Ling must spend no more than $40.00 on decorations for a party. She has spent $10.00 on streamers and wants to buy bags of balloons as well. Each bag of balloons costs $2.50. The inequality below represents x, the number of bags she can buy given the spending limit and how much she has already spent on streamers.

10 + 2.5 x less-than-or-equal-to 40

Which best describes the number of bags of balloons she can buy?
She can buy from 0 to 12 bags, but no more.
She can buy from 0 to 20 bags, but no more.
She must buy 12 or more bags.
She must buy 20 or more bags.

a. 95% confidence Interval of the True Mean Reading Score for All Fifth Graders: (76.85, 87.15)

b. 95% Confidence Interval of the Mean Reading Scores of All Fifth Graders: (77.03, 86.97)

c. 99% Confidence Interval of the Mean Reading Scores of Fifth Graders:(75.85, 88.15)

s. The 99% confidence interval is wider than the 95% confidence intervals because a higher confidence level requires a larger margin of error and a wider interval to capture the true mean with a higher degree of certainty.

To find the confidence intervals, we'll use the formula:

Confidence Interval = Mean ± (Critical Value × Standard Error)

Where:

Mean is the sample mean

Critical Value is the value corresponding to the desired confidence level and degrees of freedom

Standard Error is the standard deviation of the sample divided by the square root of the sample size

a. 95% Confidence Interval of the True Mean Reading Score for All Fifth Graders:

Since the sample size is 35, the degrees of freedom (df) will be 35 - 1 = 34.

The critical value for a 95% confidence level and 34 degrees of freedom is approximately 2.032.

Standard Error (SE) = Standard Deviation (SD) / √n

SE = 15 / √35 = 2.533

= 82 ± 5.15

= (76.85, 87.15)

b. 95% Confidence Interval of the Mean Reading Scores of All Fifth Graders:

We consider the standard error as the standard deviation of the population divided by the square root of the sample size.

Confidence Interval = 82 ± (2.032 × (15 / √35))

= 82 ± 4.97

= (77.03, 86.97)

c. 99% Confidence Interval of the Mean Reading Scores of Fifth Graders:

The critical value for a 99% confidence level and 34 degrees of freedom is approximately 2.728.

Confidence Interval = 82 ± (2.728 × (15 / √35))

=82 ± 6.15

= (75.85, 88.15)

s. Comparing the Intervals:

The 99% confidence interval is larger than the 95% confidence intervals (both for the true mean reading score and the mean reading scores of all fifth graders).

Because a higher confidence level requires a wider interval to capture the true mean with a higher degree of certainty.

As the confidence level increases, the critical value increases, resulting in a larger margin of error and a wider confidence interval.

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The process of counting the number of observations is knowns as Tabulation.

The logical representation of the numerical data written in rows and columns is known as tabulation. It helps in to facilitate the statistical analysis. The data that can be organized in the form of table is termed as tabulation. The data in the table can be represented in a systematic manner. The main objective of tabulation is to present the systematic data in a brief manner.

There are two types of tabulation. They are:

1.Simple tabulation

2.Complex tabulation

A simple example for the tabulation is, The population of the people is divided into religion, caste, gender, age etc.

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7,9,11,13,15

First, find the common difference (d)

9-7 = 11-9 = 13-11 = 15-13 = 2

d= 11

a1 = first term = 7

apply the formula:

an = a1 + (n-1) d

an = 7 + (n-1) 2

an = 7 + 2n-2

an = 2n + 5

Answer:

A = 3, B = 5.2

Step-by-step explanation:

i think that is right, i hope this helps.

The value of x would be 5 for the model 2x+4.

Rearrange unknown terms to the left side of the equation,
\(= > 2x-3x = -1 - 4\)

Combine like terms\(= -x = -1-4\)

By calculating the sum or difference : -x = -5

Lets divide both sides of the equation by the resulting coefficient 5
So x = 5

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Answer:

AAS

Step-by-step explanation:

Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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Answer:

9 x 1/12 = 4 1/2.

Step-by-step explanation:

Times 9 by 1/2.

The measure of the reference angle is: \($$\cos (\theta)=\frac{\sqrt{3}}{2}$$\)

The reference angle of an angle is the smallest acute angle between the terminal arm of a quadrant and the x-axis.

Given that:

\($$\theta=\frac{11 \pi}{6}$$\)

First, we convert to degrees

\(& \theta=\frac{11 \pi}{6} * 180 \pi \\\)

\(& \theta=\frac{11}{6} * 180 \\\)

\(& \theta=11 * 30 \\\)

\(& \theta=330^{\circ}\)

\($$\alpha=30$$\)

Hence, the measure of the reference angle Is: \($30^{\circ}\alpha=30\)$ means that the reference angle is in the first quadrant \($\theta=330^{\circ}$\) means that this angle is in the fourth quadrant

In the first and the fourth quadrants,

\($$\cos (\theta)=\cos (\alpha)$$\)

Substitute \($\alpha=30$\)

\($$\cos (\theta)=\cos (30)$$\)

In trigonometry:

\($$\cos (30)=\frac{\sqrt{3}}{2}$$\)

So:

\($$\cos (\theta)=\frac{\sqrt{3}}{2}$$\)

\($$\cos (\theta)=\frac{\sqrt{3}}{2}$$\)

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15% of the time, the probability that student who chose to walk has been late.

From the stated data-

37.5% of the 40% of students who walk to school have been late.

Thus,  37.5% of 40%

= 0.375 x 0.40

= 0.1500

= 15%

Thus, 15% of the time, the student who chose to walk has been late atleast once .

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The complete question is-

At a large high school 40 percent of the students walk to school, 32 percent of the students have been late to school at least once, and 37.5 percent of the students who walk to school have been late to school at least once. One student from the school will be selected at random. What is the probability that the student selected will be one who both walks to school and has been late to school at least once?

The derivative of f(x) = ∫ (- 2 to x) √t³ + 8) dt is, √(x³ + 8).

We have to given that,

Function is,

f (x) = ∫ (- 2 to x) √t³ + 8) dt

So, the derivative of f (x) = ∫ (- 2 to x) √t³ + 8) dt is,

By using the Fundamental Theorem of Calculus Part I, we need to evaluate the integrand at the upper limit of integration x and multiply by the derivative of the upper limit:

f'(x) = d/dx [  ∫ (- 2 to x) √t³ + 8) dt ]

f'(x) = √(x³ + 8)

Therefore, the derivative of f(x) is √(x³ + 8).

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The width of the rectangle is 1 centimeter, the length is 5 centimeters, and the area is 5 square centimeters.

To solve this problem, we will set up a system of equations using the given information.

First, we have the equation for the length of the rectangle: l = w + 4.

We are given two equations representing the area of the rectangle. The first equation is obtained using the formula for the area of a rectangle: a = \(w^2 + 4w\). The second equation models the relationship between the area and width: a = 4w + 45.

Now, we can solve this system of equations to find the values of width (w) and area (a).

Substituting the expression for length (l) in terms of width (w) into the area equation\(a = w^2 + 4w\), we get:

\(a = (w + 4)^2 + 4(w + 4)\)

\(= w^2 + 8w + 16 + 4w + 16\)

\(= w^2 + 12w + 32\)

Since this equation represents the same area as the second equation, we can equate them:

\(w^2 + 12w + 32 = 4w + 45\)

Rearranging the equation, we have:

\(w^2 + 12w + 32 = 4w + 45\)

We can solve this quadratic equation by factoring or using the quadratic formula. Factoring it, we have:

(w + 13)(w - 1) = 0

This gives two possible values for width: w = -13 or w = 1. Since width cannot be negative, we discard w = -13.

Therefore, the width of the rectangle is w = 1.

Substituting this value back into the length equation, we find:

l = w + 4

= 1 + 4

= 5

So, the length of the rectangle is l = 5.

To find the area, we substitute the width and length into either of the area equations:

\(a = w^2 + 4w\)

= 1^2 + 4(1)

= 1 + 4

= 5

Therefore, the area of the rectangle is a = 5 square centimeters.

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Answer:

There are two solutions, but only one is viable.

Step-by-step explanation:

Plato

Answer:

0.456 :)

Step-by-step explanation:

Answer:

its a commutative property becaus its just changing the order

Answer:

A = s^2

Step-by-step explanation:

The area of a square can be found by multiplying the side by its side.

A = side x side = s^2

So if the side of a square is 3, to find the are you would multiply 3 times 3. Giving you an area of 9.

The probability of randomly selecting an individual in this community who has red hair or is​ left-handed is 0.23

The probability of an event refers to the likelihood of the event occurring, expressed as a number between 0 and 1.

In other words, the probability of the union of two events can be expressed as follows:

P(A or B) = P(A) + P(B) - P(A and B)

Where A represents the event of having red hair, B represents the event of being left-handed, and P(A and B) represents the probability of the intersection of the two events. In this case, P(A) = 0.08 and P(B) = 0.15.

Therefore, to find the probability of a randomly selected individual in this community who has red hair or is left-handed, we would need to know the probability of the intersection of the two events, P(A and B).

This would allow us to subtract it from the sum of the individual probabilities, P(A) + P(B), to find the total probability of having red hair or being left-handed.

=> P(A) + P(B) = 0.08 + 0.15 = 0.23

In conclusion, to find the probability of having red hair or being left-handed in this community, we would need to know the probability of the intersection of the two events, P(A and B).

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Answer:

$80

Step-by-step explanation:

The final price of $42 was after a 25% off coupon was applied.

Therefore, $42 is 75% of the price before the coupon was applied.

So cost before coupon applied = 42/75 x 100 = $56

The price of $56 was after the 30% mark down was applied.

Therefore, $56 is 70% of the price before it was marked down.

So cost before mark down applied = 56/70 x 100 = $80

Answer:

Use the given slope and point to substitute into the point-slope formula y−y1=m(x−x1).

Slope-intercept form:

y=3x²+4x−25

Point-slope form:

y+5=(3x+10)⋅(x−2)

Step-by-step explanation:

The answer is 15.

From the question, we have

60 ÷ 4 = 15

The answer is 15.

Divide:

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

Complete question:

Solve: 60 ÷ 4

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Answer:

Pyramid

Step-by-step explanation:

Answer:

1.5 or 1/5

Step-by-step explanation:

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

The volume of the solid obtained by rotating the region bounded by y = 6x^4, x = 1, and y = 0 about the x-axis is V = 24π/5 cubic units.

To find the volume, we use the method of cylindrical shells. The volume of each shell is given by the formula V = 2π∫[a, b] x * f(x) dx, where f(x) represents the height of the shell.

In this case, the height of each shell is given by f(x) = 6x^4, and the limits of integration are from x = 0 to x = 1, as the region is bounded by x = 1 and y = 0.

Therefore, the volume can be calculated as V = 2π∫[0, 1] x * 6x^4 dx.

Simplifying, we have V = 12π∫[0, 1] x^5 dx.

Integrating x^5 with respect to x gives V = 12π * (1/6) * x^6 from 0 to 1.

Evaluating the integral, we get V = 12π * (1/6) * (1^6 - 0^6) = 2π/5.

Hence, the volume of the solid obtained by rotating the region bounded by y = 6x^4, x = 1, and y = 0 about the x-axis is V = 24π/5 cubic units.

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Answer: (w-8)(-4w+3)  

Step-by-step explanation:

Given:

4w(8 − w) + 3(w − 8)

Solution:

You need to make what's inside the parentheses the same so you can take it out as the GCF

let's change the look of (8-w) to look like (w-8)

Start:

8-w                >let's make w first, don't forget to carry signs

-w+8              >take out GCF -1 (opposite of distribution)

-1(w-8)           >now it looks more like the other parentheis,   Subsitiute in

8-w    is same as   -1(w-8)      from above

4w(8 − w) + 3(w − 8)                  >original question, now substitute

4w(-1)(w-8) + 3(w − 8)                 > simplify -1

-4w(w-8) + 3(w − 8)                     >take out w-8 as GCF

(w-8)(-4w+3)              

Answer:

y = 3/2x

Step-by-step explanation:

The slope intercept form is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-2, -3) (2,3)

We see the y increase by 6 and the x increase by 4, so the slope is

m = 6/4 = 3/2

The y-intercept is located at (0,0)

So, the equation is y = 3/2x

Answer:

a=90

c=40

b=70

Step-by-step explanation:

a is right angle so 90

c is 160-90-30=40

b is 150-80=70

Answer:

1/5

Step-by-step explanation:

Given data

Sample space

3 blue

5 white

3 red

4 purple

Sample size

=3+5+3+4

=15

Hence the probability/possibility of grabbing a white Gatorade is

=3/15

=1/5

Answer:

8 pounds total

Step-by-step explanation:

first calculate how much she used in total

1/4 + 3/8

need like denominators so multiply 1/4 by 2

2/8 + 3/8 = 5/8

so 5/8 of the total is 5 pounds, now find the total

if 5/8 = 5, then 8/8 = _8_

Answer:

If the code cannot begin with 0, we have 9 options for the first digit (1-9), 9 options for the second digit (because we previously used one digit), 8 options for the third digit, and 7 options for the fourth digit. And the list goes on

The total number of codes is:

9 x 9 x 8 x 7 = 4,536

As a result, there are 4,536 possible codes that may be generated with numbers 0-9 if each digit can only be used once and the code cannot begin with 0.