Answer: E
Step-by-step explanation:
The lifetime of a certain type of calculators is normally distributed. If the mean is 400 hours and the standard deviation is 50 hours, for a group of 5000 batteries, how many are expected to last
1.between 350 hrs to 450 hours
2.more than 300 hours
3.less than 300 hours
Answer:
1. 3413
2. 4886
3. 114
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean is 400 hours and the standard deviation is 50 hours
This means that [tex]\mu = 400, \sigma = 50[/tex]
1. Between 350 and 450 hours:
The proportion is the pvlaue of Z when X = 450 subtracted by the pvalue of Z when X = 350.
X = 450:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{450 - 400}{50}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413.
X = 350:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{350 - 400}{50}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587.
0.8413 - 0.1587 = 0.6826
Out of 5000:
0.6826 out of 5000. So
0.6826*5000 = 3413
3413 are expected to last between 350 hours and 450 hours.
2.more than 300 hours
The proportion is one subtracted by the pvalue of Z when X = 300.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{300 - 400}{50}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
1 - 0.0228 = 0.9772
Out of 5000:
0.9772of 5000 is
0.9772*5000 = 4886
4886 are expected to last more than 300 hours.
3.less than 300 hours
4886 are expected to last more than 300 hours, so 5000 - 4886 = 114 are expected to last less than 300 hours.
Find the slope that passes through the points (1,4) and (-4,14)
A: 1
B: -2
C: 1/2
D: -1
Answer:
B: -2
Step-by-step explanation:
14-4/-4-1 = 10/-5 or -2
Answer:
-2...................
The sum of 2 numbers is 11 and the difference is 5
Answer:
let no. be x and y.
we have
x+y=11.......(1)
x-y=5........(2)
adding equation 1&2
x+y+x-y=11+5
2x=16
x=16/2=8
again
8-y=5
y=8-5=3
:.
x=8,y=3
Round 367.25 to the nearest 100th of a second
does anyone do primavera online 8B i need help ASAP
lots of point
no I don't I'm sorry.....
A snake at the zoo is 4 feet long. A scale model of the snake is 2 inches long. What is the scale factor?
PLZZZZ HELP MIDDLE SCHOOL MATHHH I PROMISE I WILL GIVE BRAINLIEST!!!
Answer:
It's C
Step-by-step explanation:
Because it says to look for the number 5 on the chart and chart C is the only one that has is on there. Hope this helped!
In the year 2009, a company made $5.4 million in profit. For each consecutive year after that, their profit increased by 11%. How much would the company's profit be in the year 2012, to the nearest tenth of a million dollars?
Answer:
Hi Grif05!
Your answer is 7.1 million.
To be exact , 7182000
Step-by-step explanation:
The distance between 2009 and 2012 is 3 years so we multiply.
11x3=33.
Now we must find 33% of 5.4 million.
33 % of 5.4 million is 1782000.
33% of 5400000 = 1782000
We then add 33% of 5.4 million to itself.
We get an answer of 7182000.
Hope this helps! Tell me if I'm wrong please :)
What is volume of cube 3 2/3 all sides
Let's say you have a 4 gallon and a 10 gallon pailHow can you measure exactly 2 gallons of water?
You can fill the 10 gallon pail all the way up. After that, you can pour the water from the 10 gallon pail, into the 4 gallon pail 2 times. That will leave you with 2 gallons in the 10 gallon pail.
Please help me but no links
Answer:
I think you got to time it all togther and the answer would be 531.44m^3
Step-by-step explanation:
(5.2×7×14.6)mmm
(36.4×14.6)mmm
531.44m^3
A development expert wants to use a one-sample z interval to estimate the proportion of women aged 16 and over that are literate in Albania. They take an SRS of 50 women from this population and find that 48 are literate.
Which conditions for constructing this confidence interval did their sample meet?
Answer: The data is a random sample from the population of interest. Individual observations can be considered independent.
Step-by-step explanation:
The condition for constructing this confidence interval :
A) The data is a random sample from the population of interest.
C) Individual observations can be considered independent.
The correct options are A and C.
What is a confidence interval?A confidence interval is a range of values that are constrained by the statistic's mean and that are likely to include an unidentified population parameter. The proportion of likelihood, or certainty, that the confidence interval would include the real population parameter when a random sample is drawn several times is referred to as the confidence level.
Given:
A development expert wants to use a one-sample z interval to estimate the proportion of women aged 16 and over that are literate in Albania. They take an SRS of 50 women from this population and find that 48 are literate.
From the given choices:
The condition for constructing this confidence interval :
A) The data is a random sample from the population of interest.
C) Individual observations can be considered independent.
Therefore, A and C are the correct options.
To learn more about the confidence interval;
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The complete question:
A development expert wants to use a one-sample zzz interval to estimate the proportion of women aged 16 and over that are literate in Albania. They take an
SRS of 50 women from this population and finds that 48 are literate.
Which conditions for constructing this confidence interval did their sample meet?
Choose all answers that apply:
A
The data is a random sample from the population of interest.
B
The observed counts of successes and failures are both sufficiently large.
C
Individual observations can be considered independent.
Ice cream: A certain ice cream parlor offers fifteen flavors of ice cream. You want an ice cream cone with three scoops of ice cream, all different flavors.
Part 1 of 2
In how many ways can you choose a cone if it matters which flavor is on top, which is in the middle and which is on the bottom?
de
The number of ways to choose a cone, if order matters, is
Answer:
The number of ways to choose a cone, if order matters, is 45.
Step-by-step explanation:
Given that a certain ice cream parlor offers fifteen flavors of ice cream, and you want an ice cream cone with three scoops of ice cream, all different flavors, to determine in how many ways you can choose a cone if it matters which flavor is on. top, which is in the middle and which is on the bottom, the following calculation must be performed:
15 x 3 = X
45 = X
The number of ways to choose a cone, if order matters, is 45.
Becca and Kimberly are running at a constant speed in a marathon. Becca runs at 4.5 miles per hour. Kimberly’s progress is shown in the table.
Part A: Who runs faster?
Part B: If Becca and Kimberly are 5 hours into a marathon, how far has each run?
Answer:
Part A: Kimberly
Part B:
Becca = 22.5 miles, Kimberly = 25 miles
Step-by-step explanation:
Part A:
Given that Becca runs at a constant speed of 4.5 miles per hour, use the table to find the constant speed that Kimberly runs, and compare who runs faster.
Let x = time
y = distance
k = speed = y/x
Equation for each person can be written as: y = kx
Therefore:
✔️Equation for Becca if k = 4.5
y = 4.5x
✔️Find k (speed) of Kimberly using (2, 10):
Speed (k) = y/x
k = 10/2
k = 5 miles per hour
Equation for Kimberly would be:
y = 5x
Comparing their speed, Kimberly runs faster because she covers more miles per hour than Becca does.
Part B:
For Becca, substitute x = 5 into Becca's equation, y = 4.5x
Thus:
y = 4.5*5 = 22.5 miles
For Kimberly, substitute x = 5 into Kimberly's equation, y = 5x
Thus:
y = 5*5 = 25 miles
At Gabrielle's Restaurant, 2/5 of the dishes on the menu are vegetarian, or the vegetarian
dishes, 3/4 are pasta dishes. What fraction of the dishes on the menu are vegetarian pasta
dishes?
Hillside Travel pays its employees $16 per hour plus 8% commission on all trips booked. Tyrus worked 20 hours last week and booked trips amounting to $2,100. What was his gross pay for last week? fill in the blank 1
Answer:
$368
Step-by-step explanation:
His gross pay was $368 for last week.
What is the commission?The commission is determined by the product of the commission rate and the total sales.
Commission = Commission rate x Total sales
As per the question, we have data :
Hourly rate $10
Commission rate =8%
Number of hours worked-20
Total sales $2,100
The gross pay is the product of the hourly rate and the number of hours worked.
Gross pay Hourly rate × Number of hours worked
= $10 × 20
= $200
We know that,
Commission = Commission rate x Total sales
= 8% x $2,100
= 0.08 x $2,100
= $168
The total pay is then the gross pay increased by the commission:
Total pay = Gross pay + Commission
Total pay = $200+ $168
Total pay = $368
To learn more about the commission click here:
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Which one is the missing number?
Answer:
Step-by-step explanation:
1 or 4 im not sure
This recipe makes 6 portions of chocolate mousse.
Cali has 600 g chocolate, 36 eggs, 100 mL of lemon juice and 200 g of sugar.
Cali makes 12 portions of mousse by following this recipe.
How much of each ingredient will she have left?
Recipe: Serves 6
180 g chocolate
9 eggs
15 mL lemon juice
60 g sugar
Answer:
240 g chocolate
18 eggs
70 mL lemon juice
80 g sugar
Step-by-step explanation:
600 g choc - (2 x 180) = 240 g left
36 eggs - (2 x 9) = 18 left
100 mL lemon - (2 x 15) = 70 mL left
200 g sugar - (2 x 60) = 80 g left
Answer:
Ingredients will have left
Chocolate
600 - 2*180 = 240 gEggs
36 - 2*9 = 18Lemon juice
100 - 2*15 = 70 mlSugar
200 - 2*60 = 80 gSunny Horizon Cellular’s phone plan has a monthly fee of $10.00 and charges $0.10 for every minute used. Stephan’s bill for the month was $23.80. If the equation that models this situation is (0.10)m + 10.00 = 23.80, use inverse operations and properties of equality to find the number of minutes Stephan talked during the month.
Answer:
She talked for 138 minutes
Step-by-step explanation:
A ball is tossed into the air. The quadratic function
h(t) = -16t2 + 14t + 5 represents the situation, where t
represents the time, in seconds, after the ball is tossed
and h(t) represents the height of the ball, in feet. Which
of the following statements is NOT true?
Answer: The leading coefficient indicates that the graph of the parabola that represents the ball’s height over time will open in an upward direction
Step-by-step explanation:
Sally's bank account had a balance of 230 at the beginning of the month. She had two deposits of 50 and 420 and just one withdrawal of 190. Her balance at the end of the month was $______ ?
Answer:
510
Step-by-step explanation:
Sally bank account had a beginning balance of 230
She made two deposits of 50 and 420
50+420
= 470
She made a withdrawal of 190
Therefore her balance at the end of the month can be calculated as follows
470+230
= 700
= 700-190
= 510
Hence the balance at the end of the month is 510
Refer to the table below to answer problems 25-27.
(TABLE) Mark's Personal Running Records Distance Time (minutes:seconds)
1/4 mile: 0:58
1/2 mile: 2:12
1 mile: 5:00
If Mark set his 1-mile record by keeping a steady pace, then what was his 1/2 -mile time during the 1-mile run?
Answer:
it will be 2:50
Step-by-step explanation:
Measuring your fitness level regularly is one way to find out if you're making progress. Most fitness centers have trained staff who can evaluate your body composition, muscular strength and endurance, flexibility, and cardiovascular endurance, but it can be pricey. If you don’t have access to all the toys and tools of your gym, don’t panic. You have everything you need to measure your fitness level in your own house!
This One-Mile Walking Test measures your aerobic (cardiovascular) fitness level based on how quickly you are able to walk a mile at a submaximal (moderate) exercise intensity.
Does anyone know the answer to this?
Answer:
x=18 and y=106
Step-by-step explanation:
David’s watch broke. He decides to get it fixed instead of replacing it. The total cost to repair the watch can be represented by 0.07(45h) + 45h, where h represents the number of hours it takes to repair the watch. What part of the expression represents the amount of tax David has to pay? Explain.
What’s the answer to this question?
Answer:
the second one from up to down
Step-by-step explanation:
Can someone help me
Answer:
B: (-6, -1)
Step-by-step explanation:
6+x/2 = 0
6+x = 0
x = -6
-5+y/2 = -3
-5 + y = -6
y = -1
Answer:
(-6,-1)
Step-by-step explanation:
We can use the midpoint formula here to find the coordinates of B . Given data :-
A(6,-5) M(0,-3)Let B be B(p , q) . Then ,
=> M = ( x₁ + x₂/2 , y₁ + y ₂ /2 )
=> (0 ,-3) = ( 6 + p/2 , -5+q/2)
On comparing=> 0 = 6 + p/2
=> 6 + p = 0
=> p = (-6)
Similarly=> -3 = -5+q/2
=> -5+q = -6
=> q = 5-6
=> q = (-1)
Hence the coordinates of B is (-6,-1) .УА
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Several hours after departure the two ships described to the right are 50 miles apart. If the ship traveling south traveled 10 miles farther that the other how many miles did they each travel.
Answer:
[tex]Ship\ A = 40\ miles[/tex]
[tex]Ship\ B = 30\ miles[/tex]
Step-by-step explanation:
Given
[tex]d = 50[/tex] --- distance apart
[tex]Ship\ B = x[/tex]
[tex]Ship\ A = x + 10[/tex]
The question can be represented with the attached image.
Required
Solve for x
Using Pythagoras theorem, we have:
[tex]x^2 + (x + 10)^2 = 50^2[/tex]
Open bracket
[tex]x^2 + x^2 + 20x + 100 = 2500[/tex]
Collect like terms
[tex]x^2 + x^2 + 20x + 100 - 2500 = 0[/tex]
[tex]2x^2 + 20x -2400 = 0[/tex]
Divide through by 2
[tex]x^2 + 10x -1200 = 0[/tex]
Expand
[tex]x^2 + 40x - 30x -1200 = 0[/tex]
Factorize
[tex]x(x + 40) - 30(x +40) = 0[/tex]
Factor out x + 40
[tex](x - 30)(x +40) = 0[/tex]
Split and solve for x
[tex]x - 30 = 0\ or\ x + 40 = 0[/tex]
[tex]x = 30\ or\ x = -40[/tex]
Distance can not be negative
So:
[tex]x = 30[/tex]
Recall that:
[tex]Ship\ B = x[/tex]
[tex]Ship\ A = x + 10[/tex]
This implies that:
[tex]Ship\ B = 30\ miles[/tex]
[tex]Ship\ A = 30 + 10\ miles[/tex]
[tex]Ship\ A = 40\ miles[/tex]
The probability that it will snow on Sunday is 3/5. The probability that it will snow on both Sunday and Monday is 3/10. What is the probability that it will snow on Monday, if it snowed on Sunday?
Answer:
1/2
Step-by-step explanation:
Probability of snowing on both Sunday and Monday= probability that it will snow on Sunday × probability that it will snow on Monday.
(and usually means multiply the probabilities while or implies addition of the probabilities).
Let probability of snowing on Monday be P
Hence 3/10=3/5× P
Hence P=(3/10) divided by (3/5) = 1/2
Expand and simplify 3(y+2)+4(x-1)
Answer:
4x + 3y + 2
Step-by-step explanation:
3(y + 2) + 4(x - 1)
3y + 6 + 4x - 4
4x + 3y + 2