A flashlight battery manufacturer makes a model of battery whose mean shelf life is three years and four months, with a standard deviation of three months. The distribution is approximately normal. One production run of batteries in the factory was 25,000 batteries. How many of those batteries can be expected to last between three years and one month and three years and seven months?
a. 21,025 batteries
b. 8,525 batteries
c. 17,050 batteries
See the attached picture.
The answer is c. 17,050 batteries
The number of expected batteries to last between 3 years and one month and 3 years and seven months is 17,050 batteries.
Option C is the correct answer.
What is z-score?A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.
It measures the unusual or extreme a particular data point is compared to the rest of the distribution
We have,
First, we need to standardize the range of shelf life between three years and one month (3.08 years) and three years and seven months (3.58 years) using the formula:
z = (x - μ) / σ
where x is the shelf life in years, μ is the mean shelf life in years, and σ is the standard deviation in years.
Now,
For the lower bound:
z = (3.08 - 3.33) / 0.25
z = -1.00
For the upper bound:
z = (3.58 - 3.33) / 0.25
z = 1.00
Now,
We use a standard normal distribution table or calculator to find the area under the curve between z = -1.00 and z = 1.00, which represents the proportion of batteries that can be expected to last between three years and one month and three years and seven months.
This area is approximately 0.6826.
Finally,
We multiply this proportion by the total number of batteries in the production run to find the expected number of batteries that meet the criteria.
expected number = proportion x total number
expected number = 0.6826 * 25,000
expected number ≈ 17,065
Therefore,
The number of expected batteries is 17,050 batteries.
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Question
A train travels for 30 miles at an average speed of 25
mph. How many minutes will it take to complete
the journey?
Answer:72 minutes
Step-by-step explanation:
30/25= 1.2 * 60= 72
write a function for this table -- urgent -- I'm putting all my points into this!!!! -- bad answers reported! -- no explanation necessary
Answer:
[tex]3x^{2} -3x-6[/tex]
Step-by-step explanation:
Help please!!!! 50 points!!!!
Amara has taken out a fixed rate mortgage for $125,000 at 4.04% for 20 years, or 240 months. Her payments are $730. What is the total cost of the loan?
A. $130,050
B. $175,200
C. $211,680
D. $226,000
Answer:
182,427.03
Step-by-step explanation:
total cost = r*p*n
---------------
1- (1+r) ^-n
Where r is the loan rate, p is the principal, n is the number of payments
rate = 4.04% / 12 months
total cost = (.0404/12)* 125000* 240
------------------------------
1- (1+.0404/12)^-240
101000
-----------------
1-.44635
101000
-----------------
.55364
182,427.03
Using Payments are 730 *240 months
730*240 =175200
Timmy uses 1 1/2 cups of sugar for every 2 gallons of lemonade he makes. How many cups of sugar would Timmy use if he makes 13 gallons of lemonade?
cups of sugar
Answer:
he would have to use 19.5 cups of sugar.
Step-by-step explanation:
HELLP PLEASE!!!!!!?!?!?!???! Find the missing length of the triangle.
Answer:
11 2/3 yd.
Step-by-step explanation:
\sqrt{\left(12\frac{1}{3}^{2}-4^{2}\right)} = 35/3
35/3=11 2/3
Answer:
11.666
round up to 11.7
Step-by-step explanation:
(hypotenuse)^2 -(leg b)^2
√(12.333)^2-(4)^2
√(152.11-16)
√(136.11)
Given f(x)=x^3+2x+k.
and x+1 is a factor of f(x), then what is the value of k?
Answer:
k = 3.
Step-by-step explanation:
By the Factor Theorem. if x+a is a factor of f(x) then f(-a) = 0.
Here we use f(-1):
f(-1) = (-1)^3 + 2(-1) + k = 0
-1 - 2 + k = 0
k = 3.
Which of these statements is true? Check all that apply. CDs have a higher mean than digital. The range of digital is 800. The median of CDs is 400. Both have the same interquartile range. Both have the same median. Digital's mean is around 467.
Bar chart associated with the question is attached below
Answer:
Range of digital is 800
CDs have a higher mean than digital
Digital's mean is around 467.
Both have the same interquartile range
Step-by-step explanation:
CDs have a mean higher than digital
Range of digital is 800 (900 - 100 = 800)
Both have the same interquartile range
(Q3 - Q1)
DIGITAL :
(900+700+500+300+300+100)
700 - 300= 400
CDs:
(1000+800+800+600+400+200)
800 - 400= 400
Digital mean :
(900+700+500+300+300+100) / 6
2800/6 = 466.67 = 467
CD mean :
(1000+800+800+600+400+200) /6
=633.333
Median of CD:
1000+800+800+600+400+200
(800+600)/ 2 = 700
Median of Digital :
(500+300)/2 = 400
Answer:
A: CDs have a higher mean than digital.
B: The range of digital is 800.
D: Both have the same interquartile range.
F: Digital’s mean is around 467.
Step-by-step explanation:
edg2020
will mark BRAINLIEST for correct answer!
I have six equilateral triangles, each with a perimeter of 12cm. I fit them together to make a regular hexagon. What is the hexagon’s perimeter?
Answer:
24 cm
Step-by-step explanation:
Perimeter of equilateral triangle = 12 cm
Therefore, measure of one side of equilateral triangle = 12/3 = 4 cm
Perimeter of hexagon = 6 * measure of one side of equilateral triangle
= 6 * 4 = 24 cm
Carly's family traveled 3/10 of the distance to her grandmother's house on Saturday. They traveled 3/7 of the remaining distance on Sunday. What fraction of the total distance to her grandmother's house was traveled on Sunday?
Answer:
3/10 of the total distance to her grandmother's house was traveled on Sunday
Step-by-step explanation:
Carly's family traveled distance of Saturday = [tex]\frac{3}{10}[/tex]
Remaining distance =[tex]1-\frac{3}{10}=\frac{7}{10}[/tex]
They traveled 3/7 of the remaining distance on Sunday.
So, Distance traveled on Sunday =[tex]\frac{3}{7}(\frac{7}{10})[/tex]
Distance traveled on Sunday =[tex]\frac{3}{10}[/tex]
Fraction of the total distance to her grandmother's house was traveled on Sunday =[tex]\frac{3}{10}[/tex]
Hence 3/10 of the total distance to her grandmother's house was traveled on Sunday
HURRY PLS I NEED IT
What is the purpose of apportionment? (its ideal, value, or vision)
Answer:
An apportionment is the allocation of a loss between all of the insurance companies that insure a piece of property. This allocation is used to determine a percentage of liability for each insurer.
I'm new here! Sorry if this didn't help
Find the slope
Tysm!!! I need help asap
Answer:
2/3
Step-by-step explanation:
start at the first point and count up and then over. it is 2 squares UP, and 3 squares OVER. remember rise over run, rise (2) on top and run (3) on bottom!
Answer:
M = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The two coordinate points given are (2,2) and (-1,0).
We can use the slope formula to find the slope.
[tex]Slope(m)=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{0-2}{-1-2}[/tex]
[tex]m=\frac{-2}{-3} or \frac{2}3}[/tex]
Solve: log (7t + 2) = 2
t =
Answer:
t = 14
Step-by-step explanation:
log (7t + 2) = 2
Raise each side to the power of 10
10 ^log (7t + 2) =10^ 2
7t+2 = 100
Subtract 2 from each side
7t+2-2 = 100-2
7t = 98
Divide each side by 7
7t/7 = 98/7
t = 14
Answer:
[tex]t=14[/tex]
Step-by-step explanation:
We begin with the equation: [tex]log(7t+2)=2[/tex]
The first thing we must do is remove the log. In this case, the base of this log is 10, which means that we must have each side of this equation have a base of 10.
This gives us
[tex]10^{log(7t+2)} =10^2[/tex]
The base 10 and the log will cancel out to give us
[tex]7t+2=100[/tex]
Then we can solve for t
[tex]7t+2=100\\\\7t=98\\\\t=\frac{98}{7} \\\\t=14[/tex]
The circumference of a circle can be found using the
formula C = 2rer.
Which is an equivalent equation solved for
r = CT
Or= C(20)
O
ra
2T
2m
re
쯘
Answer:
C /2pi = r
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi*r
We want to solve for r
Divide each side by 2 pi
C / 2pi = 2*pi*r / 2pi
C /2pi = r
solve similar triangles
Answer:
7.5 ?
Step-by-step explanation:
Answer:
7.5
Step-by-step explanation:
We are given information that the two triangles are similar and we want to work out the length of "t" . Since these 2 triangles are similar, it means that a scale factor is used to enlarge the sides, we can work out the scale by dividing QP by LJ and RP by KJ so,
QP ÷ JK = 25 ÷ 5 = 5
RP ÷ JL = 22.5 ÷ 4.5 = 5
So we can see the scale factor is 5, now all we need to do is multiply the scale factor by 1.5 to find the value of t
1.5 × 5 = 7.5
The value of t is 7.5
what is a hypotenuse
Answer:
is the longest side in a triangle
Step-by-step explanation:
is the longest side in a triangle
Answer:
It is the longest side of a right triangle.
Step-by-step explanation:
A right triangle has two legs, then the (i call it a slope) hypotenuse connects the two from the top of one of leg to the end of the bottom leg.
you can calculate the hypotenuse via the Pythagorean theorem. which is A^2+B^2=C^2
Or: Leg 1^2+ Leg 2^2= Hypotenuse^2
Please help with this question. Thank you.
Answer:
t = 4
Step-by-step explanation:
Substitute the variables with the information provided.
205 = 100 + 12(6) + 5(t) + 7(4) + 5(5) - 8(5)
Simplify
205 = 100 + 72 + 5t + 28 + 25 - 40
20 = 5t
t = 4
A company is offering 1 grand prize, 3 second place prizes and 25 third place prizes. Out of 500 total entries, what is the probability of getting a third place prize?
Answer:
1/20
Step-by-step explanation:
25 prizes out of 500=25/500=1/20
Any help on these problems would be great! Thanks!
Answer:
17. 600 18. C.relative
Step-by-step explanation:
17. 900/3=300, but because she uses 2 tires at the same time you have to multiply it by 2
18. there is no actual coordinate so it wouldn't be absolute, and combination isn't a thing
I need to know these answers fast please please help!!!!
Answer:
Step-by-step explanation:
y intercept please scroll down--i need to see the rest of the graph-- y intercept is where the graph intersects with the y axis
x intercepts are x=2 and x=6
greatest value of y is y=2 and it occurs when x=4
for x between... what are the options?
if the options are greater than, equal to, or less than, the answer is greater than
I cannot figure this out for the life of me! Can someone help me out? Ignore the stuff written down.
============================================================
Explanation:
Focus on the slanted side of the parallelogram, which is 26 units long. The opposite side to this is also 26 units long since opposite sides of any parallelogram are always congruent.
Now turn your attention to the triangle formed by that dashed line. Specifically this is a right triangle. It has a legs of x and 10, where x is the unknown height (also the height of the parallelogram). The hypotenuse of this right triangle is 26 units as mentioned in the previous paragraph.
Use the pythagorean theorem to find x
a^2+b^2 = c^2
10^2+x^2 = 26^2
100+x^2 = 676
x^2 = 676-100
x^2 = 576
x = sqrt(576)
x = 24
This is a 10,24,26 right triangle, which is based on the 5,12,13 right triangle (divide every part by 2)
-------------------
Now that we know the height of the parallelogram, the area is simply base times height
area of parallelogram = base*height = 32*24 = 768
Then we subtract off the area of the shaded gray rectangle, so we subtract off 7*16 = 112 to get 768 - 112 = 656 and this is the area of the unshaded region inside the parallelogram.
-------------------
Side note: The hypotenuse of 10*sqrt(2) you wrote down would only be correct if that dashed height line was 10 units.
Factor completely.
28 - 7x^2
Answer:
7 (2 + x ) ( 2 − x )
The factored form of the given binomial is 7(x+2)(2-x)
What are the factors?A factor is a number that divides another number, leaving no remainder.
Given is a binomial, we are asked to factorize it,
28 - 7x²
7(4) - 7(x²)
= 7(4-x²)
= 7(x+2)(2-x) {∵ a² - b² = (a+b)(a-b)}
Hence, the factored form of the given binomial is 7(x+2)(2-x)
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What is the height of a pyramid (with a square base) whose side length is 12 cm and its slant
height is 10 cm?
a.) 22 cm
b.) 8 cm
c.) 2 cm
d.) None of these
We have been given that side length of pyramid the square base is 12 cm and its slant height is 10 cm. We are asked to find the height of the pyramid.
We will use slant height of a pyramid formula to solve our given problem.
[tex]s=\sqrt{h^2+\frac{1}{4}a^2}[/tex],where,
s = Slant height,
h = Height,
a = Each side of square base.
Upon substituting our given values in above formula, we will get:
[tex]10=\sqrt{h^2+\frac{1}{4}\cdot 12^2}[/tex]
[tex]10=\sqrt{h^2+\frac{1}{4}\cdot 144}[/tex]
[tex]10=\sqrt{h^2+36}[/tex]
Switch sides:
[tex]\sqrt{h^2+36}=10[/tex]
Let us square both sides:
[tex](\sqrt{h^2+36})^2=10^2[/tex]
[tex]h^2+36=100[/tex]
[tex]h^2+36-36=100-36[/tex]
[tex]h^2=64[/tex]
Now we will take positive square root of both sides.
[tex]\sqrt{h^2}=\sqrt{64}[/tex]
[tex]h=8[/tex]
Therefore, the height of the pyramid is 8 cm and option 'b' is the correct choice.
Kim's softball team was playing in the championship game. When there were 444 innings left, the team was losing by a score of 171717 to 666 points. In the last 444 innings, her team scored the same number of points per inning, and the other team did not score any more points. Kim's team won with the most points.
Write an inequality to determine the number of points per inning, ppp, Kim's team could have scored.
Answer:
Hello and welcome to Brainly! Thank you for posting your first question! I hope you enjoy your time here on Brainly!
The awnser to your question is. The required inequality is 6+4p>17
Step-by-step explanation:
Let p represent the number of runs per inning.
It is given that the team scores the same number of runs per inning and the other team did not score any more points. So, the total score of other team after last four inning is 17.
Kim's team total score in last four inning is 4p. So, the total score of Kim's team after last four inning is
Kim's team win if the total score of other team after last four inning is less than the Kim's team.
Hope this helped!!
does anybody know where i can watch baruto DUB all episode for free no downloads not 9 anime, not Hulu,!!!!!
Answer:
Im pretty sure there isnt a way to be able to watch it for free, but good luck!
Step-by-step explanation:
Answer:
i cant give you the link, but it's on for free at animelabs.
Step-by-step explanation:
How is this math?
PLZ HELP URGENT GEOMETRY QUESTION
Answer:
Step-by-step explanation:
TRUE angles are linear pairs
HELP HELP HELP Help me ASAP.. Giving branliest
Step-by-step explanation:
hope this is correct and it helps
Find cos x if sin2x-1/cosx =-1
Answer:
1
Step-by-step explanation:
a soup can has a diameter of 8 cm and a height of 12 CM what is the volume of the soup can use 3.14 for pi
Answer:
V = 602.88 cm cubed
Given that f(x)=5x+9 and g(x)=9-x^2
calculate
f(g(0))
g(f(0))