The first three terms of a geometric sequence are shown below. What is the eighth term of the sequence?

Answer:

The median is 47

Step-by-step explanation:

that line in the middle of the box is directly on 47

Answer:

Step-by-step explanation:

This is a Combination (as in permutation vs combination) question the symbol (n r) refers to "n choose r". This is sometimes written as nCr

i.e the question is asking you to find how many combinations each will yield when you chose r items from n item without repetition and order does not matter.

I will only do the first question for you and you can just follow the same steps to solve the rest of the questions.

Recall that

[tex]nCr=\frac{n!}{(r!)(n-r)!}[/tex]

Consider question a) we are given (5 1) or ₅C₁

we can see that n = 5 and r = 1

If we substitute this into the formula:

₅C₁ = (5!) / [ (1!)(5- 1)!]

= (5!) / [ (5- 1)!]

= (5!) / (4!)

= (5·4·3·2·1) / (4·3·2·1)

= 5

hence ₅C₁ = 5

Answer:

(a) 5

(b) 10

(c) 35

(d) 28

(e) 9

(f) 21

Step-by-step explanation:

[tex](\frac{n}{k} )=\frac{n!}{k!(n-k)!}[/tex]

(a)

[tex](\frac{5}{1} )=\frac{5!}{1!(5-1)!} \\\\(\frac{5}{1} )=\frac{5*4*3*2*1}{1*4!} \\\\(\frac{5}{1} )=\frac{120}{1*4*3*2*1} \\\\(\frac{5}{1} )=\frac{120}{24} \\\\(\frac{5}{1} )=5[/tex]

(b)

[tex](\frac{5}{3} )=\frac{5!}{3!(5-3)!} \\\\(\frac{5}{3} )=\frac{5*4*3*2*1}{3*2*1*2!} \\\\(\frac{5}{3} )=\frac{120}{3*2*1*2*1}\\\\(\frac{5}{3} )=\frac{120}{12} \\\\(\frac{5}{3} )=10[/tex]

(c)

[tex](\frac{7}{4} )=\frac{7!}{4!(7-4)!} \\\\(\frac{7}{4} )=\frac{7*6*5*4*3*2*1}{4*3*2*1*3!} \\\\(\frac{7}{4} )=\frac{5040}{4*3*2*1*3*2*1} \\\\(\frac{7}{4} )=\frac{5040}{144} \\\\(\frac{7}{4} )=35[/tex]

(d)

[tex](\frac{8}{2}) =\frac{8!}{2!(8-2)!} \\\\(\frac{8}{2}) =\frac{8*7*6*5*4*3*2*1}{2*1*6!} \\\\(\frac{8}{2}) =\frac{40320}{2*1*6*5*4*3*2*1}\\\\(\frac{8}{2}) =\frac{40320}{1440} \\\\(\frac{8}{2}) =28[/tex]

(e)

[tex](\frac{9}{8} )=\frac{9!}{8!(9-8)!} \\\\(\frac{9}{8} )=\frac{9*8*7*6*5*4*3*2*1}{8*7*6*5*4*3*2*1*1!} \\\\(\frac{9}{8} )=\frac{362880}{40320*1!} \\\\(\frac{9}{8} )=\frac{362880}{40320*1} \\\\(\frac{9}{8} )=\frac{362880}{40320} \\\\(\frac{9}{8} )=9[/tex]

(f)

[tex](\frac{10}{4} )=\frac{10!}{4!(10-4)!} \\\\(\frac{10}{4} )=\frac{10*9*8*7*6*5*4*3*2*1}{4*3*2*1*6!} \\\\(\frac{10}{4} )=\frac{3628800}{24*6*5*4*3*2*1} \\\\(\frac{10}{4} )=\frac{362880}{17280} \\\\(\frac{10}{4} )=21[/tex]

Answer:

d

Step-by-step explanation:

edge2020

Option D is correct. The exponential function is increasing when time goes and the total return on investment.

An exponential function is of the form aˣ where 'a' is the base of the function and 'x' is the power of the function.

A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".

According to the question,

Let 'x' is the time in years and f(x) is the total return on investment. The below table shows the function over the interval.

                    x                                                    f(x)

 a decreasing quadratic function                 10,000

 an increasing quadratic function               12,201.90

a decreasing exponential function              14,888.64

an increasing  exponential function             22,167.15            

Quadratic function f(x) = ax² +b x +c  a > 0

Exponential function f(x) = a. bˣ +q                                    

Hence, the exponential function is increasing when time goes and the total return on investment.

Learn more about exponential function here

https://brainly.com/question/27307412

#SPJ2

Answer:

B and D I dont have time to explain

I am sorry.

Thanks for question

Answer:

15552 in^3

Step-by-step explanation:

Volume formula for a cube of side length s:  V = s^3.

Then the total volume here is:

(24 in)^3 + (12 in)^3 = 15552 in^3

Answer:

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

The sum of the angles in a quadrilateral is 360 degrees

2t+t+2t+t = 360

6t = 360

Divide by 6

6t/6 = 360/6

t = 60

Angle Z = 2t

Angle Z = 2*60 = 120

Answer:

[tex]120 \: \: degrees[/tex]

Second answer is correct.

Step-by-step explanation:

The sum of the angles in a qudrilateral = 360°

[tex]t + 2t + t + 2t = 360 \\ 6t = 360 \\ \frac{6t}{6} = \frac{360}{6} \\ t = 60[/tex]

angle z

[tex]2t = 60 \times 2 \\ \: \: \: \: \: \: \: = 120[/tex]

Answer: Angle w and angle z should equal 92° to prove that r║s

Step-by-step explanation: Let us start by constructing the lines r and s, and then draw a transversal to intersect both lines as stated in the question. At the intersection of lines m and r, we have clockwise from the top angles w, x and the other two blank. This is as shown in the picture attached.

Also at the intersection of lines m and s, clockwise from the top, the angles are 92, y, z and a blank. This is also clearly marked in the picture attached.

If the two lines r and s are parallel, then it means;

(1) Angle 92 is equal to angle z (opposite angles are equal)

(2) Angle z is equal to the blank underneath angle x (corresponding angles on two parallel lines are equal)

(3) Angle 92 is equal to the blank underneath angle x (alternate angles on two parallel lines are equal)

(4) Angle 92 is equal to angle w (corresponding angles on two parallel lines are equal)

Therefore, of all four angles marked as w, x, y and z angles w and z should equal 92° to prove that line r is parallel to line s.

Answer:

Its W i took the test and got a 100

Answer: a= 40.5 b= 82.85

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

Total number of jerseys = 4 + 3 = 7

Now, the probability of picking a purple Jersey = number of purple jerseys/total number of jerseys = 3/7

Now let’s look at picking a jersey with even number

Even number jerseys are yellow two and yellow four and also purple two

So we have 3 even numbered jersey. The probability of picking an even numbered jersey is 3/7

In probability, once we have or, we add

The probability of picking an even numbered jersey or a purple jersey = 3/7 + 3/7 = 6/7

Answer:

Objective function:

Maximize profit P = [tex]35x+28y[/tex]

subject to following constraints:

[tex]x\geq 900\\y\geq 600[/tex]

[tex]x+y\leq 2000\\x\geq 0\,,\,y\geq 0[/tex]

Step-by-step explanation:

Given: The recycling plant can process up to 2000 tons of plastic a week. At least 900 tons must be processed for milk containers and at least 600 tons must be processed for soda containers.

Also, Retro earns $35 per tons for milk containers and $28 per ton for soda containers.

To find: objective function for the given situation

Solution:

Let x tons be used to make a milk container and y tones be used to make a soda container.

As at least 900 tons must be processed for milk containers and at least 600 tons must be processed for soda containers,

[tex]x\geq 900\\y\geq 600[/tex]

Also, as the recycling plant can process up to 2000 tons of plastic a week,

[tex]x+y\leq 2000[/tex]

Also, [tex]x\geq 0\,,\,y\geq 0[/tex]

Objective function:

Maximize profit P = [tex]35x+28y[/tex]

Answer:

x=5

Step-by-step explanation:

7/5=(2x-3)/x

5(2x-3)=7x

3x=15, x=5

Answer:

153°

Step-by-step explanation:

Supplementary = 180 degrees

180 - 27 = 153 degrees

Answer:

153 degrees

Step-by-step explanation:

When two angles are supplementary, their angle measures must add up to 180 degrees. Therefore:

M+N=180

M+27=180

M=180-27=153

Hope this helps!

Answer:

The answer is: 12 total candies

Step-by-step explanation

c = caramel-flavored

s = strawberry-flavored

so if there are 1/3 strawberry-flavored so that means there are 2/3 caramel-flavored. we know there are 8 caramel-flavored so if 8 is 2/3 of all the candies that means 4 is how many strawberry-flavored we have 12 total candies.

Answer:

∠3 = 140°

Step-by-step explanation:

∠4 = 40°

∠4 = ∠1 (vertical angles)

∠1 = ∠2 (alternate angles)

∠2 = 40°

So,

∠2+∠3 = 180 [Angles on a straight line add up to 180°]

40 + ∠3 = 180

∠3 = 180-40

∠3 = 140°

Answer:

Angle 3 = 140°

Step-by-step explanation:

Angle 4 is equal to 40° and on a flat surface of 180°, that is, the first horizontal line, angle A is equal to 140° because 180° - 40° = 140°. Angle A is congruent to angle 3, therefore, angle 3 is also 140°.

Answer:

f(5).g(5)

Step-by-step explanation:

(fg)=(f.g)

this is how it starts: (fg)(X)= f(x) [g(x)]

x=5

f(5).g(X)

Answer:

-39,063

Step-by-step explanation:

In this geometric, sequence, you are multiplying by -5. So, we can continue the sequence by mulitplying 375(your last value) by -5 and so on, until we have 7 total terms.

Now we add the terms together:

-3+15+-75+375+-1875+9375+-46875

=-3+15-75+375-1875+9375-46875

=-39063

Hope this helps :)

Answer: [tex]\sqrt[3]{5x}[/tex]

Answer:

b 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Manish:

[tex]Savings=\frac{1}{2}*2520\\\\= Rs.1260\\\\Amount spend at mall=\frac{1}{4}*2520\\\\=Rs.630[/tex]

Amount left with Manish = 2520 - (1260 + 630) = 2520 - 1890 = Rs. 630

Jhanavi:

Savings = (1/3) *2520 = Rs. 840

Amount spend at mall = (3/5) * 2520

                                   = 3 * 504

                                   = Rs. 1512

Amount left with Jhanavi = 2520 - (840 +1512) = 2520 - 2352

                                         = Rs. 168

Answer:

C

Step-by-step explanation:

The length of the segment is 7

2-7/2 = -3/2

(1,-3/2)

Answer:

The width of the rectangle is k+4 inches

Step-by-step explanation:

you have [tex]k^{2}+19k+60[/tex] which can be factorized to (k+4)(k+15)

if the length of the rectangle is k-5 that would mean that we can write [tex]k^{2}+19k+60[/tex] as (k-5)n which we know is false, so the only one that applies is k+4

The true statement is:

"The width of the rectangle is k + 4"

Remember that for a rectangle of length L and width W, the area is given by:

A = L*W

So we want to factorize the area equation, which is a quadratic equation, into a product of two terms.

A = k^2 + 19k + 60

The two zeros are given by Bhaskara's formula:

[tex]k = \frac{-19 \pm \sqrt{19^2 - 4*1*60} }{2} \\\\k = \frac{-19 \pm 11 }{2}[/tex]

So we have two zeros, these are:

k = (-19 - 11)/2 = -15

k = (-19 +11)/2 = -4

So we can factorize the area as:

A = (k - (-15))*(k - (-4)) = (k + 15)*(k + 4).

From this, the only statement that can be true is:

"The width of the rectangle is k + 4"

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1480401

Answer:

They Played 15 games total

Step-by-step explanation:

Make ratios:

9:60 %

x:100 %

Cross multiply: 60 times x =60x and 9x100= 900 = 60x=900

Divide to get x: 60x/60=900/60

x=15

They Played 15 games total

Please mark brainliest and have a awesome day

This is pseudo-trig.  It has a trig function but it's irrelevant.

Let y = cos X

y + 1/y = 40

Squaring,

y² + 2(y)(1/y) + 1/y² = 1600

y² + 2 + 1/y² = 1600

y² + 1/y² = 1598

cos² X + 1/cos²X = 1598

Answer: 1598

Answer:

t>28

hope this helps!

Step-by-step explanation:

t÷4 > 7

t÷4 (×4) > 7 (×4)

t > 28

Answer: 1. 2nd endpoint  (24,-18)       2. 2nd endpoint: (-19,4)

Step-by-step explanation:

1.   [tex]\frac{-10+x}{2}[/tex] = 7  x = 24

    [tex]\frac{6+y}{2}[/tex] = -6    y= -18

2nd endpoint: (24,-18)

2.  [tex]\frac{-1+x}{2}[/tex] = -10   x= -19  

   [tex]\frac{0+y}{2}[/tex] =  2     y= 4

Answer:

D = (13, - 23 )

Step-by-step explanation:

Given the translation rule

(x, y ) → (x - 4, y + 15 )

To go in the reverse direction, that is image to original, then, reverse the operations in the translation rule.

(x , y ) → (x + 4, y - 15 ) , thus

D'(9, - 8 ) → D(9 + 4, - 8 - 15 ) → D(13, - 23 )

Answer:

(13,-23)

Step-by-step explanation:

DID IT ON EDGE 2020

Answer: 30

Step-by-step explanation: To solve this problem, we're going to have to use the Pythagorean theorem...

a² + b² = c²

24² + 18² = c²

576 + 324 = c²

c² = 900

[tex]\sqrt{900}[/tex]

30

30 = c

I hope this helps!

Answer:

There is a variety of answers. you will find an example below

Step-by-step explanation:

To find the rational numbers between 2 fractions/rational numbers, we have to find the LCM of the denominator, which would increase the value of the numerator. This way you will have more rational numbers between the two.

- 5/6 = -40 / 48

5 / 8 = 30 / 48

Now, we can notice that there is a difference of 70 between the 2. this means you may choose 6 out of these. Here is an example(some of them are simplified)

5/16, 5/8, 7/48 , 1/6 , 2/6, -1/2.

Hope this helps