A survey found that women's heights are normally distributed with mean 64.2 in. and standard deviation 4.2 in. The survey also found that men's heights are normally distributed with mean 70.1 in. and standard deviation 4.1 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 63 in. Complete parts (a) and (b) below
a) find the percentage of women meeting the height requirement
b) find the percentage of men meeting the height requirement
Answer:
a
P(57 < X < 63) = 34.4%
b
P(57 < X < 63) = 4.096%
Step-by-step explanation:
From the question we are told that
The mean of women's height is [tex]\mu_ 1 = 64.2[/tex]
The standard deviation is [tex]\sigma_1 = 4.2 \ in[/tex]
The mean of men' height is [tex]\mu_2 = 70.1 \ in[/tex]
The standard deviation of men's height is [tex]\sigma_2 = 4.1 \ in[/tex]
The minimum height requirement is a = 57 in
The maximum height requirement is b = 63 in
Generally the percentage of women meeting the height requirement is mathematically represented as
[tex]P(57 < X < 63) = P(\frac{ 57 - 64.2}{ 4.2} < \frac{X - \mu_1}{\sigma_1} < \frac{ 63 - 64.2}{ 4.2} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
So
[tex]P(57 < X < 63) = P( -1.7143 < Z <-0.2857)[/tex]
=> [tex]P(57 < X < 63) = P ( Z <-0.2857) - P(Z < -1.7143)[/tex]
Generally from the z table the probability of ( Z <-0.2857) and (Z < -1.7143) is
P( Z <-0.2857) = 0.38755
and
P(Z < -1.7143) = 0.043237
So
P(57 < X < 63) = 0.38755 - 0.043237
=> P(57 < X < 63) = 0.3443
Converting to percentage
P(57 < X < 63) = 0.3443 * 100 = 34.4%
Generally the percentage of men meeting the height requirement is mathematically represented as
[tex]P(57 < X < 63) = P(\frac{ 57 - 70.1}{ 4.1} < \frac{X - \mu_1}{\sigma_1} < \frac{ 63 - 70.1}{ 4.1} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
So
P(57 < X < 63) = P( -3.1951 < Z <-1.7317)
=> [tex]P(57 < X < 63) = P ( Z <-1.7317) - P(Z < -3.1951)[/tex]
Generally from the z table the probability of ( Z <-0.2857) and (Z < -1.7143) is
P( Z <-1.7317) = 0.041663
and
P(Z < -3.1951 ) = 0.00069891
So
P(57 < X < 63) = 0.041663 - 0.00069891
=> P(57 < X < 63) = 0.04096
Converting to percentage
P(57 < X < 63) = 0.04096 * 100 = 4.096%
The bus to a science exposition averaged 18 miles to a gallon of gas.How far away was the exposition if they used 8 gallons of gas for the road trip
Answer:
144 miles
Step-by-step explanation.
If the bus has a consumption speed of 18 miles to a gallon, multiply 8 times 18 for the length of the trip!
Answer:
144 miles
Step-by-step explanation:
Distance = (fuel economy measure)(number of gallons of gas used)
Here,
Distance = (18 mpg)(8 gallons) = 144 miles
What is the equation of the line represented by the table below
Answer:
Step-by-step explanation:
let x =0 then it's 2 so 0.2(x+2) is a formula that works,
y = 0.2(X+2)
:) these are not easy, btw
Chloe and Charlie are taking a trip to the pet store to buy some things for their new puppy. They know that they need a bag of food that costs $7, and they also want to buy some new toys for the puppy. They find a bargain barrel containing toys that cost $2 each. Write an expression for the amount of money they will spend if the number of toys they buy is t.
Answer:
7 + t = 13$
If this is wrong I'm so sorry but that's what I think it is.
The required total cost for Chole and Charlie is y = 7 + 2t.
Given that,
Chloe and Charlie are taking a trip to the pet store to buy some things for their new puppy. They know that they need a bag of food that costs $7, and they also want to buy some new toys for the puppy. They find a bargain barrel containing toys that cost $2 each.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the total cost be y,
According to the given condition,
Total cost = 7 + 2t
where 2t is the total cost of the toys purchased.
y = 7 + 2t
Thus, the required total cost for Chole and Charlie is y = 7 + 2t.
Learn more about arithmetic here:
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The top of a ladder is placed against the side of a house. The ladder is 15 feet long and the wall is 12 feet high. How far from the wall will the base of the ladder by positioned if the top ladder meets the top of the wall?
Answer:
9 ft
Step-by-step explanation:
The ladder is 15 feet long
The wall is 12 feet high
Therefore the distance between the base of the wall and the ladder can be calculated by applying phythagoreans theory
c^2= a^2 + b^2
15^2 = a^2 + 12^2
225= a^2 + 144
225-144= a^2
a^2= 81
a= 9 ft
Answer: A
Step-by-step explanation:
Solve for x: 4 − (x + 2) −7
x < −9
Answer:
35 im mot sure
Step-by-step explanation:
Answer: x > 11/8
Step-by-step explanation: Here is why
4 − (x+2) − 7x < −9 (simplify)
-8x + 2 - 2 < -9 -2 ( subtract)
-8x < -11
-8x/-8 < -11/-8 (divide)
= x > 11/8
solve for y 7y - 2x = 35
Answer:
y=(35+2x)/7
Step-by-step explanation:
7y-2x=35
7y=35+2x
y=(35+2x)/7
What are 3 ways to find a unit rate on a graph
Answer: One way is Rise/Run or Y/X
Step-by-step explanation:
You first find two points on the graph and Y2-y1 gives you the rise and X2-X1 gives you the run you then put the rise on top and the run below to get Y/X or rise over run
Hope this helped
Mike purchased a radio priced at $90. If 6% sales tax is added to the price of the radio, how much does Mike have to pay for the radio
Answer:
95.4 dollars
Step-by-step explanation:
multiply by 1.06 to get the answer
Someone bought 2.75 pounds of ham for $14.50.
Someone bought 2.5 pounds of turkey for $26.25.
Someone bought 0.375 pounds of roast beef for $5.50.
u have to find cheapest to best
Answer:
ham is cheapest. next is turkey. then roast beef
Simplify the expression.
(-1 + 2i) - (-2 - 2i)
Answer:
1 +4
Step-by-step explanation:
-1+2= 1
-2-2=-4
1--4=1+4
Directions: if l || m solve for x and y
Answer:
x = 24
y = 15
Step-by-step explanation:
Since, angles (3x - 29)° and (6x - 7)° is a pair of consecutive exterior angles,
Therefore, (3x - 29)° + (6x - 7)° = 180°
9x - 36 = 180
9x = 180 + 36
x = [tex]\frac{216}{9}[/tex]
x = 24
Therefore, (3x - 29)° = 3(24) - 29
= 43°
Since, angles (3x - 29) and (8y + 17) is a linear pair.
(3x - 29)° + (8y + 17)° = 180°
43° + (8y + 17)° = 180°
8y + 60 = 180
8y = 120
y = 15
Therefore, x = 24 and y = 15 will be the answer.
Can someone do this for me, because like....
Answer:
B) y=10x+150
Step-by-step explanation:
pls answer both the questions in the photo
Answer:
the second one is 46 each
Step-by-step explanation:
360-(88+88)
92/2=46
Will give brainiest to the person who answers correctly and trust i will know who is right
Answer:
the answer is 5
Step-by-step explanation:
it is 5 because 2+8-3=5
Which algebraic expression is a polynomial with a degree of 3?
4x3 –
2y3 + 5y2 – 5y
3y3 –
–xy
Answer:
B
Step-by-step explanation:
i got it right on the assignment
Find the value of x.
Answer:
x = 15
Step-by-step explanation:
I am not sure this is right though?
Answer:
x=5
Step-by-step explanation:
angle a & angle c are vertical angles so they r congruent (equal)
5x-5 = 2x+10
5x=2x+15
3x=15
x=5
Solve -5a – 2 >8 or 2a +4>14.
Can someone help me please, it would mean alot!
-5a – 2 >8 equals a<−2
2a +4>14 equals a>5
Question 3
2 pts
Explain how you used the model in Question 2 to find the product for 0.3 x 2.7.
What is an equation of the line that passes through the point (2, -5) and is parallel to the line
6x + y = 6?
The required equation of the line is 6x + y = 7 which is parallel to line 6x + y = 6 and passes through the point at (2, -5).
What is the slope of the line?The slope of the line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
First, we have to determine the slope of the line 6x + y = 6 by placing it into a slope-intercept form:
6x + y = 6 ⇒ y = -6x + 6
Therefore, the slope of the line is m = - 6
Since the required line passes through the point at (2, -5).
Let the line (y - y₁) = m(x -x₁ )
Here x₁ = 2, y₁ = -5
Substitute the values in the equation,
So, y - (-5) = -6(x - 2)
⇒ y + 5 = -6x + 12
⇒ 6x + y = 7
Hence, the required equation of the line is 6x + y = 7 which is parallel to line 6x + y = 6 and passes through the point at (2, -5).
Learn more about the Slope of the Line here:
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6
1
+
7
7
It’s a fraction btw
Answer:
=7
Step-by-step explanation:
First turn your fraction into a decimal.Then add.
6/1
= 6
= 600%
-------------------------- 6+1=7
7/7
= 1
= 100%
7x+2x=68+103 help please
Answer:
19
Step-by-step explanation:
7x + 2x = 9x
9x = 68 + 103
68 + 103 = 171
9x = 171
Divide it
19
Answer:
I'm sure the correct answer is x = 19
Step-by-step explanation:
7x + 2x = 9x
68 + 103 = 171
divide both sides by 9 and the it gives you x = 19
PLEASE HELP FAST. WILL MARK AS BRAINLIEST IF GIVEN GOOD ANSWER
A game is played where a fair coin is flipped. On the first go, heads you lose, tails you get to flip again. On the second go, heads you lose and tails you win. What is the probability of winning? *
1/2
3/4
1
1/4
Answer:
im pretty sure its a 50% chance so 1/2
Step-by-step explanation:
find the value of x.
Answer:
26
Step-by-step explanation:
(3x26)=78+20=98
(5x26)=130-32=98
Answer:
B. 26Step-by-step explanation:
B. 26 is the correct answer.....Thank you ☺️
What’s the slope intercept form of this line?
Answer:
it has a gradient of 1 (or x)
Step-by-step explanation:
The measure of the missing angle is
Answer:
43
Step-by-step explanation:
92 + 45+43=180
HOPE THIS HELPS
Answer:
It looks like forty-five degrees, maybe a little lower
Step-by-step explanation:
that's my estimate without a protractor.
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
Equation:
y=-16x^2+267x+107
Answer:
The rocket will reach the maximum height after 8.34 seconds.
Step-by-step explanation:
We need to take the derivative of the function and set it to 0.
[tex]y' = -32x + 267 = 0\\32x = 267\\x = 8.34[/tex]
The maximum height of the rocket at x = 8.34375 will be 1,220.89.
What are the maxima and minima of a function?For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.
The maximum and minimum value of the function is at f'(x) = 0.
A rocket is sent off from a pinnacle. The level of the rocket, y in feet, is connected with the time after send-off, x like a flash, by the given condition.
The equation is given below.
y = -16x² + 267x + 107
Differentiate the function and put it zero to get the value of time that is 'x' will be given as,
y' = 0
(d/dx)(-16x² + 267x + 107) = 0
-32x + 267 = 0
32x = 267
x = 8.34375
Then the maximum height of the rocket at x = 8.34375 will be given as,
y = -16(8.34375)² + 267(8.34375) + 107
y = -1,113.89 + 2,227.78 + 107
y = 1,220.89
The maximum height of the rocket at x = 8.34375 will be 1,220.89.
More about the maxima and minima links are given below.
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A box of hot cocoa mix has 15 packets. Each packet has a mass of 28.3 grams. What is the mass of two boxes of the hot cocoa mix?
plz help
Answer:849grams
Step-by-step explanation:
28.3 times 15 = 424.5grams(1 box)
424.5(1st box) + 424.5(2nd box) = 849 grams
need help with math worksheet
Answer:
The answer is C
Step-by-step explanation:
Need explanation??
Answer:
y=-3x+6
Slope:-3
y-intercept:6
7t-13-2t=9+5t
solve for t
Answer:t=t
Step-by-step explanation:
rn, fr
Answer:
No Solution
Step-by-step explanation:
7t - 13 - 2t = 9 + 5t
~Combine like terms
5t - 13 = 9 + 5t
~Add 13 to both sides
5t = 24 + 5t
~Subtract 5t to both sides
0 = 24
Best of Luck!