Answer:
a. After the first bounce, the ball will be at 85% of 8 ft. After 2 bounces, it'll be at 85% of 85% of 8 feet. After 3 bounces, it'll be at (85% of) (85% of) (85% of 8 feet). You can see where this is going. After n bounces the ball will be at
[tex]h(n) = (85\%)^n 6ft = (\frac{17}{20})^n(6ft\times 12\frac{in}{ft}) = (\frac{17}{20})^n\times72'[/tex]
b. After 8 bounces we can apply the previous formula with n = 8 to get
[tex]h(8)=(\frac{17}{20})^8\times 72' = 19.62'[/tex]
c. The solution to this point requires using exponential and logarithm equations; a more basic way would be trial and error using the previous [tex]h(n)[/tex]increasing the value of n until we find a good value. I recommend using a spreadsheet for that; the condition will lead to the following inequality:
[tex]1>(\frac{17}{20})^n\times 72[/tex] Let's first isolate the fraction by dividing by 72.
[tex](\frac{17}{20})^n<\frac1{72}[/tex] Now, to get numbers we can plug in a calculator, let's take the natural logarithm of both sides:
[tex]ln ((\frac{17}{20})^n) < ln \frac 1{72} \rightarrow n\times ln (\frac{17}{20}) < -ln72[/tex]. Now the two quantities are known - or easy to get with any calculator, replacing them and solving for n we get:
[tex]-(0.16)n < - 4.27 \rightarrow n>26.31[/tex] Now, since n is an integer - you can't have a fraction of a bounce after all, you pick the integer right after that, or n>27.
PLEASSEE HELP:Dits for khan
What is the constant of proportionality in the equation
y
=
1
2
x
y=
2
1
xy, equals, start fraction, 1, divided by, 2, end fraction, x?
The constant of proportionality in the equation y=1/2x
is 1/2
The direct proportionality between x and y is established by :
y α x
α = proportionality symbol
y = kx - - - (1)
Where;
y and x are the variables
k = proportionality constant
Comparing (1) with the equation given : y=1/2x y=kx
The value of k aligns with 1/2 in the given equation.
Therefore, the constant of proportionality, k in the equation is 1/2
Answer:
yo yo yo! here to help :) answer is 1/2
Maribel will borrow $6250 at 13.5% APR. She chooses to pay it back in 2 years.
What will her monthly payment be? Use the table.
Use the rate table to figure out the monthly payments per one hundred dollars.
At a rate of 13.5% the interest per $100 is $ 4.778 per month.
Therefore, for two years the payment will be
$4.778 × 24 = $114.672 per $ 100
Therefore, the interest for a principal $6250 for two years;
(6250/100) × 114.672
= $7167
The monthly payment would therefore be
7167/24
= $298.625
≈$298.63
. You want to buy a book worth Php 220.50. You can buy it only by making a sacrifice of not buying a soft drink every day. If soft drinks in your school cost Php15.75, how many days do you need to save before you can buy the book? * A. 13 B. 14 C. 15 D. 16
Answer:
B-14
Step-by-step explanation:
Divide 220.50 by 15.75 and you will get 14
Hope it can help you lovelots
The triangle and the rectangle below have the same area.
6 cm
wcm
6 cm
5cm
Calculate the value of w.
Show your working.
I thought it was 10 as triangle do base x height divided by 2
Answer:
look at the photo...........................9. What are all the values for y?Plug in the x value into the equation to find 1 point
y. Equation is y=-2x + 1*
Answer: C
Step-by-step explanation: see picture
another word for collinear
Answer: words like straight, symmetrical, aligned.
There are 600 performers in a dance recital. The ratio of men to women is 4:6 many men performers were in the dance recital?
Answer:
240
Step-by-step explanation:
From the question, we are informed that there were 600 performers in a dance recital and that the ratio of men to women is 4:6.
Fraction of men at the recital = 4/10
Fraction of women at the recital = 6/10
The number of men performers that were in the dance recital will be:
= 4/10 × 600
= 240 men
Answer: 240 men
Step-by-step explanation:
From the question, we are informed that there were 600 performers in a dance recital and that the ratio of men to women is 4:6.
Fraction of men at the recital = 4/10
Fraction of women at the recital = 6/10
The number of men performers that were in the dance recital will be:
= 4/10 × 600
= 240 men
Hope it helps
Solve 6(x - 3) + 7 = -5.
The answer will be:- x = 1
Answer 15 and 16 and get 50 points
No link
Answer:
(1) x=5 (2) I think the answer to 16 is 3/5 but not 100% sure
Step-by-step explanation:
(1) 29=5x+4
Step 1: Flip the equation.
5x+4=29
Step 2: Subtract 4 from both sides.
5x+4−4=29−4
5x=25
Step 3: Divide both sides by 5.
5x /5 = 25 /5
x=5
Angie and her friends are heading to the Glacier Heights snow park. They plan to purchase the Glacier group package, which costs $76 for 8 people. That's $2 less per person than the normal cost for an individual. What is the normal cost for an individual?
Answer
The normal cost would be $11.50
Number Explanation
1) 76 ÷ 8 = 9.5
2) 9.5 + 2 = 11.5 or 11.50
Word Explanation
First, I divided the total cost 76 by the number of people 8, to find out how much it costs per person. I got 9.5! Next, I added 2 to 9.5 because in the problem it said this is $2 less than the normal cost per person. I got 11.5! That was my answer.
Solve for x then y.
y+10=-1/6(x-6)
Answer:
y= -x/6-9
x= -6y-54
Step-by-step explanation:
Petra jogs 3 miles in 30 minutes. At this rate, how long would it take her to jog 13 miles?
Answer:
390 minutes I do believe.
Step-by-step explanation:
Katie's favorite deli has a salad bar where she can make her own salad. She has to pay $1 for the container and $3 per pound for the salad.
Write an equation that shows how the total cost, y, depends on weight of the salad in pounds, x.
Do not include dollar signs in the equation
Answer:
y = 3x + 1
Step-by-step explanation:
Answer: y = 3x + 1
Step-by-step explanation:
Following the y = mx + b theory, we can find the equation (see attached image) by plugging in two points of the hypothetical graph.
For one pound of salad, Katie will pay $4 ($3 for the salad, $1 for the container). Thus, the first point will be (1,4). For two pounds, Katie will pay $7. Thus, the second point will be (2,7).
Knowing that m (slope) = [tex]\frac{y_{2}-y_{1}}{x_{2}-{x_1}}[/tex], we can get the equation m = [tex]\frac{7-4}{2-1}[/tex], thus telling us that m = [tex]\frac{3}{1}[/tex], or 3. Plug in 3 for m, and you get y = 3x + b.
To solve for b, lets' use the second point (2,7). Plug in the coordinates and you get 7 = 3(2) + b, or 7 = 6 + b. Subtract 6 from both sides and you get b = 1.
Plug in 1 for b and you end up with y = 3x + 1
3. At the bank, Sheila made 6 deposits, each in the same amount. Her sister Sherri made 5 deposits, each in the same amount. Each of Sherri's deposits was $10 more than each deposit Sheila made. Both sisters deposited the same amount in the end. How much did each sister deposit each time?
(a) Write an equation. Let x represent the amount of one of Sheila’s deposits.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.
Step-by-step explanation:
x = one deposit of Sheila
x + 10 = one deposit of Sherri
so,
6x = 5(x + 10) = 5x + 50
x = 50
x + 10 = 60
so, as check, the original equation must be true for these values :
6×50 = 5×(50 + 10) = 5×60
300 = 300
correct.
Sheila deposited 6 times $50 every time. so, in total, she deposited $300.
Sherri deposited 5 times $50+$10 = $60 every time. so, in total, she too deposited $300.
How to figure out the absolute value.
Answer:
absolute value is the same number just positive and cha never be negative.
BOWLING A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y=2.5x+3
represents the cost y of bowling x games. Interpret the parameters of the function.
The equation of line l is y=2/3x+5. The equation of line m is y=3/2x−1. What is the relationship between the two lines?
Answer:
If there is not a typo and you aren't missing a minus sign on the slopes, l and m are simmetrical relative to the line [tex]y=x+\frac{13}5[/tex]
If there is a typo nad one of the slopes is negative, they're perpendicular.
Step-by-step explanation:
The product of the slope is 1 -unless you forgot a minus sign somewhere.
In general, two lines of the form [tex]y=kx ; y= \frac1k x[/tex] are simmetrical relative to [tex]y=x[/tex]. Alas, the intercepts are different, but it's easy to spot by drawing them that they would be simmetrical to the parallel to [tex]y=x[/tex] passing through their intersection, by translation. Let's find that point
[tex]\frac23x +5 = \frac32x-1\\4x+30 =9x-6 \rightarrow 5x=36 \rightarrow x= \frac{36}5\\y=\frac 23(\frac{36}5)+5 = \frac{24}5 + \frac{25}5 = \frac{49}5[/tex] Their simmetry line - which is also their angular bisector! - is [tex]y=x+\frac{13}5[/tex]
PLS HELP ASAP ILL GIVE BRAINLKEST
Answer:
Its the bottom one x>5
Step-by-step explanation:
need desperate help thanks
Answer:
x = 158
y = 22
Step-by-step explanation:
A triangle's inside sides sum up to 180 degrees. So to find the angle y, just take 180 - the sum of the other two sides.
70 + 88 = 158
180 - 158 = 22
y = 22 degrees
Now, to find angle x, since x and y are next to each other on a straight line, it means they are supplementary angles. Supplementary angles add together to equal 180, so just substract y from 180 to get x.
180 - 22 = 158
x = 158 degrees
If the supplies on shelf A are normally $7 each and the supplies on shelf B are normally $6 each, how much will you save on each package plan from part a? Buying the first package will save $ and buying the second package will save $
Tyesha found that the z-statistic was 2. 1 and that the critical z-values were -1. 96 and 1. 96. Which of the following is a valid conclusion based on these results? One can reject the null hypothesis. One can reject the alternate hypothesis. One can accept the null hypothesis. One cannot accept or reject the null hypothesis.
The option that represents a valid conclusion based on the given results is;
One can reject the null hypothesis.
We are told that the z-statistic was 2.1.
We are also told that the critical z-values were -1.96 and 1.96.
We see that the z-value is greater than the critical z-values.
Now, in hypothesis testing, when the z-value is greater than the critical z-values, then we reject the null hypothesis.
In conclusion, we will reject the null hypothesis.
Read more about hypothesis testing at; https://brainly.com/question/15980493
Kylie went into a grocery store and bought 5 apples and 4 bananas, costing a total of $10.50. Lily went into the same grocery store and bought 10 apples and 5 bananas, costing a total of $16.50. Determine the price of each apple (x) and the price of each banana (y). Remember, write it as money, with the whole and the decimal to the hundredths place!
Answer:
Apples $0.90 / Bananas $1.50
Step-by-step explanation:
So The equations would look like this
5x + 4y = 10.5
10x + 5y = 16.5
Solving for x, we get 2.1 - 4/5y
Substitute x
10(2.1 -4/5y) +5y = 16.5
Solving for y, we get 3/2 or 1.5
Substitute y
x = 2.1 -4/5(3/2)
x = 9/10
Now check the equations with the answers
5(9/10) + 4(3/2) = 10.5 -> 21/2 = 21/2
10(9/10) + 5(3/2) = 16.5 -> 33/2 = 33/2
Which means apples cost $0.90 and bananas cost $1.50
What is Part 1 and Part 2? I think I have these correct.
Step-by-step explanation:
part 1. Alternate Exterior angle
part 2. 110°
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
The average age of kishan and dolma is 15 years and that of dolma and shaswat is 14 years .If kishan is 17 years old ,find the age of dolma and shaswat.
Help me to find answer
Answer:
dolma is 13 and shaswat is 15
Step-by-step explanation:
lets say kishan is k, dolma is d, and shaswat is 14. (k+d)/2 is 15 so k+d=30. (d+s)/2=14 so d+s=28. since k=17, d=13 and s=15
Find the circumference and the area of a circle with diameter 6 yd.
Use the value 3.14 for T, and do not round your answers. Be sure to include the correct units in your answers.
Answer:
area = 28.27433
Circumference = 18.84956
Step-by-step explanation:
I hope that this helps!!
Jin schedules 496 hours for a project. He plans to work 8 hours each day. How many days will it take to complete the project?
Answer:
62 days
Step-by-step explanation:
496/8 = 62
496/8=62
Hope this helps!
Write the word sentence as an inequality.
A number b
multiplied by −5
is at most −34
.
Answer:
-5b <= -34
Step-by-step explanation:
The inequality phrase, "at most" is same as "less than or equal to". So the algebraic inequality would be -5b <= -34. To solve for b, divide both sides by -5 and make sure to switch the inequality symbol to >= when dividing or multiplying inequalities by a negative number. So b >= 34 / 5.
im literally on my last braincell please help omg
an arithmetic sequence is given
-18, -13, -8, -3...
write an explicit formula for the nth term
Answer:
its going up by 5 every time
Step-by-step explanation:i think that would help i dont know if it was obvious
Jayla made 36 sugar cookies for the class party. Before you got to class the teachers ate 9 cookies, and then your classmates ate 1/3 of the remaining cookies. How many cookies are left for you to eat?
Answer:
9 cookies are left
Step-by-step explanation:
36 - 9 = 27
27 · 1/3 = 9
PLEASE HELP ME I REALLY NEED HELP
Answer:
no
Step-by-step explanation:
We expect you're supposed to answer, NO. This is because an angle and two sides are specified, where the angle is not between the two sides. There is no SSA theorem for congruence, so this specification is generally considered to be insufficient.
_____
Additional comment
The given information is enough to completely specify the given triangle. The reason this is true is that the given angle is opposite the longest of the given sides. A general SSA theorem cannot guarantee that will be the case, so there is no general SSA congruence theorem.
Provided that you have corresponding side and angle information for the other triangle, congruence can be determined (yes). A single triangle by itself cannot be shown congruent to anything.