Monique collects data from a random sample of seventh graders in her school and finds that 12 out of 20 seventh graders barticipate in after-school activities. Write and solve a proportion to estimate the number of seventh graders n who barticipate in after-school activities if 165 seventh graders attend Monique's

The correct answer is (B) t = 900V / (6V + 7).

To solve for t as a function of V, we can rearrange the given equation as:

V = 900t / (6t + 7)

Cross-multiplying and simplifying, we get:

6tV + 7V = 900t

Rearranging, we get:

6tV - 900t = -7V

Factoring out t on the left side, we get:

t(6V - 900) = -7V

Dividing both sides by (6V - 900), we get:

t = -7V / (6V - 900)

Multiplying numerator and denominator by -1, we get:

t = 7V / (900 - 6V)

Simplifying, we get:

t = 900V / (6V + 7)

Therefore, the equation that expresses t as a function of V is t = 900V / (6V + 7), which is option (B).

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The sum of the squares of the first 5 terms in the Fibonacci sequence is equal to [tex]Fn - Fn+1[/tex] , but the result is not true for n[tex]= 6[/tex] .

The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding numbers, starting from [tex]0[/tex] and [tex]1.[/tex]

To show that the sum of the squares of the first n terms in the Fibonacci sequence is equal to[tex]Fn - Fn+1[/tex], we can use mathematical induction.

Inductive step:

Assume that the result is true for some value of n, and consider the case where n [tex]= 5.[/tex]

[tex]0, 1, 1, 2, 3[/tex]

The fifth and sixth terms of the Fibonacci sequence are:

[tex]F5 = 5[/tex] and [tex]F6 = 8[/tex]

So,  for n = 5 is:

[tex]Fn - Fn+1[/tex]

[tex]F5 - F6 = 5 - 8 = -3[/tex]

We can also calculate[tex]Fn - Fn+1[/tex] for n = 6 using the values of F6 and F7:

[tex]F6 - F7 = 8 - 13 = -5[/tex]

So, we have:

[tex]Fn - Fn+1 = -F(n+1)[/tex]

[tex]15 = -3[/tex]

Which is not true, so the assumption that the result [tex]Fn - Fn+1,[/tex] is true for n = 5 leads to a contradiction. Therefore, we can conclude that the result is not true for n[tex]= 6[/tex].

Therefore, we have shown that the sum of the squares of the first [tex]5[/tex] terms in the Fibonacci sequence is equal to but the result is not true for n[tex]= 6.[/tex]

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The correct expansion of (-4x + 9)² is 16x² - 72x + 81.

We have,

Step 1: Start with the expression (-4x + 9)².

Step 2: To expand this expression, we use the formula for the square of a binomial: (a - b)² = a² - 2ab + b².

Step 3: In this case, a is -4x and b is 9.

Applying the formula, we have:

(-4x + 9)² = (-4x)² - 2(-4x)(9) + (9)².

Step 4: Simplify each term in the expansion:

(-4x)² = 16x² (square the first term).

-2(-4x)(9) = 72x (multiply -2, -4x, and 9 together).

(9)² = 81 (square the second term).

Step 5: Combine the simplified terms:

(-4x + 9)² = 16x² - 72x + 81.

Thus,

The correct expansion of (-4x + 9)² is 16x² - 72x + 81.

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Large MAD tells us that the average distance between each data value and the mean is large.

Given that;

The mean age of swimmers for all of these teams is 10.

Since, MAD is the mean absolute deviation (MAD) of a set, it tells the average distance between each data value and the mean.

Hence, It is a method to express the variance in the data set.

So, the large MAD tells us that the average distance between each data value and the mean is large.

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The organs of static equilibrium, also known as the maculae, are located within two expanded chambers within the vestibule called the utricle and saccule.

Utricle and saccule are filled with a gel-like substance containing tiny calcium carbonate crystals called otoliths. When the head moves, the otoliths shift and stimulate the hair cells within the maculae, which send signals to the brain regarding the body's position and movement. This allows us to maintain balance and stability, especially when standing still or moving in a straight line. Any disruptions or damage to the maculae can result in issues with balance, dizziness, and vertigo.

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The number of liters it would take to fill this box would be 1 liter .

The number of liters that would go into the box can be found by finding the volume of the box as liters are a measure of volume .

To find the volume of the box, multiply its dimensions :

Volume = width × length × height

Volume = 20 cm × 10 cm × 5 cm

Volume = 1, 000 cm³

Since 1 liter is equal to 1000 cm³, the box can fit 1 liter of liquid .

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When performing hypothesis tests on a population, you need to consider the significance level (alpha) and compare it to the p-value. The significance levels you've mentioned are 0.10, 0.05, and 0.01.

The null hypothesis (H 0) states that there is no significant difference between the sample mean (x-bar) and the population mean.

To determine whether to accept or reject H 0, follow these steps:

1. Calculate the test statistic (e.g., t or z) using the sample data.
2. Determine the p-value associated with the test statistic.
3. Compare the p-value to each of the given alpha levels (0.10, 0.05, 0.01).

Now, for each of the three alpha values, you can decide to accept or reject H 0 as follows:

- If the p-value is less than or equal to the alpha value, you reject H0. This means there is sufficient evidence to suggest a significant difference between the sample mean and the population mean.
- If the p-value is greater than the alpha value, you fail to reject H 0. This means there is not enough evidence to support a significant difference between the sample mean and the population mean.

On the graphs, you can indicate the critical regions (rejection zones) for each alpha value. These regions represent the extreme values where H 0 would be rejected. The critical regions depend on the type of hypothesis test (one-tailed or two-tailed) and the distribution of the test statistic.

For each alpha value, if the test statistic falls within the critical region(s), you would reject H 0; otherwise, you would fail to reject H 0. Remember to maintain a professional, concise, and friendly approach when explaining your conclusions.

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A confidence level is a statistical term that refers to the probability that a population mean or proportion falls within a specific range of values, called the confidence interval. The confidence level is typically expressed as a percentage and is based on the level of certainty desired by the researcher or decision-maker.

A confidence interval is a range of values around a point estimate, such as a sample mean or proportion, that is likely to contain the true population parameter with a specified level of confidence. The confidence interval is constructed by taking the point estimate and adding and subtracting the margin of error, which is based on the standard error of the estimate and the desired level of confidence.

For example, if we estimate the mean height of a population to be 65 inches with a margin of error of 2 inches and a 95% confidence level, the confidence interval would be [63, 67]. This means that we are 95% confident that the true population mean height falls between 63 and 67 inches.

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On the discussion of two customers, the comment on their opinion about the chances of spinning another 100% discount on the wheel, is that previous results won't affect the future's outcome.

Probability is calculated by dividing the favourable outcomes to the total possible outcomes. The addition rule of probability calculates the probability when the "or" operation is taking place between events. We have a spinning a wheel which based on discount to customers. Total slices on discount wheel is divided into, t = 12

Number of slices contains 10% discount,

= 6

Number of slices contains 20% discount, b = 3

Number of slices award a 40% discount, c

= 2

Number of slices award a 100% discount, d = 1

Now, We have to comment on the two customers'opinion based on the chances of spinning another 100% discount wheel. The spins are independent, that is every event is independent so if the wheel is fair the three gold winners in a row have no effect on the next persons’chances. So, The next person's chances will also remain the same Hence, previous results won't affect te future outcome.

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the randomly generated integer between 0 and 100 (inclusive). If there is a tie, the winner will be randomly selected from the tied submissions. What is the probability that a person who buys a ticket with a single submission will win the lottery

The probability that a person will win depends on the number of people who buy tickets and submit their integers. Assuming there are n participants, each person's submission has a 1/n chance of being selected as the winner.

Since there are 101 possible integers that can be generated, the probability that any given person's submission is exactly correct is 1/101. Therefore, the probability that a person who buys a ticket with a single submission will win the lottery is 1/n * 1/101.

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Answer:

Step-by-step explanation:

To divide the polynomial p(x) by d(x), we can use long division or synthetic division. Let's say we choose to use long division.

First, we need to write the polynomials in descending order of degree, with any missing terms filled in with zeros. Let's say the polynomials are:

p(x) = 3x^3 - 5x^2 + 2x + 4
d(x) = x - 2

Then, we set up the long division like this:

         3x^2 + x + 4
   x - 2 | 3x^3 - 5x^2 + 2x + 4

We divide the first term of p(x) by the first term of d(x), which gives us 3x^2. We write this above the division bar and multiply it by d(x), which gives us 3x^3 - 6x^2. We subtract this from p(x), bringing down the next term:

         3x^2 + x + 4
   x - 2 | 3x^3 - 5x^2 + 2x + 4
         - 3x^3 + 6x^2
             ----------
              -11x^2 + 2x

We repeat the process with the next term, dividing -11x^2 by x to get -11x, writing this above the division bar, and multiplying it by d(x) to get -11x + 22. We subtract this from -11x^2 + 2x, bringing down the next term:

         3x^2 + x + 4 - 11/(x-2)
   x - 2 | 3x^3 - 5x^2 + 2x + 4
         - 3x^3 + 6x^2
             ----------
              -11x^2 + 2x
              + 11x^2 - 22
              ----------
                     -20

Since we have no more terms to bring down, our remainder is -20. Therefore, the quotient p(x)/d(x) is:

p(x)/d(x) = 3x^2 + x + 4 - 11/(x-2) - 20/(x-2)^2

We can express this in the form p(x) d(x) by multiplying both sides by d(x):

p(x) = d(x) (3x^2 + x + 4 - 11/(x-2) - 20/(x-2)^2)
To answer your question, we'll first need the specific polynomials for p(x) and d(x) that you'd like to divide. However, I can still guide you through the general steps to perform the division and express the quotient.

1. Choose either synthetic or long division, depending on your preference and the complexity of the polynomials.
2. Divide p(x) by d(x) using the chosen method. Make sure to follow the steps of the division process carefully to obtain the correct quotient and remainder.
3. Once the division is complete, express the quotient p(x)/d(x) in the form p(x) = d(x) * q(x) + r(x), where q(x) is the quotient and r(x) is the remainder.

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The vertex form of the quadratic is:

y = (x - 3)^2 - 8

There we can see that the minimum value is y = -8.

To find it we need to complete squares, here we have the quadratic equation:

y = x^2 - 6x + 1

We can rewrite:

y = x^2 - 2*3*x + 1

We can add and subtract 3^2 to get:

y = x^2 - 2*3*x + 3^2 - 3^2 + 1

y = (x - 3)^2 - 9 + 1

y = (x - 3)^2 - 8

That is the vertex form, it says that the minimum value of the quadratic is y = -8.

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The school district's magnet school programs, of the 1882 qualified applicants, 52.44% were accepted, 16.41% were waitlisted, and 31.15% were turned away for lack of space.

The relative frequency for each decision made by the school district regarding their magnet school programs.
First, let's define relative frequency.

It is the fraction or proportion of the total data that belongs to a particular category or class. In this case, the categories are "accepted," "waitlisted," and "turned away."
To find the relative frequency for each decision, we need to divide the number of applicants in each category by the total number of qualified applicants, which is 1882.
So, the relative frequency for "accepted" is:
987/1882 = 0.524 or 52.4%
The relative frequency for "waitlisted" is:
309/1882 = 0.164 or 16.4%
And the relative frequency for "turned away" is:
586/1882 = 0.312 or 31.2%
To summarize the results, we can say that out of the 1882 qualified applicants for the school district's magnet school programs, 52.4% were accepted, 16.4% were waitlisted, and 31.2% were turned away due to lack of space.

This indicates that there is high demand for these programs and the school district needs to consider expanding their capacity to accommodate more students.

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There is sufficient evidence to conclude that the proportion of sales he makes to women is more than 75%.

At the 1% significance level, the critical value for a one-tailed test with 149 degrees of freedom is 2.326. Since the p-value of 0.0001 is much smaller than 0.01, we reject the null hypothesis that the proportion of sales made to women is equal to 0.75. Therefore, we can conclude that there is sufficient evidence to suggest that the proportion of sales made to women is more than 75%.

Note that we cannot conclude that the proportion of sales made to women is more than 50% because the null hypothesis assumes that the proportion is exactly 75%, not 50%. Furthermore, we have only tested the hypothesis that the proportion is greater than 75%, not whether it is greater than 50%. Therefore, the correct answer is: "There is sufficient evidence to conclude that the proportion of sales he makes to women is more than 75%."

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The loads carried by an elevator are found to follow a normal distribution with a mean weight of 1812 lbs, and a standard deviation of 105.3 lbs. The answer is c) [1606, 2018].

To answer this question, we need to use the concept of confidence intervals. A 95% confidence interval means that in 95% of all cases, the true population parameter (in this case, the weight of the elevator load) will fall within the interval.

To find the interval centered about the mean, we need to calculate the margin of error first. The formula for margin of error is:

Margin of Error = z*(standard deviation/square root of sample size)

Since we do not have a sample size here, we will use the population standard deviation instead.

For a 95% confidence level, the z-value is 1.96. So, plugging in the values we have:

Margin of Error = 1.96*(105.3/square root of 1)

Margin of Error = 205.97

Now, we can find the interval by adding and subtracting the margin of error from the mean:

Interval = [1812 - 205.97, 1812 + 205.97]

Interval = [1606.03, 2017.97]

Therefore, the answer is c) [1606, 2018].

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Answer:

-√36

Step-by-step explanation:

The first (approx. 3.567) is obviously irrational, as it continues forever; the decimal values do not end.

The next (√18) is approx. 4.243 and is irrational.

The next (π/3) is irrational because it involves an irrational number, π.

The last (-√36) is -6 and is therefore rational.

Answer:

$391.2 per owner

Step-by-step explanation:

find the total price of the items and divide it by five

The market share of the four remaining companies is 29% to the nearest percent.

The market share the four remaining companies have, to the nearest percent is calculated as follows;

The revenue of the other four companies is calculated as;

R = $4,120,500 - $2,940,000

R = $1,180,500

The market share of the four remaining companies is calculated as follows;

market share = ($1,180,500 / $4,120,500) x 100

market share = 28.65% ≈ 29%.

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If 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine,  the percent by mass of I in the sample is 75%. So, correct option is D.

The percent by mass of iodine in the sample can be calculated by dividing the mass of iodine by the total mass of the sample and then multiplying by 100.

Mass of iodine = 300 g

Mass of cesium = 100 g

Total mass of sample = 300 g + 100 g = 400 g

Percent by mass of iodine = (mass of iodine / total mass of sample) x 100

= (300 g / 400 g) x 100

= 0.75 x 100

= 75%

Therefore, the correct answer is D. 75%. This means that 75% of the total mass of the sample is iodine. It is important to note that the percent by mass of cesium in the sample is 25% because the sum of the percent by mass of all components in a sample must equal 100%.

So, correct option is D.

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The histogram that represents a set of data that is left-skewed is the one where the majority of the data is on the right side of the histogram, and the tail of the histogram extends to the left.

A left-skewed histogram is also called a negatively skewed histogram. In a left-skewed distribution, the majority of the data values are on the right side of the histogram, and the tail of the histogram extends to the left. This means that the data is clustered around higher values and gradually decreases as the values become smaller.

For example, imagine a dataset that represents the ages of a group of people. If most of the people in the group are young adults, but there are a few older individuals, the histogram would be left-skewed because the tail of the histogram (representing the older individuals) would extend to the left.

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There are many natural objects that have two or more lines of symmetry. here are two examples:

Starfish - A starfish has five arms which can be equal in shape and size, and every arm has two lines of symmetry running down the length of the arm. this means that a starfish has a total of ten strains of symmetry, with every line bisecting two fingers.

Snowflakes - Snowflakes are intricate ice crystals which can have many strains of symmetry. the precise variety of lines of symmetry depends on the form of the snowflake.

However typically, a snowflake has as a minimum six traces of symmetry that bypass via its middle factor, creating six same hands. some snowflakes could have as many as twelve strains of symmetry, making them quite symmetrical and beautiful herbal objects.

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Every even-digit palindromic number is divisible by 11.

To show that every even-digit palindromic number is divisible by 11, we'll use the divisibility rule for 11 and the properties of palindromic numbers.

An even-digit palindromic number is a number with an even number of digits, where the digits are symmetric around the center, such as 1221 or 678876.

The divisibility rule for 11 states that a number is divisible by 11 if the sum of its alternate digits (1st, 3rd, 5th, etc.) minus the sum of the remaining alternate digits (2nd, 4th, 6th, etc.) is divisible by 11.

Let's take an even-digit palindromic number with 2n digits: a₁a₂...aₙaₙ₊₁...a₂ₙ

Since it's palindromic, a₁=a₂ₙ, a₂=a₂ₙ₋₁, ... aₙ=aₙ₊₁.

Now, let's apply the divisibility rule for 11:

Difference = (a₁ + a₃ + ... + aₙ) - (a₂ + a₄ + ... + aₙ₊₁)

Since the digits are symmetric, the difference becomes:

Difference = (a₁ + a₃ + ... + aₙ) - (a₂ + a₄ + ... + aₙ₊₁) = (a₂ₙ + a₂ₙ₋₂ + ... + aₙ₊₂) - (a₂ₙ₋₁ + a₂ₙ₋₃ + ... + aₙ₊₁) = 0

The difference is 0, which is divisible by 11. Therefore, every even-digit palindromic number is divisible by 11.

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Answer:

4) 24

Step-by-step explanation:

Diagonals of a rectangle are congruent and bisect each other.

AE = x + 2

BD = 4x - 16

2AE = BD

2(x + 2) = 4x - 16

2x + 4 = 4x - 16

20 = 2x

x = 10

AC = BD = 4x - 16 = 4(10) - 16 = 40 - 16 = 24

Answer: 4) 24

cost of couch table is 732 and the cost of coffee table is 366

let the cost of coffe table is x

the cost of the couch=2×cost of coffe table

=2x

couch and coffe table=1098

2x+x=1098

3x =1098

x=366

2x=2×366=732

Answer:

cubic meter (m³)

Step-by-step explanation:

N/A

Answer:

The line that appears to be tangent to circle S is not actually tangent.

[tex] \sqrt{ {14}^{2} + {19}^{2} } = \sqrt{196 + 361} = \sqrt{557} [/tex]

√557 is not equal to 25.

Answer:

  not a tangent

Step-by-step explanation:

You want to know if a segment 19 units long from a point 25 units from the center of a circle of radius 14 units is a tangent.

A tangent to a circle forms a right angle with the radius to the point of tangency. You can easily check to see if the triangle shown is a right triangle by using the Pythagorean theorem.

If the triangle is a right triangle the sum of the squares of the short sides is equal to the square of the hypotenuse:

  14² +19² = 25²

  196 +361 = 625

  557 = 625 . . . . . . . . false — not a right triangle; not a tangent

__

Additional comment

The attached figure is drawn to scale. It shows line QR intersects the circle in 2 places, so is not a tangent. The angle at Q is obtuse.

Given 3 sides of a triangle, you can classify it as acute, right, or obtuse using the "form factor" computed as follows. Form the sum of the squares of the two shorter sides, and subtract the square of the longer side:

  f = 14² +19² -25² = 196 +361 -625 = -68

The interpretation is ...

The equation is true for any value of x! This means that no matter how many tools Victor gives to Ilay, the ratio of their tools will never be 3:4. Therefore, there is no solution to this problem.

Let's start by using algebra to represent the given information. Let's say that the number of tools Victor has is represented by the variable "v" and the number of tools Ilay has is represented by the variable "i".

According to the problem, we know two things:

The ratio of Victor's tools to Ilay's tools is 5:2, which can be written as:

v/i = 5/2

Victor has 42 more tools than Ilay, which can be written as:

v = i + 42

Now, we want to find how many tools Victor should give to Ilay so that the ratio becomes 3:4. Let's say that the amount of tools Victor gives to Ilay is represented by the variable "x".

After giving x tools to Ilay, Victor will have v-x tools, and Ilay will have i+x tools. We want to find the value of x that makes the ratio of v-x to i+x equal to 3:4.

So, we can set up the following equation:

(v-x)/(i+x) = 3/4

Now we can substitute the expression for v and the ratio of v/i to get an equation in terms of i and x:

(i+42-x)/(i+x) = 3/4

Next, we can cross-multiply to get rid of the denominators:

4(i+42-x) = 3(i+x)

Simplifying this equation:

4i + 168 - 4x = 3i + 3x

Combining like terms:

i = 7x - 168

Now we have an equation that relates the number of tools Ilay has to the number of tools Victor gives him. We can substitute this into the equation v=i+42 to get an equation that only involves x:

v = 7x - 126

Finally, we can use this equation to find the value of x that makes the ratio 3:4.

(v-x)/(i+x) = 3/4

(7x-126-x)/(i+x) = 3/4

6x-126 = (3/4)(i+x)

6x-126 = (3/4)(7x-168+x)

6x-126 = (3/4)(8x-168)

6x-126 = 6x - 126

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The inequality that determines the number of miles that Eddie can travel is $1.75 + $0.25x  ≤ $15 (first option).

The first step is to determine the inequality sign that would be used.

Here are inequality signs and what they mean:

The sign that would be used is (≤) less than or equal to

The form of the inequality is:

[flat fee + (cost per mile x number of miles)] ≤ total amount she has

$1.75 + ($0.25 × x) ≤ $15

$1.75 + $0.25x  ≤ $15

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Ortiz would be paid $1056 for working 48 hours under the given pay rate of $22 per hour.

If Ortiz worked for 48 hours at a pay rate of $22 per hour, the calculation of his total earnings can be done by multiplying the number of hours worked by the hourly rate.

To calculate Ortiz's earnings for 48 hours, we multiply 48 by $22, which gives us a total of $1056.

Therefore, Ortiz would be paid $1056 for working 48 hours under the given pay rate of $22 per hour.

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It is found that Ortiz paid $1056 for working 48 hours under the given pay rate of $22 per hour.

We are given that Ortiz worked for 48 hours at a pay rate of $22 per hour

Then the calculation of his total earnings could be done by multiplying the number of hours worked by the hourly rate.

To determine Ortiz's earnings for 48 hours, we multiply 48 by $22, that will gives us a total of $1056.

48 x 22 = 1056

Therefore, Ortiz will be paid 1056 dollars for working 48 hours under the  pay rate of $22 per hour.

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