Find the GCF

PLS HELP ASAP

In the given figure

There is a right triangle whose legs are 11, x, and its hypotenuse is y

The side opposite to the angle of measure 30 degrees is 11

The side adjacent to the angle of measure 30 degrees is x

Let us use the trigonometry ratios to find x and y

The opposite is 11 and the hypotenuse is y

By using cross multiplication

To solve the given problems, we'll use the properties of the normal distribution with mean μ = 100 and standard deviation σ = 10.

a. Probability that X > 85:

To find this probability, we need to calculate the area under the normal curve to the right of 85. We can use the standard normal distribution table or a calculator to find the corresponding z-score and then use the z-table to find the probability.

First, let's calculate the z-score:

z = (X - μ) / σ

z = (85 - 100) / 10

z = -15 / 10

z = -1.5

Using the z-table or a calculator, we find that the probability of Z > -1.5 is approximately 0.9332.

Therefore, the probability that X > 85 is 0.9332 (rounded to four decimal places).

b. Probability that X < 80:

Similarly, we'll calculate the z-score for X = 80:

z = (X - μ) / σ

z = (80 - 100) / 10

z = -20 / 10

z = -2

Using the z-table or a calculator, we find that the probability of Z < -2 is approximately 0.0228.

Therefore, the probability that X < 80 is 0.0228 (rounded to four decimal places).

c. Probability that X < 90 or X > 130:

To calculate this probability, we'll find the individual probabilities of X < 90 and X > 130, and then subtract the probability of their intersection.

For X < 90:

z = (90 - 100) / 10

z = -10 / 10

z = -1

Using the z-table or a calculator, we find that the probability of Z < -1 is approximately 0.1587.

For X > 130:

z = (130 - 100) / 10

z = 30 / 10

z = 3

Using the z-table or a calculator, we find that the probability of Z > 3 is approximately 0.0013.

Since these events are mutually exclusive, we can add their probabilities:

P(X < 90 or X > 130) = P(X < 90) + P(X > 130)

P(X < 90 or X > 130) = 0.1587 + 0.0013

P(X < 90 or X > 130) = 0.1600

Therefore, the probability that X < 90 or X > 130 is 0.1600 (rounded to four decimal places).

d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?

To find the two X-values, we need to find the corresponding z-scores for the cumulative probabilities of 0.005 and 0.995. These probabilities correspond to the tails beyond the 99% range.

For the left tail:

z = invNorm(0.005)

z ≈ -2.576

For the right tail:

z = invNorm(0.995)

z ≈ 2.576

Now we can find the corresponding X-values:

X1 = μ + z1 * σ

X1 = 100 + (-2.576) * 10

X1 = 100 - 25.76

X1 ≈ 74.24

X2 = μ + z2 * σ

X2 = 100 + 2.576 * 10

X2 = 100 + 25.76

X2 ≈ 125.76

Therefore, 99% of the values are greater than 74.24 and less than 125.76 (rounded to two decimal places).

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Answer:

C. The classmate was supposed to multiply the exponents.

Step-by-step explanation:

\( { ({2}^{3}) }^{2} = {2}^{6} = 64\)

Answer:

C

Step-by-step explanation:

your classmate multiplied the exponenets

Answer: Unclear

Step-by-step explanation: I can't see your image/sentence, so I can't help u

Answer:

the second answer is the answer

Answer:

600 ft² are x ≤ 111.02.

Step-by-step explanation:

To find the values of x for which the area of the pen is at least 600 ft², we can start by expressing the area of the pen in terms of x.

The area of the pen is equal to the product of the lengths of the two sides that are perpendicular to the barn. From the given information, we know that the length of each of these sides is 80 - x/2 ft.

Therefore, the area A(x) of the pen is given by:

A(x) = (80 - x/2) * (80 - x/2)

To find the values of x for which the area is at least 600 ft², we can set up the following inequality:

A(x) ≥ 600

(80 - x/2) * (80 - x/2) ≥ 600

Expanding the equation, we have:

(80 - x/2)^2 ≥ 600

Taking the square root of both sides, we get:

80 - x/2 ≥ √600

Simplifying, we have:

80 - x/2 ≥ 24.49

Subtracting 80 from both sides, we obtain:

-x/2 ≥ -55.51

Multiplying both sides by -2 (and flipping the inequality sign), we get:

x ≤ 111.02

Therefore, the values of x that satisfy the condition and give an area of at least 600 ft² are x ≤ 111.02.

The answer is 220%.

hope this help

Answer:

If you are doing 15 x 33 it is 495

Let me know if it isn't x and I can change my answer.

Step-by-step explanation:

Hope this helps

Just to let you know I will help you to let me know if you need help with something you can friend me or go to one of my questions and tell me in the

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The probability that the average size of the fish you caught is more than 14 inches is 0.1635 or 0.164

The size of bass caught in Strawberry Lake is normally distributed with a mean of 12 inches and a standard deviation of 5 inches.

If you catch 6 fish, the probability that the average size of the fish you caught is more than 14 inches is 0.202.

Here,

we need to find the probability that the average size of the fish you caught is more than 14 inches.

Let us denote the size of the bass caught in Strawberry Lake by X.

Then, X ~ N(μ = 12, σ = 5) represents the normal distribution of the size of bass caught in Strawberry Lake.

Let Y be the sample mean of 6 bass caught in the Strawberry Lake.

Then,

We know that Y ~ N(μ = 12, σ = 5/√6) represents the sampling distribution of the sample mean,

where σ = 5/√6

= 2.0412 (approx).

We are given that we have caught 6 fish.

Therefore, the sample size n = 6.

Then,

The probability that the average size of the fish you caught is more than 14 inches can be obtained as follows:

P(Y > 14) = P((Y - μ)/σ > (14 - μ)/σ)

= P(Z > (14 - 12)/2.0412)

= P(Z > 0.977)

= 1 - P(Z < 0.977) (as the standard normal distribution is a continuous distribution)

Using the standard normal distribution table, we get P(Z < 0.977) = 0.8365 (approx) Therefore, P(Y > 14) = 1 - P(Z < 0.977) = 1 - 0.8365 = 0.1635 (approx)

Therefore,

The probability that the average size of the fish you caught is more than 14 inches is 0.1635 or 0.164 (approx).

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Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

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Answer:

cindy is 51

Step-by-step explanation:

70 divided by 2 is 45

45+ 6 is 51

Fiona must deposit  $18,277.65 into her retirement account each year for the next 20 years in order to have a total of $600,000 by the time she retires.

percentage, a relative value indicating hundredth parts of any quantity.

The present value of an annuity is:

PV = PMT x [(1 - (1 + r)⁻ⁿ) / r]

Where PV is the present value,

PMT is the periodic payment

r is the interest rate per period (6% per year), and

n is the number of periods (20 years).

We want to find PMT, so we can rearrange the formula to solve for it:

PMT = PV x [r / (1 - (1 + r)⁻ⁿ)]

We know that PV is $600,000, r is 6% or 0.06, and n is 20.

Plugging these values into the formula, we get:

PMT = $600,000 x [0.06 / (1 - (1 + 0.06)⁻²⁰)]

PMT ≈ $18,277.65

Therefore, Fiona must deposit  $18,277.65 into her retirement account each year for the next 20 years in order to have a total of $600,000 by the time she retires.

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Answer:

x = 80

Step-by-step explanation:

All angles in a triangle add up to 180 degrees.

First, find the angle J:

60+40 = 100, J = 80 because 100+80= 180 degrees.

Now, the two angles on either side of J should also equal 180 degrees. We know that the inner angle is equal to 80 degrees. Thus, the outside angle must equal 100.

x + 20 = 100

x = 80 degrees.

Answer:

SAS postulate

Step-by-step explanation:

The triangles have two congruent sides and one congruent angle. The congruent angle is the included angle. This meets SAS criteria.

Hope this helps :-)

9514 1404 393

Answer:

  17.8 cm²

Step-by-step explanation:

The ratio of surface areas is the square of the ratio of the linear dimensions. The small/large linear dimension ratio is 2/5, so the surface area of the smaller cone is ...

  A = (2/5)²(111 cm²) = 17.76 cm²

The area of the smaller cone is about 17.8 cm².

Answer:  \(17.8 cm^{2}\)

It is anticipated that every cell in the contingency table will have an expected value of at least 5, and no cell will have an expected value of less than 1in the chi-square test.

Therefore, it is anticipated that every cell in the contingency table will have an expected value of at least 5, and no cell will have an expected value of less than 1in the chi-square test.

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Given that the length of the arc of the circle is, 9.5 ft, thus, the radius of the circle would be: 4.5 ft.

Length of arc of a circle = ∅/360 × 2πr

Radius = r.

Given:

∅ = 120°

Length of arc = 9.5 ft

Radius (r) = ?

Thus:

9.5 = 120/360 × 2× 3.14 × r

9.5 = 2.09r

r = 9.5/2.09

r = 4.5 ft

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Answer:

  3.  · (times)

Step-by-step explanation:

You want to know the operation that will give a binomial result from the expressions (3y^6 +4) and (9y^12 -12y^6 +16).

The like terms in the two expressions are 3y^6 and -12y^6, or +4 and +16. Combining these terms by addition or subtraction will not result in the elimination of either the y^6 term or the constant term. Hence addition or subtraction cannot result in a binomial.

We know that the sum of cubes is factored into the product of a binomial and a trinomial:

  a³ +b³ = (a +b)(a² -ab +b²)

Comparing this form to the given binomial and trinomial, we see that we can choose ...

  a = 3y^6

  b = 4

to make the given factors match exactly. That tells us their product will be a binomial sum:

  (3y^6 +4) × (9y^12 -12y^6 +16) = (3y^6)^3 +(4)^3 = 27y^18 +64

The operation "times" (·) will result in a binomial.

Answer:

x = 116°

y = 90°

Step-by-step explanation:

∠F = 90°, so arc EDS = 180°.

Therefore, arc EFS = 360° − 180° = 180°.  Which means ∠D = 90°.

Angles of a quadrilateral add up to 360°, so:

x + 90° + 90° + 64° = 360°

x = 116°

Answer:

The value of x is 116° and y = 90°

Step-by-step explanation:

Given that opposite supplementary angles in a cyclic quadrilateral is 180° :

\(x + 64 = 180 \\ x = 180 - 64 \\ x = 116\)

\(y + 90 = 180 \\ y = 180 - 90 \\ y = 90\)

The maximum rate of change always occurs in the direction of the gradient.

The directional derivative of a function f(x, y) in the direction of a unit vector v = ⟨a, b⟩ is defined as follows:

D_vf(x, y) = ∇f(x, y) · v

∇f(x, y) represents the gradient vector of f(x, y), which is defined as ∇f(x, y) = ⟨∂f/∂x, ∂f/∂y⟩. It is a vector that points in the direction of the steepest ascent of the function at a given point (x, y).

v = ⟨a, b⟩ is the unit vector that determines the direction in which we want to compute the derivative.

To show why the maximum rate of change of a function always occurs in the direction of the gradient, we can use the definition of the directional derivative.

Let's consider the dot product ∇f(x, y) · v, where v is a unit vector:

∇f(x, y) · v = ||∇f(x, y)|| ||v|| cosθ

In this equation, ||∇f(x, y)|| represents the magnitude (or length) of the gradient vector, ||v|| is the magnitude of the unit vector v (which is 1), and θ is the angle between ∇f(x, y) and v.

Since ||v|| = 1, the equation simplifies to:

∇f(x, y) · v = ||∇f(x, y)|| cosθ

The maximum value of the cosine function is 1, which occurs when the angle θ between the vectors is 0° (or when they are parallel). In this case, cosθ = 1, and the equation becomes:

∇f(x, y) · v = ||∇f(x, y)||

Therefore, the maximum rate of change of the function f(x, y) occurs when the angle between the gradient vector ∇f(x, y) and the direction vector v is 0°, or when they are parallel. In other words, the maximum rate of change happens when we move in the direction of the gradient.

This result is intuitive since the gradient vector points in the direction of the steepest ascent of the function. Moving in the direction of the gradient allows us to maximize the rate of change of the function at a given point.

If we were to move in a different direction, the dot product would be smaller than the magnitude of the gradient vector, resulting in a slower rate of change.

Therefore, the maximum rate of change always occurs in the direction of the gradient.

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Answer:

SA = 37.5 units^2

Step-by-step explanation:

2 1/2 = 2.5

the Surface Area of the cube

SA = 6a^2

SA = 6(2.5)^2

SA = 6(6.25)

SA = 37.5 units^2

Answer:

780 kg

Step-by-step explanation:

If 1 weights 60 kg then 13 of them should weight 780 kg

1 60 kg

13 ↗️ ?

(13 × 60) ÷ 1

Step-by-step explanation:

I think we are missing some information (angle F or B or a side length would be great).

but just the right angles are not enough to calculate specific numbers. they would depend on the angle F or e.g. the side length of AB.

without any further information F and AB can be freely changed without changing the known facts, but it changes also C, B, G

so, all I can say is C = 180 - B.

and that G = B.

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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The probability that failure A does not occur is 0.88. The probability that failures A and B occur is 0.04. The probability that failure A occurs, failure B occurs, and failure C does not occur is 0.1. The probability that at least one failure occurs is approximately 0.5408.

Let's denote the events as follows:

A: Failure of type A

B: Failure of type B

C: Failure of type C

Based on the given information, we have:

P(A) = 0.12

P(B) = 0.05

P(C) = 0.1

P(A ∪ B) = 0.13

P(A ∪ C) = 0.14

P(A ∩ C) = 0.1

1. To compute the probability that failure A does not occur, we can use the complement rule:

P(A') = 1 - P(A)

= 1 - 0.12

= 0.88

Therefore, the probability that failure A does not occur is 0.88.

2. To compute the probability that failures A and B occur, we can use the intersection rule:

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

= 0.12 + 0.05 - 0.13

= 0.04

Therefore, the probability that failures A and B occur is 0.04.

3. To compute the probability that failure A occurs, failure B occurs, and failure C does not occur, we can use the intersection and complement rules:

P(A ∩ B ∩ C') = P(A) + P(B) - P(A ∪ B) - P(A ∪ C) + P(A ∩ C)

= 0.12 + 0.05 - 0.13 - 0.14 + 0.1

= 0.1

Therefore, the probability that failure A occurs, failure B occurs, and failure C does not occur is 0.1.

4. To compute the probability that at least one failure occurs, we can use the complement rule:

P(at least one failure) = 1 - P(no failure)

= 1 - P(A' ∩ B' ∩ C')

= 1 - [P(A') * P(B') * P(C')]

= 1 - (0.88 * 0.95 * 0.9)

≈ 0.5408

Therefore, the probability that at least one failure occurs is approximately 0.5408.

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