(Hope that helps (= The given says the height distribution is normally distributed with the mean height equal to 68 inches. In this case, the bell-shaped curve has a vertical symmetry at 68 inches. This means, half of the mean exceeds 68 inches while the other half has height below 68 inches.
The height range out of which only 5% of the young American men (from age 18 to 24) lie is [63.35, 72.65] (in inches)
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
For this case, let we take:
X = height of American men from age 18 to 24[a,b] = range of height (the values of X) outside which there lies only 5% of American men.Then, according to the given data, we have:
[tex]X \sim N(\mu = 68, \sigma = 2.5)[/tex]
where [tex]\mu[/tex] is mean value of X and [tex]\sigma[/tex] is standard deviation of X (both in inches).
Also, we can write:
[tex]P(X < a) + P(X > b) = 5\% = 0.05[/tex]
Since normal distribution is symmetric about its mean, we can take a and b equidistant from the mean, so as to get a symmetric range which makes much more sense than taking an asymmetric range which doesn't comply with the nature of values of X.
Thus, we have:
[tex]\mu - a = b - \mu\\b = 2\mu - a[/tex]
From this result and [tex]P(X < a) + P(X > b) = 5\% = 0.05[/tex], we get:
[tex]P(X < a) + P(X > 2\mu -a) = 0.05[/tex]
Converting X to Z(the standard normal distribution), we get;
[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]P(X < a) + P(X > 2\mu -a) = 0.05\\\\P(Z < z = \dfrac{x-\mu}{\sigma} = \dfrac{a-68}{2.5}) + P(Z > \dfrac{2(68) - a - 68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z > \dfrac{68-a}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z > -\dfrac{a-68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) + P(Z \leq \dfrac{a-68}{2.5}) = 0.05 \: \: \: \: (\because P(Z > -k) = P(Z \leq k))\\\\2P(Z < \dfrac{a-68}{2.5}) = 0.05\\\\P(Z < \dfrac{a-68}{2.5}) = 0.025[/tex]
Using the z-tables, we get the value of Z for which p-value is 0.025 as
-1.96
Thus, we get:
[tex]\dfrac{a-68}{2.5} = -1.96\\\\a = 68 + (-1.96 \times 2.5)\\a = 63.35[/tex]
Thus, we get: [tex]b = 2\mu - a = 2(68) - 63.35 = 72.65[/tex]
Thus, the range is [a,b] = [63.35, 72.65]
Thus, the height range out of which only 5% of the young American men (from age 18 to 24) lie is [63.35, 72.65] (in inches)
Learn more about standard normal distribution here:
https://brainly.com/question/10984889
DOES ANYONE KNOW THE ANSWER TO THIS???
How do you convert an equation into slope intercept form? do you solve for x or solve for y
Answer:
An equation using the slope-intercept form would be y=mx+b. M would be the slope and b would be the intercept. For example, if slope:5 and intercept:6 the equation would be y=5x+6. Hope I helped!
which is the following solution to
x-13<18
Answer:
X < 31
Step-by-step explanation:
Answer: X<31
Hope this helps!
Foot Locker is having a sale. Buy 1 pair of Nikes for 200.00 and you get a 20% discount off the second pair. If the sales tax is 4%, how much is the first pair of Nikes?
Answer:
208
Step-by-step explanation:
200*.04=8
200+8=208 (for the first pair)
rewrite the quadratic function f(x) = (2x -3)(x+4) in standard form
Answer:
f(x) = 2x^2+5x-12
Step-by-step explanation:
This graph shows the solution to which inequality???
Answer:
B. y > (4/3)x - 2
Step-by-step explanation:
The dotted line means that the answer WILL NOT include the line itself, just the space above it. Since the shaded area is above the line, it must be greater than the line.
36,300,000 in scientific notation
Answer:
thirty-six million three hundred thousand
Step-by-step explanation:
It is just 36,300,000 in word form. Hope it helps!
Answer:
36300000 in scientific notation = 3.63 × 107.
Step-by-step explanation:
A caterer is planning a party for 64 people. The customer has $150 to spend. A $39 pan of pasta feeds 14
people and a $12 sandwich tray feeds 6 people. How many pans of pasta and trays of sandwiches should the
caterer make?
Please help me this is my first assignment in math
Answer:
1,2,3 are Natural Numbers
Step-by-step explanation:
May i please get brainiest.
The answer:
Natural Numbers
Can you please find the missing side these are similar figures.
Answer:
1.108
2.4
3.6
4.28
5.80
6. 10.5
hope this will help you
DO NOT AWNSER IF YOU DON'T KNOW
WILL GIVE BRAINLIEST, LIKE, COMMENT, AND 10 POINTS
Could you please help me with this question and explain thoroughly?
Answer:
Please don't hold me to this. I think I'm right, but I'm rusty.
Step-by-step explanation:
Constant of proportionality is how much the graph grows for each increasing x value. Slope.
Also remember, rise over run.
Slope: 2nd y- 1st y
2nd x-1st x
y=mx+b
A) 4.95-3.75 = 1.2 = about $0.09 per ounce (x=0.9)
24-10 14
For every 14 oz, the cost goes up $1.2.
B) 360-150 = 210 = 15 calories per ounce (x=15)
24-10 14
For every 14 oz, there are 210 calories in the drink.
Given that m=r-s/2nr
Make r the subject .
PLEASE I NEED IT NOW.
THANK YOU . WHOEVER ANSWERS FIRST I WILL GIVE A FOLLOW AND BRAINLIEST
Step-by-step explanation:
[tex]m = \frac{r - s}{2nr} [/tex]
m(2nr) = r-s
2×n×r×m = r-s
move the r on the right side to the left side
2nrm - r = -s
r ( 2nm - 1 ) = -s
[tex]r \: = \frac{ - s}{(2nm - 1)} [/tex]
Answer:
I think it will help you
Two men can do a work in 4 days and 6 days respectively how many days will it take if they work togatherpls tell with steps ill mark brainlist
Answer:
The answer is 12/5 days
Step-by-step explanation:
The First Man (FM) takes 4 days to complete the work
In one day he does (1/4)th portion of the work
The Second Man (SM) takes 6 days to complete the work
In one day he does (1/6)th portion of the work
The FM and SM together do [ (1/4 ) + ( 1/6) ] th portion of the work
So , [ (3+2 )/12] = ( 5 / 12 ) = 5/12 th portion in one day
Hence, FM and SM together complete the work in 12/5 = 2.4 days
Quadrilateral EFGH is a scaled copy of quadrilateral ABCD. Select all of the true statements. Original Segment EF is twice as long as segment AB. Segment CD is twice as long as segment FG The Measure fo Angle HEF is twice the measure of Angle DAB. The area of EFGH is twice the area of ABCD
The question is incomplete. Here is the complete question.
Quadrilateral EFGH is a scaled copy of quadrilateral ABCD. Select all of the true statements.
A. Segment EF is twice as long as segment AB.
B. Segment CD is twice as long as segment FG
C. The measure of angle HEF is twice the measure of angle DAB
D. The length of segment EH is 16 units.
E. The area of EFGH is twice the area of ABCD.
Answer: A. Segment EF is twice as long as segment AB
D. The length of segment EH is 16 units
E. The area of EFGH is twice the area of ABCD
Step-by-step explanation: One quadrilateral which is scaled copy of another quadrilateral means both quadrilateral are similar, i.e., they have congruent angles (same angles) but different sides lengths.
Comparing side GH with side CD, you notice GH's length is twice the side CD. This relationship between each corresponding sides is called scale factor.
Analysing statements above:
A. This statement is correct because segments EF and AB are corresponding sides, so EF will be twice as much as AB;
B. This is incorrect because they are not corresponding sides, so they are not related;
C. Is incorrect because measure of angle in similar quadrilateral has the exact same angle;
D. Statement is correct because if segment AD is 8 units, the corresponding segment EH will be:
EH = 2 x 8 = 16 units
E. Tis statement is correct because area of quadrilateral ABCD is proportional to the area of quadrilateral EFGH by the scale factor, therefore, area of EFGH is twice the area of ABCD.
Sarah has $12.45 in quarters and nickels. She has 39 more nickels than quarters.
How many of each coin does she have?
Answer:
There are 14 nickes, 24 dimes and 48 quarters
Step-by-step explanation:
let x represent the number of nickels.
As she has 10 more dimes than nickels, the number of dimes is x + 10.
As she has twice as many quarters as dimes, the number of quarters is 2(x + 10)
the total value is $15.10, so I get an equation:
0.05x + 0.1*(x + 10) + 0.25*2(x + 10) = 15.10
0.05x + 0.1x + 1 + 0.5x + 5 = 15.10
0.65x = 9.1
x = 14
x + 10 = 24
2(x + 10) = 48
Please I need your help guys anybody
Answer:
Step-by-step explanation:
sorry i cant help
Which of the following situations have a sum of zero? Select all that apply.
1. Shawna spends $20 on materials to make bracelets for her friends. She then earns $20 from selling the bracelets.
2. A diver dove down 20 1/4 feet under water and then descended 20 1/4 feet.
3. A golfer shot 2 over par (+2) on a hole. They then then shot 2 under par (−2) on the next hole.
4. You have $5.50 in your pocket and then you receive $5.50 for doing your chores.
-4j-1-5j+6= pls help me
Hello
Answer:
-9j+5
Step-by-step explanation:
=-4j-1-5j+6
=-4j-5j+6-1
=-9j+5
Cylinder A is mathematically similar to cylinder B. The height of cylinder A is 10cm and its surface area is 440cm2 . The surface area of cylinder B is 3960cm2 . Calculate the height of cylinder B
Answer:
[tex]440 = 2\pi {r}^{2} + 2\pi(r)10 \\ [/tex]
[tex]3960 = 2\pi {r}^{2} + 2\pi(r)h[/tex]
[tex] \frac{3960 = 2\pi {r}^{2} + 2\pi(r)h}{440 = 2\pi {r }^{2} + 2\pi(r)10 } [/tex]
[tex]9 = \frac{h}{10} [/tex]
h=90
The height of the cylinder B is 30 cm.
Given that:
Both cylinders A and B are similar. Similarity applies proportionate size which means we have
height of cylinder A : radius of cylinder A :: height of cylinder B: radius of cylinder B
or symbolically we have:
[tex]$\frac{h_1}{r_1} = \frac{h_2}{r_2}$\\[/tex]
or we can say we have:
[tex]r_2 = h_2\times\dfrac{r_1}{h_1} \\[/tex]
Now it is given that Cylinder A's height [tex]h_1[/tex] is 10 cm and surface area is [tex]400\rm \;cm^2[/tex]
Thus from the formula of surface area of cylinder , we have below equation for cylinder A:
[tex]2\pi \times r_1 \times 10 = 440\\or\\r_1 = \dfrac{440}{20\pi}\\\\r_1 \approx 7 \rm\: cm\\\\\\[/tex]
Also given surface area of cylinder B is 3960 [tex]\rm cm^2[/tex], thus:
[tex]2\times \pi\times r_2 \times h_2 = 3960\\\\\2\times\pi\times (h_2\times\dfrac{r_1}{h_1})\times h_2= 3960\\\\2\times\pi\times (h_2\times\dfrac{7}{10})\times h_2 = 3960\\or\\ (h_2)^2 = \dfrac{39600}{2\times\pi\times7}\\\\or\\h_2 = 30 \rm \;cm.[/tex]
Thus height of the cylinder B is 30 cm.
For more information, refer to this link:
https://brainly.com/question/1037971
for how many tickets is the cost the same for club members and non-members?
Answer:
The cost will be the same for 2 club members as for 1 non-member.
Step-by-step explanation:
There will never be a number of tickets where the price for a given number of club members is the same for the same number of non-members.
However, if two club members purchase tickets, their cost is 2($3) = $6.
If one non-member purchases a ticket, the cost is 1($6) = $6.
A sequence can be generated by using an=an−1+9, where a1=−5 and n is a whole number greater than 1. What are the first four terms in the sequence?
A.−5, 4, 13, 22
B.9, 4, −1, −6
C.−5, −45, −405, −3645
D. 9, −45, 225, −1125
Answer:
A
Step-by-step explanation:
For the sequence, the defining formula is given as;
an = Previous term + 9
So a2 will be -5 + 9 = 4
a3 will be 4 + 9 = 13
a4 will be 13 + 9 = 22
a5 will be 22 + 9 = 31
So the sequence of numbers will be;
-5, 4 , 13 , 22 , 31
Sally is 6 years older than Ali. Together the sum of their ages is 34. How old is each of them?
Answer:
34-6=?
Step-by-step explanation:
34-6=?
Answer:
Ali is 14
Sally is 20
Step-by-step explanation:
let's call Sally S.
let's call Ali A.
using what's given, you can make this equation:
A + 6 = S
(because Ali is 6 years younger than Sally)
you can also make this equation:
A + S = 34
(because the sum of their ages is 34)
now, substitute S for A + 6.
A + A + 6 = 34
2A + 6 = 34
subtract 6 from both sides of the equation
2A + 6 - 6 = 34 - 6
2A = 34 - 6
2A = 28
divide both sides of the equation by 2
2A/2 = 28/2
A = 28/2
A = 14
almost done! now you just need to substitute A for 14 in the first equation.
A + 6 = s
14 + 6 = s
20 = s
Ali is 14
Sally is 20
will give brainliest !!
Answer:
$672
Step-by-step explanation:
Answer: 42
Step-by-step explanation:
I think hope this helps
PLZ ANSWER THIS QUICK! THANKS!
Answer:
a) 300m
b) 15 miles
Step-by-step explanation:
a) 1 : 30 000
= 1x 30 000
= 30 000cm
= 30 000cm/ 100 Representing in metres
= 300m
b) 1 : 6
= 1x 2.5 : 6x 2.5
= 2.5 : 15
= 15 miles
which expression represents this model?
Answer:
3-6 I think
Step-by-step explanation:
Please help (I give brainliest and follow you)
Answer: B. (-2.0)
Step-by-step explanation:
(X,Y)
You go over -2 on the X
And stay at 0 on the Y
So it would be (-2,0)
Absolute value is DISTANCE. How many units a number is away from zero.
a.) 3
b.)4
C.) -3
d.) -4
I believe it is B) 4
The number line is going by .5 per space and there are 8 spaces in the red line segment. You can then do 8 x .5 and you will get 4.
True or False: Every number has a limited amount of factors, but an unlimited amount of multiples.
Answer:
False
Step-by-step explanation:
0 has unlimited numbers of factors because 0 times everything equals 0. If 0 is not included then the statement is true.
TIME REMAINING 01:37:16 Absalom states that 0 is a rational number. Which is a correct explanation for this statement? The number 0 is a whole number, which is part of the rational numbers. The number 0 is the center of the number line. The number 0 is a natural number, which is part of the rational numbers. The number 0 cannot be written as a fraction.
Answer:
The number 0 is a whole number, which is part of the rational numbers, is correct.
Step-by-step explanation:
Absalom states that 0 is a rational number.
As the whole numbers are 0,1,2,3,... which is starting from 0, so the stated number 0 is a part of the whole number.
As all the whole number are rational numbers, so 0 is a rational number
Hence, the explanation (i) which is,
The number 0 is a whole number, which is part of the rational numbers, is correct.
The naturals numbers are 1,2,3,... which starts from 1, so 0 is not a part of the natural number, and the number 0 can be written as a fraction like [tex]0=\frac {0}{1}[/tex].
Hence, statement (ii) The number 0 is a natural number, which is part of the rational numbers as well as the statement (iii) The number 0 cannot be written as a fraction, are wrong.
Answer:
The number 0 is a whole number, which is part of the rational numbers.
Step-by-step explanation:
List all factors of 44
Answer: Factors of 44: 1, 2, 4, 11, 22, 44
Step-by-step explanation: coz I juss know