In a school election there were four candidates: Tom, Rebecca, Olly and Wendy.
540 students voted in the election.
5% of the votes were for Tom
of the votes were for Rebecca
The ratio of the number of votes for Olly to the number of votes to Wendy was 1:2
How many votes were for Wendy?

Singam missed the target 16 times in the shooting game

Assumng A be the number of times Singam hits the target and x be the number of times he misses the target

then

A + x = 50

5A - 3x = 122

finding A in terms of x

A = 50 - x

Substituting and simplifying

5 * (50 - x) - 3x = 122

250 - 8x = 122

8B = 128

x = 16

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Answer:

b

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

√21 is the measure of the height of the cone.

According to the theorem, the square of the hypotenuse is equal to the sum of the square of other two sides.

From the given cone;

Hypotenuse = 5cm

Adjacent = 4/2. = 2cm

Determine the height

h^2 = 5^2 - 2^2

h^2 = 25 - 4

h^2 = 21

Take the square root of both sides

h = √21

Hence the measure of the height of the cone is √21

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The percentile rank of 12 means that you scored higher than 12% of the test-takers who took the same exam, and lower than the other 88%.

Percentile is a statistical measure used to compare an individual's score with the rest of the population. For example, if your score is in the 12th percentile, it means that you performed better than only 12% of the people who took the same test, while the other 88% of test-takers scored higher than you.

Percentile rank is a useful tool for comparing an individual's performance with the larger population, as it provides a clear understanding of where a person stands in comparison to others who took the same exam. It can also be used to monitor one's progress over time, and to identify areas where improvement is needed.

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The use of a "thumbs-up" gesture to symbolize the statement "good luck" is a common practice in many cultures. This gesture is typically used to express approval or agreement, but it can also be used to convey positive wishes, such as wishing someone good luck before an exam or a job interview.

It is believed that this gesture originated in ancient Rome, where it was used as a sign of approval in the gladiatorial arena. Today, the thumbs-up gesture has become a universal symbol of positivity and encouragement. So, if you want to wish someone good luck, a thumbs-up gesture is a great way to do it!

The use of a "thumbs-up" gesture to symbolize the statement "good luck" involves the following steps:

1. Extend your arm: To perform the thumbs-up gesture, first extend your arm in the direction of the person you want to wish good luck.
2. Make a fist: Close your fingers into a fist, with your thumb pointing upwards.
3. Show your thumb: Ensure that the thumb is clearly visible and pointing upwards. This represents the "thumbs-up" gesture.
4. Make eye contact: Look at the person you're wishing good luck to, so they know the gesture is directed at them.

By performing the thumbs-up gesture, you're using a universally recognized symbol to convey your positive sentiment and wish someone good luck in their endeavors.

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To integrate ∫ √(3x^3-3x) (3x^2-1) dx, we can simplify the integrand first and then apply appropriate integration techniques. So, the correct option is 1. $9/2 (3x^2-3x)^{3/2} + C

Let's simplify the integrand:

√(3x^3-3x) (3x^2-1)

= (3x^3-3x)^(1/2) (3x^2-1)

= 3x^2 (x-1)^(1/2) (3x^2-1)

= 9x^4 (x-1)^(1/2) - 3x^2 (x-1)^(1/2)

Now, we can distribute the terms and integrate each term separately.

∫ 9x^4 (x-1)^(1/2) dx - ∫ 3x^2 (x-1)^(1/2) dx

For the first integral, we can use the substitution u = x-1, du = dx:

∫ 9x^4 (x-1)^(1/2) dx = ∫ 9(x-1+1)^4 (x-1)^(1/2) dx

= ∫ 9(u+1)^4 u^(1/2) du

= 9 ∫ (u+1)^4 u^(1/2) du

= 9 ∫ (u^4 + 4u^3 + 6u^2 + 4u + 1) u^(1/2) du

= 9 ∫ (u^5/2 + 4u^4/2 + 6u^3/2 + 4u^2/2 + u^(1/2)) du

= 9 ∫ (u^5/2 + 2u^4 + 3u^3 + 2u^2 + u^(1/2)) du

= 9 (u^7/14 + 2u^6/6 + 3u^5/10 + 2u^4/8 + 2u^(3/2)/3) + C1

= 9/14 u^7 + u^6 + 9/10 u^5 + u^4 + 6u^(3/2) + C1

= 9/14 (x-1)^7/2 + (x-1)^3 + 9/10 (x-1)^(5/2) + (x-1)^2 + 6(x-1)^(3/2) + C1

For the second integral, we can again use the substitution u = x-1, du = dx:

∫ 3x^2 (x-1)^(1/2) dx = ∫ 3(x-1+1)^2 (x-1)^(1/2) dx

= ∫ 3u^2 u^(1/2) du

= 3 ∫ u^(5/2) du

= 3 (u^(7/2)/ (7/2)) + C2

= 6/7 u^(7/2) + C2

= 6/7 (x-1)^(7/2) + C2

Therefore, the integral becomes:

∫ (3x^3-3x)^(1/2) (3x^2-1) dx = 9/14 (x-1)^7/2 + (x-1)^3 + 9/10 (x-1)^(5/2) + (x-1)^2 + 6(x-1)^(3/2) - 6/7 (x-1)^(7/2) + C

We are supposed to integrate: ∫ (3x³-3x)½ (3x²-1)dx.Now, we know that a²-x²= (a-x)(a+x).Let's solve (3x²-1) by assuming it as a²- x² where a=√3x² and x=1/√3.Now, 3x²-1 can be written as 3x² - 1/3 - 2/3 i.e (a-x)(a+x). Now, we can use the standard formula:∫ (a-x)½ (a+x) dx = 1/3 (a-x)^(3/2) (a+x) + C.Using this formula we can solve for (3x²-1) as: 1/3 (3x²-1/3)^(3/2) + C.Now we substitute this value in our original expression to get:∫ (3x³-3x)½ (3x²-1)dx = ∫ (3x³-3x)½ [(3x²-1/3)^(3/2) + C]dx= 9/2 (3x²-1/3)^(3/2) + C.The main steps in three lines are as follows:We use the formula ∫ (a-x)½ (a+x) dx = 1/3 (a-x)^(3/2) (a+x) + C. We substitute this formula into our expression for 3x²-1. We integrate to get our final answer.

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The probability that a number selected at random from the first 1000 positive integers is divisible by 6 or 8 is 3/10 or 0.3.

The number of positive integers between 1 and 1000 is 1000. We can divide the number of positive integers by 6 or 8. We can start by dividing the number of positive integers by 6, then by 8.Number of integers divisible by 6:Number of positive integers between 1 and 1000 that are divisible by 6 = (1000 ÷ 6) = 166 2/3So, we can only take the integer value that is 166. The other numbers that follow the integer are not positive integers between 1 and 1000. Therefore, there are 166 positive integers between 1 and 1000 that are divisible by 6.

Number of integers divisible by 8:Number of positive integers between 1 and 1000 that are divisible by 8 = (1000 ÷ 8) = 125So, there are 125 positive integers between 1 and 1000 that are divisible by 8. Counting numbers that are divisible by both 6 and 8:Next, we will find out how many numbers are divisible by both 6 and 8.The least common multiple of 6 and 8 is 24. So, we have to find all positive integers between 1 and 1000 that are divisible by 24.Number of integers divisible by 24:Number of positive integers between 1 and 1000 that are divisible by 24 = (1000 ÷ 24) = 41So, there are 41 positive integers between 1 and 1000 that are divisible by 24.Now we can add up the total number of positive integers between 1 and 1000 that are divisible by 6 or 8.166 + 125 − 41 = 250Therefore, there are 250 positive integers between 1 and 1000 that are divisible by 6 or 8. Finally, we can calculate the probability by dividing the number of positive integers that are divisible by 6 or 8 by the total number of positive integers between 1 and 1000.250 ÷ 1000 = 0.25 or 1/4Therefore, the probability that a number selected at random from the first 1000 positive integers is divisible by 6 or 8 is 3/10 or 0.3.

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Answer:

     1.

a. 6/9 (2/3)

b. 9/6 (3/2)

     2.

a. 4/8 (1/2)

b. 8/2 (4/1)

     3.

a. 3/9 (1/3)

b. 9/3 (3/1)

     4.

a. 2/10 (1/5)

Step-by-step explanation:

Hope this helps :)

Answer:

i think the answer would be 0.5

Step-by-step explanation:

√3600 = 60

Make the base 3600 and the exponent 0.5 to get the answer:

3600 ^0.5 = 60

which would mean if your base is 60 the you switch it so that the 60 is before the equal of the exponent which would mean that the answer would be 0.5.

I hope this helps :) and if it's wrong i'm sorry

To express the events using set operations, we use the following notation: E represents event E, F represents event F, and G represents event G. The complement of an event is denoted by adding a prime symbol ('), indicating the event does not occur.

(a) For only F to occur, we need F to happen but not E and G. Thus, the expression is F and (E' ∩ G').

(b) For both E and F to occur but not G, we consider the intersection of E, F, and the complement of G. The expression is E ∩ F ∩ G'.

(c) To express at least one event occurring, we use the union of events E, F, and G. The expression is E ∪ F ∪ G.

(d) For at least two events to occur, we consider the union of all possible combinations of two events and the intersection of all three events. The expression is (E ∩ F) ∪ (E ∩ G) ∪ (F ∩ G) ∪ (E ∩ F ∩ G).

(e) All three events occurring is represented by the intersection of E, F, and G. The expression is E ∩ F ∩ G.

(f) For none of the events to occur, we need the complement of E, F, and G. The expression is (E' ∩ F' ∩ G').

(g) At most one event occurs when either none of the events occurs or only one event occurs. The expression is (E' ∩ F' ∩ G') ∪ (E ∩ F' ∩ G') ∪ (E' ∩ F ∩ G').

(h) At most two events occur when either none of the events occurs, only one event occurs, or two events occur. The expression is (E' ∩ F' ∩ G') ∪ (E ∩ F' ∩ G') ∪ (E' ∩ F ∩ G') ∪ (E' ∩ F' ∩ G) ∪ (E ∩ F ∩ G') ∪ (E ∩ F' ∩ G).

These expressions provide a way to describe various combinations and relationships among the events E, F, and G using set operations.

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Cyphon, this is the solution:

We have to multiply the following fractions:

7/12 * 4/3

7 * 4 / 12 * 3

28/36

Simplifying, we have:

7/9 (Dividing by 4 numerator and denominator)

We have to add the following fractions:

- 1/2 + 4/9

Let's find the lowest common denominator between 2 and 9, as follows:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

9, 18, 27, 36

The lowest common denominator is 18

Answer:

400 milliliters

Step-by-step explanation:

multiply 4 x 100

=400

The length of AC is given as follows:

AC = 18.3 cm.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

We look at triangle AED, with AR = 4 and hypotenuse AD = 10, hence the side length AE is given as follows:

(AE)² + 4² = 10²

\(AE = \sqrt{10^2 - 4^2}\)

AE = 9.165.

E is the midpoint of AC, hence the length AC is given as follows:

AC = 2 x 9.165

AC = 18.3 cm.

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The given number is

The scientific notation of the number is,

The equations will have the following solutions:

1.) n = -8.86; 2.) k = 17.5; 3.) a = -6.12; 4.) p = 1.66; 5.) x = -11/24;

6.) k = 4/5; 7.) k = -56; 8.) w = 45/10; 9.) y = -17/20; 10.) k = -56/15; 11) m = 44/9; 12) m = 69/20

To determine the solution of a given equation, all we need to do is to Isolate the variable to one side of the equation.

To check the equation involves plugging in the value of the variable gotten as a solution to see if makes the equation true. If true, then the solution is correct.

1 -5.51 = n + 3.35

-5.51 - 3.35 = n

n = -8.86

Plug in the value of n to check the equation if it is true:

-5.51 = -8.86 + 3.35

-5.51 = -5.51 (true)

2. -3.4k = -59.5

k = -59.5/-3.4 [division property of equality]

k = 17.5

Plug in the value of k to check the equation if it is true:

-3.4(17.5) = -59.5

-59.5 = -59.5 (true)

3. 0.85 = a/-7.2

-7.2(0.85) = a [multiplication property of equality]

a = -6.12

Plug in the value of a to check the equation if it is true:

0.85 = -6.12/-7.2

0.85 = 0.85 (true)

4. -2.25 + p = -0.59

p = -0.59 + 2.25 [addition property of equality]

p = 1.66

Plug in the value of p to check the equation if it is true:

-2.25 + 1.66 = -0.59

-0.59 = -0.59 (true)

5. x + 3/8 = -1/12

x = -1/12 - 3/8 [subtraction property of equality]

x = -11/24

Check:

-11/24 + 3/8 = -1/12

-1/12 = -1/12 (true)

6. -6/5k = -24/25

-6/5k × -5/6 = -24/25 × -5/6 [multiplication property of equality]

k = 4/5

Check:

-6/5(4/5) = -24/25

-24/25 = -24/25 (true)

7. 28 = -1/2k

28 × -2 = -1/2k × -2

k = -56

Check:

28 = -1/2(-56)

28 = 28

8. w - 4 2/5 = 1/10

w - 22/5 = 1/10

w = 1/10 + 22/5 [addition property of equality]

w = 45/10

Check:

45/10 - 4 2/5 = 1/10

1/10 = 1/10 (true)

9. -2 1/4 = -1 2/5 + y

-9/4 + 7/5 = y [addition property of equality]

y = -17/20

Check:

-2 1/4 = -1 2/5 + (-17/20)

-2 1/4 = -2 1/4

10. 1 7/15 = -11/28k

22/15 = -11/28k

22/15 × -28/11 = -11/28k × -28/11

k = -56/15

Check:

1 7/15 = -11/28(-56/15)

1 7/15 = 1 7/15 (true)

11. m - 3 2/9 = 1 2/3

m = 1 2/3 + 3 2/9 [addition property of equality]

m = 44/9

12 -5/9m = 1 11/12

-5/9m = 23/12

-5/9m × -9/5 = 23/12 × -9/5

m = 69/20

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The number of robberies in year 4 is  1.14 times the number of robberies in year 2.

the number of robberies in the year 4 is 255.

the number of robberies in year 2 is 225.

Now to find how many times the robberies took place in year 4 than in year 2 we will take the ratio as follows-

number of robberies in year 4/number of robberies in year 2 = 255/225

hence, we have,

number of robberies in year 4/number of robberies in year 2 = 17/15

number of robberies in year 4/number of robberies in year 2 = 1.13333

number of robberies in year 4/number of robberies in year 2 = 1.14

or we can say that number of robberies in year 4 = 1.14 * the number of robberies in year 2

i.e number of robberies in year 4 = 1.14 times the number of robberies in year 2.

Hence, the number of robberies in year 4 is  1.14 times the number of robberies in year 2.

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The complete question is -

how many times as many robberies were there actually in year 4 compared to year 2? round your answer to 2 decimal places.

Answer:

Top Right

Step-by-step explanation:

The greater than or equal to sign makes the line solid, and the greater than 2 makes the shading go to the right

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

Answer:

To find the center and radius of the circle given by the equation x² + y² + 4x - 6y = 5, we can complete the square for both the x and y terms.

Rearranging the equation, we have:

x² + 4x + y² - 6y = 5

To complete the square for the x-terms, we add (4/2)² = 4 to both sides of the equation:

x² + 4x + 4 + y² - 6y = 5 + 4

Similarly, to complete the square for the y-terms, we add (-6/2)² = 9 to both sides of the equation:

x² + 4x + 4 + y² - 6y + 9 = 5 + 4 + 9

Simplifying, we get:

(x + 2)² + (y - 3)² = 18

Comparing this equation to the standard form of a circle equation (x - h)² + (y - k)² = r², we can see that the center of the circle is (-2, 3) and the radius is the square root of 18, which simplifies to approximately 4.2426.

Step-by-step explanation:

To find the center and radius of the circle x²+y²+4x-6y=5, we need to complete the square for both variables:

x²+4x+y²-6y=5

(x²+4x+4) + (y²-6y+9) = 18

(x+2)² + (y-3)² = 18

Therefore, the center of the circle is (-2,3), and the radius is the square root of 18, or approximately 4.24.

Answer: did you make that up ??

Step-by-step explanation:

Answer:

A. Alternate interior

B. Transitive property

C. Converse alternate interior angles theorem.

Answer:

1/4, 3/8, 2/3

Step-by-step explanation:

Answer:

1/4. 3/8. 2/3

Step-by-step explanation:

1/4, 3/8 and 2/3

Answer:

Step-by-step explanation:

(x-60)+(x-20)+(x-40)+130+120+110=720

3X -120 + 360=720

3x +240= 720

3x= 720-240

3x=480

x= 480/3 = 160

x=160

angle F = (x-20)

angle F = 160-20=140

angle F = 140

Answer:

147

Step-by-step explanation:

Multiply the average by the number of values

85*5=425

Find the sum of the 3 values you have

102+96+80=278

Take the sum of the 3 values you have away from the sum of all 5 values

425-278=147

Answer:

Step-by-step explanation:

(102 + 96 + 80 + x + y)/5 = 85

278 + x + y = 85 × 5

278 + x + y = 425

x + y = 425 - 278

x +  y = 147

The general solution for the differential equation: -2ty 4e^-t^2 is y = √(π^3) * e^(t^2) * erf(t).

To find the general solution of the given differential equation, we'll use the method of integrating factors. The differential equation is:

-2ty + 4e^(-t^2) = 0

To solve this, we can rewrite the equation in standard form:

y' + (-2t)y = 4e^(-t^2)

The integrating factor (denoted as μ) for this differential equation is given by:

μ = e^(∫(-2t) dt) = e^(-t^2)

Now, we'll multiply both sides of the equation by the integrating factor:

e^(-t^2)y' + (-2t)e^(-t^2)y = 4e^(-t^2)e^(-t^2)

Simplifying this equation, we get:

(d/dt)(e^(-t^2)y) = 4e^(-2t^2)

Now, we can integrate both sides with respect to t:

∫(d/dt)(e^(-t^2)y) dt = ∫4e^(-2t^2) dt

Integrating the left side yields:

e^(-t^2)y = ∫4e^(-2t^2) dt

The integral on the right side is not easily solvable in terms of elementary functions. However, we can express the solution using the error function (erf), which is a special function often used in the context of integrating Gaussian distributions. The integral can be rewritten as:

e^(-t^2)y = 2√π * ∫e^(-2t^2) dt = 2√π * ∫e^(-t^2) e^(-t^2) dt

This integral can be expressed in terms of the error function:

e^(-t^2)y = 2√π * (1/2) * √(π/2) * erf(t)

Simplifying further:

e^(-t^2)y = √(π^3) * erf(t)

Finally, solving for y:

y = √(π^3) * e^(t^2) * erf(t)

Therefore, the general solution of the given differential equation is:

y = √(π^3) * e^(t^2) * erf(t)

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The spring is compressed to 95.5 cm to the right if 129 N of force are used.

In this question, we have been given the spring constant k = 283 N/m

if 129 N of force are used then we need to find distance  that the spring compressed to the right.

Let the spring stretch from the equilibrium position x.

An equation for the spring's potential energy is,

PE = 1/2 ​kx^2

129 = 1/2 * 283 * x^2

2 * 129 = 283 * x^2

258/283 = x^2

x^2 = 0.9117

x = 0.9548 m

x = 95.5 cm

Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.

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Answer:

0.60.

Step-by-step explanation:

We divide the percent by 100.

60 / 100 = 0.60.

Answer:

Angela is 12 and Micah is 28.

Step-by-step explanation:

So, the problem tells us that Micah is four more than twice Angel's age, and the sum of both their ages is 40. So, if we use a to stand for Angela's age and m to stand for Micah's age, we can safely assume our equation will look like this:

(a × 2) + 4 = m. And once that is figured out, we use a + m = 40.

For right now, we can start just randomly entering in numbers for a. Let's try 10, for example.

(10 × 2) + 4 = 24.

But does 10 + 24 = 40? No, it equals 34. So we go higher.

(12 × 2) + 4 = 28.

Does 12 + 28 = 40? Yes, yes it does.

So we can say with all certainty that Micah is 28 years old, and Angela is 12.

Answer:

\(x=2\)

Step-by-step explanation:

I believe your question is:

For what value of \(x\) does \(3^{2x}=9^{3x-4}\)?

—

First, rewrite \(9\) as \(3^2\):

\(3^{2x}=(3^2)^{3x-4}\)

Then, use exponentiation to apply the \((a^b)^c=a^{bc}\) rule:

\(3^{2x}=3^{2(3x-4)}\)

Rewrite the expression as a non-exponential one since the bases (\(3\)) are equal on both sides:

\(2x=2(3x-4)\)

Distribute the \(2\):

\(2x=6x-8\)

Subtract \(6x\) from both sides:

\(-4x=-8\)

Divide both sides by \(-4\):

\(x=2\)

Answer:

there should be 14, 45 pound boxes

Step-by-step explanation:

1000-190= 810

810/45=14 boxes

Answer:

If the rate of change is -3, just subtract -3 from 14 (or make the equation to help you).

_________________________________________________________

The equation for the first one is:

y = -3x + 14

When you plug in the x values, you get the y values:

(-2, 20), (1, 11), (3, 5), (4, 2), (6, -4)

For the second one, the start value is 2, meaning that is is y. This means that when 2 is plugged in for y, the result is 0 (x). Now we can make the equation:

y = 0.4x + 2

When you plug the x values in, you get the y values:

(-1, 1.6), (1, 2.4), (4, 3.6), (5, 4), (10, 6)

_________________________________________________________