Julia's bedroom is 10 feet by 10 feet. She wants to place a circular rug
in the corner or her room. She places a rug with a radius of 2 feet in her
room. How much of her bedroom floor, in
square feet, is not covered by the rug? Use 3.14
for r. Round to the nearest tenth.

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.

Learn more about z-score here:

https://brainly.com/question/21262765

#SPJ1

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:

https://brainly.com/question/3457976

Answer:

I'm in 10th

hope that would help, lol

[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]

Answer:

50% chance

Step-by-step explanation:

obviously

Answer:

4 and 5

Step-by-step explanation:

√20 is between 4 and 5 because 20 is between [tex]\sf 2^4[/tex] and [tex]\sf 2^5[/tex]:

[tex]\sf 2^4=16[/tex]  and  [tex]\sf 2^5=32[/tex]

Answer:

It falls in between 4 and 5

Step-by-step explanation:

Hello!

We can find the perfect squares that are before and after 20.

Perfect squares are numbers that are made by multiplying a number by itself. Numbers that are multiplied by itself 3 times are called perfect triples.

To find the square root of a number is to find out what number multiplied by itself gives us the number.

The perfect square before 20 is 16, as it is 4², or 4 x 4

The perfect square after 20 is 25, as it is 5², or 5 x 5

Therefore, the square root of 20 will fall between 4 and 5.

Answer:

9/308

Step-by-step explanation:

The probability is the area of the square divided by the area of the rectangle.

p = (3 in.)² / (22 in. × 14 in.)

p = 9/308

Answer: 4

Step-by-step explanation:

4*9=36+the 4 red =40

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.

Learn more about the expected value here;

https://brainly.com/question/15858152

Answer:

B

Step-by-step explanation:

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

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.

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:

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:

I got x= 3

[tex]m < DBE = 64\\m < CBE =26[/tex]

Step-by-step explanation:

since x= 3,

I put 3 in the equations,

first equation,

17x + 13

17*3 + 13

=64

second equation,

32-2x

32 - 2*3

=26

Answer:

It's telling you what to do...Um I can do this tho...

You do the first step...And you move on..It says..Across That tells you to go across. And you keep moving on. Do one step at a time.

I dk how to really help you.

Step-by-step explanation:

~XxRexXx~

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

Answer:

turn it

Step-by-step explanation:

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:

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:

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:

13 meters below sea level.

Step-by-step explanation:

she started at -15m.

Then she went up 7m, making it -8m.

Then down 5m, making it -13m.

the equation would look like this: -15+7-5. All the best, -Crispin

Answer:

it = -1

Step-by-step explanation:

-1

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:

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

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

Answer:

The answer is eight

Step-by-step explanation:

4*2=8

Answer:

y = -x - 1

Step-by-step explanation:

soo since we already know the slope we can subsitute it to the slope form equation

y = mx + b

y = -x + b

now to find the y intercept we have to subsitute the given point

-3 = -(2) + b

-3 = -2 + b

b = -1

Answer:

y = -x - 1

Step-by-step explanation:

Using the process of elimination, we can immediately eliminate b) (y = 2x - 3).

Why? It has a slope of 2, and our answer wants a line with a slope of -1.

y = mx + b

To find the line that goes through (2, -3), we substitute our 3 answer choices (A, C, and D) with 2 (for x-values) and -3 (for y-values).

(2, -3)

y = -x - 1

-3 = -2 - 1

-3 = -3

This statement is true

(2, -3)

y = -x - 3

-3 = -2 - 3

-3 = -5

This statement is false

(2, -3)

y = -x + 2

-3 = -2 + 2

-3 = 0

This statement is false

Therefore, the correct answer is a) y = -x - 1

*View the graph to verity the answer*

Hope this helps!