If events A and B are
independent, what must be true?

Answer:  Choice C

[tex]\frac{2x+3}{x+2}[/tex]

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

Work Shown:

[tex]h(x) = f(x) \div g(x)\\\\h(x) = \frac{f(x)}{g(x)}\\\\h(x) = \frac{2x^2-x-6}{x^2-4}\\\\h(x) = \frac{(x-2)(2x+3)}{(x-2)(x+2)}\\\\h(x) = \frac{2x+3}{x+2}\\\\[/tex]

Optional Extra Info:

Keep in mind that [tex]x \ne 2[/tex] and [tex]x \ne -2[/tex] to avoid division by zero errors. We can plug in x = 2 just fine into the simplified version of h(x), but we always need to go back to the original.

Answer:

its B. 636 to 1404

Step-by-step explanation:

Using the Empirical Rule, about 95% of the scores lie between values 636 to 1404. The correct option is c.

The standard deviation of a set of values is a measure of its variation or dispersion. The square root of the variance, which is the average of the squared differences from the mean, is used to calculate it.

According to the Empirical Rule, approximately 68% of the data for a normal distribution fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

In this case, the mean SAT score is 1020, with a standard deviation of 192. As a result, roughly 95% of the scores fall within two standard deviations of the mean, or between

(1020 - 2(192)) and (1020 + 2(192)).

Calculating, we get:

Lower bound: 1020 - 2(192) = 636

Upper bound: 1020 + 2(192) = 1404

Therefore, the answer is (b) 636 to 1404.

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Answer:

[tex]\pi = \frac{22}{7} [/tex]

Use this OK bro.

The shortest length (circumference) of the string is 18.84cm.

The circumference is that certain length that requires to enclose a  circle with respective of a fixed length known as radius. If radius of cylinder be r, then the circumference will be 2πr.

The required length of the string is the circumference of the base of the cylinder.

The radius of the cylinder is 3cm.

Taking π=3.14, the circumference will be : 2*3.14*3cm

=18.84cm

The shortest length of the string is 18.84cm.

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Answer:

[tex]x=129[/tex] °

Step-by-step explanation:

A secant is a line that intersects a circle in two places. The secants interior angle theorem states that when two secants intersect a circle inside a circle, the measure of any one of the angles formed is equal to half of the sum of the two intersecting arcs. Therefore, one can apply this theorem here:

[tex]x=\frac{204+54}{2}[/tex]

Simplify,

[tex]x=\frac{204+54}{2}[/tex]

[tex]x=\frac{258}{2}[/tex]

[tex]x=129[/tex]

Answer:

It is 45. 1000 Millileters are in a liter. 750 x 60 = 45000. 45000/1000 = 45.

Step-by-step explanation:

Let

[tex]I(m) = \displaystyle \int_0^\pi x\sin^m(x)\,\mathrm dx[/tex]

Integrate by parts, taking

u = x   ==>   du = dx

dv = sinᵐ (x) dx   ==>   v = ∫ sinᵐ (x) dx

so that

[tex]I(m) = \displaystyle uv\bigg|_{x=0}^{x=\pi} - \int_0^\pi v\,\mathrm du = -\int_0^\pi \sin^m(x)\,\mathrm dx[/tex]

There is a well-known power reduction formula for this integral. If you want to derive it for yourself, consider the cases where m is even or where m is odd.

If m is even, then m = 2k for some integer k, and we have

[tex]\sin^m(x) = \sin^{2k}(x) = \left(\sin^2(x)\right)^k = \left(\dfrac{1-\cos(2x)}2\right)^k[/tex]

Expand the binomial, then use the half-angle identity

[tex]\cos^2(x)=\dfrac{1+\cos(2x)}2[/tex]

as needed. The resulting integral can get messy for large m (or k).

If m is odd, then m = 2k + 1 for some integer k, and so

[tex]\sin^m(x) = \sin(x)\sin^{2k}(x) = \sin(x)\left(\sin^2(x)\right)^k = \sin(x)\left(1-\cos^2(x)\right)^k[/tex]

and then substitute u = cos(x) and du = -sin(x) dx, so that

[tex]I(2k+1) = \displaystyle -\int_0^\pi\sin(x)\left(1-\cos^2(x)\right)^k = \int_1^{-1}(1-u^2)^k\,\mathrm du = -\int_{-1}^1(1-u^2)^k\,\mathrm du[/tex]

Expand the binomial, and so on.

Answer:

sin ß = opposite / hypotenuse

sin45° = x / 4√2

Cross multiply

x = sin 45° × 4√2

x = √2/2 × 4√2

x = 4 × √2 ×√2 / 2

x = 4 × 2 / 2

x = 8 / 2

x = 4

Answer:

15

Step-by-step explanation:

5:22=15:66, simply multiply 3 in the right hand side

Answer:

15

Step-by-step explanation:

5 : 22 = x : 66

Product of means = product of extremes

22*x = 66*5

[tex]x = \frac{66*5}{22}[/tex]

x = 3 * 5 = 15

Answer:

9.8

Step-by-step explanation:

a geometric sequence means we multiply the previous element by a certain factor to get the next element.

so, all we need to do is determine the factor used to go from one element in the list to the next.

a1 = 9

a2 = 88.2

a3 = 864.36

a4 = 8470.728

the simplest case is usually the case from a1 to a2.

a2 = a1×f

88.2 = 9×f

f = 88.2/9 = 9.8

we are finished here.

but we can control our result and verify with the other given elements.

88.2 × 9.8 = 864.36

and that is a3. fits.

864.36 × 9.8 = 8470.728

and that is a4.

so, all fits, we are correct.

Answer:

the common ratio is 9.8

just divide the term with it's previous term

eg. 88.2/9 , 864.36/88.2

Hi, I'm happy to help!

Parallel means that two lines are lined up in the same directions and will never intersect even if they were extended forever in directions.

Let's look at the first option of AB, and AD. We can see that both lines intersect at point A, so AB and AD are not parallel.

For the next option of CD and BE, we can see that both lines don't intersect and won't ever even if the lines were extended. So, CD and BE are parallel.

For the third option, we have BC and DE. These lines don't intersect and aren't in line to ever do so. Therefore, BC and DE and parallel.

The last option is AD and BC. These two lines will never meet, but, they aren't line up in the same directions. AD is traveling upwards while BC isn't. Think about being able to make a road out of the two lines, it would never work. AD and BC are not parallel.

To sum it up: You should select the 2nd and 3rd options because those lines are parallel.

I hope this was helpful, keep learning! :D

Answer:

[tex]\frac{98p^{6}}{q}[/tex]

Step-by-step explanation:

Distribute the exponents

[tex](\frac{(7^{-2}p^{-6}q^{-8})}{2q^{-9}} )^{-1}[/tex]

[tex](\frac{q}{98p^{6}} )^{-1}[/tex]

Distribute the -1

[tex]\frac{98p^{6}}{q}[/tex]

Answer:Each of the points and the y-intercept of their perpendicular bisectors

Step-by-step explanation:

Where AB and CD are parallel lines:

the y-intercept of line AB is -56/5

the equation of line CD is: y = 7/5x - 2

If two lines are parallel, they will have the same slope (m) value in their equation, y = mx + b (slope-intercept form).

Find the slope of AB:

Slope of AB (m) = change in y / change in x = (7 - 0)/(3 - 8) = 7/5

To find the y-intercept (b) of AB, substitute (x, y) = (8, 0) and m = 7/5 into y = mx + b

0 = 7/5(8) + b

0 - 56/5 = b

b = -56/5 (y-intercept of AB)

AB is parallel to CD, so, CD will have the same slope of 7/5.

To find the equation of CD, substitute m = 7/5 and (a, b) = (5, 5) into y - b = m(x - a)

y - 5 = 7/5(x - 5)

y - 5 = 7/5x - 7

y = 7/5x - 7 + 5

y = 7/5x - 2 (equation of line CD)

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Answer:

sum is 2(a² + b²)

Step-by-step explanation:

[tex] {(a - b)}^{2} + {(a + b)}^{2} \\ = ( {a}^{2} - 2ab + {b}^{2} ) + ( {a}^{2} + 2ab + {b}^{2} ) \\ = 2 {a}^{2} + 2 {b}^{2} \\ = 2( {a}^{2} + {b}^{2} )[/tex]

the answer is she spend $18.32

Answer:

what's is the question anyway

Answer:

630 and 90 respectively

Step-by-step explanation:

Let the speed of wind be x and the plane speed be y

ATQ, (y+x)*3=2160 and (y-x)*4=2160. Solving it, we will get x=90 and y=630

The speed of the plane in still air is 630 miles per hour and the speed of the wind is 90 miles per hour.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

An airplane takes 3 hours to travel a distance of 2160 miles with the wind. The return trip takes 4 hours against the wind.

Let 'x' be the speed of the plane and 'y' be the speed of the wind. Then the equations are given as,

x + y = (2160 / 3)

x + y = 720                  ...1

x - y = (2160 / 4)

x - y = 540                  ...2

Add equations 1 and 2, then we have

2x = 720 + 540

x = 1260 / 2

x = 630 miles per hour

Then the value of 'y' is calculated as,

630 + y = 720

y = 90 miles per hour

The speed of the plane in still air is 630 miles per hour and the speed of the wind is 90 miles per hour.

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Answer:

348 km³

Step-by-step explanation:

Volume = base area×height

base area = 5.8×12/2 = 34.8 km²

volume = 34.8×10 = 348 km³

Answer:

6/23

Step-by-step explanation:

First, find the total number of marbles:

6 + 8 + 9

= 23

There are 6 red marbles out of the 23.

So, the odds of choosing one will be 6/23.

Answer:

Step-by-step explanation:

L = 9 mm

W =  9 mm

H = 10 mm

volume = LWH/3 = 9·9·10/3 = 270 mm³

Here are all of the answers to these four questions:

1. log2^64=6, or 2 to the power of 6=64.

2. log11^121=2, or 11²=121.

3. log8^512=3, or 8³=512.

4. log4^1/16=-2, or 4 to the negative second (-2) power.

I hope that this answered your question.

Yeah, so the answer is 6, 2, 3, and -2.

Answer:RPS is 90 degrees...

Answer:

round answer is : 10 ft

Step-by-step explanation:

The explanation is in the picture!

Answer:

Step-by-step explanation:

Hint:

a² - 9a + 15  = (a-7)(a-2)

a² + 9a + 15  = (a+7)(a+2)

a² + 3a - 10 = (a-2)(a+5)

a² + 5a - 14 = (a-2)(a+7)

a² - 5a - 14 = (a-7)(a+2)

[tex]3x=x+10[/tex]

We tripple something and get 10 more than something.

Put the x-es on the left and non x-es to the right,

[tex]2x=10[/tex]

Divide both sides by 2,

[tex]x=5[/tex]

Et Viòla.

Hope this helps :)

When a number is tripled, its value increases by 10 then the original number is 5.

Let's call the original number "x". According to the problem, when this number is tripled, its value increases by 10. Mathematically, we can represent this as an equation:

3x = x + 10

Now, we can solve for "x" step by step:

1. Subtract "x" from both sides of the equation:

  3x - x = 10

2. Simplify the left side:

  2x = 10

3. Divide both sides by 2 to solve for "x":

  x = 10 / 2

  x = 5

So, the original number "x" is 5.

In other words, if you take a number, triple it (multiply by 3), and then increase the result by 10, you would end up with the value 5. This can be verified by checking:

3 * 5 = 15

15 + 10 = 25

The equation 3x = x + 10 represents the relationship between the original number and its tripled value with an increase of 10. Solving this equation helps us find the original value that satisfies the given condition.

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Answer:

the answer is 4

Step-by-step explanation:

the answer will be positive

Answer:

150

Step-by-step explanation:

Increase = New Number - Original Number.

divide the increase by the original number and multiply the answer by 100.