Alexandra and Austin applied to the same university. They looked up the average SAT score of students admitted to that university. Alexandra's SAT score was 40 points above the average score. Austin's SAT score was 330 points below the average score. Which expression represents the difference in their scores?

Answer:

\(\frac{1}{10}\)

Step-by-step explanation:

note that in terms of the given fraction

1 = \(\frac{10}{10}\) , then

\(\frac{9}{10}\) + \(\frac{1}{10}\) = \(\frac{10}{10}\) = 1

Answer:

\( \frac{9}{10} + x = 1 \\ x = 1 - \frac{9}{10} \\ x = \frac{(10 - 9)}{10} \\ \boxed{x = \frac{1}{10} } \: is \: the \: required \: number\)

Answer:

y=4x-2

Step-by-step explanation:

Putting all the given values in the formula, we get:n = [1.96² x 0.21 x 0.79] / 0.03²On solving, we get,n = 2734.84 ≈ 2735Therefore, 2735 public accountants should be contacted to update the study with a margin of error of 3% and a 95% level of confidence. Answer: 2735.

Given Information :A study conducted several years ago reported that 21% of public accountants changed companies within 3 years.

The American Institute of CPAs would like to update the study.

They would like to estimate the population proportion of public accountants who changed companies within 3 years with a margin of error of 3% and a 95% level of confidence.

Required:a. To update this study, how many public accountants should be contacted? Solution: Given that: the percentage of public accountants changed companies within 3 years is 21%.The level of confidence is 95%.

The margin of error is 3%.We have to find out the sample size.To find the sample size we use the formula :n = [Z² x p x q ] / E²

Where, Z = Standard normal deviation corresponding to a 95% confidence level is 1.96.p = proportion = 21/100 = 0.21q = 1-p = 1-0.21 = 0.79E = margin of error = 3/100 = 0.03

Putting all the given values in the formula, we get:n = [1.96² x 0.21 x 0.79] / 0.03²On solving, we get,n = 2734.84 ≈ 2735Therefore, 2735 public accountants should be contacted to update the study with a margin of error of 3% and a 95% level of confidence. Answer: 2735.

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All of the criteria's are fulfilled the survey is valid.

We have the information from the question:

The proportion of college football players who have had at least one concussion is estimated to be 34% in the united states.

Then, 34% = 0.34

The sample size of the data is = 100

p: the ‘proportion’ of ‘college’

The required conditions for testing the hypothesis of population proportion are,

(i) The population is larger than the sample

(ii) np > 10

=> 100 × 0.34

      =34

(iii) n(1-p) > 10

100 × (1 - 0.34)

=> 100 × 0.66

      =66

iv)The ‘sample’ is drawn randomly from the population.

Since all of the above criteria's are fulfilled the survey is valid.

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Answer:

Step-by-step explanation:

so the base times the height Princessa ,   b/c there are 2 triangles we don't have to take 1/2 like you would normally for a triangle

for the volume:

the end triangles are 4x6 = 24

length is 10

24*10=240 \(cm^{3}\)   for the volume

for the surface:

2*(10*5) = 100

1*(10*6)=60

2*(4*6)=48

208 \(cm^{2}\)   for the surface area

The chances of player A winning and player B winning are equal, each with a probability of 5/36.

For player A to win. There are 6 possible outcomes for player A's throw and 6 possible outcomes for player B's throw, resulting in 36 possible combinations of throws. Out of these 36 combinations, there are 5 combinations where player A's throw is greater than player B's throw: (1,1), (2,1), (2,1), (3,1), and (3,2).

For player B to win. There are 5 possible combinations where player B's throw is greater than player A's throw: (1,7), (2,7), (3,7), (4,3), and (4,3).

For a draw, the outcome of the two throws must be equal. There are 2 possible combinations for a draw: (1,1) and (2,2).

The probability of player A winning in any given round is 5/36

The probability of player B winning in any given round is 5/36

The probability of a draw in any given round is 2/36

So, The chances winning of player A and player B are equal.

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The average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

Explanation:

The average acceleration of a body over a given time interval is defined as the change in velocity divided by the time interval. In this case, we are given the velocity function vA(t) for Train A, and we want to find its average acceleration over the interval 2 ≤ t ≤ 8.

To find the change in velocity over this interval, we can subtract the velocity at t=2 from the velocity at t=8:

Δv = vA(8) - vA(2) = (-120) - 100 = -220 meters per minute

To find the time interval, we can subtract 2 from 8:

Δt = 8 - 2 = 6 minutes

Now we can use the formula for average acceleration:

a = Δv/Δt = (-220)/6 = -40 meters per minute squared

Therefore, the average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.

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The sampling method used in this scenario is convenience sampling.

Convenience sampling is a non-probability sampling method where the researcher selects participants who are easily accessible and readily available to participate in the study. In this scenario, the woman at the daycare is only asking parents who are standing near the front door and waiting patiently for their children to finish their art project. She is not asking parents who are leaving early or who are in a hurry, nor is she selecting parents randomly. Instead, she is selecting parents who are convenient for her to approach and who are more likely to have positive views of the daycare's service since they are patiently waiting for their children to finish their art project. The problem with this sampling method is that it may not be representative of the entire population, and it may lead to biased results. Therefore, it is not a recommended sampling method for most studies.

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The Total surface of triangular prism  is 112 inches.

To calculate the surface area of a triangular prism, you need the measurements of the base and the height of the triangular faces, as well as the length of the prism.

The given measurements are;

Base ; 5 inches and  4 inches

height is 8 inches

Length of the prism is 2 inches.

To find the total surface area, we sum up the areas of all the faces:

Total surface area = area of triangular  faces + area of rectangular faces + area of lateral faces.

area of triangular faces = 5 inches × 4 inches = 20 inches.

area of the two faces = 20 ×2 =40

Area rectangular faces = 5 inches × 8 inches/ 2 = 40 inches.

Area of lateral faces = 8 inches ×2 = 16 square inches

for the two lateral faces is 16 × 2 = 32 square inches.

Total surface area = 40 square inches + 40 inches + 32 square inches = 112 square inches.

The Total surface of triangular prism  is 112 inches.

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Answer:

It falls in the integer category. The attached picture is a chart if you want to specify a number in a category.

Hope this helps :)

To find the cost per ounce for the 40 oz jar, divide the price by the number of ounces: $5.25/40 oz = $0.13 per oz.

To find the cost per ounce for the 15 oz jar, divide the price by the number of ounces: $2.10/15 oz = $0.14 per oz.

Therefore, the 40 oz jar is the better deal because it has a lower cost per ounce.

Subtract the fee from the total:

674 - 299 = 375

Now divide by the cost per square yard:

375 / 15 = 25

The answer is 25 square yards.

Answer:

45 square yards

Step-by-step explanation:

divide 674 by 15

The maximum height of the diver as calculated from the function is   14.54 feet.

The function that represents the position of the diver is

h(t) = -16t² + vt + 10

The diver is at a height of 10 feet.

So at t=0 , h=10

Now we will find the rest of the solutions from the graph which follows the path of a parabola .

at t=1.42 , h(t)=0

Therefore 0 = -16(1.42)² + 1.42t + 10

or, V =15.68 ft/s

Again:

For h(t) to be maximum we have to find t for which h'(t)=0 , so we diff

h'(t) = -32t +15.68

or, t = -15.68 / 32

or, t = 0.49 seconds

Now h(0.49) =  16(0.49)² + 1.42 × 0.49 + 10 = 14.54 feet

Hence the maximum height of function is 14.54 feet

Therefore the diver has an initial velocity of 15.68 ft/sec and the diver reached a height of 14.54 feet at the maximum point.

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Step-by-step explanation:

oh oh can you capture a picture of it because you don't understand

Susi's answer of 5 7/1 is not reasonable because it should be written as 5 7/1 or 6 2/3. This means that Susi made an error in her subtraction. The correct difference between 8 1/3 and 3 3/4 is actually 4 5/12, which is closer to our estimate of 4.

To estimate 8 1/3 - 3 3/4, we can round the mixed numbers to the nearest whole numbers, which are 8 and 4, respectively. Then, we can subtract 4 from 8 to get an estimate of 4.

However, to find the actual difference between the two mixed numbers, we need to subtract them by finding a common denominator. In this case, we can convert 1/3 to 4/12 by multiplying the numerator and denominator by 4, and 3/4 to 9/12 by multiplying the numerator and denominator by 3. Then, we can subtract the fractions and simplify the result to get:

8 1/3 - 3 3/4 = 8 - 3 + 1/3 - 3/4 = 5 + (4/12 - 3/4) = 5 + (1/12) = 4 5/12

Therefore, the actual difference between 8 1/3 and 3 3/4 is 4 5/12, which is closer to our estimate of 4 than Susi's answer of 5 7/1 or 6 2/3. Her answer of 5 7/1 is not reasonable because it is not a proper mixed number and should be written as 6 2/3. Additionally, her answer is greater than our estimate and the actual difference, which suggests that she made an error in her subtraction.

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\(\\ \sf\bull\longmapsto f(x)=4x+10\)

\(\\ \sf\bull\longmapsto f(3)\)

\(\\ \sf\bull\longmapsto 4(3)+10\)

\(\\ \sf\bull\longmapsto 12+10\)

\(\\ \sf\bull\longmapsto 22\)

Answer:

f(3) = 22

Step-by-step explanation:

Substitute x = 3 into f(x) , that is

f(3) = 4(3) + 10 = 12 + 10 = 22

Jake is presently \(0\) years old and the year is \(2036\), which is not a relevant response or there may be some missing details in the question.

A span of time that is equivalent to one year on the Calender but starts at a different period. A cycle of 365 and 366 day split into twelve month starting in January and ending in December.

Every monthly on the calender has four complete weeks since every month has at least 28 days. A few month have a few more days, but these extra days don't add up to a full week, therefore they aren't counted.

Let's first find the current year, given that the year in which their ages will sum up to \(16x\) is\(2036\).

\(2036 - (y - 2036) = 2*2036 - y\)

Simplifying this expression, we get:

\(2*2036 - y = 4072 - y\)

\(2y = 4072\)

\(y = 2036\)

Now, let's find Jake's current age by subtracting his birth year from the current year \(y - (2036 - 7x)\)

Since their ages sum up to 16x in 2036, we have:

\(x + 7x = 16x\)

\(8x = 16x\)

\(x = 0\)

This means that Jake is currently \(0\) years old, which is not a meaningful answer.

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Prior to placing an order to buy ABCD stock at a lower price, the investment adviser must conduct thorough research and analysis, set a target price, and determine an appropriate entry point for the purchase.

The investment adviser's primary responsibility is to act in the best interest of their client and make informed investment decisions. In this case, where the adviser believes ABCD stock is appropriate only if the price falls to $35 per share, several steps need to be taken before placing an order.

Firstly, the adviser should conduct comprehensive research on ABCD stock to understand its historical performance, financial health, industry trends, and any relevant news or events that might impact its future prospects. This research will help validate the adviser's belief that the stock is worth considering at a lower price.

Secondly, the adviser should establish a target price of $35 per share based on their analysis and the client's investment objectives. This target price serves as a reference point and provides a clear criterion for initiating the purchase.

Lastly, the adviser needs to identify an appropriate entry point for the purchase. This involves monitoring the stock's price movements and market conditions closely. The adviser may choose to set a limit order at $35 per share or implement a strategy to take advantage of potential price declines, such as dollar-cost averaging.

By following these steps, the investment adviser ensures that they have thoroughly evaluated the investment opportunity and have a plan in place before placing an order to buy ABCD stock for the client's account.

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The resulting units are kilograms grams milligrams, mole grams liter, ft^2g mL ft gmL

To evaluate the given unit expressions, we can apply the rules of multiplying units similar to multiplying fractions.

(kilogram)(kilogram grams)(gram milligrams):

The units cancel out as follows:

(kilogram)(kilogram grams)(gram milligrams) = (kilogram)(grams)(milligrams)

Therefore, the resulting units are kilograms grams milligrams.

(mole)(mole grams)(gram liter):

The units cancel out as follows:

(mole)(mole grams)(gram liter) = (mole)(grams)(liter)

Therefore, the resulting units are mole grams liter.

(mL)(cmmg)(mLcm3):

The units cancel out as follows:

(mL)(cmmg)(mLcm3) = (mL)(cm mg)(cm^3)

Therefore, the resulting units are mL cm mg cm^3.

(f^2g)(mLft)(gmL):

The units cancel out as follows:

(f^2g)(mLft)(gmL) = (ft^2g)(mLft)(gmL)

Therefore, the resulting units are ft^2g mL ft gmL.

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Answer:

  375

Step-by-step explanation:

You want to know the number of integers from 1 to 1000 that are multiples of 4 or 6.

Assuming the ends of the range are not multiples of interest, we can find the number of multiples of a given number by dividing the range by that number. Doing this for 4, 6, and (4×6), we find that in [1, 1000], there are ...

The number of multiples of 4 or 6 will be the total of multiples of 4 and multiples of 6, less the number of multiples of both 4 and 6. That is, the first sum counts those multiples of 24 twice.

  250 +166 -41 = 375

There are 375 multiples of 4 or 6 in the range 1 to 1000.

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Answer:

(11 , -23)

Step-by-step explanation:

i hope this is right

Answer:x=11 and y= −23 (11,-23)

Answer:

60°

Step-by-step explanation:

Data obtained from the question include the following:

Angle H =.?

Opposite = 2√21

Adjacent = 2√7

The value of angle H can be obtained as follow

Tan H = Opposite /Adjacent

Tan H = 2√21 / 2√7

Tan H = √(21 / 7)

Tan H = √3

Tak the inverse of Tan.

H = Tan¯¹ √3

H = 60

Therefore, the value of angle H is 60°

Answer:

D. He answers the same number of questions correctly in both rounds and the same number of questions incorrectly in both rounds​.

Step-by-step explanation:

In the first equation he earns 5 points and loses 3 points. The value of one question is 5 points, and the value of losing one question is 3 points. The same goes for the second equation except the fact that its 10 points and 4 points lost instead.

Answer:

18 Games

Step-by-step explanation:

For this problem we will have to use the same percentage Therom again, except this time we are solving for a diffrent variable.

Total Games * Percentage won in fraction form = Games won

Fill the values.

30 * 3/5 = X

Simplify

18=X

Yes, y=x has an inverse.

Yes, y=x passes the horizontal line test.

If it didn't pass the horizontal line test, it would not have an inverse.

Answer:

y = 1.5

Step-by-step explanation:

Given x is inversely proportional to \(\sqrt{1+x}\) , then the equation relating them is

y = \(\frac{k}{\sqrt{1+x} }\) ← k is the constant of proportion

To find k use the condition when x = 8, y = 2

2 = \(\frac{k}{\sqrt{1+8} }\) = \(\frac{k}{\sqrt{9} }\) = \(\frac{k}{3}\) ( multiply both sides by 3 )

6 = k

y = \(\frac{6}{\sqrt{1+x} }\) ← equation of proportion

When x = 15 , then

y = \(\frac{6}{\sqrt{1+15} }\) = \(\frac{6}{\sqrt{16} }\) = \(\frac{6}{4}\) = \(\frac{3}{2}\) = 1.5