Answer:
a) 15.9%
b) 2.3%
Step-by-step explanation:
We solving using z score formula. This formula is given as:
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. Calculate the percent of batteries with a useful life of less than 45 months. (Round your answer to the nearest tenth percent.)
x = 45, μ = 48, σ = 3
z = 45 - 48/3
= -1
Probability value from Z-Table:
The probability of batteries with a useful life of less than 45 months so
P(x<45) = 0.15866
Converting to percentage
0.15866 × 100 = 15.866
Approximately to the nearest tenth of a percent = 15.9%
b. Calculate the percent of batteries that will last longer than 54 months. (Round your answer to the nearest tenth percent.)
x = 58, μ = 48, σ = 3
z = 58 - 48/3
= 2
Probability value from Z-Table:
P(x<54) = 0.97725
P(x>54) = 1 - P(x<54)
= 0.02275
The probability of batteries that will last longer than 54 months is 0.02275
Converting to percentage
0.02275 × 100
= 2.275%
Approximately to the nearest tenth of a percentage = 2.3%
Use the limit definition to find an equation of a tangent line of f(x)= 1/(x-1) at the given point (2,1)
By "limit definition", I assume you mean the derivative. We have
[tex]f'(c) = \displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}[/tex]
For [tex]f(x)=\frac1{x-1}[/tex] and c = 2, we have
[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{\frac1{x-1}-1}{x-2}[/tex]
[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{\frac{1-(x-1)}{x-1}}{x-2}[/tex]
[tex]f'(2)=\displaystyle\lim_{x\to2}\frac{2-x}{(x-1)(x-2)}[/tex]
[tex]f'(2)=\displaystyle\lim_{x\to2}\frac1{1-x}=-1[/tex]
The tangent line to (2, 1) has slope -1. Using the point-slope formula, it has equation
y - 1 = - (x - 2)
y = - x + 3
Adrianna can read 7 pages in 10 minutes. At this rate,
how many pages can she read in 25 minutes?
Answer:
17.5 page in 25 minutes
Step-by-step explanation:
We can use ratios to solve
7 pages x pages
------------- = ----------------
10 minutes 25 minutes
7 * 25 = 10 x
175 = 10x
Divide by 10
175/10 = 10x/10
17.5 =x
17.5 page in 25 minutes
Answer:
17.5 pages
Step-by-step explanation:
What I did was I multiplied 7 by two then separately I divided seven by 2 and it gave me 3.5 so I added 14 and 3.5
On a number line, what is the distance between -1.75 and 2.5 help meerr
Answer:
4.25
Step-by-step explanation:
-1.75+x=2.5
x=4.25
50 BRAINLY POINTS PLS HELP
Answer:
Hello!!! erz here ^^
Step-by-step explanation:
I believe the answer is y = 8x - 3 (Option B)
Hope this helps!! :D
What is the value of y?
B
60°
12
12
ro
60°
А
12 to 60
answer 60°
solve:180°-(60°+60°)
180°-120°
60°##
Order from least to greatest.
0.67, 0.5, 3/5
Answer:
0.5, 0.6(3/5), 0.67
WORTH 15 POINTS
Explain why 3(x + 4) - 3(x - 5) has no solution. Choose the best response below
Place a check mark in each row to indicate
the number of solutions for each equation
below.
No
Infinitely
One
Solution Solution
Many
Solutions
5x5x+3
A. The x-terms are the same, but the constant terms are different.
B. The x-terms are different, but the constant terms are the same.
C. The x-terms are the same, and the constant terms are same.
D. The x-terms are different, and the constant terms are different.
5x+6 - 6x +5
5x+ 6 = 5x + 6
What values of a and b would make the equation shown have infinitely many
solutions?
2x+ 4 = 4x+2
2x+4 - 2x + 4
3x = ax + b
2x2x+4
Answer:
Question 2: A
Question 3: 3x=3x+0
Step-by-step explanation:
For the chart use (symbolab) it is a site that can help you with finding out the solutions by typing in the equation and it will give you an answer if it is no solution, one solution or, infinite
A rectangle has a height of 5 and a width of 4x^2-2x-6.Express the area of the entire rectangle. Expression should be expanded.
Answer:
The area of the entire rectangle is [tex]20x^2-10x-30[/tex]
Step-by-step explanation:
Area of a Rectangle
The area of a rectangle of height H and width W is:
A=H.W
The rectangle has a height of H=5 and a width of [tex]W=4x^2-2x-6[/tex]. Calculate the area:
[tex]A=5*(4x^2-2x-6)[/tex]
Expand the product:
[tex]A=20x^2-10x-30[/tex]
The area of the entire rectangle is [tex]20x^2-10x-30[/tex]
ASTRONOMY-
what would happen if the moon didn't revolve around the earth although its rotation on its axis remained the same.
WIll mark brainliest pls help
Answer:
I believe this would have a affect on the ocean as the moon controls the waves and i believe it would also affect the wind as well
Step-by-step explanation:
What is the value of m ?
Answer:
20
Step-by-step explanation:
its 20 but i.need to explain so 180-110-40=20
The solution to the system -2x+5y=-15 and 5x+2y=-6 is what
Step-by-step explanation:
−2x+5y=−15 and 5x+2y=−6
Rewrite equations:
−2x+5y=−15;5x+2y=−6
Step: Solve−2x+5y=−15for x:
−2x+5y=−15
−2x+5y+−5y=−15+−5y(Add -5y to both sides)
−2x=−5y−15
−2x−2=−5y−15−2(Divide both sides by -2)
x=52y+152
Step: Substitute52y+152forxin5x+2y=−6:
5x+2y=−6
5(52y+152)+2y=−6
292y+752=−6(Simplify both sides of the equation)
292y+752+−752=−6+−752(Add (-75)/2 to both sides)
292y=−872
292y292=−872292(Divide both sides by 29/2)
y=−3
Step: Substitute−3foryinx=52y+152:
x=52y+152
x=52(−3)+152
x=0(Simplify both sides of the equation)
Answer:
x=0 and y=−3
What type of connection can you make between markups and tips or taxes? What type of connection can you make between markdowns and discounts? Explain your answer.
Answer:
Markdowns are the same as discounts. The type of connection between markdowns and discounts is that they all take a percent off a bill or a check, which can involve subtracting and/or dividing. On the other hand, tips and taxes add money. (this is the same with markups.)
Step-by-step explanation:
XD i used this "explanation" and got it correct, it's basically exactly what that guy said but this version is more elaborate, and won't make your teachers suspect anything...xDDD
The police department of UCR is looking to collect more fines for speeders on campus. (They are turning to speeding because they cannot extract any more money out of people for parking illegally!) They record the speeds on West Campus Drive for a year and find that the average speed is 31.0 miles per hour with a standard deviation of 2.0. The data is approximated by a normal distribution. The top five percent (5%) of speeders will get tickets. What speed must you be going before getting a ticket
Answer:
≥ 34.29 mph
Step-by-step explanation:
Given that:
Distribution is normal :
Mean(m) = 31 mph
Standard deviation = 2 mph
Speed of top 5%
Top 5% = bottom (100% - 5%) = 95% = 0.95
Zscore which corresponds to 0.95 = 1.645
Using the Z formula:
Zscore = (score - mean) / standard deviation
1.645 = ( score - 31) / 2
Croas multiply:
2 * 1.645 = score - 31
3.29 = score - 31
3.29 + 31 = score
34.29 = score
Hence, speed must be greater than or equal to 34.29 mph
Bob wants to rent a car for one day. He contacted two companies. Enterprise Rentals charges $100 plus $3 per mile. Hertz Rental charge $8 per mile. After how many will the total cost for both companies be the same ?
Answer:
20 miles.
Step-by-step explanation:
To solve this problem, we will have to set two expressions representative of Enterprise Rentals & Hertz Rental equal to each other.
Let [tex]m[/tex] equal the number of miles.
If Enterprise Rentals charges $100 plus $3 per mile, we can represent this as:
[tex]100+3m[/tex]
If Hertz Rental charges $8 per mile, we can represent this as:
[tex]8m[/tex]
Set the expressions equal to each other:
[tex]8m=100+3m[/tex]
Subtract [tex]3m[/tex] from both sides of the equation:
[tex]5m=100[/tex]
Divide both sides of the equation by the coefficient of [tex]m[/tex], which is [tex]5[/tex]:
[tex]m=20[/tex]
Therefore, after 20 miles, the total cost for both companies will be the same.
_
Check your work by substituting the solved value of [tex]m[/tex] (20), into the initial equation:
[tex]8(20)=100+3(20)[/tex]
[tex]160=100+60[/tex]
[tex]160=160[/tex]
As the total costs are equal to each other, our answer is correct!
Answer:
20 miles
Step-by-step explanation:
160=$3(20)=100
8x20=160
what is the pattern 2 10 40 120
Answer:
2 plus 3
Step-by-step explanation:
5 square root of 2 help please
PLEASE HURRY!!!! WILL MARK BRAINLIST!!!!!!d. Using the equation for average rate above, determine the cheetah's average rate for the entire
trip.
Answer:
Average Rate = 55mph
Step-by-step explanation:
Now it’s time to tackle the original question. Going from point A to point B, the cheetah traveled at an average rate of 70 mph. Returning to point A, the cheetah traveled at an average rate of 40 mph.
Can we say that this cheetah’s average rate was 55 mph?
a.The average rate for the trip is equal to the total distance traveled divided by the total time traveled.
Average Rate = 70+ 40/2= 110/2 = 55mph
Yes the average rate of the cheetah is 55 mph
The following equations represent the distance traveled on each leg of the trip.
First leg of trip: td=r1 t1= 70*t
Second leg of trip: td=r2 t2= 40*t
Write an equation for the average rate for the trip. Remember, the cheetah runs from point A to point B and back to point A.
Total distance = r1 t1+ r2 t2
Average rate = Total distance / total time
= r1 t1+ r2 t2/ t1+ t2
=70t+ 40t/ 2t
=110t/2t
= 55mph
Answer:
the answer is 55 mph
Step-by-step explanation:
Average rate = Total distance / total time
= r1 t1+ r2 t2/ t1+ t2
=70t+ 40t/ 2t
=110t/2t
A plating company has two silver plating systems with variances σ12 and σ22. You, as the manager, desired to compare the variability in the silver plating done by System-1 with that done by System-2. An independent random sample of size n1= 12 of the System-1 yields s1 = 0.038 mil and sample of size n2= 10 of System-2 yields s2 = 0.042 mil. We need to decide whether σ12= σ22 with α = 0.05. What is the rejection region?
Answer:
The rejection region is
[tex]F_{cal} < F_{{1-\frac{\alpha}{2}} , df_1 , df_2 }[/tex]
or [tex]F_{cal} > F_{{\frac{\alpha}{2}} , df_1 , df_2 }[/tex]
and
From the value obtained we see that
[tex] F_{cal} < F_{\frac{\alpha }{n} , df_1 , df_2 } [/tex] Hence
The decision rule
Fail to reject the null hypothesis
The conclusion
This no sufficient evidence to conclude that there is a difference between the two variance
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 12[/tex]
The first sample standard deviation is [tex]s_1 = 0.038 \ mil[/tex]
The second sample size is [tex]n_2 = 10[/tex]
The first sample standard deviation is [tex]s_2 = 0.042 \ mil[/tex]
The significance level is [tex]\alpha =0.05[/tex]
The null hypothesis is [tex]H_o : \sigma^2_1 = \sigma^2_2[/tex]
The alternative hypothesis is [tex]H_o : \sigma^2_1 \ne \sigma^2_2[/tex]
Generally the test statistics is mathematically represented as
[tex]F_{cal} = \frac{s_1^2 }{s_2^2}[/tex]
=> [tex]F_{cal} = \frac{ 0.038^2 }{0.042^2}[/tex]
=> [tex]F_{cal} = 0.81859[/tex]
Generally the first degree of freedom is [tex]df_1 = n_1 -1 = 12-1 = 11[/tex]
Generally the second degree of freedom is [tex]df_2 = n_2 -1 = 10 -1 = 9[/tex]
From the F-table the critical value of [tex] \frac{\alpha}{2}[/tex] at the degrees of freedom of [tex]df_1 = 11[/tex] and [tex]df_2 =9 [/tex] is
[tex]F_{\frac{\alpha }{n} , df_1 , df_2 } = 3.91207[/tex]
The rejection region is
[tex]F_{cal} < F_{{1-\frac{\alpha}{2}} , df_1 , df_2 }[/tex]
or [tex]F_{cal} > F_{{\frac{\alpha}{2}} , df_1 , df_2 }[/tex]
and
From the value obtained we see that
[tex] F_{cal} < F_{\frac{\alpha }{n} , df_1 , df_2 } [/tex] Hence
The decision rule
Fail to reject the null hypothesis
The conclusion
This no sufficient evidence to conclude that there is a difference between the two variance
Rewrite each equation in slope-intercept form, if necessary. Then determine whether the lines are perpendicular. x = 9 y = -1 Are the lines perpendicular?
Answer:
[tex]x = 9[/tex] and [tex]y = -1[/tex] are perpendicular to each other.
Step-by-step explanation:
From Analytical Geometry we know that horizontal lines are of the form:
[tex]y = a[/tex], [tex]\forall \,a\in\mathbb{R}[/tex] (Eq. 1)
Where:
[tex]y[/tex] - Dependent variable, dimensionless.
Which means that for all value of [tex]x[/tex] (independent variable) has [tex]a[/tex] as their image. If we write this equation in slope-intercept form, we get that:
[tex]y = 0\cdot x + a[/tex] (Eq. 1b)
Where slope is the ratio of the change in dependent variable to the change in independent variable.
Whereas vertical lines have the following one:
[tex]x = b[/tex], [tex]\forall \,b\in\mathbb{R}[/tex] (Eq. 2)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
Which means that for all value of [tex]y[/tex] (dependent variable) has [tex]b[/tex] as their image.
If we write this equation in slope-intercept form, we get that:
[tex]x = 0\cdot y + a[/tex] (Eq. 2b)
Where slope is the ratio of the change in independent variable to the change in independent variable.
In addition, we must remember that two lines perpendicular to each other observe the following relation:
[tex]m_{A} = -\frac{1}{m_{B}}[/tex] (Eq. 3)
Where [tex]m_{A}[/tex] and [tex]m_{B}[/tex] are the slopes of each line. It is quite evident that if [tex]m_{A} = 0[/tex], corresponding to a horizontal line, then [tex]m_{B}[/tex] becomes undefined, corresponding to a vertical line.
In consequence, we come to the conclusion that [tex]x = 9[/tex] and [tex]y = -1[/tex] are perpendicular to each other.
Find the slope plus extra pts
Answer:
The Slope is -4
m = -4
Step-by-step explanation:
Hopefully this Helps! If this wasn't the answer you were looking for please don't hesitate to either comment here or private message me! Have a nice day/night! :))
Solve each problem. Show all your steps
-2 1/2 dived by 1 7/8
Answer:
1.4
Step-by-step explanation:
1+2 charliedamelioo0
Answer:
eEEE
Step-by-step explanation:
HELP IM GIVING BRAINLIEST
In order to receive credit for an English assignment, Alex must reflect on AT LEAST 5 out of 7 passages. In how many ways can this be done?
Answer:
expressionism I just took that test trust you got a workout and English and I'm miss that I hope we close at Johnny's and I'm miss that I hope we close again for the one that was a big deal for me to hit the road and I'm miss that I hope we close again for the one time of day or so he can come over for a lol you want to text cause I'm miss that I hope we close again for the one that was a if he can come over for a lol you want to text Leo and I'm miss that I hope we close again for the one that 5th to text cause I'm miss that I hope.
Which equation would you choose in order to most easily identify the vertex?
K
y = 9x4 + 6x2 +1
y = x2 + 6x + 9
y = (x + 6)(x + 9)
y = (x + 6)2 +9
a 5
Answer:
last
Step-by-step explanation:
how many solutions does this equation have? 2x+7=2x
Answer:
no solution
Step-by-step explanation:
If a certain sum of money can become
5 times of its principal in 10 years, then
the rate of interest is
Select the correct answer to 35 2/7 x 5:
1. 174
2. 176 3/7
3. 175 5/7
4. 174 5/7
Answer:
2
Step-by-step explanation:
I can't exactly explain my thinking but I estimates and the closet i got was answer 2 hoped this helped
Because everyone is always driving above the speed limit, the police implement a new policy: ticket anyone who drives 1.5 standard deviations above the average. At a major freeway, the average speed in the evening is 75 MPH. The standard deviation is 7 MPH. Michael finds himself driving at 84 MPH during an evening on this freeway. At a major street, the average speed is 43 MPH. The standard deviation is 4 MPH. Nico finds himself driving at 50 MPH. Use the information above to determine who will get a speeding ticket?
Answer:
Michael is within the speed limit regulation he won´t get any ticket
Nico is over speed limit then he should be ticket
Step-by-step explanation:
Case A conditions in a freeway evening average speed 75 MPH the
standard deviation is 7 MPH
Then according to new policy 75 + 7* ( 1,5 ) = 75 + 10,5 = 85,5 MPH
Michael is driving at 84 MPH then he has no problem at all
Case B conditions in a major street average speed 43 MPH the standard deviation is 4 MPH
According to the new policy 43 + 4 *(1,5) = 43 + 6 = 49 MPH
Nico is driving at 50 MPH then Nico will be ticket
6. Rachel's garden is square in shape. The length of one side of her garden is 52 feet. What is the area of her garden in square feet? Express your answer using exponents.
Answer:
52^ 2 because this is equal to the area which is 2704 sq ft. So 52 to the second power is your answer.
Step-by-step explanation:
