Answer:
See below.
Step-by-step explanation:
The 0.7 represents the fact that the ball bounces to 70% of its previous height with each bounce.
The ball is dropped from 9 feet then after the first bounce ( when n = 1) it climbs to 9(0.7)^1 = 6.3 feet , after the second bounce it climbs to 9(0.7)^2
= 4.41 feet and so on.
Given that the sum of the first n terms of the provided series is 6560 determine the value of n (2,6,18,54....)
Answer:
n = 8
Step-by-step explanation:
The given sequence, 2, 6, 18, 54. . ., is a geometric sequence.
It has a common ratio of 3 => [tex] \frac{6}{2} = \frac{18}{6} = \frac{54}{18} = 3 [/tex]
Thus, the sum of the first n terms of a geometric sequence is given as [tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
Where,
[tex] a_1 [/tex] = first term of the series = 2
r = common ratio = 3
[tex] S_n [/tex] = sum of the first n terms = 6,560
Plug in the above values into the formula
[tex]6,560 = \frac{2(1 - 3^n)}{1 - 3}[/tex]
[tex] 6,560 = \frac{2(1 - 3^n)}{-2} [/tex]
[tex] 6,560 = \frac{1 - 3^n}{-1} [/tex]
Multiply both sides by -1
[tex] -6,560 = 1 - 3^n [/tex]
Subtract 1 from both sides
[tex] -6,560 - 1 = - 3^n [/tex]
[tex] -6,561 = - 3^n [/tex]
[tex] 6,561 = 3^n [/tex]
Evaluate
[tex] 3^8 = 3^n [/tex]
3 cancels 3
[tex] 8 = n [/tex]
The value of n = 8
PLS HELP, ASAP what is x when 3 -2x = 11
Answer:
[tex]x = - \frac{9}{2} [/tex]
Step-by-step explanation:
3 - 2x = 11
Group the constants at the right side of the equation
That's
- 2x = 11 - 3
- 2x = 9
Divide both sides by - 2
[tex]x = - \frac{9}{2} [/tex]
Or[tex]x = - 4 \frac{1}{2} [/tex]
Hope this helps you
Management at a home improvement store randomly selected 95 customers and observed their shopping habits.They recorded the number of items each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the managers of the home improvement store.
a. number of items-discrete: total time-discrete
b. number of items-continuous; total time-discrete
c. number of items-continuous; total time-continuous
d. number of items-discrete; total time-continuous
Answer:
d. number of items-discrete; total time-continuous
Step-by-step explanation:
Continuous:
Real numbers, can be integer, decimal, etc.
Discrete:
Only integer(countable values). So can be 0,1,2...
In this question:
You can purchase 0, 1, 2,...,10,...,100,... items, so the number of items is discrete.
You can spend for example, 0.5 hours in the store, or 2.5 minutes, that is, can be decimal numbers. So the total time is continuous
The correct answer is:
d. number of items-discrete; total time-continuous
Find the first four terms of the sequence defined by a(n subscript)= 1/n (separated by a comma).
Answer:
1,1/2,1/3,1/4
Step-by-step explanation:
an = 1/n
n is the term number
a1 = 1/1 =1
a2 = 1/2
a3= 1/3
a4 = 1/4
The first 4 terms are 1,1/2,1/3,1/4
In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The
longest and the shortest days of the year vary by 2 hours 53 minutes from the equinox.
In this year, the equinox falls on March 21. In this task, you'll use a trigonometric function
to model the hours of daylight hours on certain days of the year in New York City.
Identify the independent and dependent variables find amplitude and the period of the function create a trigonometric function that describes the hours of sunlight for each day of the year and then use the function you built to find how fewer daylight hours February 10 will have then March 21
Answer:
independent: day number; dependent: hours of daylight
d(t) = 12.133 +2.883sin(2π(t-80)/365.25)
1.79 fewer hours on Feb 10
Step-by-step explanation:
a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).
__
b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,
March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...
d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))
d(t) = 12.133 +2.883sin(2π(t-80)/365.25)
__
c) d(41) = 10.34, so February 10 will have ...
12.13 -10.34 = 1.79
hours less daylight.
When the sun is at a certain angle in the sky, a 100 foot building will cast a 25 foot shadow. How y’all is a person if he casts a 1.5 foot shadow at the same time?
Answer:
6 ft
Step-by-step explanation:
The building height of 100 ft is 4 times the shadow length of 25 ft. At the same ratio, the person's height is 4 times the 1.5 ft shadow length, so is ...
4 × (1.5 ft) = 6.0 ft
The person is 6 ft tall.
HELP WITH THIS QUESTION(I know the answer I just need to double check)
Answer:
-5, -3, -1 , 1 , 3
Step-by-step explanation:
2a -a + 1 =
x + y + x + 2 =
2(x + 4) + 2x =
3x + 2(x - 2) =
Answer:
Step-by-step explanation:
Please, share the instructions that come with each problem. Thanks.
2a -a + 1 = can be simplified to a + 1.
x + y + x + 2 = cannot be simplified.
2(x + 4) + 2x =
3x + 2(x - 2) = can be expanded and then simplified:
3x + 2x - 4 = 5x - 4
A sum lent out at simple interest becomes rs4480 in 3 years and rs 4800 in 5years.find the rate of interest
Answer: rate = 4%
Step-by-step explanation:
SI = 4800 - 4480 = 320 for two years
For 1 year, it is 320/2 = 160
For 5 years, it is 160 * 5 = 800
Principal = Amount -SI
P = 4800 - 800 = 4000
SI = prt / 100
800 = (4000 * r * 5) / 1000
r = 800 * 100 / 4000 * 5
r = 4%
Answer:
Rate of intrest = 4%
Step-by-step explanation:
Short forms
Simple intrest=SI Year= Y Rate= r
SI= 4800-4480
= 320
1 year= 320/2 = 160
5year= 160 x 5
= 800
P= Amount-SI
P= 4800-800
= 4000
SI=PRT/100
800=(4000 X r X 5)/1000
r=800 x 100/4000 x 5
r= 4%
Hope it was Helpful!
Mark me as Brainliest!
Identify the axis of symmetry of the given quadratic
y= -3x^2 - 12
Answer:
[tex]\frac{d}{dy}(-3x^{2} -12) = -6x[/tex]
0 = -6x
0 = x
[tex]-3(0)^{2} -12 = -12[/tex]
(0,-12)
Step-by-step explanation:
6x^2-2x=20 use ac method
Answer:
Cannot be factored
Step-by-step explanation:
For the functions f(x)=−9x^2+9 and g(x)=8x^2+9x, find (f+g)(x) and (f+g)(−1)
Answer:
f(x) = - 9x² + 9
g(x) = 8x² + 9x
To find (f+g)(x) add g(x) to f(x)
That's
(f+g)(x) = -9x² + 9 + 8x² + 9x
Group like terms
(f+g)(x) = - 9x² + 8x² + 9x + 9
(f+g)(x) = - x² + 9x + 9To find (f + g)(- 1) substitute - 1 into (f+g)(x)
That's
(f + g)(- 1) = -(-1)² + 9(-1) + 9
= - 1 - 9 + 9
= - 1Hope this helps you
Mr. Rosenberger asked his students to use the distributive property to rewrite the expression 18 (24) by using friendlier numbers. The table below shows the expressions that four students created. Expressions Created by Students Student Expression Aaron 10 + 8 times 4 + 20 Brian 10 + 8 (4 + 20) Cece 18 (4 + 6) Diana 18 (4 + 20)
Answer:
diana
Step-by-step explanation:
Answer:
I think it’s Diana I’m sorry if I’m wrong :P
A retail store sells two types of shoes, sneakers and sandals. The store owner pays $8 for the sneakers and $14 for the sandals. The sneakers can be sold for $10 and the sandals can be sold for $17. The owner of the store estimates that she won't sell more than 200 shoes each month, and doesn't plan to invest more that $2,000 on inventory of the shoes. Let x= the number of sneakers in stock, and y=the number of sandals in stock. Write an equation to show the profit she will make on sneakers and sandals. P = [answer0]
Answer:
The equation that shows the profit: P = 2x + 3y
Step-by-step explanation:
The number of sneaker = x
The number of sandals = y
Cost of sneaker = 8 dollars.
Cost of sandals = 14 dollars.
Selling price of sneaker = $10
Selling price of sandals = $17
Total revenue = $10x + $17y
Total cost = $8x + $14y
Profit (P) = Total revenue - Total cost.
Profit = ($10x + $17y) – ($8x + $14y)
P = 10x +17y – 8x – 14y
P = 2x + 3y
Less than 51% of workers got their job through networking. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage). H0 : p H1 : p
Use the following codes to enter the following symbols:
≥≥ enter >=
≤≤ enter <=
≠≠ enter !=
Answer:
Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 51%
Alternate Hypothesis, [tex]H_A[/tex] : p < 51%
Step-by-step explanation:
We are given that less than 51% of workers got their job through networking. We have to express the null and alternative hypotheses in symbolic form for this claim.
Let p = population proportion of workers who got their job through networking
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 51%
Alternate Hypothesis, [tex]H_A[/tex] : p < 51%
Here, the null hypothesis states that greater than or equal to 51% of workers got their job through networking.
On the other hand, the alternate hypothesis states that less than 51% of workers got their job through networking.
Hence, this is the appropriate hypothesis that can be used.
Can someone help with this I can't fail.
Answer: B
Step-by-step explanation:
(f-g)(x) is f(x)-g(x). Since we have f(x) and g(x), we can directly subtract them.
5x-2-(2x+1) [distribute -1]
5x-2-2x-1 [combine like terms]
3x-3
25e +-6e7 =
What the answer
Answer:
-6511.8
Step-by-step explanation:
A department store finds that in a random sample of 200 customers, 60% of the sampled customers had browsed its website prior to visiting the store. Based on this data, a 90% confidence interval for the population proportion of customers that browse the store’s website prior to visiting the store will be between
Answer:
between 108-110?
Step-by-step explanation:
60% or 200 = 120 people
90% of 120 = 108
question doesnt look complete so this is the best I could come up with...♀️
Need help with this question thanks!
A student randomly guesses the answers to a 10 question true or false quiz. The observation in the student’s answer (T or F) for each question. Describe the sample space
Answer:
in this experiment we only have two sample space which is only true or false.
because all the answers will have to fall between this sample space.
Step-by-step explanation:
we cannot actually or fully understand the above answer without first of all defining or explaining what sample space actually means.
Sample space: this is the set of all possible outcome that may come from an experiment.or we can say simply say it is the range of values that the experiment depends on.
The graph of F(x) shown below resembles the graph of G(x) = K, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
F(x)=?
G(X) = 1x1
O A. F(X) = 3M+3
O B. F(X) --
O C. F(x) = -3M-3
O D. F(X) = 3W-3
Step-by-step explanation:
O D. F(X) = 3W-3 the answer is D
The function that represents the situation is F(x) = -x² - 3.
The correct option is A.
What is transformation on the graphs?Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification of algebraic equations.
here, we have,
Let the functions f(x) and g(x) be two real functions.
And g (x) = f (x) + k, where k is real numbers.
The function can be sketched by shifting f (x), k units vertically.
The value of k can find the direction of shift:
if k > 0, the base graph shifts k units up, and
if k < 0, the base graph shifts k units down.
Given that ,
the parent function is g(x) = x².
To find the transformed function F(x):
The function's diagram is in the opposite direction.
That means the function is -x².
And the function is shifted 3 units down vertically.
From the definition the required function is,
F(x) = -x² - 3.
Therefore, F(x) = -x² - 3.
To learn more about the transformation on the graphs;
brainly.com/question/19040905
#SPJ7
complete question:
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?
A.
F(x) = –x2 – 3
B.
F(x) = x2 – 3
C.
F(x) = –(x + 3)2
D.
F(x) = –(x – 3)2
Need help with the problem 77
Hey there! :)
Answer:
∠A = 15.6°
Step-by-step explanation:
Use trigonometry to solve for ∠A. Since this involves the opposite and adjacent sides, tangent will be used. Therefore:
24/86 = arc tan x (inverse of tangent)
0.279 = arc tan x
x = 15.59° ≈ 15.6°.
Therefore:
∠A = 15.6°
If segment ac and segment bc are tangent to circle o,find the value of x
Answer:
160°
Step-by-step explanation:
1/2 (Major arc AB - Minor arc AB) = 20°
Major arc AB = 200°
Minor arc AB = 160°
central angle = minor arc AB = 160°
The value of variable x is,
⇒ x = 150°
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
Line segment ac and segment bc are tangent to circle O.
Now, We get;
∠A + ∠B + ∠C + ∠O = 360°
90° + 90° + 30° + x = 360°
x = 360° - 210°
x = 150°
Hence, The value of variable x is,
⇒ x = 150°
Learn more about the angle visit:;
https://brainly.com/question/25716982
#SPJ7
If x, y, and z are positive integers and 3x=4y=7z, then the least possible value of x+y+z is?
A. 33
B. 40
C. 49
D. 61
E. 84
Answer:
D
Step-by-step explanation:
3x, 4y, and 7z must be equal to the LCM of 3, 4, and 7 in order to be the smallest value. The LCM is 84 which means x = 28, y = 21 and z = 12. 28 + 21 + 12 = 61.
Answer:
61
Step-by-step explanation:
3x=4y=7z
x =4/3 y
x = 7/3 z
Since they have to be integers
y and z must be multiples of 3
y = 7/4 z
Since they have to be integers
z must be multiple of 4
Z must be a multiple of 12
Let z = 12
Then
y = 7/4 *12
y = 21
x = 7/3 *12
x = 28
x+y+z
28+ 21+12
61
A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds.
A sample of seven infants is randomly selected, and their weights at birth are recorded as:
9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds.
If Alpha = 0.05,
1. What is the critical t-value?
2. What is the decision for a statistically significant change in average weights at birth at the 5% level of significance?
Answer:
1. Critical value t=±2.447
2. The null hypothesis is failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the birth weight significantly differs from 6.6 lbs.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the birth weight significantly differs from 6.6 lbs.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=6.6\\\\H_a:\mu\neq 6.6[/tex]
The significance level is 0.05.
The sample has a size n=7.
The sample mean is M=7.56.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1.18.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{1.18}{\sqrt{7}}=0.446[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{7.56-6.6}{0.446}=\dfrac{0.96}{0.446}=2.152[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=7-1=6[/tex]
For a two-tailed test with 5% level of significance and 6 degrees of freedom, the critical value for t is ±2.447.
As the test statistic t=2.152 is under 2.447 and over -2.447, it falls in the acceptance region, so the effect is not significant. The null hypothesis is failed to be rejected.
At a significance level of 0.05, there is not enough evidence to support the claim that the birth weight significantly differs from 6.6 lbs.
Sample mean and standard deviation calculations:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{7}(9+7.3+6+. . .+6.6)\\\\\\M=\dfrac{52.9}{7}\\\\\\M=7.56\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{6}((9-7.56)^2+(7.3-7.56)^2+(6-7.56)^2+. . . +(6.6-7.56)^2)}\\\\\\s=\sqrt{\dfrac{8.32}{6}}\\\\\\s=\sqrt{1.39}=1.18\\\\\\[/tex]
A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 141 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
Answer:
Length = 47 in
Radius = 47/π in
Step-by-step explanation:
Let 'h' be the length of the package, and 'r' be the radius of the cross section.
The length and girth combined are:
[tex]L+G=141=h+2\pi r\\h=141-2\pi r[/tex]
The volume of the cylindrical package is:
[tex]V=A_b*h\\V=\pi r^2*h[/tex]
Rewriting the volume as a function of 'r':
[tex]V=\pi r^2*h\\V=\pi r^2*(141-2\pi r)\\V=141\pi r^2-2\pi^2 r^3[/tex]
The value of 'r' for which the derivate of the volume function is zero yields the maximum volume:
[tex]V=141\pi r^2-2\pi^2 r^3\\\frac{dV}{dr}=282\pi r-6\pi^2r^2=0\\ 6\pi r=282\\r=\frac{47}{\pi} \ in[/tex]
The length is:
[tex]h=141-2\pi r=141-2\pi*\frac{47}{\pi}\\h=47\ in[/tex]
The dimensions that yield the maximum volume are:
Length = 47 in
Radius = 47/π in
Trish conducts an analysis which shows that the level of alcohol consumption affects reaction times more when a person is sleep-deprived than when a person is well-rested. This is an example of ______.
a. interaction
b. confounding
c. bias
d. main effect
Answer:
a. interaction
Step-by-step explanation:
In statistics, interaction occurs when the effect of one variable depends on the value of another variable.
In this case, Trish's analysis shows that the effect of alcohol consumption in a persons reaction time also depends on that person's quality of sleep, highlighting a clear case of interaction.
match each function on the left to all points on the right ! Please help!
Answer:
f(x)=2x-2 with =( -1, 4)
f(x)=2(x^2) -2 with (-1,0)
f(x)=2√(x-2) with (2,0)
Step-by-step explanation:
f(x)=2x-2
(2,0)
0=2(2)-2=2 0=2
(-1,-4)
4=2(-1)-2=-4 -4 = -4 f(x)=2(x^2) -2
(2,0)
0=2(2^2)-2=6 0=6
(-1,0)
0=2(-1^2)-2=0 0=0 f(x)=2√(x-2) (2,0)
0=2√(2-2)=0 0=0
The function f ´( x ), which would be read `` f -prime of x '', means the derivative of f ( x ) with respect to x .
What is f(x) ?A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value, or independent variable, is represented by the letter x. The output value, also known as the dependent variable, is denoted by the letter y, or f(x).
f(x)=2x-2\s(2,0)
0=2(2)
-2=2 0=2
(-1,-4)
4=2(-1)-2=-4 -4 = -4 f(x)=2(x^2) -2\s(2,0) (2,0)
0=2(2^2)
-2=6 0=6\s(-1,0)
0=2(-1^2)
-2=0 0=0 f(x)=2 √(x-2) (2,0) (2,0)
0=2√(2-2)=0 0=0
The phrase "f (x)" denotes a formula with x serving as its input variable. Not "multiply f and x," though! Never try to "multiply" the function name with its parenthesized input and avoid embarrassing yourself by pronouncing (or thinking of) "f (x)" as being "f times x".
Assume that military aircraft use ejection seats designed for men weighing between 141.8 lb and 218 lb. If women's weights are normally distributed with a mean of 173.6 lb and a standard deviation of 49.8 lb, what percentage of women have weights that are within those limits? Are many women excluded with those specifications?
Answer:
[tex]P(141.8<X<218)=P(\frac{141.8-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{218-\mu}{\sigma})=P(\frac{141.8-173.6}{49.8}<Z<\frac{218-173.6}{49.8})=P(-0.639<z<0.892)[/tex]
And we can find this probability with this difference and using the normal standard table:
[tex]P(-0.639<z<0.892)=P(z<0.892)-P(z<-0.639)=0.814-0.261= 0.553[/tex]
Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(173.6,49.8)[/tex]
Where [tex]\mu=173.6[/tex] and [tex]\sigma=49.8[/tex]
We are interested on this probability
[tex]P(141.8<X<2188)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(141.8<X<218)=P(\frac{141.8-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{218-\mu}{\sigma})=P(\frac{141.8-173.6}{49.8}<Z<\frac{218-173.6}{49.8})=P(-0.639<z<0.892)[/tex]
And we can find this probability with this difference and using the normal standard table:
[tex]P(-0.639<z<0.892)=P(z<0.892)-P(z<-0.639)=0.814-0.261= 0.553[/tex]
Then the answer would be approximately 55.3% of women between the specifications. And that represent more than the half of women
Chase scored 14 points on Monday, and he doubled his score each day thereafter. How many points did he score on Thursday?
Answer:
112
Step-by-step explanation:
Original Score equals 14 right?
If chase doubles his original Score daily it will be
14*2 (Tuesday)=28
28×2 (Wednesday)=56
56×2 (Thursday)=112
Therefore,
Chase's Final score Equals 112
The number of points did he score on Thursday is 112.
Given that,
Chase scored 14 points on Monday. And he doubled his score each day thereafter.Based on the above information, the calculation is as follows:
On Monday = 14
On Tuesday = (14) (2) = 28
On Wednesday = (28) (2) = 56
On Thursday = (56) (2) = 112
Therefore, we can conclude that the number of points did he score on Thursday is 112.
Learn more: brainly.com/question/24169758