A custom cake baker charges a flat fee for each job, plus an hourly rate for the
number of hours the job takes to complete. The total amount of her bill to the customer can be expressed by 40 + 25h
where h is the hours it takes for the job.what does the coefficient of h, in the expression represent

Answer:

See below

Step-by-step explanation:

Where the graph crosses the x-axis will solve the equation

The center of the circumscribed circle is (1, 5).

We calculate the midpoint and slope of the line segment AB:

Midpoint of AB = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Midpoint of AB = ((2 + 0) / 2, (8 + 8) / 2)

Midpoint of AB = (1, 8)

Slope of AB = (y₂ - y₁) / (x₂ - x₁)

= (8 - 8) / (0 - 2)

Slope= 0

We can notice that the equation of the perpendicular bisector of AB is x = 1.

We also find midpoint and slope of the line segment  BC

Midpoint of BC = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

= ((0 + 2) / 2, (8 + 2) / 2)

= (1, 5)

Slope of BC = (y₂ - y₁) / (x₂ - x₁)

= (2 - 8) / (2 - 0)

= -3

y - 5 = -3(x - 1)

y - 5 = -3x + 3

3x + y = 8

we have the equations of two perpendicular bisectors which are

x = 1 and 3x + y = 8.

We Substitute x = 1 into 3x + y = 8:

3(1) + y = 8

3 + y = 8

y = 5

In conclusion, center of the circumscribed circle is (1, 5).

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If h(x) = f(–x), this is saying that your graph will be reflected over the y-axis.  In other words, the x-values of every point on the graph of y=f(x) will be switched to the opposite sign.  The graph will be flipped over sideways.

For example, if (1,-4) is a point on y=f(x), then y=h(x) will have (–1,-4) on it.

If h(x) = –f(x), this is saying that your graph will be reflected over the x-axis.  In other words, the y-values of every point on the graph of y=f(x) will be switched to the opposite sign.  The graph will be flipped upside-down.

For example, if (1,–4) is a point on y=f(x), then y=h(x) will have (1,4) on it.

While you are given the equation for f(x) in each exercise, the function f(x) does not impact the transformation at all.  What is said above is true for all functions.  

If you want to graph them, then for 4:

    f(x) = -3 - x

   h(x) = f(-x) = -3 + x

For #5:

    f(x) = 1/3 x + 1

    h(x) = -f(x) = -1/3 x - 1

Answer: The answer is...

y = -2/3 x + 1

Step-by-step explanation:

The others would have crossed paths with y = -2/3 x + 10

The height of the average fourth grader is 137cm 1mm. This height can be determined by multiplying 3 by the average height of a newborn baby.

Given information,

The average height of babies = 45 cm 7mm

45 cm 7 mm is equivalent to 45.7 cm (since there are 10 millimeters in a centimeter).

Let the height of a fourth grader be x.

According to the question,

The height of a fourth grader (x) = 3 × the average height of a newborn baby

The height of a fourth grader (x) = 3 × 45.7

The height of a fourth grader (x)= 137.1 = 137cm 1mm

Therefore, the height of a fourth grader is 137cm 1mm.

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The calculated measure of the angle 1 is 43 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

Also, we have

The line AB tangent to the circle

This means that

Angle 1 = 1/2 * the arc subtended by the line

So, we have

Angle 1 = 1/2 * 86

Evaluate

Angle 1 = 43

Hence, the measure of the angle 1 is 43 degrees

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The value of x indicated in the right angle of EFG is determined as 36.

option D.

The value of x is calculated by applying the principle of sum of angles in a right angle triangle as follows;

A right triangle has a right angle and two angles that are complementary.

If angle EFG is a right angle, then the sum of angles at point F is 90 degrees.

The value of x is calculated by setting up the following equations;

2x + 6 + 12 = 90

2x + 18 = 90

2x = 90 - 18

2x = 72

x = 72/2

x = 36

Thus, the value of x is calculated by applying the principle of sum of angles in a right angle triangle.

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The quadratic equation shown in the graph is:

y = x² + 2x - 8

Here we want to find the graph of the given quadratic equation, where we only know the zeros of it.

Remember that if a quadratic equation has the zeros:

x = a

x = b

Then we can write it as:

y = (x - a)*(x - b)

Here the zeros are:

x = -4

x = 2

Then we can write:

y = (x + 4)*(x - 2)

Expanding that we will get the standard form:

y = x² + 4x - 2x - 8

y = x² + 2x - 8

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The graph that shows only a translation is (c)

From the question, we have the following parameters that can be used in our computation:

The list of options

The general rule of translation it that

Using the above as a guide, we have the following:

the graph that shows only a translation is (c)

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The given information indicates that country y's unemployment rate equals 10 %.

The formula to calculate the unemployment rate is:

Unemployment Rate = ( Number of Unemployed Individuals / Civilian Labor Force ) × 100

In this case, the number of unemployed individuals actively seeking jobs is 400,000, and the civilian labor force is 4,000,000.

Unemployment Rate = ( 400, 000 / 4, 000, 000) × 100

Simplifying the calculation :

= 0. 1 x 100

= 10 %

In conclusion, the unemployment rate in Country Y is 10%.

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The mathematical statement that represents "17 more than a number n is 26" can be written as: n + 17 = 26

Given that a statement we need to convert it into a mathematical statement,

The mathematical statement that represents "17 more than a number n is 26" can be written as:

n + 17 = 26

To solve for n, we can subtract 17 from both sides of the equation:

n + 17 - 17 = 26 - 17

Simplifying the equation gives:

n = 9

Therefore, the number n is 9.

Hence the mathematical statement that represents "17 more than a number n is 26" can be written as: n + 17 = 26

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The area of the Rhombus-shaped keychain is 3 square centimeters.

The area of the rhombus-shaped keychain,

we can use the formula:

Area = (diagonal1 * diagonal2) / 2

Given that the horizontal diagonal has a length of 2 centimeters and

the vertical diagonal has a length of 3 centimeters,

we can substitute these values into the formula:

Area = (2 * 3) / 2

    = 6 / 2

    = 3 cm^2

Therefore, the area of the rhombus-shaped keychain is 3 square centimeters.

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Answer:

[tex]x^2+2y=1[/tex]

Step-by-step explanation:

The equation of a parabola with a vertical axis of symmetry,

focus (h, k+p), and directrix x=h-p is given by:

[tex](x - h)^2 = 4p(y - k)[/tex]

In this case, the focus is (0, 1) and the directrix is x =3.

Comparing this to the general equation,

we have

h = 0, k = 1, and x = h - p = 3.

From x = h - p, we can solve for p:

3 = 0 - p

p = -3

Substituting the values of h, k, and p into the equation, we get:

[tex](x - 0)^2 = 4(-3)(y - 1)[/tex]

Simplifying further:

[tex]x^2 = -12(y - 1)[/tex]

[tex]x^2=-12y+1[/tex]

[tex]x^2+12y=1[/tex]

Therefore, the parabola equation is [tex]x^2+2y=1[/tex]

The sound emitted from the jet plane has a sound intensity of approximately 149.13 decibels.

Using the formula:

D = 10 * log(I/I0),

where D represents the sound intensity in decibels, I is the given sound intensity, and I0 is the reference intensity of 10^-12 watts per square meter.

Substituting the given values:

D = 10 * log(8.2*10^2 / 10^-12).

To simplify the calculation, we can rewrite the division as multiplication by the reciprocal:

D = 10 * log(8.2*10^2 * 10^12).

Using the logarithm property log(a * b) = log(a) + log(b):

D = 10 * (log(8.2) + log(10^2) + log(10^12)).

Using the logarithm property log(a^b) = b * log(a):

D = 10 * (log(8.2) + 2 * log(10) + 12 * log(10)).

Since log(10) = 1:

D = 10 * (log(8.2) + 2 + 12).

D = 10 * (log(8.2) + 14).

Using a calculator or logarithm table, we can find log(8.2) ≈ 0.913.

D = 10 * (0.913 + 14).

D = 10 * 14.913.

D ≈ 149.13.

Therefore, the sound emitted from the jet plane has a sound intensity of approximately 149.13 decibels.

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Answer:

measure of angle 7 + measure of angle 8 = 180°.

Solving a system of equations we can see that the costs are:

For a chair, 3/2 dollars.

For a table, 25/4 dollars.

Here we can define the variables:

x = cost of rending a chair.

y = cost of renting a table.

Here we can write a system of equations:

8x + 4y = 37

3x + 2y = 17

We can subtract two times the second equation from the first one:

8x + 4y - 2*(3x + 2y) = 37 - 2*17

2x = 3

x = 3/2

And the value of y is:

3*(3/2) + 2*y = 17

2y = 17 - 9/2 = 25/2

y = 25/2/2

y = 25/4

These are the costs in dolllars.

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Answer:

Step-by-step explanation:

the of of 50 percent of people is married

Answer:

What the other guy said

Step-by-step explanation:

400Answer:

Step-by-step explanation:

This one's a special case of a right angled triangle with sides (3, 4, and 5 units)

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} [/tex]

Now, check the triangle, sin 37° = 3/5

therefore,

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) [/tex]

[ convert degrees on right side to radians ]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) [/tex]

There are three more possible values as :

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} [/tex]

or in decimals :

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167[/tex]

[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]

similarly,

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 2.385[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = -5.385[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 8.385[/tex]

" x can have infinite number of values here with the same result, here are the four values as you requested "

I hope it was helpful ~

The lateral surface area of the triangular base prism is 288 m².

The lateral area of the triangular base prism can be found as follows:

Lateral area of the triangular base prism = (a + b + c)h

where

Therefore,

a = 7 m

b = 8 m

c = 9 m

h = 12 m

Therefore,

Lateral area of the triangular base prism = (7 + 8 + 9)12

Lateral area of the triangular base prism = 24 × 12

Lateral area of the triangular base prism = 288 m²

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Answer: Area = = 38.5 - Perimeter - 29.6819.

Step-by-step explanation:

To find the perimeter and area of a triangle with vertices L(5,5), M(-2,-4), and N(5,-6), we can use the distance formula and the formula for the area of a triangle.

Perimeter:

The perimeter of a triangle is the sum of the lengths of its sides. We can find the lengths of each side using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can calculate the lengths of LM, MN, and NL:

LM = √((-2 - 5)^2 + (-4 - 5)^2)

= √((-7)^2 + (-9)^2)

= √(49 + 81)

= √130

MN = √((5 - (-2))^2 + (-6 - (-4))^2)

= √((7)^2 + (-2)^2)

= √(49 + 4)

= √53

NL = √((5 - 5)^2 + (-6 - 5)^2)

= √((0)^2 + (-11)^2)

= √(0 + 121)

= √121

= 11

The perimeter of the triangle is the sum of these three sides:

Perimeter = LM + MN + NL

= √130 + √53 + 11 = 29.6819

Area:

To calculate the area of the triangle, we can use the formula for the area of a triangle using the coordinates of its vertices. The formula is given by:

Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Using the coordinates of L(5,5), M(-2,-4), and N(5,-6), we can calculate the area:

Area = 0.5 * |5(-4 - (-6)) + (-2)(-6 - 5) + 5(5 - (-4))|

= 0.5 * |5(2) + (-2)(-11) + 5(9)|

= 0.5 * |10 + 22 + 45|

= 0.5 * |77|

= 38.5

Therefore, the perimeter of the triangle is given by √130 + √53 + 11 = 29.6819 units, and the area of the triangle is 38.5 square units.

The Horizontal distance from the base of the skyscraper to the ship is approximately 403.81 feet.

We can use trigonometry and the concept of angles of depression. We can consider the height of the observation deck as the opposite side and the horizontal distance to the ship as the adjacent side of a right triangle.

Given that the angle of depression is 67 degrees and the height of the observation deck is 955 feet, we want to find the horizontal distance (adjacent side).

Using the trigonometric function tangent, we can set up the following equation:

tan(67°) = opposite/adjacent

tan(67°) = 955/adjacent

To find the value of the adjacent side (horizontal distance), we can rearrange the equation:

adjacent = 955/tan(67°)

Using a calculator, we can evaluate the tangent of 67 degrees:

tan(67°) ≈ 2.3693

Now we can substitute this value into the equation:

adjacent = 955/2.3693

adjacent ≈ 403.81

Therefore, the horizontal distance from the base of the skyscraper to the ship is approximately 403.81 feet.

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The dollar value of total revenue at each price is $[tex]0[/tex], $[tex]10[/tex], $[tex]12[/tex], $[tex]12[/tex], $[tex]10[/tex], and $[tex]6[/tex]. Total revenue will be the greatest at a price of $[tex]4[/tex], with [tex]3[/tex] units sold.

To find the dollar value of total revenue at each price, we can multiply the price by the corresponding quantity in the demand schedule:

Price: $[tex]6[/tex]

Quantity: [tex]0[/tex]

Total Revenue: $[tex]6 \times 0[/tex] = $[tex]0[/tex]

Price: $[tex]5[/tex]

Quantity: [tex]2[/tex]

Total Revenue: $[tex]5 \times 2[/tex] = $[tex]10[/tex]

Price: $[tex]4[/tex]

Quantity: [tex]3[/tex]

Total Revenue: $[tex]4 \times 3[/tex] = $[tex]12[/tex]

Price: $[tex]3[/tex]

Quantity: [tex]4[/tex]

Total Revenue: $[tex]3 \times 4[/tex] = $[tex]12[/tex]

Price: $[tex]2[/tex]

Quantity: [tex]5[/tex]

Total Revenue: $[tex]2 \times 5[/tex] = $[tex]10[/tex]

Price: $[tex]1[/tex]

Quantity: [tex]6[/tex]

Total Revenue: $[tex]1 \times 6[/tex] = $[tex]6[/tex]

To determine at which price the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $[tex]3[/tex], and the corresponding quantity sold is [tex]4[/tex] units.

Therefore, at a price of $[tex]3[/tex], the total revenue will be the greatest, with [tex]4[/tex] units sold.

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Step-by-step explanation:

To solve this problem, we need to calculate the probability of the first student being a boy and the second student being a girl.

There are a total of 13 boys and 15 girls in the class, making a total of 28 students.

The probability of the first student being a boy is given by:

P(boy) = Number of boys / Total number of students = 13 / 28

After the first student is selected, there are now 27 students remaining (since one student has already been selected). Out of these 27 students, there are still 15 girls remaining.

The probability of the second student being a girl, given that the first student was a boy, is given by:

P(girl|boy) = Number of girls / Remaining number of students = 15 / 27

To find the probability of both events occurring (the first student being a boy and the second student being a girl), we multiply the individual probabilities:

P(boy and girl) = P(boy) * P(girl|boy) = (13/28) * (15/27)

Calculating this expression:

P(boy and girl) ≈ 0.2041

Therefore, the probability that the first student is a boy and the second student is a girl is approximately 0.2041 or 20.41%.

Answer:

Angles 3 and 5 are consecutive interior angles.

The critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. Therefore, the correct answer is option B.

The null hypothesis in this case would be that there is independence between the type of sleeping pill and the presence of any adverse health condition.

The critical value needed to test for this is the chi-squared statistic with a significance level of 0.05.

To calculate the critical value, we first need to calculate the degrees of freedom,  which is calculated by (rows-1) * (columns-1).  In this case, the degrees of freedom is (2-1)*(2-1) = 1.

The critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. This means that if the calculated chi-squared statistic is greater than 3.84, then we can reject the null hypothesis and claim that there is a significant relationship between the type of sleeping pill and the presence of any adverse health condition.

Therefore, the critical value of the chi-squared statistic with a significance level of 0.05 is 3.84. Therefore, the correct answer is option B.

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Answer:

250πcm³

Step-by-step explanation:

Length of bigger = k X length of smaller (k is a constant)

Area of bigger = k² X area of smaller (k is a constant)

Volume of bigger = k³ X volume of smaller (k is a constant)

ratio of 3:5 means that there are 3 + 5 = 8 parts.

Length of bigger = k X length of smaller

5 = 3k

k = 5/3.

Volume of bigger = k³ X volume of smaller

= (5/3)³ 54π

= 250πcm³