Find the sum of the first eight terms of the geometric series 1 + 2 + 4 + ...

Answer: 0.353

Step-by-step explanation:

We know that 42% of all the female students participate in 2 sports this season. (58% is the percent that did not)

This means that if we select a random student, there is a 0.42 probability that the student did participate in 2 sports this season.

Other thing that i will use is that, if we have a group of N objects, and we want to create a group of K objects out of the N, the number of combinations is:

[tex]c = \frac{N!}{(N - K)!*K!}[/tex]

Now, out of 5, we want to find the proability that, at least 3 of them, did participate in at least 2 sports this season.

The probability that all 5 of them participated, is equal to the product of the individual probabilities. (so N = 5, and K = 5)

P = (0.42^5)*1 = 0.013

Now, if only 4 of them did participate (N = 5, k = 4), the probability is equal to:

P = (0.42^4)*(0.58)*5!/4! = (0.42^4)*(0.58)*5 = 0.09

The probability for only 3 is: (N = 5 and K = 3)

P = (0.42^3)*(0.58^2)*5!/(3!*2!) = (0.42^3)*(0.58^2)*(5*4/2) = 0.25

Then the total probability is:

P = 0.013 + 0.09 + 0.25 = 0.353

Answer:

The range of the box plot is 10.

Step-by-step explanation:

To find the range subtract the highest value to the lowest value.

Since 13 is the highest and 3 is the lowest the answer is 10

Hope this helps.

Answer: -5

Step-by-step explanation: Let me know if you need an explanation.

Answer:

Distance remaining = 3.1 miles

Step-by-step explanation:

Distance between A(3, 2) and B(8.2, 2) can be calculated by the formula,

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

AB = [tex]\sqrt{(8.2-3)^2+(2-2)^2}[/tex]

     = 5.2 mi

Since you have hiked for "90 minutes or 1.5 hours" at the rate of 1.4 mph,

From the formula,

Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]

1.4 = [tex]\frac{\text{Distance}}{1.5}[/tex]

Distance traveled = 1.4 × 1.5

                             = 2.1 miles

Distance remaining to travel = 5.2 - 2.1

                                               = 3.1 miles

Therefore, distance remaining to travel = 3.1 miles

Answer:

108 - 84i

Step-by-step explanation:

12( 9-7i)

Distribute

12*9 - 12*7i

108 - 84i

Answer:

x=0

Step-by-step explanation:

combine like terms

-8+8x=-8

add 8 to both sides

8x=0

x=0

The solution is 0

Answer:

x = 0

Step-by-step explanation:

When we combine like terms on the left side we get -8 + 8x = -8. Adding 8 to both sides to get rid of the -8 we get 8x = 0, and dividing the whole equation by 8 to get rid of the coefficient of x we get x = 0.

Answer:

x = -5/3 and y = -1

Step-by-step explanation:

write it as a system and simplify

-4 for the first equation (in the photo but when putting it into a system of equations it would be 2nd)

So it's

-3x-2y=7

-3x+2y=3

then it's -6x=10

then divide oth sides by -6 to get x then plug that into whatever equation and solve for y.

i hope this is right and helps

Answer:

x=-14 (im pretty sure its right )

Step-by-step explanation:

like terms :p

Answer:

Option D is the correct answer

Step-by-step explanation:

[tex](3 {m}^{ - 4} )^{3} (3 {m}^{5} ) \\ \\ = {3}^{3} {m}^{ - 4 \times 3} \times 3 {m}^{5} \\ \\ = 27 \times 3 \times {m}^{ - 12 + 5} \\ \\ = 81 {m}^{ - 7} \\ \\ = \frac{81}{ {m}^{7} } [/tex]

Answer:

the correct answer is D

Step-by-step explanation:

distribute the exponent on the left to get the expression ((3^3)(m^-12))(3(m^5))

bring the negative exponent to the denominator to get (3^4)(m^5)/(m^12)

subtract the exponents of m to get an answer of 81/(m^7)

Answer:

157.98  [tex]in^2[/tex]

Step-by-step explanation:

Given: volume of pyramid is equal to 100 cubic inches and height of the pyramid is 5 inches

To find: surface area of the pyramid

Solution:

Let h denotes the height of the pyramid and 'a' denotes side of the square base of the pyramid.

Volume of the pyramid = [tex]\frac{1}{3}a^2h[/tex]

Also,

Volume of the pyramid = 100 cubic inches

[tex]\frac{1}{3}a^2h=100\\\frac{1}{3}a^2(5)=100\\a^2=\frac{100\times 3}{5}=60\\a=\sqrt{60}[/tex]

Surface area of the pyramid  [tex](S) =a\sqrt{4h^2+a^2}+a^2[/tex]

So,

[tex]S=\sqrt{60}\sqrt{100+60}+60\\=\sqrt{60}\sqrt{160}+60\\=\sqrt{9600}+60\\=97.9796+60\\=157.9796\\\approx 157.98[/tex]

Surface area = 157.98  [tex]in^2[/tex]

Answer:

Surface area of the pyramid = 157.99 in²

Step-by-step explanation:

Volume of a pyramid is given by the formula,

Volume = [tex]\frac{1}{3}(\text{Area of the base})\times \text{height}[/tex]

100 = [tex]\frac{1}{3}\text{(Side)}^{2} \times \text{height}[/tex]

300 = s² × 5

s² = 60

s = √60

s = 2√15 in ≈ 7.746 in

Now surface area of the pyramid = Area of base + 4×(Area of one lateral side)

Area of square base = (Side)² = 60 in

Area of one lateral side = [tex]\frac{1}{2}(\text{Base})(\text{Lateral height})[/tex]

Since Lateral height = [tex]\sqrt{(h)^{2}+(\frac{S}{2})^{2}}[/tex] [By applying Pythagoras theorem in the given triangle]

                                  = [tex]\sqrt{(5)^{2}+(3.873)^{2}}[/tex]

                                  = [tex]\sqrt{25+15}[/tex]

                                  = [tex]\sqrt{40}[/tex]

                                  = 6.325 in.

Now area of lateral side = [tex]\frac{1}{2}(7.746)(6.325)[/tex]

                                        = 24.497 in²

Surface area of the pyramid = 60 + (4×24.497)

                                               = 60 + 97.987

                                               = 157.987 in²

                                               ≈ 157.99 in²

Answer:

45 degrees

Step-by-step explanation:

Think of this web as a circle. This circle is divided into 8 equal pieces.

A circle has 360 degrees in it. If we divide 360 by 8, we get 45. This means that each wedge is 45 degrees, which means that in order to rotate the image to look the same, we must rotate it by 45 degrees.

Answer:

45 degrees

Step-by-step explanation:

Answer:

p = 13

Step-by-step explanation:

When a polynomial f(x) is divided by (x + h) then the remainder is f(- h)

Here both polynomials are divided by (x + 1)

Evaluate them both for x = - 1

3(- 1)³ - 5(- 1)² - 4(- 1) + p, that is

- 3 - 5 + 4 + p

= p - 4 → A

6(- 1)³ + p(- 1)² + 9(- 1) + 5, that is

- 6 + p - 9 + 5

= p - 10 → B

Given that A = 3B, then

p - 4 = 3(p - 10)

p - 4 = 3p - 30 ( subtract 3p from both sides )

- 2p - 4 = - 30 ( add 4 to both sides )

- 2p = - 26 ( divide both sides by - 2 )

p = 13

Answer:

The sample loses [tex]\frac{1}{3}[/tex] of its mass every [tex]\frac{1}{3}[/tex] days.

Step-by-step explanation:

Expression that shows the relation between final mass of the element after 't' days is,

M(t) = [tex]900(\frac{8}{27})^t[/tex]

If M(t) = two third of the initial mass [After the loss of one third of the initial mass remaining mass of the element = 1 - [tex]\frac{1}{3}[/tex] = [tex]\frac{2}{3}[/tex]rd of the initial mass]

[tex]900\times \frac{2}{3}=900(\frac{8}{27})^t[/tex]

[tex]\frac{2}{3}=(\frac{8}{27})^t[/tex]

[tex]\frac{2}{3}=[(\frac{2}{3})^3]^t[/tex]

[tex](\frac{2}{3})^1=(\frac{2}{3})^{3t}[/tex]

By comparing powers on both the sides

3t = 1

t = [tex]\frac{1}{3}[/tex] day

Therefore, The sample loses [tex]\frac{1}{3}[/tex] of its mass every [tex]\frac{1}{3}[/tex] days.

Answer:

8/20

Step-by-step explanation

boys left handed=3

boys right handed=9

girls left handed=2

girls right handed=6

what is the probability that a student chosen from random is a girl? give answer as a fraction please and include step by step process

girls left handed: 2

girls right handed: 6

6+2=8

total all students 20

8/20

Answer:

–9xy2 – 6x2y + 5x3

–9xy2 – 6x2y – 5x3

9xy2 + 6x2y + 5x3

9xy2 – 6x2y + 5x3

the answer is 9xy2 – 6x2y + 5x3

Step-by-step explanation:

Answer:

A. 0

Step-by-step explanation:

y= mx+b

with same slope, m= same for both

if b  is different, then the lines are parallel

so no solution, option A. 0

Answer:

Scale Factor- 4/15

Missing length- 9.6

Step-by-step explanation: Got it right on Edge.

The missing length of the rectangle B is 9.6 feet and the proportion is 3.75

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the area of the rectangle 1 be represented as A = 24 x 36

where the width = 24 feet and length = 36 feet

Now , the area of the second rectangle 2 = 6.4 x y

The width = 6.4 feet

So , the scale factor is given by the proportion equation ,

k = 24 / 6.4 = 3.75

So , the scale factor k = 3.75

Now , the length of the second rectangle = 36 / 3.75 = 9.6 feet

Hence , the proportion is k = 3.75

To learn more about proportion click :

https://brainly.com/question/7096655

#SPJ6

Answer:

a= -8.33

Step-by-step explanation:

it will be deceleration because he was 12 m/s then go to 4.5 m/s

and by applying moving equation

[tex]v_{2}[/tex]=[tex]v_{1}[/tex]+at

we have all but not have a  

Answer:

10%

Step-by-step explanation:

if you times the 5 people to get it to the 25 that means that you also have to times the 2 by 5 which = 10!

hope this helped Willow!

Answer:

38

Step-by-step explanation:

Find the values of each function.

f(-9)= 4

g(6)=6

Then plug them in.

-1 x 4 + 7 x 6

-4+42

38!

Answer:

Step-by-step explanation:

Slope is the rise (y) over the run (x) between 2 points on a graph. This means that from one point go up (or down) first, then count over from that first point right (or left). A positive number on top indicates "up" and a negative number on top indicates "down"; a positive number on bottom indicates "right" while a negative number on bottom indicates "left". Keep in mind the following:

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

It doesn't matter where you "put" the negative, your slope will come out correct as long as you are moving from one point to the other correctly.

Our given slope is 4/5. They are both positive, so that means from the red point on the left ("read" a graph from left to right, just like you're reading this) we will go up 4 units. From where we "land" we will go right 5 units. As you can see, the only graph that lands on the red dot on the right when we follow that slope is the second one.

Answer:

radius is 3, center is (4,-5)

Step-by-step explanation:

when you graph this, put the first point at (4,-5) and then expand three squares up.

Answer:

wgtvwthrr

Step-by-step explanation:

Step-by-step explanation:

[tex]cylinder \: area \: = (2 \times \frac{\pi}{4} \times {dia}^{2} ) + (\pi \times dia \times hieght) \\ = (2 \times \frac{\pi}{4} \times {3.8}^{2} ) + (\pi \times 3.8 \times 12.7) \\ = 22.7 + 151.5 \\ = 174.2 \: {m}^{2} [/tex]

Answer:

3+4+5+11= 56

Step-by-step explanation:

Answer:

20.48mL

Step-by-step explanation:

Multiply 64mL by 0.32

Answer:

20.48

Step-by-step explanation:

32/100*64