explain the process of finding the mean of a data set in your own words.

The indicated probabilities. f(x) = x in the interval [0, 2] is 1.

Explanation: -

Given the probability density function f(x), we need to find the indicated probabilities over the interval [0, 2].

f(x) is defined as follows:
f(x) = x if 0 ≤ x ≤ 1
f(x) = 2 - x if 1 ≤ x ≤ 2

Step 1: Check if f(x) is a valid probability density function.
To be a valid pdf, the integral of f(x) over the entire interval should be equal to 1.

Let's check that:

∫(0 to 1) x dx + ∫(1 to 2) (2 - x) dx

For the first integral, we have:
∫x dx = (1/2)x^2 evaluated from 0 to 1 = (1/2)(1)^2 - (1/2)(0)^2 = 1/2

For the second integral, we have:
∫(2 - x) dx = 2x - (1/2)x^2 evaluated from 1 to 2 = (2(2) - (1/2)(2)^2) - (2(1) - (1/2)(1)^2) = 1/2

Total probability = 1/2 + 1/2 = 1. Since the integral is equal to 1, f(x) is a valid probability density function.

Step 2: Find the probabilities for the interval [0, 2].
Since we're looking for probabilities over the entire interval, the answer is simply the integral of f(x) over [0, 2], which we've already found to be equal to 1.

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Answer:

y=2/3x+4

Step-by-step explanation:

The sequence of pseudorandom numbers starting with x_0=3 and generated by the linear congruential generator x_(n+1)=(4x_n+1) mod 7 is:
3, 5, 6, 3, 5, 6, 3, 5, 6, 3, ... (repeating)

The sequence of pseudorandom numbers generated using the linear congruential generator x_(n+1)=(4x_n+1) mod 7 with seed x_0=3 is:

x_0 = 3
x_1 = (4x_0+1) mod 7 = (4*3+1) mod 7 = 5
x_2 = (4x_1+1) mod 7 = (4*5+1) mod 7 = 6
x_3 = (4x_2+1) mod 7 = (4*6+1) mod 7 = 3
x_4 = (4x_3+1) mod 7 = (4*3+1) mod 7 = 5
x_5 = (4x_4+1) mod 7 = (4*5+1) mod 7 = 6
x_6 = (4x_5+1) mod 7 = (4*6+1) mod 7 = 3
x_7 = (4x_6+1) mod 7 = (4*3+1) mod 7 = 5
x_8 = (4x_7+1) mod 7 = (4*5+1) mod 7 = 6
x_9 = (4x_8+1) mod 7 = (4*6+1) mod 7 = 3
and so on...

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Answer:

1. How to Solve using Algebra

Make both equations into "y =" format.

Set them equal to each other.

Simplify into "= 0" format (like a standard Quadratic Equation)

Solve the Quadratic Equation!

Use the linear equation to calculate matching "y" values, so we get (x,y) points as answers.

Algebraic method is more easy to do

2. linear functions have constant first differences. quadratic functions have constant second differences. exponential functions have a constant ratio.

A net for the pyramid is drawn and labeled. The surface area of the pyramid is found using the formula and the given measurements is 96 square units. The number of boxes of papers Nico can pack into the back of his truck is 135 boxes.

The labeled pyramid is shown in image.

To find the surface area of the pyramid, we need to find the area of each face and add them together. The area of the base is a square with side length 6, so its area is

6² = 36 square units.

The area of each triangular face can be found by using the formula for the area of a triangle, which is 1/2 times base times height.

The height of each face is the slant height of the pyramid, which we can find using the Pythagorean Theorem.

The base of each face is one of the sides of the base of the pyramid, which has length 6.

The slant height of the pyramid can be found by drawing the height from the apex to the center of the base and then using the Pythagorean Theorem to find the length of the hypotenuse of the right triangle formed by the height, half the base (3), and the slant height. We get

slant height = √(4² + 3²) = 5

So the area of each triangular face is 1/2 times base times height = 1/2 times 6 times 5 = 15 square units. Since there are four triangular faces, the total surface area of the pyramid is

4(15) + 36 = 96 square units.

Therefore, the surface area of the pyramid is 96 square units.

The volume of one box of papers is 1.5 x 1.5 x 1.5 = 3.375 cubic feet. The volume of the truck is 9.5 x 6 x 8 = 456 cubic feet. The number of boxes Nico can pack into the truck is therefore

456 / 3.375 = 135.11

Since Nico cannot pack a fraction of a box, he can fit a maximum of 135 boxes of papers in his truck.

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Gustavo's percent increase in points is 75%.

To calculate the percent increase, we need to find the difference between the new value and the original value, divide that difference by the original value, and then multiply by 100.

Gustavo's original score was 8000 points, and his new score is 14,000 points. The difference between the new score and the original score is 14,000 - 8000 = 6000 points.

To find the percent increase, we divide the difference by the original score: 6000 / 8000 = 0.75.

To express this as a percentage, we multiply by 100: 0.75 * 100 = 75%.

Therefore, Gustavo's percent increase in points is 75%. He has increased his points by 75% from 8000 to 14,000 points.

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Answer:

11 elevenths equal a whole meatloaf

11/11=1

Answer:

11 11ths

Step-by-step explanation:

11/11 = 1 whole

The expression that best estimates 6 3/4 divided by 1 2/3 is 7/2. 6 3/4 (or 6.75) divided by 1 2/3 (or 1.66...) comes out to 4 1/20 (or 4.05). The closest value to this in the options available is 7/2 (or 3.5). This answer is only .55 away from the correct value, while the rest of the options are far less close.

Answer:

7/2 or

7 dived by 2

Step-by-step explanation:

bruh A

Answer:

C)

Step-by-step explanation:

The correct answer is C: Tony did not use the property correctly because he did not multiply every term on both sides of the equals sign by 1/4.

To solve the equation 4x = 12x + 20, Tony used the multiplicative property of equality but made an error in the application. The correct approach would be to multiply every term on both sides of the equals sign by the reciprocal of the coefficient of x, which is 1/4 in this case.

However, Tony only multiplied one term on each side by 1/4, resulting in equation x = 3x + 20. This action is incorrect because it does not apply the property to every term containing x. To solve the equation correctly, Tony should have multiplied both sides by 1/4, resulting in x/4 = (3x + 20)/4.

Answer:

96 cm³

Step-by-step explanation:

V=1/2×6×8×4=196/2=96cm³

The implicit solution to the differential equation yy' + x = 3 √(x^2 + y^2) is given by x^2 + y^2 = (x^2 + y^2)^(3/2) + C, where C is a constant of integration.

To solve the given differential equation, we'll rewrite it in a standard form. Dividing both sides of the equation by √(x^2 + y^2), we have yy'/(√(x^2 + y^2)) + x/(√(x^2 + y^2)) = 3. Notice that the left side of the equation represents the derivative of √(x^2 + y^2) with respect to x. Applying the chain rule, we obtain d(√(x^2 + y^2))/dx = 3. Integrating both sides with respect to x, we get √(x^2 + y^2) = 3x + C, where C is a constant of integration.

Squaring both sides of the equation yields x^2 + y^2 = (3x + C)^2. Simplifying further, we have x^2 + y^2 = 9x^2 + 6Cx + C^2. Rearranging the terms, we obtain x^2 + y^2 - 9x^2 - 6Cx - C^2 = 0, which can be rewritten as x^2 + y^2 = (x^2 + y^2)^(3/2) + C. Thus, this equation represents the implicit solution to the given differential equation.

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The difference in the cost will be $3. It is obtained by calculating the total cost of both the restaurant.

A cost is the worth of money that has been used to produce something or supply a service and is thus no longer accessible for use in production, research, retail, or accounting.

In business, a cost can be an acquisition cost, in which case the money spent to acquire it is reported as a cost.

If the cost of pizza is $ x and the delivery fees is $ y;

Cost of pizza at the restaurant 1;

C₁=X+Y

C₁=$10.99 +  $3.00 = $13.99

For restaurant 2;

C₂=X+Y

C₂=$10.99 +  $0 = $10.99

The difference in the cost will be;

\(\rm C= C_1-C_2 \\\\\ 13.99-10.99 \\\\ C= \$ \ 3\)

Hence, the  difference in the cost will be $3.

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Answer: the rectangle is 23 x 41

Step-by-step explanation:

x = length

2x - 5 =  width

A = length x width = (x)(2x-5) = 943

2\(x^{2}\) - 5x - 943 = 0

use quadratic equation to solve for x:

a = 2, b = -5, c = -943

roots are 23, -20.5

x = 23 (length)

2x - 5 = 2(23) - 5 = 46 - 5 = 41 (width)

Answer:

Step-by-step explanation:

Perimeter is all sides added together...

X+3+2x-1+3x+4

Combine like terms

X+2x+3x.. 6x

3-1+4.. 2+4.. 6

Answer:

6x+6

Answer: 10 ¹/₂ miles per gallon

Step-by-step explanation:

The gas mileage of the camper refers to the distance (in miles for this question) that the camper can travel on 1 gallon of gas.

The camper can travel 3¹/₂ miles on ¹/₃ gallons so the mileage is:

= Distance traveled/ Gallons used

= 3¹/₂ ÷ ¹/₃

= 7/2 * 3/1

= 21 / 2

= 10 ¹/₂ miles per gallon

32

Step-by-step explanation:

32

Answer:

the answer is 1/5 x as a approximate equation

Step-by-step explanation:

Answer: x=5

Step-by-step explanation:

The correct statement regarding whether the events are independent is given as follows:

The events are not independent, since P(A) x P(B) is different of P(A and B).

Two events are independent events if the multiplication of the probabilities of each event is equals to the probability of both events.

The multiplication of the probabilities in this problem is given as follows:

5/7 x 80/90 = 400/630.

The probability of both events in this problem is given as follows:

400/637.

Different probabilities, hence the events are not independent.

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Answer:

£10.80

Step-by-step explanation:

20% = \(\frac{20}{100}\) = 0.2 , then

£54 × 0.2 = £10.80

The probability is a fraction of 43/205 which is approximately 0.2098.

To calculate the probability of the next person who leaves the lecture having gray hair, we need to know the total number of people who left the lecture, as well as the number of people who have gray hair.

From the given data, we can see that there were a total of 50+40+39+33+43 = 205 people who left the lecture. We also know that there were 43 people who had gray hair.

Therefore, the probability of the next person who leaves the lecture having gray hair is:

P(gray hair) = (number of people with gray hair) / (total number of people who left the lecture)

P(gray hair) = 43/205

P(gray hair) ≈ 0.2098

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Answer:

180 cups of hot chocolate and 95 cups of coffee

Step-by-step explanation:

multiply the cups by the price and add them together and it adds up to the total sales they got

To estimate the total number of families who rent in the city, we can use the formula: Total number of renting families = (Number of households sampled / Total number of households) x Number of renting households sampled


Step 1: Calculate the sample size.
Since it's a 1-in-50 systematic sample, you would divide the total number of households by 50.
Sample size = N / 50 = 15,200 / 50 = 304 households.

Step 2: Sum the values of yi.
For this step, you would need the actual survey data, which is not provided. But let's say you have that data and you sum the yi values. Let's assume the sum of yi is S.

Step 3: Estimate the total number of families who rent.
To estimate the total number of families who rent, you would divide the sum of yi by the sample size, and then multiply by the total number of households.
Estimated renters = (S / 304) * 15,200.

Step 4: Place a bound on the error of estimation.
To place a bound on the error of estimation, you would need to calculate the standard error (SE) and use the margin of error formula. The standard error formula for this type of survey is:

SE = sqrt((p * (1 - p)) / n)

Where p is the proportion of renters in the sample (S / 304) and n is the sample size (304).

Next, you would multiply the SE by a z-score that corresponds to a desired confidence level (e.g., 1.96 for a 95% confidence interval) to find the margin of error. Then, you could calculate the lower and upper bounds of the estimation.

Please note that I cannot provide a specific numerical answer since the yi values are not provided, but these steps will help you estimate the total number of families who rent and place a bound on the error of estimation once you have the data.

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Answer:

133.33, 200, 266.66

Step-by-step explanation:

GIven data

This is a ratio problem, and we will use the part to all method to get the solution

The given ratio is

= 2: 3: 4​

the total ratio

=2+3+4

=9

Hence the first part is

2/9= x/600

cross multiply

9x= 1200

x= 1200/9

x= 133.33

The second part

3/9=x/600

1/3=x/600

3x=600

x=200

The third part

4/9=x/600

4/9=x/600

9x=600*4

9x=2400

x=2400/9

x=266.66

Therefore the figures are

133.33, 200, 266.66

Conduct a one-tailed hypothesis test with a significance level of 0.005 to determine if the population mean is greater than 78.5.

To test the claim that the population mean is greater than 78.5, you can conduct a one-tailed hypothesis test with a significance level of α = 0.005. Since you believe the population is normally distributed but do not know the standard deviation, you can use the t-distribution.

Calculate the sample mean and sample standard deviation from a representative sample. Then, calculate the t-statistic using the formula: t = (sample mean - hypothesized mean) / (sample standard deviation / √n). Compare the calculated t-statistic to the critical t-value for the given significance level and degrees of freedom (based on sample size minus 1).

If the calculated t-statistic exceeds the critical t-value, reject the null hypothesis and conclude that there is evidence to support the claim that the population mean is greater than 78.5.

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Answer:

350 ml

Step-by-step explanation:

there are 3 sugar parts so each one is worth 70

70x5 = 350

Anna wiII need 882 square inches οf wrapping paper tο wrap aII three gifts.

Surface area is the tοtaI area that the surface οf an οbject οccupies. It is the sum οf the areas οf aII the faces οr surfaces οf the οbject.

Since the bοxes are cubes with a side Iength οf 7 inches, each face οf the cube has an area οf 7 x 7 = 49 square inches. Each bοx has six faces, sο the tοtaI surface area οf each bοx is 6 x 49 = 294 square inches.

Since Anna has three bοxes, the tοtaI surface area οf the three bοxes is 3 x 294 = 882 square inches.

Therefοre, Anna wiII need 882 square inches οf wrapping paper tο wrap aII three gifts.

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

point 01 (-3, 3)

point 02 (2 , -32)

Step 02:

equation of the line (y = mx + b)

slope = m

(y - y1) = m (x - x1)

(y - 3) = -7 (x - (-3))

y - 3 = -7 (x + 3)

y = -7x - 21 + 3

y = -7x - 18

The answer is:

y = -7x - 18

Answer:

y = 156 degrees

Step-by-step explanation:

90-66=24

180-24= 156

Answer:

y is 156°.

Step-by-step explanation:

We know ∠FED is 66°, and ∠FED & ∠DEB (or z) equal 90° degrees. That means ∠z is 24° degrees as is ∠x, since it is adjacent to ∠z. ∠x and ∠y are supplementary, which meant they equal 180°. Subtract 24° (∠x's measurement ) from 180° to get your final answer of y being 156°.

I hope this helps!~

Given, the equation that represents the height of an object:

First, we will find the velocity of the object which is the first derivative of the height using the method of the limits

We will find the value of the function y(t) when t = 3, and when t = 3+h

Substitute y(3+h) and y(3) into the expression of the limit

Where a = 0

d) compute the instantaneous velocity at t = 3

So, the answer will be:

Answer:

= 12x + -15/2

Step-by-step explanation:

4x + 1/4 + 8x + -31/4

(4x+8x) + (1/4 + -31/4)

=12x+ -15/2

Answer:

12x - 15/2

Step-by-step explanation:

(4x + 1/4) + (8x - 31/4)

4x + 1/4 + 8x - 31/4

4x + 8x

12x + 1/4 - 31/4

1/4 - 31/4

12x -15/2