Twelve decreased by 8 times a number is 36. Find the number.

Answer:

Sales tax : $27

Total price : $477

Step-by-step explanation:

Given that:

Sale price of tv = $450

Sales tax = 6%

Amount of sales tax = \(\frac{6}{100}*450\)

Amount of sales tax = 0.06 * 450

Amount of sales tax = $27

Total price = Sale price + Sales tax

Total price = 450 + 27 = $477

Hence,

Sales tax : $27

Total price : $477

Answer:

u = 21

Step-by-step explanation:

\(\frac{u-5}{8}\) = 2 ( multiply both sides by 8 to clear the fraction )

u - 5 = 16 ( add 5 to both sides )

u = 21

Step-by-step explanation:

=  3900 ( 1 + .86 )^x      the .86 represents 86 %  growth increase

The range of the function shown in the graph is the set of all real numbers for y.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

The set of input values in the function is called domain and the set of output values are called range of the function.

So the range of the function will be the set of y values.

From the graph, it is clear that, the curve is passing corresponding to every y value.

In other words, if we draw a horizontal lines from curve, all the y values are touching the curve.

So the range is the set of all real numbers.

Hence the range is all the real numbers for y.

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Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given logarithmic expression

STEP 2: Find the value of x

State the rule of logarithm that applies

Apply the rule

Hence, the value of x is approximately 10.56

Answer:

Step-by-step explanation:

y + 6 = -3(x - 4)

y + 6 = -3x + 12

y = -3x + 6

To solve for the dimensions of the rectangular container, we need to set up equations based on the given volume and then minimize the surface area.

(i) Solving for the dimensions:

Let's assume the dimensions of the rectangular container are x, y, and z.

Based on the given information, the volume of the container is 50.3 m³. Therefore, we have the equation:

V = x * y * z = 50.3

To find the values of x, y, and z, we need additional information or constraints. Without any further information, we cannot uniquely determine the values of x, y, and z.

(ii) Showing the obtained values are local minimum:

Since we don't have specific values for x, y, and z, we cannot determine whether they correspond to local minimum or maximum.

(iii) Computing the surface area of the material required:

The surface area of an open rectangular container consists of the sum of the areas of its five faces (excluding the top face).

The surface area, A, can be calculated as:

A = 2(xy + xz + yz)

Substituting the values of x, y, and z, which we assume to be known, we can compute the surface area.

In summary, without further information or constraints, we cannot determine the specific values of x, y, and z. Therefore, we cannot determine whether they correspond to a local minimum or maximum. Additionally, the computation of the surface area requires specific values for the dimensions of the container.

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Given:

A roofer earns ​$25 per hour for regular hours worked and ​$30 per hour for overtime hours worked. He puts in 40 hours of regular time during a certain week and he wishes to earn ​$1140​.

Required:

To find how many hours of overtime should he​ work.

Explanation:

Let he should work x hours overtime.

Then the equation becomes:

He should work approximately 5 hours.

Final Answer:

He should work approximately 5 hours overtime.

Answer:

I think its 1 and 1/2 because 3/2 = 1 and 1/2 which equals to 1.5

The maximum value of the sine function is 1, the angle corresponding to sin^(-1)(1) is π/2 or 90 degrees.

The principal value of sin^(-1)(1) is π/2 or 90 degrees.

The function sin^(-1)(x), also known as arcsin(x) or inverse sine, represents the angle whose sine is equal to x. In this case, we are looking for the angle whose sine is 1.

Since the sine function oscillates between -1 and 1, the angle corresponding to sin^(-1)(1) is the maximum value where the sine is equal to 1.

This occurs at π/2 or 90 degrees, making it the principal value for sin^(-1)(1).

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Since the p-value for a one-sided test of the null hypothesis H0: μ = 15 is 0.03, we can reject H0 at the 5% level of significance but not at the 1% level.

The purpose of a hypothesis is to discuss a notion or assumption and see if it might be true. Before conducting any pertinent research—aside from a basic background review—the hypothesis is formulated using the scientific process.

(a) For a 99% confidence interval, the level of significance is 1% (α = 0.01), which is less than the given p-value of 0.03. Therefore, we cannot reject the null hypothesis at the 99% confidence level, and we conclude that the 99% confidence interval for μ does include 15.

(b) For a 95% confidence interval, the level of significance is 5% (α = 0.05), which is greater than the given p-value of 0.03. Therefore, we can reject the null hypothesis at the 95% confidence level. This means that the 95% confidence interval for μ does not include 15.

In summary, the 99% confidence interval includes 15, while the 95% confidence interval does not include 15. This makes sense, as the p-value of 0.03 indicates that the evidence against the null hypothesis is not very strong, but it is still significant at the 5% level.

Therefore, a wider confidence interval (with a higher level of confidence) will include the null hypothesis value, while a narrower confidence interval (with a lower level of confidence) will not.

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Answer:

b

Step-by-step explanation:

Answer:

The variable t is equal to 9.

Step-by-step explanation:

We are given t • 7 = 63.  To solve this for t, we divide both sides of this equation by 7, obtaining:

t = 63/7 = 9

The variable t is equal to 9.

Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

The area of one wall is 25 m²

The square room has a floor area of 81 m². Since the room is square, the walls sizes are the same.

The height of the room is 5 meters. Therefore,

l = length

l = 5 m

Area = 5²

Area = 25 m²

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Answer:

Step-by-step explanation:

the answer is 45 trust me

Since (A + B)² ≠ A² + 2AB + B² for this counterexample, we have disproven the statement that (A + B)² = A² + 2AB + B² holds for all 2x2 matrices A and B.

a) Given matrix A = [[1]].

To find A², we simply multiply A by itself:

A² = [[1]] * [[1]] = [[1]]

To find (A²)t, we take the transpose of A²:

(A²)t = [[1]]t = [[1]]

To find (A¹)², we raise A to the power of 1:

(A¹)² = [[1]]¹ = [[1]]

b) Given matrices A = [[3, 2], [1, 4]] and B = [[1, 1], [0, 1]].

To find A V B, we perform the matrix multiplication:

A V B = [[3, 2], [1, 4]] * [[1, 1], [0, 1]] = [[3*1 + 2*0, 3*1 + 2*1], [1*1 + 4*0, 1*1 + 4*1]] = [[3, 5], [1, 5]]

To find A ^ B, we raise matrix A to the power of B. This operation is not well-defined for matrices, so we cannot proceed with this calculation.

To find A ○ B, we perform the element-wise multiplication:

A ○ B = [[3*1, 2*1], [1*0, 4*1]] = [[3, 2], [0, 4]]

c) To prove or disprove that for all 2x2 matrices A and B, (A + B)² = A² + 2AB + B².

Let's consider counterexamples to disprove the statement.

Counterexample:

Let A = [[1, 0], [0, 1]] and B = [[0, 1], [1, 0]].

(A + B)² = [[1, 1], [1, 1]]² = [[2, 2], [2, 2]]

A² + 2AB + B² = [[1, 0], [0, 1]]² + 2[[1, 0], [0, 1]][[0, 1], [1, 0]] + [[0, 1], [1, 0]]² = [[1, 0], [0, 1]] + 2[[0, 1], [1, 0]] + [[0, 1], [1, 0]] = [[1, 1], [1, 1]]

Since (A + B)² ≠ A² + 2AB + B² for this counterexample, we have disproven the statement that (A + B)² = A² + 2AB + B² holds for all 2x2 matrices A and B.

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Answer:

1. y= -2

Step-by-step explanation:

i hope this helps :)

Answer:

option (3)

Step-by-step explanation:

The equation of a vertical line parallel to the y- axis is

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (- 2, - 5 ) and (- 2, - 4) with x- coordinates - 2 , then

x = - 2 ← equation of line

To find the radian measure of a central angle that intercepts an arc of length 12 inches in a circle with a radius of 17 inches.

In a circle, the relationship between the central angle (θ) and the arc length (s) is given by the formula s = rθ, where r is the radius of the circle. In this case, the radius (r) is 17 inches, and the arc length (s) is 12 inches.

To find the radian measure of the central angle (θ), we rearrange the formula as follows:

s = rθ  (Divide both sides by r)

θ = s/r

Substituting the given values:

θ = 12/17

Therefore, the radian measure of the central angle that intercepts an arc of length 12 inches in a circle with a radius of 17 inches is approximately 0.7059 radians.

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====================================================

Explanation:

One equation we could solve is

x/2.5 = 30/7.5

Note the x/2.5 has us dividing the vertical sides, while 30/7.5 is the same idea for the horizontal sides. The order is large over small. You could do small over large, but make sure you keep both sides consistent.

Solving for x leads to...

x/2.5 = 30/7.5

x*7.5 = 2.5*30

7.5x = 75

x = 75/7.5

x = 10  (choice A)

There are many other possible equations that lead to the same answer. One other possible equation is x/30 = 2.5/7.5

These proportions are possible due to the fact we have similar triangles.

Answer:

-10

Step-by-step explanation:

1 2/2= 2

2/(-1/5)=(-10)

Answer:

-10

Step-by-step explanation:

1 2/2 / -1/5

2 × 5 / -1/5 × 5

10 / - 1

10 × -1 / -1 × -1

-10 / 1

-10

Answer:

x = 7

Step-by-step explanation:

The indicated angles are vertical and congruent, thus

14x + 2 = 13x + 9 ( subtract 13x from both sides )

x + 2 = 9 ( subtract 2 from both sides )

x = 7

HOPE THIS IS THEANSWER YOU NEEDED

Answer:

D)  x ≥ -2

Step-by-step explanation:

Answer:

h = 13

Step-by-step explanation:

3h + 42 = 8h - 23

     + 23        + 23          Add 23 to both sides

3h + 65 = 8h

-3h           -3h            Subtract 3h from both sides

65 = 5h

h = 13               Divide both sides by 5

Answer:

35 miles per gallon.

Step-by-step explanation:

We need to simplify 175/5 into 35/1 to make it into a unit rate. So, 35 miles per gallon is the answer.

The polygon with the given vertices after the dilation is graphed on the image given at the end of the answer.

A dilation is one type of transformation that is applied to the images, changing the side lengths of the image.

The side lengths of the image are changed because each coordinate of each vertex of the original polygon is multiplied by the scale factor of the dilation.

The vertices of the original polygon in this problem are given as follows:

J(4,0), K(-8,4), L(0,-4), M(12,-8).

The scale factor is of:

k = 0.25.

Meaning that each coordinate of each vertex of the polygon is multiplied by 0.25, which is equivalent to a division by 4.

Then, the coordinates of the vertices of the image of the polygon are as follows:

J'(1,0), K'(-2,1), L'(0,-1), M'(3,-2).

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In this problem, we have that

A=L*W

dL/dt=12 in/sec ----> given

dW/dt=-2 in/sec ---> given

Find out dA/dt

dA/dt=L*dW/dt+W*dL/dt

For L=25 in and W=5 in

substitute

dA/dt=25*(-2)+5*(12)

dA/dt=-50+60

There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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Answer:

The parenthesis means to multiply the numbers. I don't understand any of these either but I hope this helps.

Step-by-step explanation:

Pie charts are effective in conveying percentages and are commonly used in data analysis and presentations.

The true statement about pie charts is that they are effective in showing percentages. Pie charts are a common data visualization tool used to represent proportions or percentages of a whole.

The chart is divided into slices, with each slice representing a specific category or data point. The size of each slice is proportional to the percentage it represents within the whole.

This visual representation makes it easier for viewers to understand the distribution and relative proportions of different categories or variables. Pie charts are therefore frequently used in data analysis and presentations because they are good at communicating percentages.

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