A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation
C(x)=0.00048(x-200)³ + 311,040
100≤x≤ 1,000
where C(x) is the cost in dollars for handling x cases per month. The average cost per case is given by C(x)=
(A) Write the equation for the average cost function C.

The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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Answer:

The bigger number is 56

Step-by-step explanation:

\(\frac{x}{y}\) = \(\frac{7}{5}\)  cross multiply

5x = 7y

y = x -16  substage x-16 in the equation above for y

5x = 7( x - 16)

5x = 7x - 112  Subtract 7x from both sides

-2x = -112  Divide both sides by -2

x = 56

Check:

y = x - 16

y = 56 - 16

y = 40

5x = 7y

5(56) = 7(40)

280 = 28

y = x - 16

40 = 45-16

40 = 40

Answer:

1.1a+3.5b

Step-by-step explanation:

The main belt is not located between these all planets.

What is orbit?

A route that an object in space follows around another is known as an orbit. A satellite is a thing that orbits the earth. An Earth- or moon-like natural satellite is one possibility. Moons are satellites that orbit many planets. A man-made satellite is also possible, such as the International Space Station.

The belt of asteroids is located between the orbits of Mars and Jupiter. The asteroids in this region, known as the main belt, are made up of small rocky bodies that orbit the sun in a region between about 2.2 and 3.2 astronomical units (AU) from the sun.

The distance from the sun to the Earth is about 1 AU, and the distance from the sun to Venus is about 0.7 AU, so the main belt is located beyond the orbits of both Venus and Earth.

The orbits of Saturn and Uranus are much farther out from the sun, at distances of about 9.5 and 19.2 AU, respectively, so the main belt is not located between these planets.

Hence, The main belt is not located between these all planets.

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The linear function is given as follows:

\(y = \sqrt{x} + 4\)

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.

By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (x, -y)

(1, -3)             →      (1, -(-3)) = (1, 3)

(3, -2)             →      (3, -(-2)) = (3, 2)

(4, -5)             →      (4, -(-5)) = (4, 5)

By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (-x, y)

(1, -3)             →        (-1, -3)

(3, -2)             →      (-3, -2)

(4, -5)             →      (-4, -5)

By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (y, x)

(1, -3)             →        (-3, 1)

(3, -2)             →      (-2, 3)

(4, -5)             →      (-5, 4)

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Answer:

Step-by-step explanation:

Cut out square on each corner has side of x.

When folded up the height of the box becomes same as the side of the cut-out square.

Sides  of the base of the box are:

The volume of the box which is the right square prism is:

Substitute the values and find the volume:

Answer:

y=−210+5x

Step-by-step explanation: easy

a. The two lines intersect at the point (-1/2, 8, 3/2).

b. The equation of the plane that passes through the two lines is -2y - 4z + 20 = 0.

a) To find the point where the two lines intersect, we need to solve the system of equations:

x = -2 + t

y = 3 + 2t

z = 4 - t

x = 3 - t

y = 4 - 2t

z = t

Equating x from the two equations, we get:

-2 + t = 3 - t

2t = 5

t = 5/2

Substituting t in either equation, we get:

x = -2 + 5/2 = -1/2

y = 3 + 2(5/2) = 8

z = 4 - 5/2 = 3/2

Therefore, the two lines intersect at the point (-1/2, 8, 3/2).

b) To obtain the equation of the plane that passes through the two lines, we first find the direction vectors of the lines. These are given by the coefficients of t in the equations:

Line 1: (-2, 3, 4) + t(1, 2, -1)

Line 2: (3, 4, 0) + t(-1, -2, 1)

The direction vectors are (1, 2, -1) and (-1, -2, 1), respectively.

The normal vector of the plane can be found by taking the cross-product of these two direction vectors:

(1, 2, -1) × (-1, -2, 1) = (0, -2, -4)

Now we use the point (-1/2, 8, 3/2) that we found in part (a) and the normal vector (0, -2, -4) to write the equation of the plane in the point-normal form:

0(x + 1/2) - 2(y - 8) - 4(z - 3/2) = 0

Simplifying, we get:

-2y - 4z + 20 = 0

Therefore, the equation of the plane that passes through the two lines is -2y - 4z + 20 = 0.

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The question is -

a) determine the point where the two lines

x=−2+t, y=3+2t, z=4−t and x=3−t, y=4−2t, z=t intersect.

b) use your results from part (a) to obtain the equation of the plane that passes through the two lines.

Answer:

396

Step-by-step explanation:

0.03n=27

n=27/0.03=900

900*0.44=396

Answer:

Step-by-step explanation:

standard deviation σ =5000

Mean μ = 36500

X = 30000

Probability that tire fails to reach 30000 miles

P(< 30000) = P( z < (30000-36500) / 5000 )

= P ( z < - 1.3 )

= .0968 ( from z table )

refund per mile = .01

refund for 30000 mile = .01 x 30000 = 300

expected cost of promotion

= 300 x .0968

= 29.04

b )

refund of $50 is equivalent to shortage of milage by 50 / .01 = 5000 miles

Probability of miles less than 30000 - 5000 = 25000

P ( X < 25000 ) = P ( z < (25000 - 36500) / 5000 )

P ( z < - 2.3 )

= 0.0107 Answer .

Therefore, the expression (7-3i) + (x - 2i)² - (4i + 2x²) in the simplest a + bi form is: -2x² - 1 - (4x + 7i)

Linear Equation                   General Form                    Example

Slope intercept form             y = mx + b                            y + 2x = 3

Point–slope form                   y – y1 = m(x – x1 )              y – 3 = 6(x – 2)

General Form                            Ax + By + C = 0               2x + 3y – 6 = 0

Intercept form                        x/a + y/b = 1                 x/2 + y/3 = 1

As a Function f(x) instead of y      f(x) = x + C                         f(x) = x + 3

The Identity Function                      f(x) = x                     f(x) = 3x

Constant Functions                      f(x) = C                       f(x) = 6

Let's start by expanding the square term (x - 2i)² using the formula for (a + b)²:

(x - 2i)² = x² - 4xi + 4i²

Note that i² = -1, so we can simplify this expression to:

(x - 2i)² = x² - 4xi - 4

Substituting this expression and the given values into the original expression, we get:

(7 - 3i) + (x² - 4xi - 4) - (4i + 2x²)

Grouping the real and imaginary terms, we get:

(7 - 4 - 2x²) + (-3i - 4i - 4x) + (x²)

Simplifying the real part, we get:

-2x² - 1

Simplifying the imaginary part, we get:

-7i - 4x

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The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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The correct value of Z for the solution to true system is -2

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

2x + 3y - z = 4

x - 3y + 2z = -3

3x + y - z = 5

Transform the third equation

So we have

2x + 3y - z = 4

x - 3y + 2z = -3

9x + 3y - 3z = 15

Eliminate y in the equations by subtraction

So we have

x - 3z = 7

10x - z = 12

Multiply x - 3z = 7 by 10

10x - 30z = 70

10x - z = 12

Subtract the equations

-29z = 58

So, we have

z = -2

Hence, the correct value of Z  is -2

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Answer:

2.25

Step-by-step explanation:

6 · 3/8 = 18/8 = 2.25

Answer:

To find the fraction of the total audience that were students or teachers, you need to add the fractions of students and teachers and simplify the result.

5/12 + 1/8 = (53) / (123) + (16) / (86) = 15/36 + 6/48 = 15/36 + 3/24 = 18/36 + 3/24 = (18+3) / (36+24) = 21/60

So 21/60 of the total audience were students or teachers.

Answer:

x < -4

-4 > x

Step-by-step explanation:

⇒ The graph shows that the x-values has to be less than -4 (also not including -4 too)

-This can be written as x < -4

-It also can be written as -4 > x because -4 has to be greater than x (also not including -4 too)

Hope this helps again! :)

Answer:

i think it is A the first option

Step-by-step explanation:

Answer:

The cost for 1 chair is $2.75 and the cost for 1 table is $8.75

Step-by-step explanation:

Use the elimination method of linear equations to find your answer.

Our equations for this problem are:

3c+5t=52 and 9c+7t=86

1. Multiply the entire first equation by -3.

-3(3c+5t=52)

2. Simplify the equation from above:

-9c-15t=-156

3. Stack the two equations on top of each other and add/subtract:

-9c-15t=-156

9c+7t=86

4. You should be left with -8t=-70. Simplify this to find the value of t:

t=8.75

5. Plug the value of t into any of the original equations and solve for c.

3c+5(8.75)=52

6. Simplify the equation above:

3c+43.75=52

7. Subtract 43.75 from both sides of the equation:

3c=8.25

8. Divide both sides by 3 to get your c value:

c=2.75

Answer:

66.390

Step-by-step explanation: 66.389 the 9 is thousandths, it rounds up to 66.390

Answer:

x = 2

Step-by-step explanation:

Step 1: Write equation

3(x + 2) = 12

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

3(2 + 2) = 12

3(4) = 12

12 = 12

Answer:

146.3m²

Step-by-step explanation:

area of quarter circle=1/4π×8²

=50.3m²

area of the square=s²

8×8=64m²

area of the triangle=1/2bh

1/2×8×8=32m²

total area=50.3+64+32=146.3m²

Answer:

So what is the question?

.......

The distance between the two ship based on the angle of depression is 42 meters.

The distance of each ship can be calculated thus:

TanX = opposite / Adjacent

The first ship:

Tan53 = distance/ 82

distance= 108.82 meters

The second ship:

Tan39 = distance/ 82

distance= 66.40 meters

The Difference between the ships are :

Therefore, the distance between the two ships is 42 meters.

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1. The trigonometric ratios are given as follows:

2. The equation to solve for x is given as follows: sin(52º) = x/13.

3. Two equations to solve for m are given as follows:

4. The length of the hypotenuse of the triangle is given as follows: 7.9 inches.

5. The lengths are given as follows:

The three trigonometric ratios are given as follows:

In the second problem, we have that the side x is opposite to the angle of 52º, while the hypotenuse is of 13, hence the equation to solve for x is given as follows:

sin(52º) = x/13.

In item 3, the Pythagorean Theorem is used to solve for m, as follows:

n² + m² = l².

m² = l² - n²

m = square root (l² - n²).

In item 4, we have that the angle opposite to the leg of length 7 inches is of 62º, hence the hypotenuse is given as follows:

sin(62º) = 7/h

h = 7/sin(62º)

h = 7.9 inches.

The length BD in item 5 is obtained as follows:

cos(30º) = BD/5

BD = 5 x cos (30º)

BD = 4.3 cm.

Then the length BC is calculated as follows:

sin(22º) = 4.3/BC

BC = 4.3/sin(22º)

BC = 11.5 cm.

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Answer:

There are about 12 people with genetic mutation.

Step-by-step explanation:

If you write out the equation, it should look like this:

600*0.02 = 12

Therefore, the answer is that there are about 12 people with genetic mutation.

Answer:

it would be d for #1 because it has no solution for the question

Answer:

D.x=-6.

Step-by-step explanation:

Answer:

4915

Step-by-step explanation:

y= 983 so multiply 983 by 5

5x983 = 4915

Answer: 4915

Step-by-step explanation: Pls brainliest.

Considering the definition of probability, the probability that the next customer will pay with a debit card is \(\frac{12}{139}\).

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases.

\(P(A)=\frac{number of favorable events}{ total number of possible events}\)

The probability of event A can only be a number between 0 and 1; although it can also be written as a percentage.

In this case, you know:

Replacing in the definition of probability:

\(P(A)=\frac{12}{ 139}\)

Finally, the probability that the next customer will pay with a debit card is \(\frac{12}{139}\).

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