The price of a package of 4 pens is $8.00. The same pens are sold at $2.50 each. If Alex bought three packages of pens rather than buying 12 pens individually, the amount he saved on 12 pens is the percent of the amount he paid is

Sharon, an 8th grader, found the following values for weekly allowances in dollars of seven of her friends: 5, 7, 10, 8, 6, 12, and 15. if Sharon wanted to construct a one-sample t-statistic, the number of degrees of freedom is

6 degrees of freedom

The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom.

When calculating degrees of freedom, one is subtracted from the total number of items in the data sample.

mathematically, for number of data, n

degree of freedom = n - 1

the given problem has n = 7

degree of freedom = 7 - 1

degree of freedom = 6

the number of degree of freedom is 6

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According to ADA guidelines, a ramp with a two-foot vertical rise should be at least 20 feet long.

This length allows for a gentle slope that is safe and accessible for individuals with mobility impairments, including those using wheelchairs or other mobility aids. The slope of the ramp should not exceed 1:12, which means that for every inch of vertical rise, the ramp should extend 12 inches horizontally.

The ADA guidelines are designed to ensure that individuals with disabilities have safe and accessible routes of travel in public spaces. Ramps with proper dimensions and slope ratios are critical for individuals with mobility impairments to access buildings and spaces that may not be accessible via stairs. Ramps should also be designed with non-slip surfaces, handrails, and other safety features to prevent accidents and ensure that all individuals can use them safely and comfortably.

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To show that a series converges, we can use an upper bound on the terms. An upper bound is a value that is greater than or equal to all the terms in the series. In this case, we are looking for an upper bound on the largest probability in the multinomial(n;1/3,1/3,1/3) distribution.

The multinomial distribution is a probability distribution that describes the outcome of a random experiment where there are multiple possible outcomes and each outcome has a fixed probability. In this case, there are three possible outcomes, each with a probability of 1/3.

The largest probability in the multinomial(n;1/3,1/3,1/3) distribution is given by the maximum value of the multinomial coefficient:

$$\binom{n}{k_1,k_2,k_3}=\frac{n!}{k_1!k_2!k_3!}$$

where $k_1$, $k_2$, and $k_3$ are the number of times each outcome occurs in the experiment.

Since each outcome has a probability of 1/3, the largest probability occurs when $k_1=k_2=k_3=n/3$. Therefore, the largest probability is given by:

$$\binom{n}{n/3,n/3,n/3}=\frac{n!}{(n/3)!(n/3)!(n/3)!}$$

This value is an upper bound on the terms in the series and can be used to show that the series converges.

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\(6x(2xy + 5) \)

Answer:

42.8

Step-by-step explanation:

(10+30)*1.07=42.8

Answer:

\(y=45+60x\)

Step-by-step explanation:

Step one:

given data

The  charge is $45 to install the cable box and $60 for each month of service

Required

The linear expression for the situation.

Step two:

let the number of months be x and let the total charges be y

Hence the expression for the total charges is

\(y=45+60x\)

The runner's rate in miles per hour is D * 4/3 miles per hour.

Distance is a measure of the physical space between two objects or points. It is the length of the shortest path between two points in space. Distance can be measured in different units, such as meters, kilometers, miles, feet, or inches, depending on the scale of the objects or the purpose of the measurement.

In geometry, the distance between two points in a Euclidean space can be calculated using the Pythagorean theorem or the distance formula. The distance formula is expressed as:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where d is the distance between two points (x1, y1) and (x2, y2) in a two-dimensional plane. This formula can be extended to three dimensions by adding a third term to the equation.

Distance can also be calculated using other methods, such as GPS (Global Positioning System) or by measuring the time it takes for an object to travel from one point to another, using the speed of light or sound.

In everyday life, distance is a fundamental concept used in various contexts, such as navigation, transportation, sports, and communication. It plays a significant role in determining the time and effort required to travel between two points and is often used as a basis for making decisions.

We can use the formula:

rate = distance / time

where distance is the distance traveled by the runner and time is the time taken to travel that distance.

Given that the runner travels 2/3 of the marathon distance in 10 minutes, we can find the total distance of the marathon by dividing the distance traveled by 2/3:

total distance = distance traveled / (2/3) = distance traveled * 3/2

Let's denote the total distance of the marathon as D. Then:

D = distance traveled * 3/2

distance traveled = D * 2/3

We know that the time taken to travel 2/3 of the distance is 10 minutes. Let's convert this to hours:

10 minutes = 10/60 hours = 1/6 hours

Now we can calculate the runner's rate:

rate = distance / time = (D * 2/3) / (1/6) = (D * 4/3) / 1 = D * 4/3

So the runner's rate in miles per hour is D * 4/3 miles per hour.

Note that we don't have a specific value for the total distance D of the marathon, so we cannot give a numerical answer. We can only express the runner's rate in terms of D as:

runner's rate = D * 4/3 miles per hour

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Option 4, where most people keep the original item, aligns with psychological tendencies such as loss aversion and the endowment effect.

Among the given options, the most likely scenario is option 4: most people will keep the original item since people tend to value what they have more than a product they do not possess. This behavior can be attributed to the concept of loss aversion and the endowment effect.

Loss aversion refers to the tendency of individuals to strongly prefer avoiding losses rather than acquiring equivalent gains. In the context of the scenario, people may perceive the act of exchanging their original item as a potential loss because they already possess and value it. As a result, they may be reluctant to give up their original item, even if the alternative item is of equal value.

The endowment effect further strengthens this inclination to keep the original item. The endowment effect suggests that people assign a higher value to items they already possess compared to identical items that they do not own. This valuation bias stems from the psychological attachment and sense of ownership associated with the original item.

Given these behavioral biases, it is reasonable to expect that most individuals will choose to keep their original item rather than exchange it for an alternative item. This preference is driven by the aversion to perceived losses and the elevated value placed on the possession of the original item.

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Answer:

2a). Height = 2 cm

2b). Surface area = 395.84 cm²

Step-by-step explanation:

2a). Volume of the cylinder = 308 cm³

      Radius of the base of the cylinder = 7 cm

      Formula to get the volume of a cylinder = πr²h

     308 = π(7)²h

     h = \(\frac{308}{49\pi }\)

     h = 2 cm

     Therefore, height of the cylinder will be 2 cm.

2b). Formula to calculate the surface area of the cylinder = \(2\pi r(r + h)\)

      By substituting the values in the given formula,

      S.A. = 2π(7)(7 + 2)

              = 395.84 cm²

     Therefore, Surface area of the cylinder is 395.84 cm².

Answer:

∠8 = 125°

Step-by-step explanation:

Angle 8 is equal to the first angle of the diagram

Hope this helps.

Answer:

X=y

x/y+2=3 because

Y+Y+Y=3 so

X=Y+Y+Y=3

Answer:

No se

Step-by-step explanation:

pero okueuekdnfjdbebf

Answer:

He will have $10.10 left !

Step-by-step explanation:

Work in photo !

Answer:

6.27 x 10 ^ 8

Step-by-step explanation:

Answer:

\(g(x)=(x-3)(x+2)(x-2)\)

Step-by-step explanation:

Given:

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a)  is a factor of f(x).

Therefore, if 3 is a zero of g(x), then g(3) = 0 and so (x - 3) is a factor of g(x):

\(\implies g(x)=(x-3)(ax^2+bx+c)\)

As the leading coefficient of g(x) is one, a = 1:

\(\implies g(x)=(x-3)(x^2+bx+c)\)

As the constant of g(x) is 12, c = 12 ÷ -3 = -4:

\(\implies g(x)=(x-3)(x^2+bx-4)\)

Expand:

\(\implies g(x)=x^3+bx^2-4x-3x^2-3bx+12\)

\(\implies g(x)=x^3+(b-3)x^2-(4+3b)x+12\)

Compare the coefficients of the terms in x² to find b:

\(-3x^2=(b-3)x^2 \implies b=0\)

Therefore:

\(\implies g(x)=(x-3)(x^2-4)\)

\(\boxed{\begin{minipage}{5 cm}\underline{Difference of Two Squares}\\\\$a^2-b^2=(a+b)(a-b)\\ \end{minipage}}\)

To factor (x² - 4), rewrite as (x² - 2²) and apply the difference of two squares:

\(\implies g(x)=(x-3)(x+2)(x-2)\)

Therefore, the function g(x) as a product of linear factors is:

Check by expanding the factored function:

\(\implies g(x)=(x-3)(x+2)(x-2)\)

\(\implies g(x)=(x^2-x-6)(x-2)\)

\(\implies g(x)=x^3-2x^2-x^2+2x-6x+12\)

\(\implies g(x)=x^3-3x^2-4x+12\)

Step-by-step explanation: To evaluate functions substitute the given number or expression function's variable.

Answer:

The rope is 94.65 feet.

Step-by-step explanation:

a) We reject the null hypothesis at the 0.05 level of significance.

b) The power of the test is approximately 0.666 or 66.6%.

c) A sample size of at least 47 to achieve a power of 0.95 when the true difference in means is 3.

(a) To test the hypothesis, we can use a two-sample t-test. The test statistic is given by:

\(t = (\overline{x}_1 - \overline{x}_2) / \sqrt{ ( \sigma_1^2/n_1 ) + ( \sigma_2^2/n_2 ) }\)

Plugging in the values given, we get:

\(t = (4.7 - 7.8) / \sqrt{ ( 9/11 ) + ( 6/14 ) } = -3.206\)

The degrees of freedom for this test are df = n1 + n2 - 2 = 23. Using a t-table or calculator, we find that the P-value is less than 0.005.

(b) The power of the test is the probability of rejecting the null hypothesis when the alternative hypothesis is true. In this case, the alternative hypothesis is that the true difference in means is 3. We can use the non-central t-distribution to calculate the power:

\(power = 1 - P( |t| < t_{1-\alpha/2,n_1+n_2-2,\delta} )\)

where\(t_{1-\alpha/2,n_1+n_2-2,\delta}\)is the critical value of the t-distribution with n1 + n2 - 2 degrees of freedom, a significance level of 0.05, and a non-centrality parameter of

Plugging in the values given, we get:

δ =\((3) / \sqrt{ ( 9/11 ) + ( 6/14 ) } = 2.198\)

\(t_{1-\alpha/2,n_1+n_2-2,\delta} = +2.074\)

Therefore, the power of the test is:

power = 1 - P( |t| < 2.074 )

Using a t-table or calculator with 23 degrees of freedom and a non-centrality parameter of 2.198, we find that P( |t| < 2.074 ) ≈ 0.334.

(c) Assuming equal sample sizes, we can use the following formula to find the sample size needed to achieve a power of 0.95:

\(n = [ (z_{1-\beta/2} + z_{1-\alpha/2}) / δ ]^2\)

where\(z_{1-\beta/2} and z_{1-\alpha/2}\) are the critical values of the standard normal distribution for a power of 0.95 and a significance level of 0.05, respectively.

Plugging in the values given, we get:

δ =\((3) / \sqrt{ ( 9/n ) + ( 6/n ) } = 0.925\)

\(z_{1-\beta/2} = 1.96\) (for a power of 0.95)

\(z_{1-\alpha/2} = 1.96\)

Solving for n, we get:

\(n = [ (1.96 + 1.96) / 0.925 ]^2 = 46.24\)

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Step-by-step explanation:

2/3 x 2/2 = 4/6

2/3 x 3/3 = 6/9

2/3 x 4/4 = 8/12

Answer:

whaddaheck

Step-by-step explanation:

Answer:

they are all 90 degree angles

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

Answer:

With that amount of butter she can make 26 pies.

For each pie she spends $1.13625 of butter.

Step-by-step explanation:

We first need to convert the total amount of butter she has from pounds to cups, to do that we need to multiply by 2, since for each pound she has 2 cups of butter, therefore:

butter in cups = 10*2 = 20 cups

Since each pie requires 3/4 cups of butter in order to calculate the number of pies she can make we need to divide the total amount of butter she has by the amount required for each pie. We have:

number of pies = total butter in cups / butter for one pie

number of pies = 20 / (3/4) = 20*(4/3) = 80/3 = 26.667

Since she can't make 0.66 pies, we will need to take only the integer part in consideration, therefore she can make 26 pies.

In order to know the cost for each pie we first need to know the cost for each pound of butter, to calculate that we take the total amount paid by her and divide it by the amount of butter she got.

price of butter per pound = 30.3/10 = 3.03

So each pound of butter costs $3.03 and is equivalent to 2 cups, we can make a rule of three to find the cost for each pie as shown below:

2 cups -> $3.03

3/4 cups -> $x

2/(3/4) = 3.03/x

2*(4/3) = 3.03/x

8/3 = 3.03/x

8x = 9.09

x = 9.09/8 = $1.13625

For each pie she spends $1.13625 of butter.

The description of the cosine function is \(\mathrm{f(x) = -10 \cos( \frac{2\pi}{3}) x + 10}\).

A cosine function's general form is given by:

\(\mathrm{f(x) = A \times cos(Bx + C)) + D}\)

where:

A stand for amplitude, or the ratio of the maximum to the minimum value.

B = 2π / period

C stands for horizontal phase shift.

(Midpoint between the Maximum and Minimum Values) D = Vertical Shift

We can determine the parameters for the specified function given the information given:

Period = 3 (This means B = 2π / 3)

Maximum value = 20

This means the amplitude A is half of this, so A = 20 / 2 = 10

Minimum value = 0

This means the vertical shift D is half of the difference between the maximum and minimum.

So, D = (20 - 0) / 2

= 10

The amplitude is negative because the function is a mirror of its parent function over the x-axis, hence A = -10.

Putting it all together, the function is:

\(\mathrm{f(x) = -10 \cos( \frac{2\pi}{3}) x + 10}\)

Hence the final expression after the transformation is \(\mathrm{f(x) = -10 \cos( \frac{2\pi}{3}) x + 10}\).

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Answer:

99 degrees

Step-by-step explanation:

angle 8 = 99 degrees because corresponding or 'f shaped' angles are equal

Answer:

∠ 8 = 99°

Step-by-step explanation:

∠ 8 and 99° are corresponding angles and are congruent , so

∠ 8 = 99°

If the calculated chi-square test statistic is greater than 4.605, we would reject the null hypothesis of equal proportions at the 10% significance level.

To find the critical value for a chi-square test at the 10% significance level, we need to use a chi-square distribution table with degrees of freedom (df) equal to the number of categories minus 1.

Suppose the instructor is testing for the equality of proportions among k categories, then the degrees of freedom will be k-1.

The critical value for a chi-square test at the 10% significance level with k-1 degrees of freedom is given by the chi-square distribution table.

For example, suppose we have k=3 categories, then the degrees of freedom will be k-1 = 2. Using a chi-square distribution table with 2 degrees of freedom and a 10% significance level, we find the critical value to be 4.605.

Therefore, if the calculated chi-square test statistic is greater than 4.605, we would reject the null hypothesis of equal proportions at the 10% significance level.

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Answer:

$372.33

Step-by-step explanation:

For 1 mile= $0.45

For 827.4 miles = $0.45 x 827.4

= $372.33

The probability the friend finds no one in the first spot is 60%.

Probability is the chance or likelihood that an expected event occurs when there are many possible outcomes or events.

For instance, the probability that when the counting friend goes to the hiding spot, they can or cannot find a friend there.

The two friends can only hide in 2 spots, leaving 3 spots with nobody.

The number of hiding spots = 5

The number of friends hiding = 2

The number of counting friends = 1

The number of spots they can hide = 2 out of 5

The probability of finding a person in a hiding spot = 2/5 or 40%

The probability of not finding a person in a hiding spot = 3/5 (1 - 2/5) or 60% (1 - 40%).

The chances that your friend finds anyone in the first spot are 60%.

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a. The width of the gap is 2cm

b. There are two ways Mr Goh can stack up 20 completed stools. And the lowest possible height is 4.8 metres.

Length of A = 3/8 × 64cm

Length of A = 24cm

Given that the volume of B and C is the same, then:

total length of B and C = 64cm - 24cm

total length of B and C = 40cm

length of B = 20cm and length of C = 20cm

a. The width of the gap in the stool is calculated by subtracting the width of B and C from the length of A

24cm - 22cm = 2cm

b. 20 completed stools can be stacked either standing or by it sides, so they can be stacked in two ways.

height of stacking 20 stools standing = 20 × (20 + 11)cm = 620cm

height of stacking 20 stools by its side = 20 × 24cm = 480cm

620cm = 6.2m

480cm = 4.8m

Therefore, the width of the gap is 2cm. There are two ways Mr Goh can stack up 20 completed stools. And the lowest possible height is 4.8 metres.

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Answer:

−

2

(

2

−

7

)

Step-by-step explanation:

Let's first write out

2s+4+(-6s)+10

now simplify

-4s+14

again

now correct