A = 100(1+r)^4
Expand the right of this formula.
appreciate your help with an explanation

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:

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:

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

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:

Following are the answer to this question:

Step-by-step explanation:

The principle vale of Arg(3)

[tex]Arg(3)=-\pi+\tan^{-1} (\frac{|Y|}{|x|})[/tex]

The principle value of the [tex]\logi= \log(0+i)\ \ \ \ \ _{where} \ \ \ x=0 \ \ y=1> 0[/tex]

So, the principle value:

a)

[tex]\to \log(i)=\log |i|+i Arg(i)\\\\[/tex]

             [tex]=\log \sqrt{0+1}+i \tan^{-1}(\frac{1}{0})\\\=\log 1 +i \tan^{-1}(\infty)\\\=0+i\frac{\pi}{2}\\\=i\frac{\pi}{2}[/tex]

b)

[tex]\to \log(-i)= \log(0-i ) \ \ \ x=0 \ \ \ y= -1<0\\[/tex]

Principle value:

[tex]\to \log(-i)= \log|-i|+iArg(-i) \\\\[/tex]

                 [tex]=\log \sqrt{0+1}+i(-\pi+\tan^{-1}(\infty))\\\\=\log1 + i(-\pi+\frac{\pi}{2})\\\\=-i\frac{\pi}{2}[/tex]

c)

[tex]\to \log(-1+i) \ \ \ \ x=-1, _{and} y=1 \ \ \ x<0 and y>0[/tex]

The principle value:

[tex]\to \log(-1+i)=\log |-1+i| + i Arg(-1+i)[/tex]

                     [tex]=\log \sqrt{1+1}+i(\pi+\tan^{-1}(\frac{1}{1}))\\\\=\log \sqrt{2} + i(\pi-\tan^{-1}\frac{\pi}{4})\\\\=\log \sqrt{2} + i\tan^{-1}\frac{3\pi}{4}\\\\[/tex]

d)

[tex]\to i^i=w\\\\w=e^{i\log i}[/tex]

The principle value:

[tex]\to \log i=i\frac{\pi}{2}\\\\\to w=e^{i(i \frac{\pi}{2})}\\\\=e^{-\frac{\pi}{2}}[/tex]

e)

[tex]\to (-i)^i\\\to w=(-i)^i\\\\w=e^{i \log (-i)}[/tex]

In this we calculate the principle value from b:

so, the final value is [tex]e^{\frac{\pi}{2}}[/tex]

f)

[tex]\to -1^i\\\\\to w=e^{i log(-1)}\\\\\ principle \ value: \\\\\to \log(-1)= \log |-1|+iArg(-i)[/tex]

                [tex]=\log \sqrt{1} + i(\pi-\tan^{-1}\frac{0}{-1})\\\\=\log \sqrt{1} + i(\pi-0)\\\\=\log \sqrt{1} + i\pi\\\\=0+i\pi\\=i\pi[/tex]

and the principle value of w is = [tex]e^{\pi}[/tex]

g)

[tex]\to -1^{-i}\\\\\to w=e^(-i \log (-1))\\\\[/tex]

from the point f the principle value is:

[tex]\to \log(-1)= i\pi\\\to w= e^{-i(i\pi)}\\\\\to w=e^{\pi}[/tex]

h)

[tex]\to \log(-1-i)\\\\\ Here x=-1 ,<0 \ \ y=-1<0\\\\ \ principle \ value \ is:\\\\ \to \log(-1-i)=\log\sqrt{1+1}+i(-\pi+\tan^{-1}(1))[/tex]

                    [tex]=\log\sqrt{2}+i(-\pi+\frac{\pi}{4})\\\\=\log\sqrt{2}+i(-\frac{3\pi}{4})\\\\=\log\sqrt{2}-i\frac{3\pi}{4})\\[/tex]

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:

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: 2neters

Step-by-step explanation: I also recently did it on Khan academy

The height of the tent of the figure is H = 2 m

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

The volume of a prism is the product of its base area and height

Volume of Prism = B x h

where B = base area of prism

h = height of prism

Given data ,

Let the volume of the tent be represented as V

Now , the value of V is

V = 4.5 m³

Let the height of the prism be H

Now , the base of the triangle B = 1.5 m

And , the length of the tent L = 3 m

So , Volume of Prism = B x h

4.5 = ( 1/2 ) x 1.5 x H x 3

On simplifying , we get

4.5 = 2.25H

Divide by 2.25 on both sides , we get

H = 2 m

Hence , the height of the tent is 2 m

To learn more about volume of prism click :

https://brainly.com/question/11336446

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The complete question is attached below :

Syrus is buying a tent with the dimensions shown below. The volume inside the tent is 4.5 m^3. Syrus isn't sure if the tent will be tall enough for him to stand inside. What is the height of the tent?

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:

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:

C. 0.0009

Step-by-step explanation:

0.09/100

= 0.0009

Answer:A

Step-by-step explanation:0.09=0.9

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:

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

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:

21

Step-by-step explanation:

Just like a dilation you want to find some sort of scale factor. Now when 7/2 is simplified it then becomes 3.5. Now multiply that by 6 since we are trying to find the ratio. when multiplied by 6 it becomes 21 so the ration of wins to losses is 21/6

Answer:

Largest possible length is 21 inches.

Step-by-step explanation:

Given:

Total material available = 60 inches

Length to be 3 more than twice of width.

To find:

Largest possible length = ?

Solution:

As it is rectangular shaped frame.

Let length = [tex]l[/tex] inches and

Width = [tex]w[/tex] inches

As per given condition:

[tex]l = 2w+3[/tex] ..... (1)

Total frame available = 60 inches.

i.e. it will be the perimeter of the rectangle.

Formula for perimeter of rectangle is given as:

[tex]P = 2 \times (Width + Length)[/tex]

Putting the given values and conditions as per equation (1):

[tex]60 = 2 \times (w+ l)\\\Rightarrow 60 = 2 \times (w+ 2w+3)\\\Rightarrow 60 = 2 \times (3w+3)\\\Rightarrow 30 = 3w+3\\\Rightarrow 3w = 27\\\Rightarrow w = 9 \ inch[/tex]

Putting in equation (1):

[tex]l = 2\times 9+3\\\Rightarrow l = 21\ inch[/tex]

So, the answer is:

Largest possible length is 21 inches.

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:

$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:

15.625 m³

Step-by-step explanation:

The volume of a cube has a formula: V = a³

V = volume

a = side length

The side length is given 2.5 meters.

V = 2.5³

Solve for V.

V = 15.625

The volume is 15.625 cubic meters.

Answer:

15.625cm^3

Step-by-step explanation:

Formula:

V=lxwxh

Given:

l=2.5m

w=2.5m

h=2.5m

Answer:

V=lxwxh

V=2.5m*2.5m*2.5m

V=6.25m^2*2.5m

V=15.625m^3

Hope this helps :)

Answer:

Step-by-step explanation:

lot = 120 face shields

sold 5/6 of 120 =

5 × 120 ÷ 6 =

600 ÷ 6 = 100 sold of the lot.

then: 120-100 = 20

They need to sell 20 protectors.

Answer:

20 face shields.

Step-by-step explanation:

You have 120 face shields.

You sell 5/6 of them. That means that you still have to sell 1 - 5/6 = 1/6 of the lot.

120 * (1/6) = 20 * 1 = 20 face shields to sell.

Hope this helps!

Answer:

x=4

Step-by-step explanation:

3/4x+ 4 = 7

Subtract 4 from each side

3/4x+ 4-4 = 7-4

3/4x = 3

Multiply each side by 4/3

4/3 * 3/4 x = 3 * 4/3

x = 4

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:

3

Step-by-step explanation:

Because the number 5 is a number that you get from 7 more than n, and 2 is the other divisor that means n must equal 10 and 7 less than 10 is 3.

When five times a number is divided by 7 more than the number and the result is 2, then the number is 14/3, which is solved using the linear equation in one variable 5x/(x+ 7) = 2, where x is the required number.

Linear equations are first-order equations. Lines in the coordinate system are determined by linear equations. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable).

In the question, we are asked to find a number, which satisfies the statement, "Five times a number is divided by 7 more than the number. The result of this division is 2".

We assume the number to be x.

Now we try to form a linear equation in one variable from the given statement.

Five times a number is 5x.

7 more than a number is x + 7.

We are said that five times a number is divided by 7 more than a number. This can be shown as 5x/(x + 7).

Now, the result is given as 2, which can be shown as:

5x/(x+ 7) = 2, which is the required linear equation in one variable.

To get the number, we solve the equation using the following steps:

5x/(x+ 7) = 2

or, {5x/(x+ 7)}*(x + 7) = 2*(x + 7) (Multiplying both sides by (x + 7))

or, 5x = 2x + 14 (Simplifying)

or, 5x - 2x = 2x + 14 - 2x (Subtracting 2x from both sides)

or, 3x = 14 (Simplifying)

or, 3x/3 = 14/3 (Dividing both sides by 3)

or, x = 14/3 (Simplifying)

∴ When five times a number is divided by 7 more than the number and the result is 2, then the number is 14/3, which is solved using the linear equation in one variable 5x/(x+ 7) = 2, where x is the required number.

Learn more about the linear equation in one variable at

https://brainly.com/question/24145091

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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:

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:  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:

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:

- 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

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 :)