Which equation is equivalent to 3[x + 3(4x – 5)] = 15x – 24?
a.15x – 15 = 15x – 24
b.15x – 5 = 15x – 24
c.39x – 45 = 15x – 24
d.39x – 15 = 15x – 24

Answer:

the amount of work that is done when the wall is moving 0.5 m is 250 jewels

Step-by-step explanation:

1) write out the equation

(W=F×d)

2) plug in the numbers into the equation

W= F×d= 500 ×0.5 m

3) solve the problem

W=F×d=500 × 0.5m =250 jewels

The probability that Belle will select two hearts is 2/15.

To find the probability of Belle selecting two hearts, we need to calculate the probability of selecting a heart on the first draw and then, given that the first card was a heart, the probability of selecting another heart on the second draw.

Total number of cards = 3 (star cards) + 4 (hearts cards) + 3 (spade cards) = 10 cards

Probability of selecting a heart on the first draw = 4 (hearts cards) / 10 (total cards) = 2/5

After selecting a heart on the first draw, there will be 9 cards remaining, with 3 hearts cards left.

Probability of selecting a heart on the second draw, given that the first card was a heart = 3 (hearts cards) / 9 (remaining cards) = 1/3

To find the probability of both events happening (selecting two hearts), we multiply the probabilities:

Probability of selecting two hearts = (2/5) x (1/3) = 2/15

Therefore, the probability that Belle will select two hearts is 2/15.

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Based on their given probabilities, e would expect the color blue or green to be spun approximately 75 times in this experiment.

To find the expected number of times the color blue or green will be spun, we first need to add their probabilities:

0.25 + 0.125 = 0.375

This means that, on average, we would expect to see blue or green spun 0.375 times for every spin. To find the expected number of times this will happen over 200 spins, we can multiply the probability by the number of spins:

0.375 x 200 = 75

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A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

+52

Step-by-step explanation:

If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.

Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.

First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:

Social Security tax = $102,000 x 0.062 = $6,324

Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:

Social Security tax = $1,100 x 0.062 = $68.20

Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.

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Answer:

Step-by-step explanation:

A = length x width = (2w + 5)(w) = 2w² + 5w

P = 2(2w + 5) + 2w = 6w + 10

To graph:  sorry, Brainly doesn't have graphing tools so I'll just have to describe it

A:  parabola, opens up, vertex at (-1.25, -3,124), crosses x axis at (-2.5, 0) and (0,0)

P:  straight line, slants up, with a slope of 6, y-intercept of 10, crosses x axis at (-1.667, 0)

FYI, the 2 graphs intersect at 2 points:  (-2, 2) and (2.5, 25)

Answer: 2w+6

Step-by-step explanation: Here you distribute. Simply multiply 2 and w which would get you 2w and 2 by 3 which would get you 6.

A store sells 5 oranges and 10 apples.

What is the cost amount?

The cost of an asset to you often serves as its basis. The cost is the sum that you pay for it using money, debt, other goods, or services. Sales tax and other purchase-related costs are included in the price.

Here, we have

Given: A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25.

We have to determine how many of each type of fruit were sold.

We, let the oranges be x.

let the apples be y.

x + y = 15...(1)

1x + 2y = 25...(2)

We subtract equation(2) from equation(1), we get

y = 10

Now we put the value of y in equation (1) and we get

x + 10 = 15

x= 5

Hence, a store sells 5 oranges and 10 apples.

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Answer: 21.15 ft²

Step-by-step explanation:

We can use the formula for the area of a triangle:

(b×h)/2

In this case, the base is 9 and the height is 4.7.

So, we substitute the variables with the numbers in this problem.

(9 × 4.7)/2

9 × 4.7 = 42.3

42.3/2 = 21.15

So, our final answer is 21.15 ft²

The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.

The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.

The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.

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Answer:

2/6; 3/9

Step-by-step explanation:

1/3

Multiply any random number of your choice to both the numerator and denominator

Example:

1/3 × 2/2

2/6

To check your multiplication, you can always take your answer and divide it by the original fraction. If you did everything correctly, you will get the product of 1.

Example:

2/6 ÷ 1/3

Copy dot flip

2/6 × 3/1

6/6

1

Step-by-step explanation:

\( - \frac{3}{2} < 3x\)

\(3x > - \frac{3}{2} \)

\(x > - \frac{3}{2} \div 3\)

\(x > - \frac{1}{2} \)

Answer:

x=6

Step-by-step explanation:

Answer: x=6

Step-by-step explanation: 5•6+3=33

Good luck! :)

From the drawing made, we can see that a triangle with a right angle is form, thus, a right triangle.

Since this is a right triangle, the properties of sine, cossine and tangent apply. RS is the leg opposite to the 80° angle, while 20m is the length of the hypotenuse. So we can use sine to find RS.

So, the closest alternative is 19.7 m.

Answer:

100cubic inches

Step-by-step explanation:

varies inversely

pv = k

Find the constant of variation:

volume of 180 cubic inches under a pressure of 5 pounds

5 * 180 = k

k = 900

volume if the pressure is increased to 9 pounds per square inch?

9v = 900

divide both sides by 9

v = 100

Dividing by a fraction is equivalent to multiply by its inverse. For example, if you want to divide 3/4 by 5/6, you have to compute 3/4 multiplied by 6/5

18/20 can be simplified by dividing each term by the same number, in this case by 2.

If you want to divide mixed numbers, first, you have to convert the mixed numbers into improper fractions, and then proceed as explained above.

Answer:

B. 273

Step-by-step explanation:

First we have to find the volume of the pencil box.

The volume formula for a rectangular prism is lwh (Length x width x height). Length (6 1/2) x Width (3 1/2) x Height (1 1/2) = 34.125 (Volume of the pencil box)

Next, we have to find the volume of the cube.

The volume formula of a cube is the same as the volume formula for a rectangular prism (lwh). However, a cube's side lengths are all the same. This means that the volume of the cube would be Length (.5) x Width (.5) x Height (.5) = .125

Last, we have to divide the volume of the pencil box by the volume of the cube.

34.125 / .125 = 273 or B.

We can claim that after answering the above question, the So, logarithm \(log4 (0.5^(1/2)) =-0.0752\)

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

Using the following property of logarithms:

\(log_a (b^c) = c * log_a (b)\\log4 (0.5^(1/2))\\(1/2) * log4 (0.5)\\log4 (0.5) = log (0.5) / log (4)\\log (0.5) ≈ -0.3010\\log (4) = 2\)

Therefore,

\(log4 (0.5) ≈ -0.3010 / 2 ≈ -0.1505\\(1/2) * log4 (0.5) ≈ (1/2) * (-0.1505) ≈ -0.0752\\\)

So, \(log4 (0.5^(1/2)) =-0.0752\)

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Answer:

y = 19.2

Step-by-step explanation:

We know there is relationship between y and x, so according to the formula \(y = kx\)

k = 12/5

we get one function y = 2.4x

when x = 8, input it into the function,

y = 2.4×8 = 19.2

The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

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Answer:

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sofiapenaloza

05/31/2023

Mathematics

College

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The equation for the line of best fit for change in temperature, y, to amount of rain, r, is given by ŷ = − 1.4r + 0.2. On Monday, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees. Find and interpret the residual.

2.66; The line of best fit overpredicts the temperature change.

2.66; The line of best fit underpredicts the temperature change.

1.94; The line of best fit underpredicts the temperature change.

−1.94; The line of best fit overpredicts the temperature change.

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joaobezerra

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The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

What are residuals?

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

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Step-by-step explanation:

Expression for given numerical is: 9+ (2/x)

Given that we have an word equation that is 9 more than the quotient of 2 and  x

A quotient is a quantity produced by the division of two numbers.

Quotient of 2 and x is \(\frac{2}{x}\).

Nine(9) more  than 2/x is = 9+ (2/x)

So we have an expression that is:

              9+ (2/x)                          

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Answer:

y≈1.778 (or y=log(3600)/2 or y=log(6)+1)

Step-by-step explanation:

10^2y=3600

log(10^2y)=log(3600)

2y=log(36)+log(100)

2y=log(6²)+2

2y=2log(6)+2

2y-2=2log(6)

y-1=log(6)

y=log(6)+1

y≈1.778

Using the binomial distribution, we have that:

a) 0.1024 = 10.24% probability that the marketing representative must select 4 people to find one who attended the last home football game.

b) 0.2621 = 26.21% probability that the marketing representative must select more than 6 people to find one who attended the last home football game.

c) The expected number of people is 4, with a variance of 20.

For each person, there are only two possible outcomes. Either they attended a game, or they did not. The probability of a person attending a game is independent of any other person, which means that the binomial distribution is used.

Binomial probability distribution  

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)  

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

The expected number of trials before q successes is given by:

\(E = \frac{q(1-p)}{p}\)

The variance is:

\(V = \frac{q(1-p)}{p^2}\)

In this problem, 0.2 probability of a finding a person who attended the last football game, thus \(p = 0.2\).

Item a:

Thus:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{3,0}.(0.2)^{0}.(0.8)^{3} = 0.512\)

\(0.2(0.512) = 0.1024\)

0.1024 = 10.24% probability that the marketing representative must select 4 people to find one who attended the last home football game.

Item b:

This is the probability that none of the first six went, which is P(X = 0) when n = 6.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{6,0}.(0.2)^{0}.(0.8)^{6} = 0.2621\)

0.2621 = 26.21% probability that the marketing representative must select more than 6 people to find one who attended the last home football game.

Item c:

The expected value is:

\(E = \frac{q(1-p)}{p} = \frac{0.8}{0.2} = 4\)

The variance is:

\(V = \frac{0.8}{0.04} = 20\)

The expected number of people is 4, with a variance of 20.

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