In an analysis of variance where the total sample size for the experiment is nTand the number of populations is k, the mean square due to error is SSE/(k-1). 0 SSTR/k

The correct statement regarding the unit rate in this problem is given as follows:

Point (1,2) shows that the unit rate is of $2 per ounce.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The point of the graph is given as follows:

(1,2) -> x = 1, y = 2.

Hence the unit rate is given as follows:

k = y/x = 2/1 = 2.

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Answer:

(-5/3)x + 6

Step-by-step explanation:

To put the equation 20x + 12y = 72 into slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept, we need to solve for "y."

Step 1: Move the term with "x" to the other side of the equation:

12y = -20x + 72

Step 2: Divide both sides of the equation by 12 to isolate "y":

y = (-20/12)x + 72/12

Simplifying the expression further:

y = (-5/3)x + 6

Therefore, the equation 20x + 12y = 72 in slope-intercept form is y = (-5/3)x + 6.

Answer:

y = \(\frac{-5}{3}\) x + 6

Step-by-step explanation:

20x + 12y = 72  Subtract 20x from both sides

20x - 20x + 12y = -20x + 72

12y = -20x + 72  Divide every term by 12

\(\frac{12y}{12}\) = \(\frac{-20}{12}\)x + \(\frac{72}{12}\)

y = \(\frac{-5}{3}\)x + 6

Simply \(\frac{-20}{12}\) by dividing the top and the bottom by 4

Simplify \(\frac{72}{12}\) by dividing the top and bottom by 12

Helping in the name of Jesus.

Percentage for each year will be 0.05%

The percentage of each year for the 2000 bottles of whiskey can be calculated as follows:

For the new product price of $50 per bottle, the percentage is calculated as the ratio of the price per bottle to the total price. The total price of the new product is given by 2000 bottles multiplied by $50 per bottle, which equals $100,000. To find the percentage for the new product price, we divide $50 by $100,000 and multiply by 100:

Percentage for new product price = ($50 / $100,000) * 100 = 0.05%

For the 20-year-old bottles priced at $500 per bottle, we follow the same calculation. The total price for these bottles is given by 2000 bottles multiplied by $500 per bottle, which equals $1,000,000. To find the percentage for the 20-year-old bottles, we divide $500 by $1,000,000 and multiply by 100:

Percentage for 20-year-old bottles = ($500 / $1,000,000) * 100 = 0.05%

Therefore, both the new product price and the 20-year-old bottles have the same percentage, which is 0.05%.

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2% decrease= 0.98

3% decrease = 0.97

Answer:

\(7^5\)

Step-by-step explanation:

When multiplying numbers with the same base (in this case the base is 7), the exponents add. So

-6+16-5=5

So the answer is \(7^5\)

Answer:

m= -3/4

Step-by-step explanation:

use point slope formula

Answer:

i think is 424. its what my mom just explain to me

Answer:

170.25

Step-by-step explanation:

The rectangle maximum area will be A=9 square units with the length=3 and the width=3.

Area is defined as the space occupied by a plane or rectangle having length and width in two dimensional plane.

It is given that the perimeter of rectangle is P=12

So from the formula of perimeter of rectangle

2(L+W)=12

L+W=6

L=6-W

Now the area of rectangle will be

A=LxW

A=(6-W)W

Now for maximum area we will find the derivative and equate to zero.

\(A=(6W-W^2})\)

\(A'=6-2W=0\)

\(W=3\)

\(L=6-W=6-3=3\)

So the area will be

\(A=3\times 3=9 \ square \ units\)

Hence the rectangle maximum area will be A=9 square units with the length=3 and the width=3.

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There are 70 different types of pizzas could be ordered

A permutation is an act of arranging the objects or numbers in order.

Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter

Given,

Number of options on crust=2

Number of options on topping= 7

Number of options on size= 5

Therefore for each type of crust there are 7 different topping, for each toppings there are 5 different sizes

The total number ways of ordering pizza=2×7×5=70

Hence, there are 70 different types of pizzas could be ordered

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Answer:

11) -x to the power of 9/y to the power of 8

ᴍᴀᴛʜᴡᴀʏ can help you with the other problems.

Hope I could help!

The elimination method is a method for solving systems of linear equations.

The method of elimination  consists of removing the same variable from two equations and then finding the value of the other variable that is not eliminated after taking the difference between the two equations.

An equation of the form Ax By = C. Here x and y are variables and A, B and C are constants.

To solve the variables of the given equations by elimination method Let's look at a short comprehensible example.

2x + y = 7 ------> (1)

x + y = 5 -------> (2)

To eliminate 'y', subtract (1) - (2),

2x + y - x - y = 7 - 5

x = 2

Substitute x = 2 in equation(1),

2(2) + y = 7

4 + y = 7

y = 3

Therefore, x = 2, y = 3

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Answer:

x = 13, y = 24.

Step-by-step explanation:

5x - 8 + 63 + 7x - 31 = 180  (interior alternate angles are equal).

12x + 24 = 180

12x = 180 - 24 = 156

x = 156/12

x = 13.

4y + 27 =  63 + 7x - 31       (interior alternate angles are equal).

4y +27 = 32 +7(13)

4y = -27 +32 + 91

4y = `96

y = 96/4

y = 24.

Answer: the person above is wrong

Step-by-step explanation: Some ratios are not fractions.

and All fractions are ratios

From Vieta's formulas, we have

\(3x^2 - 4x + 1 = 3 (x - \alpha) (x - \beta) \\\\ ~~~~~~~~~~~~~~~~~ = 3x^2 - 3 (\alpha + \beta) + 3\alpha\beta \\\\ \implies \begin{cases} \boxed{\alpha + \beta = \frac43} \\\\ \boxed{\alpha\beta = \frac13} \end{cases}\)

a) Note that

\((\alpha + \beta)^2 = \alpha^2 + 2\alpha\beta + \beta^2 \\\\ \implies \alpha^2 - \beta^2 = (\alpha+\beta)^2 - 2\alpha\beta - 2\beta^2\)

We have exact values for \(\alpha+\beta\) and \(2\alpha\beta\), but sadly not for \(-2\beta^2\). This means we'll need to solve for \(\beta\) explicitly.

By factorizing, we have

\(3x^2 - 4x + 1 = (3x - 1) (x - 1) = 0 \\\\ \implies x = \dfrac13 \text{ or } x = 1\)

Then the value of \(\alpha^2-\beta^2\) depends on which is chosen to be the larger root, and

\(\alpha^2 - \beta^2 = \dfrac1{3^2} - 1^2 = \boxed{-\dfrac89} \text{ or } \alpha^2 - \beta^2 = 1^2 - \dfrac1{3^2} = \boxed{\dfrac89}\)

While we're at it, we can also immediately find

\(\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = \left(\dfrac43\right)^2 - 2\cdot\dfrac13 = \dfrac{10}9\)

b) Combine fractions to get

\(\dfrac2{\alpha^2} + \dfrac2{\beta^2} = \dfrac{2\beta^2 + 2\alpha^2}{\alpha^2\beta^2} \\\\ ~~~~~~~~~~~~~ = 2 \cdot \dfrac{\alpha^2 + \beta^2}{(\alpha\beta)^2} \\\\ ~~~~~~~~~~~~~ = 2\cdot \dfrac{\frac{10}9}{\left(\frac13\right)^2} \\\\ ~~~~~~~~~~~~~ = \boxed{20}\)

c) Combine fractions again.

\(\dfrac2{\alpha^2} - \dfrac2{\beta^2} = 2 \cdot \dfrac{\beta^2 - \alpha^2}{(\alpha\beta)^2} \\\\ ~~~~~~~~~~~~~ = -2\cdot \dfrac{\pm\frac89}{\left(\frac13\right)^2} \\\\ ~~~~~~~~~~~~~ = \boxed{\pm16}\)

Step-by-step explanation:

60° + 80° + y = 180° ( being straight angle )

140° + y = 180°

y = 180° - 140°

y = 40°

The directional derivative of a function f(x, y) at a point (a, b) in the direction of a unit vector u = ⟨cosθ, sinθ⟩ is given by the dot product of the gradient of f at (a, b) and the unit vector u.

That is, D_uf(a, b) = ∇f(a, b) · u

Here, f(x, y) = xy^3 - x^2, so ∇f(x, y)

= ⟨y^3 - 2x, 3xy^2⟩.

At the point (1, 4), we have ∇f(1, 4) = ⟨60, 192⟩.

The direction indicated by the angle theta = π/3 is u = ⟨cos(π/3), sin(π/3)⟩ = ⟨1/2, √3/2⟩.

Therefore, the directional derivative of f at (1, 4) in the direction of u is:

D_uf(1, 4) = ∇f(1, 4) · u

= ⟨60, 192⟩ · ⟨1/2, √3/2⟩

= 60/2 + 192(√3/2)

= 30 + 96√3

So the directional derivative of f at (1, 4) in the direction of θ = π/3 is 30 + 96√3.

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Answer:

3.333333

Step-by-step explanation:

4x-x=3+7

3x=10

x=3.33333

Answer:

C. 180-degree rotation counterclockwise followed by a translation of 5 units to the left

Step-by-step explanation:

Answer:

180° counterclockwise rotation about the origin followed by a translation 5units left

Step-by-step explanation:

Rule for 180° counterclockwise rotation is

Take any point to prove

let it be A

Rotate

Translate 5 units left(change in x)

Yes verified

The probability that the sample mean of 128 adults is more than 70.3 kilogrammes is about 0.08%.

We can utilise the Central Limit Theorem to tackle this problem, which stipulates that given a high sample size, the distribution of sample means will be approximately normal, regardless of the form of the population distribution. The sample means' mean will equal the population mean, and the sample means' standard deviation (also known as the standard error) will equal the population standard deviation divided by the square root of the sample size.

Given that the population mean is 68 kilogrammes and the population standard deviation is 10 kilogrammes, the chance that the sample mean of 128 adults is more than 70.3 kilogrammes must be calculated.

To begin, we first compute the standard error of the sample means:

Standard Error = Standard Deviation of the Population / Sample Size

= 10 / √128

= 0.8839

The z-score formula may then be used to calculate the z-score corresponding to a sample mean of 70.3 kilogrammes:

(sample mean - population mean) / standard error = z

= (70.3 - 68) / 0.8839

= 3.15

We may calculate the likelihood that the z-score is greater than 3.15 using a conventional normal distribution table or a calculator. Because the standard normal distribution is symmetrical, the likelihood of the z-score being more than 3.15 is the same as the likelihood of the z-score being less than -3.15.

According to a conventional normal distribution table, the probability associated with a z-score of -3.15 is roughly 0.0008.

As a result, the chance that the sample mean of 128 adults is more than 70.3 kilogrammes is roughly 0.0008, or 0.08%.

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The probability that the sample mean of 128 adults would be greater than 70.3 kilograms is approximately 0.0008, or 0.08%.

To solve this problem, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution. The mean of the sample means will be equal to the population mean, and the standard deviation of the sample means (also known as the standard error) will be equal to the population standard deviation divided by the square root of the sample size.

Given that the population mean is 68 kilograms and the population standard deviation is 10 kilograms, we need to calculate the probability that the sample mean of 128 adults is greater than 70.3 kilograms.

First, we need to calculate the standard error of the sample means:

Standard Error = Population Standard Deviation / √Sample Size

= 10 / √128

= 0.8839

Next, we can use the z-score formula to find the z-score corresponding to a sample mean of 70.3 kilograms:

z = (sample mean - population mean) / standard error

= (70.3 - 68) / 0.8839

= 3.15

Using a standard normal distribution table or a calculator, we can find the probability that the z-score is greater than 3.15. Since the standard normal distribution is symmetrical, the probability that the z-score is greater than 3.15 is the same as the probability that the z-score is less than -3.15.

From a standard normal distribution table, we find that the probability corresponding to a z-score of -3.15 is approximately 0.0008.

Therefore, the probability that the sample mean of 128 adults would be greater than 70.3 kilograms is approximately 0.0008, or 0.08%.

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Answer:

y=−0.18x+1.4

Step-by-step explanation:

I did it on one of my own test and got it correct!!!!

The numerical result of the given integral is approximately -9489.25.

The integral of (3x³-4x³+x) dx from 3 to 14 is equal to ∫(3x³-4x³+x) dx evaluated from x = 3 to x = 14.

To evaluate this integral, we can simplify the integrand first:

3x³ - 4x³ + x = -x³ + x

Then, we can integrate the simplified expression:

∫(-x³ + x) dx = -∫x³ dx + ∫x dx

Integrating each term separately, we get:

-∫x³ dx = -1/4 * x⁴ + C1

∫x dx = 1/2 * x² + C2

where C1 and C2 are constants of integration.

Now, we can evaluate the definite integral by substituting the limits:

∫(3x³-4x³+x) dx from 3 to 14 = [-1/4 * x⁴ + 1/2 * x²] evaluated from x = 3 to x = 14

Substituting the limits:

= [-1/4 * (14)⁴ + 1/2 * (14)²] - [-1/4 * (3)⁴ + 1/2 * (3)²]

Simplifying the expression, we get the numerical result.

Substituting the limits into the expression:

= [-1/4 * (14)⁴ + 1/2 * (14)²] - [-1/4 * (3)⁴ + 1/2 * (3)²]

= [-1/4 * 38416 + 1/2 * 196] - [-1/4 * 81 + 1/2 * 9]

= [-9604 + 98] - [-20.25 + 4.5]

= -9506 - (-15.75)

= -9506 + 15.75

= -9489.25

Therefore, the numerical result of the integral ∫(3x³-4x³+x) dx from 3 to 14 is approximately -9489.25.

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Answer:

Answer mine plz

Step-by-step explanation:

Answer:

its 25

Step-by-step explanation:

I guess I was help full for u

plz follow me for more update

Answer: The function rule C = 9n + 45 represents the cost of the shirts that the Math Club is selling. The variable C represents the total cost of the order and the variable n represents the number of shirts.

The number 9 in the function represents the price per shirt, this is because as the number of shirts increases by 1, the total cost increases by 9. This tells us that the cost of each shirt is $9.

The number 45 in the function represents the initial set-up fee charged to design the shirts. This is because even if no shirts are ordered, there is still a cost of $45. This represents a fixed cost that the Math Club must pay to have the shirts designed.

Step-by-step explanation:

Answer:

y=8

Step-by-step explanation:

3y+5y=64

8y=64

y=8

Answer: Y=8

Step-by-step explanation:

Add 3y + 5y which equals 8y

Divide the 8y by 64

64/8 = 8

So y = 8

(a) The radius of the circle is the distance the wave travels since it first formed, so if g(t) is the radius of the circle at time t, then it changes at a rate according to

dg/dt = 60 cm/s

Integrate both sides with respect to t to solve for g :

∫ dg/dt dt = ∫ (60 cm/s) dt

g(t) = (60 cm/s) t + C

but C = 0 since the radius at t = 0 must be 0.

g(t) = (60 cm/s) t

(b) The area of any circle with radius r is πr ². So

f(r) = πr ²

(c) The composition of f with g represents the area of water encircled by the wave at time t :

(f o g)(t) = f(g(t)) = π g(t) ²

It's proven that \(m \angle COD=72\)° using the Vertical Angle Theorem and property of linear pairs.

What is Vertical Angle Theorem?

Here, it is given that  \(m \angle AOB=42\)° and  \(m \angle EOF=66\)°

Using the Vertical Angle Theorem, we know that \(\angle BOC\) is congruent to \(\angle EOF\)

\(\implies m\angle BOC =m \angle EOF = 66\)°

And, using the property of adjacent angle, we get

\(m\angle AOC =m \angle AOB + m \angle BOC\\\implies m\angle AOC = 42 + 66\\\)

\(\implies m\angle AOC =108\)°

Now, using the property of linear pair (supplementary angles), we get

\(m \angle AOC + m \angle COD = 180\)°

\(\implies 108+ m \angle COD = 180\\ \implies m \angle COD = 180 - 108\)

\(\implies m \angle COD =72\)°

Therefore, it is proven that  \(m \angle COD=72\)° using linear pair property and the Vertical Angle Theorem

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Answer: 2a-3

Step-by-step explanation: hope this helps!!

Answer:

Suppose $100 is invested in each of these three accounts. After one year:

Account A: $100(1.12) = $112

Account B: $100(1.11) = $111

Account C: $100(1 + (.1075/2))^2 = $110.04

Account A has the most money after one year, so the amount should be invested in account A.