(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)
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in an equation y varies directly as x varies. if y = 55 when x = 22, what is the value of x when y = 85?
Answer:
x=34
Step-by-step explanation:
If you put Y and X into a ratio then it will be
5:2
because since their GCF is 11, then we will have to divide both of the numbers by 11.
If y=85 then that means that it was multiplied by 17. If we want them to stay within the same ratio, then we will have to multiply X (2) by 17.
That will get you 34.
A set of data has a mean of 58 and only one outlier of 92. Which statement about this data set must be true?
The range is 34.
The range is 34.
The mode is equal to the mean.
The mode is equal to the mean.
The mean is greater than the median.
The mean is greater than the median.
The distribution curve is skewed to the right.
Answer:
The correct option is;
The distribution curve is skewed to the right
Step-by-step explanation:
The given parameters are;
The mean = 58
The outlier = 92
Given that the outlier, P, can be found from the following formula, we have;
P > Q₃ + 1.5·IQR = (Q₃ + 1.5 (Q₃ - Q₁)
92 > (Q₃ + 1.5 (Q₃ - Q₁)
Given that mean = 58
Therefore, the IQR, and Q₃ are relatively small compared to the outlier, and the data is skewed, with the more smaller numbers than there are large numbers which makes the distribution curve to be skewed to the right.
How do you write 8.43 × 10^-4 in standard form?
Answer:
0.000843
Step-by-step explanation:
simplify the expression:
8.43 × 0.0001
now simplify:
0.000843
If you find my answer helpful
Pls consider marking my answer as Brainliest! It would mean a lot!
Plzs help I give u BRAINLIST
Answer:
$30,170.36
Step-by-step explanation:
I'm good at math, and I double checked with someone... I am perfectly sure that $30,170.36 is the answer.
Curtis won 53 pieces of candy playing a game at the county fairAt school he gave one to each of his classmates in his English class. He only has 25 remaining. How many did he give away?
5. Do this without using a calculator
Calculate 39 × 63 + 39 × 37
A. 3,510. B. 3,900. C. 4,290. D. 97,812
Answer:
3900
Step-by-step explanation:
Not really sure how to explain this one.
Select the correct answer.
Jason is traveling by car from his home to his office. He has gone 3.5 miles so far. From this point on, he can cover 100 miles every 2 hours. What is the equation of a line that models the total miles traveled, y, in x hours after this point?
A.
y = 100x + 3.5
B.
y = 100x – 3.5
C.
y = 50x + 3.5
D.
y = -50x + 3.5
9514 1404 393
Answer:
C. y = 50x + 3.5
Step-by-step explanation:
100 miles in 2 hours is 100/2 = 50 miles per hour. Multiplying that rate by x hours gives the miles traveled in addition to the 3.5 miles so far. The appropriate equation for miles traveled is ...
y = 50x +3.5 . . . matches choice C
Answer:
Step-by-step explanation:
Mrs. Bartz was going shopping for Halloween Candy for her first grade class. If
a bag of 25 Skittle's costs $4.00, how much would one bag of Skittles cost?
Answer:
The answer is 0.16
Step-by-step explanation:
because if you add .16 25 times or if you see the other answers it cant be 6.25 or 1.05 you think it could be 0.82 but its not
Answer:
0.16
Step-by-step explanation:
is -7.8 an irrational number
Answer:
No.
Step-by-step explanation:
An irrational number has never-ending decimals.
A rational number can be written as a fraction or has a terminating decimal.
-7.8 can be rewritten into a fraction. Its decimal also terminates. Therefore, it is not irrational but rational.
Answer:
-7.8 is rational
Step-by-step explanation:
irrational numbers are nubers that repaet random numbers that you wont know what comes next like pi or the squar root of 2. hope this halps and can you take in consideration of giving me a brainliest? Thank you
help me plzzzzzzzzzzz
can you terminate 1/10
Answer:
Hope this helps...if it dosent, sorry
Step-by-step explanation:
An average swimming pool contains 19200 gallons of water. The pool needs drained at the end of the summer. Water drains from the pool at the rate of 12 gallons per minute. Which equation can be used to find the volume, V, of the water in the pool m minutes after draining begins?
Answer:
V = 19200 - 12m
Step-by-step explanation:
The pool contains 19200 gallons of water.
Now we are told that water drains from the pool at the rate of 12 gallons per minutes.
Now, we want to find the volume, V, of the water in the pool, "m" minutes after draining begins.
Since water drains at 12 gallons per minutes, it means that after "m" minutes, the total amount that would have been drained is 12m gallons.
Thus, total volume V left after m minutes can be expressed as;
V = 19200 - 12m
what is an equation equivaent to x=-2
x-2=0 answer
Step-by-step explanation:
x=-2 move constant to the left by adding its opposite to both sides
x+2=2-2 the sum of two opposites equals 0
x-2=0
ANSWER X-2=0
HELP NOW PLZZZZZ HELPPPPPPPPPPPP
Answer:
y = 4/3x -11
Step-by-step explanation:
y = -3/4 x - 8
This is in slope intercept form
y = mx+b where the slope is -3/4
We want a slope that is perpendicular
Take the negative reciprocal
-1 ( -3/4) = 4/3
The slope of the line that is perpendicular is 4/3
Using the slope intercept form of a line is
y = mx+b
y = 4/3x+b
Substituting the point into this equation
-3 = 4/3(6) +b
-3 = 8+b
Subtract 8 from each side
-3-8 = b
-11 =b
y = 4/3x -11
Find the equation of the line.
Use exact numbers.
Y=?x+?
Answer:
y=.75x-2
Step-by-step explanation:
4,1
8,4
3/4 or .75x
to check answer:
(.75*8)=6
6-2
4
The equation of the line shown in the graph is y = 4x / 5 -2.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
Points located on the graph that lies on the line are (0, -2), and (2.5, 0)
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
Substitute the value in the above equation,
m = 0+ 2 / 2.5 -0 = 20/25
m = 4 / 5
The equation of the line is given as
y - y₁ = m (x - x₁)
Substitute the one point (-2, 0) and m in the above equation,
y + 2 = 4/5 (x - 0)
y = 4x / 5 -2
Thus, the equation of the line shown in the graph is y = 4x / 5 -2.
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Graph the exponential function.
f(x) = 4^x
Plot five points on the graph of the function. Then click on the graph-a-function button.
Exponential Function doesn't have a graph that intercepts x-axis only if it is f(x) = a^x (when a>0 and a ≠ 1)
If you want to plot five points to graph the function then. I'd rather do from negative number to positive number.
Substitute from -3≤x≤1 (We get 5 points)
f(-3) = 4^-3
f(-3) = 1/4^3
f(-3) = 1/64 (First point) (-3,1/64)
f(-2) = 4^-2
f(-2) = 1/4^2 = 1/16 (Second point) (-2,1/16)
f(-1)=4^-1 = 1/4 (Third point) (-1, 1/4)
f(0) = 4^0 = 1 (Fourth point) (0, 1)
f(1) = 4^1 = 4 (Fifth point) (1,4)
Lee has decided to build a shed on a square concrete slab. The shed has the same width, w,as the slab. Its length is 2 m shorter than the width of the slab .
a) What is an expression for the area of the shed?
Answer:
w * w+2 = area of the shed
Step-by-step explanation:
Well you just do the width times the width plus two. (please Brainliest)
Libby bought three shirts that cost $6.79, $11.08, and $8.95. How much did all three shirts cost
Answer:
$26.82
Step-by-step explanation:
It's just simple addition really. You start with adding 6.79 and 11.08 to get 17.87 and then add 8.95 to 17.87 to get 26.82. Hope this helps.
Question 3 of 10
What is the slope of the line that contains the points (4.-1) and (-1,4)?
O A. 5
O B. -5
O c. 1
O D. -1
Answer:
D
Step-by-step explanation:
y=kx+m
In this case I think the slope would be k.
k=y2+y1 / x2+x1
(4,-1) and (-1,4)
k=(4-1)/(-1-4)= 3/-5= -0.6 which is about -1
A recipe calls for 4 teaspoons of salt to 12 teaspoons of red pepper flakes. How many teaspoons of salt are needed for each tablespoon of red pepper flakes?
Answer:
1 teaspoon of salt to 3 teaspoons of red pepper flake
Step-by-step explanation: 12 divided by 4
3.46x + 6.38 = -4 the answer
Answer:
x = -3
Step-by-step explanation:
start with 3.46x + 6.38 = -4. Then take away 6.38 from both sides to get 3.46x=-10.38. Then you divide both sides by 3.46 to get x = -3.
Simplify the expression.
74÷(32)
A. −218
B. 218
C. 76
D. −76
Answer:
Simplify the expression.
Exact Form:
37
16
Decimal Form:
2.3125
Mixed Number Form:
2
5
16
HELP ASAP
Jason has $2.25 worth of dimes and quarters. He has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Jason has.
Answer:
Step-by-step explanation:
let the number of dimes=x
and number of quarters=y
x=2y
0.10 x+0.25 y=2.25
or 10x+25y=225
divide by 5
2x+5y=45
2 ×2y+5y=45
4y+5y=45
9y=45
y=45/9=5
x=2y=2×5=10
Hence dimes=10
quarters=5
A ferris wheel can accommodate 70 people in 20 minutes; how many people could ride the ferris wheel in 4 hours?
Proportional Question
Answer:
840
Step-by-step explanation:
if it can hold 70 in 20 minutes it can hold 210 in 1 hour and 4x210 equals 840
Which could be the first step of an indirect proof of the conditional below?
If x2 = 25, then 5’2= 25 and x = 5,
A. Assume x=5 is true.
B. Assume 52 = 25 is true,
C. Assume x2 + 25 is true.
D. Assume 52.25 and x + 5 are true,
Answer
Option D
Step-by-step explanation
For further help (727) 335-8234
The first step of indirect proof of the conditional below
If x2 = 25, then 5’2= 25 and x = 5 is assume 5² = 25.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Conditions:
x² = 25 then 5² = 25 and x = 5
If we have to prove the above conditions indirectly, we have to prove that x² = 25 using the conditions 5² = 25 and x = 5.
So,
We have to assume,
Step 1:
5² = 25
Step 2:
x = 5
Step 3:
x² = 25
Thus,
The first step of indirect proof of the conditional below
If x2 = 25, then 5’2= 25 and x = 5 is assume 5² = 25.
Option B is the correct answer.
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Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 26 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal. A button hyperlink to the SALT program that reads: Use SALT. (a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.) Incorrect: Your answer is incorrect. % (b) If Accrotime does not want to make refunds on more than 6% of the watches it makes, how long should the guarantee period be (to the nearest month)? months
Answer:
a
[tex]P(X < 24 )= 21.186\% [/tex]
b
[tex]x = 19.78 \ months[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 26 \ months[/tex]
The standard deviation is [tex]\sigma = 4 \ months[/tex]
Generally 2 year is equal to 24 months
Generally the percentage of total production will the company expect to replace is mathematically represented as
[tex]P(X < 24 )= P(\frac{X - \mu }{ \sigma} < \frac{24 - 26}{4} )[/tex]
Generally [tex]\frac{X - \mu}{\sigma } =Z (The \ standardized \ value \ of \ X )[/tex]
[tex]P(X < 24 )= P(Z < -0.8 )[/tex]
Generally from the z-table
[tex]P(Z < -0.8) = 0.21186[/tex]
So
[tex]P(X < 24 )= 0.21186[/tex]
Converting to percentage
[tex]P(X < 24 )= 0.21186 * 100[/tex]
=> [tex]P(X < 24 )= 21.186\% [/tex]
Generally the duration that should be the guarantee period if Accrotime does not want to make refunds on more than 6% is mathematically evaluated as
[tex]P(X < x) = P(\frac{X - \mu }{\sigma} < \frac{x - 26}{4} )= 0.06[/tex]
=> [tex]P(X < x) = P(Z < \frac{x - 26}{4} )= 0.06[/tex]
From the normal distribution table the z-score for 0.06 at the lower tail is
[tex]z = -1.555[/tex]
So
[tex]\frac{x - 26}{4} = -1.555[/tex]
=> [tex]x = 19.78 \ months[/tex]
Look at the picture to see question plz help quickly and step by step
Answer: 16.6
Step-by-step explanation:
Suppose Jane's mother replaces the six bags of trail mix. She also provides the group with 18 cans of juice. Each snack pack has the same number of apples, bags of trail mix, and cans of juice. What is the greatest number of snack packs Jane can make? Explain.
Answer:
six[6] snack packs.
Step-by-step explanation:
Without mixing words, let's dive straight into the solution to the question above. So. the mathematics principle behind this question is what is known or refer to as Greatest Common Factor. The term ''Greatest Common Factor'' with acronym GCF means the highest factor in the set of numbers given.
In this question, we are given that there are 18 cans of juice, 24 apples and 36 small bags of mix trails in order to make snack packs. Thus, we have three set of values or numbers that is 18, 24 and 36. Hence, the question/problem require us to determine the greatest number of snack packs Jane can make that is to find/determine the Greatest Common Factor.
STEP ONE: DETERMINE OR LIST OUT THE FACTORS FOR THE THREE SET OF VALUES GIVEN, THAT IS 18, 24 AND 36.
The factors of 18 = 1, 2, 3, 6, 9 and 18.
The factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.
The factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36.
STEP TWO: DETERMINE THE GREATEST FACTOR COMMON TO THE THREE LISTS.
For the three lists, the greatest factor common to them is 6.
Therefore, The greatest number of snack packs Jane can make is six[6] snack packs
Mikel has a chance to win a trip on a TV game show. All he has to do is win the “Shopping Game". In
this game, Mikel is shown six grocery store items without being shown the prices. He must buy
multiples of items until he has a total between $20 and $21 inclusive. If he doesn't reach $20 with his
first item, he continues buying items and adding to his total, until he either wins by getting an amount
between $20 and $21, or he loses by going over $21 or by buying all items and being less than $20.
First, Mikel buys six bottles of shampoo.
Solve the inequality. Round each answer to the hundredths place.
Answer:
$20 <= X < = $21
Step-by-step explanation:
You are told that he loses by going over $21 or by buying all items and being less than $20.
That means the total amount of the items bought must be equal to 20 dollars or 21 dollars or be within the two amount of money.
If Mikel buys six bottles of shampoo, x represents the total amount for the six bottles of shampoo. Then, the compound inequalities for this expression will be x less than or equal to 21 dollars and x greater than or equal to 20 dollars. That is,
$20 <= X < = $21
what is the answer to 6y * 88 = 88 * 6y
Answer:
0 or No solutions
Step-by-step explanation:
hope this helps!