In the following exercises, find the greatest common factor.


15y3, 21y2, 30y

Answer:

x = 300

n = 410

p' = 0.7317

[tex]\mathbf{P' \sim Normal (\mu = 0.7317, \sigma = 0.02188)}[/tex]

Step-by-step explanation:

From the given information;

the objective is to answer the following:

(i) Enter an exact number as an integer, fraction, or decimal.

Mean x = 300

(ii) Enter an exact number as an integer, fraction, or decimal.

Sample size n = 410

(iii) Round your answer to four decimal places.

Sample proportion p' of the drivers who always claimed they buckle up is :

p' = x/n

p' = 300/410

p' = 0.7317

Which distribution should you use for this problem? (Round your answer to four decimal places.)

P' _ ( , )

The normal distribution is required to be used because we are interested in proportions and the sample size is large.

Let consider X to be the random variable that follows a normal distribution.

X represent the number of people that always claim they buckle up

∴

[tex]P' \sim Normal (\mu = p' , \sigma = \sqrt{\dfrac{p(1-p)}{n}})[/tex]

[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.7317(1-0.7317)}{410}})[/tex]

[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.7317(0.2683)}{410}})[/tex]

[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.19631511}{410}})[/tex]

[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{4.78817341*10^{-4}})[/tex]

[tex]\mathbf{P' \sim Normal (\mu = 0.7317, \sigma = 0.02188)}[/tex]

Step-by-step explanation:

Hi, there!!..

The format of report writing are given in points;

and start your body,

and write conclusion,

You may add comments on it.

Hope it helps....

Answer:

A : 10

Step-by-step explanation:

Answer:

the correct answer is 12

Step-by-step explanation:

6/8=9/x

cross multiply

6x=72

divide by six

x=12

Answer:

The answers are A. and B.

Step-by-step explanation:

Since the area of the largest square is 36. We need two numbers that equal 36. and A. had 6 and 30 so i picked it and it was right and B. is 28 and 8 which also equals 36. But, C. is 4 and 16 which is not 36. So A. and B. are the answers. Hope this helps! :)

We can use the Pythagorean theorem (a^2+b^2=c^2)(a  

2

+b  

2

=c  

2

)left parenthesis, a, squared, plus, b, squared, equals, c, squared, right parenthesis to determine possible areas of the two smaller squares.

\text{Area of a square} =\text{side}^2Area of a square=side  

2

start text, A, r, e, a, space, o, f, space, a, space, s, q, u, a, r, e, end text, equals, start text, s, i, d, e, end text, squared

So, we can substitute the areas of the squares that share side lengths with the triangle for a^2, b^2a  

2

,b  

2

a, squared, comma, b, squared and c^2c  

2

c, squared in the Pythagorean theorem.

Hint #22 / 6

For example, in the diagram above, the area of the square that shares a side with the hypotenuse is 363636 square units. So, c^2=36c  

2

=36c, squared, equals, 36.

Hint #33 / 6

Let's fill in the possible values to see if they make the equation true.

\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 6 + 30 &\stackrel{\large?}{=}36 \\\\ 36 &\stackrel{\checkmark}{=}36\\\\ \end{aligned}  

a  

2

+b  

2

a  

2

+b  

2

6+30

36

​  

=c  

2

=36

=

?

36

=

✓

36

​  

The sum of the areas of the squares connected to the two shorter triangle sides is equal to the area of the square connected to the longest side.

So, 666 and 303030 could be the areas of the smaller squares.

Hint #44 / 6

\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 8 + 28 &\stackrel{\large?}{=}36 \\\\ 36 &\stackrel{\checkmark}{=}36\\\\ \end{aligned}  

a  

2

+b  

2

a  

2

+b  

2

8+28

36

​  

=c  

2

=36

=

?

36

=

✓

36

​  

The sum of the areas of the squares connected to the two shorter triangle sides is equal to the area of the square connected to the longest side.

So, 888 and 282828 could be the areas of the smaller squares.

Hint #55 / 6

\begin{aligned} a^2 + b^2 &= c^2 \\\\ a^2 + b^2 &= 36 \\\\ 4 + 16 &\stackrel{\large?}{=}36 \\\\ 20 &\neq 36\\\\ \end{aligned}  

a  

2

+b  

2

a  

2

+b  

2

4+16

20

​  

=c  

2

=36

=

?

36



​  

=36

​  

The sum of the areas of the squares connected to the two shorter triangle sides is not equal to the area of the square connected to the longest side.

So, 444 and 161616 could not be the areas of the smaller squares.

Hint #66 / 6

The area of the smaller squares could be:

666 and 303030

888 and 2828

Step-by-step explanation:

. 345,000 cm³.

b. 124,300 hl.

c. 9,000 cm³.

d. 32.5 dm³.

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

a. 3,450 deciliters to cubic decimeters:

1 deciliter=100 cubic decimeters

(3,450dl)(\frac{100cm^{3}}{1dl})=345,000cm^{3}(3,450dl)(

1dl

100cm

3

)=345,000cm

3

b. 124.3 hectoliters to deciliters:

1 hectoliter=1,000 deciliters

(124,3hl)(\frac{1,000dl}{1hl})=124,300hl(124,3hl)(

1hl

1,000dl

)=124,300hl

c. 9 liters to cubic centimeters:

1 liter=1,000 cubic centimeters

(9L)(\frac{1,000cm^{3}}{1L})=9,000cm^{3}(9L)(

1L

1,000cm

3

)=9,000cm

3

d. 32.5 liters to cubic decimeters:

1 liter=1 cubic decimeter

32.5L=32.5dm^{3}32.5L=32.5dm

3

your answer follow me plzzz

Answer:

The first one is 345,000 cm³.

The second is 124,300 hl.

the Third is 9,000 cm³.

Anddd the fourth one is 32.5 dm³

:)

Answer:

40

Step-by-step explanation:

The measure of m∠B in the triangle is 40°.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

Since the triangles are congruent, we know that their corresponding angles are congruent as well.

Therefore, we have:

m∠B = m∠F = 40°.

Note that we also have:

m∠C = m∠A = 80° (by corresponding angles)

m∠H = m∠G = 60° (by corresponding angles)

Finally, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle D:

m∠D = 180° - m∠B - m∠C = 180° - 40° - 80° = 60°.

Therefore,

m∠B = 40°.

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Answer:

0.8390

Step-by-step explanation:

From the question,

Z score = (Value-mean)/standard deviation

Z score = (150.2-160.5)/10.4

Z score = -0.9904.

P(x>Z) = 1- P(x<Z)

From the Z table,

P(x<Z) = 0.16099

Therefore,

P(x>Z) = 1-0.16099

P(x>Z) = 0.8390

Hence the probability that a person weighs more than 150.2 pounds = 0.8390

Answer:

A. Perimeter of segment = 49 in.

B. Area of segment = 52 in².

Step-by-step explanation:

Data obtained from the question include:

Radius (r) = 24 in.

Angle at the centre (θ) = 60°

Perimeter of segment =.?

Area of segment =.?

A. Determination of the perimeter of the segment.

Perimeter of segment = length of arc + length of chord

Length of arc = θ/360 x 2πr

Length of chord = 2r x sine (θ/2)

Pi (π) = 3.14

Length of arc = θ/360 x 2πr

Length of arc = 60/360 x 2 x 3.14 x 24

Lenght of arc = 25.12 in

Length of chord = 2r x sine (θ/2)

Length of chord = 2 x 24 x sine (60/2)

Length of chord = 24 in

Perimeter of segment = length of arc + length of chord

Perimeter of segment = 25.12 + 24

Perimeter of segment = 49.12 ≈ 49 in.

B. Determination of the area of the segment.

Area of segment = Area of sector – Area of triangle.

Area of sector = θ/360 x πr²

Area of triangle = r²/2 sine θ

Area of sector = θ/360 x πr²

Area of sector = 60/360 x 3.14 x 24²

Area of sector = 301.44 in²

Area of triangle = r²/2 sine θ

Area of triangle = 24²/2 x sine 60

Area of triangle = 249.42 in².

Area of segment = Area of sector – Area of triangle.

Area of segment = 301.44 – 249.42

Area of segment = 52.02 ≈ 52 in²

​

Answer:

The maximum one-day percentage loss = -1.15%

Step-by-step explanation:

Let assume that with the  normal distribution, 95% of observations are smaller than 1.65 standard deviations above the mean.

Given that:

Cerra estimates the standard deviation of daily percentage changes of the euro to be 1 percent over the last 100 days.

if the expected percentage change of the euro tomorrow is 0.5 percent

and that Z value at 95% C.I level = 1.65

∵ The maximum one-day percentage loss = (expected percentage change -   Z-Value) × standard deviation

The maximum one-day percentage loss =  (0.5 - 1.65) ×  1

The maximum one-day percentage loss = -1.15  ×  1

The maximum one-day percentage loss = -1.15%

Answer: 189 mg.

Step-by-step explanation:

Let x be the weight of the body( in pounds) and y be the amount of medicine( in mg).

Given: A certain medicine is given in an amount proportional to patient’s body weight.

i.e. [tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]

Let [tex]x_1=116\ \ \ ,\ y_1=126[/tex] ,  [tex]x_2=174[/tex]

then,

[tex]\dfrac{116}{126}=\dfrac{174}{y_2}[/tex]

[tex]\Rightarrow\ y_2=\dfrac{174\times126}{116}\\\\\Rightarrow\ y_2=189[/tex]

Hence, he amount of medicine required by patient weighing 174 pounds = 189 mg.

Answer:

A. x-3=0  D. 6=2x  F. x^2=9

Step-by-step explanation:

Substitute x=3 into each equation

A. x-3=0   3-3 =0   0=0  x=3 is a solution

B. 1+ x=2  1+3 =2  4=2  false

C. 9-x=3 9-3 =3  6=3  false

D. 6=2x  6 = 2*3   6=6  x=3 is a solution

E. 15x=3   15*3 =3  45=3  false

F. x^2=9  3^2 = 9   9=9  x=3 is a solution

Answer:

F'(-3) = 18

Step-by-step explanation:

Let g(x) = u and apply the chain rule

[tex]F(x)=f(g(x))=f(u)\\F'(x)=\frac{df(u)}{du}[/tex]

[tex]\frac{du}{dx}=g'(x)[/tex]

[tex]\frac{df(u)}{du}*\frac{du}{dx} = \frac{df(u)}{dx}\\F'(x)= \frac{df(u)}{du}*g'(x)\\F'(x)= f'(u)*g'(x)\\F'(x)= f'(g(x))*g'(x)[/tex]

We now have all of the necessary definite values to solve the expression for x= -3:

[tex]F'(-3)= f'(g(-3))*g'(-3)\\F'(-3)= f'(-4)*6\\F'(-3)= 3*6\\F'(-3)= 18[/tex]

Finally, we have that F'(-3)= 18.

Answer:

If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.

Remember that the slope between any two points (x1,y1), (x2,y2) is

slope   =  ( y2 - y1 ) / (x2 - x1)

Step-by-step explanation:

If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.

Remember that the slope between any two points (x1,y1), (x2,y2) is

slope   =  ( y2 - y1 ) / (x2 - x1)

Answer:

x = log (7)/ 2log 5

Step-by-step explanation:

25^ x = 7

Replace 25 with 5^2

5^ 2x = 7

Take log  on each side

log (5 ^2x) = log ( 7)

We know that log a^ b = b log a

2x  log 5 = log (7)

Divide each side by log 5

2x  log 5/ log 5= log (7)/ log 5

2x = log (7)/ log 5

Divide each side by 2

x = log (7)/ 2log 5

Answer:

36 cups of Chex total.

Step-by-step explanation:

Well, he will obviously be using 12 cups of pretzels, so let's set that aside. For every cup of pretzels, there are 3 cups of chex. So, multiply 3x12. That will give you how much chex you will need.

Answer: 4

Step-by-step explanation:

Given functions:

[tex]f(x)=\dfrac{1}{5}|x-15|\\\\ g(x)=(x-2)^2[/tex]

We know that the y--intercept of a function is the value of the function at x=0.

so, put x=0 in both the functions.

The y-coordinate of the y-intercept of f(x) = [tex]f(0)=\dfrac{1}{5}|0-15|=\dfrac{15}{5}=3[/tex]

The y-coordinate of the y-intercept of g(x) = [tex]g(0)=(0-2)^2=2^2=4[/tex]

As 4 > 3, that means he y-coordinate of the greatest y-intercept is 4.

To write an inequality and show on a number line all numbers: greater than (−3) but less than or equal to 3

Let n be the number, then -3 < n ≤3 .

On number line we mark open circle at -3 (since it has a strictly less than sign) and a closed circle at 3  (since it has a less than and equal to sign) .

To the required inequality that shows all the numbers greater than (−3) but less than or equal to 3 : -3 < n ≤3 and the number line is represented below.

Answer:

[tex]\large \boxed{\sf \ \ x=0, \ \ y=-5 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We have two equations:

(1) -2x - 4y = 20

(2) -3x + 5y = -25

5*(1)+4*(2) gives

   -10x - 20y -12x + 20y = 100 - 100 = 0

   -22x = 0

   x = 0

I replace in (1)

   -4y = 20

   y = -20/4 = -5

There is one solution x = 0, y = -5

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The two equations are

-2x-4y=20

-3x+5y=-25

multiply equation 1 by 5 and equation 2 by 4

-10x-20y=100

-12x+20y=-100

-22x=0

x=0

Substitute value in either equation

y=-5

So,option 1 is correct only one solution

Step-by-step explanation:

If the order is relevant, the number of permutations is:

₁₀P₅ = 30,240

If the order is not relevant, the number of combinations is:

₁₀C₅ = 252

The number of ways to choose 5 letters among 10 without replacement will be 252 and with replacements will be 30240.

When the order of the arrangements counts, a permutation is a numerical approach that establishes the total number of alternative arrangements in a collection.

The number of alternative configurations in a collection of things when the order of the selection is irrelevant is determined by combination.

The number of ways to choose r quantity among n without replacement is given as nCr = n!/(r!(n - 1)!)

n = 10 and r = 5

10C5 = 252

The number of ways to choose r quantity among n with replacement is given as, nPr = n!/(n - r)!

n = 40 and r = 5

10P5 = 10!/(10 - 5)! = 30240

Hence "The number of ways to choose 5 letters among 10 without replacement will be 252 and with replacements will be 30240".

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Answer:

The 95% confidence interval of mean wake time for a population with treatment is between 86.2401 and  108.7599 minutes.

This interval contains the mean wake time before treatment and which does not prove to be effective

Step-by-step explanation:

GIven that :

sample size n = 17

sample mean [tex]\overline x[/tex] = 97.5

standard deviation [tex]\sigma[/tex] = 21.9

At 95% Confidence interval

the level of significance ∝ = 1 - 0.95

the level of significance ∝ =  0.05

[tex]t_{\alpha/2} = 0.025[/tex]

Degree of freedom df = n - 1

Degree of freedom df = 17 - 1

Degree of freedom df = 16

At ∝ =  0.05 and df = 16 , the two tailed critical value from the t-table [tex]t_{\alpha/2 , 16}[/tex] is :2.1199

Therefore; at 95% confidence interval; the mean wake time is:

= [tex]\overline x \pm t_{\alpha/2,df} \dfrac{s}{\sqrt{n}}[/tex]

= [tex]97.5 \pm 2.1199 \times \dfrac{21.9}{\sqrt{17}}[/tex]

= 97.5 ± 11.2599

= (86.2401 , 108.7599)

Therefore; the mean wake time before the treatment was 104.0 min

The 95% confidence interval of mean wake time for a population with treatment is between 86.2401 and  108.7599 minutes.

This interval contains the mean wake time before treatment and which does not prove to be effective

Answer:

111.33667

Step-by-step explanation:

You add percentages just like you would any other number.

122.9%   +   108.46%  +   102.65% = 334.01%

334.01%/3 = 111.33667

Answer:

The answer is #3 which is 24%.

Step-by-step explanation:

6 × 100

25

25 into 100 is 4, then 6×4 = 24%

I really hope this helps :)

Answer:

21 cases

Step-by-step explanation:

red cases=2x.    white cases=x

2x+x=81

3x=81

x=21 cases

Answer:

2 km

Step-by-step explanation:

Since we know that the TOTAL distance from Kensington to Greenville is 4.3 km, and we also that the distance from Kensington to Springfield is 2.3 km, we can subtract these values to find the distance from Springfield to Greenville.

[tex]4.3-2.3=2[/tex]

I hope this helped!

Answer:

Simple math, different numbers.

Step-by-step explanation:

Take the total distance, 4.3

And subtract it from the given segment of the road.

4.3 - 2.3 = 2.0

So the distance between Springfield and Greenville is 2 kilometers.

Answer: Franklin could end at 4 different points.

Step-by-step explanation:

Given: Franklin the fly starts at the point (0,0) in the coordinate plane.

At each point, Franklin takes a step to the right, left, up, or down.

i.e. there are 4 choices of directions [A coordinate plan has 4 quadrants]

If he moves 10 steps, then the number of different points Franklin could end up at =  choices of directions

= 4

Hence, Franklin could end at 4 different points.

Answer:

A horizontal cross-section is obtained when the plane that passes through the solid object is parallel to its base. On the other hand, a vertical cross section is found when the intersecting plane is perpendicular to the base of the solid. These are known as a parallel cross-section and perpendicular cross section.

Step-by-step explanation:

Answer:

7 cm

Step-by-step explanation:

14 / 2 = 7 cm

7cm is the distance Harry needs to walk on the map?

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.

Given that,

Harry is trying to complete his hill walking scouts badge.

He is using a map with a scale of 1 cm : 2 km.

To earn the badge he needs to walk 14 km.

Let the distance he needs to walk on the map is x.

By given data we write an equation

1/2=x/14

Apply Cross Multiplication

14/2=x

7=x

Hence, 7cm is the distance he needs to walk on the map.

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Answer:

14v - 5

Step-by-step explanation:

The product of 14 and v is 14v. 5 less than that is 14v - 5.

Answer:

7v = 119

Step-by-step explanation:

Answer:

  $2192.60

Step-by-step explanation:

March 4 is day 63 of the year. So, the amount of tax that Kelly needs to refund to Mason is the tax for the remaining 365 -63 = 302 days of the year.

Kelly will owe Mason ...

  (302/365)($2650) = $2192.6027 ≈ $2192.60