C Apply Your Knowledge (See Ex. 7)
10 A factory produces lemon-scented widgets. Each widget is
cheaper, the more that are produced, but costs will go up if
too many widgets are produced, due to storage requirements.
The accountant for the factory says that the costs for
producing x thousands of units a day can be approximated by
the formula C = 0.04x² -8.504x + 25302. Find the daily
production level that will minimize the costs. Be sure to
show your work and include units of measurement.

The range of the function f(x) = |x| - 4 is [-4, ∞).

For any function y = f(x), Domain is the set of all possible values of y that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

We have -

f(x) = |x| - 4

According to question, we have -

f(x) =  |x| - 4

We will draw the graph of the function -

f(x) = |x| + 4

Range is the set of value along the [y] - axis.

We can see that, the values of range of [y] variable is from -

[-4, ∞)

Therefore, the range of the function f(x) = |x| - 4 is [-4, ∞).

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The simplified probability that all randomly chosen student has a schedule that excludes music theory is given as follows:

p = 1/14.

The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

In the context of this problem, these numbers of outcomes are given as follows:

The symbol [tex]C_{n,x}[/tex] represents the number of combinations of x elements that can be obtained from a set of n elements, and the combination formula is presented as follows:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Considering the formula presented above, the numeric values of the combinations are obtained as follows:

Hence the simplified probability is of:

p = 4/56 = 1/14.

As the quotient of 56 and 4 is of 14.

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The amount that you have to pay for the time is $300.

From the information, the person is buying some television time and the station tells you that they reach 120,000 people and they quote you $2.50 CPM

The cost will be:

= Total people × Cost per thousand

= 120000/1000 × $2.50

= 120 × $2.50

= $300

The amount is $300.

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[tex]\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}[/tex]

The function that can easily be seen when a quadratic function is given

in the form: y = a (x − ℎ)^2 + K are

A parabola is given in factored form when it is in the form

y = a (x − ℎ)^2 + K

the factored form can be rearranged

(y - k) = a (x − ℎ)^2

The vertex is v(h, k)

the axis of symmetry of the parabola when the parabola is written in the form as in the question is of the formula x = -b/2a.

this says that the axis of symmetry is a vertical line

the focus is given by f(h, k + 1/4a)

"a" curve opens up when a is positive and down when a is negative. when (x − ℎ) = a (y − k)^2, a opens left or right

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Answer:1/5

Step-by-step explanation:

it correct

Answer:

Step-by-step explanation:

Second part to the answer is 3/20

The measure of angle A is 53.6° if angle A and angle B are supplementary angles.

According to the question,

We have the following information:

Angles A and B are supplementary.

Measure of angle B = 126.4°

We know that when two angles are supplementary then it means that the sum of these angles will be 180°.

So, we have the following expression:

Angle A + angle B = 180

Angle A+126.4 = 180

Subtracting 126.4 from both the sides of the equation:

Angle A = 180-126.4

Angle A = 53.6°

Hence, the measure of angle A is 53.6° if angle A and angle B are supplementary.

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Answer:

The correct answer is: C

The equation of the line passing through (-6,-10) and having slope m = 1/6  in Standard From is  x - 6y = 54   .

In the question ,

it is given that ,

the required line passes through the point (-6,-10) ,

and has slope(m) = 1/6 ,

So , the equation of the line that passes through the given point and slope ,

is given by ,

(y - (-10)) = 1/6(x -(-6))

(y + 10) = 1/6(x + 6)

On cross multiplication ,

we get ,

6(y + 10) = x + 6

6y + 60 = x + 6

x - 6y = 60 - 6

x - 6y = 54

Therefore , The equation of the line passing through (-6,-10) and having slope m = 1/6  in Standard From is  x - 6y = 54   .

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Factoring the given polynomial expression with the greatest common factor gives 3x⁴(6x - x³ + 4)  

From the question, we are to factor the giving polynomial expression with the greatest common factor

The given polynomial expression is

18x^5-3x^7+12x4

This can be properly written as

18x⁵ - 3x⁷ + 12x⁴

First, we will determine the greatest common factor of the coefficients in the expression.

The coefficients in the expression are 18, 3, and 12.

The greatest common factor of 18, 3, and 12 is 3.

Now, we will determine the greatest common factor of x⁵, x⁷, and x⁴.

The greatest common factor of x⁵, x⁷, and x⁴ is x⁴.

Thus,

The greatest common factor of the polynomial expression is 3x⁴.

Now,

Factoring the polynomial with the greatest common factor

18x⁵ - 3x⁷ + 12x⁴

3x⁴(6x - x³ + 4)

Hence, the result of factoring the polynomial is 3x⁴(6x - x³ + 4)  

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Answer:

4 tickets, 2 left over

Step-by-step explanation:

26/6=4.3333 round down to 4

4*6=24 so they can evenly split 24 tickets and will each get 4

26 tickets -the 24 they split evenly = 2 left over

The value of the first angle is 18

The value of the second angle is 9

The value of the third angle is 153

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Let the second angle be = x ____(1)

The measure of the first angle of this triangle is double the measure of the second angle.

This means,

First angle = 2x _____(1)

The measure of the third angle is 117​° greater than double the measure of the first angle.

This means,

Third angle = 117 + 2(2x) = 117 + 4x _____(3)

From (1) (2) and (3) we get,

x + 2x + 117 + 4x = 180

7x + 117 = 180

7x = 180 - 117

7x = 63

x = 9

The value of first angle is 2x = 2 x 9 = 18

The value of the second angle is x = 9

The value of third angle is 117 + 4x = 117 + 4 x 9 = 117 + 36 = 153

Thus,

The value of the first angle is 18

The value of the second angle is 9

The value of the third angle is 153

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Answer:

D

Step-by-step explanation:

The coefficient is the number before the varaible x.

The number of subsets that the set S , seasons of the year is 16  .

In the question ,

it is given that

the Set S have elements as the seasons of the year , that is

Set S [tex]=[/tex] { Summer , Spring , Fall , Winter }

So , the number of elements that are present in the  set S = 4 ,

we know that the number of subsets of the set having n elements is = 2ⁿ .

So , the number of subsets of the set S having 4 elements is =  2⁴ = 16

Therefore , The number of subsets that the set S , seasons of the year is 16  .

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Answer:

4

Step-by-step explanation:

3/1=3

hence 3/(3/4 )= 3 x4/3=4

Answer:

4

Step-by-step explanation:

keep switch flip

3/1 * 4/3 = 12/3 = 4

Using cosine law,

d^2 = 65^2 + 35^2 - 2(65)(35)cos140

= 8935.5022

d = sqrt(8935.5022)

= 94.5 m

Angle = inverseCos(35sin40 / 94.5) = 76.23 degrees South of East

For the 95% confidence interval for the number of toys that are from China in a random sample of 210 toys, using the z-distribution, we have that:

a) The critical value would be of z = 1.96.

b) The standard error is of: 0.0316

c) The margin of error is of: 6%.

d) The expected number of toys in the sample is of: 147.

e) The lower limit of the interval is of: 64%.

f) The upper limit of the interval is of: 76%.

A confidence interval of proportions has the bounds obtained by the rule presented below as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The estimate and the sample size for this problem are given as follows:

[tex]\pi = 0.7, n = 210[/tex]

Hence the expected number of toys in random sample of 210 toys is of:

0.7 x 210 = 147.

The standard error is calculated as follows:

[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.7(0.3)}{210}} = 0.0316[/tex]

The margin of error is the multiplication of the critical value and of the standard error, hence:

M = 1.96 x 0.0316 = 0.06 = 6%.

The bounds of the interval are the estimate plus/minus the margin of error, hence they are given as follows:

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Answer:

a_n = (4/7)(-7)^(n - 1)

Step-by-step explanation:

a1 = 4/7 = 4/7 × 1 = (4/7)(-7)^0

a2 = -4 = 4/7 × (-7) = (4/7)(-7)^1

a3 = 28 = 4/7 × (-7)(-7) = (4/7) × (-7)^2

etc.

a_n = (4/7)(-7)^(n - 1)

Answer:

The answer is 269 in.

hope this helps!

Sorry I’m late oops

Step-by-step explanation:

The value of the given trigonometric function tan30° is equal to ( 1/ √3).

As given in the question,

In the given right angled triangle,

Let us consider triangle be ABC,

Measure of angle A = 30°

Measure of angle B = 90°

Measure of angle C = 60°

Side length BC = 1

Side length AB = √3

Now in triangle ABC,

Value of trigonometric function tan30° is given by:

tan 30° = (opposite side) / ( adjacent side)

⇒tan 30° = BC / AB

⇒tan 30° = 1 / √3

Therefore, the value of the given trigonometric function tan30° is equal to ( 1/ √3 ).

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The domain of the function is real numbers.. The value is x-1 = is a real number

The domain of a function is the set of values that we are allowed to enter into our function. This set consists of the x values for a function like f. (x). The set of values that a function can accept as input is known as its range. Once we enter an x value, the function returns this list of values.

Think about the equation y = f(x), where x and y are the independent and dependent variables. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

A positive number has a positive cubic root.

Zero has a cubic root of zero.

A negative number has a negative cubic root.

Given ,

This implies that any real number's cubic root is also a real number.

y =   ³√x-1

³√x-1 = x-1 is a cubic root

x-1 = is a real number

Therefore The value of real number is x-1 = is a real number

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The two points that could be used to plot the graph of the function (0, -0.4) and (-0.874, 0)

In this question, we have been given a function f(x) = (3x³ + 2)/(x^2-5).

We need to plot the graph of the function.

We find some coordinates of point on the graph of function.

For x = 0,

f(0) =  (30³ + 2)/(0^2-5)

f(0) = 2/(-5)

f(0) = -0.4

For f(x) = 0,

0 = (3x³ + 2)/(x^2-5)

(3x³ + 2) = 0

3x³ = -2

x = -0.874

for x = 1,

f(1) = (3(1)³ + 2)/(1^2-5)

f(1) = 5/(1 - 5)

f(1) = 5/(-4)

f(1) = -1.25

The graph of function f(x) = (3x³ + 2)/(x2-5) is as shown below.

Therefore, the two points that could be used to plot the graph of the function (0, -0.4) and (-0.874, 0)

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Answer:

D

Step-by-step explanation:

a) The piece of information not required to compute the bill after tax and tip is the cost of the item purchased by the customer.

b) The total bill paid by the restaurant customer is $22.97.

The total bill the restaurant customer paid represents 100% of $1.30 plus the tip.

Proportionately, the amount can be computed using the percentage of the tip to equate the dollar amount.

The result is the cost of the item plus tax.  Then, the total bill includes the cost, tax, and tip.

Tip left by customer = $1.30

Sales tax = 6%

Cost + tax = x

Tip = 6% of x

x = $21.67 ($1.30 ÷ 6%)

The total bill paid is $22.97 ($21.67 + $1.30).

Thus, using proportions, the restaurant customer paid $22.97, which includes the item cost, tax, and tip.

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Step-by-step explanation:

secx - 2=0

secx= 2

x= π/3

that's it

The x-values that satisfy the equation Sec(x) - 2 = 0 are x = π/3 and x = 5π/3.

To verify the given equation, we need to find the value(s) of x that satisfy the equation Sec(x) - 2 = 0.

Sec(x) represents the secant function, which is the reciprocal of the cosine function.

The equation can be rewritten as follows:

Sec(x) = 2

To find the solutions, we can take the reciprocal of both sides:

1 / Cos(x) = 2

Next, we can invert the equation to get the cosine function alone:

Cos(x) = 1/2

The cosine function has a value of 1/2 at two specific angles in the interval [0, 2π]: π/3 and 5π/3.

These angles correspond to the inverse cosine function (arccos), so we have:

x = arccos(1/2) = π/3 or x = arccos(1/2) + 2π = 5π/3

Therefore, the x-values that satisfy the equation Sec(x) - 2 = 0 are x = π/3 and x = 5π/3.

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Answer: 7

Step-by-step explanation:

Median is the middle number of a data set.

You need to first start off with listing the shoe sizes in numerical order:

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9.5

You have a total of 11 numbers in the set, so you can choose the sixth number in the set, which is 7.

So, 7 is the median number.

The median of current data is 6.5 while by adding 9.5 to the data group the median changes to 6.75.

Mode is the highest frequency number while the median is the middle value of a data set after writing in either an increasing or decreasing manner.

For example;

Set { 1,2,2,3,4,5,6} here mode is 2 and median is 3.

As per the given data,

5.5, 6, 7, 8.5 6.5,6.5, 8, 7.5, 8 5

Write the above data in increasing order,

5,5.5,6,6.5,6.5,7,7.5,8,8.5

The median is the middle value thus, 6.5 will be the median.

Now let's add 9.5 to the data group,

5,5.5,6,6.5,6.5,7,7.5,8,8.5,9.5

Now we have two middle values 6.5 and 7

Median = (6.5 + 7)/2 = 6.75

Hence "The median of current data is 6.5 while by adding 9.5 to the data group the median changes to 6.75".

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The amount of milliliters of acid that are in the resulting mixture is 522 ml and the percentage of the resulting mixture is 83.6%.

a. Milliliters of acid:

Milliliters of acid = ( .18 x 125ml) +500 ml

Milliliters of acid = 522.5ml

b. Percentage of the resulting mixture

Percentage of the resulting mixture = 522.5ml /(125ml + 500 ml)

Percentage of the resulting mixture = 522.5ml  / 625 ml × 100

Percentage of the resulting mixture =83.6%

Therefore the milliliters of acid is 522.5ml.

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The length of radius of the given circle is equivalent to 6

A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that can be formed by joining the arc's two ends.

The formula for calculating the length of an arc is expressed as:

L = rФ

where

r is the radius of the circle

Ф is the angle subtended.

Given the following parameters

L = 9.42

Ф = π/2

Determine the radius

r = L/Ф

r =  9.42/(π/2)

r = 2(9.42)/(π

r = 6

This gives the length of the radius of the circle.

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Answer: 4.06

Step-by-step explanation:

if you divided 4 into 16.24 your answer will be 4.06!!

Answer:

$4.06

Step-by-step explanation:

To find the answer, divide 16.24 by 4

This gives you the answer of how much each box costs (assuming each cereal box costs the same)

The answer is 4.06

[tex]\boldsymbol{\sf{\dfrac{4}{6}+\dfrac{1}{4} }}[/tex]

We reduce the fraction 4/6 to its lowest expression by extracting and canceling 2.

    [tex]\boldsymbol{\sf{\dfrac{4}{6}=\dfrac{4\div2}{6\div2}=\dfrac{2}{3} }}[/tex]

                            [tex]\boldsymbol{\sf{\dfrac{2}{3}+\dfrac{1}{4} }}[/tex]

Convert 2/3 and 1/4 to fractions with like denominators.

                [tex]\boldsymbol{\sf{\dfrac{2\times4}{3\times4}+\dfrac{1\times3}{4\times3} \iff \ \dfrac{8}{12}+\dfrac{3}{12} }}[/tex]

Since 8/12 and 3/12 have the same numerator, we join numerators and add.

                         [tex]\boldsymbol{\sf{\dfrac{8+3}{12}= }}\boxed{\boldsymbol{\sf{\frac{11}{12} }}}[/tex]