Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet. A sample of 45 men’s step lengths is taken. Step 1 of 2 : Find the probability that an individual man’s step length is less than 1.9 feet. Round your answer to 4 decimal places, if necessary.
Answer:
0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.
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.
Normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet.
This means that [tex]\mu = 2.5, \sigma = 0.4[/tex]
Find the probability that an individual man’s step length is less than 1.9 feet.
This is the p-value of Z when X = 1.9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.9 - 2.5}{0.4}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a p-value of 0.0668
0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.
What is net cash flow
Question 3
A 70kg patient has approximately 8 pints of blood. The patient donates 470mL of blood.
Approximately what fraction of his body's blood is this? (one pint = 568mL)
Step-by-step explanation:
Given that,
The mass of a patient = 70 kg
A 70kg patient has approximately 8 pints of blood.
The patient donates 470mL of blood.
We know that,
1 pint = 568 mL
8 pints = 4544 mL
Required fraction,
[tex]\dfrac{470}{4544}=0.1\\\\=\dfrac{1}{10}[/tex]
So, the required fraction is approximately [tex]\dfrac{1}{10}[/tex].
What is the missing term in the factorization?
12x2 – 75 = 3 (2x+?)(2x – 5)
Answer:
12x2 – 75 = 3 (2x+5)(2x – 5)
Step-by-step explanation:
Determine which diagram could be used to prove triangle ABC is congruent to triangle EDC using similarity transformations
Answer:
A
Step-by-step explanation:
edge 2021
HELP HELP QUICK QUICK
Answer:
multiplication by -1 will reflect over the x-axis
multiplication by a positive number will "scale" or "stretch" the function
Step-by-step explanation:
Few drivers realize that steel is used to keep the road surface flat despite the weight of buses and trucks. Steel bars, deeply embedded in the concrete, are sinews to take the stresses so that the stresses cannot crack the slab or make it wavy. The passage best supports the statement that a concrete road
Answer: Is reinforced with other material
Step-by-step explanation:
The options are:
A is expensive to build.
B usually cracks under heavy weights.
C looks like any other road.
D is reinforced with other material.
The passage best supports the statement that a concrete road are reinforced with other material. According to the information given in the passage, steel plays a vital role in keeping the road surface flat.
Steel bars are embedded in concrete so that the stresses cannot crack the slab. Therefore, it indicates that concrete road is reinforced with other material.
Select all of the following statments that are true
Answer:
A. -¾ + 0 = -¾
B. -¾ - ¾ = -(¾ + ¾)
C. ¾ - ¾ = ¾ + (-¾)
E. -¾ + ¾ = ¾ + (-¾)
F. -¾ + ¾ = 0
Step-by-step explanation:
Let's check each equation to determine whether they are true or false.
If what we have in the both sides are equal, then the equation is true, if they're not, them it is false.
✔️-¾ + 0 = -¾
Add everything on your left together
-¾ = -¾ (TRUE)
✔️-¾ - ¾ = -(¾ + ¾)
Add everything on both sides together respectively
(-3 - 3)/4 = -(3 + 3)/4
-6/4 = -6/4 (TRUE)
✔️¾ - ¾ = ¾ + (-¾)
0 = ¾ - ¾ (+ × - = -)
0 = 0 (TRUE)
✔️-¾ + ¾ = ¾ - (-¾)
0 = ¾ + ¾ (- × - = +)
0 = 6/4 (FALSE)
✔️-¾ + ¾ = ¾ + (-¾)
0 = ¾ - ¾ (+ × - = -)
0 = 0 (TRUE)
✔️-¾ + ¾ = 0
0 = 0 (TRUE)
Help. I will be guessing on this, but I want to make sure this is on here so no one has to guess like I am. Help a brother out
Answer:
Line 3
Step-by-step explanation:
→ Calculate gradient
[tex]\frac{6-3}{4-2} =1.5[/tex]
Answer:
Line 3
Step-by-step explanation:
(0,0) & ( 4 , 6)
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{6-0}{4-0}\\\\=\frac{6}{4}\\\\=\frac{3}{2}\\\\=1\frac{1}{2}[/tex]
angle 1 is congruent to angle 2 prove p is parallel to q
You'll need 2 more lines to complete this two column proof.
---------------------
Line 4
For the "statement" portion, you'll say something like [tex]\angle 2 \cong \angle 3[/tex]
The reason for this statement is "transitive property"
We're basically combining lines 1 and 3 to form this new line.
The transitive property is the idea that if A = B and B = C, then A = C. We connect the statements like a chain.
---------------------
Line 5
The statement is what you want to prove since this is the last line.
So the statement is [tex]p || q[/tex]
The reason is "converse of corresponding angles theorem"
As you can probably guess, this theorem says "If two corresponding angles are congruent, then the lines are parallel".
what is the slope of the function, represented by the table of values below?
A. -2
B. -3
C. -4
D. -6
Answer:
B. -3
Step-by-step explanation:
solve the equation 11n - 17 = 49
Answer:
The correct answer is =6.
Step-by-step explanation:
Solution,
Given;
11−17=49
or,11n-17=49
or,11−17+17=49+17
or,11=66
or,n=66/11
#n=6
HOPE IT HELPED♥︎
A survey of 249 people asks about their favorite flavor of ice cream. The results of this survey, broken down by the age group of the respondent and their favorite flavor, are as follows:
Chocolate Vanilla Strawberry
Children 40 10 44
Teens 34 10 38
Adults 17 43 13
If one person is chosen at random, find the probability that the person:______.
a) is an adult.
b) likes chocolate the best.
c) is an adult OR likes vanilla the best.
d) is a child AND likes vanilla the best.
e) likes strawberry the best, GIVEN that the person is a child.
f) is a child, GIVEN that the person likes strawberry the best.
Answer:
a) [tex]P(Adult)=\frac{73}{249}=0.2932=29.32%[/tex]
b) [tex]P(Chocolate)=\frac{91}{249}=0.3655=36.55%[/tex]
c) [tex]P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%[/tex]
d) [tex]P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%[/tex]
e) [tex]P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%[/tex]
f) [tex]P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%[/tex]
Step-by-step explanation:
a)
In order to solve part a of the problem, we need to find the number of adults in the survey and divide them into the number of people in the survey by using the following formula>
[tex]P=\frac{desired}{possible}[/tex]
In this case we have a total of 17+43+13 adults which gives us 73 adults and a total of 249 people surveyed so we get:
[tex]P(Adults)=\frac{73}{249}=0.2932=29.32%[/tex]
b)
The same principle works for part b
there are: 40+34+17=91 people who likes chocolate ice cream the best so the probability is:
[tex]P(Chocolate)=\frac{91}{249}=0.3655=36.55%[/tex]
c)
when it comes to the or statement, we can use the following formula:
P(A or B) = P(A) + P(B) - P( A and B)
In this case:
[tex]P(Adult)=\frac{73}{249}[/tex]
[tex]P(Vanilla)=\frac{10+10+43}{249}=\frac{63}{249}[/tex]
[tex]P(AdultandVanilla)=\frac{43}{249}[/tex]
so:
[tex]P(AdultorVanilla)=\frac{73}{249}+\frac{63}{249}-\frac{43}{249}[/tex]
[tex]P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%[/tex]
d)
Is a child and likes vanilla the best.
In the table we can see that 10 children like vanilla so the probability is:
[tex]P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%[/tex]
e)
Likes strawberry the best, GIVEN that the person is a child.
In this case we can make use of the following formula:
[tex]P(B/A)=\frac{P(AandB)}{P(A)}[/tex]
so we can get the desired probabilities. First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:
[tex]P(childrenandstrawberry)=\frac{44}{249}[/tex]
Then, we know there are 40+10+44=94 children, so the probability for the person being a child is:
[tex]P(Child)=\frac{94}{249}[/tex]
Therefore:
[tex]P(Strawberry/Child)=\frac{\frac{44}{249}}{\frac{94}{249}}[/tex]
[tex]P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%[/tex]
f)
The same works for the probability of the person being a child given that the person likes strawberry the best.
First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:
[tex]P(childrenandstrawberry)=\frac{44}{249}[/tex]
Then, we know there are 44+38+13 persons like strawberry, so the probability for the person liking strawberry is:
[tex]P(Child)=\frac{95}{249}[/tex]
Therefore:
[tex]P(Child/Strawberry)=\frac{\frac{44}{249}}{\frac{95}{249}}[/tex]
[tex]P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%[/tex]
Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x = 0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.
I error l ≤
Answer:
upper bound for the error, | Error | ≤ 0.0032
Step-by-step explanation:
Given the data in the question;
[tex]e^{0.4[/tex] < e < 3
Using Taylor's Error bound formula
| Error | ≤ ( m / ( N + 1 )! ) [tex]| x-a |^{N+1[/tex]
where m = [tex]| f^{N+1 }(x) |[/tex]
so we have
| Error | ≤ ( 3 / ( 3 + 1 )! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 3 / 4! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 3 / 24 ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴
| Error | ≤ ( 0.125 ) [tex]|[/tex] -0.0256 [tex]|[/tex]
| Error | ≤ ( 0.125 ) 0.0256
| Error | ≤ 0.0032
Therefore, upper bound for the error, | Error | ≤ 0.0032
the percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.
If one person is selected from each city, what is the probability that all of them are under 18?
Answer:
0.0158 = 1.58% probability that all of them are under 18.
Step-by-step explanation:
Probability of independent events:
If three events, A, B and C are independent, the probability of all happening is the multiplication of the probabilities of each happening, that is:
[tex]P(A \cap B \cap C) = P(A)P(B)P(C)[/tex]
The percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.
This means that [tex]P(A) = 0.235, P(B) = 0.258, P(C) = 0.26[/tex]
If one person is selected from each city, what is the probability that all of them are under 18?
Since the three people are independent:
[tex]P(A \cap B \cap C) = 0.235*0.258*0.26 = 0.0158[/tex]
0.0158 = 1.58% probability that all of them are under 18.
Ngân hàng rơi vào tình trạng vỡ nợ khi nào
Answer:
.
Step-by-step explanation:
.
(a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 2 to each of the following.
(i) 2 to 3
(ii) 2 to 2.5
(iii) 2 to 2.1
(b) Find the instantaneous rate of change when r =2.
Answer:
ai) 5pi
aii) 4.5pi
aiii) 4.1pi
b) 4pi
Step-by-step explanation:
a) Area of a circle is given by pi×r^2.
The average rate of change of the area of a circle from r=b to r=a is (pi×b^2-pi×a^2)/(b-a).
Let's simplify this.
Factor pi from the terms in the numerator:
pi(b^2-a^2)/(b-a)
Factor the difference of squares in the numerator:
pi(b-a)(b+a)/(b-a)
"Cancel" common factor (b-a):
pi(b+a).
So let's write a conclusive statement about what we just came up with:
The average rate of change of the area of a circle from r=b to r=a is pi(b+a).
i) from 2 to 3 the average rate of change is pi(2+3)=5pi.
ii) from 2 to 2.5 the average rate of change is pi(2+2.5)=4.5pi.
from 2 to 2.1 the average rate of change is pi(2+2.1)=4.1pi.
b) It looks like a good guess at the instantaneous rate of change is 4pi following what the average rate of change of the area approached in parts i) through iii) as we got closer to making the other number 2.
Let's confirm by differentiating and then plugging in 2 for r.
A=pi×r^2
A'=pi×2r
At r=2, we have A'=pi×2(2)=4pi. It has been confirmed.
84 percent of students athletes attend a preseason meeting. If there are 175 students athletes how many attend the meeting
Answer:
Total no. of students =175
percent of students athletes who attend a preseason meeting =84
No. of students who attend the meeting
= 84% of 175
=147
A total of $20,000 is invested at an annual interest rate of 6%. No matter how many years this
money is invested, what is the best investment plan to earn the most money in the end?
Compounded continuously
Compounded daily
Compounded quarterly
Compounded monthly
SCALCET8 3.11.501.XP. Find the numerical value of each expression. (Round your answers to five decimal places.) (a) sinh(ln(4)) (b) sinh(4)
sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875
sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992
Rajah 1 menunjukkan lukisan pelan berskala bagi sebuah rumah
lantainya berbentuk dua segi empat sama.
Skala yang digunakan adalah 1:200. Jika
kos memasang jubin jalah Rm 30 per m3
berapakah jumlah kos memasang jubin bagi
rumah tersebut?
Answer:
RM 1200 kalau ada gambar cuba insert
5. What is the value of x if the quadrilateral is a kite? B X+2 C С 13 A Xth12 D
Answer: just had this problem! X = 11
One angle of a triangle is twice as large as another. The measure of the third angle is 60° more than that of the smallest angle. Find the measure of each angle.
The measure of the smallest angle is º
Please help :)
Answer:
The measure of the smallest angle is 30º
Step-by-step explanation:
Let the angles be:
[tex]x \to[/tex] the first angle (the smallest)
[tex]y \to[/tex] the second angle
[tex]z \to[/tex] the third angle
So, we have:
[tex]y = 2x[/tex]
[tex]z=x + 60[/tex]
Required
Find x
The angles in a triangle is:
[tex]x + y +z = 180[/tex]
Substitute values for y and z
[tex]x + 2x +x + 60 = 180[/tex]
[tex]4x + 60 = 180[/tex]
Collect like terms
[tex]4x = 180-60[/tex]
[tex]4x = 120[/tex]
Divide by 4
[tex]x = 30[/tex]
Which of the following lists of ordered pairs is a function? A. (1,8), (2, 9), (3, 10), (3, 11) B. (-1,4), (1,7), (2, 10) C. (3,7),(4, 5), (3, 8) D. (-2,3), (1, 3), (3, 7), (1, 4)
Answer:
B
Step-by-step explanation:
B is the only one that doesnt share x-values
Write the equation of the line with the given conditions. passing through (-1, -7) and perpendicular to the line with equation 4x + 5y = 31
Answer:
y = 5/4 x - 23/4
Step-by-step explanation:
4x + 5y = 31
5y = - 4x +31
y = -4/5 x + 31/5
⊥ slope = 5/4
-7 = 5/4 (-1) + B
-28 = -5 + 4b
-23 = 4B
b = -23/4
Which line is parallel to the line that passes through the points (1,7) and (-3, 4)? A. y=--x-5 B. y=+*+1 y=-x-8 O c. D. 11 v==x+3 4
Answer:
B
Step-by-step explanation:
because
find the equation of the line
Answer:
y = x + 6
Step-by-step explanation:
rise = 1
run = 1
slope = rise/run = 1
y-intercept = 6
y = mx + b
y = x + 6
find the h.c.f. if 84 and 72
Answer:
12
Step-by-step explanation:
First lets list all the factors of these numbers
72: 1,2 3,4,6,8,9,12,18,24,36,72
84: 1 , 2 , 3 ,4 , 6 , 7 , 12 , 14 , 21 , 28 , 42 , 84
Now lets find the biggest number that is a factor of both 84 and 72
as we can see the highest number that is the factor of both 84 and 72 is 12
12 is the hcf
Please help ASAP. No links
Hello my dear friend of USA !!!
DB/AD = BE/EC
=> 6/4 = x+1/x
=> 6x = 4x + 4
=> 2x = 4
=> x = 2
So x = 2
I am from INDIA.
Lots of love ❤️!!!
Have a great day ahead!
Answer:
x = 2
Step-by-step explanation:
[tex]\frac{6}{4} = \frac{x+1}{x}[/tex]
6x = 4x + 4
2x = 4
x = 2
Helppp and explain than you
Answer:
1) x = 2
Step-by-step explanation:
Hope it helps. I'll try to solve the second one too
9514 1404 393
Answer:
x = 2(-5, 4, 6)Step-by-step explanation:
1. Substitution can work for this.
2x +3(4x -5) = 13
14x = 28 . . . . . add 15
x = 2 . . . . . . . divide by 14
__
2. The equation z=6 eliminates all but the 1st and 3rd choices. Using that value in the first equation gives ...
x + y + 6 = 5
x + y = -1
Only the 3rd choice satisfies this equation.
(x, y, z) = (-5, 4, 6)
