The figure below is comprised of two congruent squares and two congruent triangles. Each side of the squares has a length of x. Each triangle has a height of x. If x equals 14 cm, what is the total area of the figure? A. 980 sq cm B. 392 sq cm C. 784 sq cm D. 588 sq cm

The requried, if the loan is paid in full at the end of the 5-year period, the borrower would have to pay back $26,130 (rounded to the nearest dollar).

The formula for the future value of an investment with compound interest is:

[tex]FV = PV * (1 + r)^n[/tex]

Where PV is the present value (the amount borrowed), r is the annual interest rate (as a decimal), and n is the number of compounding periods. In this case, since the interest is compounded annually for 5 years, n = 5.

Substitute in the values given, we get:

[tex]FV = 22,000 * (1 + 0.035)^5[/tex]

FV = 22,000 * 1.19416

FV = 26,129.09 = 26,130

Therefore, if the loan is paid in full at the end of the 5-year period, the borrower would have to pay back $26,130 (rounded to the nearest dollar).

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Answer: f(2) = -7   , g(3) = -29

Step-by-step explanation: this problem can be solved via substitution

-2(2) - 3 = -4 - 3 = -7

-3(3)^2 - 2 = -3(9) - 2 = -27 - 2 = -29

Answer:

x      f(x)      g(x)

-2       4      -4

-1        1      - 1

0       0        0

1        1         -1

2       4        -4

Step-by-step explanation:

When a point is reflected across the x-axis the reflected point will have the same x value as the pre-image point

Therefore if point(x, y) is reflected across the x-axis the reflected point will be (x, -y)

When f(x) = x² is reflected across the x-axis, the reflected function becomes

f'(x) = -f(x) = -x²

Using this information we can complete the table as follows:

x      f(x)      g(x)

-2       4      -4

-1        1      - 1

0       0        0

1        1         -1

2       4        -4

The graph of y = 2ˣ +1 -8 is the curve of the exponential function y = 2ˣ shifted downward by 8 units and shifted to the left by 1 unit along the x-axis.

The exponential function y = 2ˣ represents a curve that grows rapidly as x increases.

The graph of y = 2ˣ +1 -8 is the same curve shifted downward by 8 units and shifted to the left by 1 unit along the x-axis.

To plot some points for the graph, choose a few x-values and then calculate the corresponding y-values using the function:

When x = -2, y = 2⁻¹ - 8 = -8.5

When x = -1, y = 2⁰ - 8 = -7

When x = 0, y = 2¹ - 8 = -6

When x = 1, y = 2² - 8 = -4

When x = 2, y = 2³ - 8 = 0

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To find the values for a and b in minutes, we need to use the information given about the uniform distribution. We know that the technician takes between 30 seconds and 13 minutes to resolve the problem.

Given that the support time follows a uniform distribution and takes between 30 seconds and 13 minutes to resolve the problem, we can find the values of a and b as follows:

Step 1: Convert the time range to minutes
30 seconds = 0.5 minutes
13 minutes = 13 minutes

Step 2: Identify the values for a and b
In a uniform distribution, 'a' is the minimum value and 'b' is the maximum value.
So, a = 0.5 minutes and b = 13 minutes

The values for a and b in minutes are:
a = 0.5 minutes
b = 13.0 minutes

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The expected winning and the value of that prize, which gives an expected winning is c. $3.13 per ticket.

The expected winnings per ticket in the raffle can be calculated by adding the products of the probability of the expected value of winning each prize. The predicted wins per ticket may be computed as the total of each prize's value multiplied by its probability of winning, i.e.

Expected winnings per ticket

= (1/800) × $400 + (4/800) × $200 + (12/800) × $125 + (30/800) × $60 + (753/800) × $0

If we condense the equation, we obtain:

Calculating the total wins anticipated per ticket

= $0.50 + $1.00 + $1.88 + $0.75 + $0

Expected winnings per ticket = $3.13

Therefore, if you buy a ticket, the expected winnings per ticket are $3.13.

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Complete question:

For a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what are the expected winnings per ticket? question options:

a) $5.36

b) $5.63

c) $5.33

d) $5.66

The length of side f is  8.38 in the triangle DEF.

In a triangle, the sum of the angles is always 180 degrees.

∠D + ∠E + ∠F = 180 degrees

∠D + ∠E + 166 degrees = 180 degrees

∠D + ∠E = 14 degrees

Now, we can use the Law of Cosines to find the length of side f:

f² = d² + e² - 2de cos(∠F)

f² = (5.2 inches)² + (6.8 inches)² - 2(5.2 inches)(6.8 inches) cos(166 degrees)

f² = 70.29 inches²

Taking the square root of both sides, we get:

f = 8.38 inches

Therefore, the length of side f is  8.38 in the triangle DEF.

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The probability model of Viet, Quinn, and Lucy will change to 18/90 instead of 15/75.

Given that,

Viet, Quinn, and Lucy are going to play Bingo, using a standard game set.

They make some predictions before the game begins.

The given table shows how the numbers match with the letters B, I, N, G, and O.

Total numbers = 75

Numbers which each letter has = 15

Probability of having each number = 15/75

Now if the game changed to 90 numbers, each letter will be having 90/5 = 18 numbers.

So probability changed to 18/90.

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The value of the test statistic for the test of the manufacturer to test his bolts is -0.296.

Given that,

A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.

So population mean, μ = 4 cm

Sample size, n = 49

Sample mean, x = 3.87 cm

Population standard deviation, σ = 0.44 cm

Level of significance, α = 0.02

Test statistic, z = (x - μ) / σ

Substituting,3

z = (3.87 - 4) / 0.44 = -0.296.

Hence the value of the test statistic for the test of the manufacturer to test his bolts is -0.296.

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The length of rectangle is,

⇒ (x + 1)

We have o given that;

The rectangle has an area of x² - 6x - 7

And, a width of x - 7

Now, Let the length of rectangle = y

Hence, We get;

y = (x² - 6x - 7) / (x - 7)

y = (x + 1) (x - 7) / (x - 7)

y = (x + 1)

Thus, The length of rectangle is,

⇒ (x + 1)

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The correct answer to your question is: the p-value of a significance test is the probability, assuming the null hypothesis is true, that the sample would produce a result at least as extreme (meaning, as far away from expected) as was actually observed.

This means that the p-value represents the strength of evidence against the null hypothesis, with lower values indicating stronger evidence against the null hypothesis. It is important to note that the p-value does not tell us the probability that the null hypothesis is true or false, but rather the likelihood of observing a result as extreme as the one observed in the sample data, assuming the null hypothesis is true.
The p-value of a significance test is: the probability, assuming the null hypothesis is true, that the sample would produce a result at least as extreme (meaning, as far away from expected) as was actually observed.

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The length of the arc intercepted by a central angle of 2.9 radians is 14.5 inches. Rounded to the nearest tenth, this is 14.5 inches.

To find the length (s) of the arc intercepted by a central angle of 2.9 radians in a circle with a radius of 5 inches, you can use the following formula:

Arc length (s) = radius × central angle (in radians)

In this case, the radius is 5 inches, and the central angle is 2.9 radians. Plugging these values into the formula, we get:

s = 5 × 2.9

s ≈ 14.5 inches

Therefore, the length of the arc intercepted by a central angle of 2.9 radians in a circle with a radius of 5 inches is approximately 14.5 inches, rounded to the nearest tenth.

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The alternative hypothesis would be: The proportion of people who own cats is smaller than 90%.

The null hypothesis for this test would be: The proportion of people who own cats is equal to or greater than 90%.

To conduct the hypothesis test, we would need to collect a random sample of 1400 individuals and determine how many of them own cats. Based on this information, we could calculate the sample proportion of cat owners and use this to test the claim that the population proportion is smaller than 90%.

We would use a one-tailed hypothesis test with a significance level of 0.005. If the p-value for our test is less than 0.005, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the proportion of people who own cats is smaller than 90%.
Hi! I'd be happy to help you with this question. You want to test the claim that the proportion of people who own cats is smaller than 90% at the 0.005 significance level.

To do this, we will set up our null and alternative hypotheses as follows:

Null Hypothesis (H0): The proportion of people who own cats is equal to 90% (p = 0.90)
Alternative Hypothesis (H1): The proportion of people who own cats is smaller than 90% (p < 0.90)

Here's a step-by-step explanation of how to test this claim:

1. Determine the sample size (n) and the number of cat owners in the sample (x): In this case, n = 1400, and x = 615.

2. Calculate the sample proportion (p-hat): p-hat = x/n = 615/1400 ≈ 0.439.

3. Determine the significance level (alpha): In this case, alpha = 0.005.

4. Calculate the standard error (SE) of the sample proportion: SE = sqrt[p*(1-p)/n] = sqrt[0.9*(1-0.9)/1400] ≈ 0.008.

5. Calculate the z-score: z = (p-hat - p)/SE = (0.439 - 0.9)/0.008 ≈ -57.63.

6. Find the critical z-value for a one-tailed test at the 0.005 significance level: z-critical = -2.576 (from a standard normal distribution table).

7. Compare the calculated z-score with the critical z-value: Since the calculated z-score (-57.63) is less than the critical z-value (-2.576), we reject the null hypothesis.

In conclusion, based on this analysis, we have enough evidence to support the alternative hypothesis that the proportion of people who own cats is smaller than 90% at the 0.005 significance level.

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Answer:

  21 units

Step-by-step explanation:

You want the height (x) of a cone with base radius 9 units and volume 567π cubic units.

The volume of a cone is given by the formula ...

  V = 1/3πr²h

Solving for the height, and using x for the height, we find ...

  x = 3V/(πr²) = 3(567π units³)/(π(9 units)²) = 21 units

The height of the cone is 21 units.

Line graphs do not use bars to represent data. Instead, they use lines to show the trend or pattern of the data over time or some other continuous variable so the given sentence is false.

The statement is false. Line graphs use points connected by lines to display changes in data over time or other continuous independent variable. The line represents the trend or pattern of the data and the points indicate specific data points. The height or length of bars is typically used in bar graphs or column charts to compare data values among different categories or groups.

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The information as shown in a pie chart is found in the attachment.

The population of England is 49.8 million.

The population of England is calculated as a percentage of the total population of the United Kingdom.

The data table given shows that England has 83% of the UK population and the total population of the UK is 60 million.

Hence, the population of England is calculated as follows:

The population of England = 83% of 60 million

The population of England = (83/100) x 60,000,000

The population of England = 49,800,000

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To solve this problem, we can use the formula for the future value of an annuity:

FV = PMT * ((1 + r)^n - 1) / r

where:

PMT = the monthly payment ($300)

r = the monthly interest rate (APR / 12 = 0.035 / 12 = 0.002917)

n = the number of months (18 years x 12 months/year = 216 months)

Plugging in the values, we get:

FV = 300 * ((1 + 0.002917)^216 - 1) / 0.002917

FV ≈ $77,300.31

Therefore, after 18 years of making monthly deposits of $300 into an investment plan with an APR of 3.5%, you will have approximately $77,300.31.

To compare this amount to the total deposits made over the time period, we can calculate the total deposits as:

Total deposits = PMT * n

Total deposits = $300 * 216

Total deposits = $64,800

We can see that the total deposits made over the 18-year period were $64,800, which is less than the final value of the investment of approximately $77,300. This is because of the effect of compound interest, where the interest earned on the investment is reinvested and earns additional interest over time, resulting in a higher final value.

This stage of group development is known as forming.

The group development process is a series of stages that a group goes through as they form, develop, and eventually come to an end. The first stage of this process is known as forming. During this stage, group members are getting to know each other and trying to establish common goals and a shared understanding of how the group will operate. They may be polite and reserved, as they are still trying to feel out the dynamics of the group.

Once the group has established its purpose and members have a sense of what is expected of them, they move into the norming stage. During this stage, group members begin to work together more closely and develop norms for behavior and communication. They may start to form stronger relationships with each other and trust begins to build.

The third stage of group development is storming. During this stage, conflicts may arise as group members struggle for power and influence. There may be disagreements about how the group should function or how tasks should be completed. However, if the group is able to work through these conflicts, they will move on to the next stage of development.

The final stage of group development is adjourning. During this stage, the group comes to an end. This may be due to the completion of a task or project, or it may be due to other reasons, such as members leaving the group or the group disbanding. During this stage, members may reflect on their accomplishments and evaluate the group's overall success.

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The probability of getting a different prize in the next box you buy is: P(A) = 3 / 5 = 0.6 or 60%.

The probability of getting a different prize in the next box you buy depends on the number of prizes left and the total number of prizes.

Since there are 5 prizes in total and you have already collected 2, there are 3 remaining prizes. The probability of getting a different prize in the next box you buy is 3 out of 5, or 60%. This is because each box is equally likely to contain any one of the prizes, and you have already collected 2 out of the 5 prizes.

To calculate the probability, you can use the formula: P(A) = number of favorable outcomes / total number of possible outcomes In this case, the number of favorable outcomes is 3 (the number of remaining prizes) and the total number of possible outcomes is 5 (the total number of prizes). Therefore, the probability of getting a different prize in the next box you buy is: P(A) = 3 / 5 = 0.6 or 60%

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Answer:

75π

Step-by-step explanation:

Length of an arc formula:

Where:

Here we are given the following:

By plugging these values into the formula we acquire(Note that the answer must be in terms of π, meaning that we do not simplify it and leave it in the final answer):

The length of the arc is 75πm

The lengths of rods A, B and C are respectively;

30 cm, 10 cm and 75 cm

We are given that;

Ratio of length of Rod A to length of Rod B is; 3:2

Ratio of length of Rod A to length of rod C is 2:5

Thus;

2/3 Length of Rod A = the length of Rod B

5/2 Length of Rod A = the length of Rod C

If length of Rod A = x, then we can say that;

5x/2 is length of Rod C

⅔x is the lenggh of Rod B

Difference between longest and shortest is 55. Thus;

(5/2)x - (2/3)x = 55

Multiply through by 6 to get;

15x - 4x = 330

11x = 330

x = 330/11

x = 30 cm

Length of Rod B = (2/3) * 30

= 10 cm

Length of Rod C = (5/2) * 30

= 75 cm

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The standard deviation of the sampling distribution is called the standard error of the mean, not the median. The standard error of the median is a different measure that is used to estimate the variability of the median of a sample.

When we take a sample from a population, the values of the sample statistics, such as the mean, median, standard deviation, etc., will vary from sample to sample. The distribution of the sample statistics is called the sampling distribution.

The standard deviation of the sampling distribution of the mean is called the standard error of the mean. It is a measure of the variability of the sample means from sample to sample.

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The estimated number of pets in the town is given as follows:

Between 4750 and 9250.

The estimated number of pets is obtained applying the proportions in the context of the problem.

The average number of pets per household is 2.8 with a margin of error of ±0.9, hence the bounds of the interval are given as follows:

Considering that there are 2500 households, the bounds of the total amounts are given as follows:

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Answer:

The answer for radius is 5cm

Step-by-step explanation:

Volume of Cylinder =pir²h

225pi=pir²×9

225=9r²

divide both sides by 9

9r²/9=225/9

r²=25

√r²=√25

r=5cm

The area of this triangle has 5 significant figures. With the following formula, we can determine a triangle's area:

Area equals (1/2) x base x height.

When we enter the values we have:

(1/2) x 2.218 mm x 1.86 mm is the area.

= 2.0586 mm2 in size

With a fixed base of 2.218 mm and a height of 1.86 mm, the area of the triangle is 2.06 mm2 (rounded to the nearest hundredth).

The number of important figures in the obtained area will next be determined. Every digit is important in decimal numbers greater than or equal to 1, so we may infer that there are five significant figures in this case:

2,0,6,7, and 4 due to the fact that the number 2.06274 is greater than 1

Therefore, the area of this triangle has 5 significant figures.

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Answer: 12%

Step-by-step explanation:
2/25 is .08

3/24 is .12

Together that’s .20 so 20%
8/25 is 32

So 32-20=12%

This will highlight the cells as described, emphasizing the effect of conditional formatting. When you press the F9 key, the spreadsheet will recalculate, and the formatting will change accordingly.

To apply the conditional formatting as described:

1. In column B, highlight cells with the number of movies greater than 15 in red.
-Select the data range in column B where the number of movies is listed.
-Go to the Home tab, click on Conditional Formatting, and choose "Highlight Cells Rules."
- Select "Greater Than" and enter 15 in the input box.
- Choose "Custom Format," go to the "Font" tab, and select red from the "Standard Colors" section.
Click OK to apply the formatting.

2. In column E, change the number format for all zero values to a currency with no decimals:
- Select the data range in column E where the medical expenses are listed.
-Go to the Home tab, click on Conditional Formatting, and choose "Highlight Cells Rules."
-Select "Equal To" and enter 0 in the input box.
- Choose "Custom Format," go to the "Number" tab, select "Currency" from the "Category" list, and set the "Decimal Places" to 0.
Click OK to apply the formatting.

This will highlight the cells as described, emphasizing the effect of conditional formatting. When you press the F9 key, the spreadsheet will recalculate, and the formatting will change accordingly.

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The 90% confidence interval for the number of seeds in the fruit is (17.480, 19.920). To find the 90% confidence interval for the number of seeds in the fruit, we will follow these steps:

1. Identify the sample size (n), sample mean (x), and sample standard deviation (s): n = 70, x= 18.7, s = 6.2.

2. Since we want a 90% confidence interval, we will use a z-score of 1.645 (from a standard normal distribution table or calculator).

3. Calculate the standard error (SE) using the formula: SE = s/√n = 6.2/√70 = 0.741.

4. Calculate the margin of error (ME) using the formula: ME = z * SE = 1.645 * 0.741 =1.220.

5. Determine the confidence interval by adding and subtracting the margin of error from the sample mean: (x - ME, x+ ME) = (18.7 - 1.220, 18.7 + 1.220) = (17.480, 19.920).

Therefore, the 90% confidence interval for the number of seeds in the fruit is (17.480, 19.920).

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