Oscar is going to buy a limited-edition soccer ball that costs $30, and the sales tax is 6%. What is the total cost?

Without any more information, the first term can be any number.

Let a be the first term in the geometric progression, and let r be the common ratio between consecutive terms. Then

a + ar + ar ² + ar ³ + ar ⁴ + ar ⁵ = 9 (a + ar + ar ²)

ar ³ + ar ⁴ + ar ⁵ = 8 (a + ar + ar ²)

r ³ + r ⁴ + r ⁵ = 8 (1 + r + r ²)

r ³ (1 + r + r ²) = 8 (1 + r + r ²)

r ³ = 8

r = 2

Now with this ratio, the sum of the first six terms is

a (1 + r + r ² + r ³ + r ⁴ + r ⁵) = a (1 - r ⁶)/(1 - r) = 63a

while the sum of the first three terms is

a (1 + r + r ²) = a (1 - r ³)/(1 - r) = 7a

and of course 63a = 9 • 7a, and this is true for any a.

Answer:

9 weeks

Step-by-step explanation:

5 x 9= 45

45+16=61

5x9+16=61

Answer: The z-score = 2.46

Step-by-step explanation:

Given:  sample size : n= 10

Population mean : [tex]\mu= 29056[/tex]

population standard deviation : [tex]\sigma= 3339[/tex]

Sample mean : [tex]\overline{x} = 31650[/tex]

Formula to calculate z :

[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

Substitute all values, we get

[tex]z=\dfrac{31650-29056}{\dfrac{3339}{\sqrt{10}}}\\\\=\dfrac{2594}{\dfrac{3339}{3.16227766}}\\\\=\dfrac{2594}{3339}\times3.16227766\approx2.46[/tex]

Hence, the z-score = 2.46

Answer:

IN THIS ORDER

NO

NO

YES

YES

NO

YES

Step-by-step explanation:

Hope this helped if I got it wrong, sorry ill edit it if I did :)

Answer:

12

Step-by-step explanation:

i am not sure a just add 5 +5+2

Answer:

60

Step-by-step explanation:

all of those rounded to the nearest ten is 60

Answer:

25

0

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

A. √123 = 11.09

11.09-11 = 0.09

B. √115 = 10.72

11-10.72 = 0.28

C. √118 = 10.86

11-10.86 = 0.14

D. √120 = 10.95

11-10.95 = 0.05 ( the smallest difference )

Answer:

1

Step-by-step explanation:

Take 4 1/2 and turn it into just halves by multiplying 4•2 and then adding it to one. 9/2 then multiply that by 2 because you need the denominator to be 4 getting 18/4. Then subtract 11/4 you end up getting 9/4. So technically you have 2 pieces but if you want them both to be 11/4 you only have one

Answer:

x + 7

Step-by-step explanation:

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4

Step-by-step explanation:

so the slope equation is y2-y1 over x2-x1 so by that logic 11-7 =4 and 4-3= 1 therefore it would equal all to 4 over 1 and by dividing that you get 4.

Answer:

y=3x

Step-by-step explanation:

Answer:

im sure its y=3x

Answer:

0

Step-by-step explanation:

Answer:

1785

Step-by-step explanation:

Answer:

2.755778

Step-by-step explanation:

Just search how much pounds is 1.25 kg?

Answer:

the ratio is 1:3 for brown sugar to sugar

Answer:

False

Explanation:

It's actually 0 > -2

Answer:

4

Step-by-step explanation:

25,437 --> twenty-five thousand, four hundred and thirty seven

Answer: minimum value of f = -2  and maximum value  of f = 2

Step-by-step explanation:

Given that;

f(x, y) = xy; 4x² + y² = 8

S(x,y) = xy + λ(4x² + y² - 8)

dS/dλ = 4x² + y² - 8 = 0

dS/dx = y + 8λx = 0 -> y = -8λx  

dS/dy = x + 2yλ = 0 -> x + 2λ(-8λx) = x(1 - 16λ²) = x(1-4λ)(1+4λ) = 0

-> x = 0 , λ = 1/4 , λ = -1/4

x = 0 -> y = 0 -> it doesn't satisfy 4x² + y² = 8

λ = 1/4 -> y = -8λx = -2x -> 4x² + y² = 8x² = 8 -> x = -1 , 1 -> y = 2 , -2

λ = -1/4 -> y = -8λx = 2x -> 4x² + y² = 8x² = 8 -> x = -1 , 1 -> y = -2 , 2

we have 4 critical points:

(-1, 2) -> f = -2

(1, 2) -> f = 2

(-1, -2) -> f = 2

(1 , -2) -> f = -2  

Therefore; minimum value of f = -2  and maximum value  of f = 2

The true statement about the slope is the slope is positive.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

To find the slope take two points from the graph as (0, 4) and (5, 6)

So, Slope of line

= (6-4) / (5-0)

= 2 /5

= 0.4

Thus, the slope of line is positive.

Learn more about slope here:

https://brainly.com/question/17310554

#SPJ7

Answer:

A) DF= 11

B) JH= 13.6

C) GJ= 23.6

D) m∠F= 105

E) m∠G= 34

F) m∠J= 41

Step-by-step explanation:

Answer:

-38

Step-by-step explanation:

distribute, mutiply and add

Answer:

The first set of ordered pairs is not a function.

Step-by-step explanation:

The X value of 7 repeats, which means that it is not a function

Answer:

530 :)

Step-by-step explanation:

If you add up the dowton and center city locations and then subtract that from the amount of pizzas at the westland location, you get your answer

Answer:

A = $2,122.20

Step-by-step explanation:

A = P(1 + r/k)^kt

Where,

A = future amount

P = principal = $1,500

r = interest rate = 7%

k = number of periods compounded = 4

t = years = 5 years

A = P(1 + r/k)^kt

= 1,500 (1 + 0.07/4)^4*5

= 1,500 (1 + 0.0175)^20

= 1,500 (1.0175)^20

= 1,500 (1.4148)

= 2,122.20

A = $2,122.20

Answer:

4x – 5

4 (x – 5)

4 ( x + 5)

5 less than the sum of 4 and a number

5 less than the product of 4 and a number

the product of 4 and the difference of a number and 5

4 more than the sum of a number and 5

5 more than the product of 4 and a number

the product of 4 and the sum of a number and 5

4 more than 5 less than a number

Answer:

1712

Step-by-step explanation:

Given arithmetic sequence is: -16,2,20

Here, a = - 16, d = 2 - (-16) = 2+ 16 = 18

n = 97, [tex] a_{97}=?[/tex]

[tex]\because a_n = a + (n-1)d\\\\

\therefore a_{97}= - 16 + (97-1)\times 18\\\\

\therefore a_{97}= - 16 + 96\times 18\\\\

\therefore a_{97}= - 16 + 1728\\\\

\therefore a_{97}=1,712\\\\[/tex]

Answer:

1712

Step-by-step explanation:

Formula of the sequence:

[tex]a_{n}=18n-34\\a_{97}=18(97)-34\\a_{97}=1712[/tex]

So 1712 is the 97th term

Answer:

3ft

Step-by-step explanation:

get the ratio of longest side which is 5over9 is equal to 15 what about 1 over 9 then u equate n get 3

Answer:

≈ 5.2 ft

Step-by-step explanation:

sum the parts of the ratio, 3 + 1 + 5 = 9 parts

Divide the angle sum of a triangle by 9 to find the value of one part of the ratio.

180° ÷ 9 = 20° ← value of 1 part of the ratio, then

3 parts = 3 × 20° = 60°

5 parts = 5 × 20° = 100°

The angles of the triangle are 100°, 60° and 20°

The longest side is opposite the largest angle in the triangle

The shortest side is opposite the smallest angle in the triangle.

Thus

the longest side is opposite 100°

the shortest side is opposite 20°

let x represent the shortest side and using the Sine rule

[tex]\frac{x}{sin20}[/tex] = [tex]\frac{15}{sin100}[/tex] ( cross- multiply )

x × sin100° = 15sin20° ( divide both sides by sin100° )

x = [tex]\frac{15sin20}{sin100}[/tex] ≈ 5.2 ( to the nearest tenth )

Thus the shortest side is ≈ 5.2 ft