Greg, Albert, Joseph, and Finn are playing hide-and-seek and taking turns being 'it'. In how many different orders could the children take their turns being 'it'? orders​

Answer:

(0, 1)

Step-by-step explanation:

To find the solution to these 2 functions, we just set up an equation where they're equal to each other:

3x+2 = |x-1|+1

Then, isolate the absolute value:

3x+1 = |x-1|

Now, to get rid of the absolute value sign, we can set the right-hand side to be the positive or negative version of itself.

First, let's set it to the negative version of itself:

3x+1 = -x+1

4x = 0

x = 0

Then, let's set it to the positive version of itself:

3x+1 = x-1

2x = -2

x = -2

We can now plug the x as 0 and -2 into any of the 2 equations above to find the solution for y:

3(0)+1 = 1, so the first solution will be (0, 1)

3(-2)+2 = -4.

You might be tempted to say that -4 is the y value for the 2nd solution, but notice that |x-1| will never be less than 0, so that would not work. Therefore, x = -2 isn't a solution either, which means it's an extraneous solution.

In conclusion, the solution to these equations is (0, 2).

By finding the point where the graphs intercept, we will see that the solution of the system of equations is the point (0, 2).

The solutions of a system of equations are the points where the graphs of the different equations intercept when graphed.

Below you can see the graph of the system:

There you can see that we have only one intersection point at x = 0, y = 2, then we can conclude that our system has only one solution, and the solution is the point (0, 2).

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The number of words Gillan can read in 1 minute is,  165

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

Gillan read 3,135 words in 19 minutes

The number of words read each minute = w

Now, it has given,

Total words = 3135

Time taken = 19 minutes

For words per minute,

we need to take ratio of total words and total time taken,

Ratio =  Total words/Time taken

         =   3135/19

         =   165

Hence, the number of words in 1 minute is 165

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Answer: 1221759 ways

Step-by-step explanation:

choosing 5 out of 45

when the order doesn't matter.

45 C 5

grab your calculator

press math,

go move your section to PROB by using direction keys

press 3.

45 C 5

it should give you a value of

1221759

1. Figure STUV is congruent to Figure KLMN because rigid motions can be used to map Figure STUV onto Figure KLMN.

2. Figure STUV is also similar to Figure KLMN because rigid motions and/or dilations can be used to map Figure STUV onto Figure KLMN. The scale factor is 2.

When it is said that two figures are congruent, like the ones shown on the graph, This means that they have the same shape and size.

Similar figures have the same shape, but they may have different sizes and be located in different positions.

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Answer: So, the sales tax on the item is $49.

Step-by-step explanation:

The sales tax rate is already given as 14%. It is stated that the item costs $350 before tax, and the sales tax rate is 14%. Therefore, the sales tax amount can be calculated by multiplying the cost of the item by the tax rate:

Sales tax amount = $350 * 14% = $350 * 0.14 = $49

So, the sales tax on the item is $49.

Answer:

17.78 minutes

Step-by-step explanation:

2 1/4 = 2.25 miles

2.25 miles in 20 minutes

1  mile in 20/2.25 minutes

2 miles in 8.89*2 minutes

2 miles in 17.78 minutes

88 kilometers per hour in miles per hour is 54.68 mi/hr

Note that:

1 km = 0.6214 miles

The measurement to convert is 88 kilometers per hour

Multiply 88 kilometers per hour by 0.6214 to convert to miles per hour

88 kilometers per hour = 88 x 0.6214 miles per hour

88 kilometers per hour = 54.6832 miles per hour

88 kilometers per hour =  54.68 mi/hr

Therefore, 88 kilometers per hour in miles per hour is 54.68 mi/hr

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Answer:

583

Step-by-step explanation:

The mean of a data set is the average of the data set. It can be found by adding up all of the values and then dividing by the total number of values added. In this case, one is given the mean, and one needs to find a missing value. Since there is a missing element, add one to the total number of values in the data set. The missing element is represented by the parameter (x). Set up an equation and solve:

\(\frac{(236)+(342)+(328)+(352)+(352)+(306)+(317)+(x)}{8}=325\\\)

Simplify,

\(\frac{2233+x}{8}=352\)

Inverse operations,

\(2233+x=2816\\\\x = 583\)

Answer:

It’s 367

Step-by-step explanation:

Answer:

= ( 3 x + 5 ) ( 7 x² + 3 )

Step-by-step explanation:

Answer:

(x + i) (x - i)

Step-by-step explanation:

The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.

To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.

We can rewrite x^2 + 1 as:

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

Now, we can use the difference of squares formula to factor x^2 - (-1):

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

Therefore, the factored form of x^2 + 1 is:

(x + i)(x - i)

Answer:

6 1/3 (19/3)

Step-by-step explanation:

if they sold 3 1/6 trays of cinnamon donuts and there were 1/2 as many chocolate donuts sold wed have to do

1/2 divided by 3 1/6

3 1/6 - 19/6

1/2 divided by 19/6 = 6 1/3

hope this helped! <3

Answer:

6 1/3 (19/3)

Step-by-step explanation:

The missing fourth vertex needed to create a rectangle is (25, 3) option D.

Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.

Here, the width of one side of the rectangle;

⇒ +3 - (-6) = 9 unit                (left side y-coordinates)

Similarly the length of the rectangle;

⇒ 25 - (-15) = 40 unit             (up-side x-coordinates)

Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)

So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:

⇒ (25, -6+9) = (25, 3)

⇒ (-15+40, 3) = (25, 3)

Therefore, the missing fourth vertex is (25, 3)

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In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

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Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

Nate has a deductible of $1,000, which means he is responsible for paying that amount out of pocket before his insurance coverage kicks in. The cost of repairing his car is $7,000, which exceeds his deductible.

However, Nate's collision coverage limit is $5,000, which is the maximum amount his insurance will cover for repairs.

Since the cost of repairs exceeds Nate's coverage limit, he will have to pay the difference between the coverage limit and the actual repair cost.

In this case, Nate's out-of-pocket expenses would be $7,000 (repair cost) - $5,000 (coverage limit) = $2,000.

Therefore, Nate will have to pay a total of $2,000 out of pocket for this claim, which includes his $1,000 deductible and the additional $1,000 that exceeds his coverage limit.

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Answer:

-4

Step-by-step explanation:

I used my smarts

Answer:

Step-by-step explanation:

Step-by-step explanation:

Based on the provided information, I would recommend B&K Real Estate Company to choose the Silver Package with a sample size of 1,000 listings. This option strikes a balance between cost and accuracy, providing a reasonable margin of error while minimizing the cost for the service.

Confidence Statement:

"I am 95% confident that the true mean of the Northeast house listing prices falls within the estimated range, based on a sample size of 1,000 listings."

Factors Considered:

Cost: The cost for the Silver Package is $10,000, which is lower than the Gold Package but higher than the Bronze Package. B&K can achieve a reasonably accurate estimate of the mean listing price at a lower cost compared to the Gold Package.

Margin of Error: The margin of error for the Silver Package is $7,750. While it is larger than the Gold Package, it is significantly smaller than the Bronze Package. The margin of error represents the range within which the true mean of listing prices is likely to fall. With a smaller margin of error, the estimated mean is more precise, providing a better understanding of the Northeast home prices compared to the Bronze Package.

Sample Size: The sample size of 1,000 listings in the Silver Package is larger than the Bronze Package but smaller than the Gold Package. A larger sample size generally leads to a more accurate estimate of the population mean. Although the sample size in the Gold Package is larger, the incremental gain in accuracy is not significant enough to justify the higher cost.

Response to Peers:

Response 1:

If the agents prefer a higher confidence interval, such as 99%, compared to the management's 95% confidence interval, it would require a larger sample size to achieve the desired accuracy. This could result in increased costs for data collection. However, a higher confidence interval provides greater confidence in the estimated mean listing price, giving the agents more assurance when making decisions. The advantage is a higher level of confidence, but the disadvantage is the increased cost associated with a larger sample size.

Response 2:

If the agents prefer a lower confidence interval, such as 90%, compared to the management's 95% confidence interval, it would require a smaller sample size to achieve the desired accuracy. This could reduce the cost for data collection. However, a lower confidence interval means a wider margin of error and less certainty in the estimated mean listing price. The advantage is the cost savings, but the disadvantage is a lower level of confidence in the estimate, potentially leading to more uncertainty for the agents when making decisions

Answer:

The p-value of the test is 0.1611>0.01, which means that there is not significant evidence at the 1% significance level that less than 34% of fathers take no responsibility for child care

Step-by-step explanation:

A journal article reports that 34% of fathers take no responsibility for child care. A group of fathers believes that this estimate is too high.

At the null hypothesis, we test if the proportion is of at least 34%, that is:

\(H_0: p \geq 0.34\)

At the alternative hypothesis, we test if the proportion is less than that, that is:

\(H_1: p < 0.34\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.34 is tested at the null hypothesis:

This means that \(\mu = 0.34, \sigma = \sqrt{0.34*0.66}\)

In a random sample of 80 fathers, it was found that 23 of those fathers take no responsibility for child care.

This means that \(n = 80, X = \frac{23}{80} = 0.2875\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.2875 - 0.34}{\frac{\sqrt{0.34*0.66}}{\sqrt{80}}}\)

\(Z = -0.99\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.2875, which is the p-value of Z = -0.99.

Looking at the Z-table, Z = -0.99 has a p-value of 0.1611.

The p-value of the test is 0.1611>0.01, which means that there is not significant evidence at the 1% significance level that less than 34% of fathers take no responsibility for child care

"The correct answer is option A." The missing coordinates of point Q are (a, c/2).We are given the coordinates of points P and N as (0, c) and (2a, 0), respectively. We are also given that point Q lies on the same line as points P, Q, and N. We need to find the missing coordinates of point Q.

Since point Q lies on the same line as P, Q, and N, its x-coordinate must be halfway between the x-coordinates of points P and N. That is, the x-coordinate of Q is:

x-coordinate of Q = (x-coordinate of P + x-coordinate of N) / 2

x-coordinate of Q = (0 + 2a) / 2 = a

So, we know that the x-coordinate of point Q is a.

To find the y-coordinate of point Q, we can use the fact that point Q lies on the same line as point P, which has coordinates (0, c). The equation of the line passing through P and N is:

y - c = (0 - c) / (2a - 0) * (x - 0)

Simplifying this equation gives:

y - c = -c/2a * xy = -c/2a * x + c

Substituting x = a in this equation gives:

y = -c/2a * a + cy = -c/2 + cy = c/2

So, we know that the y-coordinate of point Q is c/2.

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Answer:

C. ±4/5

Step-by-step explanation:

25x² = 16

25x² - 16 = 16 - 16

25x² - 16 = 0

25x² + 20x - 20x - 16 = 0

(25x² + 20x) + (- 20x - 16) = 0

5x(5x + 4) - 4(5x + 4) = 0

(5x - 4)(5x + 4) = 0

5x - 4 =0

5x + 4 = 0

\(x=-\frac{4}{5}\)

\(x=\frac{4}{5}\)

± is a symbol which represents addition and subtraction.

Answer:

oh, easy it’s 25:)

Step-by-step explanation:

Answer:

12 more

Step-by-step explanation:

y-5= 6+ (x+1)

5+6+1=12

x is 12 less than y.

Five less than y is six more than x + 1,

y - 5= 6 + (x + 1)

5 + 6 + 1 = 12.

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The  interval containing the middle-most 86% of sample mean in the interval notation is  is (196.4, 203.5)

The 50 +/- 86/2 percentile will make up the center 86% of the sample means' distribution.

The 86th percentile's z-score is 1.08

sample mean population mean = 200

standard deviation from mean = 19

sample size = 33.

Standard error (SE) is equal to 19 / sqrt(33) = 3.3077.

86th percentile x can be located using the formula z = (x - population mean)/sample error.

1.08 = (x - 200)/3.3077

x = 3.3077* 1.08 + 200 = 203.57

that is the interval's upper bound.

it is 3.5721 over the population mean (203.57 - 200).

Due to the symmetry of the normal distribution, the interval's bottom bound will be 1.66 standard deviations below the population mean (200 - 3.572 = 196.428).

then the interval is (196.4, 203.5).

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We can complete the blanks with the following ratios:

(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags

Since we do not need a flag at the starting line, then 32 flags will be required in total.

To solve the problem, we would first convert 400 yds to feet and miles.

To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.

To convert to miles, we would have 0.227 miles.

Now, we divide the entire race distance by the number of miles divisions.

This gives us:

7.5 mi /0.227 mi

= 33 flags

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(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

Let A represent the number of students reading Accountancy, S represent the number of students reading Sociology, and F represent the number of students reading French.

Let X be the number of students reading all three.

From the information given:

A ∩ S = 19

A + S - 27 = 120 - 53 + 19 = 86 (number of students reading Accountancy or Sociology but not French)

S - A - X = 27

S + F - X = 53

F - X = 19

A - X = 86 - 19 = 67

Total = A + S + F - (A ∩ S) - (A ∩ F) - (S ∩ F) + X = 120

Solving, we get X = 6, A = 73, S = 52, F = 25.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

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The percent decrease in the number of ponds that support brook trout would be approximately 47.37%.

To calculate the percent decrease in the number of ponds that support brook trout, we need to determine the difference between the initial number of ponds and the final number of ponds, and then express that difference as a percentage of the initial number of ponds.

Initial number of ponds: 19

Final number of ponds: 10

To calculate the percent decrease, we can use the following formula:

Percent Decrease = (Difference / Initial Value) * 100

Let's apply this formula to the given data:

Difference = Initial number of ponds - Final number of ponds

Difference = 19 - 10

Difference = 9

Percent Decrease = (9 / 19) * 100

Now, let's calculate the percent decrease:

Percent Decrease = (9 / 19) * 100

Percent Decrease ≈ 47.37%

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When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)

First, we shall determine the value of A. Details below:

Quadratic equation is expressed as:

x² - (sum of root)x + product of root

Comparing the above with x² - 11x + 30, we have

x² - 11x + 30 = x² - (sumof root)x + product of root

Product of roots = 30

Thus,

A = 30

Next, we shall determine the value of B. details below:

f(x) = x² + 5

f(2) = 2² + 5

f(2) = 9

Thus,

B = 9

Next, we shall determine the value of C. Details below:

Let

x + 4 = 0

Thus,

x = -4

Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:

Remainder = x² - 2x - 24

Remainder = (-4)² - 2(-4) - 24

Remainder = 0

Thus,

C = 0

Finally, we shall determine value of A/5 + √(B - C). Details below:

A/5 + √(B - C) = 30/5 + √(9 - 0)

A/5 + √(B - C) = 6 + √(9

A/5 + √(B - C) = 6 + 3

A/5 + √(B - C) = 9

Thus, the value of A/5 + √(B - C) is 9 (option B)

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Here are a few examples of statistics and distributions that might be relevant for 11th-grade students:

The normal distribution: The normal distribution, also known as the Gaussian distribution, is a common probability distribution used in statistics. It is often used to model real-world phenomena, such as IQ scores, heights, or weights. It is characterized by a bell-shaped curve, with most data points clustered around the mean.

The binomial distribution: The binomial distribution is another common probability distribution, used when there are only two possible outcomes for a given event. For example, flipping a coin is a binomial experiment, with the two possible outcomes being "heads" or "tails".

The mean and median: These are measures of central tendency that are often used to summarize a data set. The mean is the average of all the data points, while the median is the value that separates the upper half of the data from the lower half.

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Answer:

2) Vertical scale does not begin with zero