Answer:
C
Step-by-step explanation:
Use the formula for the volume of a cylinder.
[tex]V=\pi r^2h[/tex]
Plug in the height, the radius, and 3.14 for [tex]\pi[/tex].
[tex]V=3.14(15^2)(5) \\ \\ V=3.14(225)(5) \\ \\ V=3.14*1125 \\ \\ V=3532.5[/tex]
If you round that number you'll get [tex]V=3533[/tex].
So the answer is answer choice C.
How long will it take you to ski a distance of 24 miles at a speed of 6 miles per 30 minutes? (Step by step please)
Answer: It will take 2 hours. 120 minutes. 4 half-hours.
What is the value of b in the equation below? 9^-8 x 9^-2 = a^b
Answer:
b= -10
Step-by-step explanation:
9^ -8 * 9^ -2
We know that a^b * a^c = a^ (b+c)
9^ (-8+-2)
9^ -10
We want it in the form a^b
a=9
b= -10
Answer:
-10
Step-by-step explanation:
1st: the
2nd: expect
3rd: said
last step: so
plzzzz answer!!! 20 points!!!
Two lines, A and B, are represented by the equations given below:
Line A: y = x – 6
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
(–5, –11), because the point satisfies both equations
(–5, –11), because the point does not lie on any axis
(–3, –5), because the point satisfies one of the equations
(–3, –5), because the point lies between the two axes
ANSWER
(–5, –11), because the point satisfies both equations
EXPLANATION
The given equations are:
Line A: y = x – 6
Line B: y = 3x + 4
We substitute (-5,-11) into both equations.
Line A: -11 = -5– 6
This implies that,
-11=-11
This statement is true.
Line B: -11= 3(-5)+ 4
-11= -15+ 4
-11=-11
This is also true.
Since this point ,(&6,-11) satisfy both equations, it is their solution.
which equation best fits these data? PLEASE HELP
Answer:
C
Step-by-step explanation:
Use a quadratic equation regression calculator.
Plugging in all the points, the equation should come somewhere close to
[tex]y=-0.32x^{2} -1.26x+15.81[/tex]
Which is answer choice C.
Answer:
The correct option is C.
Step-by-step explanation:
Answer:
The required quadratic regression model is [tex]y=x^2-2x-3[/tex].
Step-by-step explanation:
The given data points are (-6,12), (-4,15), (-3,17), (-1,17), (1,15), (2,11), (3,9), (4,6).
From the graph it is clear that the given data forms a U-shaped curve. It means we have to find the quadratic regression model.
The general form of quadratic regression model is
[tex]y=ax^2+bx+c[/tex]
Using technology we get,
[tex]a=-0.32,b=-1.26,c=15.81[/tex]
The required quadratic regression model is
[tex]y=-0.32x^2-1.26x+15.81[/tex]
Therefore the correct option is C.
24 is 0.4 of what number
Answer: 600
Step-by-step explanation:
We have, 4% × x = 24
or, 4 100 × x = 24
Multiplying both sides by 100 and dividing both sides by 4,
we have x = 24 × 100 4
x = 600
If you are using a calculator, simply enter 24×100÷4, which will give you the answer.
what is the correct answer. what is the focus point of a parabola with this equation? y=1/8(x^2-4x-12)
A. (-2,0)
B. (-2,-4)
C. (2,-2)
D. (2,0)
E. (2,4)
The answer is C. (2,-2) u just search it up online and there are million answers
Answer:
The answer would be D. (2,0)
Step-by-step explanation:
Hope this helps!
On a separate piece of graph paper, graph y = |x| - 1; then click on the graph until the correct one appears.
Answer with explanation:
y= |x| -1
|x|=x , if x≥0
and = -x , if x<0.
So,the above function can be written as
[tex]y=\left \{ {{x-1,for, x\geq 0 } \atop {-x-1,for x<0}} \right.[/tex]
First Drawing the graph of
y= x-1 for, x ≥ 0
And , then , y= -x -1 ,for x <0.
and then combining, the two we get.
Answer:
what they said
Step-by-step explanation:
Which is the operation to do second based on the order of operations?
4+5×(7−3)
A. Subtract 3 from 7
B. Add 4 to the product of 5 and the difference of 7 and 3
C. Multiply 5 by the difference of 7 and 3
D. Multiply 7 by the sum of 4 and 5
The answer to this is C.
Why do people save more when the Federal Bank sets a high interest rate on deposits? A. Spending on nonessential items decreases. B. Interest on savings can be earned. C. Financial institutions insist on a minimum balance. D. The unemployment rate goes down.
Answer: b
Step-by-step explanation:
If point A is located at (-7,5) and is rotated around 270 clockwise about the origin, then point A' is located at...
a. (5,7)
b. (-5,-7)
c. (5,7)
d. (7,5)
e. (-7,-5)
Answer:
B.(-5,-7)
Step-by-step explanation:
According to the rule of rotation if you were to have a 270* clockwise you would first switch the x and y values. Ex: (-7,5) -> (5,-7). next you would make the original y coordinate a negative. (5,-7) -> (-5,-7).
Adjacent angles are two angles that share a common what?
Answer:
that share a common vertex
A bag contains tiles with the numbers 1 through 9 on them. Tiles were drawn 65 times. The two tile was drawn 6 times, the four tile was drawn 10 times, the six tile was drawn 14 times, and the eight tile was drawn 3 times. What is the experimental probability of drawing an even number?
Answer:
33/65
Step-by-step explanation:
We know that there was a # of even numbers drawn = to 6+10+14+3, which equals 33.
This means, in 65 trials, 33 had even outcomes. This means the experimental probability is 33/65 or approximately 51% (the most precise I could get is 33/65= 0.50769230769)
3/4 times what equals 1/4
Final answer:
To find what multiplied by 3/4 equals 1/4, set up the equation 3/4 * x = 1/4 and solve for x, giving the answer x = 1/3.
Explanation:
This question demands basic understanding of multiplication and reciprocals.
The question asks, "3/4 times what equals 1/4?". To find the answer, we can set up the equation 3/4 * x = 1/4, where x is the unknown we are trying to find. Solving for x involves dividing both sides of the equation by 3/4 to isolate x.
Therefore, the equation simplifies to x = (1/4) / (3/4). Performing the division gives us x = 1/3. This means that 1/3 is the number you need to multiply by 3/4 to get 1/4.
To find what number multiplied by 3/4 equals 1/4, divide 1/4 by 3/4, which is the same as 1/4 times the reciprocal of 3/4 (4/3), resulting in 1/3.
To find out 3/4 times what equals 1/4, we are essentially looking for a number that when multiplied by 3/4 gives us 1/4. The mathematical operation we need to use is division since we want to find what 1/4 divided by 3/4 is. So, the equation we are solving is (1/4) ÷ (3/4).
When we divide fractions, we multiply by the reciprocal of the divisor. The reciprocal of 3/4 is 4/3. So, the calculation now is (1/4) × (4/3).
Multiplying the numerators and denominators separately, we get (1 × 4) / (4 × 3) which simplifies to 4/12. After simplification, 4/12 reduces to 1/3. Therefore, 3/4 times 1/3 equals 1/4.
Complete question is :
3/4 times is what equals 1/4?
the map shows Hope road and the construction site for the new library find the equation of a street that passes through the building site and is parallel to the Hope road
Answer: y=1/3x+4
You're welcome
Answer: [tex]x-3y+12.5=0[/tex]
Step-by-step explanation:
From the give en graph , the coordinates of the point marked for library =(7,6.5)
The slope of the Hope road passing from points (0,6) and (3,7) is given by :-
[tex]\text{Slope}=\dfrac{\text{Change in y-coordinate}}{\text{Change in x-coordinate}}\\\\\Rightarrow\ \text{Slope}=\dfrac{7-6}{3-0}=\dfrac{1}{3}[/tex]
Since , a street that passes through the building site and is parallel to the Hope road, then the slope of the street will be :-
[tex]m=\dfrac{1}{3}[/tex]
[ The two parallel sides have same slopes. ]
Now, the equation of line having slope [tex]m=\dfrac{1}{3}[/tex] and passing through (7,6.5) is given by :-
[tex](y-6.5)=\dfrac{1}{3}(x-7)\\\\\Rightarrow3(y-6.5)=x-7\\\\\Rightarrow\ 3y-19.5=x-7\\\\\Rightarrow x-3y+12.5=0[/tex]
Hence, the equation of a street that passes through the building site and is parallel to the Hope road : [tex]x-3y+12.5=0[/tex]
A tray of cake samples contains a variety of flavors.
chocolate
33
vanilla
9
strawberry
3
What is the probability that a randomly selected piece of cake will be vanilla?
Simplify your answer and write it as a fraction or whole number.
p( vanilla)
The total pieces of cake equal 45. 9 pieces are vanilla. This gives the fraction 9/45 which can be simplified to 1/5. P(vanilla)=1/5
please help Use the model to solve for x.
A)
no solution
B)
x = 3
C)
x = -3
D)
x = -
3
2
Answer:
A) no solutionStep-by-step explanation:
x + 1 = x - 1 - 1
x + 1 = x - 2 subtract x from both sides
x - x + 1 = x - x - 2
1 = -2 FALSE
The Kwans are saving for their daughter’s college education. If they deposit $12,000 in an account bearing 6.4% interest compounded continuously, how much will be in the account when Ann goes to college in 12 years? a. $12,768 c. $21,216.12 b. $25,865.41 d. $76,800
After 12 years there will be $25,865.41 in the bank account when Ann goes to college option (b) is correct.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
The formula for the compounded continuously:
[tex]\rm A = Pe^{rt}[/tex]
r = 6.4% = 0.064
t = 12
P = $12,0000
[tex]\rm A = 12,0000e^{0.064\times12}[/tex]
After solving:
A = $25,865.41
Thus, after 12 years there will be $25,865.41 in the bank account when Ann goes to college option (b) is correct.
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Which list is in order from least to greatest? A) 9.4 * 10^-8, 9.25 * 10^-6, 2.5 * 10^3, 7* 10^3 B) 2.5 *10^3, 7 * 10^3, 9.25 * 10^-6, 9.4 * 10^-8. C) 9.25 * 10^-6, 9.4 * 10^-8, 7 * 10^3, 2.5 * 10^3 D) 9.4 * 10^-8, 9.25 * 10^-6, 7 * 10^3, 2.5 * 10^3
ANSWER
A) 9.4 * 10^-8, 9.25 * 10^-6, 2.5 * 10^3, 7* 10^3
EXPLANATION
The numbers are given in standard form.
The first criteria we will use to order them is the exponents.
The bigger the exponents the bigger the number.
The second criteria is that, if the exponents of any two numbers are the same, then we use the numbers multiplying the powers of 10 to order.
[tex]9.4 * 10^{-8} \: < \: 9.25 * 10^{-6} \: < \: 2.5 * 10^3 \: < \: 7* 10^3[/tex]
The correct choice is A.
Answer:
Option A. [tex]9.4\times 10^{-8}< 9.25\times 10^{-6}< 2.5\times 10^{3}<7\times 10^{3}[/tex]
Step-by-step explanation:
The given numbers are [tex]9.4\times 10^{-8}, 9.25\times 10^{-6}, 2.5\times 10^{3},7\times 10^{3}[/tex].
These are numbers written in scientific notation.
To identify the order of the numbers from least to greatest we will convert the numbers into the standard from.
[tex]9.4\times 10^{-8}[/tex] = 0.000000094
[tex]9.25\times 10^{-6}[/tex] = 0.00000925
[tex]2.5\times 10^{3}[/tex] = 2500
[tex]7\times 10^{3}[/tex] = 7000
Now we can arrange then from least to greatest.
0.000000094 < 0.00000925 < 2500 < 7000
OR
[tex]9.4\times 10^{-8}< 9.25\times 10^{-6}< 2.5\times 10^{3}<7\times 10^{3}[/tex]
Option A. is the answer.
A steel pipe 100 cm long has an outside diameter of 2 cm and an inside diameter of 1.8 cm. If thee density of the steel is 7.8 grams per cm^3, what is the mass of the pipe to the nearest gram?
Answer:
The mass of the pipe is [tex]465\ g[/tex]
Step-by-step explanation:
step 1
Find the volume of the steel pipe
The volume is equal to the area of outside circle minus the area of inside circle, multiplied by the length of the pipe
so
[tex]V=\pi [r2^{2}-r1^{2}]L[/tex]
we have
[tex]r2=2/2=1\ cm[/tex] ---> the radius is half the diameter
[tex]r1=1.8/2=0.9\ cm[/tex] ---> the radius is half the diameter
[tex]L=100\ cm[/tex]
[tex]\pi=3.14[/tex]
substitute
[tex]V=(3.14)[1^{2}-0.9^{2}](100)=59.66\ cm^{3}[/tex]
step 2
Find the mass
The mass is equal to the density multiplied by the volume
so
[tex]m=7.8(59.66)=465\ g[/tex]
Answer:
466
Step-by-step explanation:
Solve the equation below for x.
-1/2(3x-4)=11
Answer:
x=-6
Step-by-step explanation:
You are given the equation
[tex]-\dfrac{1}{2}(3x-4)=11[/tex]
First, multiply it by 2 to get rid of fraction:
[tex]-(3x-4)=22[/tex]
Now open the brackets:
[tex]-3x+4=22[/tex]
Subtract 4 from both sides:
[tex]-3x+4-4=22-4\\ \\-3x=18[/tex]
Multiply it by -1:
[tex]3x=-18[/tex]
and divide by 3:
[tex]x=-6[/tex]
Answer:
[tex]\large\boxed{x=-6}[/tex]
Step-by-step explanation:
[tex]-\dfrac{1}{2}(3x-4)=11\qquad\text{multiply both sides by (-2)}\\\\(-2\!\!\!\!\1\diagup^1)\cdot\left(-\dfrac{1}{2\!\!\!\!\1\diagup_1}\right)(3x-4)=(-2)\cdot11\\\\3x-4=-22\qquad\text{add 4 to both sides}\\\\3x-4+4=-22+4\\\\3x=-18\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=-\dfrac{18}{3}\\\\x=-6[/tex]
A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?
Answer:
6% x = 8,880 : x = selling price of house.
x = $148,000 : solve for x
Step-by-step explanation:
The selling price of the house can be calculated by dividing the commission ($8,880) by the commission rate (0.06). This gives a selling price of $148,000.
Explanation:To solve this problem, you need to understand that the 6% commission the real estate agent received is based on the selling price of the house. You can find the selling price by dividing the commission by the percentage commission expressed as a decimal.
Here's the step-by-step solution:
Convert the 6% commission rate to a decimal by dividing 6 by 100, which gives 0.06.Next, divide the commission amount ($8,880) by the commission rate (0.06). Using this calculation, $8,880 / 0.06, we find that the selling price of the house is $148,000.So, the selling price of the house on which the agent earned an $8,880 commission at a rate of 6% was $148,000.
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What is the degree of the polynomial given below?
F(x)=2x^3-x^2+5x-3
A. 2
B. 5
C. 4
D. 3
Answer:
it is 3 i am pretty sure
Step-by-step explanation:
I believe the answer is 3
I need 18,19,& 20•ignore my writing
Answer:
Part 18) Option D 100 square meters
Part 19) Option A 60 cubic meters
Part 19) Option C. 212 cubic centimeters
Step-by-step explanation:
Part 18) Estimate the surface area of the prism
we know that
The surface area of the prism is equal to
[tex]SA=2B+PH[/tex]
where
B is the area of the base
P is the perimeter of the base
H is the height of the prism
Find the area of the base B
[tex]B=3.5*7=24.5\ m^{2}[/tex]
Find the perimeter of the base P
[tex]P=2*(3.5+7)=21\ m[/tex]
we have
[tex]H=2.4\ m[/tex]
substitute
[tex]SA=2(24.5)+(21)(2.4)=99.4\ m^{2}[/tex] ----> exact value
Estimate the surface area
we have
[tex]L=3.5=4\ m[/tex] ----> round up
[tex]W=7\ m[/tex]
[tex]H=2.4=2\ m[/tex] ----> round down
Estimate the area of the base B
[tex]B=4*7=28\ m^{2}[/tex]
Estimate the perimeter of the base P
[tex]P=2*(4+7)=22\ m[/tex]
substitute in the formula
[tex]SA=2(28)+(22)(2)=56+44=100\ m^{2}[/tex]
Part 19) Estimate the volume of the prism
The volume of the prism is equal to
[tex]V=BH[/tex]
we have
[tex]B=3.5*7=24.5\ m^{2}[/tex]
[tex]H=2.4\ m[/tex]
substitute
[tex]V=(24.5)(2.4)=58.8\ m^{3}[/tex] ----> exact value
Estimate the volume
we have
[tex]L=3.5=4\ m[/tex] ----> round up
[tex]W=7\ m[/tex]
[tex]H=2.4=2\ m[/tex] ----> round down
Estimate the area of the base B
[tex]B=4*7=28\ m^{2}[/tex]
substitute in the formula
[tex]V=(28)(2)=56\ m^{3}[/tex]
Part 20) The volume of the prism is equal to
[tex]V=BH[/tex]
we have
[tex]B=6*6.8=40.8\ cm^{2}[/tex]
[tex]H=5.2\ cm[/tex]
substitute
[tex]V=(40.8)(5.2)=212.16\ cm^{3}[/tex] ----> exact value
Estimate the volume
we have
[tex]L=6\ cm[/tex]
[tex]W=6.8=7\ cm[/tex] ----> round up
[tex]H=5.2=5\ cm[/tex] ----> round down
Estimate the area of the base B
[tex]B=6*7=42\ cm^{2}[/tex]
substitute in the formula
[tex]V=(42)(5)=210\ cm^{3}[/tex]
If line s and line t are parallel lines cut by transversal line r, what is the value of x?
x = 18
x cannot be determined from the information given
x = 33
x = 12
Answer:
Because s and t are parallel x=12
Step-by-step explanation:
To get this you have to solve for (4x-12)+120=180 solve for x
4x+12=60
4x=48
=12
The equation is written as 4x - 12 + 120 = 180. Then the value of the variable 'x' will be 18. Then the correct option is A.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The sum of the angle (4x - 12)° and (120)° will be equal to 180°. Then the equation is given as,
4x - 12 + 120 = 180
Simplify the equation, then we have
4x - 12 + 120 = 180
4x = 72
x = 72 / 4
x = 18
The equation is written as 4x - 12 + 120 = 180. Then the value of the variable 'x' will be 18. Then the correct option is A.
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HELP ME ASAP!
(6.15x+0.24y)÷1.5+5.9x−1.6y
simplify it!
The simplification of the equation (6.15x + 0.24y / 1.5) + 5.9x - 1.6y is 10x - 2.16y/1.5
How to simplify equation?(6.15x + 0.24y / 1.5) + 5.9x - 1.6y
= 6.15x + 0.24y + 1.5(5.9x - 1.6y) / 1.5
= (6.15x + 0.24y + 8.85x - 2.4y) / 1.5
= (6.15x + 8.85x + 0.24y - 2.4y) / 1.5
= (15x - 2.16y) / 1.5
= 10x - 2.16y/1.5
Therefore, the answer to the equation is 10x - 2.16y/1.5
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Find the x-intercept of the graph of the linear equation y=-1/2x+3
Answer:
x = 6
Step-by-step explanation:
To find the x- intercept let y = 0, that is
- [tex]\frac{1}{2}[/tex] x + 3 = 0 ( subtract 3 from both sides )
- [tex]\frac{1}{2}[/tex] x = - 3 ( multiply both sides by - 2 )
x = 6 ← value of x- intercept
Answer:
6
Step-by-step explanation:
got it right on edge
A university conducted a study and determined that a college student walks an average of 2.4 miles a day and a college graduate walks an average of 1.8 miles per day. Which of the following is the best way to represent this data? -using a bar graph where one bar has a length of 2.4 and one bar has a length of 1.8 -using a cube with a side length of 2.4 and a cube with a side length of 1.8 -using a pie chart with one section labeled 1.8 and one section label 2.4 -using a square with a side length of 2.4 and a square with a side length of 1.8
Answer:
Using a bar graph where one bar has a length of 2.4 and one bar has a length of 1.8
Step-by-step explanation:
You use a bar graph to compare things between different groups, so it is the most appropriate one to use.
You use a pie chart to compare parts of a whole, so it would not be appropriate.
The graph should represent the relative sizes of the two values (24:18 or 1.33:1). Using a square or a cube would distort the relationship. The relative area of the squares would be 1.77:1 and that of the cubes would be 2.37:1.
Charts are used to represent data graphically.
The best way to represent the data is (a) using a bar graph where one bar has a length of 2.4 and one bar has a length of 1.8
The given parameters are:
[tex]\mathbf{Student = 2.4}[/tex]
[tex]\mathbf{Graduate = 1.8}[/tex]
Both data elements, are for different people.
So, it is best to use a bar chart.
Using a pie chart will imply that, the data elements are part of a whole data for a particular person.
Squares and cubes cannot be used at all.
Hence, the correct option is (a).
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Round 3.75 to the tenths place
Answer:3.8
Step-by-step explanation: 5 or up you round up so you round up so it is 3.8
Answer:
3.8
Step-by-step explanation:
if the hundredth place is 5 or greater then turn the tenth place to 8 so 3.8
Please help me with this. TWO LINES MEET AT A POINT THAT IS ALSO THE ENDPOINT OF TWO RAY'S. SET UP AND SOLVE THE APPROPRIATE EQUATIONS FOR m AND N.
Answer:
m=47, n=52
Step-by-step explanation:
m is equal to 90-43 since 43+m is a right angle (straight angle 180 is composed of two right angles). n is equal to 90-38. If you solve of the missing angle not given a variable, you find n as well because opposite angles are congruent and have the same measure.
what is the value of s4
ANSWER
[tex]S_4 = \frac{208}{375} [/tex]
EXPLANATION
The given series is:
[tex]\sum_{n=1}^{\infty} \frac{2}{3} ( - { \frac{1}{5} })^{n - 1} [/tex]
When n=1, the first term is
[tex]a = \frac{2}{3} [/tex]
The sum of terms of a geometric sequence is given by the formula;
[tex]S_n = \frac{a {(1 - {r}^{n} )} }{1 - r} [/tex]
The sum of the first 4 terms is:
[tex]S_4= \frac{ \frac{2}{3} {(1 - { ( - \frac{1}{5} )}^{4} )} }{1 - - \frac{1}{5} } [/tex]
[tex]S_4 = \frac{208}{375} [/tex]
The value for S4 is represented by the third option, [tex]\frac{208}{375}[/tex] .
Geometric SequencesYou can define a geometric sequence when you have a common ratio between the numbers of a sequence. This common ratio can be found when you multiply or divide the previous term by the next term of the sequence and you find the same value. The formula for geometric sequences is:
[tex]a_n=a_1*r^{n-1}[/tex], where:
[tex]a_n[/tex]=[tex]n^{th}[/tex] term
[tex]a_1[/tex]= the first term
Example
2, 4,8, 16, ....
Here, you have:
[tex]a_1[/tex]= 2
[tex]r=\frac{a_2}{a_1}=\frac{a_3}{a_2}=2[/tex] , then: 2 x 2= 4; 4 x 2=8; 8 x 2=16 - Note that the numbers represent the example sequence.
For solving this exercise also it is necessary to apply the formula for the geometric sequence for finite terms since the question asks [tex]S_4[/tex], in the other words, the sum for n=4. Thus,[tex]S_n=\frac{a_1*(1-r^n)}{1-r}[/tex].
For the given series, when n=4, you have
[tex]\frac{2}{3} *(\frac{-1}{5})^{n-4} \\ \\ \frac{2}{3} *(\frac{-1}{5})^{4-4}\\ \\ \frac{2}{3} *(\frac{-1}{5})^{0}\\ \\ \frac{2}{3} *1=\frac{2}{3}[/tex]
Therefore, [tex]a_1=\frac{2}{3}[/tex].
Now, you will find S4 from the formula for the geometric sequence for finite terms
[tex]S_n=\frac{a_1*(1-r^n)}{1-r}\\ \\ =\frac{\frac{2}{3}\cdot \left(1-\left(-\frac{1}{5}\right)^4\right)}{1-\left(-\frac{1}{5}\right)}\\ \\ \frac{\frac{2}{3}\left(1-\left(-\frac{1}{5}\right)^4\right)}{1+\frac{1}{5}}=\frac{\frac{416}{625}}{\frac{6}{5}}=\frac{416\cdot \:5}{625\cdot \:6}=\frac{208}{375}[/tex]
Read more about geometric sequences here:
https://brainly.com/question/26147596
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