Find the sum of a finite geometric series. A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height. The total vertical distance down the ball has traveled when it hits the ground the fifth time is meters.

Answers

Answer 1

Answer:

19.375 m.

Step-by-step explanation:

Before the first bounce it has travelled 10 meters.

Then after just hitting the ground the second time it has travelled 10 +1/2(10) = 15 m.

The common ratio is 0.5 and we want the sum of  5 terms

= a1  (1 - r^n) / (1 - r)

= 10 * (1 - 0.5^5) / (1 - 0.5)

= 19.375 m.


Related Questions

Confidence Interval: What is the 95% confidence interval to estimate the population mean?

Answers

Answer: The 95% confidence interval  to estimate the population mean describes a range of values that a person can be 95% sure that it contains the population mean.

Step-by-step explanation:

A 95% confidence interval for population mean ([tex]\mu[/tex]) is an interval on which a person can be 95% confident that the true population mean lies in it.

i.e. The probability that it contains the true population mean is 95%.

i.e. P( Sample mean- margin of error < [tex]\mu[/tex] < Sample mean + margin of error) = 0.95.

Explain whether the function g(x) = x^9 + x^5 is borh an even function and an odd function.

A. The function g is both an odd and even function because it is a polynomial that passed through the origin
B. Although the function g is an odd function, it is not an even function because g(x) does not equal g(-x) for all x in the domain of the function.
C. Although the function g is not an even function, it is not an odd function because g(-x) does not equal -g(x) for all x in the domain of the function
D. The function g is neither an even nor odd function. The value of g(x) does not equal g(-x) for all x in the domain of the function, and g(-x) does not equal -g(x) for all x in the domain of the function.

Answers

Answer:

The answer is B

..........

Need helpppppppppp! Show work plz

Answers

Answer:

9/169

Step-by-step explanation:

JQK of 4 suits = 12 cards

12/52x12/52=

3/13x3/13=

9/169

Write a rational number in fraction form that is equivalent to -1/5

Answers

Answer & Step-by-step explanation:

You can find a rational fraction equivalent to [tex]-\frac{1}{5}[/tex]  by multiplying the numerator and denominator by the same number. The number can be any:

[tex]-\frac{1}{5} *3\\\\-\frac{1}{5}*\frac{3}{3}=-\frac{3}{15}[/tex]

This works because if you simplify the new number, it will have the same value as the first fraction.

If you simplify both fractions to a decimal value, they both equal -0.2.

Abox contains cards that are numbered from 1 to 100. What is the probability of randomly selecting a number
that is less than 12?

Answers

Answer:

11/100,      0.11,      or 11%

Step-by-step explanation:

Answer: 11/100

Explanation:

There are 11 numbers that are less than 12 from 1-11

Which mean there are 11 possibilities of choosing a number less 12 from the 100 cards.

We can write that probability:

P = 11/100

Therefore, the probability of choosing a number less than 12 in a box of 100 cards is 11/100.

Assume a healthy heart beats exactly 70 times per minute. If an individual lives to age 85 years, estimate the number of heartbeats in his or her lifetime, using scientific notation.

Answers

Answer:

3.12732 × 10⁹ beats

Step-by-step explanation:

Given that, in 1 min, the heart of an individual makes 70 beats, the number of beats the heart of the healthy individual makes in 85 years can be calculated as follows:

1 yr = 365 days, therefore,

85yrs = 85*365 = 31,025 days

1 day = 24 hours

31,025 days = 31,025*24 = 744,600 hours.

1 hr = 60 mins

744,600 hours = 744,600*60 = 44,676,000 mins

This means the individual lived for 44,676,000 mins (85yrs)

If 70 beats are made in 1 min, therefore, in 85yrs, the individual will make:

44,676,000*70 = 3,127,320,000 beats = 3.12732 × 10⁹ beats in 85yrs

Triangle A B C is reflected across line m to form triangle A prime B prime C prime. Triangle A prime B prime C prime is rotated about point A prime to form triangle A prime B double-prime C double-prime What is the composition of transformations mapping △ABC to △A'B''C''? The first transformation is . The second transformation is . △ABC is △A'B'

Answers

Answer:

reflection across line mrotation about point A'

Step-by-step explanation:

The problem statement tells you exactly what the transformations are.

The first transformation is reflection across line m.

The second transformation is rotation about point A'.

_____

These are both rigid transformations, so ΔABC ≅ A'B''C''.

Answer:

Triangle A B C is reflected across line m to form triangle A prime B prime C prime. Triangle A prime B prime C prime is rotated about point A prime to form triangle A prime B double-prime C double-prime

What is the composition of transformations mapping △ABC to △A'B''C''?

The first transformation is

✔ a reflection across m

.

The second transformation is

✔ a rotation about A'

.

△ABC is

✔ congruent to

△A'B''C''.

Step-by-step explanation:

Ben can type 25 words in half a minute. At this rate, how many words can he type in 5 minutes?

A student found the unit rate and solved the problem. The student’s work is shown below. Has the student answered the question completely?

StartFraction 25 words over One-half minute EndFraction = StartFraction 50 words over 1 minute EndFraction
No, the student should have divided the unit rate by 5.
No, the student should have multiplied the unit rate by 10.
No, the student should have multiplied the unit rate by 5.
Yes, the student found how many words he can type in 5 minutes.

Answers

Answer:

CCCC!!!!!

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Suppose "35" cars start at a car race. In how many ways can the top 3 cars finish the​ race?

Answers

Answer:

Number of ways top 3 cars finish the​ race = 39,270

Step-by-step explanation:

Given:

Total number of cars = 35

Number of top cars = 3

Find:

Number of ways top 3 cars finish the​ race

Computation:

It is a permutation based problem.

So,

npr = n! / (n-r)!

35p3 = 35! / (35! - 3!)

35p3 = 35 ! / 32!

35p3 = 35 × 34 × 33

35p3 = 39,270

Number of ways top 3 cars finish the​ race = 39,270

Money received by an employee after deductions is called

Answers

Answer:

disposal earnings I think

Step-by-step explanation:

it is the legal deduction of money by the government I think

Estimate and then solve the equation x-17 4/5=13 1/5

Answers

Answer:

x=31

Step-by-step explanation:

Help me pls- I'll give u 55 points <3

Answers

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

So we have the expression:

[tex]39\div(2+1)-2\times(4+1)[/tex]

Recall the order of operations or PEMDAS:

P: Parentheses

E: Exponents

M/D: Multiplication and Division (Whichever First)

A/S: Addition and Subtraction (Whichever First)

Thus, first do the operations inside the parentheses:

[tex]39\div(2+1)-2\times(4+1)\\=39\div(3)-2\times(5)[/tex]

Now, do division and multiplication:

[tex]39\div(3)-2\times(5)\\=13-2\times5[/tex]

And the multiplication:

[tex]13-2\times5\\=13-10[/tex]

And finally, subtract:

[tex]13-10\\=3[/tex]

1. How many percent of 50 is 10? 2. 20 Is 60% of what number?

Answers

Answer:

1. 20%

2. [tex]33.\overline{33}[/tex]

Step-by-step explanation:

We can use percentage proportions to find out these answers.

For number one, 10 is what percent of 50, we already know our two values so we can make the equation:

[tex]\frac{10}{50} = \frac{x}{100}[/tex]

Using the cross products property, we know that x is [tex](100\cdot10)\div50[/tex] which is 20.

So 10 is 20% of 50.

For number two, we know a different pair of two numbers now: we know the percent of x, and the percent it is, so the equation can become:

[tex]\frac{20}{x} = \frac{60}{100}[/tex]

Again, cross products property tells us that x is [tex](100\cdot20)\div60[/tex], which is [tex]33.\overline{33}[/tex].

Hope this helped!

Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took
7 2/3 hours, what was the speed of the bus?

Answers

Answer:

66 miles per hour

Step-by-step explanation:

To find the speed, divide the distance by the amount of time:

506 ÷ 7 2/3

= 66

= 66 miles per hour

Answer:

66

Step-by-step explanation:

Notice that the problem is asking us to find the rate for Sean's trip. Since we are also given the distance he is traveling and the travel time, we should use the distance, rate, and time formula.

d=rt

where    d=distance  r=rate  t=time

We are given

d=506 mi

r=?

t=723=233 hr

Solving for rate and then substituting the given information into the distance, rate, time formula gives

r=dt=506233=5061⋅323=66

So Sean drove at a rate of 66 mph.

Write an equation in slope-intercept form for the line with slope -3 and y-Intercept -2.

Answers

Answer:

y = -3x - 2

Step-by-step explanation:

Step 1: State what is known

Slope = m = -3

y-intercept = b = -2

Step 2: Substitute information into y = mx + b

y = (-3)x + (-2)

y = -3x -2

Therefore the equation in slop intercept form is y=-3x-2

Answer:

y = -3x-2

Step-by-step explanation:

Replace m with -3, which is the  slope replace b with -2, = y-intercept into the equation y=mx+b.

[tex]m = -3\\y - intercept = -2\\Slope\: intercept \: form :\\y =mx+c\\y = -3x-2[/tex]

a) Is it reasonable to conclude that the weather or mechanical failures caused only about ​% of recent plane​ crashes?
A.
​Yes, because there is the possibility of overlap between the categories.
B.
​No, because there is no possibility for overlap between the categories.
C.
​Yes, because there is no possibility for overlap between the categories.
D.
​No, because there is the possibility of overlap between the categories.

Answers

Answer:

Yes, because there is no possibility for overlap between the categories.

the right triangular prism and the square rectangular prism both haven't had a 10 in in the same volume. A plane slices both solid parallel to their bases. The base of the triangular prism is a right triangle with legs 8 and 9 in Long. Find the length of the side of the square prism's cross-section in inches.​

Answers

Answer:  6 inches

Step-by-step explanation:

Volume (V) = Area of the base (B) × height (h)

Both images have the same volume and the same height, therefore the Area of their bases must be equal to each other.

Area of the triangle

[tex]A=\dfrac{1}{2}\cdot b \cdot h\\\\.\quad=\dfrac{1}{2}\cdot 8 \cdot 9\\\\.\quad= 36[/tex]

Area of a square

A = s²

36 = s²

6 = s


Write "six times 3 minus 3" as an expression.

Answers

Answer:

6(3)-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

6x(−3)

a group of biologists counted the number of birds in migration patterns. The number of birds in each ob observation, but some of the data were lost. Which expression models the number of birds in the nth observation? please help me

Answers

Answer:

56 + 6(n - 1)

Step-by-step explanation:

To know which of the equation represent the nth term, we simply test each equation to see the one that will satisfy the table given above.

This can be obtained as follow:

For 56 + 6(n - 1)

1. n = 2

56 + 6(n - 1) = 56 + 6(2 - 1)

= 56 + 6(1)

= 56 + 6

= 62

2. n = 5

56 + 6(n - 1) = 56 + 6(5 - 1)

= 56 + 6(4)

= 56 + 24

= 80

For 56 + 12(n - 1)

1. n = 2

56 + 12(n - 1) = 56 + 12(2 - 1)

= 56 + 12(1)

= 56 + 12

= 68

2. n = 5

56 + 12(n - 1) = 56 + 12(5 - 1)

= 56 + 12(4)

= 56 + 48

= 56 + 24

= 104

For 62 + 6(n - 1)

1. n = 2

62 + 6(n - 1) = 62 + 6(2 - 1)

= 62 + 6(1)

= 62 + 6

= 68

2. n = 5

62 + 6(n - 1) = 62 + 6(5 - 1)

= 62 + 6(4)

= 62 + 24

= 86

For 62 + 12(n - 1)

1. n = 2

62 + 12(n - 1) = 62 + 12(2 - 1)

= 62 + 12(1)

= 62 + 12

= 74

2. n = 5

62 + 12(n - 1) = 62 + 12(5 - 1)

= 62 + 12(4)

= 62 + 48

= 110

From the illustrations made above,

Only equation 56 + 6(n - 1) satisfied the table.

Therefore, the expression 56 + 6(n - 1) can be used to obtain the nth term.

Help me please thank you

Answers

Answer: x = 10

===========================================

Explanation:

The angles 4x and 3x+10 are corresponding angles. They are on the same side of the transversal cut (above the transversal) and to the right of each parallel line.

If the corresponding angles are congruent, then line A is parallel to line B.

4x = 3x+10

4x-3x = 10

x = 10

I need some help on this question. So, would <FET equal <FDT? or what would it equal... ​

Answers

Hi Hello.....How r u......

Answer: FET = DET

Explanation:

TE is angle bisector and it bisect FED into 2 equal angle (FET = DET)

A rectangle has a hight of 4x and a with of 3x+1
.Express the area of the entire rectangle. Expression should be expanded.

Answers

The area of the rectangle is 12x^2 + 4x.

y is directly proportional with x. Write an equation that shows the relationship if x=2 and y=6. A. y=3x B. 6y=2x C. y=13x D. 3y=x

Answers

Answer:

Hey there!

The relationship can be y=3x.

Let me know if this helps :)

How many pennies could you have if: When you break the pennies into groups of 2, you have 1 penny left over, AND when you break the pennies into groups of 3, you have 1 penny left over, AND when you break the pennies into groups of 5, you have 1 penny left over, AND when you break the pennies into groups of 7, you have NO pennies left over?

Answers

Answer:

91

Step-by-step explanation:

"When you break the pennies into groups of 2, you have 1 penny left over"

You have an odd number of pennies.

"when you break the pennies into groups of 3, you have 1 penny left over"

The number of pennies is one more than a multiple of 3.

"when you break the pennies into groups of 5, you have 1 penny left over"

A number that is divisible by 5 ends in 0 or 5. You have one more penny than that, so the number will end in 1 or 6. We already know the number is odd, so it cannot end in 6. The number of pennies must end in 1.

"when you break the pennies into groups of 7, you have NO pennies left over"

The number is a multiple of 7.

We need a multiple of 7 that ends in 1.

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, ...

You could have 91.

logx - logx-1^2=2log(x-1) what is the value of x​

Answers

Answer:

Step-by-step explanation:

[tex]logx -log(x-1)^2= 2 log(x-1)[/tex]

[tex]logx-2log(x-1) = 2log(x-1)[/tex]

[tex]logx=log(x-1)^4[/tex]

[tex]x=(x-1)^4[/tex]

[tex]x^4-4x^3+6x^2+1=0[/tex]

solve this equation

Help! Please! Geometry Question 9.​

Answers

Answer:

see below

Step-by-step explanation:

|AB| = | 2 - 5.25| = 3.25

The lines starts at 2 not at 1

NEED HELP PLZ!! Use the definition, identities, and properties of imaginary numbers to simplify each of the following expressions. Match each item with its correct simplest form. 1. (i 3)5 2. -i 6 · i 3 · i -5 3. -(i 4) (i 0) (i 7) 4. (i 5 · i -2 · i 8)0 Choices: 1 -1 i -i

Answers

Answer:

-i, -1, i, 1

I think the previous answer is arranged in the order of correct answers, if that make sense. For example, next to -i, you would put 1.

Also, are you a member of Calvert? Because this layout looks familiar.

The required expressions with their correct simplest form, follow as:

1. (i³)⁵ = - i

2. - i⁶·i³·i⁵ = - 1

3. - (i)⁴·i⁰·i⁷ = 1

4.  (i⁵·i²·i⁸)⁰= 1  

What is a complex number?

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib,

where a, and b are real numbers and i is an imaginary number.

The expressions are given in the question, as follows:

1. (i³)⁵

= (i)¹⁵

= (i²)⁷ × i

As we know that i² = -1, where i is an imaginary number.

= (-1)⁷ × i

= (-1 ) × i

= - i

Similarly, further expressions are solved below.

2. - i⁶·i³·i⁵

= i⁶·i³·i⁵

=  (i)¹⁴

=  (i²)⁷

=  (-1)⁷

=  (-1)

= - 1

3. - (i)⁴·i⁰·i⁷

= - (i)¹¹

= - (i²)⁵ × i

= - (-1)⁵ × i

= - (-1 ) × i

= - (- i)

= 1

4.  (i⁵·i²·i⁸)⁰

= ((i)¹⁵)⁰

= 1

Thus, the required expressions with their correct simplest form in the above solution part.

Learn more about the complex numbers here:

brainly.com/question/19007885

#SPJ5

NEED HELP ASAP!! Angles of Elevation and Despression! Need to find x!

Answers

Answer:

80.385

Step-by-step explanation:

It requires you to use trigonometry. First, ask yourself, which of the angle relationship (between sin, cos, tan) that includes the triangle's "x" and "300", from the angle 15°.

It's tan, because in this case, tan 15° = x / 300.

You then set x = 300 tan 15°, type it on calculator, and voila you get the answer.

Answer:

Hey there!

Tangent 15=x/300

Tangent 15(300)=x

x=80.4

Let me know if this helps :)

When Mount Saint Helens erupted in 1980, the top of the mountain was blown off. A surveyor determined the height of the new summit by measuring the angle of elevation to the top to be 37°46'. She then moved 1000 feet closer to the volcano and measured the angle of elevation to be 40°30'. Find in ft the new height of Mount Saint Helens.

Answers

Answer:

Height= 8341.6 feet

Step-by-step explanation:

A surveyor determined the height of the new summit by measuring the angle of elevation to the top to be 37°46'. She then moved 1000 feet closer to the volcano and measured the angle of elevation to be 40°30'.

40°30'= 40.5°

37°46'= 37.767°

b = 180-40.5

b= 139.5°

a= 180-139.5-37.767

a= 2.733°

Using sine method

1000/Sina= y/sinB

1000/sin 2.733= y/sin 139.5

(1000*sin 139.5)/sin 2.733= y

(1000*0.6494)/0.04768= y

13619.96= y

Y= 13620 feet

Height/sin 37.767= 13620

Height=13620*sin37.767

Height= 8341.59

Height= 8341.6 feet

Find the distance that (5, 1) is from the origin. Round to three decimal places.

Answers

Answer: Distance = 2.449

Step-by-step explanation:

Given that the distance that (5, 1) is from the origin. That is (0,0) to (5,1)

where

X1 = 0

X2 = 5

Y1 = 0

Y2 = 1

The distance from the origin to the point (5, 1) can be calculated by using the formulae

Substitute all the parameters into the formular

D = [tex]\sqrt{(X2-X1) + (Y2-Y1)}[/tex]

D = [tex]\sqrt{(5-0) + (1-0)}[/tex]

D = [tex]\sqrt{5 + 1}[/tex]

D = [tex]\sqrt{6}[/tex]

D = 2.44948

D = 2.449 ( Three decimal places)

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Write the ColorfulBouncingCircle class, where you should write the constructor, setPlayingFieldSize, and tick methods, and override the overlaps method, each according to the above descriptions. You should not have to write any code which draws; instead, a test program will be provided which will animate ColorfulBouncingCircles based on your implementation. For every time tick, the test program will compare every circle against every other circle using the overlaps method Ways in which Web sites can be unethical include:_________ a. gathering information about visitors without providing a clear privacy statement. b. using slick design strategies to make a quasi-scientific organization appear credible. c. creating a professional appearance by including links to more credible Web sites. d. B and C. e. A, B and C. The decision to take less salary in a year when the company was less profitable and employees' pay was cut is an example of Nishimatsu's: a.hubris. b.dialectic inquiry. cmitment. d.illusion of control. The tendency to adjust one's behavior, attitudes, or beliefs to group norms in response to real or imagined group pressure is called: Which statement correctly identifies the importance of symbolism in a literary work?A Symbolism informs the reader by offering an allknowing perspective.B Symbolism soothes the reader's ear with repetitive rhyming patterns.C Symbolism helps the author convey important themes to the reader.D symbolism uses "like" or "as" to make a comparison between two things. Find the slope of (3,-3) and (0,3) List at least three values that you think this archetype represents. In which situation is a are food service workers not required to wash their hands A) After using the bathroom B) after their shift C) after handling raw fruit D) after handling raw meet The final lines of the two poemso define the poet's beliefo explain the implied meaningO repeat the themeo summarize the action Please help 100 points please ASAP :((( How have you been able to personalize some of the Pharmacy laws to better understand them? Use the Venn diagram to list the set of elements of A B in roster form. A _______ is conducted to determine the adequacy of system controls, ensure compliance with established security policy and procedures, detect breaches in security services, and recommend any changes that are indicated for countermeasures. Discuss the importance of fundamental rights. Tamarisk Corp. purchased machinery for $347,400 on May 1, 2020. It is estimated that it will have a useful life of 10 years, salvage value of $17,400, production of 264,000 units, and working hours of 25,000. During 2021, Tamarisk Corp. uses the machinery for 2,650 hours, and the machinery produces 29,580 units.From the information given, compute the depreciation charge for 2021 under each of the following methods. (Round intermediate calculations to 2 decimal places, eg. 5.25 and final answers to O decimal places, e.g. 45,892.) (a) Straight-line (b) Units-of-output (c) Working hours (d) Sum-of-the-years'-digits (e) Declining-balance (use 20% as the annual rate) $ . In competitive markets, price is equal to marginal cost in the long run. Explain why this statement is not true for monopolistic competition. Select the statement that is true about the temperatures -9F and -7F.A-7F,< -9F because -7F is colder than -9F.B-7F > -9F because -7F is colder than -9F.C -7F >-9F because -7F is warmer than -9F.D -7F Monochromatic light with wavelength 588 nm is incident on a slit with width 0.0351 mm. The distance from the slit to a screen is 2.7 m. Consider a point on the screen 1.3 cm from the central maximum. Calculate (a) for that point, (b) , and (c) the ratio of the intensity at that point to the intensity at the central maximum. what is an email account The six __________ of geography include places and regions and human systems. A. key areas B. essential elements C. environments D. spatial terms