Answer:
(a) the probability that an individual distance is greater than 214.80 cm is 0.1401.
(b) The probability that the mean for 15 randomly selected distances is greater than 204.00 cm is 0.2482.
(c) The normal distribution can be used because the original population has a normal distribution.
Step-by-step explanation:
We are given that the overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.6 cm.
(a) Let X = the overhead reach distances of adult females.
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean reach distance = 205.5 cm
[tex]\sigma[/tex] = standard deviation = 8.6 cm
So, X ~ Normal([tex]\mu=205.5,\sigma^{2} =8.6^{2}[/tex])
Now, the probability that an individual distance is greater than 214.80 cm is given by = P(X > 214.80 cm)
P(X > 214.80 cm) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{214.80-205.5}{8.6}[/tex] ) = P(Z > 1.08) = 1 - P(Z [tex]\leq[/tex] 1.08)
= 1 - 0.8599 = 0.1401
The above probability is calculated by looking at the value of x = 1.08 in the z table which has an area of 0.8599.
(b) Let [tex]\bar X[/tex] = the sample mean selected distances.
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean reach distance = 205.5 cm
[tex]\sigma[/tex] = standard deviation = 8.6 cm
n = sample size = 15
Now, the probability that the mean for 15 randomly selected distances is greater than 204.00 cm is given by = P([tex]\bar X[/tex] > 204.00 cm)
P([tex]\bar X[/tex] > 204 cm) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{204-205.5}{\frac{8.6}{\sqrt{15} } }[/tex] ) = P(Z > -0.68) = 1 - P(Z [tex]\leq[/tex] 0.68)
= 1 - 0.7518 = 0.2482
The above probability is calculated by looking at the value of x = 0.68 in the z table which has an area of 0.7518.
(c) The normal distribution can be used in part (b), even though the sample size does not exceed 30 because the original population has a normal distribution and the sample of 15 randomly selected distances has been taken from the population itself.
Your anula salary of $42,500 is about to he increased by 2%.Explain the steps you would take to determine your new salary.What will your new salary be?
Answer:
$43,350
Step-by-step explanation:
To find the increase in the salary we need to find the percentage.
2 percent of $42,500 = $850.
$42,500 + $850 = $43,350.
New salary = $43,350.
The following table shows scores obtained in an examination by B.Ed JHS Specialism students. Use the information to answer the questions that follow: Score 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 Frequency 10 4 10 20 30 15 3 2 1 5.a. Construct a cumulative frequency curve for the data. b. Find the; i. inter-quartile range. ii. 70th percentile class scores. iii. probability that a student scored at most 50 on the examination
Answer:
(a) The cumulative frequency curve for the data is attached below.
(b) (i) The inter-quartile range is 10.08.
(b) (ii) The 70th percentile class scores is 0.
(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.
Step-by-step explanation:
(a)
To make a cumulative frequency curve for the data first convert the class interval into continuous.
The cumulative frequencies are computed by summing the previous frequencies.
The cumulative frequency curve for the data is attached below.
(b)
(i)
The inter-quartile range is the difference between the third and the first quartile.
Compute the values of Q₁ and Q₃ as follows:
Q₁ is at the position:
[tex]\frac{\sum f}{4}=\frac{100}{4}=25[/tex]
The class interval is: 34.5 - 39.5.
The formula of first quartile is:
[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
Here,
l = lower limit of the class consisting value 25 = 34.5
(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 24
f = frequency of the class interval = 20
h = width = 39.5 - 34.5 = 5
Then the value of first quartile is:
[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
[tex]=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75[/tex]
The value of first quartile is 34.75.
Q₃ is at the position:
[tex]\frac{3\sum f}{4}=\frac{3\times100}{4}=75[/tex]
The class interval is: 44.5 - 49.5.
The formula of third quartile is:
[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
Here,
l = lower limit of the class consisting value 75 = 44.5
(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 74
f = frequency of the class interval = 15
h = width = 49.5 - 44.5 = 5
Then the value of third quartile is:
[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]
[tex]=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83[/tex]
The value of third quartile is 44.83.
Then the inter-quartile range is:
[tex]IQR = Q_{3}-Q_{1}[/tex]
[tex]=44.83-34.75\\=10.08[/tex]
Thus, the inter-quartile range is 10.08.
(ii)
The maximum upper limit of the class intervals is 69.5.
That is the maximum percentile class score is 69.5th percentile.
So, the 70th percentile class scores is 0.
(iii)
Compute the probability that a student scored at most 50 on the examination as follows:
[tex]P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}[/tex]
[tex]=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89[/tex]
Thus, the probability that a student scored at most 50 on the examination is 0.89.
(5)
(5) = 3, then (10) =???
,
3
Step-by-step explanation:
If (5) = 3
Then (10) = 6
Because 5 x 2 = 10 so 3 x 2 = 6
Find the slope of the line graphed below?
Answer:
7/5
Step-by-step explanation:
rise over run
start at the bottom point and count up along y axis and then count over along x axis
The table shows the relationship between the number of calories Raquel burns while hiking and the number of minutes she hikes.
How many calories will Raquel burn in 1 minute while hiking?
Answer:
5 calories.
Step-by-step explanation:
We begin by calculating the rate at which Raquel burns calories while hiking.
This can be obtained as follow:
Calories burned = 225 calories
Time = 45 mins
Rate =?
In this case, the Rate is simply defined as calories per unit time. Mathematically, it is expressed as:
Rate = Calorie/time
With the above formula, we can obtain the rate at which Raquel burns calories as follow:
Calories burned = 225 calories
Time = 45 mins
Rate =?
Rate = Calorie/time
Rate = 225/45
Rate = 5 cal/min
Therefore, Raquel burns Calories at a rate of 5 cal/min.
Now, we shall determine the calories burned by Raquel in 1 minutes. This is illustrated below:
Rate = 5 cal/min
Time= 1 min
Calorie =.?
Rate = Calorie /time
5 = Calorie /1
Cross multiply
Calorie = 5 x 1
Calorie = 5
Therefore, Raquel burns 5 calories in 1 minute while hiking.
What is another name for AC
Answer:
air conditioning or air cooling or climate control
hope this helps :)
Lines AB and CD are parallel. If the measure of angle W equals 124 degrees, what is the measure of angle X?
Answer:
56 degrees
Step-by-step explanation:
They are supplementary, so they add to 180. 180 - 124 = 56.
Answer:
56 degrees
Step-by-step explanation:
They are supplementary, so they add to 180. 180 - 124 = 56.
Please help. I’ll mark you as brainliest if correct
Answer: He doesn't have any money left that period point blank
Step-by-step explanation
7-6=1
1-3= you cant do that
so he doesn't get soda at all.
7 -6 =1. . . . . . . - . . . . . . = . 1-3= nope. - . . . = nahhh
What two nonnegative real numbers with a sum of 23 have the largest possible product?
The two number with the largest product would be the two numbers closest together.
Divide 23 in half:
23/2 = 11.5
Use the whole numbers on each side of 11.5, so you have 11 + 12 = 23
Multiply: 11x 12 = 132
The stem-and-leaf plot shows the number of words in the classified ads in a newspaper one day.
How many ads had at least 20, but fewer than 45, words?
1 0 3 3 5 7 9
2 0 0 1 4 5
3 3 8 8
4 7
5 2
key:1|0 = 10
A. 6
B. 3
C. 10
D. 8
Answer:
D. 8
Step-by-step explanation:
We can see the numbers from 20 (inclusive) to 45 on the plot:
20, 20, 21, 24, 25, 33, 38, 38In total 8 adsCorrect answer choice is: D. 8
Picture 1
Soap, Face, cream, Fragrance mist
Common
Consider a graph of the equation y = −3x + 4. What is the y-intercept? Answers: −3, 3, 4, −4
Answer:
When finding the y-intercept it indicates that the x-coordinate will be zero.
So,when letting x=0 you will get
y=-3(0)+4
Hence,
y=4
Step-by-step explanation:
PLZZZZZ HELP
A median of a triangle is a line or segment that passes through a vertex and
bisects the side ______ the vertex.
A. congruent to
B. opposite
C. adjacent to
D. below
factorise : 64a cube minus 27b cube minus 144a square b plus 108ab square .
Plz Answer this question
Answer:
[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]
Step-by-step explanation:
The question is not properly formatted, here is a good format for proper understanding and readability
[tex]64a^3-27b^3-144a^2+108ab^2[/tex]
let us first collect/ group like terms
[tex]64a^3-144a^2+108ab^2-27b^3[/tex]
we can now bring out the common factors we have
[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]
The simplified expression is
[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]
please help!!!!
what is the least common denominator of 1/6, 10/11, 5/12?
===================================================
Work Shown:
LCM = least common denominator
List out the prime factorization of each denominator
6 = 2*311 = 1*1112 = 2*2*3So we have the list of primes 2,3, and 11 that help form the denominators when we multiply some of them together.
The prime 2 shows up at most twice, so 2*2 = 4 is a factor of the LCM
The prime 3 shows up at most one time, meaning 3 is also a factor
The prime 11 shows up at most one time, so 11 is another factor
Multiply these factors to get 4*3*11 = 12*11 = 132
The LCM is 132
---------------------
Another Approach:
Focus on 1/6 and 10/11 for now. The LCM is 66 because 6*11 = 66. We simply multiply the denominators together. Then we divide over the GCF 1 to get 66/1 = 66.
The LCM of 1/6 and 10/11 is 66
The fractions 1/6 and 10/11 are equivalent to 11/66 and 60/66 respectively
The original list of fractions updates to 11/66, 60/66, 5/12
We've gone from 3 different denominators to now 2 different denominators.
Repeat the steps of multiplying the denominators and dividing by the GCF
66*12 = 792
792/(gcf of 66 and 12) = 792/6 = 132
So the LCM of all the fractions is 132.
A card is randomly selected from a standard
deck of playing cards. Find the probability
that it is a face card, given that a black card
is drawn.
Answer:
3 / 13
Step-by-step explanation:
Hello!
There are 52 cards in a deck with half being red and half being black. The question ask for when a black card is drawn so we divide the total by 2
52/ 2 = 26
There are 6 black face cards in a deck so to get the probability one will be drawn we put how many there are over the total amount
6/26 we can simplify this
3 / 13
The answer is 3 / 13
Hope this helps!
Answer:
3/13
Step-by-step explanation:
In a standard 52-card deck, there are 26 black cards and 26 red cards. Of the 26 black cards, 13 are spades and 13 are clubs. Each suit has 3 face cards, Jack, Queen, and King. Therefore, there are 6 black face cards out of a total of 26 black cards.
p(face given black) = 6/26 = 3/13
Great Rapids White Water Rafting Company rents rafts for $125 per hour. Explain why the point (0,0) and (1,125) are on the graph of the relationship and what these points mean in the context of the problem. How much would you pay for 12 hours? How long have you rented the rafts if you spent $750?
Answer:
$1500
6 hours
Step-by-step explanation:
There is no one off fee, therefore we got (0,0) a starting point.
(1,125) is representing the first hour of rent, so 1 hour rent costs $125.
There is a direct relationship between the time and rental fee.
As a function is will be:
f(x) = 125x, where f(x) is the total amount and x is the time in hoursFor x= 12, we get:
f(12) = 125*12= $1500So, if f(x) = 750, then:
750 = 125x x= 750/125 x= 6 hoursA norman window has the shape of a square with a semicircle mounted on it. Find the width of the window if the total area of the square and the semicircle is to be 190 ft squared?
Answer:
11.68ft or 11.68 feet
Step-by-step explanation:
From the above question, we are told that:
Area of the square and the Area semicircle is to be 190 ft squared.
We are also told in the question that:
The window has the shape of a square with a semicircle mounted on it.
Hence, the Diameter of the semicircle = Width of the Square
Let the Width of the square = x
Area of a square = Width²
= x²
Let the Diameter of the semi circle = x
Radius of the semi circle = Diameter of the semi circle/2 = x/2
Area of a semicircle = πr²/2
Area of a the semi Circle = π ×(x/2)² /2
= (πx²/4)/2
= πx²/8
Therefore,
Area of a square + Area of a semicircle = 190ft²
= x² + πx²/8 = 190
Cross Multiply
x² + πx² = 190
= x² ( 1 + π/8) = 190
x² = (190)/(1 + π/8)
x² = 136.42573798
x = √136.42573798
x = 11.680142892ft
Approximately x ≈ 11.68ft
Therefore, the width of the window = 11.68ft
DUE TONIGHT !! determine whether the statement is true or false. justify your answer. A line with a slope of -5/7 is steeper than a line with a slope of -6/7
False.
Slope is the "rise over run" (y/x) in a linear equation. Because the denominators are the same in both fractions, it means you can just focus on the numerator with the larger number as that one will be the steeper line.
What’s the answer please
Answer:
C. [tex] \sqrt {149} [/tex]
Step-by-step explanation:
Coordinates of the endpoints of the segment are (4, 4) & (-6, - 3)
By distance formula
Length of segment
[tex] = \sqrt {(4+3)^2 +(4+6)^2} [/tex]
[tex] = \sqrt {(7)^2 +(10)^2} [/tex]
[tex] = \sqrt {49 +100} [/tex]
[tex] = \sqrt {149} [/tex]
What is the equation of the line: * parallel to the line y = -¼x + 5 and * passing through the point (2, -1) y = -¼x + 4 y = ¼x + 2 y = ¼x - 1 y = -¼x - 1/2
Answer:
y=-1/4x-1/2
Step-by-step explanation:
When two lines are parallel, they have the same slope.
So for this line, we already know that the slope (m) has to equal -1/4x.
Slope intercept form is y=mx+b, where m is the slope and b is the y intercept.
in order to find the equation, we must plug in x and y to solve for b, the y intercept (the value of y when x=0).
Now, let's plug in 2 for x and -1 for y and solve for b:
-1=-1/4(2)+b=-1=-1/2+b=-1+1/2=b
b=-1/2
Hence, the answer is y=-1/4x-1/2
Answer:
The answer is -1/4x - 1/2
Step-by-step explanation:
Just took the Unit Session
The vertical position y (in feet) of a rock t seconds after it was dropped from a cliff is given by the formula y equals short dash 16 t squared plus 4 t plus 380. The base of the cliff corresponds to y equals 0. After how many seconds will the rock hit the ground at the base of the cliff?
Answer: t = 4.87s
Step-by-step explanation: The vertical position y is given by
[tex]y = -16t^{2}+380[/tex]
If y at the base of the cliff equals 0, then equation is
[tex]-16t^{2}+380=0[/tex]
[tex]-16t^{2}=-380[/tex]
[tex]t^{2}=\frac{-380}{-16}[/tex]
[tex]t=\sqrt{\frac{380}{16}}[/tex]
[tex]t=\sqrt{23.75}[/tex]
t = 4.87
Since it is time we want, the negative value of the square root can be ignored. So, at the base of the cliff, the rock will hit the ground after 4.87 seconds.
Round to the nearest thousand.
64,473
64,473 rounded to the nearest thousand is ?
Answer:
64000
Step-by-step explanation:
Answer:
64000
Step-by-step explanation:
△ABC = △DBC, AB= 10, AC=7 DC= ?
Answer:DC=7
Step-by-step explanation:
As it is written △ABC = △DBC. So the corresonding legs (the legs which are equal ) are as follows:
AC=DC AB=DB BC= BC
So DC=7 the same like AC
a cold front came in today and the temperature dropped 30 degrees. Write an algebraic expression to explain the new temperature.
Answer:
The algebraic equation describing the above
X+y= x-30
Step-by-step explanation:
The initial temperature of the environment= x degrees
Temperature of the front= y degrees
the environment dropped 30 degrees, means loosed 30 degrees.
The final temperature f the environment= x-30
The algebraic equation describing the above
X+y= x-30
Solve for x
3/4x = -9
-12 is the answer
Step-by-step explanation:
[tex] \frac{3x}{4} = - 9[/tex]
Firstly we have to take 4 to the R.H.S and multiply -9 with 4
[tex]3x = - 9 \times 4 [/tex]
[tex]3x = - 36[/tex]
Now, take 3 to R.H.S and divide 3 by -36
[tex]x = \frac{ - 36}{ \: \: 3} [/tex]
so after solving this we get our answer,
[tex]x = - 12[/tex]
Hope it helps u
What is the slope of the line with points (1, 2) and (4, 2)?
Answer:
0
Step-by-step explanation:
To find the slope of two points, here is the formula (y2-y1)/(x2-x1)
So we have (1,2) and (4,2),
We let y2 = 2 and y1 = 2 and we let x2 = 4 and x1 = 1
So, (2-2)/(4-1) = 0/3
Our slope is 0.
a=3i+4j, b=5i+4j. find a+b
Answer:
8i+8j
Step-by-step explanation:
3i+4j+5i+4j
i(3+5) + j(4+4)
Therefore 8i +8j
HAPPY TO HELP YOU
Answer:
Step-by-step explanation:
we have :
a=3i+4j
b=5i+4i
so that : a+b=3i+4j+5i+4j
=(3i+5i)+(4j+4j)
so a+b=8i+8j=8(i+j)
A box contains 9 red and 2 blue marbles. If you select one marble at random from the box, determine the odds against selecting a blue marble.
Answer:
2/11 or approx. 18%
Step-by-step explanation:
There are 2 blue marbles out of 11 total marbles, so the probability will be 2/11.
2/11 = 0.18, or 18%
So, the odds are 2/11 or approx. 18%
Answer:
9:2
Step-by-step explanation:
9 red and 2 blue
ways that an outcome cannot occur : how many ways it can occur
9 : 2 are the odds against a blue marble
What is the value of a in the function's equation?
A. -2
B. -3
C. 3
D. 2
The value of a in the function's equation is 3
What is equation function?A function is an equation that has only one answer for y for every x. A function assigns exactly one output to each input of a specified type
What is parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions,
equation of parabola is :
[tex]y= a (x-h)^{2} + k[/tex]
where ,
h= horizontal coordinate of graph
k = vertical coordinate of graph
a = the value of the coefficient
According to the question
horizontal coordinate of graph = -2
vertical coordinate of graph = 2
[tex]y= a (x-h)^{2} + k[/tex]
[tex]y= a (x+2)^{2} + 2[/tex]
now we will take one point from x and y value from the graph to take out value of coefficient a
from graph (x,y) = (-1,5)
[tex]5= a (-1+2)^{2} + 2[/tex]
[tex]\\3= a (-1+2)^{2}[/tex]
[tex]\\3= a (1)^{2}[/tex]
[tex]a = 3[/tex]
Hence, the value of a in the function's equation is 3
To know more about equation function and parabola here :
https://brainly.com/question/26227783
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