Calculate the consumers' surplus at the indicated unit price p for the demand equation. HINT (See Example 1.] (Round your answer to the nearest cent.) q = 120 - 2p; p = 10 Need Help? Read It

The length of bc is 8. The result is obtained by using the concept of conditions for similar triangles.

For two or more similar triangles, it has two conditions.

A right triangle abc with altitude bd drawn to hypotenuse ac has the length of sides as follow

Find the length of bc!

Observe the picture of triangles in the attachment! If we drawn a perpendicular line to the hypotenuse, we'll have three similar triangles.

The corresponding sides of the two triangles are

\(\frac{\overline{ac}}{\overline{bc}} = \frac{\overline{bc}}{\overline{dc}} = \frac{\overline{ab}}{\overline{bd}}\)

The length of bc is

\(({\overline{bc})^{2} = \overline{ac} \times {\overline{dc}\)

\(({\overline{bc})^{2} = 16 \times 4\)

\(({\overline{bc})^{2} = 64\)

\({\overline{bc} = \sqrt{64}\)

\({\overline{bc} = 8\)

Hence, the length side of bc on the right triangle is 8.

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IT is found that the value of x is 4 and value of y is 5.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given system of equations are

2x-6y=22

-5x+y=1

The matrix form is

\(\left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}22\\1\end{array}\right]\)

Let as assume

\(A = \left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right]\\ \\X = \left[\begin{array}{ccc}x\\y\end{array}\right] \\B = \left[\begin{array}{ccc}22\\1\end{array}\right]\)

WE know that AX = B

Then we have;

\(\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4\\5\end{array}\right]\)

Therefore, the value of x is 4 and value of y is 5.

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Answer:

\((s-r)(x)=x^2-x+1\)

Step-by-step explanation:

Answer:

There are 2 parts of the equation

The first answer to answer is (2x+1)--(-x2+3x)

The second answer is x2--x+1

Step-by-step explanation:

I hope you have a wonderful day!!

Love you all!!

Let X be the number of people who experience mild side effects after taking the drug. X follows a binomial distribution with parameters n = 100 (the number of people taking the drug) and p = 0.75 (the probability of mild side effects).

To find the probability that more than 70 people will experience mild side effects, we need to calculate:

P(X > 70) = 1 - P(X ≤ 70)

Using the cumulative distribution function (CDF) of the binomial distribution, we can find:

P(X ≤ 70) = F(70) = ∑(i=0 to 70) [nCi * p^i * (1-p)^(n-i)]

where nCi is the binomial coefficient for choosing i items out of n.

We can use a software or calculator to calculate this sum, or use an approximation like the normal approximation to the binomial distribution.

Assuming normal approximation is appropriate, with mean μ = np = 75 and standard deviation σ = sqrt(np(1-p)) = 3.354, we can calculate the z-score:

z = (70.5 - μ) / σ = (70.5 - 75) / 3.354 = -1.33

Using a standard normal distribution table or a calculator with normal distribution functions, we can find the probability of z-score less than -1.33 is 0.0918, which is the probability of 70 or fewer people experiencing mild side effects.

Therefore, the probability of more than 70 people experiencing mild side effects is:

P(X > 70) = 1 - P(X ≤ 70) = 1 - 0.0918 = 0.9082

Using the binomial distribution, there is a probability of approximately 0.9082 that more than 70 people will experience mild side effects out of 100 people who take the drug.

Answer:

14?

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

add the numbers up and get 84 then decide by the number of numbers which is 6 and you will get 14

The algebraic expression for the situation is represented as A = 7y/4

Given data ,

Let the algebraic expression be represented as A

Now , the value of A is

Let the numerator of the fraction be p

Let the denominator of the fraction be q

A = 7 times the quantity y divided by 4

So, the value of p = 7y

The value of q = 4

The value of the numerator is divided by the value of the denominator

Substituting the values in the equation , we get

A = 7y/4

So, the algebraic expression is 7y/4

Hence , the expression is A = 7y/4

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Answer:

need more information

Step-by-step explanation:

more information is needed to answer this question

Bill invested $2000 at 5% annual interest

To solve for the word problem, you need to set up two equations.

Let B and J represent how much Bill and Janette invested respectively

The interest of 5%  = 5/100 = 0.05 and 7%  = 7/100 = 0.07

Based on the given info, we can write that:

J + B = 5000 --- (1)

0.05B + 0.07J= 310 --- (2)

From (1):

J = 5000 - B --- (3)

Put (3) in (2):

0.05B + 0.07(5000 - B) = 310

0.05B + 350 - 0.07B = 310

-0.02B = 310-350

-0.02B = -40

0.02B = 40

B = 40/0.02

B = $2000

Thus, Bill invested $2000

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Answer:

3

Step-by-step explanation:

We need to isolate x in order to solve it:

First, subtract 4 from both sides

15 - 3x = 2x

Add 3x to both sides

15 = 5x

Divide each side by 5 to get x

x = 3

Answer:

<1  is 90degrees because of properties of a kite(perpendicular diagonals) <2 is 24 degrees, alternate interior angles. <3 is 66degrees from 90-24 Done!

Answer:

I think it's 1.7 hours

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

So this one is pretty much like the last one

the distance on the x values is 6 and the distance on the y values is 4

1/6 of 6 is 1 and 1/6 of 4 is .66

We subtract the coordinates from R

4-1 is 3

2 -.66 =1.33

The 1/6 point is at (-3,1.33)

Answer:

i believe it’s 7.9 miles

Step-by-step explanation:

if there’s no specific location of the house then 7.9 must be the answer

Answer:

divide 195 by 2 , 5 times. Or 195 × 0.5^5

The value of the equation is 35 = 15 + 2y , where y is the number of years and the y = 10 years

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the initial height of the weeping willow be = 15 feet

Let the final height of the weeping willow be = 35 feet

The height in feet the weeping willow grows each year = 24 inches = 2 feet

Let the number of years be = y

On simplifying the equation , we get

35 = 15 + 2y

Subtracting 15 on both sides of the equation , we get

2y = 20

Divide by 2 on both sides of the equation , we get

y = 10 years

Hence , the equation is y = 10 years

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its a fraction which is not in the answer choice

Answer:

Hi there!

Recall that slope-intercept form is:

y = mx + b

Where m = slope

In this instance, we are given a slope of 4,

therefore:

y = 4x + b

Substitute in the x and y coordinates of the point given:

0 = 4(3) + b

0 = 12 + b

Substract 12 from both side:

-12 = b

Therefore, the equation would be:

y = 4x - 12

Graph the equation by finding x and y values or using a calculator:

x = 0, y = 4(0) - 12 = 12 (0, 12)

x = 1, y = 4(1) - 12 = - 8 (1, -8)

x = 2, y = 4(2) - 12 = - 4 (2, -4)

x = 3, y = 4(3) - 12 = 0 (3, 0)

And so forth:

Thanks<8

Answer:

b-6.9 ≤ 12

Step-by-step explanation:

The length of one side of the box, in meters, is 0.138 meters.

The density of water is approximately 1000 kg/m^3 or 1 g/cm^3. If a cubic box is filled with 2650 g of water, we can find the volume of the box and then find one side length.

Volume = Mass / Density = 2650 g/(1 g/cm^3) = 2650 cm^3

Since the box is cubic, one side length is the cube root of the volume.

Side length = (Volume)^(1/3) = (2650 cm^3)^(1/3) = 13.8 cm

To convert cm to meters, divide by 100:

Side length = 13.8 cm/100 cm/m = 0.138 m

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It would take 12 men 18 days to complete the job.

1) g ∝ h

g = kh; where k is the constant of variation.

g = 64, h = 8, hence:

64 = 8k

k = 8

g = 8h

2) j ∝ 1/h

j = k/h; where k is the constant of variation.

j = 190, h = 7, hence:

190 = k/7

k = 1330

j = 1330/h

When h = 70:

j = 1330/70

j = 19

3) y represent number of men and x represent the days

y ∝ 1/x

y = k/x

9 = k/24

k = 216

y = 216/x

For 18 days:

y = 216/18 = 12 men

Hence it would take 12 men 18 days to complete the job.

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Answer:

see explanation

Step-by-step explanation:

If the line slopes upwards from left to right then positive slope

If the line slopes downwards from left to right then negative slope

Answer:

Yes!!!

Step-by-step explanation:

Well, 12/3=4 16/4=4

4=4

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Yes, the conveyors are in a proportional relationship.

Given,

A conveyor belt moves at a constant rate of 12 feet in 3 seconds.

A second conveyor belt moves 16 feet in 4 seconds.

We need to find whether the two conveyors are in proportion relationship.

What is a proportional relationship?

There is a proportional relationship if the ratios of each pair of values are the same.

We have,

- First conveyor belt

12 feet in 3 seconds.

Ratio = 12 / 3 = 4

- Second conveyor belt

16 feet in 4 seconds.

Ratio = 16 / 4 = 4

Ratios are the same.

4 = 4

Thus the conveyors are in a proportional relationship.

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(i) AB = BA but neither A nor B is 0 nor I, and A ‡ B:

Let's consider the following matrices:

A = [[1, 0],

[0, 0]]

B = [[0, 1],

[0, 0]]

To verify the conditions:

AB = [[1, 0],

[0, 0]] * [[0, 1],

[0, 0]] = [[0, 1],

[0, 0]]

BA = [[0, 1],

[0, 0]] * [[1, 0],

[0, 0]] = [[0, 0],

[0, 0]]

As we can see, AB = BA, and neither A nor B is the zero matrix or the identity matrix. Also, A is not equal to B.

(ii) AB + BA:

Let's consider the following matrices:

A = [[1, 0],

[0, 0]]

B = [[0, 1],

[1, 0]]

To verify the condition:

AB + BA = [[1, 0],

[0, 0]] * [[0, 1],

[1, 0]] + [[0, 1],

[1, 0]] * [[1, 0],

[0, 0]]

lua

Copy code

    = [[0, 1],

       [0, 0]] + [[0, 1],

                  [1, 0]]

    = [[0, 2],

       [1, 0]]

(iii) AB = AC but B ‡ C, and the matrix A has no zero entries:

Let's consider the following matrices:

A = [[1, 1],

[0, 1]]

B = [[1, 0],

[0, 1]]

C = [[1, 1],

[0, 2]]

To verify the condition:

AB = [[1, 1],

[0, 1]] * [[1, 0],

[0, 1]] = [[1, 1],

[0, 1]]

AC = [[1, 1],

[0, 1]] * [[1, 1],

[0, 2]] = [[1, 3],

[0, 1]]

As we can see, AB = AC, but B is not equal to C, and the matrix A has no zero entries.

(iv) AB = 0 but neither A nor B is 0:

Let's consider the following matrices:

A = [[1, 0],

[0, 0]]

B = [[0, 1],

[0, 0]]

To verify the condition:

AB = [[1, 0],

[0, 0]] * [[0, 1],

[0, 0]] = [[0, 1],

[0, 0]]

As we can see, AB = 0, and neither A nor B is the zero matrix.

(v) AB = I but neither A nor B is I:

Let's consider the following matrices:

A = [[0, 1],

[1, 0]]

B = [[0, 1],

[1, 0]]

To verify the condition:

AB = [[0, 1],

[1, 0]] * [[0, 1],

[1, 0]] = [[1, 0],

[0, 1]]

As we can see, AB = I, and neither A nor B is the identity matrix.

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The measures of angles 4 and 5 are:

∠5 = 104°

∠4 =76°

On the image we can see that angles 1 and 2 are next to eachother, that means that the sum of their measures must be a plane angle, that is an angle of 180°.

Then we can write the sum:

∠1 + ∠2 = 180°

(3x + 5) + (2x + 10) = 180

5x + 15 = 180

5x = 180 - 15

x = 165/5 = 33

the measure of angle 5 is the same one of angle 1 then:

∠5 = (3*33 + 5)° = 104°

And angle 4 is supplementary of angle 1, then:

∠4 + 104° = 180°

∠4 = 180 - 104= 76°

These are the measures

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Answer:

use a calculator

Step-by-step explanation:

its not that hard

The linear distance traveled in one revolution of a wheel can be calculated using the formula:

Circumference = π * Diameter

Given that the diameter of the wheel is 36 inches, we can substitute the value into the formula:

Circumference = π * 36 inches

Using an approximate value of π as 3.14159, we can calculate the circumference:

Circumference ≈ 3.14159 * 36 inches

Circumference ≈ 113.09724 inches

Therefore, the linear distance traveled in one revolution of a 36-inch diameter wheel is approximately 113.09724 inches.

Answer:

c. y = -1/3x+3

Step-by-step explanation:

i hope this helps :)

The sum of interior Angles of Hexagon is always 720°

Any hexagon's internal angles add up to 720° in all cases. By dividing 720° by 6, we may get the size of each interior angle of a regular hexagon. As a result, we have:

720°÷6 = 120°

In a regular hexagon, each inside angle is 120°.

An example of a regular hexagon with equal-length sides and angles is shown in the diagram below. By multiplying the six 120° angles together, we can demonstrate that the result is 720°.

Therefore, the interior angles of a hexagon are always added up to 720°.

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