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You want to know the number of students in your school who play a musical instrument. You survey the first 15 students who arrive at a band class.
a. What is the population of your survey? the sample?
b. Is the sample reasonable? Explain.

Determine whether you would survey the population or a sample. Explain.

3) You want to know the average height of seventh-graders in Tallahassee.
4) You want to know the favorite types of music of students in your homeroom.
5) You want to know the number of students in Florida who have summer jobs

By collecting data at these random times, you can obtain a more representative sample of the variable you are trying to determine. Analyzing this data can help identify trends or patterns, leading to a better understanding of the subject being studied.

I understand that you want to determine something by dividing the day into three parts: morning, afternoon, and evening, and taking measurements at random times. To do this, you can use a systematic approach.
First, divide the day into the three specified parts. For example, morning can be from 6 AM to 12 PM, afternoon from 12 PM to 6 PM, and evening from 6 PM to 12 AM. Next, select random time points within each part of the day to take the desired measurements. This can be achieved by using a random number generator or simply choosing times that vary each day.
By collecting data at these random times, you can obtain a more representative sample of the variable you are trying to determine. Analyzing this data can help identify trends or patterns, leading to a better understanding of the subject being studied.

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the missing coefficients are approximately c = 0.5, d = 0.7, e = -1.6, and f = -9.9.

To determine the missing coefficients in the equation x² + cy² + dx + ey + f = 0, we can use the given points on a vertical ellipse and substitute them into the equation. This will create a system of equations that we can solve to find the values of c, d, e, and f.

Let's substitute the given points into the equation:

For the point (3.75, 0):

(3.75)² + c(0)² + d(3.75) + e(0) + f = 0

14.06 + 3.75d + f = 0            -- Equation 1

For the point (0, 2.71):

(0)² + c(2.71)² + d(0) + e(2.71) + f = 0

7.35c + 2.71e + f = 0            -- Equation 2

For the point (1, -7):

(1)² + c(-7)² + d(1) + e(-7) + f = 0

1 + 49c + d - 7e + f = 0        -- Equation 3

For the point (-1, -5.725):

(-1)² + c(-5.725)² + d(-1) + e(-5.725) + f = 0

1 + 32.86c - d - 5.725e + f = 0 -- Equation 4

We now have a system of equations with four variables (c, d, e, f). By solving this system, we can find the missing coefficients.

Solving the system of equations using a numerical solver or by hand, we find the following approximate values:

c ≈ 0.5

d ≈ 0.7

e ≈ -1.6

f ≈ -9.9

Therefore, the missing coefficients are approximately c = 0.5, d = 0.7, e = -1.6, and f = -9.9.

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Answer:

k = 3 or k = -4

(Anyone can correct me if I'm wrong)

Step-by-step explanation:

\(2x=ky+2\to\ eq1\\(k+1)x=6y-3\to\ eq2\\$Change to this form: $y=mx+c\\ky=2x-2\\y=\frac{2x-2}{k}\\$gradient of eq1: $\frac{2}{k}\\6y=(k+1)x+3\\y=\frac{(k+1)x+3}{6}\\y=\frac{k+1}{6} x+\frac{3}{6}\\y= \frac{k+1}{6} x+\frac{1}{2}\\$gradient of eq1: $\frac{k+1}{6}\\$Since gradient, m, is the same for both lines,$\\\frac{2}{k}=\frac{k+1}{6}\\12=k^{2}+k\\k^{2}+k-12=0\\(k-3)(k+4)=0\\k=3 $ or $ k=-4\)

The smaller the p-value, the stronger the evidence against the Null Hypothesis is because a small p-value suggests that the null hypothesis should be rejected.

The p-value is the probability that the observed data occurred purely by chance if the null hypothesis is true, and it is a measure of the strength of the evidence against the null hypothesis.

When p is small, it implies that the possibility of obtaining data as extreme or more extreme than that observed if the null hypothesis is true is very low. This low probability indicates that the null hypothesis is unlikely to be true, and hence, the alternative hypothesis is more likely to be true.

So, when we have a small p-value, we reject the null hypothesis and accept the alternative hypothesis. On the other hand, if the p-value is large, the data do not provide sufficient evidence to reject the null hypothesis.

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Answer:

What is the set of whole numbers?

Step-by-step explanation:

Answer: 50 feet

Step-by-step explanation: it went 40 feet to get to the surface of the water then it went and extra 10 feet above water so 40+10=50

If function \(f(x) = 7x - 8\)  and  \(g(x) =4\) then the answer is \((fog)(-1) = -36.\)

In mathematics, a function is a relation between two sets of values, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). The output value of a function is determined by its input value and any relevant rules or formulas.

Formally, a function can be defined as follows: Let X and Y be two non-empty sets. A function f from X to Y is a rule or formula that assigns to each element x in X a unique element y in Y, denoted by f(x), such that for any two elements x1 and x2 in X, if x1 = x2, then f(x1) = f(x2). The set X is called the domain of the function, and the set Y is called the codomain or range of the function.

Functions can be represented graphically, algebraically, or in tabular form. The graph of a function shows how the output value of the function varies with the input value, and can be used to visualize the behaviour of the function. The algebraic representation of a function can be given by a formula or equation that expresses the output value in terms of the input value. A tabular representation of a function shows the input-output pairs in a table.

Functions are used in many areas of mathematics, science, engineering, and economics to model and describe relationships between variables. They are also used in practical applications, such as in computer programming, where they are used to define algorithms and data structures.

We need to find (fog)(-1) = f(g(-1)).

First, we find g(-1):

g(-1) = 4(-1) = -4

Then, we plug in g(-1) into f:

f(g(-1)) = f(-4) = 7(-4) - 8 = -36

Therefore, (fog)(-1) = -36.

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Answer:

Step-by-step explanation:

Transform your log to exponent form:

Base is 3, exponent is 3 and the parentheses is what it equals

3³=2x-5            >solve

27=2x-5             >add 5 to both

32=2x               >divide 2 to both

x=16

The values of u, v, u, v, and d(u, v) are given below:(a) u, v = 171(b) ||u|| = 13(c) ||v|| = 17(d) u/||u|| = (-12/13, 5/13), v/||v|| = (-8/17, 15/17)(e) d(u, v) = 2√29

Given inner product defined on Rn, u = (−12, 5), v = (−8, 15) and u, v = u · v. The values of u, v, u, v, and d(u, v) are to be calculated.

Solution: Given inner product defined on Rn, u = (−12, 5), v = (−8, 15) and u, v = u · v.

The dot product of u and v is given by u . v= (-12 * -8) + (5 * 15)u . v= 96 + 75u . v= 171

Now, we have to calculate the norm of u and v, which can be calculated as follows: ||u|| = √u1² + u2²||u|| = √(-12)² + 5²||u|| = √144 + 25||u|| = √169||u|| = 13

Similarly,||v|| = √v1² + v2²||v|| = √(-8)² + 15²||v|| = √64 + 225||v|| = √289||v|| = 17

Now, we have to calculate the unit vector of u and v. T

he unit vector of u and v is given by: u/||u|| = (-12/13, 5/13)v/||v|| = (-8/17, 15/17)Now, we have to calculate d(u, v). The formula to calculate d(u, v) is given by: d(u, v) = ||u - v||d(u, v) = √(u1 - v1)² + (u2 - v2)²d(u, v) = √(-12 - (-8))² + (5 - 15)²d(u, v) = √(-4)² + (-10)²d(u, v) = √16 + 100d(u, v) = √116d(u, v) = 2√29

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Answer:

13.9

Step-by-step explanation:

3rd side = a

a² + b² = c²

a² + 8² = 16²

a² + 64 = 256

a² = 192

\(\sqrt{a^2} =\sqrt{192}\)

a = 13.856

Rounded to tenths:

13.9

Answer: NO

Step-by-step explanation:

The line that separates the two part is a dashed line which means that the point on the lines are not in the solution

EXTRA: ONLY IF IT IS A SOLID LINE, THE POINTS WILL BE A SOLUTION

(-2,0) is on the dashed line, so it is not a solution

Answer:

b = 452.16 cm^3

Step-by-step explanation:

V = (pi)(r^2)(h) --> V= (3.14)(4^2)(9) --> 452.16

Answer:

B

Step-by-step explanation:

Answer:

x/1 is the same as x

Step-by-step explanation:

Answer:

f(7) = 6

Step-by-step explanation:

f(7) is the y coordinate of the point on the given graph of y = f(x), whose x coordinate is 7.

From the graph of y = f(x), we see that f(7) = 6.

Answer:

∠x = 60°

Step-by-step explanation:

first:

∠a = 60° was given

the sides on each side of ∠a are equal so their opposite angles are equal also.

The sum of the interior angles of any triangle is 180°

The angles opposite ∠a are (180° - 60°)/2 = 60° each

Second:

∠b = 60° was given

so the angles opposite ∠b are also 60° each

Third:

the 2 angles opposite x are both 60° each because they are both vertical angles to 60°

That leaves ∠x  to be 180° - 60° - 60° = 60°

When two rotations are performed on a single figure, the order of the rotations never affect the location of the final image.

In mathematics, rotation is defined as that of the circular movement of an object around with a center, an axis, or a fixed point. Since rotations are rigid transformations, the size, length, shape, and angle measurements of the figure are maintained.

Precession, nutation, and intrinsic rotation are the names of these rotations. The rotation of the earth on its axis is one of the greatest instances of rotation in nature.

There are broad guidelines for rotations of 90, 180, and 270 degrees around the origin that are both clockwise and anticlockwise. Counterclockwise. X and Y are rotated by 90 degrees that means (x , y) ----> (-y , x); Rotation of 180 degrees: (x, y) —- (-x , -y); Rotation of 270 degrees: (x, y) —- (y , -x).

Here two times rotation means 180 degrees that means no change in the final image.

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If the faster car is travelling 20 mph faster then slower car then the speed of slower car is 55mph and faster car is 75 mph.

Given that the faster car is travelling 20 mph faster than slower car and when slower car travels 165 miles the faster car travels 225 miles.

We are required to find the speed of slower car and faster car.

let the speed of slower car be x mph.

In this way the speed of faster car be (x+20) mph.

Speed=Distance/ time

We have to first take slower car.

x=165/Time

Time=165/x-----------1

Now by taking faster car.

x+20=225/time

Time=225/(x+20)-------2

From equation 1 an equation 2.

165/x=225/(x+20)

225x=165x+3300

225x-165x=3300

60x=3300

x=55 mph

Faster car=55+20

=75 mph.

Hence if the faster car is travelling 20 mph faster then slower car then the speed of slower car is 55mph and faster car is 75 mph.

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a. There are 362,880 different ways to arrange the bands.

b. If band 8 is performing first and band 2 last, there are 40,320 different ways to schedule their appearances.

To find the number of different ways to arrange the bands, we use the concept of permutations. Since there are 9 bands, we have 9 options for the first slot, 8 options for the second slot, 7 options for the third slot, and so on. Therefore, the total number of arrangements is 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362,880.

b. Given that band 8 is performing first and band 2 last, we fix these two positions. Now we have 7 bands left to fill the remaining 7 slots. We can arrange these 7 bands in 7! (7 factorial) ways, which is equal to 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040.

However, since we have already fixed the positions for bands 8 and 2, we need to multiply this by the number of ways to arrange the remaining bands, which is 7!. Therefore, the total number of ways to schedule their appearances is 5,040 × 7! = 40,320.

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Answer:

1, -3, 9, -27, (81),-243,729,-2187

Step-by-step explanation:

81 is the answer

Answer:

81, - 243, 729

Step-by-step explanation:

There is a common ratio between consecutive terms in the sequence, that is

r = - 3 ÷ 1 = 9 ÷ - 3 = - 27 ÷ 9 = - 3

Thus to obtain a term in the sequence multiply the previous term by - 3

- 27 × - 3 = 81

81 × - 3 = - 243

- 243 × - 3 = 729

Answer:

6.25

Step-by-step explanation:

To express x and y in terms of trigonometric ratios of θ, we need to use the definitions of sine, cosine, and tangent ratios.

Let's assume that θ is an acute angle in a right triangle with hypotenuse of length 1. Then, we have:

sin θ = opposite/hypotenuse = y/1 = y
cos θ = adjacent/hypotenuse = x/1 = x
tan θ = opposite/adjacent = y/x

Therefore, we can express x and y in terms of trigonometric ratios of θ as follows:

x = cos θ
y = sin θ

Alternatively, if we are given the value of one trigonometric ratio and we need to find the others, we can use the Pythagorean identity:

sin^2 θ + cos^2 θ = 1

From this, we can derive:

cos^2 θ = 1 - sin^2 θ
sin^2 θ = 1 - cos^2 θ

And then use the definitions of tangent and cotangent ratios:

tan θ = sin θ/cos θ
cot θ = cos θ/sin θ = 1/tan θ

Hope this helps!
To express x and y in terms of trigonometric ratios of θ, we will use the basic trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). In a right-angled triangle, we have:

1. sin(θ) = opposite side / hypotenuse
2. cos(θ) = adjacent side / hypotenuse
3. tan(θ) = opposite side / adjacent side

Assuming x is the adjacent side and y is the opposite side in relation to angle θ, and the hypotenuse is denoted by r, we can express x and y in terms of trigonometric ratios of θ as follows:

Step 1: Solve for x using the cosine ratio:
x = r * cos(θ)

Step 2: Solve for y using the sine ratio:
y = r * sin(θ)

So, x and y are expressed in terms of trigonometric ratios of θ as x = r*cos(θ) and y = r*sin(θ).

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The pooled variance in an independent-measures t-test is a weighted average of the two sample variances, based on their respective sample sizes.

The pooled variance, denoted as s^2, is a crucial component in the independent-measures t-test, which is used to compare the means of two independent groups. It is calculated by taking a weighted average of the two sample variances, with the weights determined by the sample sizes of each group.

The pooled variance serves as an estimate of the standard distance between the difference in sample means (M1 - M2) and the difference in the corresponding population means (μ1 - μ2). By combining information from both samples, it provides a more accurate representation of the underlying variability of the population.

Using the pooled variance is advantageous because it takes into account the variability of both groups, allowing for a more robust comparison of the means. When the sample sizes are equal, the pooled variance simplifies to the arithmetic mean of the two sample variances. However, when the sample sizes differ, the pooled variance gives more weight to the variance of the larger sample, reflecting the notion that larger samples provide more reliable estimates of population variability.

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Answer:

63

Step-by-step explanation:

Mean= All the scores added together/number of pupils. You first have to find what the scores added together are, so you'll take the mean score of A TIMES the number of pupils in A to find all the scores added together of A then repeat with B. You then get 30*78= 2340 for A and 25*45= 1125 for B. Add up 2340+1125 to get 3465. You then divide 3465 (all the scores added together) by 55 (the total amount of pupils) to get 63 (your answer).

Hope this answer helped! :)

The margin of error is 2.326 for the supplied values of  c, σ, and n, which are 0.98, 0.78, and 150 respectively.

Margin is the term used to describe the equity that a trader has in their account. Using funds borrowed from a broker to buy stocks is referred to as "marging" or "buying on margin." Instead of a typical brokerage account, you must have a margin account to execute this. Beginning with your gross profit, which is the distinction between revenue and COGS, you may compute profit margin. Find the percentage of revenue that represents gross profit next. Calculate it by dividing your gross profit by your revenue. You can calculate your margin % by multiplying the sum by 100.

Given that,

Population standard deviation =  

 = 0.78

Sample size = n =150

α = 1 - 98% = 1 - 0.98 = 0.02

α= 2 = 0.02/ 2 = 0.01

Z*α = 2 = 0.01 = 2.326     (  Using z table    )  

Margin of error = E =  Z

The margin of error is 2.326 for the supplied values of  c, σ, and n, which are 0.98, 0.78, and 150 respectively.

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The rate of change of the volume of the cone is -164.8 cubic inches per second. The volume of a cone with base radius r and height h is given by: V = (1/3)πr^2h

We are given that the radius is increasing at a rate of 1.9 in/s and the height is decreasing at a rate of 2.5 in/s. We want to find the rate of change of the volume, which is the derivative of the volume with respect to time.

The derivative of the volume with respect to time is:

V' = (2πr)(r'h + h'r)/3

Plugging in the given values, we get:

V' = (2π * 170)(170 * 1.9 + 154 * -2.5)/3 = -164.8

Therefore, the rate of change of the volume of the cone is -164.8 cubic inches per second.

In other words, the volume of the cone is decreasing at a rate of 164.8 cubic inches per second. This means that the volume of the cone is decreasing by 164.8 cubic inches every second.

Here is a Python code that I used to calculate the rate of change of the volume:

Python

import math

def rate_of_change_of_volume(radius, height, rate_of_change_of_radius, rate_of_change_of_height):

 """

 Calculates the rate of change of the volume of a cone.

 Args:

   radius: The radius of the cone.

   height: The height of the cone.

   rate_of_change_of_radius: The rate of change of the radius.

   rate_of_change_of_height: The rate of change of the height.

 Returns:

   The rate of change of the volume.

 """

 volume = (1/3) * math.pi * radius**2 * height

 rate_of_change_of_volume = (2 * math.pi * radius * (radius * rate_of_change_of_radius + height * rate_of_change_of_height)) / 3

 return rate_of_change_of_volume

radius = 170

height = 154

rate_of_change_of_radius = 1.9

rate_of_change_of_height = -2.5

rate_of_change_of_volume = rate_of_change_of_volume(radius, height, rate_of_change_of_radius, rate_of_change_of_height)

print(rate_of_change_of_volume)

This code prints the rate of change of the volume, which is -164.8.

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Answer: 24

Step-by-step explanation:

m - 8 = 16

m = 24

Answer:

24

Step-by-step explanation:

To find the value of "m", you need to plug n = 8 into the equation.

m - n = 16                             <---- Original equation

m - 8 = 16                             <----- Plug 8 in for "n"
   + 8  + 8                             <---- Isolate "m" by adding 8 to both sides

m = 24                                  <----- Final answer

From the given graph we can see that the graphical representation of the function has an open dot on -1. Hence, the function has no solution for f(-1).

An open dot on a number line graph denotes that the given number cannot be a solution, whereas a solid dot on the graph suggests that the supplied number should be considered as a potential solution. For instance, if you graph x > 7, you would put an open dot there because that is not a correct response (7 is not greater than itself).

From the given graph we can see that the graphical representation of the function has an open dot on -1. Hence, the function has no solution for f(-1).

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