A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of
machines made. If x machines are made, then the unit cost is given by the function C(x)=x²-440x+64,948. What is the minimum unit cost?
Do not round your answer.

The equation balancing to each steps are has follows

Step 1: ---------- C. Divide both side by 2

Step 2: --------- A. Add 3 to both sides

Step 3: ----------B. Multiply both side by  [tex]\frac{1}{6}[/tex]

Equation balancing is the accurate description of the step taking in an equation.

Step 1 : --------C . Divide both side by 2

12x - 6 = 10

6x - 3 = 5

step 2: ---------A. Add 3 to both sides

6x -3 =5

6x = 8

step 3:-----------B. Multiply both side by  [tex]\frac{1}{6}[/tex]

6x = 8

x = [tex]\frac{4}{3}[/tex]

Therefore, the matching description to each steps are:

Step 1: ---------- C. Divide both side by 2

Step 2: --------- A. Add 3 to both sides

Step 3: ----------B. Multiply both side by  [tex]\frac{1}{6}[/tex]

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The value of line JK in the triangle is 25.2

Trigonometry is the branch concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec).

In the right-angled triangle JLM, LM is the hypotenuse, JM is the adjacent and JL is the opposite to angle M

therefore JM = √(LM)^2- (JL)^2

JM = √87^2- 60^2

JM = √3968

JM = 63

sinM= LJ/LM

sinM= 60/87

sinM=0.69

M=sin^-0.69

M= 43.6

angle M is bisected into two

M/2= 43.6/2= 21.8

in Triangle JLM

sin21.8= JK/63

Jk= sin21.8×63

JK= 25.2

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Begining with the third term, each term of the sequence is the sum of the preceding two.

The discounted price of that jeans on Valentine's day is Php 780.

From the information, the original sale price of Levi's jeans at Sm Department store is Php 1 300.00 and on February 14, all jeans will have a 40% discount.

The amount of the discount will be:

= Percentage of discount × Sales amount

= 40% × 1300

= 0.4 × 1300

= 520

The discount is Php 520

Discounted Price = 1300 - 520

= Php 780

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The profit function for the company is 12x - 24000.

Given,

Cost function, C(x) = 24,000+19x

Revenue function, R(x) = 31x

Profit function, P(x) = R(x) - C(x)

                               = 31x - (24000 + 19x)

                               = 31x - 24000 - 19x

                               = 12x - 24000

Hence, P(x) = 12x - 24000.

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2 1/2 cups of milk does she need to make 6 batches of waffle mix.

Given:

A total of 12 waffles can be made from each batch of waffle mix.

Cynthia is making 6 batches for a breakfast board meeting. If the recipe requires 5/12 cups of milk for each batch.

Number of cups of milk required = number of batches*milk required for each batch.

= 6 * 5/12

= 30/12

= 15/6

= 5/2

= 2 1/2 cups.

Therefore 2 1/2 cups of milk does she need to make 6 batches of waffle mix.

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The meaning of the symbol 'n,' represents the total number of individuals or observations in the sample.

Statistics is the science that studies and develops methods for collecting, analyzing, interpreting, and presenting empirical data. Statistics is the study and manipulation of data, which includes methods for gathering, reviewing,

analyzing, and drawing conclusions from data. Statistics is divided into two categories: descriptive statistics and inferential statistics.

The primary goal of using statistics is to plan the data collected in terms of experimental designs and statistical surveys. Statistics is a mathematical science concerned with numerical data. In short, statistics is an important process that assists in making data-driven decisions.

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The inverse of the function is also a function for each part.

What is function?

a function from a group X to a group Y assigns to every component of X specifically one component of Y.

Main body:

In order to have an inverse function, a function must be one to one.

In the case of

f(x)=x⁴we find that f(1)=f(−1)=1. So f(x) is not one to one on its implicit domain R.

If we restrict the domain of

f(x) to [0,∞) then it does have an inverse function, namely:

f−1(y)=⁴√y

Some more details...

In general, if you want to find the inverse of a function

f(x) then set y=f(x) and attempt to solve for x.

In our example, put:

y=f(x)=x⁴

Then taking the square root of both ends, allowing for both possible

signs we find:

±√y=x²

Assuming that we are only interested in real values of x, we require the left hand side to be non-negative, so assume the non-negative square root.

Then take the square root of both sides again to get:

±√√y=x

That is:

x=±√√y=±⁴√y

Note that this does not give us a unique value of x in terms of y.So the inverse function is not defined, unless we have a restriction such as x≥0, i.e. restrict the domain of f(x) to be [0,∞).

Hence y = x⁴ has inverse and its inverse is also function.

Similarly for each of the parts it is true.

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If 3/8 fraction of the dishes were from China and another 12.5 percent from Japan, it implies that 50 percent were from other countries.

Firstly, we convert the proper fraction to a percentage by expressing it over 100.

Secondly, the percentages of China and Japanese dishes are added before being subtracted from 100%.

The resulting difference is the percentage of dishes from other countries.

In summary, unit conversion, expressing the fraction as a percentage, and mathematical operations of addition and subtraction are involved.

Dishes from China = 3/8 = 0.375 or 37.5% (3/8 x 100)

Dishes from Japan = 12.5%

Dishes from other countries = 50% (1 - 37.5% - 12.5%)

Thus, the percentage of dishes from other countries is 50%.

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At a food festival, 3/8 of the dishes were from China. Another 12.5% of the dishes were from Japan.

Answer:

x = -1

Step-by-step explanation:

The option that describe the quadrilateral is

The choice is made by having a good idea of the properties of the given figures

Starting with quadrilateral: this is a four sided figure, A quadrilateral may also be a parallelogram

Parallelogram refers to figures that has parallel lines

A rectangle is a special type of parallelogram that has two opposite sides equal and equal angles of 90 degrees

A rhombus is a parallelogram that has all the sides equal but only the opposite angles are equal. square is similar to rhombus but has all angles equal to 90 degrees

All other figures except Quadrilateral are parallelogram and the distinctive feature of a parallelogram here is that the adjacent angles of a parallelogram are supplementary,

None of the given pairs of angles add up to give 180 degrees hence we say they are not supplementary and not a parallelogram

All the figures can be classified quadrilateral but not all quadrilateral are parallelogram

sum of angles of a quadrilateral is 360 degrees

45 + 146 + 60 + 109 = 360

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y=5/3x -2

slope: 5/3

y-intercept: (0,-2)

Answer:

x = 15

Step-by-step explanation:

8x + 9 and 51 are same- side interior angles and sum to 180° , then

8x + 9 + 51 = 180

8x + 60 = 180 ( subtract 60 from both sides )

8x = 120 ( divide both sides by 8 )

x = 15

The average number of liters per 100 km used by Petra's car during the trip, using proportions, was of:

13.96 liters per 100 km.

A proportion represents a fraction relative to a total amount, and this fraction, which has the meaning of a unit rate, is used along basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.

The total amount of liters used by Petra on her trip was of:

45 + 35.45 + 30.5 + 30 = 140.95 liters.

The last palindromic number in the twenty-two thousands is of:

22922.

Hence the total distance traveled by Petra was of:

22,922 - 21,912 = 1010 km.

The rate of liters per km is of:

140.95/1010 = 0.1396.

Hence the rate of liters per 100 km is:

0.1396 x 100 = 13.96 liters per 100 km.

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The value of x and y will be x =  16° and y = 20°

What is Angles?

In Euclidean geometry, an angle is the shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. The plane that contains the rays contains the angles created by two beams. The meeting of two planes might also result in an angle. Dihedral angles are what these are.

We can write

(6x + y) = (x + 5y)

[By corresponding angles]

6x + y = x + 5y

6x - x = 5y - y

5x = 4y

x = 4y/5

Now by linear pair

4x + (6x + y) = 180

4x + 6x +y = 180

10x + y = 180

By putting the value of x

10(4y/5) + y = 180

8y + y = 180

9y = 180

y = 180/9

y = 20°

Putting the value of y in x we get

x = 4(20) / 5

x = 4(4)

x = 16°

Hence, value of x =  16° and y = 20°

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For each additional slice of pizza that is purchased, the total cost of lunch is increase by $2.5

First choose two points

(1, 10) and (2, 12.5)

The cost of one slice of pizza = $10

The cost of two slice of pizza = $12.5

Using these points we have to find the slope of the line

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the graph

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

Slope of the line = (12.5 - 10) / (2-1)

= 2.5/1

= $2.5

Hence, for each additional slice of pizza that is purchased, the total cost of lunch is increase by $2.5

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The given distribution would best be described as the complete sampling distribution. which is the correct answer would be option (B).

What is the sampling distribution?

In statistics, sampling distribution refers to the study of multiple random samples drawn from a particular population depending on a specified property. The acquired data paint a clear picture of the changes in the likelihood of the outcomes determined. As a consequence, the analysts are aware of the outcomes ahead of time, allowing them to plan their appropriate steps.

All available samples of two of these four movies were chosen at random, and the sample means gross profit for each of these samples was shown.

Thus, the given distribution would best be described as the complete sampling distribution.

Hence, the correct answer would be an option (B).

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The correct option regarding the correlation coefficient is that A. I can’t be confident at all; this is about as close to a random guess as you can get.

The correlation coefficient is a statistical measure of the strength of a two-variable linear relationship. Its values can range between -1 and 1. A correlation coefficient of -1 denotes a perfect negative, or inverse, correlation, in which values in one series rise while those in the other fall, and vice versa.

A coefficient of one indicates that there is a perfect positive correlation, or a direct relationship. A correlation coefficient of 0 indicates that no linear relationship exists. In science and finance, correlation coefficients are used to assess the degree of association between two variables, factors, or data sets.

In this case, the fat that the person gets 0 implies that it's probably a random guess. In conclusion, the correct option is A.

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The area of the trapezoid is 26 square units

Area of trapezoid

= (sum of parallel lines) /2 * height

Length of the longer parallel line is solved using Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

hypotenuse = 5

opposite = 4

adjacent = ?

hypotenuse = 7.2

opposite = 4

adjacent = ?

adjacent = √(hypotenuse² - opposite²  )

adjacent 1 = √(5² - 4² ) = 3

adjacent 2 = √(7.2² - 4² ) = 5.987 ≅ 6

length of the longer parallel line

= 3 + 2 + 6

= 11

Area of trapezoid

= (sum of parallel lines) /2 * height

= (2 + 11) /2 * 4

= 6.5 * 4

= 26 square units

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The time taken for the rocket to reach its maximum height according to information given is; 2.25 seconds.

The maximum height reached by the toy rocket is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

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Answer:

250.

Step-by-step explanation:

First we need to round to the nearest 100:

120 rounded to the nearest 100 is 100.

230 rounded to the nearest 100 is 200.

455 rounded to the nearest 100 is 500.

175 rounded to the nearest 100 is 200.

So, we have the numbers 100, 200, 500, and 200.

To find the average of numbers, we need to add them up and divide the number we get by how many numbers we added:

100 + 200 + 500 + 200 = 1,000

Since we added 4 numbers, we divide by 4:

1,000 divided by 4 = 250.

We don't round to the nearest 100 for 250 because the question said to only round for the original numbers. But, if i am wrong somehow, 250 rounded is 300.

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The procedure to calculate the p-value from z-score depends on one of two choices: one-tailed (which may be Left-tailed or Right-tailed) or two-tailed tests.

A z-table, otherwise termed the standard normal table, provides the area under the curve to the left of a z-score.

The technique for using z-tables to find p-values depends on the test being carried out; which may be; one- or two-tailed test.

For one-tailed tests, the directionality is also a factor.

It therefore follows that;

For a Left-tailed z-test: the p-value = Φ(Zscore)

For a Right-tailed z-test: the p-value = 1 - Φ(z-score).

For a Two-tailed z-test: the p-value = 2 * Φ(−|z-score|).

The procedure described above represents how to calculate p-value from z-score.

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The following equations are used to find the p-value from its z-score

From the question, the parameters are given as

Also, from the question, we understand that:

The p value depends on the z-score for its own value

There are three formulas for calculating the p-value from the z-score, depending on the type of test (i.e. left-tailed test, right-tailed test and two-talied test)

These formulas are:

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The picture is right here

The true statement about this system 2x - y = 0 and 5x + 3y = 22 is

The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

Pair in Order = (x,y)

x is the abscissa, the distance measure of a point from the primary axis x

y is the ordinate, the distance measure of a point from the secondary axis y

Given are two equations 2x - y = 0 and 5x + 3y = 22.

The ordered pair (7, 19) is not a solution to this system as these two equations do not intersect each other at (7, 19).

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Answer:

the answers are 2 choices

1- The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.

2- The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.

Step-by-step explanation:

i took the k12 test and got these as the answers correctly

Answer:

-4 + 18.5202592 i

Step-by-step explanation:

-4 + 18.5202592 i

there you go

The median thickness of squirrel hair is 25% more than that of rat hair.

The interquartile range of squirrel hair thicknesses is 50% less than that of rat hair.

A box and whisker plot (also known as a box plot) depicts a five-number summary of a set of data: lowest, lower quartile, median, upper quartile, and maximum.

The line (and dot) in the middle of the box represents the median.

As per the given question,

The median of squirrel hair is 35.

The median of rat hair is 28.

Thus, the median thickness of squirrel hair is 25% more than that of rat hair.

The extreme right end of the whisker represents the maximum value.

In this question,

the maximum value of squirrel hair is 37.

the maximum value of rat hair is 34.

The extreme left end of the whisker represents the minimum value.

In this question,

the minimum value of squirrel hair is 25.

the minimum value of rat hair is 19.

The interquartile range of squirrel hair = 37-25 = 12

The interquartile range of rat hair = 25 - 19 = 6

Thus, the median thickness of squirrel hair is 25% more than that of rat hair. The interquartile range of squirrel hair thicknesses is 50% less than that of rat hair.

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Answer: 573,948 memberships

Step-by-step explanation:

1. Multiply the number of memberships the year prior by 80%

318,860 * 0.8 = 255088

If they sold 80% more memberships this year, that means you would add 80% of the previous year's memberships (255088) to the number of memberships sold last year (318860).

2. Add 80% of the previous year's memberships to the number of memberships sold last year

255088 + 318860 = 573948

Answer: 88 grams

Step-by-step explanation:

The total weight of the 30 apples is [tex](30)(99)=2970[/tex] grams.

The total weight of all the apples in the box and bag is [tex]55(94)=5170[/tex] grams.

So, the weight of the apples in the bag is [tex]5170-2970=2200[/tex] grams.

Thus, the mean weight is [tex]\frac{2200}{25}=88[/tex] grams.

Answer:

[tex]s_(_t_)=\frac{1}{3}t^3+\frac{7}{2}t^2-8t+5[/tex]

Step-by-step explanation:

1.)

[tex]a_t=v'_t\\v_t=\int(a_(_t_)dt\\v_t=\int(2t+7)dt\\v_t=t^2+7t+C\\[/tex]

2.)

[tex]v_0=-8\\-8=(0)^2+7(0)+C\\C=-8\\v_t=t^2+7t-8[/tex]

3.)

[tex]v_t=s'_t\\s_t=\int(v_t)dt\\s_t=\int(t^2+7t-8)dt\\s_t=\frac{1}{3}t^3+\frac{7}{2}t^2-8t+C\\[/tex]

4.)

[tex]s_0=5\\5=\frac{1}{3}(0)^3+\frac{7}{2}(0)^2-8(0)+C\\C=5\\s_t=\frac{1}{3}t^3+\frac{7}{2}t^2-8t+5[/tex]

Answer:

v = 8

Step-by-step explanation: