what would be the null and alternative hypothesis for testing to see if there is a relatonsip between age and opinion for the question asked by gallup

You can use the distributive property of multiplication over addition and the fact that 18 is thrice of 6.

The given expression is equivalent to

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

\(a(b+c)=a\times b+a\times c\)

(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in \(2\times x=2x\))

The given expression is \(6g-18h\)

We know that we can write

\(6=2\times3\)

\(18=2\times9=3\times6\)

Thus,

\(6g-18h=6\times g-6\times 3h=6(g-3h)=-6(-g+3h)\)

\(6g-18h=2\times 3g-2\times 9h=2(3g-9h)=-2(-3g+9h)\)

\(6g-18h=3\times 2g-3\times 6h=3(2g-6h)=-3(-2g+9h)\)

All of the above forms are obtained from the same expression without altering its value but only forms, so their simplified forms are same so they are equivalent expressions.

Thus,

The given expression is equivalent to

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Answer:C & D

Step-by-step explanation:

Answer:

A.3

Step-by-step explanation:

x-11=-8

x-11+11=-8+11

x=-8+11

x=3

Hope this helps ;) ❤❤❤

Answer: \(x=3\)

Add 11 to both sides

\(x-11+11=-8+11\\x=3\)

Answer:

The conic section is a hyperbola.

The Center is at (-3, - 4)

The foci are (9.69, - 4) and (-15.69, - 4)

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

because because you have one choice out of 12 choices and that gives you 112

To find Keegan's optimal consumption bundle of pita wraps and bubble tea, we need to determine the combination that maximizes his utility while staying within his budget of $30. The price of a pita wrap is $6, and the price of a bubble tea is $3.

Step 1: Calculate the maximum quantity of each item Keegan can buy with his budget.
- Pita wraps: $30 / $6 = 5 wraps
- Bubble teas: $30 / $3 = 10 bubble teas

Step 2: List all possible combinations of pita wraps and bubble teas within the budget.
1. 0 wraps and 10 bubble teas
2. 1 wrap and 8 bubble teas
3. 2 wraps and 6 bubble teas
4. 3 wraps and 4 bubble teas
5. 4 wraps and 2 bubble teas
6. 5 wraps and 0 bubble teas

Step 3: Determine the optimal consumption bundle.
Without information about Keegan's preferences, we cannot definitively determine his optimal consumption bundle. However, these six combinations represent all possible bundles that Keegan can purchase with his $30 budget. Keegan's optimal consumption bundle would depend on his personal preferences for pita wraps and bubble teas.

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Step-by-step explanation:

First, we need to find that top angle, which we'll call angle x. We can say 26 is the hypotenuse, and 12 is the adjacent, so we know that:

\( \cos(x) = \frac{12}{26} \)

Let's solve this, to find X:

\(x = { \cos }^{ - 1}( \frac{12}{26} )\)

Now that we know what X is, we can use trig to find the missing side, which we'll call y. 48 is the adjacent, and y is the hypotenuse, therefore:

\( \cos(x) = \frac{48}{y} \)

To find y, let's rearrange:

\(y = \frac{48}{ \cos(x) } \)

And now let's figure out calculate the value of y (I'm leaving the value of X as just X for the equations, but you will need it to calculate first):

\(y = 0.767833242\)

Answer:

Below

Step-by-step explanation:

N, the number can be anything   greater than or equal to 11.5 and less than 12.5  

11.5 ≤  n < 12.5

Answer:

158ft²

Step-by-step explanation:

Break it up!

Find the area of the three smaller shapes and add them together!

12+18+128= 158

Answer:

164 ft²

Step-by-step explanation:

We can divide the figure into a rectangle and a trapezoid. Find their areas and add them up.

Area of the rectangle

= 8×16

= 128 ft²

Area of the trapezoid

= (2+8+2)×6 ÷2

= 36 ft²

Total area of the yard

= 128+36

= 164 ft²

16250 many different three-letter words—including nonsense words—have different letters in the next position.

Given that,

We have to find how many different three-letter words—including nonsense words—have different letters in the next position.

We know that,

The number of alphabets are 26

First letter has 26 choices.

Second letter can not be same has first letter so 25 choices.

Third letter can not be same has second letter so 25 choices.

So,

Total words = 26×25×25=16250

Therefore, 16250 many different three-letter words—including nonsense words—have different letters in the next position.

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3) y=3.5x

4) 3.5(72) = 252 pages for 72 min.

First we divide 21 by 6 to find the how many pages there is in 1 min. (we got 3.5) then we multiply (3.5) by the number of minutes (72) and we get 252 pages for 72 minutes.

Hope that helped:)

Answer:

about 11.5

Step-by-step explanation: i think this is right

Answer:

11.538%

Step-by-step explanation:

290 - 260 /260  x 100% = 11.538

Answer:

117

\(100\)

by taking the interior angle sum as 360

If 3 friends, Jessa, Tyree, and Ben, are collecting "canned-food" for their culinary skills class, then

(a) expression for the amount of canned food collected 3 friends is 15x² + 4xy - 1,

(b) expression for number of cans the friends still need to collect to meet their goal is 9x² - 10xy - 1.

Part (a) : To find the amount of canned food collected so far by the three friends, we add the number of cans collected by each friend:

Amount of canned food collected so far = Jessa's collection + Tyree's collection + Ben's collection;

⇒ (9x²) + (6x² - 4) + (4xy + 3),

⇒ 15x² + 4xy - 1,

Therefore, the expression to represent the amount of canned food collected so far by the three friends is 15x² + 4xy - 1.

Part (b) : To find the number of cans the friends still need to collect to meet their goal, we subtract the amount of canned food collected so far from the collection-goal expression:

⇒ Number of cans still needed = Collection goal - Amount of canned food collected so far;

⇒ (24x² - 6xy - 2) - (15x² + 4xy - 1);

⇒ 9x² - 10xy - 1

Therefore, the expression that represents the number of cans the friends still need to collect to meet their goal is 9x² - 10xy - 1.

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The given question is incomplete, the complete question is

Three friends, Jessa, Tyree, and Ben, are collecting canned food for a culinary skills class. Their canned food collection goal is represented by the expression 24x² - 6xy -2. The friends have already collected the following number of cans: Jessa: 9x², Tyree: 6x² - 4, Ben: 4xy + 3

(a) Write an expression to represent the amount of canned food collected so far by the three friends.

(b) Write an expression that represents the number of cans the friends still need to collect to meet their goal.

Answer: then the equation basically is 5+3x7  you just need to subsitute the 7 in the problem

Step-by-step explanation:Hope this helps!

Answer:

=26

Step-by-step explanation:

5+3(7)

5+21

=26

The eigenvalues of AᵀA are: λ₁ = 9 λ₂ = 16 λ₃ = 49

The eigenvalues of AᵀA, we need to find the eigenvalues of the square matrix AᵀA. Since A is given in its singular value decomposition (SVD) form, we can directly compute the eigenvalues.

The eigenvalues of AᵀA are the squares of the singular values of A, which are the diagonal elements in the middle matrix of the SVD.

From the given SVD of A: A = UΣVᵀ

where U, Σ, and V are the matrices obtained in the SVD, and Σ is a diagonal matrix containing the singular values.

In this case, Σ is given as: Σ = [3 0 0] [0 4 0] [0 0 7]

The eigenvalues of AᵀA are the squares of the singular values:

λ₁ = (3)² = 9

λ₂ = (4)² = 16

λ₃ = (7)² = 49

Therefore, the eigenvalues of AᵀA are: λ₁ = 9 λ₂ = 16 λ₃ = 49

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Answer:

13.015625

Step-by-step explanation:

Answer:

13 remainder 1.

I have attached the work to your question.

Please see the attachment below.

I hope this helps!

Using the central limit theorem, for different sample sizes, we find the probabilities Pr(Y < 68) ≈ 0.9439, Pr(68 < Y < 69) ≈ 0.0590, and Pr(Y > 66) ≈ 0.0228.

a) In a random sample of size n = 69, we can approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 69 ≈ 0.7101. To find Pr(Y < 68), we calculate the z-score using the formula z = (x - μ) / σ, where x is the value we want to find the probability for.

z = (68 - 65) / √(0.7101) ≈ 1.5953

Using a standard normal distribution table or a calculator, we find the probability associated with z = 1.5953 to be approximately 0.9439. Therefore, Pr(Y < 68) ≈ 0.9439.

b) In a random sample of size n = 124, we can again approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will still be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 124 ≈ 0.3952. To find Pr(68 < Y < 69), we calculate the z-scores for the lower and upper limits.

Lower z-score: z1 = (68 - 65) / √(0.3952) ≈ 1.5225

Upper z-score: z2 = (69 - 65) / √(0.3952) ≈ 2.5346

Using the standard normal distribution table or a calculator, we find the probability associated with z1 = 1.5225 to be approximately 0.9357 and the probability associated with z2 = 2.5346 to be approximately 0.9947. Therefore, Pr(68 < Y < 69) ≈ 0.9947 - 0.9357 ≈ 0.0590.

c) In a random sample of size n = 196, we can once again approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will still be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 196 ≈ 0.2500. To find Pr(Y > 66), we calculate the z-score.

z = (66 - 65) / √(0.2500) = 2

Using the standard normal distribution table or a calculator, we find the probability associated with z = 2 to be approximately 0.9772. Therefore, Pr(Y > 66) ≈ 1 - 0.9772 ≈ 0.0228.

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The Laplace Transform of f(t) = 10^(-4t)cos(20t * 36.9°) can be found using the formula for the Laplace Transform of a product of functions.

Step 1: Convert the angle to radians.
The angle of 36.9° should be converted to radians. 1° is equal to π/180 radians, so 36.9° is equal to (36.9 * π/180) radians.

Step 2: Rewrite the function with an angle in radians.
Let α = 36.9 * π/180. Now, f(t) = 10^(-4t)cos(20t * α).

Step 3: Find the Laplace Transform of the function.
Using the Laplace Transform formula for a product of functions, we get:

L{f(t)} = L{10^(-4t) * cos(20t * α)}

To find the Laplace Transform of the given function, we can use the following Laplace Transform properties:

1. L{e^(at)cos(bt)} = (s - a)/((s - a)^2 + b^2)
2. L{e^(at)sin(bt)} = b/((s - a)^2 + b^2)

For our function, a = -4, and b = 20α. Thus, the Laplace Transform of the function is:

L{f(t)} = (s + 4)/((s + 4)^2 + (20α)^2)

This is the Laplace Transform of f(t) = 10^(-4t)cos(20t * 36.9°).

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The given lines of equations are not perpendicular to each other. Therefore, `θ = cos⁻¹(8/(4√10))` which is approximately `28.07°`.Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

Given lines of equations:

x = −2 + 2t, y = −6, z = 2 + 6tx=−1+t,y=1+t,z=t, t∈ R.

Firstly, we need to find the direction vectors of the two given lines.For the first equation,Let `t=1`, then the point on the line is `(-2+2(1), -6, 2+6(1))`=`(0, -6, 8)`.

Let `t=2`, then the point on the line is

\(`(-2+2(2), -6, 2+6(2))`=`(2, -6,\)14)`.T

herefore, direction vector `

\(v1 = (2, -6, 14)-(0, -6, 8)`=`(2, 0, 6)`\)

For the second equation, direction vector \(`v2 = (1, 1, 1)`.\\\)

Let the angle between the direction vectors `v1` and `v2` be `θ`.

Then, we know that `v1 • v2 = |v1||v2| cosθ`, where `•` represents the dot product of the vectors, and `|.|` represents the magnitude of the vector.

Thus, we have:

(2, 0, 6) • (1, 1, 1) = √(2²+0²+6²)√(1²+1²+1²) cosθ

=> 8 = √40√3 cosθ=> cosθ = 8/(4√10)

Therefore,

`θ = cos⁻¹(8/(4√10))`

which is approximately `28.07°`.

Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

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If the 95% confidence interval for the difference in mean shelf life between Brand A and Brand B includes zero, then there is no significant difference in the shelf life of the two brands of doughnuts. If the 95% confidence interval for the difference in mean shelf life between Brand A and Brand B does not include zero, then there is a significant difference in the shelf life of the two brands.

Based on the question, a grocery store wants to determine whether there is a difference in the shelf life of two different brands of doughnuts.

They took a random sample of 40 boxes of each brand and determined the shelf life in days. A 95% confidence interval for the difference in mean shelf life between Brand A and Brand B was found.

Unfortunately, you didn't provide the actual values of the confidence interval. However, I can still explain how to interpret it.

1. If the 95% confidence interval for the difference in mean shelf life between Brand A and Brand B includes zero (e.g., -2 to 3 days), then there is no significant difference in the shelf life of the two brands of doughnuts. This means that at a 95% confidence level, we cannot conclude that one brand has a longer or shorter shelf life than the other.

2. If the 95% confidence interval for the difference in mean shelf life between Brand A and Brand B does not include zero (e.g., 1 to 4 days), then there is a significant difference in the shelf life of the two brands. This means that at a 95% confidence level, we can conclude that one brand has a longer or shorter shelf life than the other, depending on the sign of the interval (positive or negative).

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The simplified expression 1.2 - 5 is -3.8.To simplify the expression 1.2 - 5, we need to subtract 5 from 1.2. 1.2 - 5 = -3.8 Therefore, the simplified form of the expression 1.2 - 5 is -3.8.

In decimal notation, the result is -3.8, indicating that we have subtracted 5 from 1.2, resulting in a negative value. The subtraction of 5 from 1.2 yields a difference of -3.8, indicating that the result is located 3.8 units below 0 on the number line.

The subtraction process involves taking away a quantity (5) from another quantity (1.2). Since the value being subtracted (5) is greater than the initial value (1.2), the result is negative.

Therefore, the simplified expression 1.2 - 5 is -3.8.

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Answer:

The original price was 10 dollars and 59 cents.

Step-by-step explanation:

I saw that it said 8.40 and 2.19. i made the 40 and 19 into 59. then i subtracted 59 and 19 to get forty. Next then i added 8 and two ans subtracted it. The put 8. and 40 together. $8.40

Answer:

A.

Step-by-step explanation:

An irrational number is a number that goes on forever without repeating. The square root of 2 does exactly this.

The statement which could be true for the function, g as required in the task content is; Choice C; g(0) = 2.

It follows from the task content that the statement which could be true about the function g is to be identified.

Since the given function instances are; g(0) = -2 and g(-9) = 6.

Since the function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.

Hence, the statement which could be true about the function, g is; Choice C; g(0) = 2.

This is so because, 0 is in the domain of the function and 2 is in the range of the function.

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Answer:

--------------------------

Let the equal sides be both marked as ?

Use the perimeter formula to determine one of the equal sides.

Substitute the expression for the perimeter and find the value of ?

Hence the length of each of equal sides is 4x² - x + 2.