A student scored in the 54th percentile on her Calculus exam. What does this student's score mean in relation to those of the other test takers? (1 point) The student's score was 54%. The student's score was 46% The student's score was higher than 54% of the students who took the test. The student's score was lower than 46% of the students who took the test.

The cost of 10 sodas will be C(n) = 0.75n – 0.5; $7.00

Soda is on sale for $0.75 a can, and you have a coupon for $0.50 off your total purchase

Let n-----> the number of sodas

C(n) -----> the total cost

we know that

The total cost is equal to the number of sodas multiplied by the cost of one soda minus $0.50 of the coupon

so

C(n) = 0.75n – 0.5

For n=10 sodas

substitute the value of n in the equation

C(10) = 0.75(10) – 0.5

7.5 - 0.5

= 7

Therefore, the cost of 10 sodas will be C(n) = 0.75n – 0.5; $7.00

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a) The sample space for four flights selected at random, with arrival status "O" for on-time and "L" for late, is given as {OOOO, OOOL, OOLO, OOLL, OLOO,  OLOL, OLLO, OLLL, LOOO, LOOL, LLOO, LLOL, LLLO, LLLL}.

b) The probability that a randomly selected flight is from Airline A and on-time, denoted as P(A), is calculated by multiplying the probability of being on-time for Airline A (75/100) with the proportion of flights operated by Airline A out of the total (320/1000), resulting in P(A) = 24/100.

c) The probability that a randomly selected flight is either from Airline C or on-time, denoted as P(C), is obtained by dividing the sum of flights on-time (700) and flights operated by Airline C (240) by the total number of flights (1000), giving P(C) = 94/100.

d) The probability that a flight is from Airline B given that it is late, denoted as P(B | L), is computed by multiplying the proportion of late flights (300/1000) with the probability of being from Airline B (35/100), resulting in P(B | L) = 77/300.

e) The probability that a flight is late given that it is from Airline A, denoted as P(L | A), is calculated by multiplying the proportion of flights on-time for Airline A (25/100) with the proportion of flights operated by Airline A (320/1000), resulting in P(L and A) = 8/100. Therefore, P(L | A) = 1 - P(A | L) = 11/15.

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The ratio of the height of shape a to shape c is 2 : 5

From the question, we have the following parameters that can be used in our computation:

Area A = 4

Area B = 25

Take the square root of both

So, we have

Length A = 2

Length B = 5

So, we have

Ratio = 2 : 5

Hence, the ratio is 2 : 5

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Representative sample is especially important in frequency claims because they ensure the findings accurately reflect the larger population.

When making frequency claims, researchers aim to generalize their findings to a larger population. Representative sample consists of individuals who closely mirror the characteristics of the target population. By selecting a representative sample, researchers increase the likelihood that the sample's frequencies and proportions will accurately reflect those of the larger population. This ensures that the frequency claim made based on the sample data is more likely to be valid and reliable.

Representative samples help minimize bias and enhance the generalizability of the findings. If a sample is not representative, it may over- or under-represent certain groups or characteristics within the population. This can lead to misleading frequency claims that do not accurately reflect the reality of the population as a whole. For example, if a study on voting preferences only surveys young adults, the findings may not accurately represent the voting patterns of the entire electorate.

Using a representative sample is crucial to increase the external validity of frequency claims. It allows researchers to make more accurate inferences and generalizations about the target population based on the characteristics and behaviors observed in the sample. By ensuring the sample is representative, researchers can enhance the credibility and applicability of their frequency claims, providing more reliable information for decision-making, policy development, or further research.

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The rate of downloads per minute is constant because based on the given information, the number of songs is always twice the number of minutes.

Therefore, the constant of proportionality is 2.

The rational expressions [(x² + 16xz + 64z²)/(x²z + 8xz²)] ÷ [(x² + 5xz + 24z²)/(x⁴z - 9x²z³)] can be simplified as; x(x - 3z)

We want to divide the rational expressions;

[(x² + 16xz + 64z²)/(x²z + 8xz²)] ÷ [(x² + 5xz + 24z²)/(x⁴z - 9x²z³)]

Let us break down the expressions one after the other;

(x² + 16xz + 64z²) can be expressed as;

(x + 8z)²

Likewise, (x²z + 8xz²) can be expressed as;

xz(x + 8z)

Thus;

[(x² + 16xz + 64z²)/(x²z + 8xz²)] is;

(x + 8z)²/(xz(x + 8z)) = (x + 8z)/xz

(x² + 5xz + 24z²) can be expressed as;

(x + 3z)(x + 8z)

Similarly;

(x⁴z - 9x²z³) can be expressed as;

x²z(x² - 9z²)

Thus;

[(x² + 5xz + 24z²)/(x⁴z - 9x²z³)] can be expressed as;

(x + 3z)(x + 8z)/(x²z(x² - 9z²))

Then our main expression can now be expressed as;

[(x + 8z)/xz] ÷ (x + 3z)(x + 8z)/(x²z(x² - 9z²))

This can be rewritten as;

[(x + 8z)/xz] * [(x²z(x² - 9z²))]/((x + 3z)(x + 8z))

x(x² - 9z²)/(x + 3z)

This can further be simplified as;

x(x + 3z)(x - 3z)/(x + 3z) = x(x - 3z)

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The table shows the estimated digit and significant figures of each measurement and their representation with x.

Number of Measurement Estimated Digit Significant Figures

14.8 m 3 ✓

$10.25 - ✓

0.05 L - ✓

1.000 g/mL - ✓

1.200 - ✓

6200 cm - ✓

403 kg - ✓

For each measurement, the estimated digit is replaced with an x to represent the number with the correct number of significant figures. The correct representations for each measurement are:

Note that in some cases, the representation requires adding zeros to the right of the decimal point to indicate the number of significant figures. In other cases, the representation requires rounding up or down to the correct number of significant figures.

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The standard error in each of the given scenarios are 0.0803, 0.0665, 0.0494 and 0.001. The standard error measures the variability or uncertainty in sample proportions and indicates how much the sample proportion is likely to deviate from the population proportion.

To calculate the standard error in each of the given scenarios, we can use the following formula:

Standard Error = √((pi * (1 - pi)) / n)

where:

- n represents the sample size,

- pi represents the proportion of the population,

- √ denotes the square root operation.

Now, let's calculate the standard error for each scenario:

(a) n = 23, pi = 0.20

Standard Error = √((0.20 * (1 - 0.20)) / 23) ≈ 0.0803 (rounded to 4 decimal places)

(b) n = 52, pi = 0.48

Standard Error = √((0.48 * (1 - 0.48)) / 52) ≈ 0.0665 (rounded to 4 decimal places)

(c) n = 120, pi = 0.52

Standard Error = √((0.52 * (1 - 0.52)) / 120) ≈ 0.0494 (rounded to 4 decimal places)

(d) n = 488, pi = 0.002

Standard Error = √((0.002 * (1 - 0.002)) / 488) ≈ 0.001 (rounded to 4 decimal places)

The standard error measures the variability or uncertainty in sample proportions and indicates how much the sample proportion is likely to deviate from the population proportion. Smaller standard errors indicate more precise estimates, while larger standard errors suggest greater uncertainty in the estimate.

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If you are trying to earn the most money possible on your investment, you should invest in Account Cas it has the highest interest rate and compounds annually.
i. Account A: $5255.61
ii. Account B: $5221.53
iii. Account C: $5169.31
a. To determine the value of your investment after 12 years for each account, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

i. Account A:
A = $1150(1 + 0.139/1)^(1*12)
A = $1150(1.139)^12
A ≈ $5908.52

ii. Account B:
A = $1150(1 + 0.133/12)^(12*12)
A = $1150(1.011083)^144
A ≈ $6122.64

iii. Account C:
A = $1150(1 + 0.13/365)^(365*12)
A = $1150(1.000356)^4380
A ≈ $6150.15

b. If you are trying to earn the most money possible on your investment, you should invest your money in:

Account C

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Answer:

\(a =\frac{m+p}{3}\)

Step-by-step explanation:

\(3a - p = m\)

→ First plus p to both sides to isolate 3a

\(3a = m+p\)

→ Divide both sides by 3 to isolate a

\(a =\frac{m+p}{3}\)

Answer:

see explanation

Step-by-step explanation:

Mia is wrong in that she has subtracted p from both sides instead of adding p to both sides.

Given

3a - p = m ( add p to both sides )

3a = m + p ( isolate a by dividing both sides by 3 )

a = \(\frac{m+p}{3}\)

The manager wants to control the maximum probability of Type I error at 1% (i.e. the manager wants the significance level to be 1%). To calculate the critical value, we need to find the Z-score associated with a 1% significance level.
To find the critical value, we can use a Z-table or a Z-score calculator. Since the significance level is 1% (0.01), we need to find the Z-score corresponding to the area of 0.99 (1 - 0.01) in the upper tail of the standard normal distribution.
By looking up the Z-table or using a Z-score calculator, we find that the Z-score corresponding to a 0.99 cumulative probability is approximately 2.33. The critical value the manager should use to conduct the hypothesis test is 2.33.

To calculate the probability of Type II error, we need to specify an alternative hypothesis and determine the corresponding population mean value. In this case, the alternative hypothesis is that the mean daily output is greater than 200, and the specified population mean value is 205.

To calculate the probability of Type II error, we need to find the area under the null hypothesis distribution that falls to the right of the critical value. In other words, we need to find the probability that the test statistic, assuming the null hypothesis is true, falls in the rejection region. Since we are assuming the population mean is 205, we can calculate the Z-score using the formula:

Z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
Substituting the values, we get:
Z = (205 - 200) / (18 / sqrt(81)) = 5 / (18 / 9) = 5 / 2 = 2.5

Now, we can calculate the probability of Type II error by finding the area under the null hypothesis distribution to the right of the critical value, which is 2.33. Using the Z-table or a Z-score calculator, we find that the probability of Type II error is approximately 0.0062, or 0.62%.
If the sample mean turns out to be 205, we compare it to the critical value. If the sample mean is greater than the critical value (2.33), we reject the null hypothesis. In this case, since the sample mean is 205, which is greater than the critical value of 2.33, we would reject the null hypothesis. The conclusion of the test would be that there is sufficient evidence to suggest that the mean daily output is greater than 200.

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Answer: 6

Step-by-step explanation: 10/5=2 2*3=6 which means Mr. Kelly received 4 and Mr. Smith received 6 dollars.

A) The explicit rule for the value of the collection n years after it was worth $300,000 is  = $300,000 * (1.15)^n

B) Rounded to the nearest dollar, the value of Madame Dumas's art collection 7 years after she started tracking its worth is $698,285.

A) We know that the value of the art collection three years ago is $300,000, and the value of the collection two years ago is $345,000. Using these values, we can find the common ratio (r) of the geometric sequence:

r = (value two years ago) / (value three years ago)

r = 345,000 / 300,000

r = 1.15

Now that we have the common ratio, we can write the explicit rule for the value of the collection n years after it was worth $300,000:

value after n years = $300,000 * (1.15)^n

B) Using the explicit rule we found in part A, we can determine the value of the collection 7 years after it was worth $300,000:

value after 7 years = $300,000 * (1.15)^7

value after 7 years ≈ $698,285

Rounded to the nearest dollar, the value of Madame Dumas's art collection 7 years after she started tracking its worth is $698,285.

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PLUG IN

\( \frac{11}{10} \)

in the place of x in the function and simplify.

\(f( \frac{11}{10} ) = 2( \frac{11}{10} ) - 7 \\ f( \frac{11}{10} ) = \frac{22}{10} - 7 \\ f( \frac{11}{10} ) = \frac{ - 48}{10} \\ f( \frac{11}{10} ) = \frac{ - 24}{5} \)

ATTACHED IS THE SOLUTION

Hello!

To solve for f(11/10)

 ==> must simply plug '11/10' into x's position in the equation

    \(f(\dfrac{11}{10} )=2(\dfrac{11}{10} )-7=\dfrac{11}{5} -7=\dfrac{11}{5} -\dfrac{35}{5} =-\dfrac{24}{5}\)

Hope that helps!

Answer:

\(the \: scale \: is \: 2.5 \\ 4 \times 2.5 = 10 \\ \\ so \\ y = 6 \times 2.5 = 15 \\ x = 7 \times 2.5 = 17.5\)

Step-by-step explanation:

I hope that is useful for you

\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

Answer:

QSR

Step-by-step explanation:

Same letters so its the answer

Answer:

  RS = 80°

Step-by-step explanation:

The sum of the arcs of a circle is 360°.

  RS +ST +TR = 360°

  RS = 360° -ST -TR = 360° -130° -150°

  RS = 80°

Check the picture below.

first off let's check what "h" is in the triangular face.

\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{10}\\ a=\stackrel{adjacent}{6}\\ b=\stackrel{opposite}{h}\\ \end{cases}\implies 10^2=6^2+h^2 \\\\\\ 10^2-6^2=h^2\implies \sqrt{10^2-6^2}=h\implies 8=h\)

so, the gazebo has 4 squarish faces, each 12x12, recall 48 ÷ 4 = 12, and it has 4 triangular faces, each with a height of 8 and a base of 12.

notice we're skipping the top and bottom of the cube and the bottom of the pyramid because they're not part of the "surface area".

\(\stackrel{\textit{\large Areas}}{\stackrel{\textit{4 triangular faces}}{4\left[\cfrac{1}{2}(12)(8) \right]}~~~~+~~~~\stackrel{\textit{4 squarish faces}}{4[12\cdot 12]}}\implies 192+576\implies 768\)

Answer:

1/3

Step-by-step explanation:

Answer would be B, 1/3.

The advantages of an open question include:

An open question is designed to elicit a broad and unrestricted response from the respondent. It encourages them to think creatively and explore various possibilities, which can lead to the introduction of new solutions. Unlike closed-ended questions that limit respondents to predefined options, an open question provides the freedom to express ideas, perspectives, and insights that may not have been considered before.

Furthermore, an open question allows the respondent to go in-depth with their answer. It prompts them to provide detailed explanations, examples, and personal experiences, allowing for a richer and more nuanced understanding of their thoughts and perspectives. This depth of response can unveil valuable insights, uncover underlying motivations, and provide context that may not have been captured with closed-ended questions. It also encourages active engagement and reflection from the respondent, as they are encouraged to express their thoughts and feelings in a more comprehensive manner.

Overall, open questions promote creativity, critical thinking, and a deeper exploration of ideas, making them advantageous in various contexts such as research, interviews, surveys, and problem-solving discussions.

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Answer:

x=7+√15

x=7-√15

Step-by-step explanation:

To find y'(4) by implicit differentiation, we differentiate both sides of the equation 3x^2 + 3x + xy = 4 with respect to x.

Differentiating 3x^2 + 3x + xy = 4, we get:

6x + 3 + y + xy' = 0

Since we know y(4) = -14, we substitute x = 4 and y = -14 into the differentiated equation:

6(4) + 3 + (-14) + (4)(-14)' = 0

Simplifying this equation, we have:

24 + 3 - 14 - 56y' = 0

Combining like terms, we get:

13 - 56y' = 0

Solving for y', we find:

56y' = 13

y' = 13/56

Therefore, y'(4) = 13/56.

To find an equation of the tangent line to the graph at the point (4, -14), we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the point (4, -14) and m is the slope y'(4).

Substituting the values, we have:

y - (-14) = (13/56)(x - 4)

y + 14 = (13/56)(x - 4)

Simplifying, we get:

y = (13/56)x - (13/14) - 14

y = (13/56)x - (13/14) - (196/14)

y = (13/56)x - 209/14

Thus, an equation of the tangent line to the graph at the point (4, -14) is y = (13/56)x - 209/14.

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Answer:

$700

Step-by-step explanation:

1. We see the original price is $1,000.

2. Change 30% to a decimal

3. 30/100=0.30

4. Multiply the original cost of the item(mattress) by the percentage.

5. 0.3×1,000=300

6. $300 is the amount discounted.

7. For final price with discount: Take its original price($1,000) and subtract the discount from the original price

8. $1,000-$300=$700

Answer:

$300

Step-by-step explanation:

\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

The given information is as follows:A random sample of 150 teachers in an​ inner-city school district found that​ 72% of them had volunteered time to a local charitable cause within the past 12 months.

The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150

The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037

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Answer:

\( \frac{d}{t} = s\)

Step-by-step explanation:

d= the distance walked by Tom

t=the time he took to walk the distance

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