To find the total distance traveled by the swing, we use the sum of an infinite geometric series formula with the first swing distance being 9 feet and a common ratio of 0.7. The sum equals 30 feet, indicating the total distance the swing traveled.
The question involves finding the total distance traveled by a swing that starts with an initial swing length and then decreases by a certain percentage with each subsequent swing. It can be classified as a series problem in mathematics, specifically dealing with a geometric series.
First swing distance is 9 feet. Each subsequent swing is only 70% of the previous, which means the ratio is 0.7. We want to find the sum of this geometric series. The total distance traveled by the swing is the sum of the distances traveled in each direction, so the swing's distances form an infinite series. To find the total distance traveled, we use the formula for the sum of an infinite geometric series:
S = [tex]\frac{a}{1-r}[/tex]
where S is the sum of the series, a is the first term, and r is the common ratio (in this case, 0.7). Plugging in the values, we get:
S = [tex]\frac{9 feet }{(1 - 0.7)}[/tex] = 9 feet ÷ 0.3 = 30 feet
Hence, the total distance traveled by the swing is 30 feet.
In 2/3 of a hour, workers had installed 2/5 of a foor. At the rate,what fraction of the flooring is finished after 1 hour?
Use a 10-square model to solve. What percent of 80 is 40?
Jason is covering an ottoman with fabric. The ottoman is in the shape of a rectangular prism that is 37 cm long, 21 wide, and 30 cm high. How much fabric is needed to cover the sides and top of the ottoman? Explain your strategy.
Final answer:
Jason needs 4,257 square centimeters of fabric to cover the sides and top of his rectangular prism shaped ottoman, calculated by finding the area of each side and adding them together.
Explanation:
To calculate the amount of fabric needed to cover the sides and top of a rectangular prism shaped ottoman with dimensions 37 cm in length, 21 cm in width, and 30 cm in height, we start by determining the surface area of the ottoman that needs covering. We ignore the bottom surface, assuming the ottoman sits directly on the floor.
First, calculate the area of each side:
Top/bottom surface (only top applies here) = length × width = 37 cm × 21 cm = 777 cm²
Front/back surface = length × height = 37 cm × 30 cm = 1,110 cm² (two sides, so × 2)
Left/right side = width × height = 21 cm × 30 cm = 630 cm² (two sides, so × 2)
Next, add all the calculated areas together:
777 cm² (top) + 2,220 cm² (front/back) + 1,260 cm² (left/right) = 4,257 cm²
Therefore, Jason needs 4,257 square centimeters of fabric to cover the sides and top of the ottoman.
Please help choose the best answer x/-4 >6
A: x <-24
B: x >-24
C: x < 10
D: x > 2
plz help me asap!!!!
What does this equation equal to? 2010=0.507x+5.543
d=1/2at^2 ; for a
solve for a
Answer:
a = 2d/t²
Step-by-step explanation:
1- Divide by 1/2 on both sides:
(d ÷ 1/2 = d × 2/1 = 2d)
2d = at²
2- Divide by t² on both sides:
2d/t² = a
a = 2d/t²
You can do those two steps in one but I made it in two so it's easier to understand.
a $1,400 loan has a simple annual interest rate 4%. how much simple interest is paid on the loan for 1 year?
The simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year is $56.
Explanation:The subject of your question is simple interest calculation. The formula for calculating simple interest is: principal amount x interest rate x time. You are asked to calculate the simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year. Let's proceed step-by-step:
Convert the interest rate of 4% to a decimal by dividing by 100. So, 4/100 = 0.04.The time is 1 year, so you don't need to convert it.Substitute the values into the simple interest formula. Therefore, the simple interest is: $1,400 x 0.04 x 1 = $56.So, the simple interest paid on the loan for 1 year is $56.
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A rectangle field is five times as long as it is wide. If the perimeter of the field is 288 yards, what are the field's dimensions?
A number m minus 3 is more than -4
a bonsai tree grows 0.056 cm per year. If the tree is currently 10 cm tall, how tall will it be 5 years from now?
A group of people were asked if they enjoy going to concerts or movies.
The table shows the probabilities of the results.
Answer:
Option: B is the correct answer.
Enjoying movies and concerts are not independent since,
[tex]P(movies|concerts)\neq P(movies)[/tex]
and [tex]P(concerts|movies)\neq P(concerts)[/tex]
Step-by-step explanation:
We know that if two events A and B are independent then:
[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]
where P denote the probability of an event.
Now, we know that:
[tex]P(movies|concerts)=\dfrac{P(movies\bigcap Concerts)}{P(concerts)}[/tex]
Similarly:
[tex]P(concerts|movies)=\dfrac{P(movies\bigcap Concerts)}{P(movies)}[/tex]
If movies and concerts are independent then:
[tex]P(movies|concerts)=P(movies)[/tex]
Similarly:
[tex]P(concerts|movies)=P(concerts)[/tex]
We have:
[tex]P(movies)=0.6[/tex]
[tex]P(concerts)=0.55[/tex]
[tex]P(concerts|movies)=\dfrac{0.25}{0.6}[/tex]
[tex]P(movies|concerts)=\dfrac{0.25}{0.55}[/tex]
Hence,
Enjoying movies and concerts are not independent
Since,
[tex]P(movies|concerts)\neq P(movies)[/tex]
and [tex]P(concerts|movies)\neq P(concerts)[/tex]
Paul wrote a check to the dentist for $345.69. He’ll use the check register to record his transaction. What will be his new balance?
Answer:
The answer is $704.73
Step-by-step explanation:
Answer:
The answer is A. $704.73
Step-by-step explanation:
social security number contains nine digits 0 0 0 0 0 0 0 0 0 how many different Social Security numbers can be formed using in a in a numerals from 0-9
1,000,000,000 social Security numbers can be formed using the numerals 0-9.
What is combination?A combination is grouping or sub-setting of items from a set where the order in which the selection is being made does not matter.
The formula for combination is:[tex]^{n}C_r = \frac{n!}{(n-r)!r!}[/tex]
where, n = Total number of items to be selected from.
r = Number of items to be selected.
According to the given problem,
Social security number contains nine digits.
A digit can be any number between 0-9.
For the first digit there are 10 choices which is 0-9 and the amount of numbers to be chosen is 1.
Thus there are [tex]^{10}C_{1}[/tex] ways for filling up first spot.
Similarly for the second digit , numbers available are 10 and numbers to be chosen is 9.
Thus there are [tex]^{10}C_{1}[/tex] ways for achieving this.
Same for third, fourth .. . . ninth digit.
Using the formula of combination, total number of ways would be,
= [tex]9 ~times~~ ^{10}C_{1}[/tex]
= [tex](\frac{10!}{1!\times (10-1)!})^9[/tex]
= 1000,000,000 ways
Hence we can conclude that there are 1000,000,000 ways of choosing 10 numbers from 0 to 9 for nine spots.
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PLEASE someone do this math EASY picture attached
Answer:
5/18
Step-by-step explanation:
5/8 ÷ 3/2
switch 3/2 to 2/3
5/12 × 2/3
10/36 divide each 2 5/18
what is 15% of "x"
PLEASE HELP
Answer:
0.15x
Step-by-step explanation:
15% of anything is 15/100 or 0.15 of it. You find that value by multiplying the "anything" by 0.15.
Since we don't know the value of x, the best we can do is show that the number of interest is x multiplied by 0.15.
((cosx)/(1+sinx))+((1+sinx)/(cosx)=2secx
This table shows the size, in acres, of four large water parks. What is the median of the sizes of the four water parks? 60 acres 63 acres 64 acres 65 acres Park Size (in Acres) A 66 B 70 C 60 D 60
The median size of the four water parks, given as 66, 70, 60, 60 acres, is 63 acres.
Explanation:To find the median of the sizes of the four water parks, we first need to list the sizes in ascending order. Given the sizes are 66, 70, 60, 60, the arranged list becomes 60, 60, 66, 70.
As there are four numbers, the median is the average of the middle two numbers. So by adding 60 and 66 and then dividing by 2, we find that the median size of the water parks is 63 acres.
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log base 6 (2x+1) = log base 6 (x-3) + log base 6 (x+5)
Mary and Jerry are exercising on a track
-Mary is walking at a rate of 3 miles per hour
-Jerry starts jogging at a rate of 4 miles per hour after Mary has been walking for 15 minutes
-Jerry jogs 2 miles as Mary continues walking and they both stop at the same time
Enter the total distance, in miles, that Mary walks around the track
Answer:
2.25
Step-by-step explanation:
Mary walks for 15 mins which is 0.75 mi. Jerry then starts jogging for 2 miles which is 30 minutes because he is jogging at 4 mph. This means Mary walked for 30 minutes which is 1.5 mi.
0.75+1.5=2.25
what is the slope of the line through (-2,3) and (1,1)?
Help I don’t understand this
A health food store has launched a new pack of vitamins for children. The store records the number of packs ordered by a random sample of 100 online customers and the number of packs ordered by a random sample of 100 walk-in customers.
(PICTURE IS BELOW)
Which of the following inferences can be drawn about the buying pattern of the online customers versus that of the walk-in customers?
A.Online customers buy an average of four packs compared with walk-in customers, who buy an average of one pack.
B.Online customers buy an average of five packs compared with walk-in customers, who buy an average of two packs.
C.Online customers buy an average of four packs compared with walk-in customers, who buy an average of two packs.
D.Online customers buy an average of five packs compared with walk-in customers, who buy an average of one pack.
The random Sample can be drawn the buying pattern on the online customers versus that of the walk in interview, the correct option is B.
What is sample?Sample is "a small and manageable version of a larger group".
According to the question,
The number of packs ordered by random samples through the online customers = 100
The number of packs ordered by random samples through the walk-in-interview =100
To find the inferences,
Online customers buy an average of five packs compared with walk-in customers, who buy an average of two packs.
Hence, the Option B.
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If a recipe requires 3/4 cup of water and Lisa wants to make only 1/3 of the recipe.how many cups of water should she use?
I got the answer 1/4 but I just want to make sure it’s right
if y=q x 5,and if q=10,then what is y?
a.2
b.5
c.30
d.50
The value of y is 50
Using the expression given:
y = q × 5 q = 10substitute the value of q into the expression
Now we have :
y = 10 × 5
y = 50
Hence, the value of y is 50
Math Help PLEASE! ASAP
The table below shows the deliveries for Floral World for the week. What is the mean, or average, number of deliveries per day?
Answer:
The average number of deliveries per day is 16 deliveries.
Step-by-step explanation:
The mean of a data set is the average value within it. Means are used as a way of describing data and finding the central tendency. To calculate the mean of a data set, add all values of all data points, then divide the resulting number by the amount of data points.
13 + 15 + 17 + 19 + 16 = 80
80 / 5 = 16
So, the average number of deliveries made per day by Floral World is 16 deliveries.
what are the factors of 2n^2 -5n- 42
The factors of the quadratic expression 2n^2 - 5n - 42 are found by looking for two numbers that multiply to -84n^2 and add up to -5n. The correct pair is 7n and -12n, leading to the factors (2n + 7) and (n - 6).
Explanation:The factors of 2n^2 - 5n - 42 need to be determined by finding two numbers that multiply to 2n^2 times -42 (which is -84n^2) and add up to -5n. To factor this quadratic expression, we should look for a pair of numbers that meet these criteria.
Upon inspecting possible pairs, we find that 7n and -12n are the numbers that work since (7n) * (-12n) = -84n^2 and 7n + (-12n) = -5n. The quadratic trinomial can be expressed as:
2n^2 - 5n - 42 = (2n + 7)(n - 6)
By factoring this way, we have broken down the expression into its factors, which are (2n + 7) and (n - 6).
The factors of the quadratic expression [tex]\(2n^2 - 5n - 42\)[/tex] are [tex]\(2n + 7\)[/tex] and [tex]\(n - 6\)[/tex].
To find the factors of the quadratic expression \(2n^2 - 5n - 42\), we can use the factoring method. This involves finding two numbers that multiply to give the product of the coefficient of \(n^2\) (which is 2) and the constant term (which is -42), and also add up to the coefficient of \(n\) (which is -5).
The product of the coefficient of [tex]\(n^2\)[/tex] and the constant term is:
[tex]\(2 \times -42 = -84\)[/tex]
Now we need two numbers that multiply to -84 and add up to -5. These numbers are -12 and 7 because:
[tex]\(-12 \times 7 = -84\)[/tex]
[tex]\(-12 + 7 = -5\)[/tex]
Now we can rewrite the middle term of the quadratic expression using -12 and 7:
[tex]\(2n^2 - 12n + 7n - 42\)[/tex]
Next, we can factor by grouping. Group the first two terms and the last two terms:
[tex]\(2n(n - 6) + 7(n - 6)\)[/tex]
Notice that [tex]\(n - 6\)[/tex] is a common factor. We can factor this out:
[tex]\((2n + 7)(n - 6)\)[/tex].
Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4.
The coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).
Explanation:To find the coordinates of the point that divides the line segment AB in the ratio of 1:4, we can use the formula:
x = (x1 + 1/n * (4 * x2)) / (1 + 1/n)
y = (y1 + 1/n * (4 * y2)) / (1 + 1/n)
Substituting the given coordinates into the formula, we have:
x = (10 + 1/4 * (4 * 2)) / (1 + 1/4) = 8
y = (4 + 1/4 * (4 * 8)) / (1 + 1/4) = 6
Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).
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Find the greatest common factor for the list of terms 110x3, 30x4,60x8