The question deals with a sequence of movements of a golf ball falling and rebounding, which forms a geometric series. To find the total distance traveled by the ball on its 10th descent, we calculate the sum of the first 19 terms of this geometric progression.
Explanation:The student is asking about a geometric series problem, which involves a golf ball being dropped from a height and rebounding to a fraction of that height. The sequence of the distances covered by the ball forms a geometric progression.
Let's denote the initial height the ball is dropped from as a, which is 30 ft. The rebound height is one-fourth of the descent, so the rebound ratio, or common ratio r, is 1/4. The ball travels the initial height a plus the rebound distance each time it hits the pavement. This series continues with each rebound being one-fourth of the previous fall. We want to find the total distance traveled by the ball as it hits the pavement on its 10th descent.
The total distance traveled D after the ball hits the pavement for the 10th time is the sum of the first 10 terms of this geometric sequence. Using the formula for the sum of the first n terms of a geometric series, [tex]S_n = a(1-r^n)/(1-r)[/tex], where n is the number of terms, we can calculate the total distance.
For 10 descents, we have n = 19 since each descent and rebound except
the last descent counts as two movements:
[tex]S_{19} = 30(1-(1/4)^{19})/(1-(1/4))[/tex]
[tex]S_{19} = 30(1-(1/4)^{19})/(3/4)[/tex]
By calculating [tex]S_{19[/tex], we find the total distance traveled when the ball hits the pavement on its 10th descent.
Suppose that the sample space is s = {a, b, c, d, e, f, g, h} and that outcomes are equally likely. find the probability of the event e = {b, f, h}.
The probability of the event E = {b, f, h} with the sample space S = {a, b, c, d, e, f, g, h} is 3/8 or 0.375.
Explanation:The student has asked to find the probability of the event E = {b, f, h} given the sample space S = {a, b, c, d, e, f, g, h} where all outcomes are equally likely. To calculate the probability, we need to use the formula for theoretical probability, which is the number of favorable outcomes divided by the total number of possible outcomes in the sample space.
We see that the event E has 3 outcomes (b, f, h) and the sample space S has 8 outcomes. So the probability of event E is given by:
P(E) = Number of outcomes in E / Number of outcomes in S = 3 / 8 = 0.375
Jeremy saves $35 per month over the first 7 months of the year. He saves $40 per month over the next 5 months of the year. If Jeremy spends none of his savings, which expression shows how many dollars he will have saved by the end of the year?
Answer: The expression shows the number of dollars he will have saved by the end of the year is given by [tex]35(7)+40(5)=\$445[/tex]
Step-by-step explanation:
Since we have given that
Amount he saved per month over the first 7 months = $35
Amount he saved per month over the next 5 months = $40
So, total saving by the end of the year is given by
[tex]35\times 7+40\times 5\\\\=\$245+\$200\\\\=\$445[/tex]
Hence, the expression shows the number of dollars he will have saved by the end of the year is given by
[tex]35(7)+40(5)=\$445[/tex]
Solve the inequality.
s-2 ≤ 7
s - 2 ≤ 7
+2 +2
s ≤ 9
s ≤ 9
davis printed 24 photos in 8 minutes. how many photos did he print per minute
In your US History class, you have scores of 78, 89, 87 and 96 on the first four tests. To get a B, the average of the five tests must be greater than or equal to 80 and less than 90. Solve an inequality to find the range of the scores needed on the fifth test to get a B
Evaluate f - 2g for f = 4 and g = 32.
a.) 1/2
b.) 2
c.) 8
The expression f - 2g evaluates to -60, considering f = 4 and g = 32. The answer is not listed in the given multiple-choice options, suggesting a potential error in the question or options.
Explanation:The expression to evaluate is f - 2g. With the given values for f and g, f = 4 and g = 32, we can substitute these into the expression. The calculation will be:
f - 2g = 4 - 2(32)f - 2g = 4 - 64f - 2g = -60Therefore, the value of f - 2g is -60. This answer is not given in the multiple choice options, indicating a possible discrepancy between the question and the provided options. The correct evaluation should be confirmed.
There 430 people in wave pool. Write an inequality that represents how many more people p can enter the pool.
Let
p--------> number of additional people who can enter the pool
we know that
the maximum capacity of the pool is [tex]600\ people[/tex]
so
the inequality is
[tex]430+p \leq 600[/tex]
[tex]p \leq 600-430[/tex]
[tex]p \leq 170[/tex]
the solution is the interval ----------> (-∞,170]
but remember that the number of people can't be a negative number
so
the solution is the interval -------> [0,170]
therefore
the answer is
The inequality is equal to [tex]430+p \leq 600[/tex]
how do you simpify 64 raised to the 36 power
is the open sentence 3z=2z+5 true or false when z=5?
A. True
B. False
The step function f(x) is graphed. What is the value of f(0)? -2 -1 0 1
Answer: -2 is the correct answer
Explanation:
This is the graph for greatest integer function by looking at the graph we can clearly conclude that f at zero is giving the value -2
Greatest integer function gives the value that is less than or equal to the value taken inside the function
For example if we have 2.09 and is operating under greatest integer function the value comes out to be 2 because it will convert the decimal value in integer
denoted as [2.09]=2
Refer to the Venn diagram that represents the sports students chose to play at South High School last year. Select the correct description of sports that the students in the non-intersecting portion of the tennis region chose. 2_6
how much is 81% of 403? find the missing element in the following base-rate-percentage problem. round the answer to the nearest hundredth.
Find 81% of 403 by converting the percentage to a decimal (0.81) and then multiplying it by 403, which equals to 326.43 when rounded to the nearest hundredth.
Explanation:The student is asking for the solution to determine the value of 81% out of 403. This is a simple proportional math problem and could be solved with the following steps:
Convert the percentage (81%) to its decimal equivalent. This is done by dividing the percentage by 100. So, 81 divided by 100 equals 0.81.Multiply the given total number (403) by the decimal equivalent of the percentage. So, 0.81 times 403 equals 326.43.So, 81% of 403 is approximately 326.43, rounding to the nearest hundredth.
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on a map with a scale 1:100,000 the distance between two cities is 12cm. what would be the distance between these two cities on a different map with a scale 1:300,000?
Part 1)
we have
the scale is [tex]1:100,000[/tex]
the distance on a map is [tex]12\ cm[/tex]
we know that
The scale is equal to the distance on a map divided by the real distance
Let
x------> distance on a map
y-------> real distance
S-------> scale
[tex]S=\frac{x}{y}[/tex]
In this part we have
[tex]S=\frac{1}{100,000}[/tex]
[tex]x=12\ cm[/tex]
Find the value of y
[tex]y=\frac{x}{S}[/tex]
Substitute the values
[tex]y=\frac{12}{(1/100,000)}[/tex]
[tex]y=1,200,000\ cm[/tex]
Convert to kilometers
[tex]y=12\ Km[/tex]
Part 2)
In this part we have
[tex]S=\frac{1}{300,000}[/tex]
[tex]y=12\ km[/tex]
Find the value of x
[tex]x=S*y[/tex]
Substitute the values
[tex]x=(1/300,000)*12[/tex]
[tex]x=0.00004 Km[/tex]
Convert to centimeters
[tex]x=4\ cm[/tex]
therefore
the answer is
The distance is [tex]4\ cm[/tex]
Why would the owner withdraw assets from other cash?
Answer:
The owner of a business sometimes withdraw assets other than cash because cash is more liquid and can be used in transactions easily, whereas the assets after a period of times becomes liable of depreciation.
The depreciation on assets decreases the amount of the assets based on the time and wear and tear of the tangible assets.
Therefore, to retain some liquid assets in hand the tangible or intangible assets are used first.
Hence, the businessman here did the right thing.
How many prime numbers are there between 25 and 35, inclusive? 2 3 4 5
Answer:
The answer is 2
Step-by-step explanation:
A hummingbird can travel up to 15 meters per second. What is the hummingbirds speed in miles per hour? 1 mile = 1609 meters
Answer:
33.56 miles per hour.
Step-by-step explanation:
First we will see how many meters the hummingbird can travel in an hour (in meters)
it can travel up to 15 meters per second, but we know that one hour has 3600 seconds ( because an hour has 60 minutes of 60 seconds each one ( 60 x 60 = 3600)
So the hummingbird can travel 3600 x 15 = 54,000 meters in one hour.
Now, we know that 1 mile = 1609 meters, so in order to convert the 54,000 meters in miles per hour we're going to use a rule of three.
1 mile ----------- 1609 meters
x miles ---------- 54,000 meters
x miles = 54,000/1,609 = 33.56
Therefore, the hummingbird speed is 33.56 miles per hour.
Evaluate the expression for the given values of the variables.
4(2m-n)-3(2m-n);
m=-15 n=-18
A. 3
B. -3
C. -12
D. 16
The result of evaluating the expression 4(2m-n)-3(2m-n) with respect to m=-15 and n=-18 is -12.
Explanation:To evaluate the expression 4(2m-n)-3(2m-n) for m=-15 and n=-18, we first substitute these given values into the expression.
Therefore, our expression becomes 4(2*(-15) - (-18)) - 3(2*(-15) - (-18)). Simplify the expression in the parentheses first according to the order of operations (also known as BEDMAS or PEMDAS) which stands for Brackets/parentheses, Exponents/Orders, Division/Multiplication, Addition/Subtraction.
4(2*-15 - (-18)) - 3(2*-15 - (-18)) simplifies to: 4(-30 +18) - 3(-30 + 18). Further simplify to: 4*-12 - 3*-12.
Then, doing the multiplication gets: -48 - (-36), which simplifies to: -48 + 36. Therefore, the value of the expression is -12.
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The word geometry has eight letters. Three letters are chosen at random. What is the probability that two consonants and one vowel are chosen?
Answer: [tex]\dfrac{15}{28}[/tex]
Step-by-step explanation:
The given word : geometry
Total letters in the above word = 8
Number of vowels (a e i o u) in word =3
Number of consonants = 5
Number of ways to choose two consonant and one vowel is given by :-
[tex]F=^5C_2\times^3C_1\\\\=\dfrac{5!}{2!(5-2)!}\times (3)\ [ \because ^nC_1=n]\\\\=5\times2\times3=30[/tex]
Number of ways to choose any three letters from the 8 alphabets:-
[tex]T=^8C_{3}=\dfrac{8!}{3!(8-3)!}=8\times7=56[/tex]
Now, the probability that two consonants and one vowel are chosen :-
[tex]=\dfrac{F}{T}\\\\=\dfrac{30}{56}=\dfrac{15}{28}[/tex]
Hence, the required probability = [tex]\dfrac{15}{28}[/tex]
Which of the following examplebles are substantiantiated fact?
All dogs kill sheep.
Poorly bred dogs kill sheep.
Two Neighbors and saw Eliot's dog kill a sheep.
A recent survey of sheep farmers revealed that 100,000 sheep were killed by dogs last year.
The response explains which statements are substantiated facts and why. It clarifies the concept by using examples from the question.
Explanation:Substantiated facts are statements supported by evidence or proof. In the given examples:
All dogs kill sheep - Not substantiated as it is a generalization.Poorly bred dogs kill sheep - Not substantiated as it lacks evidence.Two Neighbors saw Eliot's dog kill a sheep - Substantiated as it provides specific eyewitness evidence.A recent survey of sheep farmers revealed that 100,000 sheep were killed by dogs last year - Substantiated with data from a survey.Umbrellas are highly seasonal. Their highest selling month is 325% of their lowest selling month. During their lowest selling month, they sell 980 units. How many units do they sell during the peak month?
State the property of addition that justifies each numbered step in the following simplification.
56 + (44 +79)
steven wants to buy a $565 bicycle. Steven has no money saved, but will be able to deposit $30 into a saving account when he receives his paycheck each Friday. However, before steven can buy the bike,he must give his sister $65 that he owes her. For how many weeks will steven need to deposit money into his savings account before he can pay back his sister and buy the bike?
The new york yankess sell an avergae of 42362 tickets for each of their 81 home games about how many tickts do they sell for an entire seasone of home games
multiply the number of games by the number of seats
42362 x 81 = 3,431,322 total seats
340 decreased by 20%
.help me please thanks
The sum of the measures of the angles of any triangle is 180 degrees. in triangle abc, angles a and b have the same measure, while the measure of angle c is 72 degrees larger than each of a and
b. what are the measures of the three angles?
To rent a bike there is a set fee, plus an hourly rate. Renting a bike for 4 hours costs $24. Renting it for 7 hours costs $37.50. How much to rent it for 3 hours?
By solving a system of linear equations, the set fee for renting a bike is determined to be $6 and the hourly rate is $4.50. Hence, the cost to rent the bike for 3 hours is $19.50.
Explanation:The question involves creating linear equations based on the given information to find the cost of renting a bike for a certain number of hours. We are told that renting a bike for 4 hours costs $24 and renting for 7 hours costs $37.50. We can express this situation with two equations, where x represents the set fee and y represents the hourly rate:
4y + x = 247y + x = 37.5We solve this system of equations to find the values of x and y. Subtracting the first equation from the second gives us 3y = 13.5, hence y = 13.5 / 3 = $4.50 per hour. We can then substitute y back into the first equation: 4(4.50) + x = 24, which simplifies to 18 + x = 24, hence x = $6.
To rent the bike for 3 hours, the cost would be 3(4.50) + 6 = $13.50 + $6 = $19.50.
Where the graphs of supply and demand functions intersect the market is in equilibrium
Quadrilateral WILD is inscribed in circle O.
WI is a diameter of circle O.
What is the measure of angle D?
Thye given Quadrilateral WILD is inscribed in circle O. The measure of angle D is 135 degrees.
Since the quadrilateral is inscribed inside the circle,
Where the four vertices are on the circle itself,
What is the addition opposite angle?The opposite angle addition is 180 degrees.
Angle I and Angle D are opposite angles.
They add to 180 degrees
(angle I) + (angle D) = 180
(45 degrees) + (angle D) = 180
(angle D) + 45 = 180
(angle D) + 45 - 45 = 180 - 45 ... subtract 45 from both sides.
angle D = 135
The measure of angle D is 135 degrees.
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A collection of nickels and dimes is worth $ 9.45. If the number of dimes is doubled, the value is $16.65. How many dimes and how many nickels?