A researcher asked 120 people if they preferred swimming in a pool or swimming at the beach. The data collected show that two out of 10 people preferred swimming at the beach. What was the total number of people who preferred swimming at the beach?
A. 12
B. 60
C. 2
D. 24
PLEASE ANSWER WITH EXPLANATION / WORK

Therefore, the value of the test statistic is 2.02 (rounded to two decimal places).

To test the claim that the actual percentage of computer chips that do not fail in the first 1000 hours of their use is different from the stated percentage of 44%, we can use a hypothesis test with the following null and alternative hypotheses:

Null hypothesis: The proportion of computer chips that do not fail in the first 1000 hours of their use is equal to 44%.

Alternative hypothesis: The proportion of computer chips that do not fail in the first 1000 hours of their use is not equal to 44%.

We can use a normal approximation to the binomial distribution to calculate the test statistic:

z = (p - P) / √(P(1-P)/n)

where:

p = sample proportion = 0.46

P = hypothesized proportion = 0.44

n = sample size = 900

Plugging in the values, we get:

z = (0.46 - 0.44) / √(0.44*0.56/900)

z = 2.02

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The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.

To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.

Step 1:

Convert the percentage to a decimal.
65.3 / 100 = 0.653

Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

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The horizontal distance from the observation station to the fire is approximately 290.4 feet.

In this problem, we are given the angle of depression (θ) and the vertical distance (FS) from an observation station to a fire. We need to find the horizontal distance (x) from the station to the fire.

To solve the problem, we can use the trigonometric function tangent, which relates the opposite side to the adjacent side of a right triangle. In this case, the opposite side is the vertical distance FS, and the adjacent side is the horizontal distance x.

We can set up the following equation:

tan(θ) = FS / x

We know that θ = 15 degrees and FS = 87 feet, so we can plug these values into the equation:

tan(15) = 87 / x

Next, we can solve for x by multiplying both sides of the equation by x and dividing both sides by tan(15):

x = 87 / tan(15)

Using a calculator, we can evaluate the expression and get:

x ≈ 290.4 feet

We round our answer to the nearest tenth of a foot, which is why we keep one decimal place.

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The measures that are appropriate to accurately summarize the data are the mean and the median

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

1, 8, 2, 2, 5, 6, and 4

When sorted we have

1, 2, 2, 4, 5, 6, 8

The mean is calculated as

Mean = (1 + 2 + 2 + 4 + 5 + 6 + 8)/7

Mean = 4

The median is the middle value

So, we have

Median = 4

The mode is the data with the highest frequency

So, we have

Mode = 2

Lasltly, the measures that are appropriate to accurately summarize the data are the mean and the median

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The solution that equals a in this equation is [tex]a = 3 / 8[/tex]. The Option B.

An expression means collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that:

The expression is 1 over 4a = 2 over 3.

We can then simplify as:

1 / 4a = 2 / 3

Make a cross multiplacation, we get:

3 = 2 x 4a

3 = 8a

a = 3 / 8

Therefore, the solution of the expression is a = 3 / 8

Full question "1 over 4a = 2 over 3. Which of the following equals a in this equation? 1/6, 3/8 11/12, 2 and 2/3"

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Step-by-step explanation:

(8 x 10,000=80,000)

 (5 x 1,000=5,000) 

(3 x 100=300)

(8 x 1=8)

80,000+5,000+300+8

Answer:

85308

Step-by-step explanation:

[tex]8*10000=80000[/tex]

[tex]5*1000=5000[/tex]

[tex]3*100=300[/tex]

[tex]8*1=8[/tex]

[tex]80000+5000+300+8=85308[/tex]

Hope this helps :)

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The savings account paid a simple interest rate of 25.96%.

We can use the simple interest formula:

I = Prt

where I is the interest earned, P is the principal (initial amount deposited), r is the interest rate (in decimal form), and t is the time (in years).

The interest earned in 2 years is:

I = 759.60 - 500 = 259.60

Substituting the values into the formula, we get:

259.60 = 500 × r × 2

Simplifying and solving for r, we get:

r = 0.2596 or 25.96%

Therefore, the savings account paid a simple interest rate of 25.96%.

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mario has $759.60 in the bank after 2 years. assuming he made no additional deposits or withdrawls, what simple interest rate did the savings account pay? The initial amount deposited is $500

The dimensions of the rectangle are length = 21 meters and width = 18 meters.

To find the dimensions of the rectangle meeting these conditions, we first need to set up an equation based on the given information. We know that the perimeter is 78 meters, so we can use the formula for the perimeter of a rectangle:

Perimeter = 2(length + width)

Substituting in the given information, we get:

78 = 2(3 + width + width)

Simplifying, we can combine like terms:

78 = 2(3 + 2width)

78 = 6 + 4width

Subtracting 6 from both sides:

72 = 4width

Dividing by 4:

width = 18

So we know the width of the rectangle is 18 meters. We also know that the length is 3 meters greater than the width, so:

length = width + 3 = 18 + 3 = 21

Therefore, the dimensions of the rectangle meeting the specified conditions are:

width = 18 meters

length = 21 meters

To find the dimensions of the rectangle meeting the specified conditions, we'll use the information given: the perimeter is 78 meters and the length is 3 meters greater than the width.

Step 1: Write down the formula for the perimeter of a rectangle.
Perimeter (P) = 2(Length (L) + Width (W))

Step 2: Substitute the given values and conditions into the formula.
78 = 2(L + W)
Given that the length is 3 meters greater than the width, we can write L = W + 3.

Step 3: Substitute the expression for L in terms of W into the perimeter formula.
78 = 2((W + 3) + W)

Step 4: Solve the equation for W.
78 = 2(2W + 3)
39 = 2W + 3
36 = 2W
W = 18 meters

Step 5: Find the length (L) using the expression L = W + 3.
L = 18 + 3
L = 21 meters

So, the dimensions of the rectangle are length = 21 meters and width = 18 meters.

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The equations of the graph from the figure are y = 4 and y = -2

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

The graph

On the graph, we can see that

We have two horizontal lines that pass through the points y = 4 and y = -2

This means that the equations represented on the graph are y = 4 and y = -2

So, we can conclude that none of the options are true from the options

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The five-number summary is (7, 9, 13, 21.5, 24).

A five-number summary is a set of statistics that describes a data set. It consists of the minimum, first quartile, median, third quartile, and maximum of the data12. A box plot is a graphical display of the five-number summary using a number line and a rectangular box13.

To find the five-number summary and make a box plot for your data set, you need to follow these steps:

Arrange the data in ascending order: 7, 8, 10, 10, 13, 16, 19, 23, 24

Find the minimum and maximum values: Minimum = 7, Maximum = 24

Find the median (the middle value) of the data: Median = 13

Find the first quartile (the median of the lower half of the data): First quartile = 9

Find the third quartile (the median of the upper half of the data): Third quartile = 21.5

Therefore, by the number line the answer will be (7, 9, 13, 21.5, 24).

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Answer:

The only value of n that makes the inequality true is 5.

Explanation:

To solve the inequality, we need to isolate n on one side of the inequality symbol. First, we can multiply both sides by 7/3 to get:

n > (4/3) × 27/7

Simplifying, we get:

n > 4

So any value of n greater than 4 would make the inequality true. Among the given choices, only 5 is greater than 4, so it is the only value that satisfies the inequality.

1. The people in the survey are 32

2. The problem is that there should not be a row for 57

3. There is nothing wrong with the vfrequency table

4. The teacher displays class testscores ion stem and leaf plot woyl give the most  valid conclusion

Count the frequency

8 + 10 + 12 + 2

= 32

A statistical instrument, termed as a frequency table, tabulates and illustrates how often particular elements or values belonging to numerous classifications crop up in a dataset.

In other words, it streamlines the procedure of managing and examining data, ultimately simplifying the identification of patterns and trends that may be present within the information at hand.

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The limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

To use the ratio test, we take the limit of the absolute value of the ratio of the (k+1)th term to the kth term:

lim as k approaches infinity of |(6(k+1)^4)/(6k^4)|

Simplifying this expression, we get:

lim as k approaches infinity of |(k+1)^4/k^4|

Using L'Hopital's rule, we can evaluate this limit:

lim as k approaches infinity of |4(k+1)^3/4k^3|

lim as k approaches infinity of |(k+1)/k|^3

Since the limit is less than 1, by the ratio test, the series converges absolutely.

Alternatively, we can use the root test, which involves taking the kth root of the absolute value of the kth term:

lim as k approaches infinity of |(6k^4 k)^(1/k)|

Simplifying this expression, we get:

lim as k approaches infinity of |6^(1/k) * k^(4+1/k)|

The exponent 4+1/k approaches 4 as k approaches infinity, so we can ignore the 1/k term. Taking the limit of just the k^(4) term, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k)

Using the fact that lim as k approaches infinity of 6^(1/k) = 1 and lim as k approaches infinity of k^(4/k) = 1, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k) = 1

Since the limit is less than 1, by the root test, the series converges absolutely.
To determine if the given series converges absolutely or diverges, we can use the Ratio Test. The series is given as:

Σ(6k^4 * k) for k = 1 to ∞

First, let's simplify the series:

Σ(6k^5) for k = 1 to ∞

For the Ratio Test, we need to compute the limit as k goes to infinity of the ratio of consecutive terms:

lim (k → ∞) (|a_(k+1)| / |a_k|)

For our series, a_k = 6(k+1)^5 and a_(k+1) = 6k^5. So we have:

lim (k → ∞) (|6(k+1)^5| / |6k^5|)

We can simplify by canceling the common factor of 6:

lim (k → ∞) ((k+1)^5 / k^5)

Now, let's take the limit:

lim (k → ∞) (1 + 1/k)^5 / 1 = 1^5 / 1 = 1

For the Ratio Test, if the limit is less than 1, the series converges absolutely; if it is equal to 1, the test is inconclusive; if it is greater than 1, the series diverges.

In this case, the limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

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Answer:96

Step-by-step explanation:

(4x4)+(4x4)+(4x4)+(4x4)+(4x4)+(4x4)

16+16+16+16+16+16

48+48

96

The high temperature on Tuesday was -5°F.

Given that,

On Monday, the high temperature in Sheboygan, Wisconsin, was –12°F.

The high temperature on Tuesday was 7 degrees warmer than the high temperature on Monday.

Let T be the high temperature on Tuesday and M be the high temperature on Monday.

By the given statement,

T = M + (7°F)

We have, M = -12°F

Substituting,

T = -12°F + 7°F

  = -5°F

Hence the required temperature is -5°F.

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The probability that the dealership will make a profit if 4 customers enter on Friday is approximately 24.01%.

a. You can estimate the Hypergeometric Distribution with the Binomial Distribution under the following conditions:
1. The sample size (n) is relatively small compared to the population size (N).
2. The probabilities of success (p) and failure (q) remain approximately constant throughout the sampling process.

In this case, since we're assuming sampling with replacement, identical cars, and independent trials with constant probability, it's appropriate to use the Binomial Distribution.

b. To calculate the probability that the dealership will make a profit if 4 customers enter on Friday, we can use the Binomial Distribution formula:

P(X = k) = (nCk) * (p^k) * (q^(n-k))

Where:
- P(X = k) is the probability of exactly k successes (cars sold)
- nCk is the number of combinations of n items taken k at a time
- p is the probability of success (car sold)
- q is the probability of failure (car not sold)
- n is the number of trials (customers)
- k is the number of successes (cars sold)

Here, n = 4, p = 0.70, and q = 1 - p = 0.30. We need to find the probability of selling at least 4 cars (k ≥ 4) to make a profit:

P(X ≥ 4) = P(X = 4)
P(X = 4) = (4C4) * (0.70^4) * (0.30^0)
P(X = 4) = 1 * (0.2401) * (1)
P(X = 4) = 0.2401

Therefore, the probability that the dealership will make a profit if 4 customers enter on Friday is approximately 24.01%.

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The missing sides are represented as;

AC =  4√2    O.

AB = 4    M

DE =  6√2    L

DF =  6√2   L

To determine the value of the missing sides, we need to note the following trigonometric identities and their ratios;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have that;

cos 45 = 4/AC

cross multiply the values

AC = 4÷ 1√2

Multiply the values

AC = 4× √2/1

Multiply the values

AC = 4√2

tan 45 = AB/4

AB = 4

To determine the values

sin 45 = DE/6

DE = 6√2

Then,

DF = 6√2

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The base and height of the rectangle are 80 and 60 feet.

A rectangle has a diagonal of 100 feet. The length that could be the base and height of the rectangle is as follows:

Therefore, let's use Pythagoras's theorem to find the base and the height of the triangle.

c² = a² + b²

where

Therefore,

80² + 60² = 100²

6400 + 3600 = 10000

10000 = 10000

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The scale factor used in the dilation of the triangles is 3

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

The scale factor is calculated as

Scale factor  = A'/A

Substitute the known values in the above equation, so, we have the following representation

Scale factor  = (-3, -3)/(-1, -1)

Evaluate

Scale factor  = 3

Hence, the scale factor is 3

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The total area of Cedarville is in the shaded area that is both east of the river and north of Main Street is 6/10. Option C

We know that a fraction can be seen as a part of the whole. Thus when we talk about a fraction, we mean the part that we have taken out of the whole.

If we want to get the fraction of the total area of Cedarville is in the shaded area that is both east of the river and north of Main Street, then we have to count all the boxes and this would give us ten.

Six out of this ten are shaded thus the fraction of the total area of Cedarville is in the shaded area that is both east of the river and north of Main Street is 6/10.

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The probability of receiving exactly 7 calls in the next three hours is approximately 0.104, which corresponds to answer (b).

To solve this problem, we need to use the Poisson probability formula, which is:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the number of calls, k is the desired number of calls (7 in this case), λ is the average rate of calls per time period (5 calls per hour), and e is the base of the natural logarithm (approximately 2.71828).

Since we want to know the probability of receiving 7 calls in 3 hours, we need to adjust our λ value accordingly. Since the rate is 5 calls per hour, the average rate for 3 hours would be 5 * 3 = 15 calls.

Now, we can plug these values into the formula:

[tex]P(X = 7) = (e^(-15) * 15^7) / 7![/tex]

P(X = 7) ≈ 0.104

So, the probability of receiving exactly 7 calls in the next three hours is approximately 0.104, which corresponds to answer (b).

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The time that it would take Justin to charge the batter to 100% on both devices will be 111.67 minutes

It takes about 36.67 minutes to charge the Nintendo Switch entirely.

The iPad has a residual battery life of 40%, which means it must gain an additional 60% percent increase in energy.

Since we understand that the tablet powers up by approximately 12 percentage points every quarter of an hour, the estimated duration for one hundred percent charging is close to 75 minutes.

Consequently, Justin must energize both gadgets and will need nearly 111.67 minutes or almost two hours to accomplish this task completely.

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The correct equation which represents the graph is,

⇒ y = 1/3x - 2

We know that;

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (3, -1) and (0, -2).

Now,

Since, The equation of line passes through the points (3, -1) and (0, -2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 2 - (-1)) / (0 - 3)

m = - 1 / -3

m = 1/3

Thus, The equation of line with slope 1/3 is,

⇒ y - (-1)= 1/3 (x - 3)

⇒ y + 1 = 1/3x - 1

⇒ y = 1/3x - 2

Therefore, The equation of line passes through the points ((3, -1) and

(0, -2).will be;

⇒ y = 1/3x - 2

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The equivalent fractions for 1/5 and 3/4 with a common denominator of 20 are:

1/5 = 4/20

3/4 = 15/20

To write equivalent fractions for 1/5 and 3/4 using 20 as the common denominator

we need to multiply the numerator and denominator of each fraction by the same number such that the denominator becomes 20.

For 1/5:

1/5 = (1 x 4)/(5 x 4) = 4/20

Therefore, an equivalent fraction for 1/5 with a denominator of 20 is 4/20.

For 3/4:

3/4 = (3 x 5)/(4 x 5) = 15/20

An equivalent fraction for 3/4 with a denominator of 20 is 15/20.

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Answer: Average speed is given by the formula:

speed = distance ÷ time

Given that Darlene rode her bike 8 2/5 miles in 3/4 of an hour. We need to convert the mixed number 8 2/5 to an improper fraction.

8 2/5 = (8 x 5 + 2) / 5 = 42/5

So, Darlene rode her bike a distance of 42/5 miles in a time of 3/4 hours.

Substitute speed = distance ÷ time

speed = (42/5) ÷ (3/4)

To divide by a fraction, we invert and multiply:

speed = (42/5) x (4/3)

speed = 56/5

So, Darlene's average speed was 56/5 miles per hour (mph).

To simplify this fraction, we can divide both the numerator and denominator by 1:

speed = 11/1

The correct option is (c). t (1) = C1, and t(n) = 2t(2n/3) + C2, C1 and C2 are positive constants. Here's a step-by-step explanation:

1. When n = 1, the algorithm computes a function g (M [0])) and returns an integer value, which takes constant time, represented by C1.
2. For larger values of n, the algorithm divides the input array into two subarrays starting at positions i = 0 and [n/3 - 1], each containing [2n/3] elements.
3. It runs the algorithm recursively on each subarray, returning two integers x and y, and computes g(x, y).
4. Counting all the operations for each step, we can see that there are two recursive calls with inputs of size 2n/3, and one operation for computing g(x, y).

Therefore, the recurrence relation for the running time of this algorithm is:
t(1) = C1 (base case)
t(n) = 2t(2n/3) + C2 (recursive case)

C1 and C2 are positive constants.

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(a) 50% of the packages will weigh more than 1 pound.

(b) 24.64% of the packages will weigh between .95 and 1.05 pounds.

(c) The probability that a randomly selected package of ground beef will weigh less than .80 pound is 9.18%.

(d) It would be unusual to find a package of ground beef that weighs 1.45 pounds. Such a large package could be explained by either an error in the packaging process or a deliberate attempt to provide larger packages to some customers.

a. To find the proportion of packages that weigh more than 1 pound, we need to calculate the area under the normal curve to the right of 1 pound. Using a standard normal table or calculator, we can find this probability to be:

P(Z > (1-1)/0.15) = P(Z > 0) = 0.5000

Therefore, 50% of the packages will weigh more than 1 pound.

b. To find the proportion of packages that weigh between .95 and 1.05 pounds, we need to calculate the area under the normal curve between these two values. Using a standard normal table or calculator, we can find this probability to be:

P((.95-1)/0.15 < Z < (1.05-1)/0.15) = P(-0.33 < Z < 0.33) = 0.3482

Therefore, 34.82% of the packages will weigh between .95 and 1.05 pounds.

c. To find the probability that a randomly selected package of ground beef will weigh less than .80 pound, we need to calculate the area under the normal curve to the left of .80 pound. Using a standard normal table or calculator, we can find this probability to be:

P(Z < (.80-1)/0.15) = P(Z < -1.33) = 0.0912

Therefore, there is a 9.12% chance that a randomly selected package of ground beef will weigh less than .80 pound.

d. It would be quite unusual to find a package of ground beef that weighs 1.45 pounds, as this is more than three standard deviations above the mean. The probability of finding a package that weighs 1.45 pounds or more can be calculated as:

P(Z > (1.45-1)/0.15) = P(Z > 2.67) = 0.0038

This is a very small probability, suggesting that such a large package is an outlier in the distribution. It could be due to a mistake in packaging or an intentional oversized package for a special order.

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