A recent study of 50 U.S. chess players details such things as the number of years the players have been active and the chess ratings of the players. (A chess rating is a number, with a higher number indicating greater expertise.) The chess rating data for the sample of 50 players are summarized in the following

Answer:

Definition: The distributive property lets you multiply a sum by multiplying each addend separately and then add the products. ... Consider the first example, the distributive property lets you "distribute" the 5 to both the 'x' and the '2'.

Answer:

I'm not sure but I believe it is than 0=4/5

Answer:

HEG 122° FEG 58°

Step-by-step explanation:

HEG is 122° as well, those corners are opposite each other so they have the same amount of degrees.

FEG is 58° because a straight line is 180° and HEG Is 122° so 180°-122°=58°

Answer:

Measure FEG = 58

HEG = 122

Sorry if I got the measure names wrong, I can barely see them lol

Step-by-step explanation:

Don't know if you've learned this or not, but a straight line = 180.

A linear pair equals a straight line, meaning they equal 180.

DEF and FEG are linear pairs

180-122 = 58

FEG = 58

Vertical pairs are pairs across from each other and they are congruent, meaning that they are the same.

DEF and HEG are vertical pairs

If DEF = 122, HEG also equals 122

Answer:

576 for the week

Step-by-step explanation:

First determine how many hours she worked

4/5 * 40 = 32 hours

32 hours times the hourly rate of 18

32*18 =576

Answer:

To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:

A' = (-3, 3 + 3) = (-3, 6)

B' = (0, 7 + 3) = (0, 10)

C' = (-3, 0 + 3) = (-3, 3)

Therefore, the coordinates of the vertices for the image triangle A'B'C' are A'(-3, 6), B'(0, 10), and C'(-3, 3).

So the correct answer is: A′(−3, 6), B′(0, 10), C′(−3, 3).

Answer:

a

Step-by-step explanation:

Answer:y=-3x+12. Since the line is parallel the slope is still the same 6=-3(2)+12

Step-by-step explanation:

Answer:

$26,986.29

Step-by-step explanation:

We can use the formula for calculating the depreciation of an asset over time:

wor

\(\bold{D = P(1 - \frac{r}{100} )^t}\)

where:

D= the current value of the asset

P = the initial purchase price of the asset

r = the annual depreciation rate as a decimal

t = the number of years the asset has been in use

In this case, we have:

P = $39,600

r = 12% = 0.12

t = 3 years

Substituting these values into the formula, we get:

\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)

Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.

Answer:

$26,986.29

Step-by-step explanation:

As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:

\(f(t)=39600(1-0.12)^t\)

\(f(t)=39600(0.88)^t\)

To calculate the value of the car after 3 years, substitute t = 3 into the function:

\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)

Therefore, the car is worth $26,986.29 after 3 years.

The p-value is 0.1533, so p-value>0.05 fail to reject the null hypothesis. There is insufficient evidence to support the claim p-value greater than the significance level 0.05.

Consider the above given that

⇒\(& \alpha=0.05 \quad \mathrm{n}=34 \mathrm{~s}^2=0.0005 \\\)

⇒\(H_{0} : \sigma^2 \leq 0.0004 \\\)

⇒\(H_{a} : \sigma^2 > 0.0004\)

The null and alternative hypothesis test statistic:

⇒\(& \mathrm{x}^2=\left(\frac{\mathrm{n}-1}{\sigma^2}\right) \mathrm{s}^2 \\\)

\(& =\left(\frac{34-1}{0.0004}\right) 0.0005 \\\)

⇒\(& \mathrm{x}^2=\left(\frac{33}{0.004}\right) \times 0.0005 \\\)

\(& =82,500 \times 0.0005 \\\)

⇒\(& \mathrm{x}^2=41.25\)

⇒\(h_{0} : $\sigma^2$ is that or equal to $0.0004$\)

⇒\(h_{a} : $\sigma^2$ is greater that $0.0004$\)

⇒p value=p(z>41.25)

⇒p value=0.1533

By using P Value from Chi-Square Calculator

⇒p value=0.1533

⇒P value >0.05

Fail to reject the null hypothesis.

Therefore, the p-value is 0.1533, so p-value>0.05 fail to reject the null hypothesis.

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The competitive advantage of some small Americans factories such as in tolerance contract manufacturing lies in their ability to produce parts with very narrow requirements, or tolerances, that are typical in the aerospace industry. consider a product with specifications that call for a maximum variance in the lengths of the parts of 0.0004. suppose the sample variance for 34 parts turns out to be \(s^{2}=0.0005\) . use \(\alpha=0.05\) , to test whether population variance specification is violated.

\(H_{0} \\H_{a}\)

Test statistic:

The p-value is-------.

Answer:

\(y(x)=2xe^{3x}\) (See attached graph)

Step-by-step explanation:

To solve a second-order homogeneous differential equation, we need to substitute each term with the auxiliary equation \(am^2+bm+c=0\) where the values of \(m\) are the roots:

\(y''-6y'+9y=0\\\\m^2-6m+9=0\\\\(m-3)^2=0\\\\m-3=0\\\\m=3\)

Since the values of \(m\) are equal real roots, then the general solution is \(y(x)=C_1e^{m_1x}+C_2xe^{m_1x}\).

Thus, the general solution for our given differential equation is \(y(x)=C_1e^{3x}+C_2xe^{3x}\).

To account for both initial conditions, take the derivative of \(y(x)\), thus, \(y'(x)=3C_1e^{3x}+C_2e^{3x}+3C_2xe^{3x}\)

Now, we can create our system of equations given our initial conditions:

\(y(x)=C_1e^{3x}+C_2xe^{3x}\\ \\y(0)=C_1e^{3(0)}+\frac{C_2}{6}(0)e^{3(0)}=0\\ \\C_1=0\)

\(y'(x)=3C_1e^{3x}+C_2e^{3x}+3C_2xe^{3x}\\\\y'(0)=3C_1e^{3(0)}+C_2e^{3(0)}+3C_2(0)e^{3(0)}=2\\\\3C_1+C_2=2\)

We then solve the system of equations, which becomes easy since we already know that \(C_1=0\):

\(3C_1+C_2=2\\\\3(0)+C_2=2\\\\C_2=2\)

Thus, our final solution is:

\(y(x)=C_1e^{3x}+C_2xe^{3x}\\\\y(x)=2xe^{3x}\)

The algebraic expression for the area is:

A = (2H - 8)*H/2

Here we want to write the expression:

"the area of a triangle that has a base 8 inches less than 2 times wider than the height."

Remember that for a triangle of base B and height H, the area is:

A = B*H/2

So if the base is 8 inches less than 2 times the height, we can write:

B = 2*H - 8

Replacing that in the area equation we get:

A = (2H - 8)*H/2

That is the equation for the area.

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Answer:

Step-by-step explanation:

There is no point that is NOT included in the graph of the step function.

The coat check service charges $2 for the first hour and $1 for each additional hour or fraction of an hour.

To determine the point that is NOT included in the graph of the step function, we need to consider the charging scheme and analyze the pattern of charges.

The step function can be represented as follows:

For the first hour, the charge is a flat rate of $2.

For each additional hour or fraction of an hour, the charge is $1.

Let's analyze the points included in the graph:

(1, 2): This point represents the charge for the first hour, which is $2.

Now, let's consider the additional hours:

2. (2, 3): This point represents the charge for 2 hours, which is $2 for the first hour and $1 for the additional hour.

(3, 4): This point represents the charge for 3 hours, which is $2 for the first hour and $2 for the additional 2 hours.

(4, 5): This point represents the charge for 4 hours, which is $2 for the first hour and $3 for the additional 3 hours.

Based on the charging scheme, we can observe a pattern where the charge increases by $1 for each additional hour or fraction of an hour.

Since the charging scheme allows for any additional hour or fraction of an hour, there is no specific point that is excluded from the graph. Any positive value of x greater than or equal to 1 will have a corresponding point on the graph.

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Answer:

9

Step-by-step explanation:

s=18

e=4*s=72

e+x=3(s+x)

e+x=3s+3x

e-3s=2x

18=2x

x=9

The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

You mix 1/2 quart of blue paint for every 1/3 quart of red paint to make 5 quarts of purple paint.

Let 'x' be the amount of blue paint and 'y' be the amount of red paint. Then the equations are given as,

x / y = (1/2) / (1/3)

x / y = 3/2                        ...1

x + y = 5                          ...2

From equations 1 and 2, then we have

(3/2) y + y = 5

(5/2) y = 5

y = 2 quart

Then the value of 'x' is given as

x + 2 = 5

x = 3 quart

The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.

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Answer:

The length of the diameter of this circular area is of 30 miles.

Step-by-step explanation:

The area of a circular region can be represented by the following equation:

\(A = \pi r^{2}\)

In which r is the radius. The diameter is twice the radius.

In this question:

\(A = 225\pi\)

So

\(A = \pi r^{2}\)

\(225\pi = \pi r^{2}\)

\(r^{2} = 225\)

\(r = \pm \sqrt{225}\)

The radius is a positive measure, so

\(r = 15\)

Area in squared miles, so the radius in miles.

What is the approximate length of the diameter of this circular area

D = 2r = 2*15 = 30 miles

The length of the diameter of this circular area is of 30 miles.

Answer:

The 95% confidence intervals is (0.109, 0.125).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

Out of a sample of 6,458, a total of 754 reported that they have experienced physical bullying.

This means that \(n = 6458, \pi = \frac{754}{6458} = 0.1168\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1168 - 1.96\sqrt{\frac{0.1168*0.8832}{6458}} = 0.109\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1168 + 1.96\sqrt{\frac{0.1168*0.8832}{6458}} = 0.125\)

The 95% confidence intervals is (0.109, 0.125).

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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The slope of line h that is perpendicular to line g is: -4/3.

The slope values of any two lines that are perpendicular to each other are values that are negative reciprocals to each other.

The equation of of line g is given as y = 3/4x + 3/4, it is expressed in slope-intercept form as y = mx + b. This means that the value of the slope of line g is 3/4.

The negative reciprocal of 3/4 is -4/3. Therefore, the slope of line h that is perpendicular to line g would be -4/3.

The slope of line h is: -4/3.

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Answer:

m>−78

Step-by-step explanation:

that's your answer:)

Answer:76

Step-by-step explanation:

Vince=160

Nadir=140, which =56 on another planet. 140-56=84, so there's an 84lbs weight difference.

160-84=76 pick c

Answer:

12

Step-by-step explanation:

75% = 3/4 = 9games

1/4 = 3games

4/4 = 12 games

The correct equation of the circle with center (0,0) that passes through the point (-6,-6) is:

(x + 6)² + (y + 6)² = 72

Please note that the equation represents the circle with center (0,0) and radius √72.\(\)

Answer:

The equation of a circle with center (0,0) that passes through the point (-6,-6) is:

(x - 0)² + (y - 0)² = r²

where r is the radius of the circle. Since the center of the circle is (0,0), we can use the distance formula to find the radius:

r = √(0 - (-6))² + (0 - (-6))² = √(6² + 6²) = √72

Therefore, the equation of the circle is:

x² + y² = 72

The original number in the given question solved by algebra is 39/7.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The number is divided 5 times by 7 more than that number.

Let the number be x

Then,

x+7/5x = 8

x+7=40x

7=39x

x=39/7

Therefore, by algebra the answer will be 39/7.

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Answer:

An equivalent expression for (52 • 34)3 would be (52 • 34) • (52 • 34) • (52 • 34)

Another way to express this is (52)3 • (34)3

So it can also be written as (5^32^3) * (3^44^3)

It can be also expressed as 125 * (81*64)

This expression is the result of multiplying three times the product of 5^2 and 3^4

The given measures made up a scalene triangle. Therefore, option C is the correct answer.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Given that, a triangle has one side that measures 4 ft, one side that measures 6 ft and one side that measures 9 ft.

A. All the sides are not equal, then it is not an equilateral triangle.

B. Any two sides are not equal, then it is not an isosceles triangle.

C. All the sides are equal, then it is a scalene triangle.

D. By using Pythagoras theorem,

9²=6²+4²

81≠52

So, the given measure does made up right triangle.

Therefore, option C is the correct answer.

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Answer:

Part A:

To find the percentage of survey respondents who liked neither hamburgers nor burritos, we need to calculate the frequency in the "Does not like hamburgers" and "Does not like burritos" categories.

Frequency of "Does not like hamburgers" = Total in "Does not like hamburgers" category = 135

Frequency of "Does not like burritos" = Total in "Does not like burritos" category = 54

Total respondents who liked neither hamburgers nor burritos = Frequency of "Does not like hamburgers" + Frequency of "Does not like burritos" = 135 + 54 = 189

Percentage of survey respondents who liked neither hamburgers nor burritos = (Total respondents who liked neither hamburgers nor burritos / Total respondents) x 100

Percentage = (189 / 205) x 100 = 92.2%

Therefore, 92.2% of the survey respondents liked neither hamburgers nor burritos.

Part B:

To find the marginal relative frequency of all customers who like hamburgers, we need to divide the frequency of "Likes hamburgers" by the total number of respondents.

Frequency of "Likes hamburgers" = 110 (given)

Total respondents = 205 (given)

Marginal relative frequency = Frequency of "Likes hamburgers" / Total respondents

Marginal relative frequency = 110 / 205 ≈ 0.5366 or 53.66%

Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 53.66%.

Part C:

To determine if there is an association between liking burritos and liking hamburgers, we can compare the joint and marginal frequencies.

Joint frequency of "Likes hamburgers" and "Likes burritos" = 29 (given)

Marginal frequency of "Likes hamburgers" = 110 (given)

Marginal frequency of "Likes burritos" = 70 (calculated by adding the frequency of "Likes burritos" in the table)

To assess the association, we compare the ratio of the joint frequency to the product of the marginal frequencies:

Ratio = Joint frequency / (Marginal frequency of "Likes hamburgers" x Marginal frequency of "Likes burritos")

Ratio = 29 / (110 x 70)

Ratio ≈ 0.037 (rounded to three decimal places)