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A survey of a group of seventh graders and a group of teachers at a local middle school asked how many siblings they each have. The dot plots below show the results.

Students
A dot plot titled Students. A number line going from 0 to 9 labeled number of siblings. There are 2 dots above 0, 4 above 1, 7 above 2, 5 above 3, 2 above 4, and 0 above 5, 6, 7, 8, and 9.

Teachers
A dot plot titled Teachers. A number line going from 0 to 9 labeled Number of siblings. There is 1 dot above 0, 3 dots above 1, 2 above 2, 4 above 3, 5 above 4, 3 above 5, 1 above 6, 0 above 7, 1 above 8, and 0 above 9.

Which compares the medians of the data?
The median for the students is 4 and the median for the teachers is 8.
The median for the students is 2 and the median for the teachers is 3.
The median for the students is 4 and the median for the teachers is 3.
The median for the students is 2 and the median for the teachers is 8.

Answer:

(-5,-8)

Step-by-step explanation:

Measurement of 5 quarts is equal to 20 cups.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

We have the measurement, 1 cup = 1/4 quarts

Let x be the number of quarts for 20 cups.

By using proportion,

1 / (1/4) = 20 / x

Cross multiplying,

x = 20 × (1/4)

x = 5

Hence the measurement of 20 cups is equal to 5 quarts.

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Thee measurement equals to 20 cups is 5 quarts.

Thus, option (a) is correct.

To determine which measurement is equal to 20 cups, compare the conversion factors between cups and each of the given measurements.

As, the conversion factors are:

1. 5 quarts

= 5 x  4 cups/quart

= 20 cups

2. 40 pints

= 40 x  2 cups/pint

= 80 cups

3. 1 gallon

= 1 x  16 cups/gallon

= 16 cups

4. 320 fluid ounces

= 320 x  0.125 cups/fluid ounce

= 40 cups

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Answer:

20%

Step-by-step explanation:

80 - 64 = 16

16 ÷ 80 = 0.2

0.2 × 100 = 20%

Answer:

13/15

Step-by-step explanation:

Answer:

Step-by-step explanation:

HOPE IT HELPS MUCH

Answer:

D) 5

Step-by-step explanation:

we see that every 4 hours 20 miles are traveled.

so, the rate of change of miles travels over hours is

20/4 = 5/1 = 5

in other words, the speed was 5 mph.

The false statement is: "The researchers would come to the conclusion that the programme was successful if they used a significance level of 1%."

What is significance level?

A significance level, denoted by α, is the threshold chosen by researchers to determine the level of evidence required to reject the null hypothesis. It represents the maximum acceptable probability of making a Type I error (incorrectly rejecting the null hypothesis when it is true).

In this case, the given p-value is 0.003. If the null hypothesis is true, the p-value represents the likelihood of obtaining a test statistic that is equally extreme to or more extreme than the one that was observed. It offers proof that the null hypothesis is false.

We can conclude that there is strong evidence to reject the null hypothesis in favour of the alternative hypothesis because the p-value is 0.003, which is lower than any often used significance level like 0.05 or 0.01. Thus, if the researchers apply a 5% level of significance, they would draw the conclusion that the programme was successful.

However, if the researchers use a significance level of 1%, they would require even stronger evidence to reject the null hypothesis. Since the p-value of 0.003 is greater than 0.01, they would not be able to reject the null hypothesis at the 1% significance level and would not conclude that the program was effective.

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Answer:The slope of the given line is -4

Step-by-step explanation:

Answer: 8575/2

Step-by-step explanation:

Sum of all interior angles of a triangle is 180.

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°~

<L = 133

<M = 108

<N = 119

Measures of the interior angles of the triangle

=(180 - 133) + (180 - 108) + (180-119)

= 47 + 72 + 61

= 180

Answer:

y=3/5x

Step-by-step explanation:

We use points 0, 0 and 5, 3.

With slope equation rise/run.

Rise from 0, 0 is 3.

Run from 0, 0 is 5.

so y=3/5x.

The frequency of the dominant allele in the population is 0.6.

Let's begin with the fundamental Hardy-Weinberg equations.

p + q = 1 and p² + 2pq + q² = 1

whereby "q" is the recessive allele and "p" is the dominant allele.

Recessed traits are present in 16% of people, or 0.16 percent. This indicates the percentage of the population that possesses the recessive trait,

q², is 0.16.

It is possible to calculate q using the value for q². What comes next is that q = 0.4.

This information allows for the calculation of "p".

1 − q = p , which results in "p" being 0.6.

This 0.6 is the frequency at which the dominant allele is prevalent in the population.

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The complete question is:

In a population that is in Hardy-Weinberg equilibrium, 16% of the individuals show the recessive trait. What is the frequency of the dominant allele in the population?

Answer:

180 g oats

0.9 L milk

45 g sugar

Step-by-step explanation:

those are all divided by 3/4 making just 3 portions :D

The height of the trapezoid is approximately 24.77 feet.

To find the height of a trapezoid, we can use the formula for the area of a trapezoid:

Area = (1/2) * (base1 + base2) * height

In this case, we are given the base lengths as 12 feet and 14 feet, and the area as 322 square feet. We need to find the height of the trapezoid.

Using the formula, we can rearrange it to solve for the height:

Height = (2 * Area) / (base1 + base2)

Substituting the given values:

Height = (2 * 322) / (12 + 14)

Height = 644 / 26

Height ≈ 24.77 feet

Therefore, the height of the trapezoid is approximately 24.77 feet.

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I = 0.75 ± 5 × 10⁻⁶ is approximately equal to 0.393717 ± 5 × 10⁻⁶.

We want to approximate the definite integral:

I = ∫₀¹ (1 + x³) dx

using a series to within an accuracy of 5 × 10⁻⁶, or |error| < 5 × 10⁻⁶.

We can start by expanding (1 + x³) as a power series about x = 0:

1 + x³ = 1 + x³ + 0x⁵ + 0x⁷ + ...

The integral of x^n is x^(n+1)/(n+1), so we can integrate each term of the series to get:

∫₀¹ (1 + x^3) dx = ∫₀¹ (1 + x³ + 0x⁵ + 0x⁷ + ...) dx

                      = ∫₀¹ 1 dx + ∫₀¹ x^3 dx + ∫₀¹ 0x⁵ dx + ∫₀¹ 0x⁷ dx + ...

                      = 1/2 + 1/4 + 0 + 0 + ...

                      = 3/4

So our series approximation is:

I = 3/4

To find the error, we need to estimate the remainder term of the series. The remainder term is given by the integral of the next term in the series, which is x⁵/(5!) for this problem. We can estimate the value of this integral using the alternating series bound, which says that the absolute value of the error in approximating an alternating series by truncating it after the nth term is less than or equal to the absolute value of the (n+1)th term.

So we have:

|R| = |∫₀¹ (x⁵)/(5!) dx|

    ≤ (1/(5!)) * (∫₀¹ x⁵ dx)

    = (1/(5!)) * (1/6)

    = 1/720

Since 1/720 < 5 × 10⁻⁶, our series approximation is within the desired accuracy, and the error is less than 5 × 10⁻⁶.

Therefore, we can conclude that:

I = 0.75 ± 5 × 10⁻⁶, which is approximately = 0.393717 ± 5 × 10⁻⁶.

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(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

The expected value of weekly demand is 1.3 units, the variance is 0.81, and the standard deviation is 0.9 units.

To find the expected value, variance, and standard deviation of the weekly demand, we can follow these steps:

1. Calculate the expected value (E[X]):
\(E[X] = \sum(x \times f(x))\)
= (0 * 0.2) + (1 * 0.4) + (2 * 0.3) + (3 * 0.1)
= 0 + 0.4 + 0.6 + 0.3
= 1.3

2. Calculate E[X²]:
\(E[X^2] = \sum(x^2 \times f(x))\)
= (0² * 0.2) + (1² * 0.4) + (2² * 0.3) + (3² * 0.1)
= 0 + 0.4 + 1.2 + 0.9
= 2.5

3. Calculate the variance (Var[X]):
Var[X] = E[X²] - (E[X])²
= 2.5 - (1.3)²
= 2.5 - 1.69
= 0.81

4. Calculate the standard deviation (SD[X]):
SD[X] = √(Var[X])
= √(0.81)
= 0.9

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Answer:

MO = 8 units

MP = 4 units

Step-by-step explanation:

\( In\: \triangle MOP, \\

\angle P = 90\degree ... (given) \\

\angle M = 60\degree ... (given) \\

\therefore \angle O = 30\degree(3^{rd} \: \angle \: of\: \triangle) \\

Let \huge\purple {MO = x \: units}... (1)\\

\therefore MP = \frac{1}{2} \times MO\\(side\: opposite \: to\: 30\degree) \\\\

\therefore MP = \frac{1}{2} \times x\\\\

\huge\red {\therefore MP = \frac{1}{2} x}.... (2)\\\\

\therefore PO = \frac{\sqrt 3}{2} \times MO\\(side\: opposite \: to\: 60\degree) \\\\

\therefore PO = \frac{\sqrt 3}{2} \times x\\\\

\huge\orange{\therefore PO = \frac{\sqrt 3}{2}x} \\\\

\because MP + PO + MO = P(\triangle MOP) \\\\

\therefore \frac{1}{2} x+\frac{\sqrt 3}{2}x+ x = 12+4\sqrt 3\\\\

\therefore \frac{1}{2} x+x+\frac{\sqrt 3}{2}x= 4(3+\sqrt 3)\\\\

\therefore \frac{3}{2} x+\frac{\sqrt 3}{2}x= 4(3+\sqrt 3)\\\\

\therefore \frac{(3+\sqrt 3)}{2} x= 4(3+\sqrt 3)\\\\

\therefore x = 4(3+\sqrt 3)\times \frac{2}{(3+\sqrt 3)}\\\\

\therefore x = 4\cancel{(3+\sqrt 3)}\times \frac{2}{\cancel {(3+\sqrt 3)}}\\\\

\therefore x = 4\times 2\\\\

\therefore x = 8\\\\

\huge\purple {\boxed{\implies MO = 8}} \: \\ [From\: equation \: (1)]\\\\

\because MP = \frac{1}{2} x \:

\\ [From\: equation \: (2)]\\\\

\therefore MP = \frac{1}{2} \times 8\\\\

\huge\red {\boxed{\therefore MP = 4 \: units}}

\)

Answer:

A linear relationship can be written as:

y = a*x + b

where a is the slope (also called the rate of change of y with respect to x) and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, we have the points (-3, 3.6) and (5, 2)

Then the slope will be:

a = (2 - 3.6)/(5 - (-3)) = (-1.6/8) = -0.2

Then the rate of change is -0,2

We could complete the equation for the line.

At the moment we know that:

y = -0.2*x + b

To find the value of b, we can simply replace the values of one of the points in that equation, i will use the point (5, 2)

This means that we must replace x by 5, and y by 2

2 = -0.2*5 + b

2 = -1 + b

2 + 1 = b

3 = b

Then the equation is:

y = -0.2*x + 3.

This question is based on the concept of equation of line. Therefore, the y = -0.2 x + 3 is the rate of change of y with respect to x for this function.

We need to determined the the rate of change of y with respect to x for this function.

According to the question,

A linear relationship of line can be written as:

y = a \(\bold{\times}\) x + b

Where, a is the slope ( rate of change of y with respect to x) and b is the y-axis intercept.

For a line that passes through the points\(\bold{(x_1, y_1) }\) and \(\bold{(x_2, y_2)}\). Thus, the slope can be written as:

\(a = \dfrac{(y_2- y_1) }{(x_2 - x_1)}\)

It is given that, the points are (-3, 3.6) and (5, 2) . Then the slope will be:

\(\bold{a = \dfrac{(2- 3.6) }{( 5- (-3) )} = \dfrac{-1.6}{8} = -0.2}\)

Then the rate of change is -0.2.

  Now, the equation of line become,

y = -0.2 x + b

Now, find the value of b, we can simply replace the values of one of the points in that equation, use the point (5, 2) .This means that we must replace x by 5, and y by 2.

2 = -0.2*5 + b

2 = -1 + b  

2 + 1 = b  

3 = b

Then the equation is:   y = -0.2 x + 3.

Therefore, the y = -0.2 x + 3 is the rate of change of y with respect to x for this function.

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If the scale factor is 3/4. Then the perimeter of the original triangle will be 66.67 units.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

A triangle with a perimeter of 50 units is the image of a triangle that was dilated by a scale factor of 3/4.

Then the perimeter of the preimage, the original triangle, before its

dilation will be

Let c be the perimeter of the original triangle.

Then we have

\(\rm \dfrac{3}{4} \times x = 50\\\\x = 66.67\)

Then the perimeter of the original triangle is 66.67 units.

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Answer:

9

Step-by-step explanation:

2(x-11) + 5-1

We can use the distributive property:

2x - 22 + 5 - 1

We can then simplify:

2x - 18

In this case, if 2x - 18 = 0, then 2x = 18 and x = 9.

Answer:

2x-18

Step-by-step explanation:

\(2(x-11)+5-1\\\)

Expand

\(2\left(x-11\right):\quad 2x-22\)

Slot it into the equation

\(=2x-22+5-1\)

Add/subtract the numbers

\(-22+5-1=-18\\\\=2x-18\)

\(\large \mathfrak{Solution : }\)

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\( \mathfrak{6 + 4 ( 19 - 15 )}\)

\( \mathfrak{6+4\times 4 }\)

\( \mathfrak{6+16 }\)

\( = \large\boxed{ \boxed{ \bf22 }}\)

Answer:

125 letters

Step-by-step explanation:

Hope this helps!

Answer:

-2

Step-by-step explanation:

the rate of change or slope (M) is -2

Hope this helps:P

Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Answer: 1.  a) discriminant

              4.  b) No. when < 0 it has no Real solutions

Step-by-step explanation:

All of the other answers are correct.

In the quadratic expression, the solutions are defined by the discriminant (b² - 4ac) as follows:

The midpoint of the line segment joining points A(2, -7) and B(4, 3) is (3, -2)

The points are given as:

A(2, -7) and B(4, 3).

The midpoint of the line segment joining points A(2, -7) and B(4, 3) is calculated as:

Midpoint = 0.5 * (x1 + x2, y1 + y2)

So, we have

Midpoint = 0.5 * (2 + 4, -7 + 3)

Evaluate the sum

Midpoint = 0.5 * (6, -4)

Evaluate the product

Midpoint = (3, -2)

Hence, the midpoint of the line segment joining points A(2, -7) and B(4, 3) is (3, -2)

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The probability is approximately 0.9429. Rounded to four decimal places, the probability is 0.9429. Therefore, the probability that the sample mean would be less than 107.81 liters is about 0.9429 or 94.29%.

To solve this problem, we can use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

First, we need to calculate the standard error of the mean, which is the standard deviation of the sampling distribution of the mean:

standard error = standard deviation / square root of sample size
standard error = 26 / sqrt(220)
standard error ≈ 1.756

Next, we can standardize the sample mean using the formula for z-scores:

z = (sample mean - population mean) / standard error
z = (107.81 - 105) / 1.756
z ≈ 1.574

Finally, we can use a standard normal distribution table or calculator to find the probability of getting a z-score less than 1.574.

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