The volume of a cylinder is 54 1 cm3. If the radius is 3 cm, what is the height of the cylinder? 3 cm

O A. 6 cm

O B. 3 cm

O C. 18 cm

OD. 9 cm​

[tex]x^3-2x^2-5x +6\\\\=x^3-x^2-x^2+x-6x+6\\\\=x^2(x-1)-x(x-1)-6(x-1)\\\\=(x-1)(x^2 -x -6)\\\\=(x-1)(x^2 -3x +2x -6)\\\\=(x-1)\textbf{[} x(x-3) +2(x-3)\textbf{]}\\\\=(x-1)(x-3)(x+2)[/tex]

The requried, factored form of the given expression is (x - 1)(x - 3)(x + 2).

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

To factor the polynomial f(x) = x³ – 2x² – 5x + 6 completely, we can use a combination of the rational root theorem and synthetic division.

We can use synthetic division to test each possible root and see if it is a factor of the polynomial. Starting with x = 2, we have:

2 | 1 -2 -5 6

  | 2 0 -10

  |_____________

1 0 -5 -4

Since the remainder is not zero, x = 2 is not a factor of the polynomial. Continuing with the other possible roots, we find that x = 1 and x = 3 are roots, but x = -1, x = -2, x = -3, and x = -6 are not roots.

Therefore, we can factor the polynomial as follows:

f(x) = x² – 2x² – 5x + 6

= (x - 1)(x - 3)(x + 2)

So the completely factored form of f(x) is f(x) = (x - 1)(x - 3)(x + 2).

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Answer:

A table that represents a linear equation should be your answer. This means your slope should be constant/straight not like a parabola or absolute function.

Step-by-step explanation:

When you're trying to solve something using slope-intercept you can graph it or plug numbers for (x,y).  

Graph:

Start at (0,-3)

Then plot the point since that is your Y-Intercept

Then go 5 up and 4 over to find your next point.

Once done, you should connect the dots to form a slope or a linear equation.

Answer:

turn it

Step-by-step explanation:

Answer:

2. Letter B, see the attachment?

and also, I can't answer the #1 because I can't read it. I'm sorry

Already done #1 in your other question.

#2

Comapre to slope intercept form

Parallel lines have equal slope

Equation in point slope form

Answer:

√7

Step-by-step explanation:

√7 is the only irrational number because it has the radical sign

√

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Answer:

50% chance

Step-by-step explanation:

obviously

The minimum score needed to be accepted in the university when it takes only top 15% performers where performace had mean 70 score and standard deviation of 8 is found being 78.32 approx.

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

[tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z tables, the p value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

For this case, suppose that:

X = the score a student gets in the considered university's entrance exam.

Then, we have:

[tex]X \sim N(\mu = 70, \sigma = 8)[/tex]

Let X = x be the score such that scores bigger than x is 15% of all the scores applicants get.

That means, P(X > x) = 15% of the total area the distribution of X have under its normal distribution. Or, we can say that there is 15% chance of getting scores above X = x

Now, we can rewrite this statement as:

[tex]1 - P(X \leq x) = 0.15[/tex]

Converting X to Z (standard normal variate), we get:

[tex]1 - P(X \leq x ) = 0.15\\\\1 - P\left(Z \leq z = \dfrac{x - 70}{8} \right) =0.15\\\\P(Z \leq z = (x-70)/8) = 0.85[/tex]

The value Z = z for which the p-value is approx 0.85 is found from the z-tables as:

Thus, we get:

[tex]z = \dfrac{x-70}{8}\\x = 8z + 70\\x \approx 8 \times 1.04 + 70 = 78.32[/tex]

Thus, the minimum score needed to be accepted in the university when it takes only top 15% performers where performace had mean 70 score and standard deviation of 8 is found being 78.32 approx.

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Answer:

Step-by-step explanation:

Cylinder

Start by finding the volume of the cylinder as though the spheres were not there.

Volume of a cylinder = pi r^2 h

r = 6 inches

h = 25 inches.             Put the givens in the formula

Volume = pi 6^2 * 25

Volume = pi * 36 * 25

Volume = 900 pi

One sphere

Don't try and find the volume of both spheres. Just do one and double it.

V = pi * (4/3) * r^3

r = 6 inches

V = pi * (4/3) * 6^3

V = pi * 288 Cubic inches

Two spheres

Total volume spheres = 2 * 288 pi

Total Volume of spheres = 576 pi

Volume of the shaded region.

The following will act as a formula for the answer to the question

V_shade = Volume of the cylinder - volume of the 2 spheres

Substitute values into formula

Volume shade = 900 * pi - 576* pi       Take out common factor (pi)

Volume shade = pi  * (900 - 576 )

Volume of the shaded area

Volumne shade = pi *324

pi = 3.14

Volume shade = 1017.36

Answer:

volume of the shaded region = 1018

Step-by-step explanation:

Answer:

k = 2.31

Step-by-step explanation:

You will use the Law of Cosine to determine the unknown angles, then you will use the Sine Rule to determine the unknown side.

Answer:

Green heart is 2 and blue shape is 8.

Step-by-step explanation:

We know 1 purple drop equals 3.

So 3+3 = 6

The total weight is 16 so we can do 16-6 = 10

We have 10 left. Since we need the weight to be balanced the green heart must be 2.

Because then it would be 8 on 1 side (2 purples equals 6 and 1 heart equals 2, so 6+2=8) and 8 on the other side (8+8=16).

Answer:

The answer is eight

Step-by-step explanation:

4*2=8

[tex]~~~~\dfrac{5+2\sqrt 3}{7+4\sqrt 3} = a- 6\sqrt 3\\\\\\\implies a= \dfrac{5+2\sqrt 3}{7+4\sqrt 3}+6\sqrt3 \\\\\\\implies a=\dfrac{\left(5+2\sqrt 3 \right) \left( 7-4\sqrt 3\right)}{\left(7+4\sqrt 3 \right) \left(7-4\sqrt 3 \right)}+6\sqrt 3\\\\\\\implies a = \dfrac{35-20\sqrt 3+14\sqrt 3-24}{7^2 - \left(4\sqrt 3 \right)^2}+6\sqrt 3\\\\\\\implies a=\dfrac{11-6\sqrt 3}{49-48}+6\sqrt 3\\\\\\\implies a=11-6\sqrt 3+6\sqrt 3\\\\\\\implies a = 11[/tex]

Because the transformation is a dilation, we conclude that the buildings are not congruent.

You need to remember that if the transformation applied to A is a dilation or a contraction, then the figures will not be congruent.

Where for a point (x, y), a dilation of scale factor k is written as:

(kx, ky).

The vertices of building A are:

(x₁, y₁), (x₂, y₂), (x₃, y₃), and (x₄, y₄).

And the vertices of building B are a dilation of the above ones, such that the dilation has a scale factor k = 2.

(2x₁, 2y₁), (2x₂, 2y₂), (2x₃, 2y₃), and (2x₄, 2y₄).

So, because there is a dilation, building B is not congruent to building A.

If you want to learn more about transformations, you can read:

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Selection of machines is persons choice and not arranged specifically, thus we will use Combination.

⇒ 20C5

⇒ 20!/5!(20-5)!

⇒ 15504

Use combination

total ways

[tex]\\ \rm\dashrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

[tex]\\ \rm\dashrightarrow ^{20}C_5[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{20!}{5!15!}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{20(19)(18)(17)(16)(15!)}{5(4)(3)(2)(15!}[/tex]

[tex]\\ \rm\dashrightarrow 15504[/tex]

Answer:

1.  BC = 24

  Perimeter of ABCD = 96

3. PT = 9

   ST = 7

Step-by-step explanation:

Question 1

All the side lengths of a rhombus are equal.

Therefore, BC = AB = 24

So the perimeter of ABCD = 24 × 4 = 96

Question 3

The diagonals of a rhombus bisect each other at right angles.

Bisect means to divide into two equal parts.

Therefore, PT = TR  so  PT = PR ÷ 2

As PR = 18  then  PT = 18 ÷ 2 = 9

QT = ST  so  ST = QS ÷ 2

As QS = 14  then  ST = 14 ÷ 2 = 7

Answer:

254.4

Step-by-step explanation:

if its 0.75 inch thick, then to get the radius you just times to thickness by 2 which gets 1.5.

6-1.5= 4.5

to get the radius you divide 4.5 by 2 which gets 2.25

and then put this in the formula you get=

V=πr2h=π·2.252·16≈254.469

so the answer is 254

edit:i might be wrong feel free to correct me

Answer: 254

Step-by-step explanation:

Answer:

I'm in 10th

hope that would help, lol

Step-by-step explanation:

I think you made some mistakes in the problem definition.

I guess you mean

9 = (1/27)^(a+3)

let's think about how to create 9 out of 1/27 just by using exponents.

we note that 27 is 3³. and therefore the cubic root of 27 is 3.

so,

(1/27)^(1/3) = 1/3

because the exponent 1/3 means "cubic root". an exponent 1/2 means square root. and so on.

making the exponent negative means 1/...

so,

(1/27)^(-1/3) = 3

and now, with what exponent operation can we turn 3 into 9 ?

by squaring it.

so,

((1/27)^(-1/3))² = 9

putting an exponent on an exponent means to multiply the exponents during simplification.

therefore,

((1/27)^(-1/3))² = (1/27)^(-2/3) = 9

that means

a + 3 = -2/3

a = -2/3 - 3 = -2/3 - 9/3 = -11/3

so, the first answer option is correct.

Answer:

-4/5

Step-by-step explanation:

To find the slope of a line with two points, we do y2-y1/x2-x1.

y2 is 2. y1 is 6.

2-6 = -4

x2 is 8. x1 is 3

8-3 = 5

-4/5 is the answer meaning it is the slope.

Answer:

Slope of this line = -4/5.

Step-by-step explanation:

The formula is

Slope = (y2-y1)/(x2-x1)  where (x1, y1) and (x2, y2)  are  the 2 points.

So here we have:

(6-2)/(3-8)

= -4/5.

Step-by-step explanation:

If you have any dout you can ask me.

Number of high school students which should the store expect next week, Mary predicts that the store will see 4,238 customers next week is 2392.

The expected value is the long term average of the data or the mean of the data.

In order to better decide how to market a new line of clothing, Mary is researching the demographics of the customers of a certain clothing store.

She counted the number of customers who visited the store over the course of a month, and found out how many of the customers were high school students.

Her collected data is in the table below.

Mary predicts that the store will see 4,238 customers next week.

From using the long term mean value calculator for the provided data, the predicted value of the next week we get as 2392.

Hence, the number of high school students which should the store expect next week, Mary predicts that the store will see 4,238 customers next week is 2392.

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Answer:

B

Step-by-step explanation:

B because the of the is the cool make of giga chad braincells :)

Answer:

it = -1

Step-by-step explanation:

-1

Answer:

-2x - 3

Step-by-step explanation:

f(x) = -1/2(x + 3)  is the same as  y = -1/2(x + 3)

change all y terms to x terms and all x terms to y terms

So  change  y = -1/2(x + 3) to x = -1/2(y + 3)

Now use the new equation and slove for y

x = -1/2(y + 3)

-2x = -2· -1/2 (y + 3)

-2x = y + 3

-2x - 3 = y

Rewrite your answer y = -2x - 3

Write the equation in the  inverse

Using the t-distribution, as we have the standard deviation for the sample, it is found that the 90% confidence interval is (246.6, 282.8).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 16 - 1 = 15 df, is t = 1.7531.

Researching the problem on the internet, the standard deviation was of 42.1 mg/dL, hence the parameters are as follows:

[tex]\overline{x} = 264.7, s = 41.2, n = 16[/tex]

Thus, the bounds of the interval are given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 264.7 - 1.7531\frac{41.2}{\sqrt{16}} = 246.6[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 264.7 + 1.7531\frac{41.2}{\sqrt{16}} = 282.8[/tex]

The 90% confidence interval is (246.6, 282.8).

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Using the permutation formula, as the order is important, it is found that the officers can be chosen in 6840 ways.

Each "position" is a different role(president, vice president and secretary), hence the order is important.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 people will be chosen from a set of 20, hence:

[tex]P_{20,3} = \frac{20!}{17!} = 6840[/tex]

The officers can be chosen in 6840 ways.

More can be learned about the permutation formula at https://brainly.com/question/25925367