In the following exercises, find the greatest common factor.


15y3, 21y2, 30y

Answer:

Step-by-step explanation:

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Answer:

z= 2.38

P = 0.008656

Step-by-step explanation:

Here n= 500 and p~= 464/500= 0.928 and q`= 1- 0.928 = 0.072

We formulate our null and alternate hypothesis as

H0 =  0.9 ;       H0 > 0.9

The degree of confidence = 90%

z₀.₀₅ = 1.645 for  α= 0.05

We use the test statistic

z=  x- np/√npq

z= 466-500 *0.9/ √500 * 0.9(1-0.9)

z= 466- 450/ √45

z= 16/6.7082

z= 2.38

As the calculated value of z= 2.38  is greater than α =1.645 so we reject H0.

If H0 is true the P value is calculated as

P = 1- Ф( 2.38)

P = 1-0.991344=0.008656

Answer:

You will never be able to reach the sum of 2

Step-by-step explanation:

Answer:

Null hypothesis :

[tex]H_o:p_1-p_2 = 0[/tex]

Alternative hypothesis:

[tex]H_1:p_1-p_2 \neq 0[/tex]

Decision Rule:

To reject the null hypothesis if  z < -1.65 and z > 1.65

Conclusion:

Failed to reject null hypothesis if z > -1.65 or z < 1.65

z -value = 0.33022

P-value = 0.7414

Decision Rule:

Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1

Conclusion:  we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode

Step-by-step explanation:

From the summary of the given statistical data sets.

Let consider to [tex]p_1[/tex] represent percentage of the first group ; &

[tex]p_2[/tex] represent percentage of the second group

The null and the alternative hypothesis can be stated s follows:

Null hypothesis :

[tex]H_o:p_1-p_2 = 0[/tex]

Alternative hypothesis:

[tex]H_1:p_1-p_2 \neq 0[/tex]

At the level of significance ∝ = 0.1; the two tailed critical value from the z-table

[tex]z_{\alpha/2} = 1.65[/tex]

Decision Rule:

To reject the null hypothesis if  z < -1.65 and z > 1.65

Conclusion:

Failed to reject null hypothesis if z > -1.65 or z < 1.65

However; from the question:

There are 55 people in the first group and this group will be administered the new drug.

There are 45 people in the second group and this group will be administered a placebo.

After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.

The test statistic for the for the first group who suffered from the second episode can be denoted as :

[tex]\hat p_1 = \dfrac{\overline x_1}{n_1}=0.11[/tex]

The test statistic for the for the second group who suffered from the second episode can be denoted as :

[tex]\hat p_2 = \dfrac{\overline x_2}{n_2}=0.09[/tex]

where;

[tex]n_1[/tex] = sample size of group 1 = 55

[tex]n_2[/tex] = sample size of group 2 = 45

The total probability of both group is :

[tex]\hat p = \dfrac{n_1 \hat p_1 + n_2 \hat p_2}{n_1 + n_2}[/tex]

[tex]\hat p = \dfrac{55*0.11+ 45 * 0.09}{55+45}[/tex]

[tex]\hat p = \dfrac{6.05+ 4.05}{100}[/tex]

[tex]\hat p = \dfrac{10.1}{100}[/tex]

[tex]\hat p = 0.101[/tex]

The standard error of the statistic [tex]\hat p_1 - \hat p_2[/tex] an be computed as follows:

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{ p_1 (1 - \hat p)( \dfrac{1}{n_1}+\dfrac{1}{n_2})}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101 (1 - 0.101)( \dfrac{1}{55}+\dfrac{1}{45})}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101(0.899)(0.0404)}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.0036682796}[/tex]

[tex]S.E(\hat p_1 - \hat p_2)=0.060566[/tex]

Now; The test statistics is determined to be :

[tex]z = \dfrac{(\hat p_1 - \hat p_2 ) - (p_1-p_2)}{SE(\hat p_1 - \hat p_2)}[/tex]

[tex]z = \dfrac{(0.11-0.09) - 0}{0.060566}[/tex]

z = 0.33022

Hence; the value for the test statistics =  0.33022

the value for the test statistics =  0.33

From the z value; The P-value for the test statistics can be computed as:

P-value = 2P(Z ≥ |z|)

P-value = 2P(Z ≥  0.33022)

P-value = 2 × P (Z ≤ - 0.33022)

From the z table Z ≤ - 0.33022 = 0.3707

P-value = 2 × 0.3707

P-value = 0.7414

Decision Rule:

Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1

Conclusion:  we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode

Answer:

Hey there!

The slope of a vertical line is undefined! The run is zero, and as we know, dividing by zero is undefined!

Hope this helps :)

Answer:

Undefined

Step-by-step explanation:

A vertical line has an undefined slope or there is no slope of the line.

Answer: 308 gallons of water.

Step-by-step explanation:

First find the volume of the water been.

The volume of a rectangular prism uses the formula

V= L * W *H

V = 8 * 5 * 1

V = 40 ft^3

Now we will convert 40ft into gallons using what they gave us that 1 gallon is 0.13 ft^3  

[tex]\frac{1}{x} = \frac{0.13}{40}[/tex]    which means if 1 gallon is 0.13 cubic feet how much will 40 cubic feet be when converted to gallons.

Solve by cross product.

0.13x = 40  divide both sides by 0.13  

x= 308

Answer:

[tex]\huge\boxed{f^{-1}(x)=-\dfrac{1}{8}x+1}[/tex]

Step-by-step explanation:

[tex]f(x)=-8x+8\to y=-8x+8[/tex]

change x with y

[tex]x=-8y+8[/tex]

solve for y

[tex]-8y+8=x[/tex]          subtract 8 from both sides

[tex]-8y+8-8=x-8[/tex]

[tex]-8y=x-8[\tex]        divide both sides by (-8)

[tex]\dfrac{-8y}{-8}=\dfrac{x}{-8}-\dfrac{8}{-8}\\\\y=-\dfrac{1}{8}x+1[/tex]

Answer:

width = length = 3 inches

height = 7 inches

Step-by-step explanation:

If x is the width and length of the base, and y is the height, then:

y = x + 4

The volume of the box is:

63 = x²y

The surface area of the box is:

93 = x² + 4xy

Substitute the first equation into the third.

93 = x² + 4x (x + 4)

93 = x² + 4x² + 16x

0 = 5x² + 16x − 93

0 = (x − 3) (5x + 31)

x = 3

y = 7

Use the second equation to check your answer.

63 = (3)²(7)

63 = 63

Answer:

Length=Width=3

Height=7.

Step-by-step explanation:

First, let's write some equations. So, we have an open box (with no lid) that has a square base. It has a height 4 units more of its width/length.

First, let's write the equation for the volume. The volume of a rectangular prism is:

[tex]V=lwh[/tex]

Recall that we have a square base. In other words, the length and width are exactly the same. Therefore, we can do the following substitution:

[tex]V=(w)wh=w^2(h)[/tex]

Now, recall that the height is four units more than the width/length. Therefore, we can make the following substitution:

[tex]V=w^2(w+4)\\63=w^2(w+4)[/tex]

We can't really do anything with this. Let's next find the equation for the surface area.

So, we have 5 sides (not 6 because we have no lid). The bottom side is a square, so it's area is w^2. Since we have a square base, the remaining four sides will have an area w(w+4). In other words:

[tex]93=w^2+4(w(w+4))[/tex]

The left term represents the area of the square base. The right term represents the area of one of the rectangular sides, times sides meaning four sides. Simplify:

[tex]93=w^2+4w^2+16w\\5w^2+16w-93=0[/tex]

This seems solvable. Let's try it. Trying factoring by guessing and checking.

We can see that it is indeed factor-able. -15 and 31 are the numbers:

[tex]5w^2-15w+31w-93=0\\5w(w-3)+31(w-3)=0\\(5w+3)(w-3)=0\\w=3\\h=w+4=7[/tex]

We ignore the other one because width cannot be negative.

So, the width/length is 3 and the height is 7. We can check this by plugging this into the volume formula:

[tex]63\stackrel{?}{=}(3)^2(7)\\63\stackrel{\checkmark}{=}63[/tex]

Answer:

(A) 15 centimeters

Step-by-step explanation:

A midsegment of a triangle is always 2 things:

Half the size of the bottom of the triangle (in this case AC)

Parallel to the bottom of the triangle.

Since ABC is an equilateral triangle, we know that EVERY side is 30cm, including AC.

So the midsegment of ABC, LM, must be 15 cm.

Hope this helped!

Answer:

SAS

Step-by-step explanation:

.. cuz, it just is c:

By ''SAS congruency'' theorem we can prove AD = CB.

We have to given that,

In a figure,

AB = CD

∠1 = ∠4

Now, In triangle ADC and triangle ABC,

AC = AC (Common side)

∠1 = ∠4  (Given)

AB = CD (Given)

Hence, By SAS Congruency theorem,

Δ ADC ≅ Δ ABC

So, We get;

AD = CB

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ2

Answer:

LotsofDebt, Inc Debt Ratio is 93.75%

LotsofEquity, Inc Debt Ratio is 6.25%

equity multiplier LotsofDebt, Inc is 16

equity multiplier LotsofEquity, Inc is 1.0666666667

debt-to-equity LotsofDebt, Inc is $15 million

debt-to-equity LotsofEquity, Inc. is $0.0666666667 million

Step-by-step explanation:

In order to calculate the debt ratio of LotsofDebt, Inc and LotsofEquity, Inc.  we would have to make the following calculations:

Debt Ratio = Debt/Assets

According to the given data we have the following:

LotsofDebt, Inc Debt=$30 million

LotsofDebt, Inc Asset=Debt + Equity = $30 million + $2 million = $32 million

Therefore, LotsofDebt, Inc Debt Ratio =$30 million/$ 32 million

LotsofDebt, Inc Debt Ratio= 93.75%

LotsofEquity, Inc. Debt=$2 million

LotsofEquity, Inc Asset= Debt + Equity = $2 million + $30 million

LotsofEquity, Inc Debt Ratio = $2 million/$32 million

LotsofEquity, Inc Debt Ratio = 6.25%

In order to calculate the equity multiplier of LotsofDebt, Inc and LotsofEquity, Inc.  we would have to make the following calculations:

equity multiplier =Assets/Equity

equity multiplier LotsofDebt, Inc.=$32 million/$2 million

equity multiplier LotsofDebt, Inc= 16

equity multiplier LotsofEquity, Inc=$32 million/$30 million

equity multiplier LotsofEquity, Inc = 1.0666666667

In order to calculate the debt-to-equity of LotsofDebt, Inc and LotsofEquity, Inc.  we would have to make the following calculations:

debt-to-equity LotsofDebt, Inc=Debt/Equity

debt-to-equity LotsofDebt, Inc=$30 million/$2 million

debt-to-equity LotsofDebt, Inc= $15 million

debt-to-equity LotsofEquity, Inc.= $2 million/$30 million = 0.0666666667

debt-to-equity LotsofEquity, Inc.= $0.0666666667 million

Answer:

Option d: n = 36, p = 0.97, x = 36.

Step-by-step explanation:

We are given that a soup company puts 12 ounces of soup in each can. The company has determined that 97% of can have the correct amount.

We have to describe a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled.

Let X = Number of cans that are properly filled

The above situation can be represented through binomial distribution;

[tex]P(X = x) = \binom{n}{x} \times p^{x} \times (1-p)^{n-x} ; x = 0,1,2,........[/tex]

where, n = number of trials (samples) taken = 36 cans

            x = number of success = all cans are properly filled = 36

            p = probabilitiy of success which in our question is probability that

                  can have the correct amount, i.e. p = 97%

So, X ~ Binom (n = 36, p = 0.97)

Hence, from the options given the correct option which describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled is n = 36, p = 0.97, x = 36.

Answer:

"If an angle has measure 90°, then it is a right angle" , True

Step-by-step explanation:

We have the following:

"If an angle is a right angle, then it’s measure is 90"

The idea is to write the opposite of the previous conditional statement.

We know that if the statement is "If p, then q", then its inverse will be "If q, then p".

So the opposite of our given statement will be :

"If an angle has measure 90°, then it is a right angle"

And this statement is true since every angle that measures 90 ° is considered a right angle.

Answer:

y= 4.25x + $10

Step-by-step explanation:

A tool rental shop charges a flat fee of $10.00 to rent out their chain saw

An amount of $4.25 is charged for each of the days

Let x represent the amount that is charged for each day

Let y represent the total cost of the chain saw

Since the rental fee for each day is given as $4.25 and the flat fee is given as $10 then, the equation can be expressed as

y= $4.25x + $10

Hence the equation that expresses the cost y of renting this saw if it is rented for x days is y= $4.25x + $10

Answer:

f^-1(x) = x + 5

Step-by-step explanation:

f(x) = x-5

y = x-5

Exchange x and y

x = y-5

Solve for y

x+5 = y-5+5

x+5 =y

The inverse is x+5

Answer:

The answer is

Step-by-step explanation:

(x² + 3x + 4)(3x² - 2x + 1)

Expand the terms

We have

3x⁴ - 2x³ + x² + 9x³ - 6x² + 3x + 12x² - 8x + 4

Group like terms

That's

3x⁴ - 2x³ + 9x³ + x² - 6x² + 12x² + 3x - 8x + 4

Simplify

We have the final answer as

Hope this helps you

1. The angles form a straight angle

2. A straight angle is defined to be 180 degrees

3. The three angles of any triangle always add to 180, as the diagram shows.

4. This is false. We need to add the three different angles A,B,C to get 180. Adding angle A to itself may not lead to 180. A+A = 180 only happens when angle A is a right angle (90 degree angle).

Answer:

  (x, 2 -2x)

Step-by-step explanation:

Written in standard form, both equations are ...

  2x +y = 2

Since they are both the same, there are an infinite number of solutions. We can write those solutions in terms of x as ...

  y = 2 -2x

The solutions are ...

  (x, 2 -2x)

Answer:

A

Step-by-step explanation:

To factor x² - 5x + 4, we need to find 2 numbers that have a sum of -5 and product of 4; these 2 numbers are -1 and -4 so the factored version is (x - 1)(x - 4). Since x - 4 is not an answer choice but x - 1 is, the answer is A.

Answer:

(26+92)+17 = 26 + ( 92+17)

Step-by-step explanation:

The associative property of addition is

a + (b + c) = (a + b) + c

We want to move the parentheses

(26+92)+17 = 26 + ( 92+17)

Answer:

A ) i) X control chart : upper limit = 50.475, lower limit = 49.825

    ii) R control chart : upper limit =  1.191, lower limit = 0

Step-by-step explanation:

A) Finding the control limits

grand sample mean = 1253.75 / 25 = 50.15

mean range = 14.08 / 25 = 0.5632

Based on  X control CHART

The upper control limit ( UCL ) =

grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475

The lower control limit (LCL)=

grand sample mean - A2 *  mean range = 50.15 - 0.577(0.5632) = 49.825

Based on  R control charts

The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191

The lower control limit = D3 * mean range = 0 * 0.5632 = 0  

B) estimate the process mean and standard deviation

estimated process mean = 50.15 = grand sample mean

standard deviation = mean range / d2  = 0.5632 / 2.326 = 0.2421

note d2 is obtained from control table

Answer:

125/6(In(x-25)) - 5/6(In(x+5))+C

Step-by-step explanation:

∫x2/x1−20x2−125dx

Should be

∫x²/(x²−20x−125)dx

First of all let's factorize the denominator.

x²−20x−125= x²+5x-25x-125

x²−20x−125= x(x+5) -25(x+5)

x²−20x−125= (x-25)(x+5)

∫x²/(x²−20x−125)dx= ∫x²/((x-25)(x+5))dx

x²/(x²−20x−125) =x²/((x-25)(x+5))

x²/((x-25)(x+5))= a/(x-25) +b/(x+5)

x²/= a(x+5) + b(x-25)

Let x=25

625 = a30

a= 625/30

a= 125/6

Let x= -5

25 = -30b

b= 25/-30

b= -5/6

x²/((x-25)(x+5))= 125/6(x-25) -5/6(x+5)

∫x²/(x²−20x−125)dx

=∫125/6(x-25) -∫5/6(x+5) Dx

= 125/6(In(x-25)) - 5/6(In(x+5))+C

13 since  i think it's when a single didget number has a 1 at the beginning. i might be wrong thoough

Answer:

$[58543.42; 73456.58]

Step-by-step explanation:

Hello!

For the variable

X: salary of a college graduate that took a statistics course

Out of n= 43 students, the calculated mean is [tex]\frac{}{X}[/tex]= $66000

The population standard deviation is δ= $18908

There is no information about the variable distribution, but since the sample size is big enough (n≥30), you can apply the CLT and approximate the distribution of the sample mean to normal [tex]\frac{}{X}[/tex]≈N(μ;σ²/n)

Then you can apply the approximation of the standard normal distribution to calculate the 99% CI

[tex]\frac{}{X}[/tex] ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\frac{Singma}{\sqrt{n} }[/tex]

[tex]Z_{1-\alpha /2}= Z_{0.995}= 2.586[/tex]

[tex]\frac{Singma}{\sqrt{n} }= \frac{18908}{\sqrt{43} }= 2883.44[/tex]

[66000±2.586*2883.44]

$[58543.42; 73456.58]

With a 99% confidence level you'd expect that the interval $[58543.42; 73456.58] will include the average salary of college graduates that took a course of statistics.

I hope this helps!

Answer:

   (-10, -3)

Step-by-step explanation:

Replacing x with x+1 in a function moves its graph 1 unit to the left. The point that is 1 unit to the left of (-9, -3) is (-10, -3).

Answer:

The Azimuths are 81 degrees, 6 degrees for Grid Azimuths and 269 degrees, 194 degrees for back Azimuths

Step-by-step explanation:

Stream = 89 degrees and Pond = 14 degrees

To Convert to grid Azimuth

G-M Azimuth of 89-8=81 degrees

G-M Azimuth of 14-8=6 degrees

To obtain the back Azimuth for the stream

89+180=269 degrees

To obtain the back Azimuth for the pond

14+180=194 degrees

Answer:

z = 1.55

Step-by-step explanation:

The answer is attached.

Answer:

12

Step-by-step explanation:

Well first step to finding median is order the scores from least to greatest,

0, 3, 8, 12, 14, 15, 15

Now we can start crossing the numbers off.

After we've crossed 3 numbers off from each side,

we get 12.

Thus,

12 is the median of the number set,

Hope this helps :)

Answer:

12

Step-by-step explanation:

First we need to put the numbers in order from smallest to largest

14, 15, 8, 15, 3, 0, and 12

becomes

0 , 3 , 8 , 12 , 14, 15, 15

Then the median is the middle number

There are 7 numbers

7/2 = 3.5

The middle is  the  4th number ( 3 on the left and 3 on the right)

0 , 3 , 8 ,     12 ,     14, 15, 15

The median is 12