A market researcher sends out surveys in batches of 5,000. the
table shows the number of surveys completed and returned.
what is the average number of surveys returned?
batch
# of surveys returned
1
1
1,842
2
2,357
2,135
3
2,890
4
1,931
5

The probability that the series lasts exactly five games is 2p raise to the power 4(1-p).

How to find probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The higher the probability, the more likely it is that the event will occur.

To find the probability that the series lasts exactly five games, we need to consider all possible ways in which a team can win four games in five games played.

One possible scenario is that team A wins the first four games and team B wins the fifth game. The probability of this happening is:

P(A wins the first four games and B wins the fifth game) = p⁴ * (1-p)

Another possible scenario is that team B wins the first game, team A wins the next four games. The probability of this happening is:

P(B wins the first game and A wins the next four games) = p⁴* (1-p)

Therefore, the probability that the series lasts exactly five games is the sum of these two probabilities:

P(series lasts exactly five games) = p⁴* (1-p) + p⁴ * (1-p)

Simplifying the expression, we get:

P(series lasts exactly five games) = 2p⁴(1-p)

Therefore, the probability that the series lasts exactly five games is 2p⁴(1-p).

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Considering the expression of a line, the slope of the line that passes through the points (2,4) and (9,12) is 8/7.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line is calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (2,4) and (x₂, y₂)= (9,12), the slope m can be calculated as:

m= (12 -4)÷ (9 -2)

Solving:

m= 8÷ 7= 8/7

Finally, the slope of the line is 8/7.

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Assuming that x ≥ 0 and y ≥ 0, the situation is infeasible: True.

In Mathematics, these rules are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a coordinate plane:

In this context, we can logically deduce that the given system of inequalities 5x+3y ≤ 15 and y ≥ 6 would not have a feasible solution set if they are subjected to x ≥ 0 and y ≥ 0:

Assuming the ordered pair (1, 2), we have:

y ≥ 6

2 ≥ 6 (False).

5x+3y ≤ 15

5(1) +3(2) ≤ 15

5 + 6 ≤ 15

11 ≤ 15 (True).

Therefore, it is not a feasible solution.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

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Answer:

x = 10

Step-by-step explanation:

\(\frac{1}{5}\) x - \(\frac{2}{3}\) = \(\frac{4}{3}\)

multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions

3x - 10 = 20 ( add 10 to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

Answer:

not exactly sure what the question is asking but they are all $15 dollars apart

Step-by-step explanation:

If that's the plan, you'll probably fall in the B range according to the mean and median.

The average of a group of values is referred to as the mean. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

The midway number in a set of data is known as the median. The data should first be arranged and ranked from smallest to greatest. Divide the total number of observations by two to get the midway value. The value in that location is the median if there are an odd number of observations; otherwise, round the number up.

Most educators are far too indolent to approach "curves" in a "scientific" manner. What they really mean is that they will arbitrarily "fudge" the grades to give the impression that they are capable of teaching and the pupils are capable of learning. Therefore, estimate that they may demand 50% B's and 30% A's. There were 18% Cs and 2% test failures because they didn't want anyone to receive a D or a F because that would need extra work from them and angry parents. Even more students will receive As, and few, if any, will receive Cs in a more tolerant and indulgent setting.

If that's the plan, you'll probably fall in the B range according to the mean and median.

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Answer:

  3 tents hold 2 campers

Step-by-step explanation:

The given relations can be expressed as a single equation in the number of 2-camper tents.

__

Let x represent the number of 2-camper tents. Then the number of 4-camper tents is 6-x, and the total number of campers in tents is ...

  2x +4(6 -x) = 18

  -2x +24 = 18

  -2x = -6 . . . . . . subtract 24

  x = 3 . . . . . . . divide by -2

Exactly 3 tents hold 2 campers.

_____

Additional comment

The other 3 tents hold 4 campers.

Another way to consider this is to assume that all tents hold 2 campers, and then realize there are 18 -6×2 = 6 campers left over. If these are placed 2 per tent, then there will be 6/2 = 3 tents with 4 campers. The remaining 3 tents will have 2 campers.

Answer:

last option is the right answer.

1. The inequality when the distance between 2 and 5 times a number is no less than 8 is 1. |5x−2|≥8

2. The correct option is A. Trey is not necessarily correct. He will need to ensure that the compass width remains the same for each arc drawn from P and R.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥  <  >   ≤.

The distance between 2 and 5 times a number is no less than 8.

Let the number be x

This will be |5x−2|≥8. The correct option is 1.

For the second question, it should be noted that Trey is not necessarily correct. He will need to ensure that the compass width remains the same for each arc drawn from P and R. The correct option is A.

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These are complementary angles.

If two angles are complementary, then

the sum of their measures is 90°.

Since we know that one of the angles measures 35°, we can find the measure of the other by taking 90 minus the measure of the original angle which in this case is 90 - 35.

So we have 90° - 35° which is 55°

So the measure of the other angle is 55°

A number is decreased by 8%, the result is 79. So the original number to the nearest tenth is 85.8.

These are the specified parameters:

a number is decreased by 8%, the result is 79.

Suppose, a number = x

a number - 8% a number = 79

x - 8/100 x = 79

100/100 x - 8/100 x = 79

92/100 x = 79

            x = 79 × 100/92

            x = 7900/92

            x = 85.8

So these numbers are 85.8.

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Answer:

1.5 cups

Step-by-step explanation:

We Know

Milan drank 12 fluid ounces of juice.

How much is this in cups?

Let'solve

1 ounce = 0.125 cup

12 ounces = 0.125 x 12 = 1.5 cups

So, Milan drank 1.5 cups of juice.

Answer:

y = (1/4)x

Step-by-step explanation:

Look at the point (4, 1).

For every 4 gallons of white paint, he uses 1 gallon of red paint.

You can also read it as for every gallon of white paint, he uses 1/4 gallon of red paint.

y = (1/4)x

Answer:

(x-2)^{2}=4(y-4)

Answer:

y = 1/4 (x - 2)^2 + 4

Step-by-step explanation:

The equation of a parabola is

y = a(x - h)^2 + k

This is for a parabola that opens in the y direction (up or down) If you make a sketch of the focus and directrix you'll be able to see what direction it opens. See image. The parabola kind of curls around the focus and opens away from the directrix. Also, this sketch can help you find the vertex which we need, which is actually a point on the curve and which is exactly half way between the focus and directrix.

The vertex is (h, k) for this problem it is (2, 4). h is 2 and k is 4. You will fill in the 2 and 4 in the parabola formula. Then the last thing you need is the a infront of the paranthesis on the right side of the equation.

Use the formula

a = 1/4p (the p is in the denominator).

p is the distance from the vertex to the focus, so for this question, it is 1. see image.

a = 1/4(1)

a = 1/4

Fill it in the parabola formula.

y = a (x - h)^2 + k

y = 1/4 (x - 2)^2 + 4

The two distances are equal, which means the points (2, -8) and (0, -8) are symmetric about the axis of symmetry x = 1, or the vertex (1, -9).

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The vertex of a parabola in standard form, f(x) = a(x - h)² + k, is at the point (h, k).

We can rewrite the given equation, f(x) = x² - 2x - 8, in standard form by completing the square:

f(x) = x² - 2x - 8

= (x² - 2x + 1) - 1 - 8

= (x - 1)² - 9

So the vertex of the parabola is at the point (1, -9), where h = 1 is the x-coordinate of the vertex, and k = -9 is the y-coordinate of the vertex.

To verify that points (2, -8) and (0, -8) are symmetric about the vertex, we can calculate the axis of symmetry, which is x = h, or x = 1 in this case.

The distance between the vertex (1, -9) and the point (2, -8) is the same as the distance between the vertex and the point (0, -8), since these points have the same y-coordinate:

d((1, -9), (2, -8)) = d((1, -9), (0, -8))

Using the distance formula, we can calculate the left-hand side:

d((1, -9), (2, -8)) = √((2 - 1)² + (-8 - (-9))²)

= √(1 + 1)

= √(2)

Using the distance formula again, we can calculate the right-hand side:

d((1, -9), (0, -8)) = √((0 - 1)² + (-8 - (-9))²)

= √(1 + 1)

= √(2)

Hence, the two distances are equal, which means the points (2, -8) and (0, -8) are symmetric about the axis of symmetry x = 1, or the vertex (1, -9).

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Answer: 1/3

Step-by-step explanation:

The probability of selecting a chocolate cream pie can be found by dividing the number of chocolate cream pies by the total number of pies:

Probability of selecting a chocolate cream pie = Number of chocolate cream pies / Total number of pies

Probability of selecting a chocolate cream pie = 4 / 12

Simplifying this fraction by dividing the numerator and denominator by 4 gives:

Probability of selecting a chocolate cream pie = 1/3

Therefore, the probability of selecting a chocolate cream pie from Annie's Pie Shop is 1/3.

Answer:

92

Step-by-step explanation:

Because 92 occurs the most and some of the numbers aren't even there.

Answer: .75 + .25x ≤ 7

Step-by-step explanation: The x equals the amount that you can buy for each item.

Answer:

0.8

Step-by-step explanation:

Given: \(3 \frac{3}{4}\) hours one day

To find: How much snow fell per hour?

Solution: To find how much it will snow in an hour, first convert \(3\frac{3}{4}\) to a decimal  

3.75. Now, divide 3 by 3.75

\(\frac{3}{3.75} =\)

\(3\) ÷ \(3.75\)

\(= 0.8\)

So, 0.8 snow will fall per hour

By using  Fundamental Theorem of Calculus, we find the derivative of the function g(x) = In { sqrt( t + t^3)dt } limit from x to 0 is  ln(sqrt(x + x^3)).  The derivative of the function g(x) = { In (1+t^2) dt} where limit are from x to 1 is  ln(1 + x^2).

The Fundamental Theorem of Calculus, which states that if a function is defined as the definite integral of another function, then its derivative is equal to the integrand evaluated at the upper limit of integration.

So, applying this theorem, we have:

g'(x) = d/dx [∫x_0 ln(sqrt(t + t^3)) dt]

= ln(sqrt(x + x^3)) * d/dx (x) - ln(sqrt(0 + 0^3)) * d/dx (0)

= ln(sqrt(x + x^3))

Therefore, g'(x) = ln(sqrt(x + x^3)).

Using the Fundamental Theorem of Calculus, we have:

g'(x) = d/dx [∫1_x ln(1 + t^2) dt]

= ln(1 + x^2) * d/dx (x) - ln(1 + 1^2) * d/dx (1)

= ln(1 + x^2)

Therefore, g'(x) = ln(1 + x^2).

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____The given question is incomplete, the complete question is given below:

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = In { sqrt( t + t^3)dt } limit from x to 0.  8. g(x) = { In (1+t^2) dt} where limit are from x to 1.

Answer:

The Inverse Property of Addition states that \(a + (-a) = 0\): The sum of a real number and its additive inverse is zero, the additive module.

Step-by-step explanation:

From the Algebra of Real Numbers we know that the Inverse Property of Addition, also know as Existence of Additive Inverse states that for all real number \(u\) exist only a real number \(v\) so that:

\(u+v = 0\)

Where \(v = -u\) and \(0\) is also known as additive module.

Therefore, we can complete the phrase below:

The Inverse Property of Addition states that \(a + (-a) = 0\): The sum of a real number and its additive inverse is zero, the additive module.

Answer:

The Inverse Property of Addition states that : The sum of a real number and its additive inverse is zero, the additive module.

Step-by-step explanation:

ive done it!

Answer:

Essential Elegance Candle

Step-by-step explanation:

Ratios are Lavender:Vanilla

For the Essential elegance candle the ratio is 3:6 which can be simplified to 1:2 whereas the Glory Candle is 4:10 which can be simplified to 2:5 on either one the vanilla is the bigger number but in terms of ratio it would be the essential elegance since 1/2>2/5

0.003 is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations

To calculate the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations.The mean is the expected number of calls involving a fax transmission, while the standard deviation is the measure of variability in the distribution. We then use this information to calculate the probability of exceeding the expected number by more than 2 standard deviations, which can be done using the z-score formula. The z-score for values more than 2 standard deviations away from the mean is 2.33, which corresponds to a probability of 0.003. Thus, the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations is 0.003.

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If the inflation rate is 180%, the average prices will double in less than one year.

This is because inflation measures the increase in the prices of goods and services over a period of time. Therefore, the formula for calculating how many years it will take for average prices to double at a given inflation rate is:Years to double = 70/inflation rate

In this case, the inflation rate is 180%.

Therefore:Years to double = 70/180%

Years to double = 0.389 years

This means that average prices will double in approximately 4.67 months (0.389 years multiplied by 12 months per year).

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This approach allows us to work with smaller numbers and simplifies the calculations. We find that Sara has 40 tens and -2 ones, or 38 marbles left.

To solve addition and subtraction word problems with two two-digit numbers, we can break down each number into its tens and ones digits and then perform the operations. When faced with word problems involving addition or subtraction of two two-digit numbers, it is helpful to break down each number into its tens and ones digits.

Let's consider an addition example: suppose we have the problem "Jane has 46 apples, and John gives her 27 more. We can break down 46 into 40 and 6 (4 tens and 6 ones), and 27 into 20 and 7. Adding the tens digits, we get 40 + 20 = 60, and adding the ones digits, we have 6 + 7 = 13. Combining the results, we find that Jane now has 60 tens and 13 ones, or 73 apples.

Similarly, for subtraction problems, this approach helps us simplify the calculations. Let's take an example: "Sara has 85 marbles, and she gives away 47. How many marbles does she have left?" Breaking down 85 into 80 and 5, and 47 into 40 and 7, we can subtract the tens and ones separately. Subtracting the tens, we have 80 - 40 = 40, and subtracting the ones, we get 5 - 7 = -2. Combining the results, we find that Sara has 40 tens and -2 ones, or 38 marbles left.

By breaking down two-digit numbers into their tens and ones, we can handle addition and subtraction more easily, making the calculations manageable and accurate.

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