Answer:
the probability is 0.0202
Step-by-step explanation:
The computation is shown below:
Given that
The Average life span = 17 hours
Standard deviation = 0.8 hours
Sample = 30 batteries
Sample mean = 16.7 hours
Now based on the above information
The probability is
[tex]P (\bar x \leq 16.7) = P (\frac{\bar x - \mu}{(\frac{\sigma }{\sqrt{n} } )} \leq (\frac{16.7 - \mu}{(\frac{\sigma }{\sqrt{n} } )}\\\\= P(z\leq \frac{16.7-17}{\frac{0.8}{\sqrt{30} } } )\\\\= P(\leq -2.05)\\\\= 0.0202[/tex]
Hence, the probability is 0.0202
Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distributed with mean $39725 and standard deviation $7320. Suppose a school takes a sample of 125 such graduates and records the annual starting salary of each. The probability that the sample mean would be at least $39000 is about
Answer:
0.8665 = 86.65% probability that the sample mean would be at least $39000
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean $39725 and standard deviation $7320.
This means that [tex]\mu = 39725, \sigma = 7320[/tex]
Sample of 125:
This means that [tex]n = 125, s = \frac{7320}{\sqrt{125}} = 654.72[/tex]
The probability that the sample mean would be at least $39000 is about?
This is 1 subtracted by the pvalue of Z when X = 39000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{39000 - 39725}{654.72}[/tex]
[tex]Z = -1.11[/tex]
[tex]Z = -1.11[/tex] has a pvalue of 0.1335
1 - 0.1335 = 0.8665
0.8665 = 86.65% probability that the sample mean would be at least $39000
Input(x) Output(y)
32 20
14 2
? -6
-2. -14
-10. ?
complete the function table and write the function rule. show the steps you took to get this answer
Answer:
Rule : x subtracted by 12 = y , first ? = 6 (6,-6) , second ? = -22 (-10,-22)
Chris ran 3 miles in 15 minutes and continues to run at this rate for 1 hour. Amy ran 4 miles in
30 minutes and continues to run at this rate for 1 hour. Fill in the blank to complete the
sentence.
Amy will run _____ miles in 1 hour.
A. 7.5
B. 8
C. 4
D. 10
E. Not listed
Answer:
B) 8 miles
Step-by-step explanation:
30 mins is half an hour. And she ran 4 miles if you multiply both then you get 8 miles in 1 hour.
Tell whether the statement is true or false.
{ {4, 16, 24, 7, 37} = (37, 16, 7,42,4}
Answer:
false
Step-by-step explanation:
i dont understand kinda
but if you add it,
88<106
so false
write a letter to your friend telling her how you are coping in your new senior school
Answer:
?
Step-by-step explanation:
find the highest common factor of 12,20 and 28
no links
Answer:
the highest or greatest common factor 12,20,and 28 is 4
Answer:
12, 20, 28.
Step-by-step explanation:
here is the answer
no links
no photos
just a simple answer
have a great day/night
:)
7
11 X
Find the exact value of x.
X=
Do the side lengths form a Pythagorean triple?
o yes
O no
Answer:
[tex] \sqrt{49 + 121} = \sqrt{170} [/tex]
No , The side lengths of the triangle does not form a Pythagorean triple
The value of x = 13.038 = √170
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be ΔABC
Now , the base of the triangle BC = 11
The height of the triangle AB = 7
The hypotenuse of the triangle AC = x
Now , the length of AC can be calculated from the Pythagoras Theorem
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
And , AC² = AB² + BC²
Substituting the values in the equation , we get
AC² = 11² + 7²
AC² = 121 + 49
AC² = 170
Taking square roots on both sides of the equation , we get
The value of AC = √170
The value of AC = 13.038
Therefore , the value of x = 13.038
Hence ,
No , The side lengths of the triangle does not form a Pythagorean triple
The value of x = 13.038 = √170
To learn more about triangles click :
https://brainly.com/question/16739377
#SPJ2
Solve for the missing side. Round to the nearest tenth.
10
50°
х
Answer:
15.6
Step-by-step explanation:
If 5(3x − 2) = 6, then x =
a. 2/6
b. 5/6
c. 10/15
d. 16/15
Answer:
D
Step-by-step explanation:
[tex]5(3x-2)=6\\15x-10=6\\15x=16\\x=\frac{16}{15}[/tex]
Answer:
D.) 16/15
Step-by-step explanation:
To solve we must first distribute the 5 to everything that is inside the parenthesis. To do this we can multiply 5×3x = 15x and 5×-2 = -10.We can then combine these new numbers and set them equal to 6.
5(3x-2) ---> 15x-10=6
From here we need to get the x on one side all alone. To do this we need to first move the -10. We can add 10 to both sides.
15x=6+10
Simplify...
15x=16
Then we can divide both sides by 15 to get x alone
x=16/15
could you pls tell me the answer to part a and b thx, and could you also give me a step by step explanation of how you did it?
Answer:
sure Gigi, as below
Step-by-step explanation:
A)
we want to know the rates. so this like like in MPH (Miles per hour) or feet per second but something that we can compare each walker with the other .... so we want some type of scale that makes sense. what are the given units.... they are distance in miles and time in hours.. so maybe MPH would work for this.
there is a very good, basic formula that you should just remember for this type of problem... I can it the dirt formula... partly b/c it's dirt easy.. and partly b/c it really is about how much dirt you cover.. i mean.. how far you do... in a distance .. and you can use any unit you want... like we'll use miles here.. for our units.. we will you d = rt where d= distance , r= rate and t = time.
d = rt.... notice the formula looks a lot like the word "dirt" handy huh...
use it to make all the walks have a number... their rate... the r in the formula... to compare with, so use your algebra skills to rearrange the formula... to
d/t = r now we can plug in each of the walkers and get a rate to comparr them
Aisha 5/2 = r so 5/2 MPH
Bob 7.5 / 5 = r so 7.5 = 15/2 then (15/2) / 5 = (15/2) * (1/5) ( cross cancel the 15 and 5 so you get (3/2) * (1/1) = 3/2
Bob = 3/2 MPH
Cora = 9 / 3.6 or 9 / 3[tex]\frac{6}{10}[/tex] or (9/1) / ([tex]\frac{36}{10}[/tex]) or (9/1) * (10 / 36) cross cancle the 9 and 36 so you get (1/1) * ( 10 / 4) = 10/4 = 5 /2
Cora = 5/2 MPH
Dylan = 3.75 /2.5 or 3 [tex]\frac{3}{4}[/tex] / 2[tex]\frac{1}{2}[/tex] or (15/4) / (5/2) or (15/4 ) * (2/5) cross cancel the 2 and 4 and also cross cancel the 15 and 5 then, (3/2) * ( 1/1)= 3/2
Dylan = 3/2 MPH
MPH
Aisha = 5/2
Bob = 3/2
Cora = 5/2
Dylan = 3/2
you can now make fair comparisons among the 4 people
B)
d = rt
d/t = r
Emilio = 19.2 / 6 or 19[tex]\frac{2}{10}[/tex] / 6 or (192/10 ) / (6/1) invert and multiply to bring the denominator up (192/10) * (1/6) cross cancle 6 into 192 = 32
so(32/10) * ( 1/1) = 32/10 or 16/5 = 3[tex]\frac{1}{5}[/tex] or 3[tex]\frac{2}{10}[/tex] which is 3.2 MPH
Fala = 10.5 / 3 or 10[tex]\frac{1}{2}[/tex] /3 or [tex]\frac{21}{2}[/tex] / 3 or (21/2) / (3/1) invert and multiply the denominator (21/2) * ( 1/3) , cross cancel 3 and 21 (7/2) * ( 1/1) = 7/2
so now you have all the rates.. how fast they are walking. in Miles per hour and that's what the scale of the number line is.. so, good.. just mark each of their speeds
Bob and Dylan = 3/2 or 1.5 MPH... pretty slow.. huh :P
Cora and Aisha = 5/2 or 2.5 MPH faster but not fast
Emilo 3.2 MPH pretty quick
Fala 3.5 MPH she's fast. :D speed walking
3.2 on the number line is not marked.. 3.25 is.. so just a bit below the 3.25 mark.. that's 3[tex]\frac{1}{4}[/tex] , see it?
all the others are marks on the number line.. just count marks for 1//2s
HELP ON HOMEWORK PLS
Answer:
∠LPN = 57°
Step-by-step explanation:
arc LMN = 360° - 102° - 144° = 114°
∠LPN = 114°/2 = 57°
A linear function is graphed below.
(-1, 4)
(5, -5)
What is the slope of this graphed line?
Answer:
[tex]-1\frac{1}{2}[/tex]
Step-by-step explanation:
We have two coordinate points and are asked to find a slope.
When finding slope, we can use the formula listed :
[tex]\frac{y^2-y^1}{x^2-x^1}}[/tex]
To understand what the variables are, you can take this :
[tex](x^1,y^1)[/tex]
[tex](x^2,y^2)[/tex]
Substitute the points :
[tex](-1,4)[/tex]
[tex](5,-5)[/tex]
Now substitute it into the formula :
[tex]\frac{-5-4}{5-(-1)}[/tex]
[tex]\frac{-3}{2}[/tex]
[tex]-1\frac{1}{2}[/tex]
Answer:
Step-by-step explanation:
find the slope m by using the slope formula
m = (y2 - y1) / (x2 - x1)
Point1 = ( -1,4) where it takes the form (x1,y1)
Point2 =(5, -5) where it takes the form (x2,y2)
notice the form is important
m = (-5 -4) / (5 - (-1))
m = -9 / ( 5 +1 )
m = -9 / 6
m = - 3/2
A net of a rectangular prism has 3 pairs of equal sides. The front face has an area of 30 feet squared.
Which statements about the area of the faces of the rectangular prism are true? Select all that apply.
Two of the faces have an area of 30 ft2.
There is only one face with an area of 48 ft2.
Two of the faces have an area of 40 ft2.
The front face has an area of 30 ft2.
The top face has an area of 40 ft2.
Answer:
A,C,D
Step-by-step explanation:
I took it on Edge
1
There are 31 students in a class.
14 of the students are female.
Find the percentage of the class that are female.
Give your answer to the nearest percent.
Effect
aths
Answer:
45.16%
Step-by-step explanation:
31 students is 100%
so, 14x100/31=45.16
The graph represents distance traveled varying directly with time.
What would be the distance traveled after 12 hours?
a. 40 miles
b. 540 miles
c. 480 miles
d. 600 miles
Answer:
c. 480 miles.
Step-by-step explanation:
From the graph:
after 5 hours distance travelled is 200 miles.
So by proportion distance in 12 hours = 200 * 12/ 5
= 2400/5
= 480 miles.
A biologist found the wingspans of a group of monary butterflies to be normally distributed with a mean of 52.5 mm and a standard deviation of 2.5 mm. What percent of the butterflies had the following wingspans? A. Less than 48.9 mm B. Between 49 and 55
Answer:
A. 7.5%
B. 68.26%
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 of 52.5 mm and a standard deviation of 2.5 mm.
This means that [tex]\mu = 52.5, \sigma = 2.5[/tex]
A. Less than 48.9 mm
The proportion is the pvalue of Z when X = 48.9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48.9 - 52.5}{2.5}[/tex]
[tex]Z = -1.44[/tex]
[tex]Z = -1.44[/tex] has a pvalue of 0.075
0.075*100% = 7.5%, which is the answer.
B. Between 49 and 55
The proportion is the pvalue of Z when X = 55 subtracted by the pvalue of Z when X = 49. So
X = 55
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 52.5}{2.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
X = 49
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 52.5}{2.5}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
0.6826*100% = 68.26%, which is the answer.
The percent of the butterflies had the given wingspans are;
A) 7.5%
B) 76.64%
We are given;
Population mean; μ = 52.5 mm
Population standard deviation; σ = 2.5 mm
Formula for z-score is;
z = (x' - μ)/σ
A) For less than 48.9 mm,P(X' < 48.9);
z = (48.9 - 52.5)/2.5
z = -1.44
From online p-value from z-score calculator, we have;
P(X' < 48.9) = 0.075 or 7.5%
B) For x' between 49 and 55, P(49 < X < 55)
At x' = 49;
z = (49 - 52.5)/2.5
z = -1.4
Z-score at x' = 55;
z = (55 - 52.5)/2.5
z = 1
From online p-value from z-score calculator, the p-value between the two z-scores is;
p = 0.7664 or 76.64%
Read more about z-scores at; https://brainly.com/question/6316394
Examine the diagram, where quadrilateral HIJK is inscribed in OC.
H
RD
K
112
1
J
© 2016 StrongMind. Created using GeoGebra.
If mZIJK = 112°, what is mZIHK?
Answer:
m<IHK = 68°
Step-by-step explanation:
In an inscribed quadrilateral, opposite angels are supplementary. This means that the sum of the opposite angles in am inscribed quadrilateral equals 180°. One is the supplement of the other.
Therefore,
m<IHK = 180 - m<IJK
m<IHK = 180° - 112°
m<IHK = 68°
A computer technician notes that 40% of computers fail because of the hard drive. If he repairs many computers a day, what is the probability that the first computer that has failed due to the hard drive is his 4th computer of the day?
Answer:
(B) 0.0864
Step-by-step explanation:
Correct on Edge
Last year Jacob’s total
Answer:
the answer is $ 83,634
your welcome
The length of every chord in a circle is always greater than the length of a radius.
True or False?
Answer:
the answer would be false
Please help I’ll give points + brainalist
Answer:
D
Step-by-step explanation:
median because it indicates the expected range of gas prices
What Happens to the value of the expression 100 minus X as X increases
Step-by-step explanation:
if f (x) = 100 - x;
as x increases, the value of f(x) will decrease
Answer:
100 decreases
Step-by-step explanation:
PLEASE HELP, I don’t know how to do this...like at all
Answer:
arc ? = 255°
Step-by-step explanation:
arc DB = 180° - 75° = 105°
arc ? = 360° - 105° = 255°
how do you solve 6 1/2 x 16?
Answer:
Step-by-step explanation:
Make 6 1/2 an irrational fraction: 13/2 (I dunno know if its called that )
divide 16 by 2: 8
multiply that by 13: 104
Tell me if this helps or not bc I'm not really sure, but I really hope I helped!
Height of 10th grade boys is normally distributed with a mean of 63.5 in. and a standard
deviation of 2.9 in.
The area greater than the Z-score is the probability that a randomly selected 14-year
old boy exceeds 70 in.
What is the probability that a randomly selected 10th grade boy exceeds 70 in.?
Answer:
P(Z>2.24) = P(70<X<1e99) = 1.25%
Step-by-step explanation:
Calculate Z-score:
Z=(x-μ)/σ
Z=(70-63.5)/2.9
Z=6.5/2.9
Z=2.24
Find area greater than Z-score:
P(Z>2.24) = P(70<X<1e99) = normalcdf(70,1e99,63.5,2.9) = 0.0125
So the probability that a randomly selected 10th-grade boy exceeds 70 inches is a 1.25% chance.
Find the volume of the figure. Round to the nearest tenth if necessary.
3 yd
3 yd
10 yd
Answer: 90 yards
Step-by-step explanation:
10 by 3 by 3 is 90
Solve the triangle. Round decimal answers to the nearest tenth.
Helppppppppppppp meeeee
Which statement uses words to represent 5+8x3-2
Answer:
A. Five more than the product of 8 and 3, minus 2
Step-by-step explanation:
A is the correct answer because it correctly displays "5 + 8 x 3 - 2"
Hope this helps. :D
-Luna
Help pls giving branliest
Answer:
What types of nouns should be used in effective process writing?
Step-by-step explanation: