A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x)=0.4x^2 - 104x + 13,586. How many cars must be made to minimize the unit cost? Do not round the answer

The modal mark is 16.because as we can see there are two 15, two 13,one 14, two 17 and three 16.

Answer:

  $1258.09

Step-by-step explanation:

You want the monthly annuity payment that will let you withdraw $150,000 per year forever from an account earning 8% after 30 years.

In order to withdraw an amount "forever," the withdrawal amount must be equal to the interest earned by the account.

  I = Prt

  150,000 = P(0.08)(1)

  P = 150,000/0.08 = 1,875,000

The value of an ordinary annuity is given by the formula ...

  A = P(12/r)((1 +r/12)^(12t) -1) . . . . . where P is the monthly payment, and r is the annual interest rate earned over a period of t years.

Using the values we know, we can find P:

  1875000 = P(12/0.08)((1 +0.08/12)^(12·30) -1) = 1490.359449P

  P ≈ 1258.09

You would need to deposit $1258.09 each month.

__

Additional comment

The formulas used here assume that the deposits and withdrawals occur at the end of the month.

The statement that justifies the triangles' similarity is (c) SSS similarity theorem

The triangles are given as

Triangle ABC and Triangle DBE

From the figure, we can see that the corresponding vertical lines of either triangle are parallel (but not equal)

This means that, the triangles are similar triangles

This is so because the other two sides of the smaller triangle lie completely on the bigger triangle

As a general rule, the corresponding sides of similar triangles are in proportions

So, we can say that the corresponding side lengths of the triangles are similar

The statement that justifies this is the Side-Side-Side similarity theorem

Hence, the true statement is (c) SSS similarity theorem

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The irrational numbers lying between 1/12 and 1/10 are -

For the given question;

The number are given as  1/12 and 1/10

Write both number in its decimal form.

1/12 = 0.8333333

1/10 = 0.1

Thus, write number which lies between these two.

1/12 = 0.8333333

0.456258824......

0.32547965.......

0.21448663324........

1/10 = 0.1

The dotted parts shows that the number is nether terminating nor repeating.

Thus, the irrational numbers lying between 1/12 and 1/10 are found.

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y = -1/5x +1/2 linear function has the same slope .

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.

First solve for the slope

m =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m=[tex]\frac{0-\frac{3}{5} }{\frac{1}{2} -\frac{1}{5} }[/tex]

m = [tex]\frac{-1}{5}[/tex]

Look for the linear equation with the same value of m after determining the slope (parallel equation).

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The mean = 0.2,  variance = 0.03226 and Standard deviation = 0.1796

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given:

level            x

1             0.419

2            0.276

3            0.225

4            0.068

5            0.012

So, mean = (0.419+ 0.276 + 0.225+ 0.068 + 0.012)/5

mean = 0.2

level          x        (x- mean)       (x- mean)²        

1             0.419        0.219            0.0479  

2            0.276       0.076            0.0057

3            0.225        0.025         0.000625

4            0.068       -0.268         0 .0718

5            0.012        -0.188          0.0353

So, variance = 0.032265

standard deviation = √(variance)

Standard deviation = √(0.032265)

Standard deviation = 0.1796

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Lowest degree polynomial with f(0) = 960 with zeros of -4 (multiplicity 3), 3(multiplicity 1). The polynomial is f(x)=-5(x+4)³(x-3).

Given that,

Lowest degree polynomial with f(0) = 960 with zeros of -4 (multiplicity 3), 3(multiplicity 1)

We have to find the polynomial of f(x) which satisfy the conditions.

Here,
We have the zeros of the polynomial are -4 (multiplicity 3), 3(multiplicity 1)

Which we can write as -4,-4,-4,3 are the zeros.

Then we can write the polynomial as

f(x)=ω(x+4)³(x-3)

We have to first find the value of ω.

So,

We have f(0)=960

ω(0+4)³(0-3)=960

ω(4)³(-3)=960

64ω(-3)=960

-192ω=960

ω=960/-192

ω=-5

We got the ω as -5.

The polynomial f(x)=-5(x+4)³(x-3)

Therefore, the polynomial is f(x)=-5(x+4)³(x-3).

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The actual fraction of growth-

a) population = 10 million; growth rate = 559/155.

b) population = 30 million; growth rate = 344/155

c) population = 50 million; growth rate = 126/155

The base growth rate = 4.3%.

The current carrying capacity = 62 million.

The actual fractional growth for the given values are-

growth rate = r * (1 - population/carrying capacity)

a) population = 10 million,

Put the values;

growth rate = 4.3 × (1 - 10/62)

growth rate = 559/155 is the actual fraction of growth.

b) population = 30 million,

Put the values;

growth rate = 4.3 × (1 - 30/62)

growth rate = 344/155 is the actual fraction of growth.

c) population = 50 million,

Put the values;

growth rate = 4.3 × (1 - 50/62)

growth rate = 126/155 is the actual fraction of growth.

Thus, the actual fraction of growth is estimated.

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Answer:

3/7

Hope this helps!

Have a good day :).

Time can be used to quantify, contrast, or even rank the length of events or the gaps between them. To complete the cooking at 2:00 PM, George needs to start his cooking at  12:30 PM.

Time can be defined in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be calculated, compared, or even ordered utilizing time.

Given time needed for each meals are;

Turkey = 70 min

Pumpkin pie = 17 min

Rolls = 30 sec

coffee = 45 sec

Total time = 87 min 75 sec

                = 1 hour 27min 75 sec

So in order to complete the cooking at 2:00 PM, George needs to start his cooking at  12:30 PM.

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Answer:

224

Step-by-step explanation:

The answer is 224 since 8 x 28 = 224

Answer: Terrence planted 224 flowers in total

Step-by-step explanation:  8x28

The equation is of the form y=mx+b, where m = slope and b = y-interset. Therefore, find m and b:

For m

For b

So, the equation is:

Answer: D.

Answer:

Bottom left

Step-by-step explanation:

The figure that looks like <-------------------------> is a line

Top left *------------------------* is a segment

Bottom right is a ray *---------------->

Top right is a * point or dot

I hope this helps!

An equation of the line in point-slope form is y = 6x + 50.

y = y₁ = m(x -x₁) is the equation of a straight line, where m is the slope and (x₁, y₁) are the coordinates at a given point on the line (see slope-intercept form). When you know the slope and another point on the line, the point-slope form of a linear equation is most helpful for locating a point on a line. When two other points are known, it can also be used to locate a point on a line.

Given,

y₂ = 200

y₁ = 230

x₂ = 30

x₁ = 25

Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Slope = [tex]\frac{230-200}{30-25}[/tex]

Slope = [tex]\frac{30}{5}[/tex]

Slope = 6

Equation:

y - y₁ = m(x - x₁)

y - 200 = 6(x - 25)

y - 200 = 6x - 150

y = 6x + 50

An equation of the line in point-slope form is y = 6x + 50.

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Answer:

  -8

Step-by-step explanation:

You want the value of c(3) when c(x) = (x -5)^3.

The value of a function is found by substituting the argument for the variable and doing the arithmetic.

  c(x) = (x -5)^3

  c(3) = (3 -5)^3 = (-2)^3

  c(3) = -8

Answer:

y = 1/3 x + 3

Step-by-step explanation:

1) when finding a perpendicular line, you take the slope and use the reciprocal (you flip it) and change the sign (from negative to positive or positive to negative)

-3 ---> 1/3

2) plug in the slope into a new equation

y=1/3 x + b

3) plug in the points

3= 1/3 (0) + b

b=3

4) rewrite the equation

y=1/3 x + 3

The relation which is a function among the answer choices is; A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.

A function is a relation in which each element of the domain is associated with exactly one element of the codomain.

A relation can be tagged a function if it describes that there should be only one output (y - value) for each input ( x - value). Put simply, a function is a kind of relation (defined by a set of ordered pairs) in which case, it ensures that every x-value is associated with only one y-value.

On this note, since the relation described in the first answer choice is such that every x-value is associated with only one y-value as it is a parabola (quadratic function), it is termed a function.

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Given that P is a point on the perpendicular bisector, l, of MN, we have proved that PM = PN because By the definition of reflection, point P is the image of itself and point N is the image of N.

We are given :

P is a point on the perpendicular bisector, l, of MN.

Now, we want to prove that PM = PN

A Reflection is a transformation in which the figure is the mirror image of the other. Every point is a mirror reflection of itself .

By the definition of reflection, we can deduce that point P is the image of itself , and point N is the image of M .

The line l acts as a Line of symmetry or axis of reflection.

Now, in transformations, we know that reflections preserve length and as a result, PM = PN.

Therefore, we will conclude that point N is the image of M .

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Answer: Point M

Step-by-step explanation:edge 2023

Answer:

You cant use the distributive property because it is when the equation is like this: ax(b+c) so if it was 11x(5+0) you would multiply the 5 by 11 by itself and multiply 0 with 11 then you add them and get 55. I hope that helps :)

Step-by-step explanation:

The zeros of the function f(x) = x³ + 9x² + 20x  is :

0, 5 ,4

Steps to solve quadratic equation:

Check your answer by plugging it into the original equation.

Given function,

f(x) = x³ + 9x² +20x

take x common from f(x),

=> x(x² + x - 20) = 0

=> x(x² + 5x + 4x + 20) = 0

=> x( x + 5 ) + 4 ( x +5 ) = 0

=> (x + 5)  ( x + 4 ) = 0

=> x -5 = 0 or x -4 = 0

=> x = 5 and x = 4 .

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Given:

5, 9, 96, 3, 2, 8, 79, 1, 4, 16

To determine the mode based on the given data set, we note first that mode is the number in a data set that occurs most frequently. Since each value occurs only once, there is no mode of this data set.

Therefore, the answer is: no mode or none.

Answer:

20% off

Step-by-step explanation:

22-17.60=4.4

(5)4.4=22

Answer:

bottom right

Step-by-step explanation:

bottom right

Based on the fact that the researchers are 96% confident that they are correct, then the probability that they are actually wrong is 4%.

If we are to believe the assertions of the researchers that they are 96% certain of them being correct, then the probability that they are wrong can be found by the formula:

= 1 - Percentage certainty

Solving for that probability of being wrong then gives:

= 1 - 96%

= 4%

It is worthy of note that this probability of being wrong is based on their estimates and so there is a chance that the probability of being wrong is 4%.

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Answer:

the ratio is 6.5 : 1.5

Step-by-step explanation:

it asks "what is the ratio of time spent studying in math to studying for English?"

ratio uses the ":" mark. also you put the parts like this:

first part : second part

the parts can be found by looking for the "to" as indicated bold in the question

the first part of the ratio it asks is the "time spent studying in math" in hours which is 6.5

the second part of the ratio it asks is the "time spent studying in English" in hours which is 1.5

so the answer is:

6.5 : 1.5

Answer:

Ratio of time spent studying in math to studying for English

[tex]\large \text{$=\dfrac{13}{3}$ }[/tex]

Step-by-step explanation:

What is a ratio?
We use ratios to compare two numeric quantities or quantities with the same units

Basically a ratio of one quantity x to another quantity y can be expressed in the following ways, all read as the ratio of x to y

x/ y

x to y

x : y

The most useful way of representing a ratio is by using the fractional form because it can be used in determining other quantities

In this problem you spend 6.5 hours/week  studying for math and 1.5 hours/week studying for English

Since both units are the same (hours/week) we can compute the ratio as

[tex]{\dfrac{\text{Number of hours studying math}}{\text{Number of hours studying English}}\\\\= \dfrac{6.5}{1.5}\\\\[/tex]

We can simply this fraction as follows

Multiply both numerator and denominator by 10

[tex]= \dfrac{65}{15}\\\\[/tex]

Divide both sides by 5

[tex]\dfrac{65 \div 5}{15 \div 5}\\\\= \boxed{\bold{\dfrac{13}{3}\\\\}}[/tex]

This is the same as 13:3 or 13 to 3

(Be careful what is the numerator and what is the denominator.
If the question had asked for the ratio of hours studying English to hours studying Math then the ratio would be 1.5/65 = 15/65 = 3/13)

Answer:

Is this correct??

if yes reply

The solution of the equation is x = 5.

The equation is written as follows:

- 94  = -2 (8x + 7)

The variable to be found as variable x.

A variable is a number represented with a letter in an equation.

Hence,

- 94  = -2 (8x + 7)

open the bracket on the right side of the equation

-94 = - 16x - 14

add 14 to both sides of the equation

-94 = - 16x - 14

-94 + 14 = - 16x - 14 + 14

-80 = - 16x

divide both sides by -16

x = -80 / -16

x = 5

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Answer:

P(A|B) =  1/2

Step-by-step explanation:

Sample space for B = {10, 20, 30, 40, 50, 60, 70, 80}

where B is even

Total number of elements in sample space = 8

P(A|B) = Probability of a number being 40 or less from the sample space of 8

Sample space for A|B  = {10, 20, 30, 40}

So out of a possible 8 elements in the sample space for B only 4 elements can be chosen for the sample space of A

So P(A|B) = 4/8 = 1/2

The equation of the line passing through points (-2, 5) can be written as follows

Equation of a straight line is an equation of the form y = mx + c, where

The slope is the gradient which is the ratio of the difference in the y direction to the difference in x direction.

given that the equation of the line is x + 3y = 7

rewriting the equation gives

y = -x/3 + 7/3

hence the slope is -1/3, and this is equated with the formula for slope

[tex]\frac{y-y_{1} }{x-x_{1} }=-\frac{1}{3}[/tex]

substituting the values for points  (-2,5)  and cross multiplying gives

3 (y - 5) = - ( x - -2)

y - 5 = - (x + 2 ) /3

y - 5 = -x/3 - 2/3

y = -x/3 - 2/3 + 5

y = -x/3 + 13/3

Rewriting the equation of the line in standard form is done as follows

y = -x/3 + 13/3

3y = -x + 13

x + 3y = 13

The equations are gotten from substitution the values to the formula for slope and substituting. Rearranging the equation gives the equation in slope intercept form and in standard form.

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