Select the GCF of these numbers. 48 and 60 22 ·3 2· 112 32 23 · 5 13· 193 ·232

Jane sold approximately 7.8 cups of lemonade. Since she cannot sell a fractional number of cups of lemonade, we can round up to 8 cups.

Let x be the number of cups of lemonade Jane sold.

The total earnings she made from selling x cups of lemonade is:

Total earnings = price per cup * number of cups sold

Total earnings = $0.25 * x

The total cost of making x cups of lemonade is:

Total cost = cost per cup * number of cups sold

Total cost = $1.50 * x

Jane's profit is equal to her total earnings minus her total cost:

Profit = Total earnings - Total cost

Profit = $0.25x - $1.50x

Profit = -$1.25x

We know that Jane's earnings were $9.75, so we can set up the equation:

$9.75 = -$1.25x

To solve for x, we can divide both sides by -$1.25:

-$9.75 / -$1.25 = x

x = 7.8

Jane sold approximately 7.8 cups of lemonade. Since she cannot sell a fractional number of cups of lemonade, we can round up to 8 cups.

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Answer:

d. 1 7/30...............

Answer:

D

Step-by-step explanation:

2/5 + 5/6

Make the denominator same

(2×6)/30 + (5×5)/30

12+25/30

37/30

1 7/30

The expression used  to calculate the surface area of the rectangular prism is given by option b. 2×6 + 2×10 + 2×15.

Let us consider 'l' be the length of the rectangular prism.

'w' be the width of the rectangular prism .

'h' be the height of the rectangular prism.

From the attached figure we have,

Length of the rectangular prism l = 3 units

Width of the rectangular prism w = 2 units

Height of the rectangular prism h = 5 units

Surface of the rectangular prism = 2(lw + wh + hl )

Substitute the values in the formula we get,

⇒Surface of the rectangular prism = 2 (3×2 + 2×5 + 5×3 )

⇒Surface of the rectangular prism = 2 ( 6 + 10 + 15)

⇒Surface of the rectangular prism = 2×6 + 2×10 + 2×15

Therefore, the surface area of the rectangular prism with given dimensions is equal to option b. 2×6 + 2×10 + 2×15.

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The above question is incomplete, the complete question is:

Which expression can be used to find the surface area of the following rectangular prism?

Attached figure.

The approximate p-value is 5.1250%.

P-value is the probability of obtaining a test statistic as or more extreme than what was actually observed, given that the null hypothesis is true.

Two-sided significance test, with a significance level of 2%. you then randomly sample 420 items from the production line, and find that 22 of the items are defective.

The approximate p-value for this two-sided significance test, with a significance level of 2%, is 5.1250%.

This is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This was calculated using a binomial test, which takes into account the sample size and the expected rate of defects.

This p-value indicates whether or not the observed rate of defects is significantly different from the expected rate.

In this case, the p-value is the probability of observing 22 or more defective items given that the true rate is 3.2%.

This can be calculated using a binomial test.

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The amount that each charity gets is $25.

The charity raise simply define as we raise funds in the form of small amounts of money from a huge crowd of people within a specific period of time.

For example, if 100 people donate $50 each to your crowdfunding campaign in two weeks, you will be able to raise $5000.

To find the amount that each charity got, we have to divide the total charity amount raised in the proportion given, i.e., 1/6.

Each charity gets 1/6 of the total amount raised, which is $150.

So, we need to divide $150 by 6:

$150 ÷ 6 = $25

Therefore, each charity received $25.

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A student willing to participate in a debate competition is required to fill out a registration form.

Form filling in two types of data i.e.,

Quantitative data is data that can be counted or measured in numerical values. The two main types of quantitative data are discrete data and continuous data. Height in feet, age in years, and weight in pounds are examples of quantitative data. Qualitative data is descriptive data that is not expressed numerically.

Categorical data is a collection of information that is divided into groups. i.e., if an organization or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical.

a. What is your date of birth?

Quantitative.

b. Have you participated in any debate competition previously?

Categorical.

c. If yes, how many debate competitions have you participated so far?

Quantitative.

d. Have you won any of the competitions?

Categorical.

e. If yes, how many have you won?

Quantitative.

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The given question is incomplete, complete question is:

A student willing to participate in a debate competition required to fill a registration form. State

whether each of the following information about the participant provides categorical or quantitative

data.

a. What is your date of birth?

b. Have you participated in any debate competition previously?

c. If yes, how many debate competitions have you participated so far?

d. Have you won any of the competitions?

e. If yes, how many have you won?

Please write answer in two parts. A. Main answer (correctly paraphrased, addressing all aspect of the question) B. Explanation (Step-by-step explanation)

All the possible angle measures are given as follows:

25º and 35º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

On the first quadrant, we have that:

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The best prediction possible for the number of times the spinner will not land on yellow is 18.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Assuming that the spinner is fair and all outcomes are equally likely, we can calculate the probability of the spinner not landing on yellow in one spin by adding up the probabilities of all other outcomes, which are green, blue, and red.

The probability of the spinner not landing on yellow in one spin is:

P(not yellow) = P(green) + P(blue) + P(red)

= 1/6 + 1/3 + 1/6

= 1/2

Therefore, the expected number of times the spinner will not land on yellow in 36 spins is:

E(not yellow) = 36 x P(not yellow)

= 36 x 1/2

= 18

So the best prediction possible for the number of times the spinner will not land on yellow is 18. However, it's important to note that this is just a prediction based on probabilities, and the actual number of times the spinner doesn't land on yellow in 36 spins may vary.

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Answer:

≈ $26

Step-by-step explanation:

13% = 0.13

199.99 x 0.13 = $25.9987

So, 13% markup is ≈ $26

The number of ways to arrange the letters of PENCIL when the first letter can't be N or L is option (B) 480.

The word PENCIL has 6 letters, here we have to use permutation method.  If all the letters are used, there are 6! = 720 ways to arrange them. However, the first letter can’t be N or L. This means that there are only 4 choices for the first letter (P, E, C, or I). After choosing the first letter, there are 5 letters left to arrange,

So there are 5! = 120 ways to arrange them.

Therefore, the total number of ways to arrange the letters of PENCIL when the first letter can’t be N or L is

4 x 5! = 4 x 120 = 480

Therefore, the correct option is (B) 480.

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Answer:

-2

Step-by-step explanation:

The explanation is in the picture

The probability that at most 70 switches fail during the first year is low, at around 1.3%.

The problem involves the use of the exponential distribution to model the lifetime of a certain type of electrical switch. Specifically, we are given that the average life of these switches is beta = 3.

The exponential distribution is often used to model the time between occurrences of a certain event, such as the failure of a component. In this case, we can use it to model the time between failures of the electrical switches.

To answer the question, we need to find the probability that at most 70 switches fail during the first year. Let X be the number of switches that fail during the first year. We know that X follows a Poisson distribution with parameter lambda = (1/3)*300 = 100.

This is because the expected number of failures per year for each switch is 1/3 (since the average life is 3 years), and there are 300 switches installed.

Therefore, we can use the Poisson distribution to calculate the probability that at most 70 switches fail during the first year:

P(X <= 70) = e^(-100) * (100^0/0!) + e^(-100) * (100^1/1!) + ... + e^(-100) * (100^70/70!)

This can be calculated using a calculator or software such as Excel. The answer is approximately 0.013, or 1.3%. This suggests that the switches are fairly reliable, and that it is unlikely that a large number of them will fail in a short period of time.

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The value of x is approximately 10.57 and the value of y is approximately 15.25.

In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.

The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.

In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:

105 + (7y + 1) + (7x + 1) + (4y + 14) = 180

Simplifying and solving for x and y, we get:

7x + 4y + 122 = 180

7x + 4y = 58 ......(1)

Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:

105 + (4y + 14) = 180 ......(2)

(7y + 1) + (7x + 1) = 180 ......(3)

Simplifying and solving for y in equation (2), we get:

4y + 119 = 180

4y = 61

y = 15.25

Substituting this value of y in equation (3) and solving for x, we get:

(7x + 1) + (7*15.25 + 1) = 180

7x + 106 = 180

7x = 74

x = 10.57

Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.

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Answer: 1. 48.356 2. 75.3982236862

Step-by-step explanation:

Radias*2 pi

The area of the cement part is 24 m².

Area is the region bounded by a plane shape.

To calculate the area of the part with cement. we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area is 24 m².

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The standard deviation of the ACT scores is approximately 4.2.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much the data values deviate, on average, from the mean (or average) of the data set. A higher standard deviation indicates greater variability or spread in the data, while a lower standard deviation indicates less variability or spread.

According to the given information:

To find the standard deviation of ACT scores, we can use the given information about the mean and the percentage of scores above a certain threshold.

Given:

Mean (μ) = 21.4

Percentage of scores above 26 = 15%

Since the distribution is approximately normal, we can use the Z-score formula to find the Z-score corresponding to the given percentage. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution.

Z-score formula:

Z = (X - μ) / σ

Where:

Z = Z-score

X = Value (in this case, 26)

μ = Mean (21.4)

σ = Standard deviation (to be found)

We can rearrange the formula to solve for σ:

σ = (X - μ) / Z

Substituting the given values:

X = 26

μ = 21.4

Z = Z-score corresponding to 15% (which can be found using a standard normal distribution table or a Z-score calculator)

Assuming a standard normal distribution table or calculator gives us a Z-score of approximately 1.04 for a percentage of 15%, we can plug in the values:

σ = (26 - 21.4) / 1.04

σ = 4.4 / 1.04

σ ≈ 4.2 (rounded to the nearest tenth)

So, the standard deviation of the ACT scores is approximately 4.2.

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Answer:

To graph this inequality, you can start by graphing the related function y = -x^2 - 1. This is a downward-facing parabola that opens downwards and has a vertex at (0, -1).

To graph the inequality y ≥ -x^2 - 1, you need to shade the region above the graph of the parabola. This is because any point above the parabola will have a y-coordinate that is greater than or equal to the corresponding y-coordinate on the parabola.

So, to graph the inequality, you can shade the region above the parabola. You can use a dotted line to represent the boundary of the inequality, since the inequality includes the possibility of equality (y = -x^2 - 1).

I hope this helps!

In the circle the mesaure of ∠ACF is  7

The distance from the centre of a circle to any point on the boundary is called the radius. The radius is half of the diameter; 2r=d 2 r = d . The line segment that joins two points on the circle is a chord.

If diameter of a circle bisects a chord ,then it must be perpendicular to the chord.

∴ m∠ACF = 90°  

(8x + 34)° = 90°

8x = 90 - 34

x = 56/8

x = 7

Hence,mesaure of ∠ACF = 7

Complete question : In Circle C, the diameter AB bisects the chord EF.

If m∠ACF = (8x+34)°, enter in the correct value of x.

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Answer:

Your answer should be A

The two statements are;

The area of sector 1 is  20n² + 15n square meters

The total distance around the garden is 20n + 2 meters

Option A  and C

The formula for the area of a rectangle is expressed as;

A = lw

Such that the parameters are;

For the first sector, we have that;

Length = 4n + 3

Width = 6n - 2 - 5n = n - 2

Substitute the values

Area of sector 1 = (4n + 3)(5n)

expand the expression

Area of sector 1 = 20n² + 15n square meters

Area for the sector 2

Area = (3n - 3)(n -2)

expand the bracket

Area = 3n² - 6n - 3n + 6 = 3n² - 9n + 6

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Answer:

I would say convenience sampling. It's hard to tell. Sampling every other person is like systematic sampling, BUT convenience sampling would be to sample people that are easy to reach.

Answer:

use desmos graphing calculator it helps alot

Step-by-step explanation:

x^{2}-x-6=0 has two zeros/solutions

x^{2}-x-6=0 has 1 zero/solution

x^{2}-x-6=0 has no zero/solution

we get the quotient as 161 and remainder as 11.So the missing numbers are:R = 11

9, 1, 6

First divide the greater number by the smallest number and then divide the smaller number by the remainder. We continue the process until we get 0 remainder. The divisor is the HCF of the given numbers.

To divide 5,472 by a two-digit number, we can use long division method as follows:

34) 5 4 7 2( 34

   -    4 0

     ______

       1 4 7

  -    1 3 6

      _______

            1 1

Therefore, we get the quotient as 161 and remainder as 11.

So the missing numbers are:

R = 11

9, 1, 6

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this is "Repeated measures ANOVA, which is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions.

A repeated measures ANOVA is a statistical test used to analyze data from experiments in which the same participants are measured multiple times under different conditions. This design is sometimes referred to as a "within-subjects design" because each participant is measured within the same group.

Here are the steps for conducting a repeated measures ANOVA:

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Answer: A

Explanation:

His discount and final price be $280 for his order of 140 boxes.

A discount is a drop in a product's or service's price.

It is frequently provided as a perk to customers to entice them to buy. Discounts are often stated as a percentage or dollar amount off the list price.

Depending on the sort of discount and the situation, discounts can be computed in a variety of ways.

For instance, a product that costs $100 would have a discounted price of $80 with a 20% discount applied. Similar to this, a product that costs $50 would have a discounted price of $40 if it received a $10 reduction.

In marketing and sales, discounts are frequently used to draw customers and boost sales volume.

The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his maths test.

In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage."

This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."

Exampe of Percentage :-

10% = 10/100 ( = 1/10 (or) 0.1)

25% = 25/100 ( = 1/4 (or) 0.25)

According to question

Lee qualifies for a 20% discount because his order of 140 boxes falls within the range of 100-200 boxes.

Since each box originally cost $2.50, the full price of 140 boxes, after any discounts, is:

140 * $2.50 = $350

The 20% Lee discount is determined as follows:

20% * $350 = $70

Lee's discount is therefore $70, and his adjusted price is as follows:

$350 - $70 = $280

Therefore, Lee will ultimately pay $280 for his order of 140 cartons.

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Answer:

  2

Step-by-step explanation:

You want the average rate of change of f(x) = -x² -2x +6 on the interval [-7, 3].

The average rate of change of f(x) on the interval [a, b] is computed as ...

  m = (f(b) -f(a))/(b -a)

For the given function f(x), this is ...

  m = (f(3) -f(-7))/(3 -(-7)) = (-9 -(-29))/10 = 20/10 = 2

The average rate of change of f(x) on the interval [-7, 3] is 2.

__

Additional comment

The derivative of the function is f'(x) = -2x -2. The midpoint of the interval is x = (-7 +3)/2 = -2. The value of the derivative at the midpoint is equal to the average rate of change on the interval:

  -2(-2) -2 = 4 -2 = 2 . . . . average slope between x=-7 and x=3.

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The tax on the belt buckle is $1.56

What is Rate?

In general terms, a rate is a measure of the relationship between two quantities that are measured in different units. A rate expresses how much of one thing there is per unit of another thing. For example, miles per hour is a rate that expresses how many miles are traveled in one hour.

To calculate the tax on the belt buckle, we need to multiply the price of the belt buckle by the sales tax rate:

Tax = Price x Tax rate

In this case, the price of the belt buckle is $25 and the sales tax rate is 6.25%. To convert the tax rate from a percentage to a decimal, we need to divide it by 100:

Tax rate = 6.25% ÷ 100 = 0.0625

Now we can calculate the tax on the belt buckle:

Tax = Price x Tax rate

= $25 x 0.0625

= $1.56

Therefore, the tax on the belt buckle is $1.56. The total cost of the belt buckle including tax would be $25 + $1.56 = $26.56.

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