Suppose another one of your credit cards offers 3% cash back on gas, 2% at grocery stores, and 1% on all other purchases. If you spent a total of $2,738.21 on everything, with $384.23 of that total at the grocery store and $134.92 for gas, how much would your cash back be?

An equation of the line in point-slope form that passes through the points (2, 1) and (-4, -8) is y - 1 = 3/2(x - 2).

In Mathematics and Geometry, the point-slope form of any straight line can be determined by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the slope;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-8 - 1)/(-4 - 2)

Slope (m) = -9/-6

Slope (m) = 3/2

At data point (2, 1) and a slope of 3/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 3/2(x - 2)  

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In conclusion, the solution for this question is that Adriana's actual elevation is also approximately 13.3 meters above sea level.

How to solve?

To estimate Adriana's current elevation, we can simply find 80% of the total elevation gain and add it to her starting elevation:

Total elevation gain = 25 3/4 m - (-36.5 m) = 62.25 m

80% of 62.25 m = 0.8 * 62.25 m ≈ 49.8 m

Estimated current elevation = -36.5 m + 49.8 m ≈ 13.3 m

So we estimate that Adriana's current elevation is approximately 13.3 meters above sea level.

To find her actual elevation, we can use the same method but with the actual percentage of completion:

Actual elevation gain = 80% * (25 3/4 m - (-36.5 m)) = 0.8 * 62.25 m = 49.8 m

Actual elevation = -36.5 m + 49.8 m = 13.3 m

Therefore, Adriana's actual elevation is also approximately 13.3 meters above sea level.

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Answer:

Step-by-step explanation:

y = x² -10x + 16

y = (x - 8) (x - 2)

solve each when y = 0

x - 8 = 0

x - 8 + 8 = 0 +8

x = 8

and

x - 2 = 0

x - 2 + 2 = 0 +2

x = 2

SO solutions are (8, 0) and (2, 0)

To produce the function f(x) = 2| x−1 | − 3 from the parent function f(x) = |x|, three transformations are required.

Horizontal shift: The function is shifted horizontally by 1 unit to the right. This is done by subtracting 1 from the input value of the function. The transformation is f(x) → f(x − 1).

Vertical stretch: The function is vertically stretched by a factor of 2. This is done by multiplying the output value of the function by 2. The transformation is f(x) → 2f(x − 1).

Vertical shift: The function is vertically shifted down by 3 units. This is done by subtracting 3 from the output value of the function. The transformation is f(x) → 2f(x − 1) − 3.

To find points on the function, we can substitute different values of x into the function and calculate the corresponding y-values. For example:

When x = 0: f(0) = 2|0 − 1| − 3 = -5

When x = 1: f(1) = 2|1 − 1| − 3 = -3

When x = 2: f(2) = 2|2 − 1| − 3 = -1

Using these points, we can plot the graph of the function f(x) = 2| x−1 | − 3. The graph is a V-shaped curve with the vertex at (1,-3), opening upwards. The points we found above can be plotted on the graph as (-1,-5), (1,-3), and (2,-1).

The p-value for this test is the probability of observing a z-score of -2.45 or lower, which is approximately 0.0072. Therefore, the answer is 0.0072.

The null hypothesis is a common arithmetic theory that asserts there is no statistical relationship and significance between two groups of observed data and measured phenomena for a particular set of single, observed variables.

What the researcher anticipates discovering after performing a study is expressed as a scientific hypothesis. A statistical hypothesis, on the other hand, is a prediction of what the statistician does NOT expect to discover. The term "NULL hypothesis" refers to this rationale.

We can use a one-sample proportion test with a one-tailed alternative to test this hypothesis, and calculate the p-value as the probability of observing 10 or fewer ones out of 120 rolls, assuming the null hypothesis is true.

Using a normal approximation to the binomial distribution.

(since n=120 is large and p0=1/6 is not too close to 0 or 1),

the test statistic is:

z = ([tex]\frac{10}{120}[/tex] - [tex]\frac{1}{6}[/tex]) / √([tex]\frac{\frac{1}{6} *\frac{5}{6} }{120}[/tex])

≈ -2.45

The p-value for this test is the probability of observing a z-score of -2.45 or lower, which is approximately 0.0072. Therefore, the answer is 0.0072.

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According to given information, the approximate p-value for this test is 0.0072.

What is meant by p-value?

In statistics, the p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample, assuming that the null hypothesis is true.

To determine the p-value for this test, we need to perform a hypothesis test to determine if the observed proportion of ones in the 120 rolls is significantly different from the long-run proportion of ones. We can use the following hypotheses:

Null hypothesis: p = 1/6 (assuming a fair die)

Alternative hypothesis: p < 1/6 (the calculator is producing fewer ones than it should)

To perform the test, we can use the normal approximation to the binomial distribution, since np = 120(1/6) = 20 and n*(1-p) = 120*(5/6) = 100, which are both greater than 10.

The test statistic is:

z = (x - np) / sqrt(np(1-p))

where x = 10 is the number of ones observed, np = 20 is the expected number of ones under the null hypothesis, and p = 1/6 is the hypothesized proportion of ones.

Substituting these values, we get:

z = (10 - 20/6) / sqrt(20/6 * (1 - 1/6))

z = -2.305

The p-value for this test is the probability of observing a test statistic as extreme or more extreme than -2.305, assuming the null hypothesis is true. Since this is a one-tailed test in the left tail, the p-value is the area to the left of -2.305 under the standard normal distribution. Using a table or calculator, we can find that this area is approximately 0.0106.

Therefore, the approximate p-value for this test is 0.0106, which is closest to 0.0072.

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Answer:

[tex]6.25\pi \: {ft}^{2} [/tex]

Step-by-step explanation:

Given:

d = 5 ft

Find: a (area) - ?

First, we have to find the radius (r) of the circle, which is half diameter:

r = 0,5 × d

r = 0,5 × 5 = 2,5 ft

Now we can find the area of the circle (a):

[tex]a = \pi \times {r}^{2} = \pi \times ( {2.5})^{2} = 6.25\pi \: {ft}^{2} [/tex]

Answer:  The area of the circle is 19.625

Step-by-step explanation:

The formula for area of a circle is

[tex]A = \pi r^2[/tex]

We know that the diameter is 5 ft. The radius is half of the diameter, so we take 1/2 * 5 = 2.5

So the radius is 2.5

Now we will fill in the numbers for the formula

[tex]A = 3.14 * (2.5)^2[/tex]

or (3.14)(2.5)(2.5)

When we multiply all of the numbers, the area of the circle is 19.625

The value of AD of the triangle using trigonometric ratios is: 18.7

The sum of angles in a triangle is 180 degrees. Thus:

∠ABC = 180 - (41 + 35)

∠ABC = 104°

Using sine rule, we have:

AB/sin 35 = AC/sin 104

AB = (42 * sin 35)/(sin 104)

AB = 42 * 0.5911

AB = 24.826

Now, using trigonometric ratio:

AD/AB = cos 41

AD = 24.826 * 0.7547

AD = 18.7

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When Declan selects a pupil from the list at random 100 times, the estimation on the total number of times Declan selects a pupil who studies French is equal to 20 (times).

We have a table present above which shows the probability a pupil chosen at random studies Italian, French, Russian or German. Now, Declan randomly select a pupil from the list at 100 times. We have to estimate for the total number of times Declan will select a pupil that studies French. From the table, the probability to select a pupil who studies French = 0.2

So, Total number of times Declan will select a pupil that studies French

= 0.2 × 100

= 20 times

Hence, required estimation on total number of times is 20.

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Complete question:

The above table shows the probability a pupil chosen at random studies Italian, French, Russian or German.

Subject Italian French Russian German

Probability

Declan select a pupil from the list at random 100 times. Work out an estimate for the total number of times Declan will select a pupil that studies French

Answer:

[tex]\large\boxed{\tt f(-3)=26}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to evalulate the function given the value of x.}[/tex]

[tex]\textsf{Note that because x equals -3, x will equal -3 for all the variables on the right side.}[/tex]

[tex]\large\underline{\textsf{We should have;}}[/tex]

[tex]\tt f(-3)=(-3)^{2}-3(-3)+8[/tex]

[tex]\textsf{Let's start by evaluating the right side of the function.}[/tex]

[tex]\tt f(-3)=(-3 \times -3)+9+8[/tex]

[tex]\textsf{Note that a negative multiplied by a negative equals a positive term.}[/tex]

[tex]\tt f(-3)=9+9+8[/tex]

[tex]\large\boxed{\tt f(-3)=26}[/tex]

[tex]\huge\text{Hey there!}[/tex]

If x = -3

[tex]\mathtt{f(x) = x^2 - 3x + 8}\\\\\\\mathtt{f(x) = -3^2 - 3(-3) + 8}\\\\\\\mathtt{f(x) = -3\times-3 - 3(-3) + 8}\\\\\\\mathtt{f(x) = 9 - (-9) + 8}\\\\\\\mathtt{f(x) = 9 + 9 + 8}\\\\\\\mathtt{f(x) = 18 + 8}\\\\\\\mathtt{f(x) = 26}\\\\\\\\\\\huge\text{Therefore your answer should be:}\\\\\\\huge\boxed{\mathtt{f(x) = 26}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

y=-2x+6

I determined this by first calculating the slope which turned out to be -2, and then i solved using slope intercept formula y=mx+b. Slope is -2 because i input the 2 points 0,6 and 3,0 into slope formula

Step-by-step explanation:

Brainliest maybe ? :)

The complete factorization of 3x⁵- 75x³ is:- 3x³(x + 5)(x - 5)

How to solve factor?

To factor completely the expression 3x⁵ - 75x³, we can first factor out the greatest common factor (GCF) of the two terms, which is 3x³:

3x³(x² - 25)

Next, we can factor the expression inside the parentheses using the difference of squares formula:

3x³(x + 5)(x - 5)

Therefore, the complete factorization of 3x⁵ - 75x³ is:

3x³(x + 5)(x - 5)

We can check that this is the correct factorization by using the distributive property of multiplication and verifying that the product of the factors is equal to the original expression:

3x³(x + 5)(x - 5) = 3x³(x² - 25)

= 3x³x² - 3x³(25)

= 3x⁵ - 75x³

So the factorization is correct.

In summary, to factor completely an expression like 3x⁵ - 75x³, we should first factor out the GCF and then look for further factorization opportunities using various factorization techniques such as the difference of squares formula, the sum or difference of cubes formula, or the quadratic formula. It's important to remember to check our work by multiplying the factors back together to ensure that we get the original expression.

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Answer: 12:30 P.M.

Step-by-step explanation:

50 + 50 + 50 + 90 minutes = 240 minutes
240 divided by 60 = 4
4 hours before 4:30 P.M. = 12:30 P.M.
Answer should be 12:30 P.M.

Answer:

They left the house at 1:20 P.M.

Step-by-step explanation:

The movie was an 1 1/2 so 4:30 - 1:30 = 3:00

Thy got there 50 minutes before so 3:00 - 0:50 = 2:10

It took them 50 minutes to get there so 2:10 - 0:50 = 1:20

Therefore they left the house at 1:20 P.M.

The given system of linear equations has infinite solutions. The solution has been obtained by using the elimination method.

What is the elimination method?

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

We are given a system of linear equations as -x + y = -8 and 2x - 2y = 16.

Now, on dividing the equation 2x - 2y = 16 by 2, we get

x - y = 8.

Now, on adding the first and the third equation, we get

⇒ (-x + y) + (x - y) = -8 + 8

⇒ 0 = 0

Hence, the system has infinetly many solutions.

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Question: What is the solution for the given system of linear equations?

-x + y = -8 and 2x - 2y = 16

In this case, x and y are both 27 degrees.

If I'm understanding you correctly, we have a semicircle with a triangle DEF engraved on it.

Vertex D has a 90 degree angle.

You are informed that angles D = 27 degrees, E = y degrees, and F = x degrees. You need to locate x and y.

Angle D is 90 degrees because triangle DEF is encircled by a semicircle.

Angles E and F therefore sum up to 90 degrees. Also, we are aware that angle D = 27° 2.

Angles E and F are so equal at 63 degrees and 27 degrees, respectively.

Half of a circle is a semicircle. It is a 2D shape that results from splitting a circle into two equal pieces. . A protractor, a circle folded in half, and other everyday objects are some instances of semicircles.

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The contrast coefficients would be as follows:

The farmers are interested in whether there is any difference between the low-low combination (it is the cheapest) and the average of the remaining three levels. The hypotheses they want to test are:

To test this hypothesis, the following contrast would be used:

To compare the high- to low-nitrogen content fertilizers, the following contrast would be used:

To compare the high- to low-phosphorus content fertilizers, the following contrast would be used:

To compare the ll combination to the hh combination, the following contrast would be used:

For each of the contrasts above, the contrast coefficients would be as follows:

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Answer:

To determine which trigonometric function to use in a triangle, you need to identify what sides and angles are given, and what you are trying to find. The three primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan), which relate the ratios of the sides of a right triangle to its angles.

To determine which trigonometric function to use, you can use the acronym SOH-CAH-TOA, which stands for:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Let's take an example:

Question: In a right triangle ABC, where angle B is the right angle, the length of the hypotenuse is 10 cm, and the length of the adjacent side to angle A is 6 cm. What is the value of the sine of angle A?

Solution: We are given the hypotenuse and the adjacent side to angle A, and we want to find the sine of angle A. Looking at the SOH-CAH-TOA acronym, we see that sine involves the ratio of the opposite side to the hypotenuse. In this case, the opposite side to angle A is not given, but we can use the Pythagorean theorem to find it:

a² + b² = c², where a and b are the legs of the right triangle and c is the hypotenuse.

In our triangle, we have:

a² + 6² = 10²

a² + 36 = 100

a² = 64

a = 8

Now that we know the length of the opposite side to angle A is 8 cm, we can use the sine function:

sin(A) = Opposite / Hypotenuse = 8 / 10 = 0.8

So, the value of the sine of angle A is 0.8.

In summary, to determine which trigonometric function to use, you need to identify what sides and angles are given, and what you are trying to find. You can then use the SOH-CAH-TOA acronym to match the given sides with the appropriate function, and use the Pythagorean theorem and other trigonometric identities to find any missing sides or angles.

Regenerate response

So, the rate of change of Logan's money remaining per ride paid for varies between -1/15 and -1/3, depending on the two rides that we choose to calculate the slope.

In mathematics, slope refers to the steepness of a line or a curve. More specifically, it is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or curve.

The slope of a straight line can be found by dividing the change in the y-coordinates (vertical change) by the change in the x-coordinates (horizontal change) between any two points on the line. This is often represented by the symbol "m".

by the question.

To find the rate of change of Logan's money remaining per ride paid for, we need to calculate the slope of the line that represents the relationship between the number of rides paid for and the money remaining.

We can start by plotting the data points on a coordinate plane, where the x-axis represents the number of rides paid for and the y-axis represents the money remains.

(15, 10) (30, 9)

(20, 20) (50, 10)

We can see that the two points (15, 10) and (30, 9) represent the two rides where Logan had $10 and $9 remaining, respectively, and (20, 20) and (50, 10) represent the two rides where Logan had $20 and $10 remaining, respectively.

To calculate the slope of the line that passes through these points, we can use the formula:

[tex]slope = (y_2 - y_1) / (x_2 - x_1)[/tex]

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the points (15, 10) and (30, 9), we get:

[tex]slope = (9 - 10) / (30 - 15) = -1/15[/tex]

Using the points (20, 20) and (50, 10), we get:

[tex]slope = (10 - 20) / (50 - 20) = -1/3[/tex]

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The surface area of the given cuboid is 228 cm².

What is surface area of a cuboid?

The surface area of a cuboid is a measure of the total area of its six faces. It is an important concept in geometry and is used in many real-life applications. For example, when calculating the amount of paint needed to cover the walls of a room, you would need to know the surface area of the walls. Similarly, when designing packaging for a product, you would need to know the surface area of the box to determine the amount of material required to make it.

To find the surface area of a cuboid, you need to add up the areas of all six faces.

Given the dimensions of the cuboid as,

Length = 9 cm

Breadth = 4 cm

Height = 6 cm

The surface area of the cuboid can be calculated as follows,

Area of the top face = length × breadth = 9 cm × 4 cm = 36 cm²

Area of the bottom face = length × breadth = 9 cm × 4 cm = 36 cm²

Area of the front face = breadth × height = 4 cm × 6 cm = 24 cm²

Area of the back face = breadth × height = 4 cm × 6 cm = 24 cm²

Area of the left side face = length × height = 9 cm × 6 cm = 54 cm²

Area of the right side face = length × height = 9 cm × 6 cm = 54 cm²

Therefore, the total surface area of the cuboid is the sum of all six faces, which is:

Surface Area = 2 × (length × breadth + breadth × height + length × height)

Surface Area = 2 × (9 cm × 4 cm + 4 cm × 6 cm + 9 cm × 6 cm)

Surface Area = 2 × (36 cm² + 24 cm² + 54 cm²)

Surface Area = 2 × 114 cm²

Surface Area = 228 cm²

Therefore, the surface area of the given cuboid is 228 cm².

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In conclusion Shaniyah has $159.25 for food and gas.

How to find?

First, we need to find how much Shaniyah spends on internet service and cell phone bill:

Amount spent on internet service = 21% of $325 = 0.21 x $325 = $68.25

Amount spent on cell phone bill = 3/10 of $325 = (3/10) x $325 = $97.50

The total amount spent on internet service and cell phone bill is $68.25 + $97.50 = $165.75

To find how much Shaniyah has left for food and gas, we subtract the total amount spent on internet service and cell phone bill from the total amount spent on bills:

Amount spent on food and gas = Total amount spent on bills - Amount spent on internet service and cell phone bill

Amount spent on food and gas = $325 - $165.75

Amount spent on food and gas = $159.25

Therefore, Shaniyah has $159.25 for food and gas.

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Answer:

Step-by-step explanation:

8x + 6y = 726

9x + 7y = 831

56x + 42y = 5082

-54x - 42y = -4986

2x = 95

x = 47.50 Shirt

47.50(8) + 6y = 726

380 + 6y = 726

6y = 346

y = 57.67 pants

Answer:

Step-by-step explanati

Since both terms are perfect squares, factor using the difference of  squares formula,

a

Answer:

Event 1 and Event 2 have different probabilities, and it is not possible to determine which one is higher without additional information.

Event 1 involves rolling a six-sided dice, which has six possible outcomes, each with an equal probability of 1/6. The probability of rolling a 3 on a single roll is 1/6. Therefore, the probability of rolling two 3's in a row is (1/6) x (1/6) = 1/36.

Event 2 involves drawing from a deck of 52 cards, which includes 26 red cards (13 of which are face cards). The probability of drawing a red suited face-card on the first draw is 26/52 x 4/13 = 2/13, since there are 26 red cards out of 52 total cards, and 4 face-cards out of 13 cards of each suit. On the second draw, there will be one less card in the deck, so the probability of drawing another red suited face-card will be 25/51 x 3/12 = 5/204. The probability of drawing two red suited face-cards in a row is therefore (2/13) x (5/204) = 5/663.

Comparing the two events, we see that the probability of Event 1 is higher than that of Event 2. Therefore, rolling two 3's in a row using a six sided dice is the event with the higher theoretical probability.

(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)

a. The probability that a randomly selected pipe is made of PVC is approximately 0.242 or 24.2%.

b. The probability that randomly selected pipe is a trunk is 0.104

c. The probability that randomly selected pipe is a main made of galvanized iron (gi) is 0

d. The probability that randomly selected pipe is  a submain made of asbestos cement is 0.168

What is probability?

The chance of an event can be calculated using the probability formula by simply dividing the favorable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anything between 0 and 1, as the favorable number of outcomes can never exceed the total number of outcomes.

a. The total number of pipes is 8646, and the number of pipes made of PVC is 2092. The probability of a randomly selected pipe being made of PVC is:

P(PVC) = 2092/8646 ≈ 0.242

b. The total number of pipes is 8646, and the number of trunk pipes is 903. The probability of a randomly selected pipe being a trunk is:

P(trunk) = 903/8646 ≈ 0.104

c. The total number of main pipes is 5299, and the number of main pipes made of galvanized iron (GI) is 0 (according to the table). Therefore, the probability of a randomly selected main pipe being made of GI is:

P(GI|main) = 0/5299 = 0

Note that the vertical bar "|" means "given" or "conditioned on".

d. The total number of submain pipes is 2444, and the number of submain pipes made of asbestos cement (AC) is 411. Therefore, the probability of a randomly selected submain pipe being made of AC is:

P(AC|submain) = 411/2444 ≈ 0.168

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Answer: x=1.09

Step-by-step explanation:

To solve for x, we can take the natural logarithm of both sides of the equation:

ln(e^(3x)) = ln(12)

Using the property of logarithms that ln(e^y) = y, we can simplify the left side to:

3x = ln(12)

Then, we can divide both sides by 3 to solve for x:

x = (1/3)ln(12)

Using a calculator to evaluate ln(12) and round to the nearest hundredth, we get:

x ≈ 1.09

Answer: x=0.83

Step-by-step explanation: buddy was wrong

Answer:

Step-by-step explanation:

b is now located at (3,-12)

The proportions from the sets of numbers are 66/11 = 6/1, 35/14 = 25/10, 48/12 = 4/1, 45/9 = 25/5 and 72/12 = 6/1

To create a proportion from each set of numbers, we must select 4 numbers from each set and express them as a fraction in the form of a/b = c/d.

Here are the proportions for each set:

Note: To create a proportion, we must select numbers that are related to each other in some way, such as the sides of a shape or the parts of a ratio.

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Answer:

(-8,5)(-1,-2)(1,-4)

Step-by-step explanation:Glad I could help

Looking at the back to back stem and leaf plot for the test scores, we can tell that D) The median and mean for Class A are higher than those for Class B. They have equal IQRs of 15.

The mean of Class A can be found to be :
= ( 70 + 70 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 90 + 95 + 95 + 95 + 95 + 95 + 95 + 100 + 100 + 100 ) / 22

= 92

The mean of Class B would be :

= ( 70 + 70 + 70 + 75 + 75 + 75 + 75 + 75 + 80+ 80 + 80 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90+ 90 + 95 + 95 + 100 ) / 23

= 82

The mean of Class A is therefore larger than Class B. The IQR cannot be up to 70 given that the lowest value of 70 and the highest is 100 so the correct option is option D.

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Answer:

Julianne (she owes 25 more than Rosa)

Step-by-step explanation:

Because Rosa owes -0.25 less than Julianne and because if you subtract the two balances  or do keep change flip method it will give you -0.25 meaning that when Julianne owes nothing Rosa still will owe some money (25 cents).