QUESTION 10 Identify the population of the following example. In a poll of 50,000 randomly selected college students, 74% answered yes, when asked "Do you have a television set in your dorm room?" The

Answer:

107 chocolate cupcakes sold

78 chocolate covered strawberry cupcakes sold

Step-by-step explanation:

to solve one of these questions, you need to write two equations and then substitute back and forth to get the answer.

to start, we need to write an equation.

2.75c+3.75s=586.75

and c+s=185

reworking the second equation to isolate s, we'll then substitute it into the first one.

so s=185-c

2.75c+3.75(185-c)=586.75

2.75c+693.75-3.75c=586.75

combine like terms (the ones with a c variable attachment)

2.75c-3.75c=-1c

693.75-1c=586.75

-693.75

-107=-1c

/-1

107=c

put that back into the second equation

107+s=185

78=s

a) A pulse of width 2 units, starting at t=5 and ending at t=7.

b) A sum of two pulses of width 1 unit each, one starting at t=5 and the other starting at t=7.

c) A ramp starting at t=2 and ending at t=4.

Part 2

a) A rectangular pulse of height 1, starting at t=5 and ending at t=7.

b) Two rectangular pulses of height 1, one starting at t=5 and the other starting at t=7, with a gap of 2 units between them.

c) A straight line starting at (2,0) and ending at (4,2).

In part 1, we are given three signals and asked to identify their characteristics. The first signal is a pulse of width 2 units, which means it has a duration of 2 units and starts at t=5 and ends at t=7. The second signal is a sum of two pulses of width 1 unit each, which means it has two parts, each with a duration of 1 unit, and one starts at t=5 while the other starts at t=7. The third signal is a ramp starting at t=2 and ending at t=4, which means its amplitude increases linearly from 0 to 1 over a duration of 2 units.

In part 2, we are asked to sketch the signals. The first signal can be sketched as a rectangular pulse of height 1, starting at t=5 and ending at t=7. The second signal can be sketched as two rectangular pulses of height 1, one starting at t=5 and the other starting at t=7, with a gap of 2 units between them. The third signal can be sketched as a straight line starting at (2,0) and ending at (4,2), which means its amplitude increases linearly from 0 to 2 over a duration of 2 units. It is important to note that the height or amplitude of the signals in part 2 corresponds to the value of the signal in part 1 at that particular time.

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Answer:

20, 40, 60

Step-by-step explanation:

We can find the LCM by making a list which is my favorite way.

Cell phone number 1: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60

Cell phone number 2: 5, 10, 15, 20, 25, 30, 35 40, 45, 50, 55, 60

Answer:

The first three times that the cell phones beep at the same time are the 20th, 40th and 60th minutes.

Step-by-step explanation:

Let the first cell phone be A, that is, A beeps every 4 minutes

and let the other cell phone be B, that is, B beeps every 5 minutes.

Cell phone A will be at the 4th, 8th, 12th, 16th and 20th minutes while cell phone B will beep at the 5th, 10th, 15th and 20th minutes. Hence, the first time the cell phones will beep together is the 20th minute.

Cell phone A will then beep at the 24th, 28th, 32nd, 36th and 40th minutes while cell phone B will beep at the 25th, 30th, 35th and 40th minutes. The second time the cell phones will beep together is the 40th minute.

Cell phone A will beep at the 44th, 48th, 52nd, 56th and 60th minutes while cell phone B will beep at the 45th, 50th, 55th and 60th minutes. The third time the cell phones will beep together is the 60th minute.  

Hence, the first three times that the cell phones beep at the same time are the 20th, 40th and 60th minutes.

Answer:

x= 16

Step-by-step explanation:

here!hope this helps

Answer:

10\(\sqrt{3}\), or 17.32050

Step-by-step explanation:

Answer:

The given image is a graph of an exponential function. The graph is in the form of y = ab^x, where a is the initial value (y-intercept), b is the base (growth or decay factor), and x is the exponent (input value).

In this particular graph, the function appears to be a decay function since the value of the function is decreasing as x increases. We can also see that the initial value of the function is 24, which means that when x = 0, y = 24. We can also see that the base of the function is less than 1 (approximately 0.8), which tells us that the function is decreasing at a constant rate.

To write the exponential function that represents this graph, we can use the general form of the function y = ab^x and substitute the known values:

y = 24(0.8)^x

Therefore, the exponential function that represents the given graph is y = 24(0.8)^x.

Image 2.

The given image is a graph of an exponential function. The graph is in the form of y = ab^x, where a is the initial value (y-intercept), b is the base (growth or decay factor), and x is the exponent (input value).

In this particular graph, the function appears to be a growth function since the value of the function is increasing as x increases. We can also see that the initial value of the function is 5, which means that when x = 0, y = 5. We can also see that the base of the function is greater than 1 (approximately 1.2), which tells us that the function is increasing at a constant rate.

To write the exponential function that represents this graph, we can use the general form of the function y = ab^x and substitute the known values:

y = 5(1.2)^x

Therefore, the exponential function that represents the given graph is y = 5(1.2)^x.

Answer:

  5y -10

Step-by-step explanation:

We can find the value of the desired expression by using substitution for the variables A and B.

  3A +2B

  = 3(y -4) +2(y +1) . . . . . . using y-4 for A, and y+1 for B

  = 3y -12 +2y +2 . . . . . . eliminate parentheses with the distributive property

  = (3 +2)y +(-12 +2) . . . . group like terms

  = 5y -10

An expression that equals 3A +2B is 5y -10.

_____

Additional comment

The "standard form" of a polynomial expression has the highest-degree term listed first, and others in decreasing order of degree.

Answer: 60 degrees

Step-by-step explanation:

a triangle has a interior sum of 180°
90 + 30 = 120

180 - 120 = 60

a) X is an unbiased estimator of p. b) The Var(X) is p(1-p)/n. c) The E[X(1-X)] is (n-1)[p(1-p)/n]. d) The value of c is c = 1/(n-1).

(a) To show that X = Y/n is an unbiased estimator of p, we need to show that E[X] = p.

Since Y is a sum of n iid Bern(p) random variables, we have E[Y] = np.

Now, let's find the expected value of X:

E[X] = E[Y/n] = E[Y]/n = np/n = p.

Therefore, X is an unbiased estimator of p.

(b) To find the variance of X, we'll use the fact that Var(aX) = a^2 * Var(X) for any constant a.

Var(X) = Var(Y/n) = Var(Y)/n² = np(1-p)/n² = p(1-p)/n.

(c) To show that E[X(1-X)] = (n-1)[p(1-p)/n], we expand the expression:

E[X(1-X)] = E[X - X²] = E[X] - E[X²].

We already know that E[X] = p from part (a).

Now, let's find E[X²]:

E[X²] = E[(Y/n)²] = E[(Y²)/n²] = Var(Y)/n² + (E[Y]/n)².

Using the formula for the variance of a binomial distribution, Var(Y) = np(1-p), we have:

E[X²] = np(1-p)/n² + (np/n)² = p(1-p)/n + p² = p(1-p)/n + p(1-p) = (1-p)(p + p(1-p))/n = (1-p)(p + p - p²)/n = (1-p)(2p - p²)/n = 2p(1-p)/n - p²(1-p)/n = 2p(1-p)/n - p(1-p)²/n = [2p(1-p) - p(1-p)²]/n = [p(1-p)(2 - (1-p))]/n = [p(1-p)(1+p)]/n = p(1-p)(1+p)/n = p(1-p)/n.

Therefore, E[X(1-X)] = E[X] - E[X²] = p - p(1-p)/n = (n-1)p(1-p)/n = (n-1)[p(1-p)/n].

(d) To find the value of c such that cX(1-X) is an unbiased estimator of p(1-p)/n, we need to have E[cX(1-X)] = p(1-p)/n.

E[cX(1-X)] = cE[X(1-X)] = c[(n-1)[p(1-p)/n]].

For unbiasedness, we want this to be equal to p(1-p)/n:

c[(n-1)[p(1-p)/n]] = p(1-p)/n.

Simplifying, we have:

c(n-1)p(1-p) = p(1-p).

Since this should hold for all values of p, (n-1)c = 1.

Therefore, the value of c is c = 1/(n-1).

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The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.

A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).

The area of a rectangle = (length of rectangle)(width of rectangle).

Given the following parameters for the patio and the bench:

Area to be painted = area of rectangular patio - area of rectangular bench

Area of rectangular patio = (x + 20)(x + 10)

Area of rectangular bench = (6)(2) = 12

Area to be painted = (x + 20)(x + 10) - 12

The answer is: B. A = (x + 20)(x + 10) - 12.

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Answer:

Can you give me more information to answer this?

Step-by-step explanation:

Answer:

Area: 2,088 Perimeter: 202

Step-by-step explanation:

Since it's a rectangle, both small sides are going to be the same, and both long sides are going to be the same. So for perimeter add up 29+72+29+72 to equal 202. For area you just multiply 29 times 72:)

The required statements and reasons to prove that DE is equal to CE is explained.

The triangle congruence theorem is a theorem that can be used to prove that two or more triangles are the same, considering the corresponding properties of the triangles. The properties are length of the sides, and measure of internal angles.

The statements and reasons to prove that DE is equal to CE are explained below using the triangle congruence theorem.

         STATEMENT                            REASON

1. AD = BC                                          Given

2. <BCD = <ADC                                Given

3. DC = DC                                         Reflexive property

4. ΔADC ≅ ΔBCD                              SAS

5. <EDC ≅ <ECD                                CPCTC

6. AC = BD                                          Definition of diagonal

7. DE = CE                                           Congruent sides of isosceles triangle

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The correct option is (E) None of them. Given that the vector v can be written as a linear combination of V1 and V2 such that v = C1V1 + C2V2.

We need to identify which of the following statements is always false.

(A) Cy can be as a multiple of C2.

This statement is true as we can write C1V1 + C2V2 as C2(V2) + C1(V1).

(B) C1 C2 cannot be negative.

This statement is false as C1 and C2 can be positive, negative, or zero.

(C) Cy can be a positive number.

This statement is true as both C1 and C2 can be positive numbers.

(D) v can be v = -5V2. This statement is false because v can be written as a linear combination of V1 and V2, and there is no negative coefficient in the expression.

Therefore, none of the statements are always false, and the answer is option (E) None of them.

Answer: The correct option is (E) None of them.

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Answer:

Suppose that we have two similar figures.

Then if a given side of one of the figures has a measure M, the correspondent side in the other figure has a measure M' = k*M

Where k is the scale factor.

Then if the perimeter of the first figure is P, the perimeter of the other figure will be P' = k*P

And if the area of the first figure is A, then the area of the other figure will be:

A' = k^2*A

Then the quotient between the perimeters is:

P'/P = k

And the ratio between the areas is

A'/A = k^2

So what we need to do, is find the value k.

In the image, we can see that the base of the larger figure is 30 yd, and the base of the smaller figure is 12 yd.

If we define the smaller figure as the original one, then we will have:

M = 12 yd

M' = 30 yd

M' = 30yd = k*12yd = k*M

Solving for k we get:

k = 30yd/12yd = 2.5

Then the ratio between the perimeters is:

P'/P = k = 2.5

And the ratio of the area of the larger figure (A') to the smaller figure (A) is:

A'/A = k^2 = (2.5)^2 = 6.25

Therefore, the standard error of the mean, σ= 2.53 (approx).

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.

Given: A simple random sample of 10 items resulted in a sample mean of 25.

The population standard deviation is = 8.

We have to find out the standard error of the mean, σ/Sample Size n,

so we will first calculate σ as;

σ = Population standard deviation = 8

Sample Size n = 10

Substituting values in the formula to find the standard error of the mean, we get;σ/√n = 8/√10 = 2.53 (Round off the value to two decimal places)

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Regression problems are used to predict continuous outputs. In such problems, the goal is to establish a mathematical relationship between input variables (also known as independent variables) and the corresponding output variable (dependent variable).

The regression model learns from a training dataset, identifying patterns and relationships between the input and output variables. Once trained, the model can be used to predict the output values for new, unseen input data.

This makes regression particularly useful in scenarios where the output is a continuous numerical value, such as predicting housing prices based on features like location, size, and number of rooms.

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The value of the consumer price index (CPI) in 2017 is 119.5.

To calculate the consumer price index (CPI), we need to compare the prices of a basket of goods in different years with a base year. Let's examine the given table for an average household of four people and the three products included in the basket:

Year | Product A | Product B | Product C | Total Expenditure

2015 | $100 | $50 | $80 | $230

2016 | $110 | $55 | $90 | $255

2017 | $120 | $60 | $95 | $275

2018 | $125 | $65 | $100 | $290

To calculate the CPI for 2017, we compare the total expenditure for 2017 with the total expenditure for the base year (2015) and multiply it by 100. The formula for CPI is (Total Expenditure in a given year / Total Expenditure in the base year) * 100.

CPI in 2017 = (Total Expenditure in 2017 / Total Expenditure in 2015) * 100

Plugging in the values from the table:

CPI in 2017 = ($275 / $230) * 100

= 1.195 * 100

= 119.5

Therefore, the value of the consumer price index (CPI) in 2017 is 119.5.

This indicates that the average price level for the basket of goods in 2017, compared to the base year 2015, has increased by approximately 19.5%. The CPI is a measure used to track changes in the cost of living over time, and a higher CPI value indicates a higher inflation rate or increase in prices.

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Answer:

(4, 4)

Step-by-step explanation:

On the Cartesian plane, values on the x-axis increase to the right, and values on the y-axis increase as you go vertically upwards.

x-coordinate = 2

y-coordinate = 3

•Moving 2 units to the right adds 2 to the x-coordinate.

∴ new x-coordinate = 2 + 2 = 4

• Moving 1 unit up adds 1 to the y-coordinate.

∴ new y-coordinate = 3 + 1 = 4

∴ You will end up on the point (4, 4).

slope = 5/2

The points given: (3, 8)and (1, 3)

Using the slope formula:

The null hypothesis is a statement that assumes there is no significant relationship between two variables or that there is no difference between two groups. In the context of the given question, the null hypothesis would be that the mean driving times for the three routes are the same.

This means that there is no significant difference in the average driving times for the three routes being compared. The null hypothesis is often used in statistical hypothesis testing, where it is compared against the alternative hypothesis to determine if the observed data provides enough evidence to reject the null hypothesis.

In this case, the alternative hypothesis could be that the mean driving times for the three routes are different, indicating that there is a significant difference in the average driving times for the three routes. By testing the null hypothesis, researchers can determine whether or not there is a significant difference in the data being analyzed.

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Therefore, x = 8

The image above will help you better understand why.

Answer:

x=8

Step-by-step explanation:

It is really easy just try to multiply

Answer:

1.) Carries energy

Step-by-step explanation:

A good summary of an ATP molecule is a molecule that transfers energy between cells... meaning it carries energy from cell to cell. Furthermore, energy cannot be destroyed, and cannot be absorbed, only changed and transformed. This leaves us with two options, (1. Carries energy, and 4. None of the above). Since we already have a basic understanding of what an ATP molecule does, we can confidently determine that the correct answer is that an ATP molecule can best be described as carrying energy.

The formula for y in terms of x is y = 3/x³.

Inversely Proportional:

When two variables are inversely proportional to each other, then the value of one quantity increases with respect to decrease in other or vice-versa.

So, it can be written as,

y = k/x

where,

y is inversely proportional to x and k is the constant of proportionality.

Given,

Y is inversely proportional to the cube of x.

Here we need to find the formula for y in terms of x.

We know that, y is inversely proportional to the cube of x.

So, it can be written as

=> y = k / x³

Where k is the constant.

To find the formula of y,

First we need to find the value of k,

By applying the value of x and y,

So,

=> 24 = k / (1/2)³

=> 24 = k / 1/8

=> 24/8 = k

=> k = 3

Therefore, the formula for y in terms of x is,

=> y = 3/ x³

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The exponential form of given number 121200 is 1.212 × \(10^5\)

And the earth sun distance in kilometers in powers of 10 notation is 1.5 × \(10^8\)

For given question,

We need to express 121,200 in exponential (powers of 10) notation.

To use scientific notation, pick a value between 1 and 10, then multiply it by 10ˣ.

The number between 1 and 10 in 121200 is 1.212 with 5 decimal points.

So, the exponential notation of given number would be,

121,200 = 1.212 × \(10^5\)

Earth's average distance from the Sun is around 93 million miles (150 million kilometers). That's one AU.

So the number between 1 and 10 in 150,000,000 is 1.5, with 8 decimal points.

So, the distance between he Earth and the Sun is:

150,000,000 = 1.5 × 10⁸

Therefore, the exponential form of given number 121200 is 1.212 × \(10^5\)

And the earth sun distance in kilometers in powers of 10 notation is 1.5 × \(10^8\)

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Answer:7

Step-by-step explanation:Divide 84 by 12 and it gives you 7.

Hope it helps :)

Therefore, the unit rate of \(\frac{84}{12}\) is \(7\).

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

As per the given information

\(\frac{84}{12}=7\)

Hence, the unit rate of \(\frac{84}{12}\) is \(7\).

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1/4 + 2/3

= 3/12 + 8/12

=11/12

1–11/12

you have 1/12 left

Answer:

one-quarter left

Step-by-step explanation

pretty sure this is the answer, but i could be wrong

The smallest amount that Caleb could have converted will be £ 59.

We are given that:

At shop A, Gavin converted £ 30 into € 36.60

At shop B, Amna converted £ 73 into € 86.14

Also, Caleb converted some pounds and got € 71.98.

Rate of conversion at shop A is:

£ 30 = € 36.60

£ 1 = € 36.60 / 30

£ 1 = € 1.22

rate of conversion at shop B is:

£ 73 = € 86.14

£ 1 = € 86.14 / 73

£ 1 = € 1.18

Now, we can see that the rate of conversion is more at shop A.

So, the smallest amount that Caleb might have converted will be:

Pounds = € 71.98 / € 1.22

Pounds = £ 59

Therefore, the smallest amount that Caleb could have converted will be £ 59.

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Answer: The radius of convergence, r, is 1. So the series converges for -1 < x < 1 and diverges for |x| ≥ 1.

Step-by-step explanation:

Here, we can use the ratio test.

Let's apply the ratio test to the given series:

|(n+1)^2 x^(n+1) 2*4*6*...*(2n)*(2n+2)/(n^2 x^n 2*4*6*...*(2n))| n->∞

Simplifying the expression, we get:

|(n+1)^2 / n^2| * |x| * |2n+2|/|2n| n->∞

Taking the limit as n approaches infinity, we get:

|(n+1)^2 / n^2| * |x| * |2n+2|/|2n| n->∞

Note that |2n+2|/|2n| = |n+1|/|n|, so we can simplify the expression in (1) to:

|(n+1)^2 / n^2| * |x| * |n+1|/|n| n->∞

Simplifying further, we get: |(n+1) / n| * |(n+1) / n| * |x| n->∞

Note that (n+1)/n approaches 1 as n approaches infinity, so we can simplify the expression to:

 1 * 1 * |x| n->∞

Therefore, the series converges if: |x| < 1 n->∞

Which means the radius of convergence, r, is 1. So the series converges for -1 < x < 1 and diverges for |x| ≥ 1.

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The y intercept is where a line on a graph crosses the y axis when the x coordinate is 0.

Answer:

The point where the line is on the Y axis

Step-by-step explanation:

for example in the equation y=mx+b, b would be the y-intercept or in the equation y=4x+7, the y-intercept would be 7.