Find the DOMAIN and RANGE from this graph.

Option (D), the last option is the correct statement, If heights in inches of 200 graduating seniors were summarized in the frequency table;

The median height is greater than or equal to 60 inches but less than 66 inches.

The median is the number value that separates the lower and upper values to halves. The median height is determined by arranging all the given heights in order either from the smallest to highest or from highest to smallest without skipping any measurement of the heights.

After arranging all the heights in order, the median height is usually at the middle.

The reason as to why the median height is greater than or equal to 60 inches but less than 66 inches is because the middle height should not be same as the largest height of 66 inches. It is possible to have multiple 60 inch heights from the 200 seniors. It is also possible to have multiple 66 inch of heights from the 200 seniors.

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the data described, preference ratings, are quantitative (involving numerical values) and ordinal (representing relative ranking or ordering).

Preference ratings involve assigning numerical values to items based on their perceived importance or preference. This numerical scale allows for the ranking or ordering of items, indicating a quantitative aspect. Furthermore, the ratings are ordinal in nature since they represent a relative ranking or ordering rather than precise numerical measurements.

Quantitative data is data that can be measured numerically, and in this case, the preference ratings are assigned numerical values. Ordinal data refers to data that can be ordered or ranked, such as in this case where items are rated on a scale from least to most important.

Therefore, the data described, preference ratings, are quantitative (involving numerical values) and ordinal (representing relative ranking or ordering). They are not continuous or discrete as the focus is on the ordinal relationship rather than precise numerical measurement or specific data points.

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The charity needs to consider a range of prices that will guarantee it a monthly profit of at least $3000. To determine the range of prices that can generate such profit, we need to make use of the total cost function and the revenue function.

These functions can help us identify the price range that will provide a profit margin of $3000 or more.Let’s consider the total cost function first:Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC)In this problem, the fixed cost is given as $8000. Variable cost is calculated as VC = $20x (where x is the number of units of books sold).So, TC = $8000 + $20xFor the revenue function, the price per book is given as $30. We also know that the number of books sold is equal to the number of books printed and that the book printer requires a minimum order of 1000 books before they can start printing.

Therefore, the revenue function is given as R = $30x, where x is the number of units of books sold.Using these two functions, we can now calculate the profit function:Profit = Revenue - Total CostP = R - TCP = $30x - ($8000 + $20x)P = $10x - $8000We want to determine the range of prices that will generate a monthly profit of at least $3000. Therefore, we can set up an inequality and solve for x as follows:$10x - $8000 ≥ $3000$10x ≥ $11000x ≥ 1100Hence, x should be greater than or equal to 1100 to generate a profit of $3000 or more. Since the book printer requires a minimum order of 1000 books, the charity should set its price such that it will sell more than 1000 books to achieve the profit target.

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Answer:

x = 1.04, w = 2

Step-by-step explanation:

104 = 1.04 × 10²

Answer:

1.04 x \(10^{2}\), so your answer is x = 1.04, w=2

The completely factored form of the polynomial is 7x² (x + 6) (x - 4)

Given,

The polynomial ; 7x⁴ + 14x³ - 168x²

We have to find the complete factored form of this polynomial;

Polynomial;

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here,

The polynomial is  7x⁴ + 14x³ - 168x²

Now,

Factorize the polynomial using common factors;

That is,

7x⁴ + 14x³ - 168x²

7x² (x² + 2x - 24)

Solve x² + 2x - 24 using quadratic formula;

That is,

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2

Now,

Solve

-2 + √-92 / 2 = 3.79 ≈ 4

Solve

-2 - √-92 / 2 = -5.79 ≈ -6

Then,

The factors will be (x - 4) and (x + 6)

So,

7x² (x + 6) (x - 4) will be the factored form of the polynomial.

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Answer:

Option 2

Step-by-step explanation:

Hello!

In the table we are given a root of the equation, or the x-value that when plugged in will result in a y-value of 0.

We can plug in (4,0) into all equations and see which one has that point included.

Only the first two equations accept the root (4,0).

Now if we take a look at the graph, we see that all y-values are positive. The only function between the two options is the 2nd one, as being squared will always result in a positive number.

The correct option is the 2nd function.

We want to solve the proportion:

For doing so, we remember that solving a proportion equivals to find the variable x. We will multiply means and extremes:

This means that the value of x is 8, which is the solution of the proportion.

One would expect log₃ 20 to be between 2 and 3. None of the options provided is correct.

To determine between which two integer values we would expect to find log₃ 20, we can use the fact that logarithms represent the exponent to which the base must be raised to obtain the given value.

In this case, we want to find the exponent to which 3 must be raised to obtain 20. So, we are looking for an integer value x such that 3^x = 20.

We can approximate this value by calculating the logarithm of 20 to the base 3:

log₃ 20 ≈ 2.7268

Since the base is 3, the value of the logarithm will increase as the exponent increases. Therefore, we would expect log₃ 20 to be between 2 and 3.

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Answer:

-45a + 27b

Step-by-step explanation:

9(-5a + 3b)

⇒ -45a + 27b

Answer: -10a+6b2-4b+3

Answer:

Yes yes no no

Step-by-step explanation:

This image should help

Answer:

The answers should be:

LRS = 137.5

NRS = 42.5

QRN = 137.5

MNR = 42.5

RNP = 137.5

KNP = 42.5

MNK = 137.5

Step-by-step explanation:

180 - 42.5 = 137.5

Answer:

ok this is going to be kinda confusing but here:

angle lrs: 137.5

angle nrs:42.5

angle nrq:137.5

angle knp:42.5

angle rnm: 42.5

angle mnk: 137.5

angle pnr: 137.5

Step-by-step explanation:

basically everything is either 137.5 or 42.5

Answer:

answers B

Step-by-step explanation:

According to the given information for the normal distribution, we can expect that the corresponding z-score may be negative.

It is given to us that -

The normal distribution has mean 11

The normal distribution has data value of 9

We have to find out if the corresponding z-score is to be positive or negative.

The z-score calculates the number of standard deviations higher or lower the mean, the data point is present.

The formula for z-score is given by -

\(z=\frac{data point - mean}{standard deviation}\)

Although we do not have the value of standard deviation in the question, we can see that the value of

data point - mean = 9-11 = -2

So, we can see that the numerator of the z-value formula is already negative.

Thus, we can expect that the corresponding z-score may be negative according to the information provided for the normal distribution.

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Answer:

16.9265381881

Step-by-step explanation:

Tangent = Opposite/Adjacent.

Thus, tan62 = x/9 --> tan62 = 1.88072646535, multiply by 9 to get x, 1.88072646535* 9 = 16.9265381881

Since 1/4 is greater than 1/6 we can infer that Tiffany painted more of the room's wall.

Since most walls are square or rectangular, their surface area may be calculated by multiplying the width and height values, then taking out any spaces for doors or windows. However, unusual architecture and design might lead to the combination of the rectangle with triangular, round, or trapezoidal shapes. Using the fundamental formulas for estimating the area of two-dimensional forms is the key to accurately determining the surface area of a wall.

We must determine the precise dimensions of the parts Tiffany and Roberto painted in order to compare the quantity of each.

Assume for the moment that the wall is one unit in size. Tiffany then painted 1/4.

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Answer:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C\)

Step-by-step explanation:

we want to integrate the following integration:

\( \displaystyle \int {x}^{2} \cdot {e}^{x} dx\)

notice that, the integrand is in the multiplication of two different function in that case we can consider integration by parts given by:

\( \rm \displaystyle \int u \cdot v \: dx = u \int vdx - \int u' \left( \int v dx \right)dx\)

where u' can be defined by the differentiation of u

now we have to choose our u and v

which can be chosen by using the guideline:ILATE Inverse trig. , Logarithm, Algebraic expression, Trigonometry, Exponent.

since x comes first thus,

\( \displaystyle u = {x}^{2} \quad\text{and} \quad v = {e}^{x} \)

by figuring out the defferentiation of u,we acquire:

\( \displaystyle u' = 2x\)

altogether we get:

\( \rm \displaystyle \int {x}^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int 2x \left( \int {e}^{x} dx \right)dx\)

by figuring out the parentheses integration

we get:

\( \rm \displaystyle \int x^2 \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int2x \cdot {e}^{x} dx\)

now we again have integration of two different functions so let's choose our u and v once again which can be done using the guideline

\( \displaystyle u = 2x \quad\text{and} \quad v = {e}^{x} \)

by figuring out the defferentiation of u

we acquire:

\( \displaystyle \: u' = 2\)

altogether we get:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x \int{e}^{x} dx- \int2 \left( \int{e}^{x}dx \right) dx \right)\)

by solving parentheses we get

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x {e}^{x} - 2 e^{x} dx \right)\)

by figuring out the integral we get:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- \left( 2x {e}^{x} - 2 e^{x} \right)\)

remove parentheses:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} \)

at last we of course have to add constant of integration:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C\)

and we are done!

Answer:

\(\displaystyle \int {x^2e^x} \, dx = e^x(x^2 - 2x + 2) + C\)

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)

Basic Power Rule:

Integration

Integration by Parts:                                                                                               \(\displaystyle \int {u} \, dv = uv - \int {v} \, du\)

Step-by-step explanation:

*Note:

The answer below me is correct, but there is a simpler method of obtaining the answer.

Step 1: Define

Identify

\(\displaystyle \int {x^2e^x} \, dx\)

Step 2: Integrate

Use tabular integration.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Factorise means to carry over the common number or letter to the outside of a set of brackets, whilst keeping the rest of the equation inside the brackets.

Answer:

Carry f to the outside, meaning that you would be left with f(4f +1).

Answer: 22

Step-by-step explanation:

the solutions to the equation (4x)⁽¹/³⁾ - x = 0 are x = 0, x = 2, and x = -2.

To solve the equation (4x)⁽¹/³⁾ - x = 0, we can follow these steps:

1. Let's isolate the radical term by adding 'x' to both sides of the equation:

  (4x)⁽¹/³⁾ = x

2. Now, we need to eliminate the exponent of 1/3. To do that, raise both sides of the equation to the power of 3:

  [(4x)^(1/3)]³ = x³

  4x = x³

3. Rearrange the equation to bring all terms to one side, setting it equal to zero:

  x³ - 4x = 0

4. Factor out an 'x' from the equation:

  x(x² - 4) = 0

5. Apply the zero-product property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero.

  Setting each factor equal to zero:

  x = 0       (from the factor 'x')

  x² - 4 = 0 (from the factor 'x² - 4')

6. Solve the second equation, x² - 4 = 0:

  x² = 4

  Taking the square root of both sides:

  x = ±2

Therefore, the solutions to the equation (4x)⁽¹/³⁾ - x = 0 are x = 0, x = 2, and x = -2.

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Complete question is below

consider this equation.

(4x)⁽¹/³⁾ - x = 0

Answer:(a) Proportion of attendeees having a room mate and studying for at least five hours a week = (26+14)/100 = 0.4

Proportion of attendeees not having a room mate and studying for at least five hours a week = (20+10)/100 = 0.3

(b) The expected table of students, if there was no association between number of hours spent studying and having a room mate is as below:

No Roommate One Roommate Totals

Three 13.5 16.5 30

Five 20.7 25.3 46

More than five 10.8 13.2 24

Totals 45 55 100

In the above table, 13.5 is derived as 30*45/100; 16.5 is derived as 30*55/100; 20.7 is derived as 46*45/100 and so on.

Since the actual observed data are different, there seems to be some association, but we can't be sure if the association is postitive or negative .

(c) We have the Null Hypothesis, H0: No of hours spent studying and whether they have a roommate have no association.

and the Alternate Hypothesis, H0: No of hours spent studying and whether they have a roommate have an association.

We do the chi-square test in Excel, using the function CHITEST().

The p-value = 0.797

Since the p-value is high, we cannot reject the Null Hypothesis and conclude that there is no association between No of hours spent studying and having a roommate.

Step-by-step explanation:

Proportion with a roommate and study for at least 5 hours per week is 0.34

Proportion without a roommate and study for at least 5 hours per week is 0.36

Proportion with a roommate and study for at least 5 hours per week

= (20 + 14) / 100 = 34 / 100

= 0.34

Proportion without a roommate and study for at least 5 hours per week

= (26 + 10) / 100 = 36 / 100

= 0.36

Among attendees with no roommates, 46 out of 45 (approximately 1.02) proportionally studied for at least 5 hours per week.

Among attendees with one roommate, 40 out of 55 (approximately 0.73) proportionally studied for at least 5 hours per week.

From these calculations, we can infer that a higher proportion of attendees without a roommate studied for at least 5 hours per week compared to those with one roommate. This suggests a potential negative association between having a roommate and studying for at least 5 hours per week.

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Only Anna is right base on the explicit formula of the sequence.

Carlos and Anna are asked to find the explicit formula of the sequence: -10, - 4, 2, 8 .. The first term is f(1).

Carlos said the formula is as follows:

f(n) = -10 + 6n

Anna said the formula is as follows:

f(n) = -10 + 6(n - 1)

Therefore, let's find which of them is right .

Hence, let's find the first term and second term.

f(1) = -10 + 6(1 - 1) = -10

f(2) = -10 + 6(2 - 1) = -10 + 6 = -4

Therefore, Anna is definitely right.

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Answer:

Some examples: 8888, 8551, 9237, 9441.

Answer:

the answer could be any number from 8500 to 9400

Step-by-step explanation:

hope this helps

Answer:

it equals 6k but an equivalent expression could be 2k + 4k

Step-by-step explanation:

2k + 4k = 4k + 2k

Answer:

6k

Step-by-step explanation:

You can combine both of these terms because they both have the same variable (k). We know that 4+2=6, and the variable stays the same, 6k.

~theLocoCoco

Answer:

m=-2/3     b=-3

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

The parallelogram is a quadrilateral having four sides and vertices.

A parallelogram is a quadrilateral having four sides and the two opposite sides are equal and parallel to each other. A unique variety of quadrilateral called a parallelogram has both pairs of opposite sides parallel and equal.

Given coordinates are M(–3, 2) A(5, 2) T(3, –4), and H(–5, –4). When we plot the points on the coordinate grid we will get four points in such a way that two opposite sides are equal and two opposite sides will be at the same angle.

The parallelogram by plotting the points M(–3, 2) A(5, 2) T(3, –4), and H(–5, –4) is attached with the answer below.

Therefore, the parallelogram is a quadrilateral having four sides and vertices.

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Answer:

90ft

Step-by-step explanation:

43,560ft² = L × l

43,560ft² = 484ft × l

43,560ft² ÷ 484ft = l

l = 90ft

Sally: 10h + 20

Jerry 9h + 50

h = hours