Please help, find x.

Answer: The length of the major axis = 18 units.

Step-by-step explanation:

For equation ellipse: \(\dfrac{(x-a)^2}{m^2}+\dfrac{(y-b)^2}{n^2}=1\)

If n>m , then length of major axis = 2n

Otherwise 2m

Given equation:

\(\dfrac{(x+2)^2}{64}+\dfrac{(y-1)^2}{81}=1\ \text{ ,which is an ellipse.}\\\\\Rightarrow\ \dfrac{(x+2)^2}{8^2}+\dfrac{(y-1)^2}{9^2}=1\)

9>8

So, the length of the major axis = 2(9) = 18 units.

Answer:

a₇ = \(\frac{1}{216}\)

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

\(\frac{a_{2} }{a_{1} }\) = \(\frac{36}{216}\) = \(\frac{1}{6}\)

\(\frac{a_{3} }{a_{2} }\) = \(\frac{6}{36}\) = \(\frac{1}{6}\)

this indicates the sequence is geometric with nth term

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term and r the common ratio

here a₁ = 216 and r = \(\frac{1}{6}\) , then

a₇ = 216 × \((\frac{1}{6}) ^{6}\) = 6³ × \(\frac{1}{6^6}\) = 6³ × \(6^{-6}\) = \(6^{-3}\) = \(\frac{1}{6^3}\) = \(\frac{1}{216}\)

Answer: 10,077,696

Step-by-step explanation: U7=216(6)^6

Un=U1(r)^(n-1)

n=7

r=6

n is your nth term

r is your common ratio

The values of \(x\) are \(1+\sqrt{89}\) and \(1-\sqrt{89}\).

To find the values of x:

Given equation: \((x+7)(x-9)=25\)

Then: \(x(x-9)+7(x-9)=25\)

Using the distributive property: \(a.(b+c)=a.b+a.c\)

\(x^{2} -9x+7x-63=25\)

Combine like terms:

\(x^{2} -2x-63=25\)

Subtract 25 from both sides and obtain:

\(x^{2} -2x-88=0\)

Using completing square form:

Add and subtract \((\frac{2}{2} )^{2} =1\) we have:

\(x^{2} -2x-88+1-1=0\\(x-1)^{2} -89=0\)

Add 89 to both sides we have:

\((x-1)^{2} =89\)

Taking square roots on both sides, obtain:

\(x-1=\) ± \(\sqrt{89}\)

Add 1 to both sides we have:

\(x=1\)±\(\sqrt{89}\)

Therefore, the values of \(x\) are \(1+\sqrt{89}\) and \(1-\sqrt{89}\).

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The complete question is given below:

Use completing the square to solve (x + 7)(x – 9) = 25 for x.

The cartesian equation of the curve defined by x = sin(t) and y = csc(t), 0 < t < π/2,  is y = √(1 - x²).

To eliminate the parameter t, we can use the trigonometric identity

csc(t) = 1/sin(t).

Substituting this into the equation y = csc(t), we have y = 1/sin(t).

Rearranging the equation, we get sin(t) = 1/y. Now, we can substitute the expression for x from the equation x = sin(t) into this equation. This gives sin(t) = 1/y = x.

Taking the square of both sides, we have

sin²(t) = (1/y)²

= x².

Using the Pythagorean identity sin²(t) + cos²(t) = 1,

we can rewrite the equation as cos²(t) = 1 - x².

Since cos²(t) = 1 - sin²(t), we can substitute this into the equation to get

1 - sin²(t) = 1 - x².

Simplifying, we have sin²(t) = x².

Taking the square root of both sides, we get sin(t) = ±x.

Finally, substituting sin(t) with its expression x in the equation y = csc(t), we have y = 1/sin(t) = 1/(±x).

Simplifying further, we have y = ±(1/x).

Hence, the cartesian equation of the curve is y = ±(1/x), or equivalently,

y = √(1 - x²) for the positive root.

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The required value of x is 125° for the given pentagon.

The external angle of a pentagon is formed by extending one of its sides, and it is supplementary to the adjacent interior angle of the pentagon.

According to the given figure,

We have been given that a pentagon, which has five sides is shown.

As we know that the sum of the external angles of any polygon is always 360 degrees.

So, x° + 40° + 65° + 60° + 70° = 360°

x° + 235° = 360°

x° = 360° - 235°

Apply the subtraction operation, and we get

x = 125°

Therefore, the required value of x is 125°.

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Answer:

1,200

Steps down below

Step-by-step explanation:

Steps

1:  48=4% loaded on truck and they have 96% left to load

2: so set up a proportion and it should look like this

3: 48 over x = 4 over 100

4: 48/x=4/100

6: do cross multiplication 100×48= 4,800÷ 4 = 1,200 total on truck

Answer: 1,200 total on truck

Hope this helps.

Answer:

letter A po

Step-by-step explanation:

thanks for brain less

As sample variance increases, the likelihood of rejecting the null hypothesis and the effect on measures of effect size such as r2 and Cohen's d can be described by the likelihood increases and measures of effect size increase. So, the correct option is A.

here, we have,

As sample variance increases, the data points are more spread out, making it more likely to detect a significant difference between groups, thus increasing the likelihood of rejecting the null hypothesis.

Additionally, the larger variance may also lead to larger effect sizes, as r2 and Cohen's d both consider the magnitude of differences in the data. Hence Option A is the correct answer.

Answer :A. The likelihood increases and measures of effect size increase.

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complete question:

As sample variance increases, what happens to the likelihood of rejecting the null hypothesis and what happens to measures of effect size such as r2 and Cohen's d? Answer A. The likelihood increases and measures of effect size increase. B. The likelihood increases and measures of effect size decrease. C. The likelihood decreases and measures of effect size increase. D. The likelihood decreases and measures of effect size decrease.

Answer:

12n-20

Step-by-step explanation:

Answer:

y= -x+9

Step-by-step explanation:

1. A. These are directly proportional quantities.

2. B. They are indirectly proportional quantities.

3. D. These are inversely squared proportional quantities.

1. In the equation U = TS/A², the relationship between quantity U and quantity T is these are directly proportional quantities.

When the value of T increases, the value of U increases.

Similarly, when the value of T decreases, the value of U decreases.

This inverse relationship indicates that they are directly proportional.

2. In the equation U = TS/A², the relationship between quantity T and quantity S is they are indirectly proportional quantities.

When the value of T increases, the value of U also increases. Conversely, when the value of T decreases, the value of U decreases as well. This direct relationship indicates that they are directly proportional.

3. In the equation U = TS/A², the relationship between quantity U and quantity A is these are inversly  squared proportional quantities.

When the value of A increases, the value of U decreases.

On the other hand, when the value of A decreases, the value of U increases.

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1. In the following equation: U=TS/A².

How is quantity U related to quantity T ?

A. These are directly proportional quantities.

B. These are indirectly proportional quantities.

c. These are inversely proportional quantities.

D. These are inversely squared proportional quantities.

2. In the following equation: U=TS/A². How is quantity T related to quantity S ?

A. They are directly proportional quantities.

b. They are indirectly proportional quantities.

c. They are inversely proportional quantities.

d. They are inversely squared proportional quantities.

3. 1. In the following equation: U=TS/A².

How is quantity U related to quantity A ?

A. These are directly proportional quantities.

B. These are indirectly proportional quantities.

c. These are inversely proportional quantities.

D. These are inversely squared proportional quantities.

- U is directly proportional to T (answer A).
- T is inversely proportional to S (answer C).
- U is directly proportional to A (answer C).

In the given equation U = A^2 * TS, let's analyze the relationship between the quantities.

For the first question, "how is quantity U related to quantity T?", we can see that U is directly proportional to T.

This means that as T increases, U also increases, and as T decreases, U decreases.

The correct answer is A.

These are directly proportional quantities.

Moving on to the second question, "how is quantity T related to quantity S?", we can see that T and S are inversely proportional to each other.

This means that as T increases, S decreases, and vice versa.

The correct answer is C. They are inversely proportional quantities.

Finally, for the third question, "how is quantity U related to quantity A?", we can see that U is directly proportional to A.

This means that as A increases, U also increases, and as A decreases, U decreases.

The correct answer is C. These are directly proportional quantities.

In summary:
- U is directly proportional to T (answer A).
- T is inversely proportional to S (answer C).
- U is directly proportional to A (answer C).

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To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .

What is normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The normal distribution appears as a "bell curve" on a graph.

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Answer:

10/7

Step-by-step explanation:

5x+2x=10

7x=10

x=10/7

Answer:28

Step-by-step explanation:

Break it up! 6x3 is 18. Then 18 + 10 is 28 :P

Hope this helps :D

Answer:

12x^5 +28X^4 + 20x^3 + 27x^2 + 63x + 45

Step-by-step explanation:

(4x^3)(3x^2) + (4x^3)(7x) + (4x^3)(5) + (9)(3x^2) + (9)(7x) + (9)(5) =

12x^5 +28X^4 + 20x^3 + 27x^2 + 63x + 45

The computer virus initially infects one file, then for every minute the number files gets tripled. So the first term will be 1, the second will be 3, the third will be 9 and so on. The sequence is:

This is a geometric sequence, where each term is related to its previous by the product of a constant number. For these cases we can represent the sequence as shown below:

To find how many files will be infected after 15 minutes we need to make n=15 and solve for a, we have:

Therefore , the solution to the given problem of trigonometry comes out to be  angle of elevation : 62.3°.

The area of mathematics called trigonometry examines the correlation between triangle length l. The field first came into existence in the Classical world, presumably in the third-century BC, as a result of the integration of geometry with astronomy studies. Precise approaches mathematics deals with certain trigonometric equations and possible uses of them in calculations. There are six common trigonometric functions in trigonometry. They are known by their respective names and abbreviations sine, trigonometry, tangent, secant, etc. cosecant (csc). The studies of triangle aspects, particularly those right triangles, is known as trigonometry. However, studying geometry entails learning about all polygons' characteristics.

Here,

given  :

An aircraft is being followed by two radar stations, which are 4.3 miles apart.

Station A is 9.6 miles away from the plane in a straight line.

Thus,

To find the angle of elevation  from station A to plane :

Using Trigonometric ratios:

=> Sin A  = 8.5 / 9.6

=> Sin A = 85/96

=> A =  \(Sin^{-1}\)(85/96 )

=> A = 62.302840124651483 °

=> A = 62.3°

Therefore , the solution to the given problem of trigonometry comes out to be  angle of elevation : 62.3°.

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a. A graph of the functions f(x) and g(x) is shown in the image attached below.

b. A function that could be described as exponential is f(x).

c. The value of x for which the function values are equal is -2.678.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

In this scenario, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

Part b.

By critically observing the graph of the functions f(x) and g(x), we can logically deduce that only f(x) represent an exponential function.

Part c.

For the value of x for which the function values are equal, we have:

\(0.3333x + 7 = 1.1487e^{-0.624x}\\\\7 = 1.1487e^{-0.624x}-0.3333x\)

x = -2.678.

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Answer:

D

Step-by-step explanation:

ndndndnddndndnjdndjdjdjdjjddjdjdjdjddjjdjdd

Answer/Step-by-step explanation:

Length of AC:

Given that AB = x + 2, and BC = 7x - 3, therefore,

\( (x + 2) + (7x - 3) = AC \) (segment addition postulate)

Simply the expression for the length of segment AC

\( x + 2 + 7x - 3 = AC \)

Collect like terms

\( x + 7x + 2 - 3 = AC \)

\( 8x - 1 = AC \)

Length of QR:

Given that PQ = 8y + 5, and PR = 13y + 25, therefore,

QR = (13y + 25) - (8y + 5) (PQ + QR = PR)

Simplify the expression to for the length of segment QR

QR = 13y + 25 - 8y - 5

Collect like terms

QR = 13y - 8y + 25 - 5

QR = 5y + 20

The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

what is triangle ?

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

Given, side length, a = 12 units.

the height of equilateral triangle, h = (a√3)/2.

Substituting the value of 'a',

h = (12√3)/2 = 6√3 =

10.39 units.

The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.

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Answer:

9/10 of a dollar

Step-by-step explanation:

50/100=5/10,

so 5/10+4/10=9/10

Together they will have 9/10 part a dollar.

What is proportion ?

A proportion is an equation based on the equality of two ratios.

Here, Carmen has 4/10 of a dollar and Try says he has 50/100 part of a dollar,  now to calculate the fraction of dollar together they will be having will be the sum of Carmen and Troy part of dollar :

\(\begin{aligned}\frac{4}{10}+\frac{50}{100}&=\frac{4}{10}+\frac{5}{10}\\&=\frac{9}{10}\end{aligned}\)

Therefore, together they will have 9/10 part a dollar.

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Answer:

Step-by-step explanation:

Let the number of chefs is x and the number of customers is y.

Regular rolls

Equation:

Vegetarian rolls

Equation:

We have a system.

Solve it by elimination, multiply the first one by 4 and the second one by 3:

Compare the equations:

Substitute the value of y into first equation and solve for x:

Answer:2 Chefs and 13 customers.

Step-by-step explanation:

The probability that the bit will fail before 10 hours of usage is:

P(X < 10) = F(10) = 1 - e^(-(10/50)^2) ≈ 0.3935

The Weibull distribution is given by the probability density function:

f(x) = (a/B) * (x/B)^(a-1) * e^(-(x/B)^a)

where a and B are the shape and scale parameters, respectively.

In this case, a = 2 and B = 50. We want to find the probability that the bit will fail before 10 hours of usage, i.e., P(X < 10), where X is the random variable representing the length of life of the drill bit.

Using the cumulative distribution function (CDF) of the Weibull distribution, we have:

F(x) = 1 - e^(-(x/B)^a)

Substituting the values of a and B, we get:

F(x) = 1 - e^(-(x/50)^2)

So the answer is approximately 0.4.

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Answer:

$2100

Step-by-step explanation:

I = prt

I = $1500(0.05)(8)

I = $1500(0.4)

I = $600

$1500 + $600

= $2100

Using the Principle of permutations it is found that, there are 720 ways in which the horses can finish in first, second, and third place.

This is an example of a permutation problem, where we are interested in the number of ways to order a set of objects.

In this case, we have 10 horses racing at the championship, and we want to determine how many ways they can finish in first, second, and third place.

To solve this problem, we can use the permutation formula:

P(n, r) = n! / (n - r)!

where n is the total number of objects and r is the number of objects we want to choose and arrange in order.

In this case, we want to choose 3 horses from 10 to finish in a particular order. Therefore, we have:

P(10, 3) = 10! / (10 - 3)!

= 10! / 7!

= 10 x 9 x 8

= 720

Therefore, there are 720 ways in which the horses can finish in first, second, and third place.

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Answer:

the simplest form of 15/20 is 3/4

If we select three balls, the probability of selecting exactly one white one is 16.

There are 6 balls in a box.

2 white and 4 black.

If we select three balls, then we have to determine the probability of selecting exactly one white.

First we determine the number of ways of selecting three balls in total of 6 balls. So

\(^{6}C_{3} = \frac{6!}{3!(6-3)!}\)

\(^{6}C_{3} = \frac{6!}{3!3!}\)

\(^{6}C_{3} = \frac{6\times5\times4\times3!}{3\times2\times1\times3!}\)

Simplify

\(^{6}C_{3}\) = 5 × 4

\(^{6}C_{3}\) = 20

Now determining the probability of selecting the 3 balls out of non white balls.

\(^{4}C_{3}=\frac{4!}{3!(4-3)!}\)

\(^{4}C_{3}=\frac{4!}{3!1!}\)

Simplify

\(^{4}C_{3}=\frac{4\times3!}{3!\times1}\)

\(^{4}C_{3}\) = 4

Now, the probability of selecting exactly one white one = The number of ways of selecting three balls in total of 6 balls - The probability of selecting the 3 balls out of non white balls

The probability of selecting exactly one white one = 20 - 4

The probability of selecting exactly one white one = 16

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Answer:

35

Step-by-step explanation:

f(x)=5x^3-2x^2+3

f(2)=5x2^3-2x2^2+3

=5x8-2x4+3

=40-8+3

=40-5

=35

Answer:

35

Step-by-step explanation:

F(x) = 5x^3 -2x^2 + 3

Let x=2

F(2) = 5(2)^3 -2(2)^2 + 3

       = 5*8 -2(4) +3

       = 40 -8+3

       = 32+3

      = 35

Answer:

30

Step-by-step explanation:

3:7

30 students

3\10×30=9

7\10×30=21

9+21=30