What is the slope of the graph ? Leave your answer as a reduced fraction .

Answer:

(a) the probability that an individual distance is greater than 214.80 cm is 0.1401.

(b) The probability that the mean for 15 randomly selected distances is greater than 204.00 cm is 0.2482.

(c) The normal distribution can be used because the original population has a normal distribution.

Step-by-step explanation:

We are given that the overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.6 cm.

(a) Let X = the overhead reach distances of adult females.

The z-score probability distribution for the normal distribution is given by;

                         Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)  

where, [tex]\mu[/tex] = population mean reach distance = 205.5 cm  

           [tex]\sigma[/tex] = standard deviation = 8.6 cm

So, X ~ Normal([tex]\mu=205.5,\sigma^{2} =8.6^{2}[/tex])

Now, the probability that an individual distance is greater than 214.80 cm is given by = P(X > 214.80 cm)

    P(X > 214.80 cm) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{214.80-205.5}{8.6}[/tex] ) = P(Z > 1.08) = 1 - P(Z [tex]\leq[/tex] 1.08)

                                                                    = 1 - 0.8599 = 0.1401

The above probability is calculated by looking at the value of x = 1.08 in the z table which has an area of 0.8599.

(b) Let [tex]\bar X[/tex] = the sample mean selected distances.

The z-score probability distribution for the sample mean is given by;

                                   Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)  

where, [tex]\mu[/tex] = population mean reach distance = 205.5 cm  

           [tex]\sigma[/tex] = standard deviation = 8.6 cm

           n = sample size = 15

Now, the probability that the mean for 15 randomly selected distances is greater than 204.00 cm is given by = P([tex]\bar X[/tex] > 204.00 cm)

    P([tex]\bar X[/tex] > 204 cm) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{204-205.5}{\frac{8.6}{\sqrt{15} } }[/tex] ) = P(Z > -0.68) = 1 - P(Z [tex]\leq[/tex] 0.68)

                                                                    = 1 - 0.7518 = 0.2482

The above probability is calculated by looking at the value of x = 0.68 in the z table which has an area of 0.7518.

(c) The normal distribution can be used in part​ (b), even though the sample size does not exceed​ 30 because the original population has a normal distribution and the sample of 15 randomly selected distances has been taken from the population itself.

Answer:

Step-by-step explanation:

-7y = -10x - 8

y = 10/7x + 8/7

Answer:

x = -1

Step-by-step explanation:

[tex]Midpoint =(1,2)= (x,y)\\J(3,-3)=(x_1,y_1) \:and\:K(x,7)= (x_2,y_2)\\\\x = \frac{x_1+x_2}{2} \\\\1 = \frac{3+x}{2}\\ \\Cross\:Multiply \\2\times 1 = 3+x\\2 =3+x\\2-3=x\\-1=x\\\\x =-1[/tex]

Answer:

What

Step-by-step explanation:

What Do You Mean Bro

Answer:

Step-by-step explanation:

Let the amount spent by Tim be x and the amount spent by Nikko be y

If Tim spent $55 more than 2/3 of the amount that Nikko spent for his computer, then amount spent by Tim will be x = 55+2/3 y

Since the total amount that Tim and Nikko spent for their computers was $2,870 then;

x+y = $2,870

Substituting  x = 55+2/3y into the equation above, we will have;

55+2y/3 + y = 2,870

(165 + 2y)/3 + y = 2,870

(165 + 2y+3y)/3 = 2,870

cross multiply

165 + 2y+3y =  3*2870

165+5y = 8610

5y = 8610-165

5y = 8445

y = 8445/5

y = 1689

Hence Nikko spent  a sum of $1,689.00 on his computer.

Answer:

[tex] \dfrac{df^{1}(16)}{dx} = \pm \dfrac{1}{10} [/tex]

Step-by-step explanation:

[tex] f(x) = x^2 + 4x - 5 [/tex]

First we find the inverse function.

[tex] y = x^2 + 4x - 5 [/tex]

[tex] x = y^2 + 4y - 5 [/tex]

[tex] y^2 + 4y - 5 = x [/tex]

[tex] y^2 + 4y = x + 5 [/tex]

[tex] y^2 + 4y + 4 = x + 5 + 4 [/tex]

[tex] (y + 2)^2 = x + 9 [/tex]

[tex] y + 2 = \pm\sqrt{x + 9} [/tex]

[tex] y = -2 \pm\sqrt{x + 9} [/tex]

[tex]f^{-1}(x) = -2 \pm\sqrt{x + 9}[/tex]

[tex]f^{-1}(x) = -2 \pm (x + 9)^{\frac{1}{2}}[/tex]

Now we find the derivative of the inverse function.

[tex]\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2}(x + 9)^{-\frac{1}{2}}[/tex]

[tex]\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2\sqrt{x + 9}}[/tex]

Now we evaluate the derivative of the inverse function at x = 16.

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{16 + 9}}[/tex]

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{25}}[/tex]

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2 \times 5 }[/tex]

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{10}[/tex]

Look it up then u get the answer

Answer:

hey mate!

kindly see attached picture

hope it helped you:)

Answer:

.= 157

Step-by-step explanation:

There are three clock summing up to 21

One clock=21/3

One clock= 7

There are three calculator summing up to 30

One calculator= 30/3

One calculator= 10

There are three light bulb summing up to 15

One light bulb =15/3

One light bulb= 5

So the problem expression is

Clock +calculator *3bulb

= Clock +(calculator*3bulb)

= 7+(10*3(5))

= 7 +(10*15)

= 7 + 150

.= 157

Answer:

[tex] p = \dfrac{I}{rt} [/tex]

Step-by-step explanation:

I = prt

Switch sides.

prt = I

We are solving for p. We want p alone on the left side. p is being multiplied by r and t, so we divide both sides by r and t.

[tex] \dfrac{prt}{rt} = \dfrac{I}{rt} [/tex]

[tex] p = \dfrac{I}{rt} [/tex]

Answer: It will be 4 or -5.

Step-by-step explanation:

Answer:

x = 4, -5

Step-by-step explanation:

Step 1: Write out expression

0 = (x - 4)(x + 5)

Step 2: Find roots

x - 4 = 0

x = 4

x + 5 = 0

x = -5

Answer:

  see attached

Step-by-step explanation:

This is asking you to recognize the symbols used to designate a point, line segment, ray, angle, line, and plane.

The point is designated by its letter.

A line segment is designated by the letters of its endpoints, with an overline.

A ray is designated by the endpoint and a point on the ray. The endpoint is listed first. The letters have an arrow over them pointing in the direction from the endpoint.

An angle is designated using the symbol ∠. If three letters are used to identify the angle, the middle one is the vertex.

A line is designated using its name, or by the letters of two points on the line. If the letters are used, there may be a double-ended arrow over them.

A plane is designated by 3 non-collinear points, for example, "plane ABC". It may also be designated by the name of the plane.

Answer:

Step-by-step explanation:

[tex]4 - 2(3 + 2) ^{2} \\ 4 - 2( {5}^{2} ) \\ 4 - 2(25) \\ 4 - 50 = - 46[/tex]

Answer:

Hello! Answer below.

Step-by-step explanation:

The answer to your question is:

18 9/10 or 18.9

Steps below...

You have to do this first.

1. Convert the mixed number to fraction.

2. [tex]7/2[/tex]

Multiplied by

[tex]27/5[/tex]

This will equal, 189/10

If you divide this the answer will be 18 9/10

So the answer is 18 9/10 or 18.9

Hope this helps!

By, BrainlyMagic

Answer:

[tex]x_n=7(-3)^{n-1}[/tex]

Step-by-step explanation:

First, write some equations so we can figure out the common ratio and the initial term. The standard explicit formula for a geometric sequence is:

[tex]x_n=ar^{n-1}[/tex]

Where xₙ is the nth term, a is the initial value, and r is the common ratio.

We know that the second and fifth terms are -21 and 567, respectively. Thus:

[tex]a_2=-21\\a_5=567[/tex]

Substitute them into the equations:

[tex]x_2=ar^{(2)-1}\\-21=ar[/tex]

And:

[tex]a^5=ar^{(5)-1}\\567=ar^4[/tex]

To find a and r, divide both sides by a in the first equation:

[tex]r=-\frac{21}{a}[/tex]

And substitute this into the second equation:

[tex]567=a(\frac{-21}{a} )^4[/tex]

Simplify:

[tex]567=a(\frac{(-21)^4}{a^4})[/tex]

The as cancel out. (-21)^4 is 194481:

[tex]\frac{567}{1}=\frac{194481}{a^3}[/tex]

Cross multiply:

[tex]194481=567a^3\\a^3=194481/567=343[/tex]

Take the cube root of both sides:

[tex]a=\sqrt[3]{343} =7[/tex]

Therefore, the initial value is 7.

And the common ratio is (going back to the equation previously):

[tex]r=-21/a\\r=-21/(7)\\r=-3[/tex]

Thus, the common ratio is -3.

Therefore, the equation is:

[tex]x_n=7(-3)^{n-1}[/tex]

Answer:

(x-4)*(x+5) : x =4,-5

Step-by-step explanation:

a= 1

b= 1

c= -20

x1,2 = (-1+-(1 - (4*1*-20))^0.5)/2

x1,2 = (-1+-(1+80)^0.5)/2

x1,2 = (-1+-(81^0.5))/2

x1,2 =(-1+-9)/2

x1 = 8/2 = 4 x2 = -10/2 = -5

Answer:

Step-by-step explanation:

Circumference of a circle = πd

where

d is the diameter of the circle

From the question

Circumference = 56.52 inches

π = 3.14

To find the diameter substitute the value of the circumstance into the above formula and solve for the diameter

That's

56.52 = πd

[tex]d = \frac{56.52}{\pi} \\ d = \frac{56.52}{3.14} [/tex]

We have the final answer as

Hope this helps you

The diameter of Dion's bicycle tire is 18 inches.

The length of the perimeter of the circle is known as the Circumference. Mathematically, [tex]C=2\pi r[/tex]

The circumference of the bicycle tire is 56.52 inches.

So,

[tex]2\pi r=56.52\\r=\dfrac{56.52}{2\times 3.14}\\r=9 inches[/tex]

So, the diameter of the bicycle tire is [tex]9\times 2= 18[/tex] inches.

Thus, the diameter of the bicycle tire is 18 inches.

Learn more about diameter here- https://brainly.com/question/5501950

#SPJ2

Answer:

The length and width of the parking lot are [tex]\frac{46}{3}[/tex] meters and [tex]\frac{23}{2}[/tex] meters, respectively.

Step-by-step explanation:

The surface formula ([tex]A[/tex]) for the rectangular parking lot is represented by:

[tex]A = w\cdot l[/tex]

Where:

[tex]w[/tex] - Width of the rectangle, measured in meters.

[tex]l[/tex] - Length of the rectangle, measured in meters.

Since, surface formula is a second-order polynomial, in which each binomial is associated with width and length. If [tex]A = 6\cdot x^{2}-19\cdot x -7[/tex], the factorized form is:

[tex]A = \left(x-\frac{7}{2}\,m \right)\cdot \left(x+\frac{1}{3}\,m \right)[/tex]

Now, let consider that [tex]w = \left(x-\frac{7}{2}\,m \right)[/tex] and [tex]l = \left(x+\frac{1}{3}\,m \right)[/tex], if [tex]x = 15\,m[/tex], the length and width of the parking lot are, respectively:

[tex]w =\left(15\,m-\frac{7}{2}\,m \right)[/tex]

[tex]w = \frac{23}{2}\,m[/tex]

[tex]l =\left(15\,m+\frac{1}{3}\,m \right)[/tex]

[tex]l = \frac{46}{3}\,m[/tex]

The length and width of the parking lot are [tex]\frac{46}{3}[/tex] meters and [tex]\frac{23}{2}[/tex] meters, respectively.

Answer:

last option ie all of the above are true

Lines s and t are intersect at P. Therefor, option D is the correct answer.

In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.

Straight lines s and t are intersect at P.

P is called point of intersection.

Therefor, option D is the correct answer.

Learn more about intersection of lines here:

brainly.com/question/11297403.

#SPJ2

Answer:

[tex] y = 0 [/tex]

Step-by-step explanation:

To find the given asymptote of the given function, [tex] f(x) = \frac{x^2 - 2x + 1}{x^3 + x - 7} [/tex], first, compare the degrees of the lead term of the polynomial of the numerator and that of the denominator.

The numerator has a 2nd degree polynomial (x²).

The denominator has a 3rd degree polynomial (x³).

The polynomial of the numerator has a lower degree compared to the denominator, therefore, the horizontal asymptote is y = 0.

Divide distance walked by time:

2 1/4 miles / 2/3 hours = 3 3/8 miles per hour

Answer:

100 ounces(hope it help)

Step-by-step explanation:

because there is only 100 ounces in the jar.

Answer:

Step-by-step explanation:

(b-(a-a)) ÷ 3

a = 6 , b = 3

Substitute the values into the above formula

That's

[tex](3 - (6 - 6)) \div 3[/tex]

Using PEDMAS solve the terms in the bracket first

That's

[tex](3 - 0) \div 3[/tex]

We have

3 ÷ 3

Hope this helps you

Answer:  82 sq. units .

Step-by-step explanation:

Let A (9, −1), B (−1, 7), C(−5, 2), D(5, −6) are the vertices of rectangle.

Then we plot them on graph ( as provided in attachment)

Length = AB [tex]=\sqrt{(9+1)^2+(-1-7)^2}[/tex] units  [By distance formula : [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]]

[tex]=\sqrt{(10)^2+(-8)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}[/tex] units

Width = BC = [tex]\sqrt{(-1+5)^2+(7-2)^2}[/tex] units

[tex]=\sqrt{4^2+5^2}\\\\=\sqrt{16+25}\\\\=\sqrt{41}[/tex]

Area = length x width

= [tex]2\sqrt{41}\times\sqrt{41}=2\times41= 82\text{ sq. units}[/tex]

Hence, the  area of the rectangle is 82 sq. units .

Answer:

apples:bananas: strawberries

3     :             6       :         7

Step-by-step explanation:

apples:bananas: strawberries

6              12                  14

Divide each by 2

6/2           12/2               14/2

3                 6                      7

The ratio is

3     :             6       :         7

Answer:

3:6:7  

Step-by-step explanation

The answer is 3:6:7 because if you divide the numbers by 2, you will get a answer of 3, 6, and 7, the simplest form of the ratio.

Hope this helped!

~Emilie Greene

Answer:

[tex]\Huge \boxed{x=-1}[/tex]

Step-by-step explanation:

[tex]x^2+2x=-1[/tex]

Adding 1 to both sides of the equation.

[tex]x^2+2x+1=-1+1[/tex]

[tex]x^2 +2x+1=0[/tex]

Factoring the left side of the equation.

[tex]x^2 +1x+1x+1=0[/tex]

[tex]x(x+1)+1(x+1)=0[/tex]

[tex](x+1)(x+1) = 0[/tex]

[tex](x+1)^2 =0[/tex]

Taking the square root of both sides of the equation.

[tex]\sqrt{(x+1)^2} =\sqrt{0}[/tex]

[tex]x+1=0[/tex]

Subtracting 1 from both sides of the equation.

[tex]x+1-1=0-1[/tex]

[tex]x=-1[/tex]

Answer:

x = -1

Step-by-step explanation:

[tex]x^2+2x = -1\\=0\\=x^2+2x+1 \\= (x+1)(x+1)\\=(x+1)^2\\\\0 = \sqrt{(x+1)^2} \\= x+1\\\\x+1=0\\x=-1[/tex]

Answer:

Step-by-step explanation:

12x - 2 + 20x - 10 = 180

32x - 12 = 180

32x = 192

x = 6

12*6 - 2

72 - 2 = 70

the solution is b

Step-by-step explanation:

6 x 1/7 is Less than 1 since 6 x 1/7 is equal to 6/7 in decimal form is 0.8571429.

4 x 4/9 is greater than 1 since 4 x 4/9 is equal to 1 7/9 in decimal form is 1.777...

8 x 1/8 is equal to 1 since 8 x 1/8 is equal to 1.

7 x 1/5 is greater than 1 since 7 x 1/5 is equal to 1 2/5 in decimal form is 1.4

3 x 1/2 is greater than 1 since 3 x 12 is equal to 1 1/2 in decimal form is 1.5

1 x 3/4 is is less than 1 since 1 x 3/4 is equal to 3/4 in decimal form is 0.75

Answer:

24 ft.

Step-by-step explanation:

10x2=20. 20+4=24

Answer:

24 FT.

Step-by-step explanation:

10x2=20. 20+4=24

Answer:

Net

Step-by-step explanation:

The definition of "Net Income" is a person's income after deductions and taxes. Hence it is also sometimes know as the "Take-Home" income. i.e the amount of money that you actually take home.