Mathematics College

How to find the (r) or difference in this scenario:
Aliens Away is a new video game where a player must eliminate a certain number of aliens on the screen by scaring them with an adorable house cat. When James plays the game, he eliminates 64 aliens in the first level and 216 aliens in the fourth level. If the number of aliens are destroyed in a geometric sequence from one level to the next, how many total aliens will James have wiped out by the end of the sixth level?

It is given that it is a geometric sequence, if I am not mistaken it is the explicit formula.

IF YOU COULD PLASE EXPLAIN:)

Answers

Answer 1

Total number of aliens James have wiped out by the end of the sixth level is 1330

The number of aliens eliminated in first level a = 64

The number of aliens eliminated in the fourth level = 216

The sequence is in geometric sequence

The nth term of the geometric sequence is

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

The fourth term is 216

216 = [tex]64r^3[/tex]

[tex]r^{3}[/tex] = 216/64

r = 3/2

Then we have to find the total alien James killed by the end of sixth level

Sum of n terms = [tex]\frac{a(r^n-1)}{r-1}[/tex]

Substitute the values in the equation

= [tex]\frac{64(1.5^6-1)}{1.5-1}[/tex]

= 665/0.5

= 1330

Hence, total number of aliens James have wiped out by the end of the sixth level is 1330

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Related Questions

(−1/2x+7/10)−(−3/4x−1/5)

Answers

The expression (−1/2x + 7/10) − (−3/4x − 1/5) has a value of 1/4x + 9/10 when simplified

How to evaluate the expression?

From the question, the expression is given as

(−1/2x+7/10)−(−3/4x−1/5)

Rewrite the expression properly to make it legible

So, we have

(−1/2x + 7/10) − (−3/4x − 1/5)

Expression the above parameter as an equation

This is represented as

(−1/2x + 7/10) − (−3/4x − 1/5) = (−1/2x + 7/10) − (−3/4x − 1/5)

Open the brackets

So, we have the following equation

(−1/2x + 7/10) − (−3/4x − 1/5) = −1/2x + 7/10 + 3/4x + 1/5

Collect the like terms in the equation

(−1/2x + 7/10) − (−3/4x − 1/5) = 3/4x − 1/2x + 7/10 + 1/5

Evaluate

(−1/2x + 7/10) − (−3/4x − 1/5) = 1/4x + 9/10

The expression cannot be further simplified

Hence, the solution to the expression (−1/2x + 7/10) − (−3/4x − 1/5) is 1/4x + 9/10

Answers

Answer:

answer is -0.8333

round about -0.834

Step-by-step explanation: I hope this helps.

Answer:

Short steps pleaseFind the mean and variance of the binomial experiment in which n 5 and p 0.7. a. Mean b. Variance

Answers

Given

n= 5

p = 0.7

Find:

a. mean

b. variance

sol:

Mean d

[tex]\begin{gathered} mean\text{ =n}\times\text{p} \\ \\ \text{ = 5}\times\text{0.7} \\ \\ \text{ =3.5} \end{gathered}[/tex][tex]\begin{gathered} variance=np(1-p) \\ \\ =\text{ }5\times0.7(1-0.7) \\ \\ =3.5(0.3) \\ \\ =1.05 \\ \\ \end{gathered}[/tex]

Two cyclists, 108 miles apart, start riding toward each other at the same time. One cycles 2 times asfast as the other. If they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?

Answers

Initial distance: 108 miles

We know that they start riding toward each other, and one of them is 2 times as fast as the other. Then, if the speed of the slowest is v, the speed of the faster cyclist is 2v. The combined speed is:

[tex]v_T=v+2v=3v[/tex]

The speed and the distance are related by the equation:

[tex]V=\frac{D}{t}[/tex]

They meet 4 hours later, thus:

[tex]\begin{gathered} D=108 \\ t=4 \end{gathered}[/tex]

Finally, using the previous equation:

[tex]\begin{gathered} 3v=\frac{108}{4} \\ \Rightarrow v=9\text{ mi/h} \end{gathered}[/tex]

The speed of the faster cyclist (2v) is 18 mi/h.

Given f(x)=3x+2 find f(-4)

Answers

Step-by-step explanation:

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LanaCharles almn on the coordinate plane what is the perimeter of a ALMN round to the nearest unit

Answers

The Solution:

Given the graph below:

We are required to find the perimeter of the triangle LMN rounded to the nearest unit.

Step 1:

Find the distance LM, where L(-3,2) and M(3,5)

By the formula for distance between two points, we have

[tex]LM=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where,

[tex]\begin{gathered} x_1=-3 \\ y_1=2 \\ x_2=3 \\ y_2=5 \end{gathered}[/tex]

Substituting, we get

[tex]LM=\sqrt[]{(3--3)^2+(5-2)^2}=\text{ }\sqrt[]{6^2+7^2}=\text{ }\sqrt[]{85}=9.2195[/tex]

Step 2:

Find the distance LN:

[tex]LN=12[/tex]

Step 3:

Find the distance MN, where M(3,5) and N(9,2)

[tex]MN=\sqrt[]{(9-3)^2+(2-5)^2}=\text{ }\sqrt[]{6^2+(-3)^2}=\text{ }\sqrt[]{45}=6.7082[/tex]

Step 4:

The perimeter is:

[tex]\text{ Perimeter=LM+MN+LN=9.2195+6.7082+12=27.9277}\approx28\text{ units}[/tex]

Therefore, the correct answer is 28 units.

A number cube is rolled once, {1,2,3,4,5,6)Determine the likelihood of each situation,Column AColumn B1.rolling an even numbera. unlikely2.rolling a 7b. impossible3.rolling a number greater than 0Ccertain4.rolling a number that is greater than 2d. likely5.rolling a 2 or 3e equally likely

Answers

The likelihood of the following situations:

1. rolling an even number is likely.

2. rolling a 7 is impossible.

3. rolling a number greater than 0 is certain.

4. rolling a number that is greater than 2 is likely.

5. rolling a 2 or 3 is equally likely

Out of 3500 students at a college 1760 are enrolled in a computer class. What is the per cent of students taking the computer class?

Answers

Using percentages we can conclude that 50.2% of students are taking a computer class.

What is the percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

So, the percentage of students taking computer classes:

The total number of students is 3500.The number of students enrolled in a computer class is 1760.

Now, calculate as follows:

1760/3500 × 1000.502 × 10050.2

Therefore, using percentages we can conclude that 50.2% of students are taking a computer class.

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use the graph to complete the ordered pair solution (0,_) for f.

Answers

we must look the value of the graph when x=0

the graph trought x=0 when y=-1 so, the point is

[tex](0,-1)[/tex]

2. I want to find the area of a basketball free throw lane, and I am trying to use this formula:
Area =(6 ft) + (12 ft)(19 ft).
Clearly explain how you can tell this is wrong without knowing any area formulas.

Answers

Answer:

Down Here

Step-by-step explanation:

Hello!

Area is measured in units². Here, the units are feet, so the area would be written as feet² (ft²).

Simplifying the expression:

6ft + (12ft)(19ft)6ft + 228ft²

You can't simplify this because the units are not the same, and this can't measure area because all units of the area have to be squared. The term 6ft has non-squared units.

What is the value of p in the proportion below? 20/6 = p/12O 2 O 10O 40O 72

Answers

20/6 = p/12

cross-multiply

p x 6 = 20 x 12

6p = 240

divide both-side of the equation by 6

p = 240/6

p = 40

Solve |x4|+6 = 13.
O A. x
11 and x = -11
OB. x = 11 and x = -3
OC. x = -11 and x = -3
OD. x = -11 and x = 3

Answers

Answer:

Step-by-step explanation:

| x - 4 | + 6 = 13

x - 4 + 6 = 13

x = 11

4 - x + 6 = 13

x = -3

how to find a volume of a cylinder that has a radius of 10 and a base of 4 Khan academy

Answers

Question:

Find a volume of a cylinder:

Solution:

Remember that the volume of the cylinder with radius r and height h is given by the following formula:

[tex]V\text{ = }\pi r^2h[/tex]

then, replacing the data of the problem into the previous equation, we get:

[tex]V\text{ = }\pi(4^2)(10)\text{ = 3.14 (16)(10) = 502.4}[/tex]

thus, we can conclude that the correct answer is:

[tex]V\text{ = 502.4}[/tex]

If lines L=4x and M=x are perpendicular, what is the value of x?

Answers

Those angles are complementary, therefore, we can conclude:

[tex]\begin{gathered} 4x+x=90 \\ add_{\text{ }}like_{\text{ }}terms: \\ 5x=90 \\ Solve_{\text{ }}for_{\text{ }}x: \\ x=\frac{90}{5} \\ x=18 \end{gathered}[/tex]

Answer:

x = 18

Which of the following is the position vector for a vector that has an initial point of (10, 2) andterminal point of (-8, -7)?

Answers

initial point = (10,2)

Terminal point = (-8,-7)

subtract the coordinates of the initial point from the coordinates of the terminal point

Position vector = ( -8-10 , -7-2 ) = <-18,-9>

Which of the following statements are equivalent to "Some politicians are not crooked"? Select all that apply:All politicians are crooked.Some politicians are crooked.Not all politicians are crooked.All politicians are not crooked.

Answers

SOLUTION

The given statement is

"Some politicians are not crooked"

The equivalent statement is

Not all politicians are crooked

And

All politicians are not crooked.

The equivalent statement is

Not all politicians are crooked

And

All politicians are not crooked.

Answer: Not all politicians are crooked

It is equivalent to saying that "Some politicians are not crooked". Both are implying that not every politician is crooked and some of them are good.

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The equation of a curve is y=f(x)
The vertex of the curve is at (2,-3)
Write down the coordinates of the vertex of the curve with the equation
a) f(x)+5
b) -f(x)

Answers

The rigid transformations of the vertex of the curve are listed below:

(i) (2, 2).

(ii) (2, 3).

How to determine the coordinates of the vertex

In this problem we find the value of a point of a curve f(x), this point (the vertex) must be transformed by using rigid transformations. There are two cases: (i) Vertical translation, (ii) Reflection about the x-axis. The formulas for each case are described below:

Vertical translation

P'(x, y) = P(x, y) + (0, k)

Reflection about the x-axis

P'(x, y) = P(x, y) + (0, - 2 · p)

Where p is the y-coordinate of point P.

If we know that P(x, y) = (2, - 3), then the coordinates for each case are, respectively:

Vertical translation

P'(x, y) = (2, - 3) + (0, 5)

P'(x, y) = (2, 2)

Reflection about the x-axis

P'(x, y) = (2, - 3) + (0, 6)

P'(x, y) = (2, 3)

The transformations of the vertex of the curve are (i) (2, 2) and (ii) (2, 3).

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This table shows the top athletes that play both basketball and track. What is the intersection between the set of basketball players and the set of track athletes? Basketball Track Arnold Berenson Nickerson Eaton Yun Tadesse McDonald Jones Tadesse Nickerson Yang Martin

Answers

The intersection between the set of basketball players and the set of track athletes is given by:

{Tadesse, Nickerson}

What is the intersection between two sets?

The intersection between two sets is the set containing the elements that belong to both sets which we are calculating the intersection.

In the context of this problem, the sets are given as follows:

List of basketball players: {Arnold, Nickerson, Yun, McDonald, Jones, Tadesse}List of track athletes: {Berenson, Eaton, Tadesse, Nickerson, Yang, Martin}.

The intersection is composed by athletes that are both basketball players and track athletes, hence it is given as follows:

{Tadesse, Nickerson}

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Which graph shows the same linear equation shown in the table below?

Answers

I'm drawing now

_______________________

Option C

Mr. and Mrs. Tournas know that their son will attend a college, in 14 years, that they estimate to cost approximately $250,000How much should they deposit now if they assume that they can earn 8.5% compounded annually?

Answers

Compound interest formula:

[tex]A\text{ = }P(1+i)^n[/tex]

where:

A is the final amount, here = $250,000

P is the principal amount

i is the interest rate per year (in decimal form), here = 0.085

n is the number of years invested, here = 14

Replacing into the equation and solving for P, we get:

[tex]250000=P(1+0.085)^{14}[/tex][tex]\frac{250000}{1.085^{14}}=P[/tex]

P = $79,785.5

Graph transformation of the following line given the transformation: g(x)= -f(x) -2

Answers

Transformation of a Function

We are given the function:

[tex]y=f(x)=\frac{2}{3}x+8[/tex]

And it's required to find another function g(x) according to the transformation:

g(x) = -f(x) - 2

First, we calculate the negative of f(x):

[tex]-f(x)=-(\frac{2}{3}x+8)=-\frac{2}{3}x-8[/tex]

And now we subtract 2 to find g(x):

[tex]g(x)=-\frac{2}{3}x-8-2=-\frac{2}{3}x-10[/tex]

The equation above is in the slope-intercept form where the slope is m=-2/3 and the y-intercept = -10

Answer:

[tex]g(x)=-\frac{2}{3}x-10[/tex]

2,000 deposit,compound interest,compounded anually,at 6% for 2 years. What is the total balance(A=Principal+Interest)?

Answers

Given a principal P, compounded anually at r% for t years. Then the

8 Madison has two plants. She waters the spider plant every 4 days and the cactus every 6 daysShe water bo November 30. What is the next day that she will water both plants?

Answers

Two plants

Spider plant 4 days

Cactus plant 6 days

Then find when

4X = 6Y

find m.c.m (minimum common multiple) of 4 and 6

m.c.m (4,6) = 12

SO therefore, if both plants were watered November 30, then

add 12 days to Nov 30

12 days after Nov 30 = December 12

I only need help for letter b, the question is on the picture

Answers

Part B

Remember that

z =(x - μ)/(σ/√n)

where

n=21

we have

μ=1,700

σ=200

For X=1,500

Find out the value of Z1

Z1=(1,500-1,700)/(200/√21)

Z1=-4.5826

For X=1,900

Z2=(1,900-1,700)//(200/√21)

Z2=4.5826

Using a z-score table value

P(1,500therefore

The answer is 21 out of 21

Event A, Event B, and Event Care provided. Event A and Event B aremutually exclusive. Event A and Event C are not mutually exclusive.P(A) = 0.45P(B) = 0.30P(C) = 0.25What is the probability of the union of A and B?

Answers

Given data:

The probability of A is P(A)=0.45.

The probability of B is P(B)=0.30.

The expression for the mutually exclusive events is,

[tex]P(A\cap B)=0[/tex]

The expression for the probability of A union B is,

[tex]\begin{gathered} P(A\cup B)=P(A)+P(B)-P(A\cap B) \\ =0.45+0.30-0 \\ =0.75 \end{gathered}[/tex]

Thus, the probability of (AUB) is 0.75.

Look at the photograph and if you need anything let me know

Answers

Observe that the triangles have one pair of congruent angles, and two pair of congruent sides. This means we can demonstrate the congruence using SAS postulate, that is, Side-Angle-Side.

Therefore, the answer is the first option.

The Ruiz family took a summer trip.
In 4 days, they drove 1,600 miles. If they drove an equal
number of miles each day, how many miles did they drive
each day? Describe the basic fact you use to find your
answer and how many zeros you add from the dividend.

Answers

Answer:

400 miles each day

Step-by-step explanation:

You have 1600 miles divided into four days.

1600 / 4

We can use the basic fact that multiplying a number by ten simply means shifting everything to the left, for example 2 x 10 = 20, we just shifted 2 to the left and inserted a 0.

So for this problem, we can do the same. Divide 1600 by 100, or 10 x 10, then divide by 4.

1600/16 = 100

16/4 = 4.

Now, since we divided by ten twice before, we can get the right answer by multiplying by ten twice.

4 x 10 = 40

40 x 10 = 400

Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. sin 16° = ___

Answers

We have round of to 100th place means up to 3 places

[tex]\sin (16\text{ degre}e)=0.27563[/tex]

Now we will reduce the digit from right side upto 3 places

As last digit is 3 which is less than 5 so it will remove directly

[tex]\sin (16\text{ degr}e)=0.2756[/tex]

Now the last digit is 6 which is greater than 5. So and is even so change we will simply remove this

[tex]\sin (16\text{ degre}e)=0.275[/tex]

What is 2 2/3 - 3/5? 7/154 4/152 1/15 1 2/5

Answers

[tex]\begin{gathered} 2\text{ }\frac{2}{3}-\frac{3}{5}=\frac{8}{3}-\frac{3}{5} \\ \frac{8}{3}-\frac{3}{5}=\frac{40-9}{15}=\frac{31}{15}=2\text{ }\frac{1}{15} \end{gathered}[/tex]

4) The half-life of a medication is the amount of time for half of the drug to be eliminated from the body. The half-life of Advil or ibuprofen is represented by the equation 2 ) 5 . 0 ( t M R = , where R is the amount of Advil remaining in the body, M is the initial dosage, and t is time in hours.

Answers

Based on the half-life, 35.36 mg will remain at 6:00P PM in the body

The amount of the medication that will remain at 6:00P PM?

The details that complete the question are added as an attachment

From the question, we have

Initial dosage = 200 mg

This means that

M = 200

Also, we have

Initial time =1 : 00 pm

This means that the number of hours, is

n = 6pm - 1pm

n = 5

Recall that the function is given as

R = M(0.5)ⁿ/²

So, we have the following equation

R = 200 x (0.5)⁵/²

Evaluate the quotient of the exponents

So, we have the following equation

R = 200 x (0.5)².⁵

Evaluate the products

R = 35.36 mg

Using the above computation as a guide, we have the remaining amount to be 35.36 mg

Hence, the amount of the medication that will remain at 6:00P PM is 35.36 mg