A rectangle measures 2
1
2
inches by 1
5
16
inches. What is its area?

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

Answer:

√7

Step-by-step explanation:

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

√

https://brainly.com/question/19242625

Answer:

189.9394

Step-by-step explanation:

Since 6 is >= 5, the 3 thurns into a 4

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:

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:

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]

The amount of the gross pay of the employee is 726.80 dollars. Then the correct option is D.

Taking two or more numbers and adding them together, or the entire amount of two or more numbers in addition.

A statement of an employee's biweekly earnings is given below. earnings deductions week ended regular is shown below.

$62.00, $45.06, $10.54, $12.40, $596.80

Then their sum will be

→ $62.00 + $45.06 + $10.54 + $12.40 + $596.80 = 726.80

More about the addition link is given below.

https://brainly.com/question/14092461

[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).

Learn more about Factors here:

https://brainly.com/question/24182713

#SPJ7

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:

Question 6 answer is 35

Step-by-step explanation:

using pythagoras theorem, hypotenuse²= opposite²+ adjacent²

since it is said that we're looking for the hypotenuse then the values given are for opposite and adjacent.

therefore, hyp²= 21²+28²

hyp²= 1225 take square root of both sides to eliminate square and find hypotenuse

hyp= 35

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:

-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.

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:

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:

Step-by-step explanation:

Perpendicular formula

m1 * m2 = - 1

Givens

m1 = - 7

m2 = ??

Solution

-7 * m2 = -1

m2 = 1/7

y = 1/7 x + b

x = 8

y = -3                     Substitute these values into y = 1/7 x + b

-3 = (1/7)*8 + b    

-3 = 8/7 + b          Subtract 8/7  from both sides

-3 - 8/7 = b

-4 1/7 = b

Answer (perpendicular line) y = (1/7) x - 4 1/7  or

Answer (perpendicular line) y = (1/7) x - 4.14

Parallel line

Nothing changes except you have a different y intercept.

y = -7x + b

x = 8

y = -3                           Substitute these values into y = -7x + b

-3 = -7*8 + b

-3 = - 56 + b

-3 + 56 = b

b = 53

Equation Parallel line: y = -7x + 53

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).

More can be learned about the t-distribution at https://brainly.com/question/16162795

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:

50% chance

Step-by-step explanation:

obviously

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.

Step-by-step explanation:

If you have any dout you can ask me.

Answer:

The answer is eight

Step-by-step explanation:

4*2=8

The approximate measure of angle acb in right triangle abc in which the length of the hypotenuse, line segment ac is 25 cm is 53.1 degrees.

In a right angle triangle, ratio of the adjacent side to the hypotenuse side is equal to the cosine angle between them.

[tex]\cos\theta=\dfrac{b}{c}[/tex]

Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.

The right triangle abc is given, in which,

According to the right angle triangle property,

[tex]\cos(acb)=\dfrac{bc}{ac}\\\cos(acb)=\dfrac{15}{25}\\\angle acb=\cos^{-1}(0.6)\\\angle acb=53.1^o[/tex]

Hence, the approximate measure of angle acb in right triangle abc in which the length of the hypotenuse, line segment ac is 25 cm is 53.1 degrees.

Learn more about the right angle triangle property here;

https://brainly.com/question/22790996

Answer:

53.1 degrees.

Step-by-step explanation:

Answer:

turn it

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