a store sells jump ropes. each jump rope costs the same amount. during a sale, the store reduces the price of each jump rope by $1.90. marc spends $12.78 on 2 jump ropes at the sale price. what was the price of 1 jump rope before the sale

Answer:

$221.1

Step-by-step explanation:

Divide 73.70 by 5 pounds so that you can get the price of 1 pound beef

After diving the price for one pound of beef is $14.74.

Now, you have the price of 1 pound beef, you can just multiply it with 15 pounds.

15 x 14.74 = 221.1

Answer:

$221.1

Step-by-step explanation:

you multiplie it buy 5

The probability that the sample average is more than 8.40 is 1.02% as per the given pH of the water in the reservoir at a certain level.

The Given data is as follows:

The mean (μ)  = 8.5

The standard deviation (σ)  = 0.22

Sample size (n) = 37

The level of significance (α) = 0.05

We need to calculate  the probability of the sample average that should be more than 8.40.

sample distribution (z) = (x - μ) / (σ/√n)

z = (8.40 - 8.5) / (0.22/√37)

z = -2.57

By using the standard normal table, we can able to find that the probability of  z-score of -2.57. Assuming that this is a two-tailed test, the probability of getting a z-score of 2.57.

The probability of the sample average = 0.0051 + 0.0051 = 0.0102.

Therefore we can conclude that  the probability that the sample average is more than 8.40 is 1.02%.

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In mathematics, differentiation refers to the process of finding the derivative of a function. The basic means of differentiation include:

Limit definition: The derivative of a function is defined as the limit of the difference quotient as the interval over which the quotient is taken approaches zero.

Power rule: The derivative of a function of the form f(x) = xⁿ is given by f'(x) = nx⁽ⁿ⁻¹⁾

Product rule: The derivative of a product of two functions u(x) and v(x) is given by (u × v)'(x) = u'(x) × v(x) + u(x) × v'(x).

Quotient rule: The derivative of a quotient of two functions u(x) and v(x) is given by (u/v)'(x) = [u'(x) × v(x) - u(x) × v'(x)] / v(x)².

Chain rule: The derivative of a composition of functions f(g(x)) is given by f'(g(x)) × g'(x).

These basic means of differentiation are essential tools for analyzing and modeling functions in calculus and related fields.

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Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

The depth of the water in the Monterey Bay, California, can be modeled as a function of time in half-hours after midnight, denoted as y.

To find the equation that models the depth of the water in the Monterey Bay, we need more information about the function. Please provide the details or the equation that defines the relationship between the depth and time. To model the depth of the water in the Monterey Bay as a function of time, we need to gather data or information about the relationship between the two variables. Without this data, it is not possible to provide a specific equation. However, in general, the depth of the water in a bay can be influenced by several factors such as tides, weather conditions, and geography. Tides are primarily caused by the gravitational forces exerted by the moon and the sun on the Earth. The Monterey Bay is known for extreme tides due to its unique geography and the interaction of tidal currents with the underwater canyon system. The depth of the water can vary significantly throughout the day due to the tidal cycle. To accurately model the depth, it is necessary to consider the local tide tables or consult scientific studies that provide specific equations or formulas.

In conclusion, without specific information about the relationship between the depth of the water and time, it is not possible to provide an equation to model the depth of the water in the Monterey Bay accurately. To obtain accurate modeling, it is recommended to refer to local tide tables or consult scientific studies that provide specific equations or formulas based on the geographical and tidal characteristics of the bay.

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An equation that represent the graph is: D. y equals negative 2 times x plus two.

A graph that represent the linear equation y equals one fourth times x plus 1 on the coordinate plane is: D. graph of a line passing through the points 0 comma 1 and negative 4 comma 0.

A graph that shows the solution to the system of linear equations is: C. coordinate plane with one line that passes through the points 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 0 and 3 comma 1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁) or \(y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\)

Where:

At data point (0, 2), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

\(y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y +2 = \frac{(2+2)}{(-2 -0)}(x -0)\\\\y +2 = -2(x -0)\)

y = -2x - 2 (y equals negative 2 times x plus two).

For y equals one fourth times x plus 1, we have:

y = 1/4(x) + 1

Lastly, we would determine the solution to the system of linear equations;

y equals one third times x ⇒ y = 1/3(x)

x + 3y = 6

x + 3(x/3) = 6

x + 3x/3 = 6

6x/3 = 6

6x = 18

x = 3

y = 1/3(x)

y = 1/3(3)

y = 1.

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Answer:

D. They never intersect

Step-by-step explanation:

Answer:

seventy and six hundred eighty-one thousandths

Answer:

seventy thousand six hundred eighty one.

Step-by-step explanation: that is your answer

Answer:

y=-1/5x+3 or slope = -1/5

Step-by-step explanation:

Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

The  statement (f) is proved

To prove each of the statements (a)-(f):

(a) If n≡0(mod7), then n2≡0(mod7):
- Let n be any integer that is congruent to 0 modulo 7.
- This means n can be written as \(n = 7k\) for some integer k.
- Now, we can find n^2 and see if it is congruent to 0 modulo 7.
- \(n^2 = (7k)^2 = 49k^2 = 7(7k^2).\)
- We can see that n^2 is divisible by 7, which means \(n^2≡0(mod7)\).
- Therefore, statement (a) is proved.

(b) If n≡1(mod7), then n2≡1(mod7):
- Let n be any integer that is congruent to 1 modulo 7.
- This means n can be written as n = 7k + 1 for some integer k.
- Now, we can find n^2 and see if it is congruent to 1 modulo 7.
- \(n^2 = (7k + 1)^2 = 49k^2 + 14k + 1 = 7(7k^2 + 2k) + 1.\)
- We can see that n^2 leaves a remainder of 1 when divided by 7, which means \(n^2≡1(mod7).\)

- Therefore, statement (b) is proved.

(c) If n≡2(mod7), then n2≡4(mod7):
- Let n be any integer that is congruent to 2 modulo 7.
- This means n can be written as n = 7k + 2 for some integer k.
- Now, we can find n^2 and see if it is congruent to 4 modulo 7.
-\(n^2 = (7k + 2)^2 = 49k^2 + 28k + 4 = 7(7k^2 + 4k) + 4.\)
- We can see that n^2 leaves a remainder of 4 when divided by 7, which means\(n^2≡4(mod7).\)
- Therefore, statement (c) is proved.

(d) If n≡3(mod7), then n2≡2(mod7):
- Let n be any integer that is congruent to 3 modulo 7.
- This means n can be written as n = 7k + 3 for some integer k.
- Now, we can find n^2 and see if it is congruent to 2 modulo 7.
-\(n^2 = (7k + 3)^2 = 49k^2 + 42k + 9 = 7(7k^2 + 6k + 1) + 2.\)
- We can see that n^2 leaves a remainder of 2 when divided by 7, which means\(n^2≡2(mod7).\)
- Therefore, statement (d) is proved.

(e) For each integer n\(, n^2≡(7−n)^2(mod7):\)
- Let n be any integer.
- We can expand\((7-n)^2 to get (7-n)^2 = 49 - 14n + n^2 = n^2 - 14n + 49.\)
- Now, we can compare n^2 with\((7-n)^2.\)
- We can see that both expressions have the same remainder when divided by 7.
- Therefore, \(n^2≡(7-n)^2(\)mod7) for every integer n.
- Therefore, statement (e) is proved.

(f) For every integer n, n^2 is congruent to exactly one of 0,1,2, or 4 modulo 7:
- We have already proved statements (a)-(e), which cover all possible remainders modulo 7.
- Therefore, for every integer n, n^2 is congruent to exactly one of 0,1,2, or 4 modulo 7.
- Therefore, statement (f) is proved

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The radius R of the cylinder is 2/3 r when its volume is maximum.

Consider a right circular cone with height h and radius r. A right circular cylinder is inscribed in the cone such that its axis is perpendicular to the base of the cone and its upper end coincides with the upper slant edge of the cone.

To find the radius R of the cylinder when the volume is at a maximum, we need to differentiate the equation for the volume of the cylinder to R and set the derivative equal to zero. We also need to check that the resulting value for R produces a maximum volume. Let V be the volume of the cylinder.

Then the volume of the cylinder is given by:

V = πR²hLet the radius of the cone be r. Then the height of the cone is given by:

h = √(r² - R²)

So the volume of the cylinder becomes:

V = πR²√(r² - R²)

To find the maximum volume, we need to differentiate the volume equation to R and set the derivative equal to zero:

dV/dR = π(2R√(r² - R²) - R²/r)/2√(r² - R²) = 0

R² = (2/3)r²

R = (2/3)r

Therefore, the radius R of the cylinder is 2/3 r when its volume is maximum.

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Step-by-step explanation:

Step one:

The farmer sells his corn for $230 a metric ton

small surcharge = $25.

let the amount per metric ton be x

and let the total cost per x metric ton be y

the total cost function is

y=230x+25--------------1

The neighbor sells her corn for $230 a metric ton

he gives $15 rebate------A rebate is a partial refund of the cost of an item

let the amount per metric ton be x

and let the total cost per x metric ton be y

the total cost function is

y=230x-15----------------2

Step two:

Equating the two equation above

230x+25=230x-15

230x-230x=25+15

0=40

The result shows that based on the cost function of both farmer, there will never be an amount of corn that would make them have the same cost

a. The probability is approximately 0.1226

b. The probability is approximately 0.7196

c. Distribution of sample means follows a normal distribution

a. To find the probability that an individual distance is greater than 212.50 cm, we need to calculate the area under the normal distribution curve to the right of 212.50 cm.

First, we need to standardize the value using the z-score formula: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.

z = (212.50 - 202.5) / 8.6 = 1.1628

Using a standard normal distribution table or a calculator, we can find the area to the right of the z-score of 1.1628. This area represents the probability that an individual distance is greater than 212.50 cm. The probability is approximately 0.1226.

b. To find the probability that the mean for 15 randomly selected distances is greater than 201.20 cm, we can use the central limit theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

The mean of the sample means will be the same as the population mean, μ = 202.5 cm. The standard deviation of the sample means, also known as the standard error of the mean, can be calculated as σ / sqrt(n), where σ is the population standard deviation and n is the sample size.

standard error = 8.6 / sqrt(15) ≈ 2.22

Next, we standardize the value using the z-score formula:

z = (201.20 - 202.5) / 2.22 ≈ -0.5848

Using a standard normal distribution table or a calculator, we can find the area to the right of the z-score of -0.5848. This area represents the probability that the mean for 15 randomly selected distances is greater than 201.20 cm. The probability is approximately 0.7196.

c. The normal distribution can be used in part (b) even though the sample size does not exceed 30 because of the central limit theorem. According to the central limit theorem, as the sample size increases, the distribution of sample means approaches a normal distribution, regardless of the shape of the population distribution.

In this case, the sample size is 15, which is reasonably large enough for the central limit theorem to hold. Therefore, we can assume that the distribution of sample means follows a normal distribution, allowing us to use the properties of the normal distribution to calculate probabilities.

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The equation of the tangent plane to the surface at the point V is x + y + z = 3.

As per the question given,  

To find the equation of the tangent plane to the surface at the point V, we need to first find the partial derivatives of the surface with respect to u and v, and evaluate them at the point V.

r(u, v) = u^2 i + 3u sin(v) j cos(v) k

∂r/∂u = 2u i + 3sin(v)jcos(v)k

∂r/∂v = 3u cos(v)j(-sin(v))k + 3u sin(v)(-sin(v))j(-cos(v))k

At V, u = 0 and v = π/2, so

r(0, π/2) = 0 i + 0 j + 3k

∂r/∂u(0, π/2) = 0 i + 0 j + 3k

∂r/∂v(0, π/2) = 0 j + 0 i + 0 k

The tangent plane to the surface at V is given by the equation:

r(0, π/2) + ∂r/∂u(0, π/2)(u - 0) + ∂r/∂v(0, π/2)(v - π/2) = 0

Substituting the values, we get:

3k + 0u + 0v - 0i - 0j = 0

Simplifying, we get:

x - 0 + y - 0 + z - 3 = 0

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The volume of the square pyramid, to the nearest tenth, is determined as: 1.5 cubic inch.

Volume of a pyramid is given as, V = 1/3 × a² × h, where:

a = side length of the square base

h = height of the pyramid

Given the following:

Perimeter of the base = 5.1 in.

Side length of the square base = 5.1/4

The height of the pyramid = 2.7 in.

Plug in the values into V = 1/3 × a² × h:

Volume of the square pyramid = 1/3 × (5.1/4)² × 2.7

Volume of the square pyramid = 1/3 × 1.625625 × 2.7

Volume of the square pyramid = 1.4630625

Volume of the square pyramid = 1.5 cubic inch (to the nearest tenth of a cubic inch).

Thus, the volume of the square pyramid with the given perimeter, to the nearest tenth, is determined as: 1.5 cubic inch.

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Comparing the calculated density of the gold bar (19.085 g/cm^3) to the known density of pure gold (19.3 g/cm^3), we can conclude that the gold bar is likely to be pure gold.

Let's calculate the density correctly.The given information is as follows: Mass of the gold bar = 2990 g

Dimensions of the gold bar: 2.81 cm × 17.6 cm × 3.13 cm

To find the volume, we multiply the three dimensions:

Volume = 2.81 cm × 17.6 cm × 3.13 cm Now, let's calculate the volume:

Volume = 2.81 cm × 17.6 cm × 3.13 cm ≈ 156.709152 cm^3

Next, we can calculate the density of the gold bar using the formula:

Density = Mass / Volume ,Density = 2990 g / 156.709152 cm^3

Now we can calculate the density: Density ≈ 19.085 g/cm^3

The known density of pure gold is approximately 19.3 g/cm^3.

Comparing the calculated density of the gold bar (19.085 g/cm^3) to the known density of pure gold (19.3 g/cm^3), we can conclude that the gold bar is likely to be pure gold.

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(a) The probability that x > 1/7 is 4/7

(b) The probability that x < 1 + 7y is 1/9.

(a) To find the probability that x > 1/7, we need to integrate the joint density function over the region where x > 1/7 and y is between 0 and 1:

\(P(x > 1/7) = \int \int _{x > 1/7} p(x,y) dx dy\)

\(= \int_{1/7}^1 \int _0^1 2/3 (x + 2y) dx dy (since p(x,y) = 2/3 (x + 2y)\)for 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and 0 otherwise)

\(= (2/3) \int_{1/7}^1 (\int_0^1 x dx + 2 \int_0^1 y dx) dy\)

\(= (2/3) \int_{1/7}^1 (1/2 + 2/2) dy\)

\(= (2/3) \int _{1/7}^1 3/2 dy\)

= (2/3) (1 - 1/14)

= 12/21

= 4/7

Therefore, the probability that x > 1/7 is 4/7.

(b) To find the probability that x < 1 + 7y, we need to integrate the joint density function over the region where x is between 0 and 1 + 7y and y is between 0 and 1:

\(P(x < 1 + 7y) = \int \int_{x < 1+7y} p(x,y) dx dy\)

=\(\int_0^1 \int_0^{(x-1)/7} 2/3 (x + 2y) dy dx\)(since p(x,y) = 2/3 (x + 2y) for 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and 0 otherwise)

= \((2/3) \int_0^1 (\int_{7y+1}^1 x dy + 2 \int_0^y y dy) dx\)

= \((2/3) \int_0^1 [(1/2 - 7/2y^2) - (7y/2 + 1/2)] dx\)

= \((2/3) \int_0^1 (-6y^2/2 - 6y/2 + 1/2) dy\)

=\((2/3) \int_0^1 (-3y^2 - 3y + 1/2) dy\)

= (2/3) (-1/3 - 1/2 + 1/2)

= -2/9 + 1/3

= 1/9

Therefore, the probability that x < 1 + 7y is 1/9.

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Answer:

12(2m-p+6)

Step-by-step explanation:

Answer:

\(x^3\)

Step-by-step explanation:

To find the greatest common factor of a set of numbers, we need to find the greatest number, that when it's used as a divisor for all the numbers, returns an integer value.

We have the numbers \(x^3, x^6,\) and \(x^9\).

Exponent rules tell us that \(a^b \div a^c = a^{b-c}\).

This means that each of these values must be raised to the power of three. Therefore, each of them can be divided by \(x^3\).

\(x^3 \div x^3 = 1\)

\(x^6 \div x^3 = x^3\)

\(x^9 \div x^3 = x^6\)

So \(x^3\) is the GCF.

Hope this helped!

The amount Connor and Ashley need to make to have the same amount saved is $144

Let

Ashley:

1/4x + 11

Connor:

3/8x - 7

1/4x + 11 = 3/8x - 7

11 + 7 = 3/8x - 1/4x

18 = (3x-2x) / 8

18 = 1/8x

x = 18 ÷ 1/8

x = 18 × 8/1

x = $144

Therefore, the amount Connor and Ashley need to make to have the same amount saved is $144

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Answer:

38/55

Step-by-step explanation:

the probably is P(A)

2x4+2x5+4x5

11x10

2

8+10+20

55

38/55

Answer:

38/55

Step-by-step explanation:

hope its help

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The probability that the 5th child is a girl = 1/2

Before the first birth, the probability that the woman would give birth to 5 girls in a row = 0.03125

Step - by - Step expalanation

What to find?

• The probability that the 5th child is a girl.

• Before the first birth, the probability that the woman would give birth to 5 girls in a row.

Probability = required outcome / all possible outcome.

For the first part of the question, the 5th child could either be a boy or girl.

So, all possible outcome = 2 and the required outcome = 1

Hence, the probability that the fifth child is a girl = 1/2

For the second part of the question,

Before, the first birth, the probabilty that the woman would give birth to 5 girls in a row will simply =(probability of given birth to a girl)^no. of times she will give birth.

That is;

The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

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Answer:

1. Is -3, or answer choice C

For given six number cards, three pairs with the same total:

(8, -4), (6, -2) and (5, -1)

In this question, we have been given six number cards.

-4 -2 -1 5 6 8

We need to arrange the cards into three pairs with the same total in brackets.

Arranging cards with numbers  -4, -2, -1, 5, 6, 8 making pair with the same total.

i.e.  8 - 4 = 4

so the first pair is (8, -4)

6 - 2 = 4

so the second pair is (6,-2)

5 - 1 = 4

and the last pair is (5,-1)

Therefore, for given six number cards, three pairs with the same total:

(8, -4), (6, -2) and (5, -1)

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Answer:

-5

Step-by-step explanation:

Answer: -5

Answer if it is multiplication: 1.5555...(If it is additon don't pay attention to this answer)

Step-by-step explanation: -9 + -5 = -14.

Answer:

\(2x^{2}\) is your answer

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor (GCF).

By using Pythagorean identities the expression can be written as

         -8 (sin ( x ) + 1 -sin 2x)

The Pythagorean identity is an important identity in trigonometry derived from the Pythagorean theorem. These identities are used to solve many trigonometric problems where, given a trigonometric ratio, other ratios can be found. The basic Pythagorean identity, which gives the relationship between sin and cos, is the most commonly used Pythagorean identity:

sin2θ + cos2θ = 1 (gives the relationship between sin and cos)

There are two other Pythagorean identities as follows :

sec2θ - tan2θ = 1 (gives the relationship between sec and tan)

csc2θ - cot2θ = 1 (gives the relationship between csc and cot)

Given expression is:

-8tanx/ 1 +tan2x

we know that:

By the Pythagorean Theorem:

1 + tan²x = sec²x

and tan x = sin x/cos x

and, sec x = 1/cos x

Now, we can write as:

   -8tanx / 1 +tan²x

= -8 tan x / sec²x

= -8 sin x /cos x ÷ 1/cos²x

= -8 sin x/cos x × cos²x/1

= -8 (sin ( x ) + 1 -sin 2x)

Complete Question:

Use appropriate identities to rewrite the following expression in terms containing only first powers of sine:

−8tan 1 + tan2x.

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(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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