Question: You are playing your favorite video game, Hero's Quest. In the game, you can complete missions to earn experience points. You may complete a mission as many times as you would like, but each time you do, you only receive 80% as much experience as the previous time. The first time that you complete Mission A, you earn 1000 experience, points. The second time you complete it, you earn 800 experience points. How many times can you complete the mission before you earn less than 400 points? Explain your answer​

Answers

Answer 1

Using a geometric sequence, it is found that you can complete the mission 5 times before you earn less than 400 points.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, the amount of points after n times is a geometric sequence with [tex]a_1 = 1000, q = 0.8[/tex], hence the equation is:

[tex]a_n = 1000(0.8)^{n-1}[/tex]

You will earn less than 400 points when:

[tex]a_n < 400[/tex]

Hence:

[tex]1000(0.8)^{n-1} < 400[/tex]

[tex](0.8)^{n-1} < 0.4[/tex]

[tex]\frac{0.8^n}{0.8} < 0.4[/tex]

[tex]0.8^n < 0.32[/tex]

[tex]\log{0.8^n} < \log{0.32}[/tex]

[tex]n > \frac{\log{0.32}}{\log{0.8}}[/tex]

[tex]n > 5.1[/tex]

You can complete the mission 5 times before you earn less than 400 points.

More can be learned about geometric sequences at https://brainly.com/question/11847927


Related Questions

Hugo began his science experiment with 22 grams of sugar crystals. During the experiment, the change in the mass of the sugar crystals was

6 grams.
What is the final mass of the sugar crystals?

Answers

Answer:

its actually 16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Please help! Will be marking brainliest!

Answers

Answer:

integer and rational

Step-by-step explanation:

(4 ² +24) = |(3 - 7) - 16|=
3
5
1
2

Answers

Answer:

The equality is not true.

Step-by-step explanation:

[tex](4^2 +24) = |(3 - 7) - 16|[/tex]

[tex](16 +24) = |(3 - 7) - 16|[/tex]

[tex]40 = |(3 - 7) - 16|[/tex]

[tex]40 = |(- 4) - 16|[/tex]

[tex]40 = |-20|[/tex]

[tex]40 = 20[/tex]

But

[tex]40 \neq 20[/tex]

If the measure of angle 1=4x-3 and the measure of angle 2=3x+8, find the value of x so that the measure of angle 1 is supplementary to the measure of angle 2.​

Answers

Answer:

hujikmnjhu

Step-by-step explanation:

egyiru9epojgtur9iokejrue

What is the value of x in the equation -6x-5x+22?
-22
-2
2
22
What is the answer

Answers

Answer:

theres no answer

Step-by-step explanation:

is there more?

PLease help me(: !!!!!!!!!!!!!!!!!!!!

Answers

Answer:

should be 65

Step-by-step explanation:

if not then hmu

Each time the 5 moves one place to the left, it is worth ___________as
much

A. 10 times
B. 100 times
C. One-tenth
D. One hundredth

Answers

Answer:

A. 10 times

Step-by-step explanation:

Answer:

A. Ten times.

Step-by-step explanation:

If it was one place to the right, it would have been one-tenth, so that's gone. If it was moved twice in place of either direction, it would be hundredths, so those are also eliminated. So, It's 10 times.

Easy 1 through 3 ! 17 points

Answers

1. (1.) -24, (2.) 6, (3.) -3

2. Positive

3. Difference = Subtraction

Product = Multiplication

Quotient = Division

Find the area of the semicircle please .

Answers

Answer:

39.25

Step-by-step explanation:

the formula is a = (3.14 × [tex]r^{2}[/tex]) / 2

the equation is a = (3.14 ×[tex]5^{2}[/tex]) / 2

5 is the radius

1. [tex]5^{2}[/tex] = 25

2. 3.14 × 25 = 78.5

3. 78.5 / 2 = 39.25

I hope this helped! :)

Answer:

12.5π or 39.25

Step-by-step explanation:

10 is diameter, we first find the radius which is 10/2 = 5 and so we know the area formula of the circle is πr^2 so 5^2 is 25 and then there's a π at the end so 25π, but it's a semicircle so 25π/2 which is 12.5π, if it's in base 10 (decimal form) then simply do 12.5 x 3.14 = 39.25

What is an equation of the line that passes through the points (3,3) and (-2,6)
F.y=-3/5x + 24/5
G.y=-3/5x - 24/5
H.y=3/5x + 24/5
J.y=3/5x - 24/5

Answers

Answer:

F

Step-by-step explanation:

x - x1/ x2-x1= y - y1/ y2 -y1

x - 3 / -2 -3= y -3/6-3

x-3/-5=y-3/3

3(x-3)= -5(y-3)

3x-9= -5y +15

5y = -3x +24

y= -3x/5 +24/5

What is the range of the following relation
(9,-2) (4,3) (8,10) (-4,8)

A- 2,3,8,10
B-(9, -2) (4,3)
C - -4,4,8,9
D- (8,10) (-4, 8)

Answers

Answer:

Step-by-step explanation:

i believe it would be A...

If m ZAEB = 88°, find m2AED.

Answers

The correct answer is C.

Step-by-step explanation:

Hey there!

Here;

Given is; angle AEB = 88°

angle AEB + angle AED = 180° { being linear pair}

88° + angle AED = 180°

angle AED = 180° - 88°

Therefore, angle AED = 92°

Therefore, answer is Option C.

Hope it helps...


What is an equation of the line that passes through the point (-6, -7) and is
perpendicular to the line 6x + 5y = 30?

Answers

Answer:

Step-by-step explanation:

Product of slope of perpendicular lines = -1

6x + 5y = 30

Write this equation in y = mx + b  form

        5y = -6x + 30

          y = [tex]\frac{-6}{5}x+\frac{30}{5}[/tex]

          [tex]y=\frac{-6}{5}x + 6[/tex]

Slope of this line m₁ = -6/5

m₁ * m₂ = -1

      m₂ = -1÷m₁ = -1 * [tex]\frac{5}{-6}[/tex]  

[tex]m_{2}=\frac{5}{6}[/tex]     & (-6 , -7)

Equation of the required line: y - y₁ = m (x - x₁)

[tex]y - (-7) = \frac{5}{6}(x - [-6])\\\\y + 7 = \frac{5}{6}x + 6 *\frac{5}{6}\\\\y = \frac{5}{6}x +5-7\\\\y=\frac{5}{6}x-2[/tex]

Question 4 fast please

Answers

Answer:

X=-10

Step-by-step explanation:

Collinear points are points on the same line.

Use the equation of gradient to find the gradient. Then use the gradient to find X

[tex]\frac{Y2-Y1}{X2-X1}=Gradient of a slope[/tex]

[tex]\frac{2-(-4)}{3-0}=\frac{2+4}{3}=\frac{6}{3}=2[/tex]

[tex]\frac{x+4}{-3-0}=2[/tex]

Multiply both sides of the equation to get rid of the fraction.

[tex]\frac{x+4}{-3}*-3 =2*-3[/tex]

x+4=-6

x=-6-4

x=-10

–8 ÷ 2 =
answer now and free r

Answers

Answer:

-4

Step-by-step explanation:

Tell whether each number is divisible by 2, 3, 5, 6, 9, and/or 10.

a. 8,435


b. 981

Answers

Step-by-step explanation:

a. 8,435 is divisible by 5

b. 981 is divisible by 3 and 9

Need help with this algebra problem 15 points will give brainiest if right

Answers

Answer:

b is the lowest and d is the highest y axis

Step-by-step explanation:

Which of the following is square root of 0.000081?

(A) 0.9

(B) 0.09

(C) 0.009

(D) 9

Find the value of square root of 64/225?

(A) 8/17

(B) 8/15

(C) 13/8

(D) 8/11

Which number is not a perfect square?

(A) 4

(B) 9

(C) 111

(D) 81

Which of the following is square root of 1/25?

(A) 1/2

(B) 1/3

(C) 1/4

(D) 1/5

What is square root of 36/49?

(A) 3/4

(B) 6/7

(C) 7/6

(D) 5/8

What is square root of 36/121?

(A) 6/11

(B) 3/5

(C) 2/3

(D) 6/121

Answers

Answer:

1. C) 0.009

2. B) 8/15

3. C) 111

4. D) 1/5

5. B) 6/7

6. A) 6/11

Hope this helps and have a nice day.

Write as a single exponent.
1. ( 1/10 x 1/10 x 1/10 x 1/10 )^2
2. ( 1/10 x 1/10 x 1/10 )^3
3. ( 10 x 10 x 10 )^-2

Answers

Step-by-step explanation:

1. (1/10 × 1/10 × 1/10 × 1/10)^2

(10^-4)^2

10^-8

2. (1/10 × 1/10 × 1/10)^3

(10^-3)^3

10^-6

3. (10 × 10 × 10)^-2

(10^3)^-2

10^-6

Question

Write as a single exponent.

1. ( 1/10 x 1/10 x 1/10 x 1/10 )^2

2. ( 1/10 x 1/10 x 1/10 )^3

3. ( 10 x 10 x 10 )^-2

I can’t.....help. I’m gay, I don’t understand math.

Answers

Answer:

i cant help i do not know answer

Answer:i-

Step-by-step explanation: good luck

What is the equation of the line that is perpendicular to y = -2/3x + 4 and that passes through (–2,–2)?
y = 3/2x - 3/10
y = 3/2x - 5
y = 3/2x + 1
y = 3/2x - 2/3

Answers

Answer:  y = 3/2x + 1

Step-by-step explanation:  For a perpendicular line, take the reciprocal of  "m"  and reverse the sign.

- 2/3 becomes +3/2

Then substitute the y and x values of the given coordinate into the equation and solve for "b"

y = mx + b

-2 = 3/2(-2) + b

-2 = -3 + b

-2 +3 = b

+1 = b   Substitute for b in y = (3/2)x + 1

can someone help me figure this out ?

Answers

Answer: AAS

Step-by-step explanation:

Lets call the intersection point between AC and DE F.

I think he meant the two triangles AFE and DFC.

We know angle A is congruent to angle D.

We also know AE is congruent to DC.

There is also a hidden piece of evidence which is AFE is congruent to DFC due to vertical angles.

We know two angles and 1 side, so we can use AAS to figure out that the two smaller triangles are congruent.

Josh but a total of 30 cans of cola and root beer. There were twice as many cans of cola is cans of root beer. How many cans of color did he buy?

Answers

Answer:

20

Step-by-step explanation:

start by using system of equations

x = cola

y = root beer

x + y = 30

x = 2y

now either use substitution or elimination. for me, substitution is easier.

the second equation already has one variable isolated ( x ) so, plug that into the first equation.

2y + y = 30

y = 10

now plug your answer into the original equation.

x + 10 = 30

x = 20

hope this helps :)

Robert believes the lines graphed at right are perpendicular, but Mario is not convinced. What is the slope of each line? Explain how you know whether or not the lines are perpendicular. ​

Answers

Answer/Step-by-step explanation:

An easy way to be sure two lines are perpendicular is if the product of both slopes equals -1.

That is: [tex] (m_1)(m_2) = -1 [/tex]. Where, m1 and m2 are slopes of both lines respectively.

Let's find the slope of the both lines.

Slope of the line that slants upward from left to right using coordinates (0, 0) and (2, 2) of two points on the line:

[tex] m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{2 - 0} = \frac{2}{2} [/tex]

[tex] m_1 = 1 [/tex]

Slope of the line that slants downwards from left to right using coordinates (2, 2) and (0, 4) of two points on the line:

[tex] m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 2}{0 - 2} = \frac{2}{-2} [/tex]

[tex] m_2 = -1 [/tex]

Find the product of both slopes

[tex] (m_1)(m_2) = (1)(-1) = -1 [/tex]

Therefore, we know the lines are perpendicular because [tex] (m_1)(m_2) = -1 [/tex].

can someone plz help im strugging

Answers

Answer:

a. the measure of angle A is 113 degrees

the measure of angle B is 67 degrees

Step-by-step explanation:

Remember, linear pairs have a sum of 180 degrees when added. So, if you add your angle measures and set it equal to 180, then you just need to solve from there.

7x-13+3x+13=180

combine like terms

(7x+3x)+(-13+13)=180

10x+0=180

10x=180

divide both sides by 10 to isolate x

x=18

now that you have x, plug it into your angle measures

m<a: 7(18)-13

126-13

113

m<b: 3(18)-13

54+13

67

1. Which graphs could represent a proportional relationship?

A. A
B. B
C. C
D. D

Answers

Answer:

a

Step-by-step explanation:

proportional relationship start from the origin (0,0)

they also have a line that goes upwards in an even relationship

they also can make points

follows the slope

The answer is to your question is A

10. Points D, E, and F are non-collinear. How many lines can be drawn that pass through F and are perpendicular
to DE ? Use a diagram to illustrate your answer.

Answers

Given:

Points D, E, and F are non-collinear.

To find:

Number of lines that pass through F and are perpendicular  to DE.

Solution:

Points D, E, and F are non-collinear. It means points D, E and F are not lie on a  single straight line.

We know that, the number of perpendicular lines on a line from a particular point is 1.

So, number of lines that pass through F and are perpendicular  to DE is 1 as shown in the below figure.



2.

Which polynomial function gets larger and larger in the negative direction as x gets

larger and larger in the negative direction?

a. f(x) = 5x2 – 2x + 1

b. f(x) = 6x3 + 4x2 – 15x + 32

c. f(x) = 7x4 – 2x3 + 3x2 + 8x – 10

d. f(x) = 8x6 + 1

Answers

Given:

x gets  larger and larger in the negative direction.

To find:

The polynomial function which gets larger and larger in the negative direction.

Solution:

In options a, c and d, degree of polynomials are even and leading coefficient is positive. So,

[tex]f(x)\to \infty\text{ as }x\to -\infty[/tex]

In option b, degree of polynomial is odd and leading coefficient is positive. So,

[tex]f(x)\to -\infty\text{ as }x\to -\infty[/tex]

Therefore, the function in option b, [tex]f(x)=6x^3+4x^2-15x+32[/tex] gets larger and larger in the negative direction as x gets  larger and larger in the negative direction.

Hence, the correct option is b.

We want to see which polynomial function gets larger and larger as the variable increases in the negative direction. We will see that the correct option is d: f(x) = 8x^6 + 1

Here you need to remember two things.

As the larger the exponent is, the faster the polynomial grows.

When we evaluate a negative number in an even exponent, the outcome is always positive.

Then the polynomials that get larger and larger as x increases in the negative direction are all the polynomials with a even leading exponent, particularly, the one that increases faster is the one with the largest leading exponent, which is:

d. f(x) = 8x^6 + 1

If you want to learn more, you can read:

https://brainly.com/question/23792383

A farm processes 6,000 gallons of milk every hour. Which equation represents the amount of milk, y, that the farm processes in x hours?
A. y=6,000+x
B. y=x6,000
C. y=6,000x
D. y=6,000x

Answers

y = 6000x is correct.
C is the answer to that problem

The temperature dropped 6°C every hour for 9 hours. What was the total number of degrees the
temperature changed in the 9 hours?

Answers

Answer:

What is the starting temp?

Step-by-step explanation:

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