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 the ball has traveled when it hits the ground the fifth time is meters.

Answers

Answer 1
10 + 5 + 5 + 2.5 + 2.5 + 1.25 + 1.25 + 0.625 + 0.625 = 28.75 meters
Answer 2
[tex].625+.625[/tex][tex] 5+5, 2.5+2.5, 1.25 + 1.25[/tex]
[tex](10 + 5 + 5 + 2.5 + 2.5 + 1.25 + 1.25 + 0.625 + 0.625) = 28.75 [/tex]

Related Questions

The cruise control function on Georgina's car should keep the speed of the car within 3 miles per hour of the set speed. The set speed is 55 miles per hour. Write a compound inequality to show the leaves that are within each range. Then graph the solutions.

Answers

This should help. Sorry I had to make this rn.

Answer:

Given,

Set speed of car = 55,

∵ The speed of the car within 3 miles per hour of the set speed.

So, the maximum speed of car = 55 + 3,

And, the minimum speed of car = 55 - 3

Let x shows the current speed of car,

x ≤ 55 + 3 or x ≥ 55 - 3

x - 55 ≤ 3 or x - 55 ≥ - 3

x - 55 ≤ 3 or -(x-55) ≤ 3

| x-55 | ≤ 3

Which is the required compound inequality,

Now, 55 - 3 ≤ x ≤ 55 + 3

52 ≤ x ≤ 58

[52, 58]

Which is the solution of the above compound inequality.

Also, the graph is shown below.

If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so forth, how much money will be in the bank after 40 days? $8.20 $16.40 $0.40 $4.10

Answers

this is an arithmetic sequence with the common difference being 1

and if u have 1 cent on day 1 and 2 cents on day 2....then on day 40, u would have 40 cents....but we need the sum of all the days..

the sum of an arithmetic sequence can be found using the formula :
sn = n(a1 + an) / 2
n = number of terms = 40
a1 = first term = 1
an = last term = 40

now we sub
s(40) = 40(1 + 40) / 2
s(40) = 40(41)/2
s(40) = 1640/2
s(40) = 820.....820 cents = $ 8.20 <== the sum

Laura drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 8 hours. when laura drove home, there was no traffic and the trip only took 6 hours. if her average rate was 16 miles per hour faster on the trip home, how far away does laura live from the mountains

Answers

Final answer:

To find the distance Laura lives from the mountains, calculate her average speed when driving to the mountains and use the time taken during the trip. With the given speeds and travel times, the distance can be determined using a simple equation.

Explanation:

To find the distance Laura lives from the mountains:

Let x be Laura's average speed when driving to the mountains.Since Laura drove 16 mph faster on the way home, her speed returning was x+16 mph.Distance to mountains = x * 8 (hours) and distance from mountains = (x+16) * 6 (hours).Set up the equation: x * 8 = (x+16) * 6 to solve for x.Once x is found, the distance Laura lives from the mountains can be calculated as x * 8.

How to multiply a whole number into a fraction?

Answers

Greetings!

To multiply a fraction, both terms must be a fraction.
To turn a whole number into a fraction (without changing the value of the number), we put 1 as the denominator:

Example:
8=8/1

Now that you have terms as fractions, you can multiply them by eachother:
8/1*2/5
=16/5

Hope this helps.
-Benjamin

Evaluate the following expression. 5^-1/5^0

Answers

EVALUATE.

Exact form:
1/5

Decimal Form: 0.2
I think you mean [tex]\frac{5^{-1}}{5^0}[/tex]

ok, know some stuff
[tex]x^0=1[/tex] for all real values of x
[tex]x^{-m}=\frac{1}{x^m}[/tex]

so

[tex]\frac{5^{-1}}{5^0}=[/tex]
[tex]\frac{\frac{1}{5^1}}{5^0}=[/tex]
[tex]\frac{\frac{1}{5}}{5^0}=[/tex]
[tex]\frac{\frac{1}{5}}{1}=[/tex]
[tex]\frac{1}{5}[/tex]

it results in 1/5


or, we could have done
[tex]\frac{x^m}{x^n}=x^{m-n}[/tex] and
[tex]x^{-m}=\frac{1}{x^m}[/tex]
so
[tex]\frac{5^{-1}}{5^0}=5^{-1-0}=5^{-1}=\frac{1}{5^1}=\frac{1}{5}[/tex]



the result is [tex]\frac{1}{5}[/tex]

Subtract the polynomials: (3x2 + 2x + 4) - (x2 + 2x + 1). Enter your answer as a polynomial in descending order below, and use the caret (^) for exponents. For example, you would write as 4x^2.

Answers

Line up the like terms like so

3x^2  +  2x  + 4
x^2    +  2x   + 1

Now subtract straight down
3x^2 - x^2 = 3x^2 - 1x^2 = 2x^2
2x - 2x = 0x = 0
4 - 1 = 3

The results of 2x^2, 0 and 3 are added up to get 2x^2 + 0 + 3 and that turns into 2x^2 + 3

Answer: 2x^2 + 3

Write an equation that represents degrees fahrenheit in terms of degrees celsius. let xx represent the temperature in degrees celsius and let yy represent the temperature in degrees fahrenheit.

Answers

As we know Conversion from fahrenheit to celsius is
[tex]F - 32 = \frac{9C}{5} [/tex]

We can write it also as

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

F as y and C as x then we can write it as

[tex]y = \frac{9x}{5} + 32 [/tex]

An equation is formed of two equal expressions. An equation that represents degrees Fahrenheit in terms of degrees celsius is y=(9/5)x+32.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The equation to covert degrees fahrenheit to degrees celsius is given as,

(C × 9/5) + 32 = F

where C represents temperature in degrees Celcius and F represents the temperature in degrees Fahrenheit.

Now, we need to represent the degree Celcius by x, while the degree Fahrenheit by y. Therefore, the above equation can be rewritten as,

y = (x × 9/5) + 32

y = (9/5)x + 32

Hence, an equation that represents degrees Fahrenheit in terms of degrees celsius is y=(9/5)x+32.

Learn more about Equation here:

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in the chorus there 12 more girl than boys there 32 student in chorus how many boys are there and how many girls are there

Answers

This can be represented by this equation:
x + (x + 12) = 32
Now simplify:
2x + 12 = 32
Then subtract:
2x = 20
Now divide to find x:
x = 10
Plug back in to find the amounts:
10 boys
22 girls

Hope this helps!! :)

The penny size d is given by the literal equation d = 4n - 2, solve for n

Answers

Thanks for your question!

d = 4n -2
d + 2 = 4n
(d+2)/4 = n

Hope this helped!

if a and b are the measures of two first quadrant angles and sin a = 4/9 and sin b = 2/5 find sin (a+b)

Answers

The sine of the sum of two angles a and b, with sin a = 4/9 and sin b = 2/5, is calculated using the sine addition formula and is approximately 32.24/45.

To find sin(a+b) when given sin a = 4/9 and sin b = 2/5, we use the sine addition formula:

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

Since we have the sine values, but not the cosine values, we need to find cos(a) and cos(b). Knowing that [tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]for any angle theta, we can find the cosines:

For cos(a): [tex]cos^2(a) = 1 - sin^2(a) = 1 - (4/9)^2 = 1 - 16/81 = 65/81[/tex]. So, [tex]cos(a) = \sqrt{(65/81)} = 8/9[/tex] (since a is in the first quadrant where cosine is positive).For cos(b): [tex]cos^2(b) = 1 - sin^2(b) = 1 - (2/5)^2 = 1 - 4/25 = 21/25[/tex]. So, cos(b) = [tex]\sqrt{(21/25)}= 4.6/5[/tex] (since b is in the first quadrant where cosine is positive).

Now, we plug these values into the formula:

sin(a+b) = (4/9)(4.6/5) + (8/9)(2/5) = 16.24/45 + 16/45 = 32.24/45

Thus, the sine of the sum of the two angles a and b is approximately 32.24/45.

the perimeter of a square picture frame is 48 inches. one side length of the frame is 30.48 centimeters. how many centimeters are in an inch?
The answer is 2.54 centimeters but i need help with my work

Answers

Since the perimeter is 4 times a side in a square, we get 48/4=12 inches per side, and 12 in= 30.48 cm. Dividing both sides by 12,we get 1in= 2.54 cm

Determine the 3-day sma for the ten consecutive day closing prices of sprint nextel corp listed below. $7.78, $8.08, $7.99, $8.02, $7.89, $8.72, $9.19, $9.16, $8.98, $9.38

Answers

The 3-day moving average is the average 3 number moiving one place each time.

The 3-day sma for the ten consecutive day closing prices is given by of sprint nextel corp:

(1st day price + 2nd day price + 3rd day price) / 3 = ($7.78 + $8.08 + $7.99) / 3 = $23.85 / 3 = $7.95

(2nd day price + 3rd day price + 4th day price) / 3 = ($8.08 + $7.99 + $8.02) / 3 = $24.09 / 3 = $8.03

(3rd day price + 4th day price + 5th day price) / 3 = ($7.99 + $8.02 + $7.89) / 3 = $23.90 / 3 = $7.97

(4th day price + 5th day price + 6th day price) / 3 = ($8.02 + $7.89 + $8.72) / 3 = $24.63 / 3 = $8.21

(5th day price + 6th day price + 7th day price) / 3 = ($7.89 + $8.72 + $9.19) / 3 = $25.80 / 3 = $8.60

(6th day price + 7th day price + 8th day price) / 3 = ($8.72 + $9.19 + $9.16) / 3 = $25.80 / 3 = $27.07 / 3 = $9.02

(7th day price + 8th day price + 9th day price) / 3 = ($9.19 + $9.16 + $8.98) / 3 = $27.33 / 3 = $27.33 / 3 = $9.11

(8th day price + 9th day price + 10th day price) / 3 = ($9.16 + $8.98 + $9.38) / 3 = $27.33 / 3 = $27.52 / 3 = $9.17

Therefore, the 3-day sma for the ten consecutive day closing prices of sprint nextel corp are $7.95, $8.03, $7.97, $8.21, $8.60, $9.02, $9.11, $9.17

Answer:

Step-by-step explanation:

The 3-day moving average is the average 3 number moiving one place each time.

The 3-day sma for the ten consecutive day closing prices is given by of sprint nextel corp:

(1st day price + 2nd day price + 3rd day price) / 3 = ($7.78 + $8.08 + $7.99) / 3 = $23.85 / 3 = $7.95

(2nd day price + 3rd day price + 4th day price) / 3 = ($8.08 + $7.99 + $8.02) / 3 = $24.09 / 3 = $8.03

(3rd day price + 4th day price + 5th day price) / 3 = ($7.99 + $8.02 + $7.89) / 3 = $23.90 / 3 = $7.97

(4th day price + 5th day price + 6th day price) / 3 = ($8.02 + $7.89 + $8.72) / 3 = $24.63 / 3 = $8.21

(5th day price + 6th day price + 7th day price) / 3 = ($7.89 + $8.72 + $9.19) / 3 = $25.80 / 3 = $8.60

(6th day price + 7th day price + 8th day price) / 3 = ($8.72 + $9.19 + $9.16) / 3 = $25.80 / 3 = $27.07 / 3 = $9.02

(7th day price + 8th day price + 9th day price) / 3 = ($9.19 + $9.16 + $8.98) / 3 = $27.33 / 3 = $27.33 / 3 = $9.11

(8th day price + 9th day price + 10th day price) / 3 = ($9.16 + $8.98 + $9.38) / 3 = $27.33 / 3 = $27.52 / 3 = $9.17

Therefore, the 3-day sma for the ten consecutive day closing prices of sprint nextel corp are $7.95, $8.03, $7.97, $8.21, $8.60, $9.02, $9.11, $9.17

Jana is thinking of a number. If she divides her number by 12 and then multiplies the quotient by 8, the result is 520. What number is Jana thinking of?

Answers

You would do the reverse of what was done so you would do 520/8 and then multiply that by 12 so you get 780

Suppose that you have he option to buy an item with either cash or credit. Under which condition would you use credit?

Answers

if they didn't take cash

Answer:

If you want to build a good credit history

Step-by-step explanation:

Buying something in order to build a good credit history does not benefit in the short run such as any financial or non-financial benefit.

However, when need arises to make request for a large sum of loan in the long run (such as buying house, purchasing vehicle or capital for investing in business) from the financial institution or any other credit providers, then the good credit history would be winning key factor for obtaining the loan.

What is 7,130 divided by 86?

Answers

the answer is 82.906

Write the function y = 3(x - 1)2 + 2 in standard form.

Answers

3 x 2 = 6

6(x-1) = 6x - 6

6x - 6 + 2

6x -4

hope this helps

What is767,074 rounded to the nearest hundred thousand

Answers

800,000 is the answer
800,000 is the rounded answer.

Find the perimeter of the polygon with the vertices g(2, 4), h(2,−3), j(−2,−3), g(2, 4), h(2,−3), j(−2,−3), and k(−2, 4)k(−2, 4).

Answers

The distance between g and h is sqrt[(2-2)^2+(4+3)^2]=7 The distance between h and j is sqrt[(2+2)^2+(-3+3)^2]=4 The distance between j and k is sqrt[(-2+2)^2+(-3-4)^2]=7 The distance between k and g is sqrt[(-2-2)^2+(4-4)^2]=4 The perimeter of the polygon is 7+4+7+4=22

A 9-ft light pole casts a 15-ft shadow. Find thw height of a nearby tree that is cadtinh a 40-ft shadow.

Answers

The 40 foot tree cast a shadow that was 34 feet.

Help In Math Please!!
The graphic shows the average number of points scored per game for ten players in the NBA.

What is the interquartile range (IQR) of the data set.
A) 1.1
B) 4.9
C) 6.9
D) 9.8

Answers

To calculate the interquartile range of a dataset, we first arrange the dataset in order:

Since the given dataset is already arranged in order.

We obtain the Q1 and the Q3 data values.

The Q1 value is the value for which 25% of the datavalues lie below it. For the given dataset, the Q1 value is 24.

Similarly, the Q3 value is the value for which 25% of the datavalues lie above it. For the given dataset, the Q1 value is 28.9.

The interquartile range is given by

IQR = Q3 - Q1 = 28.9 - 24 = 4.9

Therefore, the interquartile range (IQR) of the data set is 4.9.

Answer:

The other answer for USA TP is 26.25

Step-by-step explanation:

The mean is the average of the numbers.

29.8 + 29.6 + 28.9 + 27.1 + 26.4 + 25.5 + 24.5 + 24.0 + 23.8 + 22.9

10

= 26.25

what is the area of a circular mirror with a radius of 10 cm?

Answers

area=pi r squared
area=3.14 x 10squared 
area= 314
the answer is 314

Final answer:

The area of a circular mirror with a radius of 10 cm is calculated using the formula πr², which results in an area of 314.16 cm².

Explanation:

The area of a circular mirror can be calculated using the formula πr², where π (pi) is approximately 3.1416 and r is the radius of the circle. Given the radius of the circular mirror as 10 cm, we can substitute this value into the formula to find the area.

Area = π × (10 cm)²
A = 3.1416 × 100 cm²
A = 314.16 cm²

Therefore, the area of the circular mirror is 314.16 cm².

Amy leaves a rest stop at 2 PM traveling west, at 45 miles per hour. Sarah leaves 2 hours later, also traveling west, but at 55 miles per hour. At what time will Sarah catch up with Amy?

Answers

55(t-2) =45t

55t-110 = 45t

-110 = -10t

t = 11 hours

 2 pm plus 11 hours = 1 am

Answer: mathematics, central tendency is the tendency of data values to cluster around some central value. What does a measure of variability tell you about the central tendency of a set of data? ... If the range and IQR are small, the values are clustering around some central value.

Step-by-step explanation:

if you live in Dallas then you live in Texas what is the biconditional of this

Answers

you live in Dallas, if and only if you live in Texas
Final answer:

The biconditional of the statement 'If you live in Dallas then you live in Texas' is 'You live in Dallas if and only if you live in Texas'. This means that living in Dallas is both necessary and sufficient for living in Texas.

Explanation:

The biconditional of the statement 'If you live in Dallas then you live in Texas' would be 'You live in Dallas if and only if you live in Texas'. In other words, living in Dallas is both necessary and sufficient for living in Texas. This means that if one condition is true, then the other must also be true. Similarly, if one condition is false, then the other must also be false. A biconditional statement essentially equates the truth of two conditions.

Learn more about biconditional here:

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Over the past ten years, the town's population doubled in size. The population is currently 12,000. What was the population ten years ago?

Which of the following represents the given word problem if "P" represents the population ten years ago?

Answers

I think the answer is 2P = 12,000 but I might be wrong

Find the value of d in the triangle

Answers

d = 3/ sin(15)

d= 11.5911 feet

round answer as needed

Considering the one-time deposit and monthly rent, the equation y=1200+400x can be used to represent y, the total cost of renting an apartment for x months. What is the amount of the deposit?
A. $30
B. $400
C. $800
D. $1200 <--- My answer ( Check this please ^_^

Answers

In this item, we are given with the equation,
    y = 1200 + 400x

where y is the total amount of rent and x is the number of months. 

There are two terms in the right-hand side of the equation: 1200, and 400x. It is observed that the value of the first term is constant at 1200 while that of the second term is variable depending on the number of months. The first term therefore can be attributed as the deposited value. 

Therefore, the answer to the question is letter D. 

What is 7 more than five times the number 9 divided by 15?

Answers

Answer:

7 more than five times the number 9 divided by 15 is, 10

Step-by-step explanation:

As per the statement:

7 more than five times the number 9 divided by 15

"five times the number 9" translated to [tex]5 \times 9 = 45[/tex]

"five times the number 9 divided by 15" translated to [tex]\frac{45}{15} = 3[/tex]

then;

"7 more than five times the number 9" divided by 15 means 7 + 3 = 10

Therefore,  7 more than five times the number 9 divided by 15 is, 10

Answer:

10

Step-by-step explanation:

Hope this helps!

What's the next three terms of the following sequence 160,136,112,88

Answers

Every number gets subtracted by 12. Therefore the next three numbers after 88 are 88-24, which is 64, then 64 - 24, which is 40, and 40-24, which is 16.
the next three terms are 64, 40, and 16.
On each number from the sequence you are subtracting 24 from it. So 160-24= 136 then 136-24= 112 then 112-24 = 88 then 88-24 = 64 and so on

Solve the literal equation 2a-b=8b-4a for a

Answers

a = 1.5b
Have a great day!


firs you need to look for the like terms (look at the a terms) then you will need to look for any other like terms in this case look at the b and the 8b it would probably be easier to add or subtract the smallest number. then if you answer turns out to be 2/3 your correct. HOPE IT HELPS SORRY IF YOU DONT GET IT.

What is the length of line RS? Use the law of sines to find the answer.Round to the nearest tenth.

Answers

Using the law of sines,
sin80°/3.1 = sin∠QSR/2.4
∠QSR = sin^-1(2.4sin80°/3.1)
≈ 49.679°
∠SQR = 180° - 80° - 49.679° (angles in a triangle)
= 50.321°
sin50.321°/RS = sin80°/3.1
RS = (3.1sin50.321°/sin80°)
= 2.4 units (nearest tenth)
The length of line RS is 2.4 units.
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