Answer:
97.5%
Step-by-step explanation:
Solution:-
- Denote a random variable,
X: Scores of all juniors in a school district centralized test.
- The random variable ( X ) follows normal distribution with the corresponding parameters:
X ~ Norm ( μ , σ^2 )
Where, μ = Mean score
σ = standard deviation of scores secured
- The given parameters for the normal distribution are:
X ~ Norm ( 74 , 8^2 )
- To draw a Normal curve we need to draw a bell shaped curve and annotate the following descriptions:
Mean ( μ ) : The vertical center-line that bifurcates the normal curve
1st standard deviation ( μ ± σ ) : First small division to the left and right about the mean ( μ ). [ 74 - 8 , 74 + 8 ] = [ 66 , 82 ]
2nd standard deviation ( μ ± 2σ ) : Second small division to the left and right about the mean ( μ ). [ 74 - 16 , 74 + 16 ] = [ 58 , 90 ]
3rd standard deviation ( μ ± 3σ ) : Third small division to the left and right about the mean ( μ ) - tailed. [ 74 - 24 , 74 + 24 ] = [ 50 , 98 ]
- Mark the associated percentage of scores that lies between 1st, 2nd and 3rd standard deviations from the mean ( μ ). Apply the Empirical rule of statistics. Which states:
p ( μ - σ , μ + σ ) = p ( 66 , 82 ) = 67 %
p ( μ - 2σ , μ + 2σ ) = p ( 58 , 90 ) = 95 %
p ( μ - 3σ , μ + 3σ ) = p ( 50 , 98 ) = 99.7 %
- See the attachment for the complete diagram.
- To determine the percentage of students who scored no more than 90 on the test.
- Employ the use of standardizing the required probability by using the following relation:
p ( X < x ) = p ( Z < [ (x - μ) / σ ] )
p ( X < 90 ) = p ( Z < [ (90 - 74) / 8 ] )
= p ( Z < [ (90 - 74) / 8 ] )
= p ( Z < 2 )
- We will employ the use of Empirical rule of second deviation ( μ ± 2σ ) to evaluate the required percentage:
p ( μ - 2σ < X < μ + 2σ ) = p ( 58 , 90 ) = 95 %
1 - p ( 58 < X < 90 ) = 1 - 0.95 = 0.05
p ( X > μ + 2σ ) = p ( X > 90 ) = [ 1 - p ( 58 < X < 90 ) ] / 2
= [ 1 - 0.95 ] / 2
= 0.05 / 2
= 0.025
Hence,
p ( X < 90 ) = p ( Z < 2 ) = 1 - p ( X > 90 )
= 1 - 0.025
Answer = 0.975 ( 97.5 )%
A 48-inch board is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece. The shorter piece is ______
inches long.
Answer:
12 inches long
Step-by-step explanation:
So you have the ratio x : 3x
4x = 48
x = 12
Plug in:
12 * 1 = 12
The length of the shorter piece is 12 inches if the 48-inch board is cut into two pieces. One piece is three times the length of the other.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A 48-inch board is cut into two pieces. One piece is three times the length of the other.
Let x and y be the length.
x = 3y
x + y = 48
3y + y = 48
y = 12 inches
x = 36 inches
Thus, the length of the shorter piece is 12 inches if the 48-inch board is cut into two pieces. One piece is three times the length of the other.
Learn more about the linear equation here:
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Veronica is choosing between two health clubs. After how many months will the total cost for each health club be the same?
Yoga Studio A. Membership $26 Monthly $23.25
Yoga Studio B. Membership $59 Monthly $17.75
An angle measuring 32 degrees has a complement that measures ( 2x-16 ) degrees. What is the value
Answer:
x=37
Step-by-step explanation:
Complementary angles add up to 90 degrees.
Let's first find the measure of the complement.
90-32=58
Now we can set the numerical value of it equal to the expression it gave us.
2x-16=58
We have to isolate x.
Lets add 16 to both sides
2x=74
Divide both sides by 2.
x=37
OMG, I'm so confused. Help me pls!
1.) -9u( -4)(-w)
2.) -b(-12)(11)
3.) -h(-jk)
4.) (-1)(-a)(-bc)
Answer:
-36uw
132b
hjk
-abc
Step-by-step explanation:
When you multiply a negative by another negative, the negative is cancelled out. When you multiply a negative by a positive, the negative is kept.
1.) -9u(-4)(-w)
36u(-w)
-36uw
2.) -b(-12)(11)
12b(11)
132b
3.) -h(-jk)
hjk
4.) -1(-a)(-bc)
1a(-bc)
-1abc
-abc
Hope this helps! :)
PLEASE HELP due in 5 minutes thank you!!
Answer:
x = 180 - 76 - 63
x = 41°
Step-by-step explanation:
Answer:
x =41
Step-by-step explanation:
The three angles form a straight line so they add to 180 degrees
76+ x+ 63 = 180
Combine like terms
139 + x = 180
Subtract 139 from each side
139-139 + x = 180-139
x =41
which ones are the correct ones , please help me thank you !
Answer:
A) is the last option 5/7.
Step-by-step explanation:
B) the third and last option. 7/-9 and -7/9
please help me out here! Thank you! I’ll give brainliest!
Answer:for the first one it is 5/9
and for the second one it is 4/9
Step-by-step explanation:
Answer:
For first 0.56 and for second 0.44
Plz mark me brainliest
Step-by-step explanation:
if four out of ten people vote than a town with two hundred thousand people how many will vote
Answer:
80,000 people will vote. I'm pretty sure
Step-by-step explanation:
You first divided 200,000 by 10 then multiply it by 4 and you get 80,000. You're welcome, if its right.
Answer:
80.000 peple will vote
Step-by-step explanation:
Four out of ten is equivalent to the fraction 4/10 in which when simplified it can be written as 2/5 (I simplified the fraction to make it easier), then you just multiply the fraction by the amount of people =200,000. When multiplied you will get the result 80.000. Hope this helps :)
Find the distance between (−7, 1) and (0, −6). Round your answer to the nearest tenth.
Answer:
9.90
Step-by-step explanation:
a2+b2=c2
(7)2+(7)2=c2
49+49=c2
98=c2
√98=√c2
9.90=c
what is the next term of the geometric sequence? 5,10,20
Answer:
40
Step-by-step explanation:
To find the common ratio, take the second term and divide by the first term
10/5 = 2
We multiply the last term given by the common ratio to get the next term
20* 2= 40
What is a correct name for the angle shown? Line segments R S and S T combine to form an angle. Angle R Angle S Angle R T S Angle S R T
Answer:
(B)Angle S
Step-by-step explanation:
Given that line segments RS and ST combine to form an angle.
The angle formed by the two line segments occur at the common end point of the two segments which in this case is S.
Therefore the angle is formed at S.
This can be written in the following ways:
[tex]\angle RST, \angle TSR$ or simply \angle S.[/tex]
The correct option is B.
Answer:
What is a correct name for the angle shown? Option B
(A) Angle R
( B) Angle S <====== Option B Hope this helps
(C) Angle R T S
(D) Angle S R T
Step-by-step explanation:
Of all 840 sixth grade students in a math school, 700 participated in the math Olympiad. Of all 910 fifth grade students, 745 participated in it.From which grade did more students participate in the Olympiad?
Answer:Sixth grade
Step-by-step explanation:
Given
There are [tex]840[/tex] sixth grade students out of which [tex]700[/tex] Participated in math olympiad
also no of fifth grade students[tex]=910[/tex]
Fifth graders who participated in math olympiad [tex]=745[/tex]
Since [tex]745>740[/tex]
There are more fifth graders in Olympiad [Numerically]
Percentage wise
Percenteage of sixth graders who participated in Math olympiad[tex]=\dfrac{700}{840}\times 100=83.33\ \%[/tex]
Percenteage of Fifth graders who participated in Math olympiad[tex]=\dfrac{745}{910}\times 100=81.86\ \%[/tex]
So, a greater Population of Sixth graders participated in math olympiad compared to Fifth graders as [tex]83.33\ \%>81.86\ \%[/tex]
Kyle believes that the equation of the line of best fit for the scatterplot below is Which statement best summarizes why Kyle is incorrect? Kyle's equation has a negative y-intercept, but the scatterplot shows a point on the y-axis with a positive y-value. Kyle's equation has a negative y-intercept, but the scatterplot shows a positive correlation. Kyle's equation has a negative slope, but the scatterplot shows a point on the y-axis with a positive y-value. Kyle's equation has a negative slope, but the scatterplot shows a positive correlation.
Answer:
D
Step-by-step explanation:
kyles equation has a negative slope, but the scatter plot shows a positive correlation
The statement best summarizes why Kyle is incorrect:
Kyle's equation has a negative slope, but the scatterplot shows a positive correlation.
What is Scatterplot?A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.
How to solve?
As we can conclude that;
Kyle's equation has a negative slope, but the scatter plot shows a positive correlation
Learn more about Scatter Plot:
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Which expression is the best estimate of Four-fifths times 22.01?
One-fifth times 20
Four-fifths times 20
4 × 20
5 × 20
Answer:
the second one four fifth times 20
Step-by-step explanation:
4/5×22.01=17.68 which is approximately equal with 4/5×20=16.
Answer:
Its four fifths times 20 i took the test.
Step-by-step explanation:
-6 + m = -23
I need work and answer
Will give the bainliest
Answer:
The answer for [tex]m[/tex] :
[tex]m = -17[/tex]
Step-by-step explanation:
Solve for [tex]m[/tex] :
[tex]-6 + m = -23[/tex]
Add both sides by 6:
[tex]-6 + 6 + m = -23 + 6[/tex]
[tex]m = -17[/tex]
So, the answer is [tex]x = -17[/tex]
Which expression is the best estimate of Four-fifths times 22.01?
One-fifth times 20
Four-fifths times 20
4 × 20
5 × 20
Please awnserill give brainliest
Answer:
four fifth times 20
Step-by-step explanation:
17.60=16
the value of a car is 28,000 bit it is depreciating 12% per year how much will the car be worth in 8 years
Answer:
The value of the car in 8 years is : v(t)=69,326 rounded to the nearest dollar, yet if not rounded to the nearest dollar then it is 69,326.968936
Step-by-step explanation:
v(t)=28,000(1.12)^8
v(8)=69,326
while hiking you see a 100ft observation tower on top of a 1100ft hill. The angle of elevation to the top of the tower is 6. How far away is the tower?.
Answer:692.82 ft
Step-by-step explanation:
Given
Height of tower is [tex]h=100\ ft[/tex]
Tower is mounted at the top of [tex]H=1100\ ft[/tex] hill
angle of elevation [tex]\theta =60^{\circ}[/tex]
Using figure we can write
[tex]\tan \theta =\dfrac{h+H}{\text{Distance}}[/tex]
[tex]\tan 60^{\circ}=\dfrac{100+1100}{\text{Distance}}[/tex]
[tex]Distance =\frac{1200}{\tan 60^{\circ}}[/tex]
[tex]Distance=\frac{1200}{\sqrt{3}}[/tex]
[tex]Distance=692.82\ ft[/tex]
PLS HURRY I NEED THIS ANSWERED RIGHT NOW!!! Brittney has twice as much money as Sun. Together, they have $60. Let x represent the amount of money Sun has. What expression represents the amount of money Brittney has? What expression represents the amount of money that Brittney and Sun have together? What is the equation described in this problem?
Sun's money = x
Brittney's money = 2x
x + 2x = $60
3x = $60
3x/3 = 60/3
x = 20
So amount that Brittney has is 2x.
The amount they have together is 3x
The equation that describes the problem is 3x = $60
Answer:
Brittney has twice as much money as Sun. Together, they have $60. Let x represent the amount of money Sun has.
What expression represents the amount of money Brittney has?
✔ 2x
What expression represents the amount of money that Brittney and Sun have together?
✔ 2x + x
What is the equation described in this problem?
✔ 2x + x = 60
Step-by-step explanation:
Which inequality represents the graph below
Answer:
nhyh
Step-by-step explanation:
h
mhhhygvvvx VC ghv h h h b
Solve the following equation 5x+3/4 - 2x-4/3=5
Answer: X= 67/36
Step-by-step explanation:
Drag each expression to show whether it can be used to find the surface area, volume, or neiWhich product is equal to 3x2 – 9x + 6?
(3x – 3)(x – 3)
(3x – 3)(x – 2)
(3x + 3)(-x + 3)
(3x – 2)(x + 3)ther.
Answer:
(3x - 3)(x - 2)
Step-by-step explanation:
3x² - 9x + 6
3x² - 6x - 3x + 6
3x(x - 2) - 3(x - 2)
(3x - 3)(x - 2)
James takes 75 minutes to complete a writing assignment, and 15 minutes to complete a science assignment. James is required to spend more than 300 minutes on his assignments. According to his schedule, he can complete at most 20 assignments this week.
Which system of inequalities can be used to determine the number of writing assignments (w) and the number of science assignments (s) James can complete this week?
A. 75w+15s>300
w+s≤20
B. 15w+75s<300
w+x≤20
C. 75w+15s≥300
w+s≥20
D.
15w+75s>300
w+s≤20
Answer:
75w + 15s > 300
w+s ≤20
Step-by-step explanation:
writing assignments (w)
science assignments (s)
the time is more than 300 minutes
75w + 15s > 300
at most 20 assignments
w+s ≤20
Which of the points shown below are on the line given by the equation y = 3x? Check all that apply.
Answer:
Step-by-step explanation:
Only A and D. Draw a line through A and D and you will see that this is a proportional relationship; the line goes through the origin.
the value of a car is 28,000 bit it is depreciating 12% per year how much will the car be worth in 8 years
Answer:
Hello,
10,070
Step-by-step explanation:
100% - 12% = 88% = 0.88
28,000 x 0.88^8 = 10,069.76...
Albert uses 4One-half ounces of paint on a sculpture. His cousin Tony uses 0.8 as much paint as Albert on a portrait.
Together, how much paint do Tony and Albert use?
3.6 ounces
5.3 ounces
8.1 ounces
8.2 ounces
PLEASE AWNSER ASAP WITH GIVE BRAINLEST IF U DO
Answer:
3.6 ounces.
Step-by-step explanation:
4 one half ounces = 2 ounces of paint.
So Albert uses 2 ounce and Tony uses 2 * 0.8 = 1.6 ounces.
So together they use 2+ 1.6 = 3.6 ounces.
Answer:
8.1 ounces
Step-by-step explanation:
what is x³+y³+z³x23-34/2=8?
Answer:
Step-by-step explanation:
Solve for u.
10 + 6u = 7u
u =
Answer:
u = 10
Step-by-step explanation:
10 + 6u = 7u
10 = u
Just subtract 6u on both sides.
if a cylinder has a volume of approximately 125.6 cubic cm and has a height of 10cm what is the length of the radius
Answer:
radius = 4 cm
Step-by-step explanation:
To find the length of the radius, we will follow the step below;
First, write down the formula for finding the volume of a cylinder
v=πr²h
where v is the volume of a cylinder
r is the radius and
h is the height of the cylinder
from the question given,
v=125.6 and h = 10 cm
we can now proceed to insert the values into the formula and solve for r
note that π is a constant which is equal to 3.14
v=πr²h
125.6 =3.14×r×10
125.6 =31.4 r
Divide both-side of the equation by 31.4
125.6/31.4 =31.4 r/31.4
4 = r
r =4 cm
The length of the radius = 4 cm
Based on the above table, what is the fastest growing listed occupation for those without a college degree?
a. Gaming and sports book writers and runners
b. Dental assistants
C. Marriage and family therapists
Manicurists and pedicurists
d.
Answer:
Step-by-step explanation:
Dental assistants
Answer:
Dental assistants
Step-by-step explanation: