You are testing H0:μ=100 H 0 : μ = 100 against Ha:μ<100 H a : μ < 100 with degrees of freedom of 24. The t statistic is -2.63 . The P-value for the statistic falls between ... and ...?

sinθ = -0.9798 (rounded to two decimal places).

What is the Trigonometry ?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the trigonometric functions that describe those relationships.

We can use the identity sin²θ + cos²θ = 1 to find sinθ, since we know cosθ:

sin²θ + cos²θ = 1

sin²θ + 0.2² = 1 (substituting cosθ = 0.2)

sin²θ = 0.96

Taking the square root of both sides, we get:

sinθ = ± 0.9798

Since θ is in the second quadrant, sinθ is negative.

Hence, sinθ = -0.9798 (rounded to two decimal places).

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Answer:

The answer is the second option

Step-by-step explanation:

All you have to do is replace x with the data given.

Example: f(x) = 3\(x^{2}\) - 6

x = 0 => f(x) = 3 x \(0^{2}\) - 6 = 3 x 0 - 6 = -6

x = 1 => f(x) = 3 x \(1^{2}\) - 6 = 3 x 1 - 6 = 3 - 6 = -3

x = 2 => f(x) = 3 x \(2^{2}\) - 6 = 3 x 4 - 6 = 12 - 6 =  6

When f(x) = 4, then, the value of x = 2 (domain = 2, range = 4).

According to the mapping above, the given relationship is bijective (one-to-one and onto or one-to-one correspondence) because each element of the range is mapped to by exactly one element of the domain.

When we say a relationship is bijective, it means the satisfies both the injective (one-to-one function) and surjective function (onto function) properties. Therefore, as a result, f(x)=4 implies f(2)=4 or simply x=2.

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Answer:

Step-by-step explanation:

The length of BD is 15 units. Hence option D is correct.

According to the figure, we know that,

Let the intersection point of AC and BD be 'O'

Hence AO = 4 units,

OC = 4.5 units,

AC = radius of the circle = 8.5 units

We know that, If a radius is perpendicular to a chord in the circle, then the radius bisects the chord.

Hence BO = OD

By using Pythagoras' theorem,

\(AB^{2} = AO^2+BO^2\\ \Rightarrow BO^2 =AB^2 - AO^2 \\\Rightarrow BO^2 = radius^2 - AO^2\\\Rightarrow BO^2 = AC^2 - AO^2\\\Rightarrow BO^2 = (8.5)^2 - (4)^2\\\Rightarrow BO^2 = 72.25 - 16\\\Rightarrow BO^2 = 56.25\\\Rightarrow BO = 7.5\\\)

Hence BD = BO + OD = 7.5 + 7.5 = 15 units

Hence option D is correct.

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False. The statement you described is not an equivalent form for a conditional statement. The process you mentioned, which is reversing and negating the antecedent and consequent, is known as forming the contrapositive of the statement.

A conditional statement has the form "If P, then Q," where P is the antecedent and Q is the consequent. The contrapositive is formed by negating both the antecedent and consequent, and reversing their order: "If not Q, then not P." The contrapositive is equivalent to the original conditional statement.

However, simply reversing the antecedent and consequent without negating them gives you the converse, which is "If Q, then P." The converse is not equivalent to the original conditional statement.

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Explanation:

There are 8 letters in the word "GEOMETRY".

Use the nPr permutation formula with n = 8 and r = 7 and you'll find that 8P7 = 40320.

Or you can compute it like this 8*7*6*5*4*3*2 = 40320

This would be the answer if we could tell the E's apart.

However, we cannot tell the E's apart, so we have to divide by 2 to correct for the double-counting.

There are 40320/2 = 20160 different seven letter combinations possible.

The running time wοrst case οf deleting a minimum element frοm a (min) binary heap with N elements is O(lοgN). Therefοre, the cοrrect answer is c. O(lοgN).

When deleting the minimum element frοm a binary heap, the heap needs tο be restructured tο maintain its heap prοperty. This restructuring prοcess invοlves mοving elements within the heap and pοtentially swapping elements tο maintain the heap's structure and οrdering.

Since a binary heap is a cοmplete binary tree and has a height οf lοgN, the wοrst-case running time fοr deleting the minimum element is prοpοrtiοnal tο the height οf the heap, which is O(lοgN). This is because the number οf cοmparisοns and swaps required during the restructuring prοcess is dependent οn the height οf the heap.

Therefοre, the cοrrect answer is c. O(lοgN).

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From the statement, we have a right triangle with:

• angle θ,

• opposite side OS = 7,

• hypotenuse H = 12,

and we must find the value of angle θ.

We also have Tom's resolution of the problem.

(1) From the resolution, we see that Tom computes the angle θ using the following formula:

Adding the data above the sides, we have:

From trigonometry, we know that this equation is wrong. The correct trigonometric relation is:

(2) Replacing the values OS = 7 and H = 12 in the correct trigonometric relation, we have:

Solving for θ, we get:

• The mistake in Tom's resolution is that he used the incorrect trigonometric relation for the angle, the opposite side and the hypotenuse.

• Using the correct trigonometric relation, which involves a sine function instead of the cosine, we get θ ≅ 35.7°.

exponential graphs grow faster

Answer:

c

Step-by-step explanation:

a. Optimal solution: X1 = 140, X2 = 0, X3 = 80, Objective Function Value = 4700.000.

b. The first constraint (4X1 + 5X2 + 8X3 < 1200) is binding.

c. The dual price for the second constraint is 2.333, indicating that for each unit increase in its right-hand side value, the objective function value increases by 2.333.

d. The objective function coefficient of X2 can vary between 30 and 40 without changing the optimal solution

a. The complete optimal solution is:

X1 = 140

X2 = 0

X3 = 80

Objective Function Value = 4700.000

b. The first constraint (4X1 + 5X2 + 8X3 < 1200) is binding because it has a slack/surplus value of 0.

c. The dual price for the second constraint (9X1 + 15X2 + 3X3 < 1500) is 2.333. This means that for each unit increase in the right-hand side value of the second constraint, the objective function value will increase by 2.333 units, assuming all other variables and constraints remain constant.

d. The objective function coefficient of X2 can vary between 30 and 40 before a new solution point becomes optimal. This means that as long as the coefficient remains within this range, the current solution will still be optimal. However, if the coefficient of X2 goes below 30 or above 40, a new optimal solution may be obtained.

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MJ Supply distributes bags of dog food to pet stores. Its markup rate is 28%. Which equation represents the nee price of a bag, y, given an original price, p?​

we know that

100%+28%=128%=128/100=1.28

so

the value of y is equal to

Answer:

484 cars

Step-by-step explanation:

sum the parts of the ratio, 8 + 12 = 20 parts

Divide the total made by 20 to find the value of one part of the ratio

1210 ÷ 20 = 60.5 ← value of 1 part of the ratio , then

number of cars = 8 × 60.5 = 484

Answer:

Larger hose will take 18 minutes and 45 seconds

Step-by-step explanation:

ONE smaller hose fills the pool in 5*15 = 75 minutes.One large hose can do this job in  75/4 minutes = 18 3/4 minutes = 18 minutes and 45 seconds

The larger hose will take 18 minutes and 45 seconds.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

One smaller hose fills the pool in 5 x 15 = 75 minutes.

One large hose can do this job,

Time = 75/4 minutes = 18 3/4 minutes

Time = 18 minutes and 45 seconds

Therefore, the larger hose will take 18 minutes and 45 seconds.

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Answers:

The ~ mark means "similar"

=====================================================

The red angle markings tell us which angles are congruent to one another. We have these two pairs of congruent angles

Because we have two pairs of congruent angles, we use the AA similarity theorem. AA stands for angle angle. We could use three pairs, but two pairs is the minimum needed for similarity statements.

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To figure out what goes in the third answer box, note how the order HGF is given to us. The order is important.

We have H first, G second, F third.

H being first, and it having a single arc, means that whatever has a single arc on the other triangle must be first. That would be H. Unfortunately they reuse angle H which makes things confusing a bit.

G is second in HGF, and G has the double arc marking. Note how M also has this double arc marking. Therefore we have M second in the answer. So far we have HM as part of the third answer.

The only thing left is N. Therefore, we have triangle HMN as the answer for the third box.

Put another way, we have these pairings:

This is why the order is important. So we can see how the angles pair up in the order that they do.

This is why triangle HGF is similar to triangle HMN.

We can write that as triangle HGF ~ triangle HMN

The ~ mark means "similar"

We don't have enough information to prove that the triangles are congruent or not. So we cannot say \(\triangle HGF \cong \triangle HMN\). Your teacher made a typo when using the congruence symbol \(\cong\)

Instead, it should be \(\triangle HGF \sim \triangle HMN\)

Answer:

B.61kg

Step-by-step explanation:

use the formula

force÷acceleration=mass

183÷3=61kg

a) The minimum number of dogs that could have a mass of more than 27 kg is 4.

b) The maximum number of dogs that could have a mass of more than 27 kg is 17.

The given table shows information about the masses of some dogs.

a) Because we need the minimum number of dogs,

Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the minimum value out of 13 and 4 is 4.

b) Because we need the maximum number of dogs,

Let's assume all dogs present in the interval 20 to 40 have a mass of more than 27kg so the maximum of the values present in the interval 20 to 40 is 13 + 4 = 17

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Answer:

Step3

-by-step explanation:

Answer:

41.36% decrease

Step-by-step explanation:

Since it told us that the total amount of people was 1,100 people, we know our percentage is going to have to be x/1100.

We calculate how many less people came to the pool after the weeks have passed, which totals up to 455 people (455 people decrease).

So,

455/1100 = 0.413636 or 41.36% decrease.

Answer:

60

Step-by-step explanation:

Answer:

k = -2.

Step-by-step explanation:

By the Factor Theorem, if x - 1 is a factor then p(1) = 0.

So, p(1) = (1)^2 + 1  + k = 0

k = -1 - 1

k = -2.

The total amount that would be found in the account after 4 years, would be $ 641. 69

The total amount after 4 years in Arik's account can be found by the formula :

= A = Amount invested x ( 1 + r /n )ⁿ

The variables are:

Amount invested = $ 500

r = 6.25% = 0. 0625

n = 12

t = 4 years

The total amount is then :

A = 500 x ( 1 + 0. 0625 / 12 ) ^ ⁽¹² ˣ ⁴ ⁾

A = $ 641. 69

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Answer:

1.  x=-7/3 + 4y/3

2. x= 6- 3y/4

Step-by-step explanation:

to isolate the variable you simply solve for it by moving all the terms which don't contain x to the right by multiplying, subtracting, adding, and dividing

Answer:

14 = c

Step-by-step explanation:

it is just like u said;

a + b = c

6 + 8 = c = 14

(it could also be 8-6 = c = 2)

The probability of Greg winding up wearing the white shirt and tan pants when getting dressed in the dark is 1/8 or 12.5%.

The probability of Greg wearing the white shirt and tan pants when getting dressed in the dark can be calculated by finding the probability of each event occurring independently and then multiplying those probabilities together.

First, let's find the probability of Greg choosing the white shirt. He has 4 shirts to choose from, so the probability of picking the white shirt is 1/4 (one white shirt out of four total shirts).

Next, let's find the probability of Greg choosing the tan pants. He has 2 pairs of pants to choose from, so the probability of picking the tan pants is 1/2 (one tan pair out of two total pairs).

Now, we can multiply the two probabilities together to find the overall probability of Greg wearing the white shirt and tan pants: (1/4) * (1/2) = 1/8.

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Answer:

25x

Step-by-step explanation:

6x and 19x are like terms so we can add them

6x+19x = 25x

\(8. \: \: \: \: 2 {x}^{2} + 14 = 22 \\ \\ = > 2 {x}^{2} = 22 - 14 \\ \\ = > 2 {x}^{2} = 8 \\ \\ = > {x}^{2} = \frac{8}{2} \\ \\ = > {x}^{2} = 4 \\ \\ = > x = \underline{+}\sqrt{4} \\ \\ = > \green {\boxed{x = 2\: or \: (-2)}} \\ \\ \\ \\ \\ 9. \: \: \: \: 8 {x}^{2} + 19 = 54 + 3 {x}^{2} \\ \\ = > 8 {x}^{2} - 3 {x}^{2} = 54 - 19 \\ \\ = > 5 {x}^{2} = 35 \\ \\ = > {x}^{2} = \frac{35}{5} \\ \\ = > {x}^{2} = 7 \\ \\ = > x = \underline{ + } \sqrt{7} \\ \\ = > \green{\boxed{ x = \sqrt{7} \: or \: ( - \sqrt{7} )}} \)\(\\\\\\\\10. \: \: \: 7 {x}^{2} + 12 = 51 - 4 {x}^{2} \\ \\ = > 7 {x}^{2} + 4 {x}^{2} = 51 - 12 \\ \\ = > 11 {x}^{2} = 39 \\ \\ = > {x}^{2} = \frac{39}{11} \\ \\ = > {x} = \underline{+ }\sqrt{ \frac{39}{11} } \\ \\ = > \green{\boxed{ x = \sqrt{ \frac{39}{11} } \: or \: (- \sqrt{ \frac{39}{11} } )}}\)

Answer:

√n²=±n

-√9y²=±3y

is a required answer.

n is less than 0

but for any number square means greater than or equal to 0

Hence it's

#2

First, we need to determine an equation for both Arcade X and Arcade Y.

Arcade X: 0.65t + 5 = P

Arcade Y: 0.45t + 10 = P

If you graph both lines, we will find the solution to be (25, 21.25), which means that D. 25 tokens will need to be bought in order for the total cost in both arcades to be the same.

I have included the graph here.

Answer:

Step-by-step explanation:

32/13 = 2 6/13

Answer:

She spend $7 a month on downloads.

Step-by-step explanation:

y = the total spent on downloads

x = number of months

m = the amount spent each month

y = mx

45.50 = m(6.5)  Divide both sides by 6.5

7 = m