In general, how many variables are there in an experiment? O a. Many including independent and dependent variables n O b. One independent variable and one dependent variable O c. None because experiments are controlled for the best results O d. Moisture and temperature are the only variables

Answer:

15.6

Step-by-step explanation:

The mean weight of the team was found to be 222.47 pounds. The standard deviation was 28.32 pounds. 3 standard deviations below the mean were 136.83 pounds. Player A was approximately 0.20 standard deviations above the mean.

(i) Mean:

mean = (sum of all weights) / (number of weights) = (177 + 203 + 211 + 211 + 232 + 205 + 185 + 185 + 178 + 210 + 206 + 212 + 184 + 174 + 185 + 242 + 188 + 212 + 215 + 247 + 241 + 223 + 220 + 260 + 245 + 259 + 278 + 270 + 280 + 295 + 275 + 285 + 290 + 272 + 273 + 280 + 285 + 286 + 200 + 215 + 185 + 230 + 250 + 241 + 190 + 260 + 250 + 302 + 265 + 290 + 276 + 228) / (55) = 222.47

So, the mean weight of the team members of Football Team A was approximately 222.47 pounds.

(ii) Standard deviation:

We need to calculate the deviation from the mean for each weight and then find the square of the deviations. We can then find the sum of the squared deviations, divide by the number of weights minus 1, and then find the square root of the result.

Deviation from the mean:

177 - 222.47 = -45.47,

203 - 222.47 = -19.47,

211 - 222.47 = -11.47, and so on till,

228 - 222.47 = 5.53

Squared deviation:

(-45.47)^2 = 2070.5489,

(-19.47)^2 = 379.3409,

(-11.47)^2 = 131.4409, and so on till,

(5.53)^2 = 30.6409.

Sum of squared deviations:

sum = 2070.5489 + 379.3409 + 131.4409 + ... + 30.6409

sum = 30589.6409

standard deviation = square root of [(sum of squares of deviations from the mean) / (number of observations - 1)]

standard deviation = square root of [(30589.6409) / (55 - 1)]

standard deviation = 28.32

So, the standard deviation of the weights of the team members of Football Team A was approximately 28.32 pounds.

(iii) 3 standard deviations below the mean:

3 standard deviations below the mean = mean - (3 * standard deviation) = 222.47 - (3 * 28.32) = 136.83

So, a weight that is 3 standard deviations below the mean is approximately 136.83 pounds.

(iv) Player A's weight in terms of standard deviations:

Player A's weight = 228 pounds

Player A's deviation from the mean = 228 - 222.47 = 5.53

Player A's weight in terms of standard deviations = 5.53 / 28.32 = 0.20

So, Player A was approximately 0.20 standard deviations above the mean.

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Complete question: Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year. 177; 203; 211; 211; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230; 250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265 Assume the population was Football Team A. Find the following. (Round your answers to two decimal places.) (i) the population mean (ii) the population standard deviation (iii) the weight that is 3 standard deviations below the mean (iv) When Player A played football, he weighed 228 pounds. How many standard deviations above or below the mean was he?

Answer:

603.2

Step-by-step explanation: Use the radius of the cylinder and height and plug it into the volume formula for a cylinder and solve

Compare the prime factorizations:

25 • 5 • 11 = 5² • 5 • 11 = 5³ • 11

23 • 52 • 7 = 23 • (2² • 13) • 7 = 2² • 7 • 13 • 23

Clearly these products have no common prime factors, so their GCF is 1.

But I'm guessing this a multiple choice question, and the numbers you listed are already prime factorizations. In that case, we have

2⁵ • 5 • 11 = 2³ • 2² • 5 • 11

2³ • 5² • 7 = 2³ • 5 • 5 • 7

with the common factors underlined, so that the GCF is 2³ • 5.

To solve for the angles that satisfy the equation 9 tan 0+13= 2 tan 0 + 6, we need to first simplify the equation. We can start by moving all the terms involving tan 0 to one side of the equation and the constant terms to the other side. This gives us: 7 tan 0 = -7

Next, we can isolate tan 0 by dividing both sides by 7: tan 0 = -1 Now we can find the angles that satisfy this equation by using a calculator or reference table to find the angle whose tangent is -1. This angle is -45 degrees or 315 degrees, since the tangent function has a period of 180 degrees and the tangent of an angle in the second quadrant is negative. Therefore, the two angles that satisfy the equation are -45 degrees and 315 degrees.
To find all angles that satisfy the given equation, 9tan(θ)+13 = 2tan(θ)+6, first isolate the tan(θ) term:
9tan(θ) - 2tan(θ) = 6 - 13 7tan(θ) = -7 tan(θ) = -1 Now, use the arctangent function to find the principal angle (in degrees) that corresponds to a tangent value of -1: θ = arctan(-1) ≈ -45° Since tangent has a period of 180°, we can find all angles between 0° and 360° by adding multiples of 180° to the principal angle: θ1 = -45° + 180° = 135 θ2 = -45° + 360° = 315°
So, the angles that satisfy the equation are approximately 135° and 315°.

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The value of new_list is [1, 4, 9, 16].

The code given creates a new list called new_list by using a list comprehension to iterate over the values in my_list and squaring each value using the exponent operator (**).

This means that the first value in my_list (which is 1) is squared to 1, the second value (which is 2) is squared to 4, the third value (which is 3) is squared to 9, and the fourth value (which is 4) is squared to 16.

These squared values are then added to the new_list one by one, resulting in the final value of [1, 4, 9, 16].

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Answer:

1 : 2

Step-by-step explanation:

9 : 18

Both numbers are divisible by 9, thus:

9/9 : 18/2

[1 : 2]

Answer: 18

Step-by-step explanation:

In order to compute eigenvalues of symmetric matrices, Householder reflections are indeed used to transform the matrix into a tridiagonal form.

This is an important step because it simplifies the computation and takes advantage of the inherent properties of symmetric matrices.

However, Householder reflections alone cannot fully diagonalize the matrix. After obtaining the tridiagonal matrix using Householder reflections, other numerical methods, such as the QR algorithm or the Lanczos method, are required to perform the diagonalization. These methods iteratively transform the tridiagonal matrix into an even more simplified form, ultimately converging to a diagonal matrix.

The reason Householder reflections cannot fully diagonalize the matrix is because they are primarily designed to introduce zeros below the main diagonal, without altering the eigenvalues. The method aims to maintain orthogonality during the process, preserving the properties of symmetric matrices.

To complete the diagonalization, further iterative methods are necessary to isolate the eigenvalues along the main diagonal of the matrix.

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a. The number of bricks required for the top step is 795.

b. The total number of bricks required for all the steps is 2250.

(a) To find the number of bricks required for the top step, we need to use the information that each successive step requires two less bricks than the prior step.

So, we can start by finding the total number of bricks required for all the steps and then subtracting the number of bricks required for the bottom 29 steps.

The total number of bricks required for all the steps can be found using the formula for the sum of an arithmetic sequence:

S = n/2 * (a1 + an)

where S is the sum, n is the number of terms, a1 is the first term, and an is the nth term.

In this case, we have:

n = 30 (since there are 30 steps)

a1 = 100 (since the bottom step requires 100 bricks)

d = -2 (since each successive step requires 2 less bricks than the prior step)

an = a1 + (n-1)d = 100 + (30-1)(-2) = 40.

Plugging these values into the formula, we get:

S = 30/2 * (100 + 40) = 2250

So, the total number of bricks required for all the steps is 2250.

To find the number of bricks required for the top step, we subtract the number of bricks required for the bottom 29 steps from the total number of bricks required for all the steps:

number of bricks required for top step = total number of bricks - number of bricks for bottom 29 steps

= 2250 - [100 + 98 + 96 + ... + 6 + 4 + 2]

= 2250 - 1455

= 795

Therefore, the number of bricks required for the top step is 795.

(b) To find the total number of bricks required to build the staircase, we simply add up the number of bricks required for each step. We can use the formula for the sum of an arithmetic series again to simplify the calculation:

S = n/2 * (a1 + an)

where S is the sum, n is the number of terms, a1 is the first term, and an is the nth term.

In this case, we have:

n = 30 (since there are 30 steps)

a1 = 100 (since the bottom step requires 100 bricks)

d = -2 (since each successive step requires 2 less bricks than the prior step)

an = a1 + (n-1)d = 100 + (30-1)(-2) = 40

Plugging these values into the formula, we get:

S = 30/2 * (100 + 40) = 2250

Therefore, the total number of bricks required to build the staircase is 2250.

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Answer:

405 bagels 27 an hour

Step-by-step explanation:

this is because when you divide 270 by 10 you get 27 which is how much per hour then multiply the # of bagels and the # of hours you get is 405. In other words you first want to know how many bagels it took to get to 270 bagels in 10 hours.Hope it helped.

The flour that Karina's mother has won't be enough for the recipe and she requires extra 3/20 together with the quality owed by the mother.

Flour is defined as a food product that is the main ingredient for baking of different recipes such as cakes, breads, plate pies just to mention a few.

The amount of flour needed by Karina for the recipe= 3/5 = 0.6.

The amount of flour owed by the mother = 3/7 = 0.45

The difference between the available flour = 0.6 - 0.45 = 0.15

This shows that extra flour of 0.15 or 3/20 is needed in addition to the quantity of flour owed by the mother to be able to make the recipe.

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Sarah's company started out with a $350 value and is currently changing at a rate of $100 annually.

The annual fee is expressed as an equation in slope-intercept form:

y = 100x + 350.

y = mx + b, where m is the line's slope and b is its y-intercept, is the formula for a straight line.

Given details:

The table displays the prices that Sarah charged each client during the course of her business's first two years:

Year                            Annual Dog-walking Fee

2010                            $350

2014                            $750

A.

Sarah has so increased the cost by $400 over the past four years.

For Sarah's company, its rate of change called slope will be,

m = 750 - 350 / 4

m = 100

Therefore, Sarah is raising the cost by $100 yearly.

Due to the payment she received for the first year, the calculated values of a business is $350.

B. Define x as the period of time that has passed since she began her business in 2010.

Consequently, the annual fee equation can be expressed in slope-intercept form as,

y = mx + c

where y stands for the cost she must pay after x years.

Her company's baseline value is therefore $350, and its rate of change is $100 annually.

The annual fee is expressed as an equation in slope-intercept form.: y = 100x + 350.

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Answer:

B

Step-by-step explanation: dilated means get bigger so (0,10) times 3 is (0,30) and (8,6) times 3 is (24,18) and (4,2) times 3 is (12,6)

pls mark me branliest

Answer: B

Step-by-step explanation:

it's very much correct :)

The equation of the line is y = -1x + -1, where m is the slope and c is the y-intercept.

The equation of a line can be found by using the two given points and the slope-intercept formula, y = mx + c. The slope (m) of a line is the change in y divided by the change in x. To find the slope, we subtract the y-coordinates of the two points given, (-3 - (-4)) and divide by the change in x, (3 - 1). This gives us -1 as the slope of the line. The y-intercept (c) is the point at which the line crosses the y-axis. To find the y-intercept, we can substitute the given x-coordinate of one of the points, 1, and its y-coordinate, -3, into the equation. This gives us the y-intercept of -1. Therefore, the equation of the line is y = -1x + -1. This equation can be used to plot any point on the line and to determine the x- and y-coordinates of any point on the line.

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the answer is v= -5x + 1136

A point that is √2 away from (-1, 5) is (-1 + √2, 5)

Here, we have,

to name a point that is √2 away from (-1, 5):

The point is given as:

(x, y) = (-1, 5)

The distance is given as:

Distance = √2

The distance is calculated as:

Distance = √(x2 - x1)^2 + (y2 - y1)^2

So, we have:

√(x + 1)^2 + (y - 5)^2 = √2

Square both sides

(x + 1)^2 + (y - 5)^2 = 2

Let y = 5

So, we have:

(x + 1)^2 + (5 - 5)^2 = 2

This gives

(x + 1)^2 = 2

Take the square root

x = -1 + √2

Hence, a point that is √2 away from (-1, 5) is (-1 + √2, 5)

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Answer:

5

Step-by-step explanation:

Basically, we need to find the number that 443,520 is divisible by out of our four choices. Let's try to divide 443,530 by each of our choices.

443,530 / 3 = 147843.3333.....

443,530 / 4 = 110882.5

443,530 / 5 = 88706

Therefore, the answer is 5.

Another way to solve this question is to apply the divisibility rules of the four choices. Automatically, if you know that the divisibility rule of 5 is that the number must end in either 5 or 0, you will know that the answer is 5 because the number 443520 ends in 0.

Answer: the bird went 128 metres in 15 sec and took 4 sec to descend

Step-by-step explanation: plz mark me brainliest

Answer:

To see why, we can compare the graphs of the two functions. The graph of ƒ(x) = e^x is an exponential function that starts at the point (0,1) and increases rapidly as x increases. The graph of g(x) = 5e^x is also an exponential function, but it starts at the point (0,5), which is five times higher than the starting point of ƒ(x). This means that g(x) is a vertical stretch of ƒ(x) by a factor of 5.

Option a) g(x) = e^x + 7 is a vertical shift of ƒ(x) by 7 units, but it does not represent a vertical stretch.

Option b) g(x) = 1/3e^x is a vertical compression of ƒ(x) by a factor of 1/3, rather than a vertical stretch.

Option d) g(x) = e^4x represents a horizontal stretch of ƒ(x) by a factor of 1/4, but it does not represent a vertical stretch.

We need to verify the equality 1 [f(x) + g(x)] dx = f(x) dx + g(x) dx for each pair of functions given: (a) f(x) = x, g(x) = 1, (b) f(x) = 1, g(x) = x², (c) f(x) = e^x, g(x) = 1, and (d) f(x) = x².

(a) f(x) = x, g(x) = 1:

Using the properties of integration, we have ∫[f(x) + g(x)] dx = ∫(x + 1) dx = (x²/2 + x) + C.

Also, ∫f(x) dx = ∫x dx = x²/2 + C₁, and ∫g(x) dx = ∫1 dx = x + C₂.

Adding the integrals, we get f(x) dx + g(x) dx = (x²/2 + C₁) + (x + C₂) = x²/2 + x + C.

Therefore, 1 [f(x) + g(x)] dx = f(x) dx + g(x) dx is verified.

(b) f(x) = 1, g(x) = x²:

Using the same approach, we have ∫[f(x) + g(x)] dx = ∫(1 + x²) dx = (x + x³/3) + C.

Also, ∫f(x) dx = ∫1 dx = x + C₁, and ∫g(x) dx = ∫x² dx = x³/3 + C₂.

Adding the integrals, we get f(x) dx + g(x) dx = (x + C₁) + (x³/3 + C₂) = x + x³/3 + C.

Therefore, 1 [f(x) + g(x)] dx = f(x) dx + g(x) dx is verified.

(c) f(x) = e^x, g(x) = 1:

Using the same approach, we have ∫[f(x) + g(x)] dx = ∫(e^x + 1) dx = (e^x + x) + C.

Also, ∫f(x) dx = ∫e^x dx = e^x + C₁, and ∫g(x) dx = ∫1 dx = x + C₂.

Adding the integrals, we get f(x) dx + g(x) dx = (e^x + C₁) + (x + C₂) = e^x + x + C.

Therefore, 1 [f(x) + g(x)] dx = f(x) dx + g(x) dx is verified.

(d) f(x) = x²:

Using the same approach, we have ∫[f(x) + g(x)] dx = ∫(x² + x²) dx = (2x³/3) + C.

Also, ∫f(x) dx = ∫x² dx = x³/3 + C₁, and ∫g(x) dx = ∫x² dx = x³/3 + C₂.

Adding the integrals, we get f(x) dx + g(x) dx = (x³/3 + C₁) + (x³/3 + C₂) = 2x³/3 + C.

Therefore, 1 [f(x) + g(x)] dx = f(x) dx + g(x) dx is verified.

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Answer:

Step-by-step explanation:

Problem 1

Set Up the Proportion

3 cm / 8 km = x / 20 km                Cross multiply

3*20 = 8x                                        Combine the left

60 = 8x                                           Divide by 8

60/8 = x

7 4/8  = x

7 1/2 km = x

7.5 km  = x

Problem 2

3 cm / 8km = 12 cm / x                  Cross multiply

3x = 12 * 8                                      Combine the right

3x = 96                                          Divide by 3

3x/3 = 96/3

x = 32 km

Answer: 10 hours

Let's use the fact that the number of caterpillars eating the bush and the time it takes to eat the bush are inversely proportional to each other, since all the caterpillars eat at the same pace.

This means that if we increase the number of caterpillars, the time it takes to eat the bush will decrease, and vice versa.

Now, we can set up the proportion:

number of caterpillars * time to eat the bush = constant ( fixed number )

We know that 36 caterpillars can eat the bush in 15 hours, so the constant is:

36 * 15 = 540

To find how long it would take 54 caterpillars to eat the same bush, we can plug in the values into the formula and solve for the time:

54 * t = 540

t = 540 / 54

t = 10

It would take 54 caterpillars 10 hours to eat all the leaves on the bush in Violetta's front yard

10 HOURS

Step-by-step explanation:

hope this helps!1!1!!!!

Answer:

33% or with 10th place decimal 33.3%

Step-by-step explanation:

1/3 has a continuous decimal form of .333333...

So, it is usually rounded to .33

Hope this helps!

Answer: 33.33%

Step-by-step explanation:

Option (c) is the correct option.

9/10 is rational and a real no. but not an integer.

What is a rational number?

A number with the form p/q, where p and q are integers and q is not equal to 0, is said to be rational.

What is an integer?

In the category of real numbers are irrational numbers, fractions, and rational numbers like positive and negative integers.

What is a real number?

Integers, which can be both negative and positive and include zero, are numbers without a decimal or fractional component.

Our objective is to find a number which is rational and a real number but not an integer.

√2 is not rational and not a real number.

-5 is rational and a real number but It is an integer.

9/10 is rational and a real number and also not an integer.

Hence, (c) is the correct option.

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Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. The value of the account on January 1, 2021, would be $2,331.57.

To calculate the value of the account on January 1, 2021, we need to consider the compounding interest for each year.

First, we calculate the value of the initial deposit after three years (12 quarters) using the formula for compound interest:

Principal = $1,000

Rate of interest per period = 8% / 4 = 2% per quarter

Number of periods = 12 quarters

Value after three years = Principal * (1 + Rate of interest per period)^(Number of periods)

                           = $1,000 * (1 + 0.02)^12

                           ≈ $1,166.41

Next, we calculate the value of the additional $1,000 deposit made on January 1, 2019, after two years (8 quarters):

Principal = $1,000

Rate of interest per period = 2% per quarter

Number of periods = 8 quarters

Value after two years = Principal * (1 + Rate of interest per period)^(Number of periods)

                         = $1,000 * (1 + 0.02)^8

                         ≈ $1,165.16

Finally, we add the two values to find the total value of the account on January 1, 2021:

Total value = Value after three years + Value after two years

                ≈ $1,166.41 + $1,165.16

                ≈ $2,331.57

Therefore, the value of the account on January 1, 2021, is approximately $2,331.57.

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