Donnie, Karim, and Shawn run on the cross-country team. At yesterday’s practice, Donnie ran 200% as far as Karim. The ratio of the distance that Karim ran to the distance that Shawn ran is 4 : 3.

If you add the distance that all three boys ran, you get a sum of 45 miles. How far did each boy run individually?



this is ratio problem

Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

Answer:

40

Step-by-step explanation:

280 divided by 7

The regression equation of the formula regarding tuition will be given as y = 34000 - 2300x.

Regression method of writing an equation is used to show relation between two variables. The two variables include an independent variable and a dependent variable. The dependent variable is related to the independent variable and their relation and changes can be shown with the help of regression model. According to the question

the charge for tuition = $32000

Charge deduced from tuition per year = $2300

So we assume the tuition cost as y and the number of years as x.

The regression equation will be

y = 34000 - 2300x

where y is the tuition cost and x is the number of years in school and y is dependent variable and x is independent variable.

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Answer:

To find the answers you just need to multiply each value by 3. This is as we are given the information that y is equal to 3x. If we know this and we know the values of x we can easily work out the output (y)!!

We can also see a pattern of +3 going upwards!!

Hope this helps, have a great day!

An important measure of location for categorical data is the mode.

While the mean and median can only be determined for numeric data, the mode can be used to describe categorical variables. The mode's principal benefit as a gauge of central tendency is this. When continuous or discrete variables are expressed as intervals, it is also helpful.

The mode represents the value that occurs most often in a dataset.

A dataset can have no mode (if no value repeats), one mode, or multiple modes.

A set of data values' mode is the value that appears the most frequently. The value x (i.e., X = x) at which the probability mass function takes its maximum value is known as the mode if X is a discrete random variable. In other words, it is the value that will be sampled most frequently.

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Yes there was an error made and it is a type II error

What is type i and ii error in Hypotheses testing?

A Type I mistake in statistics is a false positive finding, whereas a Type II error is a false negative finding.

The possibility of making these mistakes is inherent in hypothesis testing since making a statistical choice always entails some level of uncertainty.

The significance level, or alpha (), determines the likelihood of a Type I mistake, whereas beta () determines the likelihood of a Type II error. These dangers can be reduced by carefully designing the layout of your study.

Comparison of Type I and Type II errors

Considering your minor symptoms, you decide to get checked for COVID-19. There are two mistakes that could happen:

False positives of type I are when a test indicates you have a coronavirus when you don't.

False negative type II errors occur when the test results indicate that you don't have coronavirus but in fact you have.

The null and alternate hypotheses are provided below for the scenario:

H0: The average amount of tooth whitening achieved by toothpaste is four shades.

Ha: The average amount of colors your teeth lighten after using toothpaste is less than four.

H0: µ = 4

Ha: µ < 4

While we reject the null hypothesis when it is true, we made a type I error, according to the definition.

The failure to reject the null hypothesis when the null hypothesis is false is what is referred to as a type II error .

In the hypothetical situation, it is said that the average number of shades that toothpaste whitens teeth is three. This implies,

There are less than four hues. This proves that the null hypothesis is untrue.

This indicates that when the null hypothesis is false, we are unable to reject it.

It is a type II error as a result.

Yes, a type II error.

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Answer:

22

Step-by-step explanation:

Answer:

cheese is cheese

The equation of the ellipse in the graph, with center at (0, 0), and semi  major and minor axis of 3 and 2 can be presented as follows;

[tex]\dfrac{x^2}{2^2} +\dfrac{y^2}{3^2 } = 1[/tex]

An ellipse is the locus of a point that moves such that the sum of the distance from two points is constant.

The standard form of the equation of an ellipse can be presented as follows;

[tex]\dfrac{(x - h)^2}{b^2} + \dfrac{(y - k)^2}{a^2} = 1[/tex]

Where;

(h, k) = The coordinates of the center of the ellipse

a = The semi major axis

b = The semi minor axis

From the attached graph the coordinates of the center of the ellipse is; (0, 0)

The semi major axis, a  = 3

The semi minor axis, b = 2

Therefore;

[tex]\dfrac{(x - 0)^2}{2^2} + \dfrac{(y - 0)^2}{3^2} = 1[/tex]

The equation of the ellipse in standard form is therefore;

[tex]\dfrac{x^2}{2^2} + \dfrac{y ^2}{3^2} = 1[/tex]

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Answer:

43.152

Step-by-step explanation:

6/5*35.96=43.152

The table of values and the linear equations indicates

4. Andy is correct, the equation of the table of values is; y = 2·x + 4

5. The Three equations are the same

A linear equation is an equation that produces a straight line graph, when plotted on the coordinate plane and can be expressed in the form; y = m·x + c

Where;

m = The slope of the straight line graph of the equation

c = The y-intercept

4. The values in the table indicate that the difference between consecutive terms in the x-values and the first difference in the y-value is constant, therefore, the values represent a linear relationship.

The slope, m, of the linear relationship is constant and it can be found using any two pair of points as follows;

m = (4 - 2)/(0 - (-1))  = 2

The equation is therefore;

y - 2 = 2·(x - (-1)) = 2·(x + 1) = 2·x + 2

y = 2·x + 2 + 2 = 2·x + 4

The equation, y = 2·x + 4 is in the form y = m·x + c, therefore;

Andy is correct

5. The slope-intercept form of the equation of a straight line is; y = m·x + c

Therefore;

y + 1 = 2·x -3

y + 1 - 1 = 2·x - 3 - 1 (subtraction property)

y = 2·x - 4

The equation, y = 2·x - 4, is in the form, y = m·x + c

2·x - 3 = y + 1

2·x - 3 - 1 = y + 1 - 1 (subtraction property)

2·x - 4 = y

y = 2·x - 4 (symmetric property)

The equation, y = 2·x - 4 is in the form, y = m·x + c, which is the same as the first equation

2·y + 2 = 4·x - 6

2·y + 2 - 2 = 4·x - 6 - 2 (subtraction property of equality)

2·y = 4·x - 8

2·y ÷ 2 = (4·x - 8) ÷ 2 (division property)

y = 2·x - 4

The above equation is the same as the first two equations, therefore, the equations are the same

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True, A P-value of 0.07 is less than that significance requirement of 0.1, suggesting that there is sufficient evidence to conclude that people who have a significant other are happier than single people.

The hypothesis being examined was that those who have a significant other are happier on average than those who do not. To test this hypothesis, data from a sample size of persons were collected and evaluated to compute the P-value.

The P-value of 0.07 was determined to be less than the level of significance established at 0.1, implying that there is sufficient evidence to support the hypothesis that persons with a significant other are happier on average than solitary people.

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The number of packages that can be wrapped with 12 feet of ribbon is 24.

For the stated question.

Total length of the ribbon = 12 feet.

Ribbon required to wrap a one box = 1/2 foot.

Number of boxes = Total length / required ribbon for one box

Number of boxes = 12/ (1/2)

Number of boxes = 12 x 2

Number of boxes = 24

Thus, the number of packages that can be wrapped with 12 feet of ribbon is 24.

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Answer:

394

Step-by-step explanation:

because 14,203 divided by 36 is 394.527777778 but the complete number of necklaces he can make is 394.

Answer: B. Angle Bisector

Why: the line from D to be is intersecting or bisecting the 90 degree angle

Why you lie you say 30 but give a 15

it is false that that when the direction of bias is towards love it means that the error causes the true measure of association to be overestimated

A Measurement process is biased if it systematically overstates or understates the true value of the measurement

Systematic error due to difference in accuracy or completeness of recall to memory of past or experience is the most associated with recall bias.

Positive association is biased toward the null null value it means that the error causes the true value of association to be underestimated

but in the given given question the statement states that when the direction of the bias is toward the null it means that the error causes the true measure of association to be overestimated which is false

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Answer: One solution

Step-by-step explanation:

6x+16=2x+30

4x=14

x=7/2

Given surd [tex]\frac{7}{\sqrt{7} }[/tex] after rationalization we get it as [tex]\sqrt{7}[/tex]

The process of rationalization can be thought of as the removal of a radical or an imaginary number from the denominator of an algebraic fraction. In other words, eliminate the radicals from a fraction so that the denominator is solely composed of rational numbers.

Here we use the Rationalization technique

Given surds,

[tex]\frac{7}{\sqrt{7} }[/tex]

Multiplying Numerator and Denominator [tex]\sqrt{7}[/tex]

Then,

[tex]\frac{7}{\sqrt{7} }[/tex] × [tex]\frac{\sqrt[]{7} }{\sqrt{7} }[/tex]

We get the result as [tex]\frac{7\sqrt{7} }{7}[/tex] which is equal to √7

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An expression that would represent the number of frames he has left for him to make would be = X = n - ⅔.

A fraction is an expression that is used to represent the part of a whole structure or an object such as the wooden frame.

The total number of wooden frames to be made= n.

The number of frames that Mr. Brown has made= ⅔

The number that is left to be made = X

But, n = ⅔ + X

To find X, make X the subject of formula;

X = n - ⅔.

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The value of the integral ∫x²dV using cylindrical coordinates is 512π / 3 .

In this case, the solid is positioned between the cylinder x² + y² = 4 and will be evaluated by using the cone z²= 16x² + 16y² .

Cylindric coordinates will be used to calculate this integral  [tex]\int\limits_e {x^2} \, dx[/tex].

The distance from the origin to the point (x, y, 0) and the angle the point (x, y, 0) makes with the x-axis, respectively, are provided by the formulas.

x = r cos θ

y= r sin θ

With these coordinates, we shall characterize the solid E.

The boundary is then x² + y² = r²

The boundary also becomes r² = 4 or ( 0 ≤ θ ≤ r² )

Again z = 16r²

The original integral must now be translated into terms of these new coordinates. It is necessary to multiply the function by the Jacobian of the change in coordinates in order to ensure that the result remains the same. The value for the cylindric coordinates is r. Then

[tex]\int_ex^2 dx = \int\limits^{2\pi}_0\int\limits^2_0\int\limits^{16r^2}_0 r(r^2cos^2\theta)dzdrd\theta[/tex]

[tex]=\int _0^{2\pi }\int _0^216r^5\cos ^2\theta drd\theta[/tex]

[tex]=\int _0^{2\pi }\frac{512}{3}\cos ^2\theta d\theta[/tex]

= 512/3 π

Hence the volume of the solid that is enclosed by the integral is given by 512/3 π .

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a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700 then average total cost is $ 0.61

The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:

1. 1,000 units per day at a total cost of $700.

ATC = Total cost/output

ATC = $700/1000

ATC = $0.58

2. If the firm produced 500 units per day, its total cost would be $450.

ATC = Total cost/output

ATC = $450/500

ATC = $0.45

3. If it produced 700 units per day, its total cost would be $425.

ATC = Total cost/output

ATC = $425/700

ATC = $0.61

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Answer:

3(n+6)

Step-by-step explanation:

3n+18= 3(n+6)

The null hypothesis and the alternate hypothesis for the set of elementary school children is given by H₀ :  μ₁ = 2 and H₁ : μ₂  ≠ 0 and the p-value is 0.136 .

Given x₁ = 74 , x₂ = 72

s₁ = 9 , s₂ = 11 (standard deviation)

n₁ = 50 ,n₂ = 50

Let μ₁ be the true mean for x₁

Let μ₂ be the true mean for x₂

null and alternate hypothesis:

H₀ :  μ₁ - μ₂  = 0

H₁ : μ₁ - μ₂  ≠ 0

Test statistic ,

Z = (x₁ - x₂ - D₀ ) / (√σˣ₁² /n₁ + √σˣ₂² /n₂ )

Now we will substitute the values to calculate the the test statistic.

D₀ = μ₁ - μ₂

hence Z₀ = (74 - 72) / √(81/80+121/50)

or,  Z₀ = 1.49256..

or,  Z₀ ≈ 1.49

Now we will calculate the p-value using the z-score.

p-value:

= 2P(Z > Z₀)

= 2P(Z>1.49)

= 2 {1-0.93189}

= 0.1362...

≈ 0.136

Hence the p-value is 0.136 .

A hypothesis is presented as a theory to explain a certain phenomenon. A hypothesis cannot be said to as a scientific hypothesis if it cannot be tested using the scientific process.

History-based observations that can't currently be fully explained by existing bodies of knowledge are typically where science starts. A hypothesis is a theory put out to explain an observed occurrence or a proven assertion regarding the relationship between two or more variables in a scientific field.

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The possible amount of time that it could take Wyatt to husk 72 dozen ears of corn is 4 to 6 hours.

What are time and work?

Time is the span of any action or work that occurs or is ongoing. Work is a task or series of activities carried out to accomplish a specific goal.

Given, Wyatt can husk anywhere from  12 to  18 dozen ears of corn per hour.

Thus, to find the time taken to husk 72 dozen ears of corn,

the maximum time = 72/12 =6 hours

And, the minimum time =  72/18 =4 hours

Thus, depending on his speed, Wyatt takes anywhere from  4  to 6 hours to husk  72 dozen ears of corn.

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The simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

The given statement is "7-radical 7 over10+radical 3".

Write the statement in mathematical form and simplify:
[tex]\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\\\\\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\times\frac{10 - \sqrt{3}}{10 -\sqrt{3}}\\\\\frac{(7 - \sqrt{7})(10-\sqrt{3})}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex]

Hence, the simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].

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The triple integral f(x, y, z)dV for the following function f is 256π(256 - x - y)² as an iterated integral in cylindrical coordinates.

In two-dimensional space R2, a point with rectangular coordinates (x, y) can be identified with (r, θ) in polar coordinates and vice versa, where x=rcosθ, y=rsinθ, r2=x2+y2 and tanθ=(y.x) are the relationships between the variables.

In three-dimensional space R3, a point with rectangular coordinates (x, y, z) can be identified with cylindrical coordinates (r,θ,z) and vice versa. We can use these same conversion relationships, adding z as the vertical distance to the point from the x y-plane

According to the question:

The integrated integral in cylindrical coordinates is given by:

∫∫∫f(ρ, θ, z)dV = ∫∫∫xρcos(θ)ρsin(θ)zdρdθdz

Evaluating the integral yields:

∫∫∫f(ρ, θ, z)dV = 256π∫zdz

= 256πz²

= 256π(256 - x - y)²

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The margin of error for the population mean is 5.601

What does the term "margin of error" mean?

Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.

Given c = 0.95

The significance level is obtained as follows:

alpha = 1 - c

alpha = 1 - 0.95

alpha = 0.05

Also, it is given that n = 150 and sigma = 35 .

The critical value of Z distribution at 0.05 level of significance can be computed in MS Excel using + NORMS INV (alpha/2) function as follows:

Thus, [tex]Z_{0.005/2}=1.96[/tex]

Now, the margin of error can be computed as follows: ME = Critical Value x Standard Error

[tex]Z_{0.005/2}*\frac{sigma}{\sqrt{n} } \\= 1.96 * \frac{35}{\sqrt{150} } \\= 5.601[/tex]

Thus, the margin of error for the population mean is 5.601

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