Using the normal distribution, it is found that:
a) 4.46% of finish times was higher than 72 minutes.
b) 55.11% of finish times was between 52 and 70 minutes.
c) The 40th percentile of finish times is 52.5 minutes.
d) The 95th percentile of finish times is 71.45 minutes.
In a normal distribution 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]
It 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, which is the percentile of X.In this problem:
The mean is of 55 minutes, hence [tex]\mu = 55[/tex].The standard deviation is of 10 minutes, hence [tex]\sigma = 10[/tex]Item a:
The proportion is 1 subtracted by the p-value of Z when X = 72, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{72 - 55}{10}[/tex]
[tex]Z = 1.7[/tex]
[tex]Z = 1.7[/tex] has a p-value of 0.9554
1 - 0.9554 = 0.0446
0.0446 x 100% = 4.46%
4.46% of finish times was higher than 72 minutes.
Item b:
Th proportion is the p-value of Z when X = 70 subtracted by the p-value of Z when X = 52, hence:
X = 70:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 55}{10}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
X = 52:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{52 - 55}{10}[/tex]
[tex]Z = -0.3[/tex]
[tex]Z = -0.3[/tex] has a p-value of 0.3821.
0.9332 - 0.3821 = 0.5511
0.5511 x 100% = 55.11%
55.11% of finish times was between 52 and 70 minutes.
Item c:
The 40th percentile is X when Z has a p-value of 0.4, so X when Z = -0.253.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.253 = \frac{X - 55}{10}[/tex]
[tex]X - 55 = -0.253(10)[/tex]
[tex]X = 52.5[/tex]
The 40th percentile of finish times is 52.5 minutes.
Item d:
The 95th percentile is X when Z has a p-value of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 55}{10}[/tex]
[tex]X - 55 = 1.645(10)[/tex]
[tex]X = 71.45[/tex]
The 95th percentile of finish times is 71.45 minutes.
A similar problem is given at https://brainly.com/question/24663213
What is the slope of the function?
O-6
O 4
O 4
O 6
Answer:
12/2 = 6
Step-by-step explanation:
2 ways to do it, graph it, or do the slop finding formula y2-y1/x2-x1
answer:
Step-by-step explanation:
I hope she is correct answer
15. A farmer records the number of eggs that chickens on the farm produce each week. The table
shows the results.
143
160
117
137
152
108
128
If during the next week, the chickens on the farm produce 60 eggs, which statement is true?
A The value 60 is an outlier that will skew the data to the left.
B The value 60 is an outlier that will skew the data to the right.
С The value 60 is not an outlier, and it will not skew the data in either direction.
D
The value 60 is not an outlier, and the effect on the data is unknown.
m 130 degrees n 130 degrees what is t
Answer:
50 degrees
Step-by-step explanation:
that line is a 180 degree and 180-130=50
help me due today it is math
Answer:
2
Step-by-step explanation:
sum of digits=1+2+5+8=16
smallest term to be added to make it divisible by 9 is 2
∵16+2=18÷9=2
5
which ratio is greater than 5/8
12/24
3/4
15/24
4/12
Answer:(B)
Explanation: 3/4. Hope this helped :)
make the subject x of the formula y = 7x + 4
Answer:
[tex]x = \frac{y - 4}{7}[/tex]
Step-by-step explanation:
[tex]y = 7x + 4 \\\\y - 4 = 7x\\\\\frac{y - 4}{7} = \frac{7x}{7}\\ \\ \frac{y - 4}{7} = x[/tex]
Write as a fraction
3÷151
Answer:
3/151
Step-by-step explanation:
That's the answer
which two expressions are equivalent to 7(t + 5)?
A). 7 • 5 • t
B). 7 • 5 + t
C). 7 • 5 + 7 • t
D). (5 + t) • 7
E). 5(t + 7)
Answer:
7.5+7.t
and
(5+t).7
are equivalent to 7(t+5)
Option D and E are equivalent to 7(t + 5) That is :
(5 + t) • 7 and 5(t + 7)
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
The given equation is :
7(t + 5)
7(t+5) multiply 7 with inside the parenthesis
7(t+5) = 7t + 7x5
this result is equivalent to option D and E which will give the same result.
Therefore, Option D and E are equivalent to 7(t + 5).
Read more about expressions at :
https://brainly.com/question/12030750
#SPJ2
Which equation reprints a line passing through the point (8,16) with a slope of 3
Plz help me on this qustin. Slove for w 2w ≥ -12
Answer:
w > -6
Step-by-step explanation:
divide each term n 2x > -12 by 2 then simplify
Gven: f(x) = 4x +1 and (x)= x^2 + 1.
find (fog)(x)
Answer:
Step-by-step explanation:
27836?+_68_729+_8978
help with this i dont understand please
Answer:
see explanation
Step-by-step explanation:
The rule explains what happens to the input value in order to obtain the output.
input = 4 , then divide by 4
4 ÷ 4 = 1 , then add 2
1 + 2 = 3
---------------------------------------
input = 6 , divide by 4
6 ÷ 4 = 1,5 . now add 2
1.5 + 2 = 3.5
-----------------------------------------
input = 8 , divide by 4
8 ÷ 4 = 2 , now add 2
2 + 2 = 4
-------------------------------------------
input = 10 , divide by 4
10 ÷ 4 = 2.5 , now add 2
2.5 + 2 = 4.5
--------------------------------------------
input | 0 | 2 | 4 | 6 | 8 | 10
------------------------------------------
output| 0 | 2.5 | 3 | 3.5 | 4 | 4.5
Answer:
Ok, Dear This is the most easy question.
Focus with me , Ill tell you the answer and explain it
First answer :3
Secound answer:3.5
Third answer:4
Last one :4.5
Step-by-step explanation:
So Baisicly,
First answer : We Devide 4 by 4 so its equal to 1 and then we add 2 then its equal to 3.
Secound answer: We divide 6 by 4 so it becomes 1.5 and then add 2 so itll become 3.5.
Thid answer: We divide 4 by 8 and so it becomes equal to 2 and then we add 2 so its 4.
Last one: We divide 4 by 10 and so it becomes 2.5 and then we add 2 so itll become 4.5.
Find the area of the figure. (Sides meet at right angles.)
4 m
Бm
4 m
10 m
8 m
Simplify the algebraic
expression
4(x + 1) + 7(x + 3).
a. 11x + 4
b. 2x + 215
C. 11x + 25
d. 5x + 11
Someone help pleaseeee
Answer:
C.
Step-by-step explanation:
4(x + 1) + 7(x + 3)= 4*x+4*1 + 7*x+7*3 = 4x+4 +7x +21 = 11x + 25
C
Step-by-step explanation:
4x+4+7x+21
11x+25
you have to combine like terms
x/-5+6 is greater than or equal to 2
Answer:
[tex]x\geq 2[/tex]
Step-by-step explanation:
Write out the problem
[tex]\frac{x}{-5+6} \geq 2[/tex]
Simplifiy -5 + 6 = 1
[tex]\frac{x}{1} \geq 2[/tex]
Remember that any fraction with a denominator of 1 is equilvalent to the numerator, so
[tex]\frac{x}{1} =x[/tex]
[tex]x\geq 2[/tex]
Jacob travels to the shops 5 miles from his home, then he travels to the
post office 3 miles from the shops. Afterwards he travels home. What is
the total distance Jacob traveled? What is the total displacement of
Jacob?*
Distance 8 miles : Displacement 8 Mlles
Distance 16 Miles: Displacement 0
Distance 8 Miles: Displacement 8 Miles
Distance 6 miles : Displacement 8 miles
Answer:
[tex]\huge\boxed{Distance:16mi}\\\huge\boxed{Displacement: 0mi}[/tex]
Step-by-step explanation:
Because Jacob starts and ends at his house, his total displacement is 0mi, because the distance from his house to his house is 0 mi.
Because Jacob travels 5 miles to the shops, then (N.B. I'm inferring here) in a straight line, 3 more miles to the post office, a total distance of 8 miles, then another 8 backwards, he travels a total distance of 16mi.
Hope it helps :) and let me know if you want me to elaborate.
5. Aaron sold 126 boxes of cookies. This is 14 more than twice the
number of boxes his sister, Victoria, sold. How many boxes of
cookies did Victoria sell?
Answer:
56 boxes
Step-by-step explanation:
1. First subtract 14 from 126 to get 112 boxes
2. Now divide 112 by 2 to get Victoria's total of 56
I need help with elementary statistics
the sum of x and 4y is 9
Answer:
y= -1/4x +9/4
Step-by-step explanation:
I don't know which form you wanted, so heres the slope form
What is
[tex] \frac{4}{60} [/tex]
simplified?
Answer:
1/15
Step-by-step explanation:
4/60
Divide the top and bottom by 4
4/4 =1
60/4= 15
1/15
what is the speed of light?
Answer:
The universal physical constant c, or the speed of light in vacuum, is essential in many fields of physics. It has a precise value of 299792458 metres per second.
Step-by-step explanation:
Answer:
299 792 458 m / s
Step-by-step explanation:
In terms of sig figs, it can be 3.0 * 10^8 m/s
Find the average rate of change of the function from x=1 to x=2.
f(x)=−10/x^2
Enter the exact answer.
Average rate of change =
Answer:
Average rate of change = [tex]\frac{15}{2}[/tex]
Step-by-step explanation:
For a closed interval [tex][a,b][/tex] in a function, the average rate of change is [tex]m=\frac{f(b)-f(a)}{b-a}[/tex].
Thus, given our interval of [tex][1,2][/tex] from the directions, we determine that [tex]f(b)=f(2)=-\frac{10}{(2)^2}=-\frac{10}{4}=-\frac{5}{2}[/tex] and [tex]f(a)=f(1)=-\frac{10}{(1)^2}=-\frac{10}{1}=-10[/tex].
Hence, [tex]m=\frac{f(b)-f(a)}{b-a}=\frac{(-\frac{5}{2})-(-10) }{2-1}=\frac{\frac{15}{2}}{1}=\frac{15}{2}[/tex].
In conclusion, the average rate of change of the function from x=1 to x=2 is [tex]\frac{15}{2}[/tex].
In this problem, I did part a) correctly, but I got 7 points off in part b) but I don’t know why?
Answer: You need to prove that ABCD is a rhombus because it's diagonals are always perpendicular, no matter what.
A rhombus is a quadrilateral and:
- its opposite angles have equal measure.
- The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral.
- Its diagonals bisect opposite angles.
What is the reciprocal of
5/6
Answer:
6/5
Step-by-step explanation:
I need 425 divided by 5 with the algorithm please!
Answer:
85
Step-by-step explanation:
I attached my work in a picture below!
Hope this helps :D
In a school there are 200 boys and 800 girls. Find the percentage of girls in that school.
Answer:
80% girls.
Step-by-step explanation:
20% boy.
80%+20%= 100%
Set Question involving real and natural numbers
Only two real numbers satisfy x² = 23, so A is the set {-√23, √23}. B is the set of all non-negative real numbers. Then you can write the intersection in various ways, like
(i) A ∩ B = {√23} = {x ∈ R | x = √23} = {x ∈ R | x² = 23 and x > 0}
√23 is positive and so is already contained in B, so the union with A adds -√23 to the set B. Then
(ii) A U B = {-√23} U B = {x ∈ R | (x² = 23 and x < 0) or x ≥ 0}
A - B is the complement of B in A; that is, all elements of A not belonging to B. This means we remove √23 from A, so that
(iii) A - B = {-√23} = {x ∈ R | x² = 23 and x < 0}
I'm not entirely sure what you mean by "for µ = R" - possibly µ is used to mean "universal set"? If so, then
(iv.a) Aᶜ = {x ∈ R | x² ≠ 23} and Bᶜ = {x ∈ R | x < 0}.
N is a subset of B, so
(iv.b) N - B = N = {1, 2, 3, ...}
For all horizontal lines the range is
When you have a function where y equals a constant, your graph is a truly horizontal line,
In that case, the range is just that one and only value. No other possible values can come out of that function! Many other functions have limited ranges.
7. Solve. *
Tommy had 3 pounds of peanuts. If he split the peanuts up between himself
and his three friends, how many pounds of peanuts would each person gets
Answer:
0.75 is what they each get.
Step-by-step explanation:
You need to divide 3 by 4.
helppp please!!!!!!!!!!!!!!
Answer:
No
No
Yes
Yes
No
Step-by-step explanation:
In this case we are looking at substitution, so any where you find x put three(3) in replace of it.
And remember the answer should be 36,
I find it difficult to type the answer so I will take a picture instead.
