A, B, C and D form the vertices of a
quadrilateral. Calculate the area of the
quadrilateral rounded to 1 DP.
AB = 23.6m
AD = 7.8m
BC = 9.7m
CD = 14.9m
Angle ABC = 59⁰

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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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 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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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 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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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.

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

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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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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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 most specific classification of the fraction 9/3 is: Rational Numbers

A rational number is defined as a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero,

The fraction we are given as: 9/3

Now, we know that 9 and 3 are classified as integers and as such we can easily classify them as rational numbers.

Thus, the best specific classification of 9/3 is really rational numbers.

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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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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

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 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 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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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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Answer:

[tex]\frac{1}{21}[/tex]

Step-by-step explanation:

To start, let's divide [tex]-\frac{1}{6}[/tex] by [tex]-\frac{7}{4}[/tex]. To do this, we're going to have to flip around the second number and multiply it by the first one (this is how to divide fractions).

[tex]-\frac{1}{6}[/tex] × [tex]-\frac{4}{7} = \frac{4}{42} =\frac{2}{21}[/tex]

Now, it's time for us to multiply that result by 0.5. As you may already know, 0.5 is equivalent to [tex]\frac{1}{2}[/tex], so let's use that value instead.

[tex]\frac{2}{21}[/tex] × [tex]\frac{1}{2} = \frac{2}{42} = \frac{1}{21}[/tex]

So, our final answer is [tex]\frac{1}{21}[/tex]. Let me know if you need more help!

Answer:0.00298

Step-by-step explan

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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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.

The parametric function for your location on the Ferris wheel at any given time:
x(t) = 80 * sin(2π * (t/2))
y(t) = 80 * cos(2π * (t/2)) + 3

To create a parametric function that models your location on the Ferris wheel at a given time, we need to come up with equations that describe your horizontal and vertical positions as functions of time.

Let's start with the horizontal position. Since the Ferris wheel rotates counter-clockwise, we know that your position on the wheel will increase as time goes on. We can express this as:

x(t) = 80cos(2πt/120)

Here, t represents time in seconds, and the factor of 2π/120 ensures that the function completes one full cycle (i.e. one trip around the wheel) in 120 seconds, or 2 minutes. The cosine function gives us a smooth, periodic curve that oscillates between -80 and 80, corresponding to your position on either side of the wheel's center.

Next, let's consider your vertical position. We know that you start at a height of 3 feet above the ground, and as the wheel rotates, your height will vary sinusoidally over time. We can express this as:

y(t) = 80sin(2πt/120) + 3

Here, the sine function gives us a smooth, periodic curve that oscillates between 77 and 83 feet (i.e. the radius of the wheel plus or minus 3 feet).

So, putting it all together, our parametric function for your location on the Ferris wheel at a given time t is:

(r(t), θ(t)) = (80cos(2πt/120), 80sin(2πt/120) + 3)

Here, r(t) and θ(t) represent your radial distance from the center of the wheel and the angle you've rotated from the starting position, respectively. This parametric function describes a smooth, periodic curve that traces out your path on the Ferris wheel as it rotates counter-clockwise.

Given the information, we know the Ferris wheel has a radius of 80 feet, the bottom is 3 feet above the ground, it rotates counter-clockwise, and has a period of 2 minutes.

To create a parametric function, we need two equations, one for the x-coordinate (horizontal) and one for the y-coordinate (vertical). Let's denote the time variable as t, measured in minutes.

1. X-coordinate (horizontal position):
Since the Ferris wheel rotates counter-clockwise, we can use the following equation for the x-coordinate:
x(t) = 80 * sin(2π * (t/2))

2. Y-coordinate (vertical position):
To account for the bottom of the Ferris wheel being 3 feet above the ground, we need to add 3 to the vertical equation:
y(t) = 80 * cos(2π * (t/2)) + 3

Now, we have the parametric function for your location on the Ferris wheel at any given time:
x(t) = 80 * sin(2π * (t/2))
y(t) = 80 * cos(2π * (t/2)) + 3

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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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Answer:

[tex]2 \frac{1}{3} + 1 \frac{3}{4} [/tex]

[tex]2 \frac{4}{12} + 1 \frac{9}{12} = 3\frac{13}{12} = 4 \frac{1}{12} [/tex]

The correct answer is A.

The Volume of the solid = 601.83 m³

The Surface area of the solid = 266.9 m²

The solid is composed of a cylinder and a cone, therefore, we would need the following formulas:

Volume of cone = 1/3 * πr²h

Volume of Cylinder = πr²h

Surface area of cone = πrl

Surface area of cylinder = 2πr(h + r)

Volume of the solid = 1/3 * πr²h + πr²h

radius (r) = 5 m

height of cone (h) = 5 m

Height of cylinder (h) = 6 m

π = 3.14

Plug in the values:

Volume of the solid = 1/3 * 3.14 * 5² * 5 + 3.14 * 5² * 6

Volume of the solid = 130.83 + 471 = 601.83 m³

Surface area of the solid = πrl + 2πr(h + r) - 2(πr²)

r = 5 m

l = 5m

π = 3.14

h = 6 m

Plug in the values:

Surface area of the solid = 3.14 * 5 * 5 + 2 * 3.14 * 5(6 + 5) - 2(3.14 * 5²)

= 78.5 + 345.4 - 157

= 266.9 m²

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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 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 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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Answer:

<

Step-by-step explanation:

because 42.18 is smaller than 42.7

Answer:

We know that, if in a distribution one tail is longer than the other, the distribution is skewed.

Here in the given histogram, it has a long right tail which is in the positive direction on the x axis. So it is right skewed distribution. That is also known as positive skewed distribution.

Step-by-step explanation:

So here we have got the required answer. Option C is correct.

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