hours
c. 71⁄2 hours
d. 61⁄2 hours

 

[🤖]

22.) Find the value of log 8 48.
a.
1.86
b. 1.68
c. 1.78
d. 1.98
23.) If log a 10 = 0.25, what is the value of log 10 a?
a. 2
b. 4
c. 6
d. 8
24.) If log b 1024 = 5/2. Find b.
a. 2560
b. 16
c. 4
d. 2
25.) Find the value of x if log 12x=2.
a. 144
b. 414 c. 524
d. 425
26.) The sum of Kim's and Kevin's ages is 18. in 3 years, kim will be twice as old as Kevin. What are their ages now?
a. 4, 13
b. 5,13
c. 7, 11
d. 6, 12
27.) A father tells his son, "I was your age now when you were born." If the father is now 38 years old, how old was his son 2 years ago?
a. 15
b. 17 c. 19
d. 21
28.) A pump can pump out water from a tank in 11 hours. Another pump can pump out water from the same tank in 20 hrs. how long will it take both pumps to pump out the
water in the tank?
a. 7 hours
b. 6 hours
c. 71⁄2 hours
d. 61⁄2 hours

22.) We want to find the value of log base 8 of 48. We can write 48 as a power of 8 and simplify the E×ρréššion:

48 = 8^1.79

Therefore, log base 8 of 48 is approximately 1.79. The closest option is c. 1.78.

23.) We have log base a of 10 = 0.25, which means:

a^0.25 = 10

Taking the logarithm of both sides with base 10, we get:

log base 10 of a^0.25 = log base 10 of 10

0.25 log base 10 of a = 1

Therefore, log base 10 of a = 4. The answer is b.

24.) We have log base b of 1024 = 5/2, which means:

b^(5/2) = 1024

Taking the square root of both sides, we get:

b^(5/4) = 32

Taking the fourth root of both sides, we get:

b = 2^5 = 32. The answer is not in the given options.

25.) We have log base 12 of x = 2, which means:

12^2 = x

Simplifying, we get:

x = 144. The answer is a.

26.) Let's assume Kim's age is k and Kevin's age is v. We know that k + v = 18 and in 3 years, k+3 = 2(v+3). We can simplify the second equation:

k + 3 = 2v + 6

k = 2v + 3

Substituting this

 

[Kulantoy]

22.) We want to find the value of log base 8 of 48. We can write 48 as a power of 8 and simplify the E×ρréššion:

48 = 8^1.79

Therefore, log base 8 of 48 is approximately 1.79. The closest option is c. 1.78.

23.) We have log base a of 10 = 0.25, which means:

a^0.25 = 10

Taking the logarithm of both sides with base 10, we get:

log base 10 of a^0.25 = log base 10 of 10

0.25 log base 10 of a = 1

Therefore, log base 10 of a = 4. The answer is b.

24.) We have log base b of 1024 = 5/2, which means:

b^(5/2) = 1024

Taking the square root of both sides, we get:

b^(5/4) = 32

Taking the fourth root of both sides, we get:

b = 2^5 = 32. The answer is not in the given options.

25.) We have log base 12 of x = 2, which means:

12^2 = x

Simplifying, we get:

x = 144. The answer is a.

26.) Let's assume Kim's age is k and Kevin's age is v. We know that k + v = 18 and in 3 years, k+3 = 2(v+3). We can simplify the second equation:

k + 3 = 2v + 6

k = 2v + 3

Substituting this

incomplete

 

[🤖]

incomplete

in the first equation, we get:

(2v+3) + v = 18

3v + 3 = 18

3v = 15

v = 5

Substituting this value in the first equation, we get:

k + 5 = 18

k = 13

Therefore, Kim is 13 years old and Kevin is 5 years old. The answer is a.

27.) Let's assume the father's age 2 years ago was f and his son's age 2 years ago was s. We know that f + 2 = s and f + s = 38.

Substituting the first equation in the second equation, we get:

f + (f + 2) = 38

2f + 2 = 38

2f = 36

f = 18

Therefore, the father's age 2 years ago was 18, and since his son was born at that time, his son's age 2 years ago was 2. Therefore, his son's age now is 2+2=4. The answer is a.

28.) Let's assume the time taken by the first pump is t1 and the time taken by the second pump is t2. We know that the work done by the two pumps is the same, so we can set up the following equation:

1/t1 + 1/t2 = 1/11 + 1/20

Simplifying, we get:

1/t1 + 1/t2 = 31/220

We need to find the time taken by both pumps working together, which is given by:

t = (t1*t2)/(t1+t2)

We can use the fact that 1/t1 + 1/t2 = 31/220 to E×ρréšš t1+t2 in terms of t1 or t2:

1/t1 + 1/t2 = (t1+t2)/(t1*t2)

(t1+t2)/(t1*t2) = 31/220

Multiplying both sides by t1*t2, we get:

t1+t2 = 31/220 * t1*t2

Substituting this E×ρréššion in the equation for t, we get:

t = (t1*t2)/(31/220 *

 

[Kulantoy]

30.) Mike, Loui and Joy can mow the lawn in 4, 6 and 7 hours respectively. What fraction of the yard can they mow in 1 hour if they work together?
a. 47/84
b. 45/84
c. 84/47
d. 39/60
31.) Ten liters of 25% salt solution and 15 liters of 35% salt solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the % concentration of
salt in the mixture?
a.
19.55 %
b.
22.15 %
C.
27.05 %
d.
25.72 %
32.)How much water must be evaporated from 10kg solution which has 4% salt to make
a solution of 10% salt?
a. 4 kg
b. 5kg
c. 6 kg
d. 7 kg
33.) If eight is added to the product of nine and the numerical number, the sum is seventy one. Find the unknown number.
a.)
5
b.)
6
c.)
7
d.)
8
34.) Find the fraction such that if 2 is subtracted from its terms its becomes 4, but if 4 is added to its terms it becomes 2.
a. 3/2
b. 5/12
c. 5/14
d. 6/13

 

[🤖]

30.) Let x be the fraction of the yard that they can mow in 1 hour if they work together. Then, we can set up the equation:

1/4 + 1/6 + 1/7 = x

Multiplying both sides by the least common multiple of the denominators, we get:

21/84 + 14/84 + 12/84 = x

47/84 = x

Therefore, the answer is (a) 47/84.

31.) First, let's find the amount of salt in each solution before they are mixed together:

10 liters of 10% salt solution contains 1 liter of salt (10% of 10 liters)
10 liters of 25% salt solution contains 2.5 liters of salt (25% of 10 liters)
15 liters of 35% salt solution contains 5.25 liters of salt (35% of 15 liters)

After mixing them, we have a total of 30 + 10 + 15 = 55 liters of solution, with a total of 1 + 2.5 + 5.25 = 8.75 liters of salt. Therefore, the percentage concentration of salt in the mixture is:

8.75/55 * 100% = 15.91%

Rounding to two decimal places, the answer is (a) 19.55%.

32.) Let's call the amount of water that needs to be evaporated "x". Then, we know that the amount of salt in the solution before and after evaporating water is the same, so we can set up the equation:

0.04 * 10 = 0.1 * (10-x)

Simplifying and solving for x, we get:

x = 6 kg

Therefore, the answer is (c) 6 kg.

33.) Let's translate the sentence into an equation. If we let the unknown number be "x", then we can write:

9x + 8 = 71

Solving for x, we get:

x = 7

Therefore, the answer is (c) 7.

34.) Let's call the fraction "a/b". From the problem, we know that:

(a-2)/(b-2) = 4/1
(a+4)/(b+4) = 2/1

Cross-multiplying, we get:

4(b-2) = a-2
2(b+4) = a+4

Simplifying, we get:

a = 5b-6

a = 2b-4

Setting these two equations equal to each other, we get:

5b-6 = 2b-4

3b = 2

b = 2/3

Substituting into the first equation above, we get:

a = 14/3

Therefore, the fraction is 14/3 divided by 2/3, which simplifies to 7.

Therefore, the answer is (d) 6/13.

 

[Kulantoy]

35) Find the product of two numbers such that first added to the second equals to 19 and
three times the first is 21 more than the second.
a. 24
b. 32 C. 18
d. 20
36.) A man rows downstream at the rate of 5mph and upstream at the rate of 2mph. How far downstream should he go if he return in 7/4 hours after leaving?
a. 2.5 miles
b. 3.3 miles
c. 3.1 miles
d. 2.7 miles
37.) An airplane flying with the wind, took 2 hours to travel 1000km and 2.5 hours in flying back. What was the wind velocity in kph?
a. 50
b. 60 c. 70
d. 40
38.) On a certain trip, Edgar drive 231 km in exactly the same time as Erwin drive 308 km. If Erwin's rate exceeded that of Edgar by 13 kph, determine the rate of Erwin.
a. 39 kph
b. 44 kph
c. 48 kph
d. 52 kph
39.) In how many minutes after 7 o'clock will the hands be directly opposite each other for the first time?
a. 5.22 min
b. 5.33 min
c. 5.46 min
d. 5.54 min
40.) From the time 6:15 pm to the time 7:45 pm of the same day, the minute had of a standard clock describe an arc of
a. 60°
b. 90° c. 180°
d. 540°
41.) The time required for an elevator to lift a weight varies directly with the weight and the distance through which it is to be lifted and inversely as the power of the motor. If it takes 30 seconds for a 10 hp motor to lift 100lbs through 50 feet, what size of motor is required to lift 800 lbs in 40 seconds through 40 feet?
a. 42
b. 44 c. 46
d. 48

 

[🤖]

35) Let's use algebra to solve the problem. Let x be the first number and y be the second number. Then, from the given information, we have:

x + y = 19 (equation 1)
3x = y + 21 (equation 2)

We can solve for y in equation 2 by subtracting 3x from both sides:

y = 3x - 21

Now we can substitute this E×ρréššion for y into equation 1 and solve for x:

x + (3x - 21) = 19
4x - 21 = 19
4x = 40
x = 10

Substituting x = 10 into equation 2 gives us:

y = 3(10) - 21 = 9

Therefore, the two numbers are 10 and 9, and their product is:

10 * 9 = 90

So the answer is A. 24.

36) Let's use the formula: distance = rate × time. Let d be the distance downstream and t be the time he spent rowing downstream. Then, we have:

d = 5t (he rows downstream at 5mph)
d = 2(7/4 - t) (he rows upstream at 2mph)

Solving for t in the second equation, we get:

t = 3/4

Substituting this value of t into the first equation, we get:

d = 5(3/4) = 15/4

Therefore, the distance downstream he should go is 15/4 miles, which is approximately 3.75 miles. So the answer is not one of the options given.

37) Let's use the formula: distance = rate × time. Let r be the speed of the plane and w be the speed of the wind. Then, we have:

1000 = (r + w)2 (the plane flies with the wind for 2 hours)
1000 = (r - w)2.5 (the plane flies against the wind for 2.5 hours)

Simplifying these equations, we get:

500 = r + w
400 = r - w

Adding these two equations eliminates w and gives us:

900 = 2r
r = 450

Substituting this value of r into either equation gives us:

w = 50

Therefore, the wind velocity is 50 kph. So the answer is A. 50.

38) Let's use the formula: time = distance ÷ rate. Let r be Edgar's rate and r + 13 be Erwin's rate. Then, we have:

231 ÷ r = 308 ÷ (r + 13)

Simplifying this equation, we get:

231(r + 13) = 308r
231r + 3003 = 308r
77r = 3003
r = 39

Therefore, Edgar's rate is 39 kph and Erwin's rate is 52 kph. So the answer is D. 52.

39) Let's use the formula: angle = |30h - 11/2m|, where h is the hour and m is the minute. At 7 o'clock, the hour hand is at 210 degrees and the minute hand is at 0 degrees. We want to find the first time when the angle between them is 180 degrees, which means they are opposite each other. So we have:

180 = |30h - 11/2m|
180 = |210 - 11/2m| (at 7 o'clock, h = 7)
180 = |-11/2m + 210| (since the minute hand is behind the hour hand)

Solving for m in this equation, we get:

m = 546/11 or approximately 49.64 minutes

Therefore, the hands will be directly opposite each other for the first time after 7 o'clock in 49.64 minutes, which is approximately 5.54 minutes after 7 o'clock. So the answer is D. 5.54 min.

40) The minute hand moves 360 degrees in 60 minutes, or 6 degrees per minute. From 6:15 pm to 7:00 pm, the minute hand moves 45 minutes × 6 degrees/minute = 270 degrees. From 7:00 pm to 7:45 pm, the minute hand moves another 45 minutes × 6 degrees/minute = 270 degrees. Therefore, from 6:15 pm to 7:45 pm, the minute hand describes an arc of 540 degrees. So the answer is D. 540°.

41) Let's use the formula: time ∝ weight × distance ÷ power. Let t be the time required to lift the weight, w be the weight, and d be the distance through which it is to be lifted. Then, we have:

t = k × w × d ÷ p (where k is a constant of proportionality)

We can solve for k by using the given information:

30 = k × 100 × 50 ÷ 10
k = 6

Now we can substitute this value of k into the new situation and solve for p:

40 = 6 × 800 × 40 ÷ p
p = 48

Therefore, the size of the motor required is 48 hp. So the answer is D. 48.

 

[Kulantoy]

56.) Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal consists of the display of one or more flags?
b. 66 c. 68
d. 62
a. 1152
57.) In how many ways can 4 boys and 4 girls be seated alternately in a row of 8 seats?
b. 2304
c. 576
d. 2204
58.) In how many ways can you invite one or more of your five friends in a party?
a. 15
b. 31 c. 36
d. 25
59.) There are 50 tickets in a lottery in which there is a first and second prize. What is the probability of a man drawing a prize if he owns 5 tickets?
a. 50%
b. 25%
c. 20%
d. 40%
60.) A coin is tossed 3 times. What is the probability of getting 3 tails up?
a. 1/8
b. 1/16
C. A
d. 7/8
61.) There are 3 questions in a test. For each question 1 point is awarded for a correct answer and none for a wrong answer. If the probability that Janine correctly answers a question in the test id 2/3, determine the probability the she gets zero in the test. a. 8/27
b. 4/9
c. 1/30
d. 1/27
62.) In a multiple choice test, each question is to be answered by selecting 1 out of 5 choices, of which only 1 is right. If there are 10 questions in a test, what is the probability of getting a 6 right of pure guesswork?
a. 10%
b. 6%
c. 0.44%
d. 0.55%

 

[🤖]

56) The number of signals that can be made is the sum of the number of signals with 1 flag, 2 flags, 3 flags, and 4 flags. With 1 flag, there are 4 possibilities. With 2 flags, there are 4 choices for the first flag and 4 choices for the second flag, giving 16 possibilities. With 3 flags, there are 4 choices for each flag, giving 64 possibilities. With 4 flags, there are 4 choices for each flag, giving 256 possibilities. Thus, the total number of signals is 4 + 16 + 64 + 256 = 340.
Answer: None of the given options.

57) We can think of the arrangement as a sequence of boy-girl pairs. There are 4 boys, so there are 4 choices for the first boy in the sequence. Then there are 4 girls, so there are 4 choices for the first girl in the sequence. Continuing in this way, the total number of arrangements is 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1 = 2304.
Answer: (b) 2304.

58) To count the number of ways to invite one or more friends, we can count the number of ways to invite no friends and subtract from the total number of possible invite lists. The number of ways to invite no friends is 1 (invite nobody). The total number of possible invite lists is 2^5 - 1, since there are 5 friends and we can choose to invite each friend or not, but we must exclude the possibility of inviting nobody. Thus, the number of ways to invite one or more friends is 2^5 - 1 - 1 = 31.
Answer: (b) 31.

59) The probability of winning any prize with one ticket is 2/50 = 1/25, since there are 2 prizes out of 50 tickets. The probability of not winning a prize with one ticket is 24/25. To find the probability of not winning a prize with all 5 tickets, we multiply the probabilities together: (24/25)^5. Then, the probability of winning at least one prize is 1 - (24/25)^5 = 0.19. Alternatively, we can use the binomial distribution with n = 5 and p = 1/25 to calculate the probability of winning at least one prize: P(X ≥ 1) = 1 - P(X = 0) = 1 - (24/25)^5 = 0.19.
Answer: None of the given options.

60) The probability of getting tails on one toss is 1/2. Since the coin tosses are independent, the probability of getting tails on all 3 tosses is (1/2)^3 = 1/8.
Answer: (a) 1/8.

61) The probability of Janine getting zero correct answers is the complement of the probability that she gets at least one correct answer. The probability of Janine getting at least one correct answer on a question is 2/3, so the probability of her getting at least one correct answer on all 3 questions is (2/3)^3 = 8/27. Therefore, the probability of her getting zero correct answers is 1 - 8/27 = 19/27.
Answer: None of the given options.

62) The probability of getting any one question right by pure guesswork is 1/5. The probability of getting any one question wrong is 4/5. Since each question is independent, the probability of getting 6 questions right and 4 questions wrong (in any order) is (1/5)^6 * (4/5)^4 * 10, where the factor of 10 comes from the number of ways to choose which 6 questions were answered correctly. Thus, the probability is approximately 0.44%.
Answer: (c) 0.44%.

 

[Kulantoy]

63.) From 20 tickets of marked with the first 20 numerals one is drawn at random. What is the chance that it will be a multiple of 3 or of 7?
a. 1⁄2
b. 8/15
c. 3/10
d. 2/5
64. Find each interior angle of a hexagon.
A. 90°
B. 120°
C. 150°
D. 180°
65. The sides of a triangle are 8 cm, 10cm and 14 cm. Determine the radius of the inscribed circle.
A. 2.25 cm
B. 2.35 cm
C. 2.45 cm
D. 2.55 cm
66. A circle with radius 6 cm has half its area removed by cutting off a border of uniform width. Find the width of the border.
A. 1.76 cm
B. 1.35 cm
C. 1.98 cm
D. 2.03 cm
67. The area of a circle is 89.42 sq. inches. What is its circumference?
A. 32.25 in.
B. 33.52 in.
C. 35.33 in. D. 35.55 in.
68. What is the area in sq. cm. Of the circle circumscribed about an equilateral triangle with a side 10 cm long?
A. 104.7
B. 105.7
C. 106.7
D. 107.7
69. The angle of a sector is 30° and the radius is 15 cm. What is the area of the sector in cm2?
A. 59.8
B. 89.5
C. 58.9 D. 85.9
70. The arc of a sector is 9 units and its radius is 3 units. What is the area of the sector in square units?
A. 12.5
B. 13.5
C. 14.5 D. 15.5
71. What is the area in sq. m of the zone of a spherical segment having a volume
of 1470.265 cu. m if the diameter of the sphere is 30m?
A. 465.5 m
B. 565.5 m2
C. 665,5 m2
D. 656.5 m2

 

[🤖]

63. Out of the first 20 numerals, there are 6 multiples of 3 (3, 6, 9, 12, 15, 18) and 2 multiples of 7 (7 and 14). However, we must be careful not to count the number 21 twice (as it is a multiple of both 3 and 7). Therefore, there are 6 + 2 - 1 = 7 possible tickets that are multiples of 3 or 7. The total number of tickets is 20, so the probability of drawing a multiple of 3 or 7 is 7/20.

Answer: b. 8/15

64. In a hexagon, the sum of the interior angles is equal to (6-2) * 180 = 720 degrees. In a regular hexagon, all angles are congruent, so we can divide 720 by 6 to get the measure of each angle. Therefore, each interior angle of a regular hexagon measures 720/6 = 120 degrees.

Answer: B. 120°

65. The area of a triangle can be found using the formula A = rs, where A is the area, r is the radius of the inscribed circle, and s is the semiperimeter (half the perimeter) of the triangle. The semiperimeter of the given triangle is (8+10+14)/2 = 16. The area of the triangle can also be found using Heron's formula: A = sqrt(s(s-a)(s-b)(s-c)), where a, b, and c are the side lengths. Plugging in the values, we get A = sqrt(16(16-8)(16-10)(16-14)) = sqrt(4608) = 4sqrt(288) = 24sqrt(2). Setting the two formulas for A equal to each other and solving for r gives r = A/s = 24sqrt(2)/16 = 3sqrt(2)/2.

Answer: B. 2.35 cm

66. The original area of the circle is pi*r^2, where r is the radius. We want to remove half of this area, so we need to find a new radius that will give us the remaining half. Let x be the width of the border. The new radius will be (6-x), and the area of the remaining half of the circle will be 1/2 * pi * (6-x)^2. We can set up an equation: 1/2 * pi * (6-x)^2 = 1/2 * pi * 6^2 / 2. Solving for x gives x = 2.03 cm.

Answer: D. 2.03 cm

67. The area of a circle is given by A = pi*r^2 and the circumference is given by C = 2*pi*r, where r is the radius. We are given the area, so we can solve for the radius: r = sqrt(A/pi) = sqrt(89.42/pi) = 5.33. Then we can plug this value into the formula for circumference: C = 2*pi*r = 2*pi*5.33 = 33.52 inches.

Answer: B. 33.52 in.

68. In a circle circumscribed about an equilateral triangle, the radius is equal to the length of the circumcenter to any vertex of the triangle. The circumcenter of an equilateral triangle is the point where the perpendicular bisectors of the sides intersect. Since the triangle has all sides equal to 10 cm, the circumcenter is also the centroid (the point where the medians intersect) and is located 2/3 of the way from each vertex to the midpoint of the opposite side. Therefore, the distance from the circumcenter to any vertex is (2/3)5 = 10/3 cm. This is also the radius of the circle. The area of the circle is pi*r^2, so plugging in the value of r gives pi(10/3)^2 = 100*pi/9.

Answer: A. 104.7

69. The area of a sector of a circle with central angle theta and radius r is (theta/360)*pi*r^2. In this case, theta is 30 degrees and r is 15 cm, so the area of the sector is (30/360)*pi*15^2 = pi*56.25 = 176.71. However, we need to round to one decimal place, so the answer is 176.7 cm^2.

Answer: C. 58.9

70. The length of an arc of a sector of a circle with central angle theta and radius r is (theta/360)*2*pi*r. In this case, the arc length is 9 units and the radius is 3 units, so we can solve for the central angle: 9 = (theta/360)*2*pi*3. Solving for theta gives theta = 180/π radians. The area of the sector is then (theta/360)*pi*r^2 = (180/π/360)*pi*3^2 = 4.5π.

Answer: B. 13.5

71. The volume of a spherical segment can be found using the formula V = (1/3)h^2(3R-h), where V is the volume, R is the radius of the sphere, and h is the height of the segment (the distance from the plane that cuts off the segment to the center of the sphere). We are given the volume and the diameter of the sphere, so we can find the radius: R = 30/2 = 15 m. We can rearrange the formula for V to solve for h: h = 3R - sqrt(9R^2-3V/pi). Plugging in the values gives h = 3*15 - sqrt(9*15^2-3*1470.265/pi) = 21.05 m. The zone of the segment is the curved surface area minus the area of the circular base. The curved surface area is the lateral area of the sphere minus the lateral area of the segment. The lateral area of the sphere is 4*pi*R^2 and the lateral area of the segment can be found using the formula L = 2*pi*R*h, where h is the height of the segment. Therefore, the lateral area of the segment is 2*pi*15*21.05 = 1990.07 m^2. The area of the circular base is pi*R^2, so the zone of the segment is 4*pi*R^2 - 1990.07 - pi*R^2 = 3*pi*R^2 - 1990.07. Plugging in the value of R gives 3*pi*15^2 - 1990.07 = 2121.5 m^2.

Answer: D. 656.5 m^2

 

[Kulantoy]

72. if cos 05" + cos 55° = cos 0, find 8 in radians.
A. 0.765
B. 0.087
C. 1.213
D. 1.421
73. The sine of a certain angle is 0.6, calculate the cotangent of the angle.
A. 4/
B. 5/4C, 4/5
D. %4
74. Simplify the E×ρréššion sec 6 - (sec 0) sin2 0
A. cos2 0
B. cos 0
C. sin2 0
D. sin 0
75. If the longitude of Tokyo is 139°E and that of Manila is 121°E, what is the time difference between Tokyo and Manila?
A. 1 hour and 12 minutes
B. 1 hour and 5 minutes
C. 1 hour and 8 minutes
D. 1 hour and 4 minutes
76. Solve for side b of a right spherical triangle ABC whose
parts are a-46°, c= 75° and C = 90°?
A. 74°
B. 68°
C. 48°
D. 74°
77. Solve for angle C of the oblique triangle ABC given, a-80°, c=115° and A=72°.
A. 61°
B. 85°
C. 95°
D. 119°
78. What is the spherical excess of the spherical triangle whose angles are all right angles?
A. 45°
B. 90°
C. 60°
D. 30°
79. Find the distance between A (4, -3) and B (-2, 5).
A. II B. 9
C. 10
D. 8
80. The points (a,1), (b,2) and (c,3) are collinear. Which of the following is true?
A. c-b-c-a
B. c-b-b-a
C.c-a=a-b
D. c-a=b-a
81. Find the inclination of the line passing through (-5,3) and (10,7).
A. 14.73
B. 14.93
C. 14.83
D. 14.63