A(2,3),B(6,3),C(6,−4) ,and D(2,−4)
. Find the area of rectangle ABCD.

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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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 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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There are 21 kilograms of potash in a bag of fertilizer that weighs 49 kilograms.

The total number of parts of the fertilizer is calculated as;

total parts =  is 2+3+2

total parts = 7

The mass of potash in a bag of fertilizer is calculated by using the fraction of the mixture that is potash, and multiply it by the total weight of the bag.

The fraction of the mixture that is potash  =3/7.

The mass is calculated as follows;

mass = (3/7) x 49 kg

mass = 21 kg

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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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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.

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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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.

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 standard deviation of the data-set is given as follows:

s = 4.14.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The data-set in this problem is given as follows:

3, 4, 5, 7, 10, 12, 15.

Hence the mean is:

Mean = (3 + 4 + 5 + 7 + 10 + 12 + 15)/7

Mean = 8.

The sum of the differences squared for the data-set is given as follows:

SS = (3 - 8)² + (4 - 8)² + (5 - 8)² + (7 - 8)² + (10 - 8)² + (12 - 8)² + (15 - 8)²

SS = 120.

The standard deviation is given by the square root of the sum of the differences squared divided by the cardinality, hence:

s = sqrt(120/7)

s = 4.14.

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The required standard form of the function is f(x) = 3x² - 48x + 32.

The vertex form of a quadratic function is:

f(x) = a(x - h)² + k

Where (h, k) is the vertex of the parabola and a is a coefficient that determines the shape of the parabola.

In the given function, we can see that the vertex is at (8, -160) and a is 3. So we have:

f(x) = 3(x - 8)² - 160 (vertex form)

Expanding the square, we get:

f(x) = 3(x - 8)(x - 8) - 160

f(x) = 3(x² - 16x + 64) - 160

Distributing the 3, we get:

f(x) = 3x² - 48x + 192 - 160

Simplifying, we get:

f(x) = 3x² - 48x + 32

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Answer:

In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM.

A coin is tossed three times in a row. The observation is how the coin lands (H for heads or T for tails) on each toss. The sample space, using set notation, is:
S = {(H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T)}

A basketball player shoots three consecutive free throws. The observation is the result of each free throw (S for success, F for failure). The sample space, using set notation, is:
S = {(S, S, S), (S, S, F), (S, F, S), (S, F, F), (F, S, S), (F, S, F), (F, F, S), (F, F, F)}

A coin is tossed three times in a row. The observation is the number of times the coin comes up tails. The sample space, using set notation, is:
S = {0, 1, 2, 3}

A basketball player shoots three consecutive free throws. The observation is the number of successes. The sample space, using set notation, is:
S = {0, 1, 2, 3}

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Answer:

the answer is true. may I get brainliest

TRUE. The critical value of a hypothesis test is based on the researcher's selected level of significance.

The critical value of a hypothesis test is based on the researcher's selected level of significance. The level of significance represents the probability of rejecting a true null hypothesis, and it determines the critical value, which is the point beyond which we reject the null hypothesis. Therefore, the higher the level of significance, the lower the critical value, and the easier it is to reject the null hypothesis.
True, the critical value of a hypothesis test is based on the researcher's selected level of significance. The level of significance determines the threshold for rejecting or failing to reject the null hypothesis, and the critical value is a point on the test statistic's distribution that corresponds to this threshold.

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True. The cofactor expansion of the determinant of a matrix A along any row or column will yield the same result.

The cofactor expansion of the determinant of a matrix A along a row or a column is given by the formula:

```
det(A) = a1j * C1j + a2j * C2j + ... + anj * Cnj
```

where `aij` is the element in the ith row and jth column of A, and `Cij` is the (i,j)-cofactor of A.

The (i,j)-cofactor of A is defined as `(-1)^(i+j) * Mij`, where `Mij` is the determinant of the (n-1) by (n-1) matrix obtained by deleting the ith row and jth column of A.

To see why the cofactor expansion is independent of the row or column chosen, consider the formula for the determinant of a matrix obtained by transposing A:

```
det(A^T) = det([a11, a21, ..., an1],
               [a12, a22, ..., an2],
               ...,
               [a1n, a2n, ..., ann])
```

By the cofactor expansion along the first row of A^T, we have:

```
det(A^T) = a11 * C11' + a12 * C12' + ... + a1n * C1n'
```

where `Cij'` is the (i,j)-cofactor of A^T.

Now note that `Cij' = (-1)^(i+j) * Mji`, where `Mji` is the determinant of the (n-1) by (n-1) matrix obtained by deleting the jth row and ith column of A. But this is precisely the (j,i)-cofactor of A. Therefore, we have:

```
det(A^T) = a11 * C11 + a21 * C21 + ... + an1 * Cn1
```

which is the cofactor expansion of det A along the first column of A. Since the transpose of a matrix has the same determinant as the original matrix, we conclude that the cofactor expansion of det A along any row is equal to the cofactor expansion along any other row.

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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

Answer:

<

Step-by-step explanation:

because 42.18 is smaller than 42.7

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 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 oatmeal bar has a volume of 16 cubic inches.

A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.

The volume of a rectangular prism is expressed as;

V = w × h × l

V = base area × height

Where w is the width, h is height and l is length

To find the volume of the rectangular prism oatmeal bar, we need to multiply the base area by the height.

So, the volume of the oatmeal bar can be calculated as:

Volume = Base Area × Height

Volume = 4 in² × 4 in

Volume = 16 in³

Therefore, the volume of 16 cubic inches.

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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

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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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 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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Using the graph provided, the value f (-1) is -3; option B.

Using the graph provided, the value of f (-4) is -4; option C.

Using the graph provided, the value of x is when f(x)=3 is 2; option C.

A function from one set X to another allocates exactly one element of the other set Y to each element of X.

The set X is known as the function's domain, while the set Y is known as the function's codomain.

The 4 categories of functions are:

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Answer: To show that the number 52.470817081708 is rational, we need to express it as a ratio of two integers.

Let x = 52.470817081708. We can write x as a sum of its integer part and fractional part:

x = 52 + 0.470817081708

To convert the fractional part to a fraction, we can multiply both numerator and denominator by a power of 10 that will eliminate the decimal point. In this case, we can multiply by 10^12:

0.470817081708 = 470817081708 / 10^12

Therefore, we can write:

x = 52 + 470817081708 / 10^12

We can simplify the fraction by dividing both numerator and denominator by their greatest common divisor:

x = 52 + 163717 / 3125000

So we have expressed x as a ratio of two integers, 163717 and 3125000. Therefore, 52.470817081708 is a rational number.

The number 52.470817081708 is rational because it can be expressed as a ratio of two integers: 52470817081708

To show that 52.470817081708 is rational, we need to write it as a ratio of two integers.

First, we can see that the number has a repeating pattern of digits after the decimal point, which tells us that it can be expressed as a fraction. To do this, we'll count the number of decimal places in the repeating pattern, which is 12 in this case.

Next, we'll use the following formula to convert the repeating decimal to a fraction:

x = a + b/(10^n - 1)

Where:

- x is the repeating decimal
- a is the non-repeating part of the decimal (in this case, it's just the whole number 52)
- b is the repeating part of the decimal (in this case, it's the digits 470817081708)
- n is the number of digits in the repeating pattern (in this case, it's 12)

So plugging in our values, we get:

52.470817081708 = 52 + 470817081708/(10^12 - 1)

Simplifying the denominator, we get:

52.470817081708 = 52 + 470817081708/999999999999

To write this as a ratio of two integers, we'll simplify the fraction:

52.470817081708 = 52 + 235408540854/499999999999

So the number 52.470817081708 can be written as the fraction 52 + 235408540854/499999999999, which is a ratio of two integers. Therefore, we have shown that 52.470817081708 is rational.

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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: 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 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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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.