Write a simplified polynomial expression in standard form to represent the area of the rectangle below.
X - 4
5X + 2

Therefore, the only claim that the interval would tend to refute is option E: The population mean is less than 125.

Based on the 90% confidence interval of 135 to 160, we can conclude that the population mean is likely to be within this interval with a 90% degree of confidence.

A. The claim that the population mean is more than 110 is not refuted by the confidence interval since the lower limit of the interval is above 110.

B. The claim that the population mean is less than 150 is not refuted by the confidence interval since the upper limit of the interval is above 150.

C. The claim that the population mean is between 140 and 150 is not refuted by the confidence interval since both values are within the interval.

D. The claim that the population mean is more than 140 is not refuted by the confidence interval since the lower limit of the interval is above 140.

E. The claim that the population mean is less than 125 is refuted by the confidence interval since the lower limit of the interval is above 125.

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Answer:

6.75

Step-by-step explanation:

We are given that function

\(f(x)=\frac{9x-18}{4}\)

5 is an element in the domain of f(x)

i.e

x=5

We have to find the corresponding element of 5 in the range of f(x).

Substitute x=5 in the given function

\(f(5)=\frac{9\times 5-18}{4}\)

\(f(5)=6.75\)

Hence, the corresponding element of 5 is 6.75 in the range.

My first step is to draw a picture

We know that the length is 2 times the width

L = 2w

We are given a width of 4.6 yards

L = 2(4.6) = 9.2 yards

We can find the area by using the formula

A = l*w

A = 9.2 * 4.6

A =42.32 yd^2

Answer: The question seems unclear on what answer is actually wanted however I'll try showing some steps which make the inequality true but in reversed manner.

y > x2 + 3x – 4
y+4 > x2 + 3x
y + 4 - 3x > x2
4 - 3x > x2 - y
- 3x > x2 - y - 4
x < (x2 - y - 4)/-3

The above ways are some inequalities which can show the inequality true

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The median of the data is 5 if the all class widths are 1, option (C) is correct.

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.

In the histogram, 15 data values are given:

1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 8, 9

The mid-value is 5 which is on the 8th place

Thus, the median of the data is 5 if the all class widths are 1, option (C) is correct.

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xy+xb+ya+ab = 32

x(y+b) + a(y+b) = 32

(x+a) (y+b) = 32

4.(y+b) = 32

(y+b) =32/4

(y+b) = 8

OPTION C

The probability of getting a green ball and purple ball is 4/27

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

Probability = sample space /Total outcome

total outcome = 4+3+2 = 9

For the first draw,

probability of picking a green = 4/9

for the second draw;

probability of picking a purple = 3/9 = 1/3

The probability of getting a green and a purple = 1/3 × 4/9

= 4/27

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That the equation of the line is y = 7x - 50.

The equation of a line with slope m passing through the point (x1, y1) is given by: y - y1 = m(x - x1).

In this case, the line has a slope of 7 and passes through (8, 6). Therefore, we can plug in the values for m, x1, and y1 into the equation above to find the desired equation.

Substituting in 7 for m, 8 for x1, and 6 for y1, we can rewrite the equation as: y - 6 = 7(x - 8).

Simplifying, we find that the equation of the line is y = 7x - 50.

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Answer:7,874

Step-by-step explanation: Because if he naps for 254 mins a day and there are 31 days, you multiply 254 by 31

Answer:

The point M(Mx, My) is mid-point of GH with G(Gx, Gy) and H(Hx, Hy).

=> 2*Mx = Gx + Hx => 2*4 = -2 + Hx => Hx = 10

=> 2*My = Gy + Hy => 2*(-3) = 2 + Hy => Hy = -8

=> H(10, -8)

Hope this helps!

:)

The coordinate of the point H is (10, -8) if the midpoint, M, of segment GH is M(4, -3). Endpoint G has the coordinates G(-2, 2).

A segment bisector is a line, ray, line segment, or point that divides a line segment into two equal halves at its center.

It is given that:

The midpoint, M, of segment GH is M(4, -3). Endpoint G has the coordinates G(-2, 2).

Let (x, y) be the coordinates of endpoint H

H(x, y)

(x - 2)/2 = 4

x - 2 = 8

x = 8 + 2

x = 10

(y + 2)/2 = -3

y + 2 = -6

y = -8

Thus, the coordinate of the point H is (10, -8) if the midpoint, M, of segment GH is M(4, -3). Endpoint G has the coordinates G(-2, 2).

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Answer:

that  be 34 because you multiply

Step-by-step explanation:

The values of the missing sides is DE = 12 and AC = 6.5

Two triangles are said to be similar if the ratio of their corresponding sides are in the same proportion. Also all the corresponding angles are congruent.

Using Pythagoras:

AC² = AB² + BC²

AC² = 2.5² + 6²

AC = 6.5

Using similar triangles:

BC / DE = AB / EF

6/DE = 2.5/5

DE = 12

The values of the missing sides is DE = 12 and AC = 6.5

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The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

r + ¾ = ⁷/₈

r = ⁷/₈ - ¾

⁷/₈ - ⁶₈ = ¹/₈

r = ¹/₈

Step-by-step explanation:

but my original answer was 4/4

Answer:

If it's AL to A'L' then its 1/2

If it's A'L' to AL then its 2

Answer:

15 ml

Step-by-step explanation:

We are told

Solution A = 15% of water

Solution B = 20% of water

Let's assume, the entire solution = 100ml

We are told that in the beaker we have 10 ml of Solution A already

Mathematically,

100 ml = 15%

10 ml = X

100ml × X = 15 × 10

X = 150/ 100

X = 1.5%

Hence in the beaker, we have 1.5% of water from Solution A

We are asked to find how many ml of solution B must be added to make the solution have 18% of water

Let y = number of ml of solution B

Hence

10 ml × 15%(0.15) = 1.5 ml of water - Equation 1

y ml × 20%( 0.20) = 0.20y ml of water ...... Equation 2

Add up the above equation

10ml + y ml ×18% (0.18) = 1.5 + 0.20y

(10 + y)(0.18) = 1.5 + 0.20y

1.8 + 0.18y = 1.5 + 0.20y

Collect like terms

1.8 - 1.5  = 0.20y - 0.18y

0.3 = 0.02y

y = 0.3/0.02

y = 15ml                              

Therefore,15mL of solution B must be added to the beaker in order to create a mixture that is 18% water

Answer:

0.9 liters.

Step-by-step explanation:

The difference between 20% of 3 and 50% of 3 is 30%. 30% of 3 liters is 0.9 liters so this is what you add to can A.

A zero vertical asymptote removable discontinuity means that there is a zero of the function at the input value where the vertical asymptote would occur,

A zero of a function occurs when the value of the function is zero. A vertical asymptote of a function occurs when the value of the function becomes unbounded (either positive or negative) as the input approaches a certain value.

A removable discontinuity of a function occurs when there is a hole in the graph of the function at a certain input value, but the function can be made continuous at that point by defining its value at that input.

In the case of a zero vertical asymptote removable discontinuity, this means that there is a zero of the function at the input value where the vertical asymptote would occur, and the function can be made continuous at that input value by defining its value to be the value of the function at that input.

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Anwser 52 degrees

Step-by-step explanation:

first you figure out the 2 angles the triangle is missing so 28-90 would be 62

then to find the other unknown angle you solver for the larger triangle

so 90+48=138

180-138=42

42+62=104

104+2y-30=180

add 30

104+2y=210

-104

2y=106

divide by 2

y=53

I did it wrong :) don't pay attention to this comment XP

Therefore, When ratios have the same units, we call that ratio a unit ratio.

When ratios have the same units, we call that ratio a unit ratio. An explanation of what is meant by the term ratio would be helpful. A ratio compares the relative sizes of two or more quantities. If the numbers being compared have the same units, then it is called a unit ratio. Unit ratios are ratios that relate to each other in terms of the same measurement unit. They are also sometimes known as unit rates or unit fractions. They are frequently used to compare the relative size of one quantity to another when they are measured in the same units. For example, when we say that there are two apples for every five oranges, we are expressing a ratio between apples and oranges. However, when we say that there are two apples per five oranges, we are using a unit ratio.

Therefore, When ratios have the same units, we call that ratio a unit ratio.

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On graphing the inequality , a dotted line and the shaded area is seen which means all the values above that line is included.

When two algebraic expressions are equated using inequality operators < ,> etc , the statement formed is called Linear Inequality.

The inequality given is

y > - 3x+8

On graphing the inequality , a dotted line and the shaded area is seen which means all the values above that line is included.

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Answer: Zak - Resp after 24 months = $4,344.00

              Zak - Technology Fund after 24 months = $1,102.98

              Zak's Technology Fund has enough money to buy a laptop.

              Zak's Savings (Resp) will last less than 6 months

Step-by-step explanation for Zak:

January - June 2019

$15/hr x 20 hr x 4 wks x 6 months = $7200 Gross Income

Taxable Income is $7200 - $1080 = $6120    (Annual Income $12,240)

→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income

Tech Fund (5%): $5486.40(0.05) = $274.32

Food Expense (30%): $5486.40(0.3) = $1,645.92

Clothing Expense (30%): $5486.40(0.3) = $1,645.92

Entertainment Expense (25%): $5486.40(0.25) = $1,371.60

Miscellaneous Expense (10%): $5486.40(0.1) = $548.64      

                                               Other Expenses: $5,212.08

July - December 2019 (excluding August)

$16/hr x 20 hr x 4 wks x 5 months = $6400 Gross Income

Taxable Income is $6400 - $960 = $5440    (Annual Income $11,560)

→ $6,400 - ($960 + $320 + $128 + $0 + $75.20) = $4,916.80 Net Income

Tech Fund (5%): $4916.80(0.05) = $245.84

Food Expense (30%): $4916.80(0.3) = $1,475.04

Clothing Expense (30%): $4916.80(0.3) = $1,475.04

Entertainment Expense (25%): $4916.80(0.25) = $1,229.20

Miscellaneous Expense (10%): $4916.80(0.1) = $491.68      

                                              Other Expenses: $4,670.96

January - June 2020

$17/hr x 20 hr x 4 wks x 6 months = $8160 Gross Income

Taxable Income is $8160 - $1224 = $6936    (Annual Income $13,872)

→ $8,160 - ($1224 + $408 + $163.20 + $0 + $194.88) = $6,169.92 Net Income

Tech Fund (5%): $6169.92(0.05) = $308.50

Food Expense (30%): $6169.92(0.3) = $1,850.98

Clothing Expense (30%): $6169.92(0.3) = $1,850.98

Entertainment Expense (25%): $6169.92(0.25) = $1,542.48

Miscellaneous Expense (10%): $6169.92(0.1) = $616.98      

                                               Other Expenses: $5,861.42

July - December 2020 (excluding August)

$18/hr x 20 hr x 4 wks x 5 months = $7200 Gross Income

Taxable Income is $7200 - $1080 = $6120    (Annual Income $13,056)

→ $7,200 - ($1080 + $360 + $144 + $0 + $129.60) = $5,486.40 Net Income

Tech Fund (5%): $4916.80(0.05) = $274.32

Food Expense (30%): $5486.40(0.3) = $1,645.92

Clothing Expense (30%): $5486.40(0.3) = $1,645.92

Entertainment Expense (25%): $5486.40(0.25) = $1,371.60

Miscellaneous Expense (10%): $5486.40(0.1) = $548.64      

                                              Other Expenses: $5,212.08

\(\boxed{\begin{array}{l|r|r|r|r||r}\underline{ZAK}&\underline{Jan-Jun'19}&\underline{Jul-Dec'19}&\underline{Jan-Jun'20}&\underline{Jul-Dec'20}&\underline{Totals\quad }\\Gross&\$7200.00&\$6400.00&\$8160.00&\$7200.00&\$28960.00\\Resp&\$1080.00&\$960.00&\$1224.00&\$1080.00&\$4344.00\\Net&\$5486.40&\$4916.80&\$6169.92&\$5486.40&\$22059.52\\Other&\$5212.08&\$4670.96&\$5861.42&\$5212.08&\$20956.54\\Tech&\$274.32&\$245.84&\$308.50&\$274.32&\$1102.98\end{array}}\)

The probability that the sample mean exceeds 45 is approximately 0.

By the central limit theorem, the sample mean of a large sample size from any distribution with a finite mean and variance is approximately normally distributed.

Since the exponential distribution has a mean of 4 and a variance of 16, we can approximate the distribution of the sample mean as a normal distribution with mean 4 and standard deviation 4/sqrt(225) = 4/15.

To find the probability that the sample mean exceeds 45, we can standardize the distribution using the z-score formula:

z = (45 - 4) / (4/15) = 10.625

Using a standard normal distribution table or a calculator, we can find the probability that a standard normal random variable exceeds 10.625:

P(Z > 10.625) ≈ 0

Therefore, the probability that the sample mean exceeds 45 is approximately 0.

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(112)3 =336

(211)3 =633

sum of the numbers:

(112)3 +(211)3=

336+633=

969

product of the numbers:

(112)3 × (211)3=

336×633=

212688

Answer:

x = 7  x = -6

Step-by-step explanation:

x^2−x−42=0

Factor

What two numbers multiply to -42 and add to -1

-7*6 = -42

-7+6 = -1

(x-7) (x+6) =0

Using the zero product property

x-7 =0   x+6 =0

x = 7  x = -6

The correct label for the angle formed by line segments BC and BA measuring 65 degrees is ∠CBA.

In the given statement, line segments BC and BA are mentioned as the forming elements of the angle. When labeling an angle, the convention is to use three letters, with the middle letter representing the vertex of the angle. In this case, the vertex of the angle is point B. Therefore, the correct label for the angle would include B as the middle letter.

Among the options provided, ∠CBA correctly represents the angle formed by line segments BC and BA. It indicates that the vertex of the angle is B, with C and A being the endpoints of the two line segments. The order of the letters in the angle label follows a counter-clockwise direction, starting from the initial side (BC) and moving towards the terminal side (BA).

Options A (∠A), B (∠BCA), and C (∠b) do not accurately represent the given angle or follow the convention of labeling angles. Hence, the correct label for the angle formed by line segments BC and BA, measuring 65 degrees, is ∠CBA.

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The correct label for the angle formed by line segments BC and BA, measuring 65 degrees, is ∠CBA. The name of an angle starts at one ray, passes through the vertex, and ends at the other ray.

When we talk about angles, the label or name for an angle usually starts at one ray, passes through the vertex, and ends at the other ray. In this question, the angle is generated by the line segment BC (the one side of the angle), and line segment BA (the other side of the angle), with the vertex being at point B. Therefore, the correct label for this angle is ∠CBA or ∠ABC. The choice D.) ∠CBA is correct.

Note that the letters can be reversed (starting at A and ending at C) because angle measures are the same in both directions. The first and the last letters of the label name (C and A in this case) refer to the rays or line segments forming the angle, whereas the middle letter (B) refers to the vertex of the angle.

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Symmetry is a way of measuring the shape of a data set. It is defined as the similarity between the upper and lower halves of a distribution.

A symmetric distribution is one where the data is equally distributed around a central point. To calculate this, you need to subtract the mean (the average of the values) from each data point and then divide by the standard deviation (the measure of how much the data is spread out). The formula for symmetry is: (x-mean)/standard deviation. An example of a symmetric distribution would be the scores of a group of students on an easy test. If the mean score was 70 and the standard deviation was 10, then any score between 60 and 80 would be considered symmetric.

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The data collected from the customers in restaurants about the quality of food is an example of a(n); Observational Study

There are four types of statistical studies namely;

Observational studies

Surveys

Experiments

Meta-analytical studies.

1) An observational study involves observing and recording data on some variable(s) of interest.

2) A (sample) survey uses questioning to gather data.

3) An experiment also referred to as experimental study attempts to give an answer to a statistical question by manipulating all or part of the sample.

Now, we are told that some data was collected from the customers in restaurants about the quality of food.

This is a type of observational study because it involves observing and recording data on an interest which is quality of food

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