Find the sum of the following infinite geometric series.

Find The Sum Of The Following Infinite Geometric Series.

Answers

Answer 1

Answer:

Final answer is [tex]\frac{80}{3}[/tex].

Step-by-step explanation:

We have been given an infinite geometric series.

Now we need to find it's sum.

common ratio [tex]r=-\frac{1}{5}[/tex].

plug n=1 to get the first term

[tex]a_n=32\left(-\frac{1}{5}\right)^{\left(n-1\right)}[/tex]

[tex]a_1=32\left(-\frac{1}{5}\right)^{\left(1-1\right)}[/tex]

[tex]a_1=32\left(-\frac{1}{5}\right)^{\left(0\right)}[/tex]

[tex]a_1=32\left(1\right)[/tex]

[tex]a_1=32[/tex]

Now plug these values into infinite sum formula

[tex]S_{\infty}=\frac{a_1}{1-r}=\frac{32}{1-\left(-\frac{1}{5}\right)}=\frac{32}{1.2}=\frac{320}{12}=\frac{80}{3}[/tex]

Hence final answer is [tex]\frac{80}{3}[/tex].

Answer 2

The sum of the infinite geometric series given in the problem is 26.6

7.

A geometric series is a sequence of terms in which each term is obtained by multiplying the previous term by a constant ratio. It is a specific type of series where the terms follow a geometric progression.

Formally, a geometric series is expressed as:

a, ar, a[tex]r^2[/tex], a[tex]r^3[/tex], ...

To solve the geometric series sum of the form:

S = a + ar + a[tex]r^2[/tex] + a[tex]r^3[/tex] + ...,

where a is the first term and r is the common ratio, we can use the formula for the sum of an infinite geometric series:

S = [tex]\frac{a}{1 - r}[/tex].

In this case, the given series is:

S = 32[tex]\times \frac{-1}{5}^(^n^ -^ 1^)[/tex],

Comparing this to the standard geometric series form, we can identify that the first term a is 32, and the common ratio r is [tex]\frac{-1}{5}[/tex].

Substituting these values into the formula, we get:

S =  32[tex]\times \frac{-1}{5}^(^n^ -^ 1^)[/tex],

S = [tex]\frac{32}{(1 +\frac{1}{5})}[/tex],

S = [tex]\frac{32}{\frac{6}{5} }[/tex],

S = 32 [tex]\times \frac{5}{6}[/tex],

S = [tex]\frac{160}{6}[/tex]

S = [tex]\frac{80}{3}[/tex] = 26.67.

Therefore, the sum of the given geometric series is 80/3 or approximately 26.67.

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Related Questions

a computers value declines about 7% yearly. sally bought a computer for $800 in 2005. How much is it worth in 2009?

Answers

Final answer:

The computer is worth approximately $599.83 in 2009.

Explanation:

To find out how much the computer is worth in 2009, we need to determine the value after each year's decline. The computer's value declines by 7% each year, so we can calculate the worth of the computer in 2009 by multiplying the original value by (1 - 0.07) four times since there are four years between 2005 and 2009.

Year 1: $800 * (1 - 0.07) = $800 * 0.93 = $744

Year 2: $744 * (1 - 0.07) = $744 * 0.93 = $692.64

Year 3: $692.64 * (1 - 0.07) = $692.64 * 0.93 = $644.86

Year 4 (2009): $644.86 * (1 - 0.07) = $644.86 * 0.93 = $599.83

Therefore, the computer is worth approximately $599.83 in 2009.

Final answer:

To find the value of a computer in 2009 that Sally bought for $800 in 2005 with a 7% annual decline, we use the exponential decay formula. The computer would be worth approximately $598.48 in 2009.

Explanation:

The question asks to calculate the value of a computer after a specific period of time, considering a yearly depreciation. Sally bought a computer for $800 in 2005, and its value declines by 7% yearly. To find its value in 2009, we can use the formula for exponential decay:

Value = Initial Value × [tex](1 - Decline \ Rate)^{Years}[/tex]

Plugging in the values:

Value = $800 × [tex](1 - 0.07)^4[/tex]

Value = $800 ×  [tex](0.93)^4[/tex]

Value = $800 × 0.7481

Value = $598.48

Therefore, the value of the computer in 2009 is approximately $598.48.

Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer.​

Answers

First make a table of values of the function’s coordinates, and try to avoid coordinates that include decimals.

Second, find the first differences from the table you constructed. ( it should be 1)

There should be a 2 point gap in the x column if you chose the points (2,-4)(4,-3)(6,-2) (8,-2) and that is your denominator

Last, the y intercept (-5) is your b variable (y=mx +b)

The equation is

Y= x/2 -5

Sorry about my English

John, Rick, and Molli can paint a room working together in 6 hours. Alone, John can paint the room in
12 hours. If Rick works alone, he can paint the room in 15 hours. Write an equation comparing the
group rate to the sum of the individual rates. Then find how long it will take Molli to paint the room if
working alone.

a. What is the equation?

b. What is the lowest common denominator for the equation in part a?

c. Show all work below in solving equation from part a.

Answers

Answer

a. [tex]\frac{1}{m}(6)+\frac{1}{12} (6)+\frac{1}{15} (6) =1[/tex]

b. 60hrs

Step-by-step explanation:

Let the time Molli will take to pint the room to be = t

Thus the amount of room that Molli can paint in 1 hour= 1/m

The amount of room John can paint is 1 hour= 1/12

The amount of room Rick can paint in 1 hour = 1/15

The equation for working together at a rate x time per work done will be;

[tex]\frac{1}{m} *6+\frac{1}{12} *6+\frac{1}{15} *6=1[/tex]

You multiply by 6 in the three terms of the equation because it takes 6 hours for John, Rick and Molli to complete painting.

[tex]\frac{6}{m} +\frac{1}{2} +\frac{2}{5} =1[/tex]

multiply by 10m in every part of the expression because 10m is the Least Common Multiple(LCM) is this case

Collect like terms and find value of m

[tex]60+5m+4m=10m\\\\60+9m=10m\\\\60=10m-9m\\\\60=m[/tex]

Molli will take 60 hours to paint the room if working alone

Given the quadratic function g(x)=x^2, find g(3x-2).

Answers

Answer:

[tex]g(3x-2) = (3x-2)^{2}[/tex]

Step-by-step explanation:

[tex]g(x)=x^{2}[/tex]

To do this, you must substitute [tex]3x-2[/tex] for x in the equation g(x)

[tex]g(3x-2) = (3x-2)^{2}[/tex]

Simplified this would be

[tex]9x^{2} -12x+4[/tex]

What is the function rule for the following situation? Rex paid $20 for a membership to the pool and pays $300 each time he goes to the pool.
y = 20x + 3
20 = 3x + y
y = x + 20
none of these

Answers

The function rule for the situation is none of the given options

What is the function rule for the situation

From the question, we have the following parameters that can be used in our computation:

Membership = $20

Payment each time = $300 per visit

using the above as a guide, we have the following:

f(x) = Membership + Payment each time * x

substitute the known values in the above equation, so, we have the following representation

f(x) = 20 + 300* x

Evaluate

f(x) = 20 + 300x

Hence, the expression is f(x) = 20 + 300x

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none of the given options

None of the provided options in the question are correct.

The function rule that correctly represents Rex's situation, given that he paid a $20 membership fee and pays $300 each time he goes to the pool, would be a linear equation that includes a one-time fee (membership) and a per-visit cost. Let's define x as the number of times Rex goes to the pool and y as the total cost. Therefore, the equation should include the initial membership fee and the per-visit cost multiplied by the number of visits.

The correct function rule is y = 20 + 300x, where 20 represents the one-time membership fee and 300 represents the cost per pool visit. None of the provided options are correct. The equation signifies that for every visit to the pool, the total cost increases by $300, and the initial membership cost is $20.

Please help me! Its for my big test tomorrow!

Answers

QUESTION 11

Given : [tex]\ln(3x-8)=\ln(x+6)[/tex]

We take antilogarithm of both sides to get:

[tex]3x-8=x+6[/tex]

Group similar terms to get:

[tex]3x-x=6+8[/tex]

Simplify both sides to get:

[tex]2x=14[/tex]

Divide both sides by 2 to obtain:

[tex]x=7[/tex]

12.  Given; [tex]\log_3(9x-2)=\log_3(4x+3)[/tex]

We take antilogarithm to obtain:

[tex](9x-2)=(4x+3)[/tex]

Group similar terms to get:

[tex]9x-4x=3+2[/tex]

[tex]5x=5[/tex]

We divide both sides by 5 to get:

[tex]x=1[/tex]

13.  [tex]\log(4x+1)=\log25[/tex]

We take antilogarithm to get:

[tex](4x+1)=25[/tex]

Group similar terms

[tex]4x=25-1[/tex]

[tex]4x=24[/tex]

Divide both sides by 4

[tex]x=6[/tex]

14. Given ; [tex]\log_6(5x+4)=2[/tex]

We take antilogarithm to get:

[tex](5x+4)=6^2[/tex]

Simplify:

[tex](5x+4)=36[/tex]

[tex]5x=36-4[/tex]

[tex]5x=32[/tex]

Divide both sides by 5

[tex]x=\frac{32}{5}[/tex]

Or

[tex]x=6\frac{2}{5}[/tex]

15. Given: [tex]\log(10x-7)=3[/tex]

We rewrite in the exponential form to get:

[tex](10x-7)=10^3[/tex]

[tex](10x-7)=1000[/tex]

[tex]10x=1000+7[/tex]

[tex]10x=1007[/tex]

Divide both sides by 10

[tex]x=\frac{1007}{10}[/tex]

16. Given:   [tex]\log_3(4x+2)=\log_3(6x)[/tex]

We take antilogarithm to obtain:

[tex](4x+2)=(6x)[/tex]

[tex]2=6x-4x[/tex]

Simplify

[tex]2=2x[/tex]

Divide both sides by 2

[tex]1=x[/tex]

17. Given [tex]\log_2(3x+12)=4[/tex].

We rewrite in exponential form:

[tex](3x+12)=2^4[/tex]

[tex](3x+12)=16[/tex]

[tex]3x=16-12[/tex]

[tex]3x=4[/tex]

Divide both sides by 3

[tex]x=\frac{4}{3}[/tex]

18. Given [tex]\log_3(3x+7)=\log_3(10x)[/tex]

We take antilogarithm to get:

[tex](3x+7)=(10x)[/tex]

Group similar terms:

[tex]7=10x-3x[/tex]

[tex]7=7x[/tex]

We divide both sides by 7

[tex]x=1[/tex]

19.  Given: [tex]\log_2x+\log_2(x-3)=2[/tex]

Apply the product rule to simplify the left hand side

[tex]\log_2x(x-3)=2[/tex]

We take antilogarithm to obtain:

[tex]x(x-3)=2^2[/tex]

[tex]x^2-3x=4[/tex]

[tex]x^2-3x-4=0[/tex]

[tex](x-4)(x+1)=0[/tex]

x=-1 or x=4

But x>0, therefore x=4

20. Given  [tex]\ln x+ \ln (x+4)=3[/tex]

Apply product rule to the LHS

[tex]\ln x(x+4)=3[/tex]

Rewrite in the exponential form to get:

[tex]x(x+4)=e^3[/tex]

[tex]x^2+4x=e^3[/tex]

[tex]x^2+4x-e^3=0[/tex]

This implies that:

[tex]x=-6.91[/tex] or [tex]x=2.91[/tex]

Find the diameter of a circle with an area of
95.03 square feet.

Answers

For this case we have that the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle

By clearing the radio we have:

[tex]r = \pm \sqrt {\frac {A} {\pi}}[/tex]

We take the positive value:

[tex]r = \sqrt {\frac {A} {\pi}}\\r = \sqrt {\frac {95.03} {\pi}}\\r = 5.50 \ ft[/tex]

The diameter is twice the radius:

[tex]d = 11[/tex]

Answer:

[tex]11 \ ft[/tex]

Answer:

11 feet

Step-by-step explanation:

We are given the area of a circle and we are to find the diameter of this circle.

We know that the area of a circle is given by [tex]\pi r^2[/tex] so equating its given value to get:

[tex]\pi \times r^2 = 95.03[/tex]

[tex] r ^ 2 = \frac {95.03} {\pi } [/tex] [tex] r = \sqrt {30.25} [/tex]

[tex] r = 5 . 5 [/tex]

Therefore, our required diameter will be [tex]5.5 \times 2[/tex] = 11 feet

you can only move forward 5 and backward 2 and 6. If you start at 2 and want to get to 24, what's the least possible number of moves you need.

Answers

Answer:

9

Step-by-step explanation:

2-2+5+5+5+5+5+5-6

the answer is 9. ——-

Ivan and Tanya share £150 in the ration 4 : 1
work out how much more Ivan gets compared to Tanya.

Answers

Add the ratio to get total shares: 4 +1 = 5

Divide the total amount to share by the total shares:

150 / 5 = 30

Now multiply each set of shares by that:

4 x 30 = 120

1 x 30 = 30

120-30 = 90 more

Where is the Great Barrier Reef located?

Answers

Answer:

The Great Barrier Reef is located in Australia.

The Great Barrier Reef is located off the northeastern coast of Australia.

It stretches for approximately 1,600 miles and is home to a diverse range of sea creatures and fish, attracting millions of tourists, scuba divers, and water enthusiasts each year.

This natural wonder is a significant tourist attraction and plays an important role in the Australian economy.

Additionally, the Great Barrier Reef has been designated as a United Nations World Heritage Site due to its ecological importance.

help me with this please ​

Answers

It’s the fourth one

Answer:

None of these

Step-by-step explanation:

This is because the answer can't have anything to do with perpendicular because you don't know if any of the angles are 90 degrees (and honestly none of them look right anyways... pun intended) and the only answer that isn't perpendicular is wrong because the lines are intersececting.

Given: x - 8 > -3.

Choose the solution set.

1.{x | x R, x > -9}
2.{x | x R, x > -5}
3.{x | x R, x > 5}
4.{x | x R, x > 14}

Answers

Answer:

x-8>-3 {x|R, x>5 is right answer

For this case we must find the solutions of the following inequality:

[tex]x-8> -3[/tex]

Adding 8 to both sides of the inequality we have:

[tex]x> -3 + 8\\x> 5[/tex]

Thus, the solutions of the variable "x" are given by all the real numbers greater than 5.

Answer:

Option C

Travis traveled a total distance of 3 1/2miles. He rode the bus 1 1/4mile.He walked 2/3 mile.He rode in a car the remainder of the 3 1/2 miles. How far in miles did he ride in a car?

Answers

Answer: 1  5/12

Step-by-step explanation: You need to find a common denominator 3 and 4 are the denominators you can do 3 times 4 is 12 and 4 times 3 is 12, but whatever you do to the denominator needs to be done to the numerator so 2 times 4 is 8 and 1 times 4 is 4 then you have the fractions 8/12 and 3/12 then you just subtract and you get 1  5/12.

*Hard to explain*

How many cubes with side lengths of 1/3 to fill the prism

I dont have the image yet but here are the numbers in the problem


1 Cm, 2 2/3 Cm, 2/3 Cm
I will mark brainliest, dont delete my problem

Answers

I believe I am correct.

Multiply the side values together to get the volume of the prism.

1 x 2 2/3x 2/3 = 1.7(repeating)

Then divide 1.7(repeating) by 1/3 and you end up with 5 1/3.

Hope this helps!

Simplify (2z^5)(12z^3)/4z^4

Answers

Answer:

[tex]6z^{4}[/tex]

Step-by-step explanation:

Given in the question an expression,

[tex]\frac{ (2z^5)(12z^3)}{4z^4}[/tex]

Step 1

Apply exponential "product rule"

[tex]x^{m}x^{n}=x^{m+n}[/tex]

[tex]\frac{ 12(2)z^5)(z^3)}{4z^4}[/tex]

[tex]\frac{ (24)z^5)(z^3)}{4z^4}[/tex]

[tex]\frac{ 24(z^{(5+3)})}{4z^4}[/tex]

[tex]\frac{ 24(z^{8})}{4z^4}[/tex]

Step 2

Apply exponential " divide rule"

[tex]\frac{x^{m}}{x^{n}}=x^{m-n}[/tex]

[tex]\frac{24/4(z^{8})}{z^4}[/tex]

[tex]\frac{6(z^{8})}{z^4}[/tex]

[tex]\frac{6(z^{8-4})}{1}[/tex]

[tex]6z^{4}[/tex]

7. What is the interquartile range for the data set?
37, 4, 53, 79, 25, 48, 78, 65, 5, 6, 42, 61.
please show how you the answer.

8. What is the standard deviation for the data set?
112, 149, 112, 148, 139, 121, 116, 134, 148.
Express your answer as a decimal to the nearest tenth.
please show how you got the answer

Answers

The given data set is:

37, 4, 53, 79, 25, 48, 78, 65, 5, 6, 42, 61

We arrange the data set in ascending order of magnitude {4,5,6,25,37,42,48,53,61,65,78,79}

The median is 45.

The lower half of the data set is

{4,5,6,25,37,42}

The first quartile is the median of the lower half set;

[tex]Q_1=15.5[/tex]

The upper half of the data set is:

{48,53,61,65,78,79}

The median of the upper half is [tex]Q_3=63[/tex].

The inter-quartile range  [tex]Q_3-Q_1=63-15.5=47.5[/tex]

8. The given data set is 112, 149, 112, 148, 139, 121, 116, 134, 148.

The mean of the data set is [tex]\bar X =\frac{\sum x}{n}[/tex]

[tex]\bar X =\frac{112+149+112+148+139+121+116+134+148}{9}[/tex]

[tex]\bar X =\frac{179}{9}=131[/tex]

The standard deviation is given by:

[tex]s=\sqrt{\frac{\sum (x-\bar X)^2}{n} }[/tex]

[tex]s=\sqrt{\frac{(-19)^2+(18)^2+(-19)^2+(17)^2+(8)^2+(-10)^2+(-15)^2+(3)^2+(18)^2}{9} }[/tex]

[tex]s={\frac{\sqrt{2022}}{3}=14.98888477[/tex]

The standard deviation is 15.0 to the nearest tenth.

a civil engineer has laid a graph down over the stretch of a new road system. a circular rotary has a diamater with endpoints (-3,5) and (5,11) what are the center and raduis of the rotary

Answers

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{11}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{5-3}{2}~~,~~\cfrac{11+5}{2} \right)\implies \left(\cfrac{2}{2}~,~ \cfrac{16}{2}\right)\implies \stackrel{center}{(1,8)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{endpoint}{(\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})}\qquad \stackrel{center}{(\stackrel{x_2}{1}~,~\stackrel{y_2}{8})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[1-(-3)]^2+[8-5]^2}\implies r=\sqrt{(1+3)^2+(8-5)^2} \\\\\\ r=\sqrt{16+9}\implies r=\sqrt{25}\implies r=5[/tex]

Do the midpoint formula. Which will give you (1,8)

Rewrite the expression using the distributive property.

8(4x+6y-2z)

A. 12x + 14y - 6z
B. -4x + -2y - 10z
C. 32x + 48y - 16z
D. 0.5x + 0.75y - 0.25z

Answers

Answer:

32x + 48y - 16z

Step-by-step explanation:

SOME ONE PLZ HELP): I need help on my apex y’all

Answers

Answer:

[tex]\large\boxed{A.\ 2^0}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m}:\\\\\dfrac{2^6}{2^6}=2^{6-6}=2^0=1[/tex]

John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33o . How tall is the tree?

Answers

Answer:

3300

Step-by-step explanation:

100 * 33

Use the substitution method to find the solution to the system of linear equations.

Answers

Answer: answer is d

Step-by-step explanation: input in calculator or set both equal to y and then set them equal to each other

-17 + n/5 = 33. solve this please

Answers

For this case we must solve the following equation:

[tex]-17+ \frac {n} {5} = 33[/tex]

Adding 17 to both sides of the equation we have:

[tex]\frac {n} {5} = 33 + 17\\\frac {n} {5} = 50[/tex]

Multiplying by 5 on both sides of the equation:

[tex]n = 50 * 5\\n = 250[/tex]

Thus, the value of n is 250

ANswer:

[tex]n = 250[/tex]

The solution to the equation -17 + n/5 = 33 is n = 250.

We have,

To solve the equation, we can start by isolating the variable term.

Here's the step-by-step solution:

-17 + n/5 = 33

First, let's get rid of the constant term (-17) by adding 17 to both sides of the equation:

-17 + 17 + n/5 = 33 + 17

Simplifying, we have:

n/5 = 50

To isolate n, we can multiply both sides of the equation by 5:

5 * (n/5) = 5 * 50

This simplifies to:

n = 250

Therefore,

The solution to the equation -17 + n/5 = 33 is n = 250.

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15. The temperature C, in degrees, that is equivalent to a temperature of F degrees Fahrenheit is given by graph of this equation shows the temperature in Celsius for the corresponding temperatures in Fahrenheit.
a. Explain how linear equations can be used in temperature conversion.
b. Explain how could you could use the conversion graph to find the normal body temperature in degrees Celsius, which is 98.6°F.

Answers

Answer:

A. How can the equation be used in temperature conversion?

You take the conversion equation C = (5/9) (F - 32) and you replace the F by the value of Fahrenheit degrees...  then solve the calculations to get the degrees in Celsius.

For example, if you have 80°F to convert in °C:

C = (5/9) (80 - 32) = (5/9) (48) = 26.66 °C

B. How can you use the graph to find the body temp in C?

Using the graph will give a very imprecise measure due the scale of the graph.

But you would have to find 98.6 on the axis of X (it represents the °F), then go upwards until you find the line....

Then report that position on the line on the Y-axis (representing the °C) to get your measure.

Answer:

For A: The linear equation is [tex]C=\frac{5}{9}F-\frac{32}{9}[/tex]

For B: The temperature of normal body in degree Celsius is 37° C.

Explanation:

For A:

Linear equations are defined as the equations in which the highest power of a variable is '1'. The general equation for a linear equation is:

[tex]y=mx+c[/tex]

where,

y = Y-coordinate

m = slope of the line

x = X - coordinate

c = intercept on y-axis

For the given equation:

[tex]C=\frac{5}{9}(F-32)[/tex]

The linear equation representation for the given equation is:

[tex]C=\frac{5}{9}F-\frac{32}{9}[/tex]

For B:

We are given a value of temperature in degree Fahrenheit. To calculate its value in degree Celsius, we use the equation above.

Putting value of F = 98.6 in above equation, we get:

[tex]C=(\frac{5}{9}\times 98.6)-\frac{32}{9}\\\\C=37[/tex]

Hence, the temperature of normal body in degree Celsius is 37° C.

I need help please!!!!??

Answers

Check the picture below.

On the Y axis. The first number is on the X axis and the other is on the Y

I am a two dimensional shape that has less than 4 sides. All of my sides are straight. What shape am I.

Answers

Final answer:

A two-dimensional shape with less than four sides and all straight sides is a triangle. Triangles are basic geometric shapes with three edges and three vertices.

Explanation:

If you are a two-dimensional shape with less than four sides and all your sides are straight, the shape you are describing is a triangle. A triangle is a simple polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with all three sides of equal length is an equilateral triangle, if only two sides are equal it's called an isosceles triangle, and if all sides are of different lengths, it is called a scalene triangle.

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The president of a certain University receives a salary that is three times the salary of one of the department heads the total of the two salaries is 190000 what is the salary of the president of the University

Answers

Answer:

$142500

Step-by-step explanation:

We are given that the resident of a certain University receives a salary that is three times the salary of one of the department heads.

If the sum of the two salaries is $190000, we are to find the salary of the president of the University.

Let [tex]x[/tex] to be the department head's salary, we can write an equation:

[tex]3x+x=190000[/tex]

[tex]4x=190000[/tex]

[tex]x=47500[/tex]

Salary of the president of the University = [tex]3(47500)[/tex] = $142500

Answer:

$142,500

Step-by-step explanation:

Let's say x is the salary of the department head.... so the salary of the president of the university can be described as 3x.

Then, we know the total of the two salaries is 190,000.  We can express this as:

3x + x = 190,000

4x = 190,000

x = 47,500

x is for the department head.  To get the president's salary, we have to multiply that by 3:

p = 3 (47,500) = 142,500

The salary of the president is then of $142,500.

What is the volume of the prism that can be constructed from this net?

184 units³

120 units³

124 units³

64 units³

Answers

Check the picture below.

so the net once folded up, will look more or less like the box there on the bottom-right.

Length = 2, Width = 10, Height = 6.

volume is then 2*10*6 = 120.

Answer:10,126,272 units

Step-by-step explanation:

184*184*184=6,229,504

120*120*120=1,728,000

124*124*124=1,906,624

64*64*64=262,144

6,229,504+1,728,000+1,906,624+262,144=10,126,272

In a population of 300 pigeons, 55% are female. If 40% of the male pigeons are not white, how many male pigeons are white? 135 180 81

Answers

Answer:

81

Step-by-step explanation:

Assuming the pigeons are either male or female, the 45% of them that are not female are male. Of those, there are 40% that are not white, so 60% are white. Then the number of white male pigeons is ...

60% of 45% of 300 = 0.60 · 0.45 · 300 = 81

The figure is made up of a cylinder, a cone, and a half sphere. The radius of the half sphere is 3 inches. What is the volume of the composite figure?

Answers

Given.

Radius of the Half sphere is 3 inches.

From the figure;

Radius of half sphere= Radius of cylinder= Radius of cone=3inches

Height of cone= 4inches.

Height of cylinder=6inches.

Volume of cone=(πr²h)/3

=(π3²×4)/3

=(12π) inch³

volume of cylinder= πr²h=π3²6=54π inch³

Volume of half sphere= (4/3) π r³=π(4×3³)/3 (1/2)=π×4×9/2=18π inch³

Total area of Composite figure=(12π +54π +18π) inch³

=84π inch³

=(84)× 22/7inch³

=12×22 inch³

=264inch³

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

The volume of the composite figure is 84π ≅ 263.89 inches³

Step-by-step explanation:

Lets revise the rules of the volume of some figures

- The composite figure consists of :

# Half sphere with radius 3 inches

# Cylinder with radius 3 inches and height 6 inches

# Cone with radius 3 inches and height 4 inches

- The volume of the sphere is 4/3 π r³

∴ The volume of the half sphere = 1/2 × 4/3 π r³ = 2/3 π r³

- The volume of the cylinder is π r² h

- The volume of the cone is 1/3 π r² h

* Now lets solve the problem

- The volume of the half sphere

∵ The radius of the half sphere = 3 inches

∵ The volume of it = 2/3 π r³

∴ The volume = 2/3 × π × (3)³ = 18π inches³

- The volume of the cylinder

∵ The radius of the cylinder = 3 inches

∵ The height of the cylinder = 6 inches

∵ The volume of it = π r² h

∴ Its volume = π × (3)² × 6 = 54π inches³

- The volume of the cone

∵ The radius of the cone = 3 inches

∵ The height of the cone = 4 inches

∵ The volume of it = 1/3 π r² h

∴ Its volume = 1/3 π × (3)² × 4 = 12π inches³

- Add all the volumes to find the volume of the composite figure

∴ The volume = 18π + 54π + 12π = 84π = 263.89 inches³

* The volume of the composite figure is 84π ≅ 263.89 inches³

given that ABCDEF = PQRSTU , solve for z

Answers

the answer is z=7 (as 3z-4=17)

Answer:

A. 5

Step-by-step explanation:

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