Find the dimensions of a rectangle with area 512 m2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)

Answer:

The standard error  S.E of the mean is 5

Step-by-step explanation:

From the given data;

Fifty students are enrolled in a Business Statistics class.

After he first examination, a random sample of 5 papers was selected.

Now; let consider a random sample of 5 papers was selected. with the following grades : 60, 75, 80, 70, and 90

The objective of this question is to determine the standard error of the mean

In order to achieve this ; we need to find the mean and the standard deviation from the given data.

TO start with the mean;

Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{n} \sum x_i[/tex]

Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{5} (60+75+80+70+90)[/tex]

Mean [tex]\overline X[/tex] = 0.2(375)

Mean [tex]\overline X[/tex] = 75

On the other hand; the standard deviation is :

[tex]s = \sqrt{\dfrac{1}{n-1}\sum(x_i - \overline X)^2}[/tex]

[tex]s = \sqrt{\dfrac{1}{5-1}((60-75)^2+(75-75)^2+(80-75)^2+(70-75)^2+(90-75)^2 )}[/tex]

[tex]s = \sqrt{\dfrac{1}{4}(225+0+25+25+225 )}[/tex]

[tex]s = \sqrt{\dfrac{1}{4}(500 )}[/tex]

[tex]s = \sqrt{125}[/tex]

s = 11.18

Finally; the standard error  S.E of the mean is:

[tex]S.E = \dfrac{s}{\sqrt{n}}[/tex]

[tex]S.E = \dfrac{11.18}{\sqrt{5}}[/tex]

[tex]S.E = \dfrac{11.18}{2.236}[/tex]

[tex]S.E = 5[/tex]

The standard error  S.E of the mean is 5

First,

[tex]9x+15y+15z=45\implies 3x+5y+5z=15[/tex]

The volume is given by the integral (one of 6 possible combinations),

[tex]\displaystyle\int_0^5\int_0^{\frac{15-3x}5}\int_0^{\frac{15-3x-5y}5}\mathrm dz\,\mathrm dy\,\mathrm dx=\boxed{\frac{15}2}[/tex]

Answer:

centre = (13,0)

radius = 8

Step-by-step explanation:

The standard equation of the circle is

(x-x0)^2 + (y-y0)^2 = r^2 ...............(1)

where

(x0,y0) is the centre,

r is the radius.

For

(x-13)^2 + y^2 = 64  ..............(2)

we rewrite (2)

(x-13)^2 + (y-0)^2 = 8^2 ...............(3)

and compare (3) with (1)

to identify

x0 = 13, y0 = 0, and r = 8

Therefore

centre = (13,0)

radius = 8

Answer:

[tex]\huge\boxed{z=3}[/tex]

Step-by-step explanation:

If two polygons are similar, then corresponding sides are in proportion.

The corresponding sides:

4 → x

y → 15

3 → w

2 → 6

z → 9

therefore:

[tex]\dfrac{z}{9}=\dfrac{2}{6}[/tex]         cross multiply

[tex](z)(6)=(9)(2)[/tex]

[tex]6z=18[/tex]         divide both sides by 6

[tex]z=3[/tex]

Answer:

Step-by-step explanation:

Answer:

69 meters

Step-by-step explanation:

Answer:

Please privately chat to us why you chose to cheat during online class, otherwise we will contact your parents and kick you out of our program for the reason stated.

Step-by-step explanation:

Please contact your Quantitive Reasoning teacher at her email, as stated in Google Classroom.

Answer:

A

Step-by-step explanation:

A function is that of which has only one x value. Therefore you are looking for the graph that does not have multiple x values. Doing a vertical line test to see whether there is more than one point on a line of the graph will show you that A is the only one that has one answer for each x value that is given. All the other graphs have two points for some of the x's, which makes them not a function.

Answer:

k = 44

Step-by-step explanation:

k/4 + 3 = 14

k/4 = 11

k = 44

Answer:

[tex]\boxed{\sf k=44}[/tex]

Step-by-step explanation:

[tex]\sf \frac{k}{4} +3=14[/tex]

Subtract 3 from both sides.

[tex]\sf \frac{k}{4} +3-3=14-3[/tex]

[tex]\sf \frac{k}{4}=11[/tex]

Multiply both sides by 4.

[tex]\sf \frac{k}{4}(4)=11(4)[/tex]

[tex]\sf k=44[/tex]

Answer:

C) |-9| != |9|

Step-by-step explanation:

The definition of absolute value is simply the non-negative value of the argument without regards to the sign.  With this in mind, let's walk through these options.

A) -2/2 < 3 ==> -1 < 3 which is True

B) |-1| >= 0 ==> 1 >= 0 which is True since 1 is > 0

C) |-9| != |9| ==> 9 != 9 which is False since 9 == 9

D) -7 <= -5  which is True since -7 is < -5

Cheers

Answer:

H0: p=0.85;

Ha: p>0.85

Step-by-step explanation:

What was being tested is that:

the coach wanted to know if the proportion of basketball players who are over 72 inches is more than 85%.

The null hypothesis which we are testing against would be that the proportion of basketball players who are over 72 inches is 85%.

H0: p=0.85;

Ha: p>0.85

Answer:

lmkjhvjgcfnhjkhbmgnc gfghh

Step-by-step explanation:

Answer: $1284 per quarter

Step-by-step explanation:

Answer:

$5136

step by step:

this year tuition-1200

in a year there are 4 quarters

so total this yr is 1200×4=4800

Next year

tuition is 100%+7%per 4months

so

1.07×1200=1284per month

per year 1284×4=5136

Answer:

work is pictured and shown

Answer:

Infinitely many solutions.

Step-by-step explanation:

To solve the system of equation using the substitution method, the problem has already given us a solution for x:

x = -4y - 9

Using this, we can plug that into the first equation and solve for y:

3x + 12y = -27

3(-4y - 9) + 12y = -27

-12y - 27 + 12y = -27

-27 = -27

The fact that our solution indicate -27 = -27 means that these two equations have infinitely many solutions for the value y.  This simply means that no matter what we put in for y, the statement will always be true.

Notice that these two equations are in fact the same equation:

x = -4y - 9 ==> x + 4y = -9 ==> 3x + 12y = -27

Since these two equations are the same, then there are infinitely many solutions.

I'm not sure quite what they want for the form in terms of y, but let's solve for y since they already solved for x:

x = -4y - 9

x + 9 = -4y

y = (-1 / 4) (x + 9)

Cheers.

Answer:

[tex]y=\frac{4}{3}x-1.75[/tex]

Step-by-step explanation:

If the slope of a line is 4/3,

and we wanna find the equation of a line that is parallel to it and crosses through (5,5).

So we already have the slope because the slope of 2 parallel lines are the same.

y = 4/3x

Look at the image below↓

So now we just need to find the y-intercept.

After some numbers we got,

[tex]y=\frac{4}{3}x-1.75[/tex]

Look at the other image below↓

Thus,

the equation of the parallel line is [tex]y=\frac{4}{3}x-1.75[/tex].

Hope this helps :)

Answer:

Reject H0

Age and pressure are related

Step-by-step explanation:

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. In the given scenario we reject the null hypothesis because job pressure and age are related to each other.

Answer:

The answer is A.

Step-by-step explanation:

You have to multiply by converting the second fraction into upside down :

[tex] \frac{4x + 1}{6x} \div \frac{x}{3x - 1} [/tex]

[tex] = \frac{4x + 1}{6x} \times \frac{3x - 1}{x} [/tex]

[tex] = \frac{(4x + 1)(3x - 1)}{x(6x)} [/tex]

[tex] = \frac{12 {x}^{2} - 4x + 3x - 1}{6 {x}^{2} } [/tex]

[tex] = \frac{12 {x}^{2} - x - 1 }{6 {x}^{2} } [/tex]

Answer:  3/(28) ≈ 10.7%

Step-by-step explanation:

3 blue + 2 red + 3 green = 8 total pens

   First pick    and           Second pick

 [tex]\dfrac{3\ blue\ pens}{8\ total\ pens}\quad \times \quad \dfrac{2\ remaining\ blue\ pens}{7\ remaining\ total\ pens}\quad =\large\boxed{\dfrac{3}{28}}[/tex]  

Answer:

1. Pattern (rule) : y = x-6

2. Pattern (rule) : y=x^2+1

3. Pattern (rule)  : y = -3x

4. Pattern (rule) : y = 2x-2

5. Pattern (rule) : y = x^2

Step-by-step explanation:

Note: question number correspond to your order of questions.

1. Pattern (rule) : y = x-6

for missing parts, see attached table.

2. Pattern (rule) : y=x^2+1

3. Pattern (rule)  : y = -3x

4. Pattern (rule) : y = 2x-2

5. Pattern (rule) : y = x^2

Answer:

[tex]Perimeter = 14 + 7\sqrt{2}[/tex]

Step-by-step explanation:

Given:

Area of the square = 49 in²

Required

Determine the perimeter of the one of the congruent triangles

First, we'll determine the length of the square;

[tex]Area = Length * Length[/tex]

Substitute 49 for Area

[tex]49 = Length * Length[/tex]

[tex]49 = Length^2[/tex]

Take Square root of both sides

[tex]7 = Length[/tex]

[tex]Length = 7[/tex]

When the square is divided into two equal triangles through the diameter;

2 sides of the square remains and the diagonal of the square forms the hypotenuse of the triangle;

Calculating the diagonal, we have;

[tex]Hypotenuse^2 = Length^2 + Length^2[/tex] -- Pythagoras Theorem

[tex]Hypotenuse^2 = 7^2 + 7^2[/tex]

[tex]Hypotenuse^2 = 2(7^2)[/tex]

Take square root of both sides

[tex]Hypotenuse = \sqrt{2} * \sqrt{7^2}[/tex]

[tex]Hypotenuse = \sqrt{2} * 7[/tex]

[tex]Hypotenuse = 7\sqrt{2}[/tex]

The perimeter of one of the triangles is the sum of the 2 Lengths and the Hypotenuse

[tex]Perimeter = Length + Length + Hypotenuse[/tex]

[tex]Perimeter = 7 + 7 + 7\sqrt{2}[/tex]

[tex]Perimeter = 14 + 7\sqrt{2}[/tex]

Answer:

The 90%  confidence level is  [tex]19.15< L < 20.85[/tex]

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 64[/tex]

     The mean age is  [tex]\= x = 20 \ years[/tex]

      The standard deviation  is   [tex]\sigma = 4 \ years[/tex]

Generally  the degree of freedom for this data set is mathematically represented as

        [tex]df = n - 1[/tex]

substituting values

        [tex]df = 64 - 1[/tex]

        [tex]df = 63[/tex]

Given that the level of confidence is  90%  the significance level is mathematically evaluated as

          [tex]\alpha = 100 - 90[/tex]

         [tex]\alpha =[/tex]10 %  

         [tex]\alpha = 0.10[/tex]

Now   [tex]\frac{\alpha }{2} = \frac{0.10}{2} = 0.05[/tex]

Since we are considering a on tail experiment

The  critical value for half of  this significance level at the calculated  degree of freedom is obtained from the critical value table as

           [tex]t_{df, \frac{ \alpha}{2} } = t_{63, 0.05 } = 1.669[/tex]

   The margin for error is mathematically represented as

          [tex]MOE = t_{df , \frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

substituting values  

          [tex]MOE = 1.699 * \frac{4 }{\sqrt{64} }[/tex]

         [tex]MOE = 0.85[/tex]

he 90% confidence interval for the true average age of all students in the university is evaluated as follows

           [tex]\= x - MOE < L < \= x + E[/tex]

substituting values  

         [tex]20 - 0. 85 < L < 20 + 0.85[/tex]

         [tex]19.15< L < 20.85[/tex]

Answer: 680

Step-by-step explanation:

When order doesn't matter,then the number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Given: Total participants = 17

From these, a group of 3 participants is to be tested under a special condition.

Number of groups of 3 participants chosen = [tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\[/tex]

[tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\\\\=\dfrac{17\times16\times15\times14!}{3\times2\times14!}\\\\=680[/tex]

Hence, there are 680 groups of 3 participants can  be chosen,.

Answer:

The variables X and Y are dependent.

Step-by-step explanation:

The variable X denotes number of face cards . That is it can take values,

X = {0, 1, 2 }

Compute the probability for all he values of X as follows:

P [X = 0] = P (None of the 12 card is chosen in either draw)

              = (40/52)×(39/51)

              = 1560/2652

              = 0.5882

P [X = 1] = P (One of the card is face card is selected)

              = 2×(40/52)×(12/51)

              = 960/2652

              = 0.3619

P [X = 2] = P (Two of the 12 card is chosen in the draw)

              = (12/52)×(11/51)

              = 132/2652

              = 0.0498

The variable Y denotes number of cards numbered 10 . Thus, it can take values:

Y = {0, 1, 2 }

P [Y = 0] = P (None of the 4 card is chosen in either draw)

              = (48/52)×(47/51)

              = 2256/2652

              = 0.8507

P [Y = 1] = P (One of the 4 card is chosen in either draw)

              = 2×(4/52)×(48/51)

              = 384/2652

              = 0.1448

P [Y = 2] = P (Two of the 4 card is chosen in the draw)

              = (4/52)×(3/51)

              = 12/2652

              = 0.0045

Now compute the probability of (X and Y).

P [X = 0 and Y = 0] = P(None of the 16 card is chosen in either draw)

                              = (36/52)×(35/51)

                              = 1260/2652

                              = 0.4751

The variables X and Y are independent if,

P [X = 0 and Y = 0]  = P [X = 0] × P [Y = 0]

                               =  P [X = 0] × P [Y = 0]

                               = 0.8507 × 0.5882

                               = 0.5204

The two values are not equal.

Hence, the variables X and Y are not independent.

Answer:

A.

{-4 ≤ x ≤ 4}

{-4 ≤ y ≤ 4}

Step-by-step explanation:

We’ll domain is the amount of x values,

Range is the amount of y values

_______________________________

Domain:

Starts from -4 to 4

{-4 ≤ x ≤ 4}

I made the sign less than or equal to because the circle lines are solid.

Range:

This starts from -4 to 4 also.

{-4 ≤ y ≤ 4}

Thus,

answer choices A. is correct

Hope this helps :)

Hey there! I'm happy to help!

Note that this is not a function because some inputs can have more than one output, that's why they say relation, not function! :D

DOMAIN

The domain is all of the possible x-values of the relation.  We see that the lowest x-value is -4, while the highest is 4. If you plug in these two or any number in between, there will be at least one corresponding output.

This domain can be written as -4 ≤ x ≤ 4.

RANGE

The range is all of the possible outputs or y-values. We see that the minimum y-value is -4 and that the highest is 4. Therefore, we will just write it the same as the domain but use a different variable.

-4 ≤ y ≤ 4.

This matches with Option A.

I hope that this helps! Have a wonderful day!

Answer:

70.5°

Step-by-step explanation:

22² = (20)²+(18)² - 2(20)(18) cos X

484 = 400 + 324 - 720 cos X

-240 = -720 cosx

1/3 = cos X

[tex]cos^{-1}(\frac{1}{3})[/tex] = X

X = 70.52877937

Answer:

Consistent.

Step-by-step explanation:

Since there is one solution ( the lines intersect), the equations are consistent

They would be inconsistent if the lines do not intersect

The would be equivalent if they are the same line

The answer would be consistent.

Step-by-step explanation:

In the graph shown here, there is only one solution

because the lines intersect at the point (5, 3).

In order for the lines to be inconsistent, the lines would have to not

meet or intersect each other but notice that this is not the case here.

The would be equivalent if they are the same exact line

so it would look like there would just be one line.

Answer:

$7

Step-by-step explanation:

Simple interest formula:

I = Prt

6 months = 6 * 30 days = 180 days

1 year = 360 days

t = (180 days)/(360 days) = 0.5

I = $7000 * 0.002 * 0.5

I = $7

Answer:

$7

Step-by-step explanation:

Recall that simple interest is given by

I = Prt,

Where :

I = interest (we are asked to find this)

P = principal amount = given as $7000

r = rate = given as 0.2% = 0.002

t = time in years = given as 6 months = 0.5 years

SImply substitute the known values into the equation above:

I = Prt

= (7000)(0.002)(0.5)

= $7

Answer:

For 0,90 of Confidence we reject H₀

For  0,95 CI we reject H₀

Step-by-step explanation:

To evaluate a difference between two proportion with big sample sizes we proceed as follows

1.-Proportion 1

n = 2160

243 had rear license  p₁ = 243/2160     p₁ = 0,1125

2.Proportion 2

n = 358

55   had rear license   p₂ = 55/ 358     p₂ = 0,1536

Test Hypothesis

Null Hypothesis                            H₀      ⇒   p₂   =  p₁

Alternative Hypothesis                Hₐ     ⇒    p₂  >  p₁

With signficance level  of  0,05  means  z(c) = 1,64

T calculate   z(s)

z(s) =  ( p₂ - p₁ ) / √ p*q ( 1/n₁  +  1/n₂ )

p = ( x₁  +  x₂ ) / n₁  +  n₂

p = 243  +  55 / 2160 + 358

p = 0,1183     and then    q = 1 -  p     q =  0,8817

z(s) =  ( 0,1536 - 0,1125 ) / √ 0,1043 ( 1/ 2160   +  1 / 358)

z(s) =  0,0411 /√ 0,1043*0,003256

z(s) = 0,0411 / 0,01843

z(s) =  2,23

Then  z(s) > z(c)      2,23  >  1,64

z(s) is in the rejection region we reject H₀

If we construct a CI for  0,95   α = 0,05   α/2  =  0,025

z (score ) is  from z- table    z = 1,96

CI = ( p ±  z(0,025*SE)

CI = ( 0,1536 ± 1,96*√ 0,1043*0,003256 )

CI = ( 0,1536 ± 1.96*0,01843)

CI = ( 0,1536 ± 0,03612 )

CI = ( 0,11748  ;  0,18972 )

In the new CI we don´t find  0 value so we have enough evidence to reject H₀

Answer:

The probability is 1

Step-by-step explanation:

Given

Number of flips = 8

Outcomes = 8 heads

Required

Probability of getting a head in the next row

This problem can be attributed to experimental probability and it'll be solved using experimental probability formula, which goes as follows;

[tex]Probability = \frac{Number\ of\ Occurence}{Total\ Trials}[/tex]

Let [tex]P(Head)[/tex] represents the probability of getting a head in the next row;

[tex]P(Head)= \frac{Outcome\ of\ head}{Total\ Flips}[/tex]

[tex]P(Head)= \frac{8}{8}[/tex]

[tex]P(Head)= 1[/tex]

Hence, the probability of obtaining a head in the next flip is 1

Explanation:

The tickmarks show which pieces are congruent to one another, which in turn show the segments have been bisected (cut in half). The square angle markers show we have perpendicular segments. So we have three perpendicular bisectors. The perpendicular bisectors intersect at the circumcenter. The circumcenter is the center of the circumcircle. This circle goes through all three vertex points of the triangle.

A useful application is let's say you had 2 friends and you three wanted to pick a location to meet for lunch. Each person traveling from their house to the circumcenter's location will have each person travel the same distance. We say the circumcenter is equidistant from each vertex point of the triangle. In terms of the diagram, LH = LJ = LK.

Answer: B.) Circumcenter

Step-by-step explanation:

Answer:

- 29 / 20

Step-by-step explanation

The cosec (x) = 1 / sin(x)

There are 2 ways to do this:

Either using a calculator:

sin^-1(20 / 29) = 43.60281897

so inputting into 1/sin(-x) where x = 43.6.....

This gives: -29 / 20

OR

1 / sin(x) = cosec ( x)

so cosec (x) = 1/(20/29)

= 29/20

By observing the cosec(x) graph, we see that to get cosec (-x), all we need to do is to minus our answer seeing as the graph is symmetrical across the axes. Therefore x = -29/20