Answer:
Im assuming youre trying to answer what is the 60% height, it would be 3ft
Step-by-step explanation:
The height of the ball follows a geometric sequence where each subsequent bounce reaches 60% of the height of the previous bounce. The height continues to decrease but does so following a consistent pattern of 60% reduction with each bounce.
Explanation:The problem presented involves the bouncing of a ball and is described as a geometric sequence because each bounce is a constant ratio (60% or 0.6) of the previous height. To understand this sequence, we need to look at it step by step.
Initially, the ball is dropped from a height of 5ft therefore, the initial height is 5ft. With each subsequent bounce, the ball bounces to 60% of its previous height. The height after the first bounce would be 0.6 times the initial height, which equals to 0.6*5 = 3ft. After the second bounce, the height would be again 60% of the previous height, which calculates to 0.6*3 = 1.8ft. This continues for each subsequent bounce.
So, the height of the ball after each bounce decreases but it follows a constant pattern - every next height is 60%, or 0.6, of the previous one, which is a characteristic of geometric sequences.
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Identify the value of p. Give your answers in simplest radical form. HELP PLEASE!!
Answer:
C
Step-by-step explanation:
using the cosine ratio to find p
cos 45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{p}[/tex]
cross- multiplying gives
p × cos45° = 6 → [ cos 45° = [tex]\frac{1}{\sqrt{2} }[/tex]]
p × [tex]\frac{1}{\sqrt{2} }[/tex] = 6
multiply both sides by [tex]\sqrt{2}[/tex]
⇒ p = 6[tex]\sqrt{2}[/tex] ( third option on list )
To determine the value of p in simplest radical form, solve the equation by simplifying the denominator and taking the square root of both sides. The value of p is 2.
Explanation:To identify the value of p, we need to solve the equation and simplify it to the simplest radical form. Let's start by simplifying the denominator and expressing it as a perfect square.
Next, we can take the square root of both sides of the equation to eliminate the square. This will help us isolate p. Once we do that, we can solve for p by getting rid of the square root on the left side of the equation. After simplifying, we find that p = 2.
So, the value of p is 2.
In △ABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . Find the length of DE if perimeter of ABDE is 30 cm and AB = 12 cm
Answer:
DE = 6 cm
Step-by-step explanation:
Let DE = x cm.
Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)
As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.
Therefore, from (1) We get , m∠EAD = m∠ADE and m∠EBD = m∠BED.
So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.
So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then
12 + x + x + x = 30
⇒ 12 + 3x = 30
⇒ x = 6
Hence, the length of DE is 6 cm.
Answer:
DE=6cm
Step-by-step explanation:
Let x=DE, since AB║DE, therefore ∠BAD=∠ADE and ∠ABE=∠BED. (1)
Also, we are given that AD is the angle bisector of ∠A and BE is the angle bisector of ∠B,
Therefore, ∠EAD=∠DAB and ∠ABE=∠EBD (2)
From (1) and (2), ∠EAD=∠ADE and ∠EBD=∠BED
⇒The ΔADE and ΔEDB then becomes the isosceles triangle with AE=Ed and ED=DB (Sides opposite to equal angles are always equal)
Therefore, AE=DE=DB=x
We are given that the perimeter of ABDE is 30 cm, therefore,
Perimeter of ABDE= sum of all the sides of ABDE
⇒30=AB+BD+DE+AE
⇒30=12+3x
⇒30-12=3x
⇒x=6cm
Therefore, the length of DE= 6cm
If the length of one base of a trapezoid is 5, the length of the other base is 2x + 7, and the length of the midsegment is 6x – 24, what is the value of x? Show equations and all work that leads to your answer.
Answer:
x = 6
Step-by-step explanation:
The midsegment of a trapezoid is the line parallel to the parallel sides of the trapezoid, which connects the midpoints of the non-parallel sides.
The length of the midsegment of the trapezoid is half the sum of the length of the parallel sides.
i.e,
Length of the midsegment = (1/2) *(Length of base1 + Length of base2)
6x - 24 = (1/2) * (5 + 2x + 7)
12x - 48 = 2x + 12
10x = 60
x=6
∴ x = 6
A certain type of bacteria increases continuously at a rate proportional to the number present. if there are 500 present at a given time and 1,000 present 2 hours later, how many hours (from the initial given time) will it take for the numbers to be 2,500
The number of hours from the initial given time that will take for the bacteria to grow to 2500 number is 4.64 hours approx.
How to calculate the instantaneous rate of growth of a function?Suppose that a function is defined as;
[tex]y = f(x)[/tex]
Then, suppose that we want to know the instantaneous rate of the growth of the function with respect to the change in x, then its instantaneous rate is given as:
[tex]\dfrac{dy}{dx} = \dfrac{d(f(x))}{dx}[/tex]
Assuming that the bacterial growth can be approximated by a continous and differentiable function y = f(x), where x represents the number of hours spent from the initial time, we're given that:
[tex]\dfrac{dy}{dx} \propto y[/tex]Supposing the proportionality constant be k, then we get:
[tex]\dfrac{dy}{dx} = ky[/tex]
Solving this differential equation, we get:
[tex]\dfrac{dy}{y} = kdx\\\\\text{Integrating both the sides without limits}\\\\\int \dfrac{dy}{y} = \int x dx\\\\\ln(y) + \ln(c) = kx\\\\\ln(yc) =kx\\ yc = e^{kx}\\y = \dfrac{e^{kx}}{c}[/tex]
where ln(c) represents the integration constant. (we took ln(c) because, firstly, ln's range is whole real number (which gives us the access to use it as integration constant), and secondly that it can merge with ln(y) to simplify the work)
Since we're given that:
At x = t (for some value of t in hours), we're given that y = 500,
and for x = t+2, y = 1000,
so we get two equations as:
[tex]\\500 = \dfrac{e^{kt}}{c}\\\\1000 = \dfrac{e^{k(t+2)}}{c}\\[/tex]
Thus, we get:
[tex]\dfrac{e^{kt}}{500} = \dfrac{e^{k(t+2)}}{1000} \\\\kt = \ln(0.5) + k(t+2)\\\\k = \dfrac{-\ln(0.5)}{2}} \approx 0.3465[/tex]
Thus, we get:
[tex]\\500 = \dfrac{e^{kt}}{c} \\\\c = \dfrac{e^{0.3465t}}{500}[/tex]
Thus, we get:
[tex]y = \dfrac{e^{0.3465x}}{\dfrac{e^{0.3465t}}{500}} = 500e^{0.3465(x-t)[/tex]
Let from the initial given time t, it takes h hours more for bacterias to be 2500, then we get:
[tex]2500 = 500 \times e^{0.3465 (t+h - t)}\\0.3465(h) = \ln(5)\\\\h = \dfrac{\ln(5)}{0.3465} = 4.644 \: \rm hours \: approx.[/tex]
Thus, the number of hours from the initial given time that will take for the bacteria to grow to 2500 number is 4.64 hours approx.
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Fill in the value of the function, when the input is 2: y = −4 + 2
Answer:
y=-6
Step-by-step explanation:
y=-4(2)+2
y=-8+2
y=-6
(2,-6)
Answer:
y = - 6
Step-by-step explanation: You have to substitute 2 for x in order for you to get your solution.
y = - 4x + 2
y = - 4(2) + 2
y = - 8 + 2
y = - 6
Remember, a negative times a positive, becomes a negativeHope this helps you!!! :)
Please check out my question
Answer: Choice D) x intercept of f(x) is larger then the x intercept of g(x)
===================================
Explanation:
A) False. The x intercept of f is 1 while the x intercept of g is -1. The x intercept happens when y = 0. Visually, this is where the graph crosses the x axis.
B) False. The y intercept of f(x) is -1, compared to the y intercept of g(x) is +1. The y intercept happens when x = 0, which is when the graph crosses the y axis.
C) False. The y intercept of f(x) is actually smaller than the y intercept for g(x)
D) True. The x intercept of f(x) is larger than the x intercept of g(x). Compare 1 and -1, which are the x intercepts for f and g in that order.
Answer: D
Step-by-step explanation:
NOTES:
x-intercept is when y = 0y-intercept is when x = 0f(x) g(x)
x-int: 1 -1
y-int: -1 1
A) x-intercepts are not equal so FALSE
B) y-intercepts are not equal so FALSE
C) y-intercept of f(x) is not greater than g(x) so FALSE
D) x-intercept of f(x) is greater than g(x) so TRUE
help please 15 points
Answer:
its called line FGH
Step-by-step explanation:
its because the line is FGH
Hope this helps :)
A line is named by two of the points on the line, with a line drawn above the letters.
For the line in the attached image, the answer would be the first choice.
Determine which of the given numbers are roots of the polynomial f(x)=6x^2+x-1.
A. 1/2, 1
B. -1/2, 2
C. -1/2
D. 1
Answer:
Step-by-step explanation:
factor the trinomial: (3x-1)(2x+1)=0
x = 1/3 or -1/2
How much pizza will each person get if 4 people share 3 4 of a pizza equally? A) 1 3 B) 1 4 C) 1 6 D) 3 16
The coldest surface temperature on the moon is 57 degrees colder than twice the coldest surface on Earth. What is the coldest surface temperature on Earth if the coldest temperature on the moon is -116 degrees?
Answer:
Step-by-step explanation:
Answer:
The problem can not be solved since information is missing.
The coldest surface temperature of the moon needs to be given in the text.
THIS IS THE ACTUAL ANSWER
NO JOKE
A bond purchased at $500.00 now has a value of $650.00 what is the percent increase of its value?
Answer: A bond purchased at $500.00 now has a value of $650.00 what is the percent increase of its value?
To make it simple for you, the final ANSWER is a 30% increase, due to the fact that taking $500.00 and multiplying that by 0.3 gives you 150, which you add on to 500, giving you 650. Hope that helps!
Answer: The required percent increase in the bond's value is 30%.
Step-by-step explanation: Given that a bond purchased at $500.00 now has a value of $650.00.
We are to find the percent increase of the value of bond.
According to the given information, we have
Purchasing value of the bond = $500.00
and
present value of the bond = $650.00.
So, increase in the value of the bond = $(650.00 - 500.00) = $150.00.
Therefore, the percent increase of the bond's value is given by
[tex]\dfrac{150.00}{500.00}\times 100\%=\dfrac{3}{10}\times 100\%=30\%.[/tex]
Thus, the required percent increase in the bond's value is 30%.
Translate the graph according to the rule (x, y) → (x – 2, y). The first graph goes with the question.
Look at the picture.
(x, y) → (x + 2, y)
Translate the graph of f(x) 2 units right.
-------------------------------------------------------------
(x, y) → (x, y + n) - translate the graph n units up
(x, y) → (x, y - n) - translate the graph n units down
(x, y) → (x - n, y) - translate the graph n units left
(x, y) → (x + n, y) - translate the graph n units right
The graph shows the exponential regression model for data representing a rabbit population after x years. Which is true of the regression model?
The graph of the regression model is limited to whole-number values for x.
The graph of the regression model is limited to whole-number values for y.
The graph of the regression model cannot be used to approximate the population size for year 1.
The graph of the regression model can be used to predict the population size for any number of years in the future.
Answer:it’s B
Step-by-step explanation:
Geometry problem below
Answer:
Answer D. "ASA"
Step-by-step explanation:
Answer:
ASA
Step-by-step explanation:
When looking at the postulates, we need to know what they stand for
SSS, is side side side
SAS is Side angle side
AAS is angle angle side
ASA is Angle side angle (the side is between the angles)
In the picture we know 2 angles and the included side
so we will use ASA
The price of a smart watch is $109.99 and the sales tax is 6.5%. What is the total cost of the smart watch? Enter your answer in the box.
if you know any other answer on quiz plz give them itll be appreciated greatly :)
Which ordered pair COULD represent point P on the graph?
A) (2, 6)
B) (-3, 6)
C) (-2, -5)
D) (3, -5)
Answer:
the answer is d
Step-by-step explanation:
you can tell because it's past 2 and close to 3. it's -5 because it's past -4. so their is your answer to why it's d
The ordered pair that represents point P on the graph is **D) (3, -5)**. Point P lies in the fourth quadrant, where both the x-coordinate (3) and the y-coordinate (-5) are positive.
The ordered pair that could represent point P on the graph is **D) (3, -5)**. Point P is located in the fourth quadrant where both x and y coordinates are positive. The graph shows a Cartesian plane with axes labelled and scaled. Point P appears to be close to coordinates (3, -5), indicating it's located at a positive distance along the x-axis and a negative distance along the y-axis.Kasia wants to create a triangle with angles measuring 37 degrees, 62 degrees, and 81 degrees. She says that only one unique triangle is possible given these angle measures. Which statement about Kasia’s claim is true?
Kasia is incorrect. Since the angles sum to 180 degrees and no side lengths are given, multiple triangles can be drawn with these angle measures.
Kasia is incorrect. No triangle can be made with these angle measures because they do not sum to 180 degrees.
Kasia is correct. Since the angles sum to 180 degrees and no measurements are given, only one unique triangle is possible.
Kasia is correct. Since the angles do not sum to 180 degrees, only one unique triangle is possible.
Answer:
option: A is correct
Step-by-step explanation:
kaisa's claim is incorrect. clearly the sum of the three angles is 180 degrees therefore we could easily create a triangle with the help of this information but we can't say that this traingle will be unique so we need to know some more information regarding its side.hence multiple triangles could be drawn with these angle measures.
hence option A is correct.
Answer:
A
Step-by-step explanation:
A solution to an equation is a number when substituted back into the original equation produces a what statement
Answer:
true statement
Step-by-step explanation:
Substituting a solution back into the original equation will make the equation true.
What is the length of the midsegment of the trapezoid made by the vertices A(0, 5), B(3, 3), C(5, -2) and D(-1, 2). Show equations and all work that leads to your answer.
Answer:
[tex]\frac{3\sqrt{13} }{2}[/tex]
Step-by-step explanation:
First we have to identify the parallel sides of the trapezium.
We know that the slopes are equal for parallel lines.
Slope of (x₁,y₁) and (x₂,y₂) is given by
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Slope of AB:
[tex]m_{AB} = \frac{3-5}{3-0}=-\frac{2}{3}[/tex]
Slope of BC:
[tex]m_{BC} = \frac{-2-3}{5-3}=-\frac{5}{2}[/tex]
Slope of CD:
[tex]m_{CD} = \frac{2+2}{-1-5}=-\frac{4}{6}=-\frac{2}{3}[/tex]
Slope of DA:
[tex]m_{DA} = \frac{2-5}{-1-0}=3[/tex]
We see that the slopes of AB and CD are equal, so, AB and CD are the parallel sides.
The length of the midsegment = (1/2)*(length of base1 + length of base2 )
Length of the bases can be calculated using distance formula,
[tex]d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
AB = [tex]\sqrt{(3-0)^{2}+(3-5)^{2}}= \sqrt{9+4} =\sqrt{13}[/tex]
CD = [tex]\sqrt{(-1-5)^{2}+(2+2)^{2}}= \sqrt{36+16} =\sqrt{52}=2 \sqrt{13}[/tex]
Length of the midsegment = (1/2) (√13 + 2√13) =3√13/2
how do u do this one?
Answer: 200 messages
========================================================
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Plan A's cost equation is y = 0.10x + 30
Plan B's cost equation is y = 50
Equate the two right hand sides, then solve for x
0.10x + 30 = 50
0.10x = 50-30
0.10x = 20
x = 20/0.10
x = 200
If you send/receive 200 messages, then the two plans will both cost the same ($50) per month.
Which of this fraction are greater then1/2 but less then 3/4 .7/8 .2/5 .1/3 .5/8 .3/6
Answer: 7/8
Step-by-step explanation:
think of each faction as a pie or pizza.
each one will have the number of slices as the bottom number of the fraction.
now shade in the top numbers and see if it more than your 1/2
you will see 7/8 is the answer since it will be one piece left from being complete or "gone"
hope this helped angel!!
Which number is written in scientific notation?
A) 7.8 x 10^-5
B) 3.4 x 100^2
C) 0.84 x 10^6
D) -5 x 10^-12
Answer:
I would say A. 7.8 x 10^-5
Step-by-step explanation:
7.8 x 10^-5 can also be written as 7.8 times 10 to the negative fifth power or the exponent of negative five. But, if you solve it you would get 0.000078 as the real number.
A salesperson at a clothing store earns a commission of 2.5% on all the sales he makes. Which inequalities represent the sales, s, in dollars, he needs to make to earn a commission of more than $100
Answer:
Option A is correct.
Inequality represents the sale s in dollars:
[tex]0.025s\geq 100[/tex]
[tex]s> 4000[/tex]
Step-by-step explanation:
Let s represents the sales in dollars.
Given :A salesperson at a clothing store earns a commission of 2.5% on all the sales he makes.
Earns a Commission = 2.5% of s = [tex]\frac{2.5}{100} \times s = \frac{25s}{1000} = 0.025s[/tex]
It is also given that he needs to make to earn a commission of more than $100
then, we have an inequality:
[tex]0.025s\geq 100[/tex]
divide both sides by 0.025 we get;
[tex]s> 4000[/tex]
Therefore, an inequality represents the sales in dollar ; [tex]0.025s\geq 100[/tex] or [tex]s> 4000[/tex]
Answer:
s > 4,000, s > 4,000
Step-by-step explanation:
Since he needs to make $100 the choices that give him $100 or more are correct.
can someone PLEASE HELP ME ASAP
Answer: The correct answer for number 1. is 11
PLEASE HELP! 100 POINTS! WILL GIVE BRAINLIESTT!
Your local shoe store anticipated giving away 2,500 pairs of shoes in one month, but they only sold 2,215 pairs of shoes. What was the approximate percent error? Show your work to find the percent error.
Answer:
= 11.4%
Step-by-step explanation:
Percent error = (target - actual)/target * 100
target = 2500
actual = 2215
Lets substitute in
Percent error = (2500-2215)/2500 * 100
= 285/2500*100
=.114 * 100
= 11.4%
Answer:
11.4%
Step-by-step explanation:
Find the perimeter of the rectangle.
104
26
52
208
Answer:
P = 124 inches
Step-by-step explanation:
We will need to use the Pythagorean theorem to find the bottom of the rectangle.
a^2 + b^2 = c^2
14^2 + b^2 = 50^2
196 + b^2 = 2500
Subtract 196 from each side
b^2 = 2500 -196
b^2 =2304
Take the square root of each side
sqrt(b^2) =sqrt(2304)
b=48
The perimeter is equal to
P =2(l+w)
P =2(14+48)
= 2(62)
= 124
Tossing coins imagine tossing a fair coin 3 times. (a) what is the sample space for this chance process? (b) what is the assignment of probabilities to outcomes in this sample space?
Answer:
We are given that a fair coin is tossed 3 times.
We know that if a fair coin is tossed 3 times, then there are 8 possible outcomes.
(a) what is the sample space for this chance process?
The sample space associated with tossing a fair coin three times are:
Ω = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Where:
H denotes the head and T denotes the tail.
(b) what is the assignment of probabilities to outcomes in this sample space?
We are given that a fair coin is tossed 3 times, which means that all the possible outcomes in the above mentioned sample space has equal chance being selected. Therefore, the assignment of probabilities to outcomes in this sample space is same for all outcomes and is given below:
[tex]p= \frac{1}{8}[/tex]
Orlando invested $16,000 in an eight-year CD bearing 6.5% simple annual interest, but needed to withdraw $3,500 after five years. If the CD’s penalty for early withdrawal was one year’s worth of interest on the amount withdrawn, when the CD reached maturity, how much less money did Orlando earn total than if he had not made his early withdrawal? a. $227.50 b. $682.50 c. $910.00 d. $455.00
Answer:
Therefore, the correct option is OPTION C.
Step-by-step explanation:
If Orlando had not made his early withdrawal, the amount of money he would have earned is:
F = 0.065($16,000)(8) = $8.320
Given that he withdraw $3500, he now earns:
F1 = (0.065)($16,000)(5) + ($12,500)(0.065)(3)
F1 = $5200 + $2437.5 = $7637.5
And now we have to take into acount the year of penalty, which is one year’s worth of interest on the amount withdrawn.
Penalty= $3500(0.065)(1) = $227.5
So the total money he earns now is: $7637.5 - $227.5 = $7410
Then, the amunt of money he could have earn but he didn't is:
Money = $8.320 - $7410 = $910
Therefore, the correct option is OPTION C.
Answer:
Its C
Step-by-step explanation:
Use the domain and range of each of the following relations to determine which is a function.
A. {3,7,-7,9}
B. { (3,9), (7,-4), (-7,7) }
C. { (3,9), (7,-4), (-7,7) }
D. { (3,9), (7,-4), (7,6), (-7,7) }
Answer:
B
Step-by-step explanation:
i took a test with this question
We want to see which one of the given relations is a function.
The correct options are:
B and C.
To see this, we first need to define what a function is.
A function is a relationship that maps elements from one set, the domain, into another set, the range.
Such that each element in the domain can be mapped into only one element on the range.
The standard notation to these relations is (x, y).
This means that x, from the domain, is being mapped into y, from the range.
Now let's analyze the given options:
A) {3,7,-7,9}
This is just a set of values, no relation there, so this is not a function.
B) { (3,9), (7,-4), (-7,7) }
Here we have a relation, and we can see that each element on the domain is being mapped into only one element from the range, so this is a function.
C) { (3,9), (7,-4), (-7,7) }
This is the exact same set as the one on B.
D) { (3,9), (7,-4), (7,6), (-7,7) }
Here we can see that the element x = 7 is mapped into two different values, so this is not a function.
Then the options that represent functions are B and C.
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A contaminant is found in a solution at a level of 3/500%. What fraction of the solution is this
Answer:3/5
Step-by-step explanation:
First we change 500% to fractions
Changing percentage to fraction is dividing the number by 100
500% = 500/100
Putting this we get 3/(500/100)
Then when a number is being divided by a fraction, to get the answer, we multiply the number by the inverse of the fraction
3/(500/100) = 3 x 100/500 = 300/500 = 3/5
If contaminant is found in a solution at a level of 3/500%. Then 3/5 is fraction of the solution
What is Fraction?A fraction represents a part of a whole.
Given,
A contaminant is found in a solution at a level of 3/500%
Let us convert five hundred percentage to a fraction.
500% is converted to fraction by dividing 500/100
So let us divide three by 500/100
3/ (500/100)
When a fraction is divided with another fraction, then the denominator is multiplied inversely with numerator
3×100/500
=300/500
3/5
Hence if contaminant is found in a solution at a level of 3/500%. Then 3/5 is fraction of the solution
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