Answer:
The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they are willing to pay more for the service, or they are not. Customers are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
40% of the customers are willing to pay more for the service.
This means that [tex]p = 0.4[/tex]
Now we have selected 10 customers randomly.
This means that [tex]n = 10[/tex]
What are the expected value and standard deviation
[tex]E(X) = np = 10*0.4 = 4[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.4*0.6} = 1.55[/tex]
The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.
Based on historical data, your manager believes that 39% of the company's orders come from first-time customers. A random sample of 171 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.21 and 0.32
Answer:
[tex] z= \frac{0.21- 0.39}{0.0373}= -4.829[/tex]
[tex] z= \frac{0.32- 0.39}{0.0373}=-1.877[/tex]
And we can find the probability with this difference:
[tex] P(-4.829<z< -1.877) = P(Z<-1.877) -P(Z<-4.829)=0.0303- 6.86x10^{-7}=0.0303[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n = 171[/tex] represent the sample size
[tex]p =0.39[/tex] the proportion of interest
We want to find the following probability:
[tex] P( 0.21 < \hat p < 0.32)[/tex]
We can use the normal approximation for this case since np >10 and n (1-p) >10
For this case we know that the distribution for the sample proportion is given by:
[tex]\hat p \sim N( p , \sqrt{\frac{p (1-p)}{n}} )[/tex]
And we can use the following parameters:
[tex] \mu_{\hat p}= 0.39[/tex]
[tex] \sigma_{\hat p} =\sqrt{\frac{0.39*(1-0.39)}{171}}= 0.0373[/tex]
And we can apply the z score formula given by:
[tex] z = \frac{p \\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
And using this formula we got:
[tex] z= \frac{0.21- 0.39}{0.0373}= -4.829[/tex]
[tex] z= \frac{0.32- 0.39}{0.0373}=-1.877[/tex]
And we can find the probability with this difference:
[tex] P(-4.829<z< -1.877) = P(Z<-1.877) -P(Z<-4.829)=0.0303- 6.86x10^{-7}=0.0303[/tex]
A square has an area of 349.69m2.
Work out the perimeter of the square.
Answer:
[tex]74.8m[/tex]
Step-by-step explanation:
[tex]A=a^2\\P=4a\\P=4\sqrt{A} \\=4*\sqrt{349.69} \\=74.8m[/tex]
Ares is making 14 jars of honey peanut butter. He wants to use 45 milliliter (ML) of honey in each jar. How much honey (in ML) will ares use in all?
Answer:
630 milliliters.
Step-by-step explanation:
The statement tells us that the final product is 14 jars of honey peanut butter and that in each jar use 45 mliliters of honey. This means that to know the total honey to be used, the required quantity for each jar must be multiplied by the total number of jars, that is:
14 * 45 = 630
Which means that he would spend a total of 630 milliliters.
Step-by-step explanation:
Ares uses 630 ml of honey, because 14×45=630
1. Ryan budgets $35 a week for lunch for 5 days. What
is his average lunch expense each day?
Answer: $7
Step-by-step explanation:
35/ 5 = 7
Answer:
$7
Step-by-step explanation:
Bc/ 35/5=7
Let D= {(x,y) | x^2+y^2 ≤ 4x} Using polar coordinates, What is the integral: ∬y^2/ (x^2+y^2)dxdy?
In polar coordinates, the inequality changes to
[tex]x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta[/tex]
which is a circle of radius 2 and centered at (2, 0). The set D is then
[tex]D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}[/tex]
The integral is then
[tex]\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta[/tex]
[tex]=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta[/tex]
There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,
[tex]\sin(2\theta)=2\sin\theta\cos\theta[/tex]
so that the integral is
[tex]=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta[/tex]
Then invoke another double-angle formula,
[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]
to change the integral to
[tex]=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta[/tex]
[tex]=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}[/tex]
please answer this correctly
Answer:
557
Step-by-step explanation:
l x w
13x24
13x7
22x7
557
The graph shows the relationship between the number of hours that Michelle has been driving and the distance that she has left to travel to get to her destination. A graph on a coordinate plane titled Distance Remaining Over Time. The x-axis is labeled time (in hours), numbered 1 to 8, and the y-axis is labeled miles to destination, numbered 50 to 400. A straight line with a negative slope starts at point (0, 350) and ends at point (7, 0). Which statement is true? It took Michelle 6 hours to complete the trip. For each hour that Michelle drove, she traveled an additional 50 miles. In the first 6 hours, Michelle had traveled a total of 50 miles. In the first 3 hours, Michelle had traveled a total of 200 miles.
Answer:
For each hour that Michelle drove, she traveled an additional 50 miles.
Step-by-step explanation:
The point (0, 350) tells you Michelle's trip is 350 miles long. The point (7, 0) tells you she completed it in 7 hours. The point (6, 50) on the graph tells you she has 50 miles remaining of the original 350 after 6 hours.
True: for each hour Michelle drove, she traveled an additional 50 miles.
Answer:
B. For each hour that Michelle drove, she traveled an additional 50 miles.
Step-by-step explanation:
What’s the correct answer for this?
Answer:
E:
Step-by-step explanation:
The equation of circles is
(x-a)²+(y-b)²=r²
Where
Center = (a,b) = (-6,-3) and r = 12
Now
The equation becomes
(x+6)²+(x+3)²=144
Graph the equation below by plotting the
y-intercept and a second point on the
line.
Answer:
Step-by-step explanation:
On the y-axis, graph the point on (0,4). Then from there, go up one, and to the right 4.
The table below represents the total cost of leasing a car at the end each month.
Month 1 -------- 3 -------- 8 -------- 12
Cost $1,859 --- $2,577 --- $4,372 --- $5,808
Write an equation in slope-intercept form to represent the total cost, y, of leasing a car for x months.
Answer:
y= 359 x+1500
Step-by-step explanation:
find the slope m= (2577-1859)÷(3-1) = 359
y=mx+b
find b : substitute x ,y, and m
get b = 1857 - 359*1 = 1500
Answer:
y= 359 x+1500
Step-by-step explanation:
verify clairaut's theorem for u=e^xysiny
Find the characteristic polynomial and the eigenvalues of the matrix. [Start 2 By 2 Matrix 1st Row 1st Column 11 2nd Column 2 2nd Row 1st Column 2 2nd Column 11 EndMatrix ]The characteristic polynomial is nothing.
Answer:
Step-by-step explanation:
The answer is 3x 987 colunm 2
Which graph represents this equation-3x + 4y= -12
Answer:
C
Step-by-step explanation:
-3x+4y=-12
Add 3x to both sides:
4y=3x-12
Divide both sides by 4 to isolate y:
y=3/4x-3
This means that the line described has a slope of 3/4 and a y intercept of -3. The only graph that matches this is choice C. Hope this helps!
Answer: c
Step-by-step explanation:
For each of the following research scenarios, decide whether the design uses a related sample. If the design uses a related sample, identify whether it uses matched subjects or repeated measures.
1. You are interested in a potential treatment for compulsive hoarding. You treat a group of 50 compulsive hoarders and compare their scores on the Hoarding Severity scale before and after the treatment. You want to see if the treatment will lead to lower hoarding scores. The design described__________a, b, or c________.
a. uses a related sample - repeated measures
b. uses a related sample - matched subjects
c. does not use a related sample
2. John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample to lonely people to the sleep quality of a random sample of nonlonely people. The design described______a, b, or c_______.
a. does not use a related sample
b. uses a related sample (repeated measures)
c. uses a related sample (matched subjects)
Answer:1. uses a related sample - repeated measures
2. . does not use a related sample--a
Step-by-step explanation:
Question 1.
step1 A repeated measure design is a design which measures a given sample repeatedly over a given time using different conditions or related measures.
step 2:In the treatment for compulsive hoarding, Here, measures are taken two times ie before and after treatment on the same 50 hoarders which shows a repeated measure, also the design is a within related sample of the same 50 hoarders to give measurement at different conditions of treatment for high and low hoarding scores so the design describes a related sample - repeated measures
Question 2:
step 1 ; An unrelated sample occurs when Samples being measured do not depend on each other
Step 2; 1st Sample for comparison by John are random lonely people and Second Sample are random non lonely people. so the two samples are independent on each other and will give different measurement based on quality of sleep. So the design does not use a related sample
what is the diagonal of asquare with length 3cm
Answer:
3√2
Step-by-step explanation:
If you draw the diagonal, you have a 45°45°90° triangle.
The two legs are 3, so the hypotenuse is 3√2
Find the measure of x:
Answer:
x=7
Step-by-step explanation:
Do the equation 8x+5 + 3x+8 = 90 and do the math to come out with 7
Hope this helps :)
Answer:
7*
Step-by-step explanation:
8x + 3x + 8 * + 5*=11x+13*
90*-13*=77*
77*= 11x
x= 77*/11=7*
* = degree
Mary is three quarters of Cameron's age. Mary is 24 years old. How old is Cameron?
Answer:
32 years oldStep-by-step explanation:
3/4=24 so 1/4= 24÷3= 8
1/4=8
So to get 4/4 or Cameron's age it is 8×4=32yrs
[tex]answer \\ 32 \: years \: old \\ solution \\ mary's \: age = 24 \\ let \: cameron's \: age \: be \: x \\ given \\ \frac{3}{4} x = 24 \\ or \: x = 24 \times \frac{4}{3} \\ x = 32 \\ hope \: it \: helps[/tex]
A thermometer shows a temperature of Negative 20 and three-fourths degrees. A chemist recorded this temperature in her notebook using a decimal. Which number did the chemist write in the notebook?
Answer:
20.75
Step-by-step explanation:
Answer:
C. -20.75
Step-by-step explanation:
Which expression best represents the situation?
Select the expression that best matches the scenario.
O4 + x + 3
4(x + 3)
4.3
4x + 3
Tyson bought a burger for himself and
each of his 3 friends. He left a tip of $3.
Which expression could represent
the amount of money Tyson spent?
Explain your thinking.
Help plz
Answer:509
Step-by-step explanation:600
Find the area of a regular hexagon with a side length of 5cm, Round to the nearest tenth.
Answer:
i think its 64.95cm
Step-by-step explanation:
Help asap giving branlist!!!
Answer:
Option A.
The heartbeat has a pattern of 60 + (5 x minutes) and linear graphs are straight. The only way the linear graph is straight if there is a pattern.
Step-by-step explanation:
What is the slope intercept form.
Answer:
y = 1/4x + 2
Step-by-step explanation:
Since they gave you point slope form already, all you need to do is convert that into slope-intercept form. Just distribute the parenthesis and move the 4 over. Once you do so, you should get C/3rd option as your answer.
Peter has invented a game with paper cups. He lines up 121 cups face down in a straight line from left to right and consecutively labels them from 1 to 121. He then walks from left to right down the line of cups, flipping all of the cups over. He returns to the left end of the line, then makes a second pass from left to right, this time flipping cups 2,4,6,8... On the third pass, he flips cups 3,6,9,12.... He continues like this: On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.) After 121 passes, how many cups are face up?
Answer:
After 121 passes, there will be 11 cups facing up
Step-by-step explanation:
Given that:
Peter initially lines up 121 cups facing down in a straight line from left to right and consecutively labels them from 1 to 121.
We can have an inequality ; i.e 1 ≤ n ≤ 121; if n represents the divisor including n itself for which n = odd number. Thus at the end of this claim, the cup will be facing up.
On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.)
For each divisor on the ith pass of n;
[tex]i \ th \ pass \ = \ n \ \to \ p |n[/tex] since we are dealing with possibility of having an odds number:
Thus; [tex]p =i[/tex] and [tex]i^2 = n[/tex] where ; n = perfect square.
Thus ; we will realize that between 1 to 121 ; there exist 11 perfect squares. Therefore; as a result of that ; 11 cups will definitely be facing up after 121 passes
The base of a rectangular prism has an area of 24 square millimeters. The volume of the prism is 144 cubic millimeters. The shape is a cube. What is the height of the prism?
Answer:
height = 6 mm
Step-by-step explanation:
The prism is a rectangular prism. The base area of the prism is 24 mm². The volume of the prism is given as 144 mm³.
The height of the prism can be solved as follows.
Volume of the rectangular prism = Bh
where
B = base area
h = height
Volume = 144 mm³
B = 24 mm²
volume = Bh
144 = 24 × h
144 = 24h
divide both sides by 24
h = 144/24
h = 6 mm
Answer:
c
Step-by-step explanation:
edg 2022
A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 17 minutes. For 60 randomly selected runs, bus line B was observed to be off schedule an average of 60 minutes, with standard deviation 13 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.
a. Level of significance, null and alternative hypothesis
b. What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
c. Find or estimate the P-value
d. Based on your answers to part a and c will you reject or fail to reject the null hypothesis? Are the data statistically significant at level alpha?
e. Interpret your conclusion in the context of the application
Answer:
a) Level of significance α=0.05
Two-tailed test, with null and alternative hypothesis:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
b) Student's t distribution. We assume equal variances for both populations, independent sampled values and populations normally distributed.
Test statistic t=-2.4
c) P-value = 0.018
d) Rejection of the null hypothesis.
The data is statistically significant.
e) There is evidence to conclude there is significant difference in average off-schedule times between the bus lines. The difference we see in the samples seems not due to pure chance.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that there is a significant difference in average off-schedule times for this bus lines.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is 0.05.
The sample 1 (bus line A), of size n1=51 has a mean of 53 and a standard deviation of 17.
The sample 2 (bus line B), of size n2=60 has a mean of 60 and a standard deviation of 13.
The difference between sample means is Md=-7.
[tex]M_d=M_1-M_2=53-60=-7[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{17^2}{51}+\dfrac{13^2}{60}}\\\\\\s_{M_d}=\sqrt{5.667+2.817}=\sqrt{8.483}=2.913[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-7-0}{2.913}=\dfrac{-7}{2.913}=-2.4[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=51+60-2=109[/tex]
This test is a two-tailed test, with 109 degrees of freedom and t=-2.4, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.4)=0.018[/tex]
As the P-value (0.018) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant difference in average off-schedule times for this bus lines.
Please help! Correct answer only, please! Consider the matrix shown below: Find the determinant of the matrix Q. A. -67 B. -65 C. 65 D. 67
Answer: d) 67
Step-by-step explanation:
[tex]determinant\ \left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&j\end{array}\right] = a\cdot det\left[\begin{array}{cc}e&f\\h&j\end{array}\right] -\ b\cdot det\left[\begin{array}{cc}d&f\\g&j\end{array}\right] +\ c\cdot det\left[\begin{array}{cc}d&e\\g&h\end{array}\right][/tex]
[tex]determinant\ \left[\begin{array}{ccc}2&3&4\\-3&2&1\\5&-1&6\end{array}\right] \\\\\\= 2\cdot det\left[\begin{array}{cc}2&1\\-1&6\end{array}\right] -\ 3\cdot det\left[\begin{array}{cc}-3&1\\5&6\end{array}\right] +\ 4\cdot det\left[\begin{array}{cc}-3&2\\5&-1\end{array}\right]\\\\\\=2[2(6)-1(-1)]-3[-3(6)-1(5)]+4[3(-1)-2(5)]\\\\\\=2(13)-3(-23)+4(-7)\\\\\\=26+69-28\\\\\\=\large\boxed{67}[/tex]
rearrange the equation t = vf - vi /a
to make acceleration appear on the left hand side
Answer:
a= (vf - vi)/t
Step-by-step explanation:
t = vf - vi /a
a* t =(vf - vi /a)*a
at = vf - vi
at/t = (vf - vi)/t
a = (vf - vi)/t
Hope it works
What’s the correct answer for this?
Answer:
s = 4.43
Step-by-step explanation:
Using formula for bigger circle
s =r∅
Where s is the Arc length, r is rdius and ∅ is theta(angle)
8.84=5∅
∅= 8.84/5
Angle = 1.77 radians
So both angles equal to 1.77 radians
Now again
Using formula
s = r∅
Where s is the Arc length, r is rdius and ∅ is theta(angle)
s = (2.5)(1.77)
s ≈ 4.43
Are the two terms on each tile like terms? Sort the tiles into the appropriate categories.
-7y^2and y^2
-4p and p^2
0.5kt and -10kt
6 and 9
5x and 5
3ad and 2bd
Answer:
LIKE TERMS: 6 and 9, 0.5kt and -10kt, and -7y2 and y2. UNLIKE TERMS: 3ad and 2bd, 5x and 5, and the last one is -4p and p2
Step-by-step explanation:
Answer: like terms: 6&9 , 0.5kt&-10kt , -7y^2&y^2
unlike terms 3ad&2bd, 5x&5, -4p&p^2
Step-by-step explanation:
passed
Which value of a in the exponential function below would cause the function to shrink? f(x) = a(three-halves) Superscript x Four-fifths Five-fourths Three-halves Seven-fourths
Answer:
Four-fifths
Step-by-step explanation:
As we know that
By multiplying the function by a constant, we may expand or shrink the function in the y-direction.
Now we have
[tex]y=a(b^{x})[/tex]
if [tex]a> 1[/tex] > the function would enlarge
if [tex]0< a < 1[/tex] > the function would shrinks
Now
For case A
[tex]a = \frac{4}{5}[/tex]
[tex]0 < (\frac{4}{5} )< 1[/tex] ....... > the function would shrinks
For case B
[tex]a = \frac{5}{4}[/tex]
[tex](\frac{5}{4} )>1[/tex] .......> the function would enlarge
For case C
[tex]a = \frac{3}{2}[/tex]
[tex](\frac{3}{2} )>1[/tex] .........> the function would enlarge
For case D
[tex]a = \frac{7}{4}[/tex]
[tex](\frac{7}{4} )>1[/tex] .........> the function would enlarge
Therefore the second option is correct
Answer: 4/5
Step-by-step explanation: E2020
