Answer:
Step-by-step explanation:
Hello!
The given data corresponds to the variables
Y: Annual Maintenance Expense ($100s)
X: Weekly Usage (hours)
n= 10
∑X= 253; ∑X²= 7347; [tex]\frac{}{X}[/tex]= ∑X/n= 253/10= 25.3 Hours
∑Y= 346.50; ∑Y²= 13010.75; [tex]\frac{}{Y}[/tex]= ∑Y/n= 346.50/10= 34.65 $100s
∑XY= 9668.5
a)
To estimate the slope and y-intercept you have to apply the following formulas:
[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{9668.5-\frac{253*346.5}{10} }{7347-\frac{(253)^2}{10} }= 0.95[/tex]
[tex]a= \frac{}{Y} -b\frac{}{X} = 34.65-0.95*25.3= 10.53[/tex]
^Y= a + bX
^Y= 10.53 + 0.95X
b)
H₀: β = 0
H₁: β ≠ 0
α:0.05
[tex]F= \frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg}; Df_{Error}}[/tex]
F= 47.62
p-value: 0.0001
To decide using the p-value you have to compare it against the level of significance:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The decision is to reject the null hypothesis.
At a 5% significance level you can conclude that the average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.
b= 0.95 $100s/hours is the variation of the estimated average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.
a= 10.53 $ 100s is the value of the average annual maintenance expense of the computer wheel alignment and balancing machine when the weekly usage is zero.
c)
The value that determines the % of the variability of the dependent variable that is explained by the response variable is the coefficient of determination. You can calculate it manually using the formula:
[tex]R^2 = \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]} = \frac{0.95^2[7347-\frac{(253)^2}{10} ]}{[13010.75-\frac{(346.50)^2}{10} ]} = 0.86[/tex]
This means that 86% of the variability of the annual maintenance expense of the computer wheel alignment and balancing machine is explained by the weekly usage under the estimated model ^Y= 10.53 + 0.95X
d)
Without usage, you'd expect the annual maintenance expense to be $1053
If used 100 hours weekly the expected maintenance expense will be 10.53+0.95*100= 105.53 $100s⇒ $10553
If used 1000 hours weekly the expected maintenance expense will be $96053
It is recommendable to purchase the contract only if the weekly usage of the computer is greater than 100 hours weekly.
Kendra can make 120 soccer kicks in 3 minutes. Jovani can make 100 soccer kicks in 4 minutes. How long will it take them to make 1300 soccer kicks together?
The time it takes them to make 1300 soccer kicks together is 51 minutes
Let the number of soccer kicks be yLet the time taken be x
Writing this as a coordinate (x, y). If Kendra can make 120 soccer kicks in 3 minutes and Jovani can make 100 soccer kicks in 4 minutes, this can be written in a coordinate form as (3, 120) and (4, 100)
The standard linear equation is given as y = mx + b
Get the slope:
m = 100-120/4-3
m = -20/1
m = -20
Get the y-intercept:
Recall that y = mx + b
120 = -20(3) + b
120 = -60 + b
b = 180
The required equation is g(x) = -20x + 180
To determine the time it will take them to make 1300 soccer kicks together, substitute g(x) = 1300 and find "x"
1300 = -20x + 180
20x = 1200 - 180
20x = 1020
x = 51 minutes
Hence the time it takes them to make 1300 soccer kicks together is 51 minutes
Learn more on equations here: https://brainly.com/question/11408596
Find the circumference of a circle with a radius of 15 centimeters. Round your answer to the nearest centimeter
Answer:
94 cm
Step-by-step explanation:
The formula for finding the circumference of a circle is;
Circumference = 2πr
where π = [tex]\frac{22}{7}[/tex] or 3.14 and
r = radius
Here radius is 15 cm so;
Circumference = [tex]2 * \frac{22}{7} * 15[/tex]
= [tex]\frac{660}{7}[/tex]cm
= 94.28cm
= 94 cm ( rounded to the nearest centimetre )
Support requests arrive at a software company at the rate of 1 every 30 minutes. Assume that the requests arrive as events in a Poisson process.
a) What is the probability that the number of requests in an hour is between 2 and 4 inclusive? Give your answer to four decimal places.
b) What is the expected number of requests in a 10 hour work day? Give an exact answer.
c) What is the probability that the number of requests in a 10 hour work day is between 20 and 24 inclusive? Give your answer to four decimal places.
d) What is the standard deviation of the number of requests in a 10 hour work day? Give your answer to four decimal places.
Answer:
a. 0.5413
b. 20
c. 0.3724
d. 4.4721
Step-by-step explanation:
Solution:-
- We will start by defining a random variable X.
X : The number of support requests arrived
- The event defined by the random variable ( X ) is assumed to follow Poisson distribution. This means the number of request in two distinct time intervals are independent from one another. Also the probability of success is linear within a time interval.
- The time interval is basically the time required for a poisson event to occur. Consequently, each distributions is defined by its parameter(s).
- Poisson distribution is defined by " Rate at which the event occurs " - ( λ ). So in our case the rate at which a support request arrives in a defined time interval. We define our distributions as follows:
X ~ Po ( λ )
Where, λ = 1 / 30 mins
Hence,
X ~ Po ( 1/30 )
a)
- We see that the time interval for events has been expanded from 30 minutes to 1 hour. However, the rate ( λ ) is given per 30 mins. In such cases we utilize the second property of Poisson distribution i.e the probability of occurrence is proportional within a time interval. Then we scale the given rate to a larger time interval as follows:
λ* = [tex]\frac{1}{\frac{1}{2} hr} = \frac{2}{1hr}[/tex]
- We redefine our distribution as follows:
X ~ Po ( 2/1 hr )
- Next we utilize the probability density function for poisson process and accumulate the probability for 2 to 4 request in an hour.
[tex]P ( X = x ) = \frac{e^-^l^a^m^b^d^a . lambda^x}{x!}[/tex]
- The required probability is:
[tex]P ( 2 \leq X \leq 4 ) = P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 )\\\\P ( 2 \leq X \leq 4 ) = \frac{e^-^2 . 2^2}{2!} + \frac{e^-^2 . 2^3}{3!} + \frac{e^-^2 . 2^4}{4!}\\\\P ( 2 \leq X \leq 4 ) = 0.27067 + 0.18044 + 0.09022\\\\P ( 2 \leq X \leq 4 ) = 0.5413[/tex] Answer
b)
We will repeat the process we did in the previous part and scale the poisson parameter ( λ ) to a 10 hour work interval as follows:
λ* = [tex]\frac{2}{1 hr} * \frac{10}{10} = \frac{20}{10 hr}[/tex]
- The expected value of the poisson distribution is given as:
E ( X ) = λ
Hence,
E ( X ) = 20 (10 hour work day) .... Answer
c)
- We redefine our distribution as follows:
X ~ Po ( 20/10 hr )
- Next we utilize the probability density function for poisson process and accumulate the probability for 20 to 24 request in an 10 hour work day.
[tex]P ( X = x ) = \frac{e^-^l^a^m^b^d^a . lambda^x}{x!}[/tex]
- The required probability is:
[tex]P ( 20 \leq X \leq 24 ) = P ( X = 20 ) + P ( X = 21 ) + P ( X = 22 )+P ( X = 23 ) + P ( X = 24 )\\\\P ( 20 \leq X \leq 24 ) = \frac{e^-^2^0 . 20^2^0}{20!} + \frac{e^-^2^0 . 20^2^1}{21!} + \frac{e^-^2^0 . 20^2^2}{22!} + \frac{e^-^2^0 . 20^2^3}{23!} + \frac{e^-^2^0 . 20^2^4}{24!} \\\\P ( 20 \leq X \leq 24 ) = 0.0883 +0.08460 +0.07691 +0.06688+0.05573\\\\P ( 20 \leq X \leq 24 ) = 0.3724[/tex] Answer
c)
The standard deviation of the poisson process is determined from the application of Poisson Limit theorem. I.e Normal approximation of Poisson distribution. The results are:
σ = √λ
σ = √20
σ = 4.4721 ... Answer
pls help me pls pls pls
Answer: 1x + 2y = 4
Step-by-step explanation:
The equation of the line is y = -1/2x + 2.
First, let's make 4 on one side of the equation. First, bring x to the left. y + 1/2x = 2. Then multiply the whole equation by two. Thus, 1x + 2y = 4.
Hope it helps <3
What will happen (other things being equal) if you increase the sample size used to construct a given confidence interval?
Answer:
So if you increase the sample size used to construct a given confidence interval, the confidence interval will be narrower, that is, more precise.
Step-by-step explanation:
The sample size is important to find the margin of errror of a confidence interval.
The margin of error is given by a formula in the following format:
[tex]M = \frac{c*s}{\sqrt{n}}[/tex]
In which c is the critical value(depends on the distribution used, can be T or Z), s is the standard deviation(of the sample or the population) and n is the size of the sample.
As n increases, M decreases, which leads to a lower margin of error.
The lower the margin of error, the more precise the interval is.
So if you increase the sample size used to construct a given confidence interval, the confidence interval will be narrower, that is, more precise.
What steps would you take to determine if these figures are similar? Check all that apply. Use a scale factor of 2. Multiply the vertices of polygon ABCD by One-half. Translate the intermediate image 4 units down. Perform two different dilations. Reflect the intermediate image.
Answer:
Well I took it"s Reflect the intermediate image. and Multiply the vertices of polygon ABCD by One-half.
Step-by-step explanation:
Answer:
2 and 5 or B and E
Step-by-step explanation:
i did it on edge! ; )
Find the missing side. Round your answer to the nearest tenth.
Answer:12.4
Step-by-step explanation:
hyp=16,opp=x
sin 51°=[tex]\frac{x}{16}[/tex]
cross multipy
sin 51° x 16 = x
x=0.7771 x 16
x≅12.4
hey one more for my friend :)
Answer:
Third graph from the top
Step-by-step explanation:
A proportional relationship is a straight line that goes through the point (0,0)
Answer:
The third graphStep-by-step explanation:
The third straight graph, since a proportion is a relationship in which a second variable is changed by a same value all the time (linear).
Hope this helps, if not, tell me and I shall try again
Which of the following are exterior angles? Check all that apply.
Answer:<5 and <4 are exterior angles
Step-by-step explanation:
Because they are the only ones outside it they are the only ones that are exterior angles!
<!> Brainliest is appreciated! <!>
Answer:
for AL Its 3 and 4
Plz answer what is in the screen shot!
Answer:
([tex]\sqrt{15}[/tex])/7
Step-by-step explanation:
Let b be the tird side of the triangle
tanθ= b/c
using the pythagorian theorem we get :
a²+b²= c² ⇒ b²= c²-a²= 8²-7²=15 ⇒b=√15
so: tanθ= √15/7
What is the equation of the graphed line written in
standard form?
O 2x - y = -4
O 2x - y = 4
O y = 2x – 4
O y=x-4
Answer:
2x-y=4
Step-by-step explanation:
Standard form of a line: Ax+by=c
Use slope intercept form: y=mx+b
slope= 2
y=2x-4
Add 4 to both sides.
y+4=2x
subtract y from both sides.
4=2x-y
Rotate the equation
2x-y=4
Answer:
2x-y=4
Step-by-step explanation:
y=2x-4 is the slope intercept.
y-2x=-4
-2x+y=-4
2x-y=4
how many are 5 x 5 ?
Ahmad makes compost by mixing 0.5 kg of sand with 2 kg of peat. Write the ratio of sand to peat. Give your answer in its simplest form.
Answer:
0.5kg
2kg
0.7kg
b668_*;
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Help me pls pls pls pls
Answer:
Inequality Form:
x≥130
Step-by-step explanation:
isolate the variable by dividing each side by factors that don’t contain the variable.
the class mean was 72 with a standard deviation of 4.2. Calculate the z-score (to 2 decimal places) for a person who received score of 59. Is it usual or unusual?
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Michelle, a student studying music, randomly sampled fellow music majors and asked whether they listen to music while they study. The resulting confidence interval for the proportion of music students who listen to music while studying is (0.09,0.26). What is the margin of error?
Answer:
The margin of error of this confidence interval is MOE=0.085.
Step-by-step explanation:
The confidence interval bounds are usually calculated from a sample statistic substracting (for the lower bound) or adding (for the upper bound) the margin of error. This margin of error depends on the confidence level, the standard deviation and the sample size.
Then, if the lower and upper bound are calculated this way, we can calculate the margin of error as:
[tex]LB=p-MOE\\\\UB=p+MOE\\\\UB-LB=(p+MOE)-(p-MOE)=2\cdot MOE\\\\\\MOE=\dfrac{UB-LB}{2}=\dfrac{0.26-0.09}{2}=\dfrac{0.17}{2}=0.085[/tex]
what is the answer to the problem i need help with?
Answer:
C
Step-by-step explanation:
Recall the equation for a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex], where the center is (h,k) and the radius is r.
The given equation is:
[tex](x+5)^2+(y+7)^2=21^2[/tex]
Another way to write this is:
[tex](x-(-5))^2+(y-(-7))^2=21^2[/tex]
Thus, we can see that h=-5 and k=-7.
The center is at (-5, -7).
someone please help me!!!
Explanation:
Surface area of a cone = pi*r^2 + pi*r*sqrt(r^2+h^2)
r = radius
h = height of cone
In this case,
r = 8 is the radius
h = 41
So,
SA = surface area
SA = pi*r^2 + pi*r*sqrt(r^2+h^2)
SA = pi*8^2 + pi*8*sqrt(8^2+41^2)
SA = 1250.936884057 use a calculator for this step
SA = 1251 square meters approximately
not sure how I would solve this
Fill in the missing information. Tim Worker is doing his budget. He discovers that the average miscellaneous expense is $45.00 with a standard deviation of $16.00. What percent of his expense in this category would he expect to fall between $38.60 and $57.80?
Answer:
[tex] P(38.6 <X <57.8)[/tex]
And we can assume a normal distribution and then we can solve the problem with the z score formula given by:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{38.6- 45}{16}= -0.4[/tex]
[tex] z=\frac{57.8- 45}{16}= 0.8[/tex]
We can find the probability of interest using the normal standard table and with the following difference:
[tex] P(-0.4 <z<0.8)= P(z<0.8) -P(z<-0.4) = 0.788-0.345= 0.443[/tex]
Step-by-step explanation:
Let X the random variable who represent the expense and we assume the following parameters:
[tex]\mu = 45, \sigma 16[/tex]
And for this case we want to find the percent of his expense between 38.6 and 57.8 so we want this probability:
[tex] P(38.6 <X <57.8)[/tex]
And we can assume a normal distribution and then we can solve the problem with the z score formula given by:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{38.6- 45}{16}= -0.4[/tex]
[tex] z=\frac{57.8- 45}{16}= 0.8[/tex]
We can find the probability of interest using the normal standard table and with the following difference:
[tex] P(-0.4 <z<0.8)= P(z<0.8) -P(z<-0.4) = 0.788-0.345= 0.443[/tex]
[tex](2 + 6)(2 + 3)[/tex]
Answer:
40 because (8)(5)=40 when you add the numbers inside the parenthesis
Step-by-step explanation:
Look at my picture for the written work for ANOTHER method
To solve this problem, you use the method called FOIL.
F= multiply the FIRST terms
O= multiply the OUTTER terms
I= multiply the INNER terms
L= multiply the LAST terms
Please rate this the brainlist if this helped, thanks!
Answer:
[tex]40[/tex]
Step-by-step explanation:
[tex](2+6)(2+3)[/tex]
Solve brackets.
[tex](8)(5)[/tex]
Multiply.
[tex]=40[/tex]
4(x+1)=16 HELP MEEEEEE
Answer:
4(x + 1) = 16
x + 1 = 4 (Divide equation by 4)
x = 3 (subtract 1)
Answer:
x = 3
Step-by-step explanation:
4(x + 1)=16
Expand the brackets.
4x + 4 = 16
Subtract 4 on both sides.
4x + 4 - 4 = 16 - 4
4x = 12
Divide both sides by 4.
4x/4 = 12/4
x = 3
Determine the function which corresponds to the given graph. (3 points) a natural logarithmic function crossing the x axis at negative two and y axis at one. The asymptote is x = -3
Answer:
[tex]y=\log_3{(x+3)}[/tex]
Step-by-step explanation:
The parent log function has a vertical asymptote at x=0, so the asymptote at x=-3 indicates a left shift of 3 units.
The parent log function crosses the x-axis 1 unit to the right of the vertical asymptote, which this one does, indicating there is no vertical shift.
The parent log function has an x-value equal to its base when it has a y-value of 1. Here, the y-value of 1 corresponds to an x-value 3 units to the right of the vertical asymptote, so the base of this logarithm is 3.
The function is ...
[tex]\boxed{y=\log_3{(x+3)}}[/tex]
Find the least number which is exactly divisible by 72 and 108
Step-by-step explanation:
2 is the answer because:
72/2=36
108/2=54
Answer:
2
Step-by-step explanation:
Well divisible means the lowest numbers it can be divided by.
So we can make a chart.
72 - 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
108 - 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
So besides 1, 2 is the lowest divisible number between 108 and 72.
If f(x) = 7 + 4x and g (x) = StartFraction 1 Over 2 x EndFraction, what is the value of (StartFraction f Over g EndFraction) (5)?
Answer:
270
Step-by-step explanation:
f(5) = 7 +4·5 = 27
g(5) = 1/(2·5) = 1/10
The ratio of functions is the ratio of their individual values:
(f/g)(5) = f(5)/g(5) = 27/(1/10)
(f/g)(5) = 270
If x ∥ y and y ∥ z, then _____
Answer:
x ║ z
Step-by-step explanation:
Lines parallel to the same line are parallel to each other.
x and z are both parallel to y, so are parallel to each other:
x ║ z
WHY CAN'T ANYONE HELP ME PLEASE?? The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $3, sales will reach 8000 Fun Noodles per day during the summer. Raising the price to $6 will cause the sales to fall to 5000 Fun Noodles per day. a. Assume that the relationship between sales price, x, and number of Fun Noodles sold, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (sales price, number sold).
Answer:
y = -1000x +11000
Step-by-step explanation:
Given:
(x, y) = (sales price, number sold) = (3, 8000), (6, 5000)
Find:
slope-intercept equation for a line through these points
Solution:
When given two points, it often works well to start with the 2-point form of the equation for a line.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Filling in the given points, you have ...
y = (5000 -8000)/(6 -3)/(x -3) +8000
y = (-3000/3)(x -3) +8000
y = -1000x +3000 +8000 . . . . eliminate parentheses
y = -1000x +11000 . . . . the desired equation
What is the inverse of the function f(x) = 2x + 1?
1
1
h(x) =
X-
2
2
1
1
Oh(x) =
- x +
O h(x) =
3x-2
Oh(x) =
= {x+2
Mark this and return
Save and Exit
Next
Submit
Answer:
[tex]f^{-1} = \frac{x-1}{2}[/tex]
Step-by-step explanation:
[tex]f(x) = 2x+1[/tex]
Replace it with y
[tex]y = 2x+1[/tex]
Exchange the values of x and y
[tex]x = 2y+1[/tex]
Solve for y
[tex]x = 2y+1[/tex]
Subtracting 1 from both sides
[tex]2y = x-1[/tex]
Dividing both sides by 2
[tex]y = \frac{x-1}{2}[/tex]
Replace it by [tex]f^{-1}[/tex]
So,
[tex]f^{-1} = \frac{x-1}{2}[/tex]
Answer:
[tex]\displaystyle f^{-1}(x)= \frac{1}{2}x - \frac{1}{2}[/tex]
Step-by-step explanation:
f(x) = 2x + 1
f(x) = y (output)
y = 2x + 1
Solve for x.
y - 1 = 2x
Divide 2 on both sides.
y/2 - 1/2 = x
1/2y - 1/2 = x
Switch variables.
1/2x - 1/2 = y
[tex]f^{-1}(x)= \frac{1}{2}x - \frac{1}{2}[/tex]
Not sure of how to solve this
Answer:
undefined
Step-by-step explanation:
Using the slope formula
m = (y2-y1)/ (x2-x1)
and the given points
m = ( 8 - -1)/( 2-2)
= (8+1) / 0
We cannot divide by 0 so the slope is undefined
how to simplify -8+5w=27
Answer:
w=7
Step-by-step explanation:
1. -8+5w=27
2. add 8 to both sides: 8+-8+5w=27+8
3. Simplify: 5w=35
4. Divide both sides by 5: 5w/5=35/5
5. w=7
Hope This Helps :)
Answer:
w = 7
Step-by-step explanation:
-8 + 5w = 27
Add 8 on both sides.
-8 + 5w + 8 = 27 + 8
5w = 35
Divide both sides by 5.
5w/5 = 35/5
w = 7