Answer:
a. 72
b. 816
c. 570
d. 30
Step-by-step explanation:
Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.
Please refer the figure for a better understanding.
a. In a normal distribution, Mean = Median = Mode
Therefore, Median = Mean = 72
b. We have to know that 68% of the values are within the first standard deviation of the mean.
i.e., 68% values are between Mean Standard Deviation (SD).
Scores between 63 and 81 :
Note that 72 - 9 = 63 and
72 + 9 = 81
This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.
Now, Scores between 63 and 81 =
= 68 X 12 = 816.
That means 816 students have scored between 63 and 81.
c. We have to know that 95% of the values lie between second Standard Deviation of the mean.
i.e., 95% values are between Mean 2(SD).
Note that 90 = 72 + 2(9) = 72 + 18
Also, 54 = 63 - 18.
Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to of the values.
Therefore, Scores between 72 and 90 =
= 570.
That is a total of 570 students scored between 72 and 90.
d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.
In this case, 5 % of the values lie between below 54 and above 90.
Since, we are asked to find scores below 54. It should be 2.5% of the values.
So, Scores below 54 =
= 2.5 X 12 = 30.
That is, 30 students have scored below 54.
Step-by-step explanation:
It is found that score of 62 is not within one standard deviation of the mean.
What is z - score?The Z-score measures how many standard deviations the measure is from the mean. 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]then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
In a set with mean and standard deviation, the z- score of a measure X is given by:
[tex]Z = \dfrac{X - \mu}{\sigma},[/tex]
Z-score, we look at the z-score table and find the p-value associated with this z-score.
Given that Mean score of 54 and a standard deviation of 6.
This means to see if a score of 62 is within one standard deviation of the mean.
Is Z between -1 and 1 when X = 62.
[tex]Z = \dfrac{X - \mu}{\sigma},\\Z = \dfrac{62 - 54}{6},[/tex]
Z = 1.33
Therefore, It is found that score of 62 is not within one standard deviation of the mean.
Learn more about z-score here:
https://brainly.com/question/21262765
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Which fraction is not equivalent to 9/12
PLEASE SOMEBODY HELP ASAP
Answer:
15/20 I am studying with international schooling so you can ask me anything anytime
Answer:
16/24 is NOT equivalent to 9/12
Step-by-step explanation:
9/12 ÷ 3 = 3/4
3/4 × 2 = 6/8
3/4 × 5 = 15/20
3/4 × 8 = 24/32
find the slope of the graphed line
Answer:
rise over run
Step-by-step explanation:
In this case it is undefined
please tell me the answer
Answer:
so so so so srry i cant see that pic
Step-by-step explanation:
x/3-1/2=5/6 solve for the variable
Answer:
4/3 - 1/2= 5/6 hope this helped
multiply the complex number by this complex conjugate.
16. 8+i
17. 3 - 2i
18. -7- 5i
1. During October, William Korth worked 160 regular time hours at $9.28 an hour and 18 overtime hours at time-
and-a-half. What is William’s gross pay for October?
2. Last year, Ida Zolen worked 2,000 hours at regular time pay of $8.20 an hour. She also worked 75 hours over time
at double his regular rate. What was Ida’s gross pay last year?
3. Alan Kirbaum works on an 8-hour day basis and is paid $8 an hour for regular time work and time-and-a half for
overtime work. Last week he worked these hours: Monday:9 ; Tuesday:6 ; Wednesday:11 ; Thursday:8 ; Friday:9.
A) How many regular hours did he work?
B) How many overtime?
C) What is his overtime rate?
D) What is his overtime pay?
E) Find Alan’s gross pay.
4. Stephen Woll’s regular pay is $20 an hour. He is paid time and a half for overtime work beyond 40 hours a week. He
worked: Monday:11 ; Tuesday:10 ; Wednesday:10 ; Friday:12. Find Stephen
Answer:
Kindly check explanation
Step-by-step explanation:
1.) regular time hours = 160
Overtime hours = 18
Gross pay = (9.28 * 160) + (1.5 * 9.28 * 18) = $1735.36
2.) Last year, Ida Zolen worked 2,000 hours at regular time pay of $8.20 an hour. She also worked 75 hours over time at double his regular rate. What was Ida’s gross pay last year?
Gross pay:
(2000 * 8.20) + (2 * 8.20 * 75) = $17,630
3. Alan Kirbaum works on an 8-hour day basis and is paid $8 an hour for regular time work and time-and-a half for overtime work. Last week he worked these hours: Monday:9 ; Tuesday:6 ; Wednesday:11 ; Thursday:8 ; Friday:9.
A) How many regular hours did he work?
Regular hours = (8 + 6 + 8 + 8 + 8).= 38 hours
B) How many overtime?
Overtime = (1 + 3 + 1). = 5 hours
C) What is his overtime rate?
2.5 * $8 = $20
D) What is his overtime pay?
$20 * 5 = $100
E) Find Alan’s gross pay.
(38 * $8) + $100 = $404
4. Stephen Woll’s regular pay is $20 an hour. He is paid time and a half for overtime work beyond 40 hours a week. He
worked: Monday:11 ; Tuesday:10 ; Wednesday:10 ; Friday:12. Find Stephen
Total Hour = (11 + 10 + 10 + 12) = 43 hours
The ratio of the number of boys to the number of girls I just school is 5 to 8 if there are 208 students in the school how many girls can you expect
Answer:
128 girls
Step-by-step explanation:
boys : girls = 5 : 8
Number of boys = 5x
Number of girls = 8x
Total students = 208
5x + 8x = 208
13x = 208
x = 208/13
x = 16
Number of girls = 8x = 8 * 16 = 16 * 8
= 128
Answer:
12
Step-by-step explanation:
Marcel was writing an article for his school paper and read a report that said 2 out of every 20 items purchased at a clothing store were returned. What percent of items were returned to the clothing store?
Answer:
0.1% were returned
PLEASE ANSWER ASAP I ONLY HAVE 30 MINUTES please
18
8
13
7
Find the area of the white granite area in the picture above.
Answer: 178
Step-by-step explanation:
18x13
234 area of white granite
8x7
56 area of blue granite
234-56 to find the area of the white granite
i’ll mark brainlest:( i need help!
Answer: Choice A) [tex]3 \sqrt{26}[/tex]
==================================================
Work Shown:
[tex]\text{The two points are } (x_1,y_1) = (6,7) \text{ and } (x_2,y_2) = (3,-8)\\\\d = \text{Distance between } (x_1,y_1) \text{ and } (x_2,y_2)\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} = \text{Distance Formula}\\\\d = \sqrt{(6-3)^2+(7-(-8))^2}\\\\d = \sqrt{(6-3)^2+(7+8)^2}\\\\[/tex]
[tex]d = \sqrt{(3)^2+(15)^2}\\\\d = \sqrt{9+225}\\\\d = \sqrt{234}\\\\d = \sqrt{9*26}\\\\d = \sqrt{9}*\sqrt{26}\\\\d = 3\sqrt{26}\\\\[/tex]
When going from 234 to 9*26, the idea here is to factor where one factor is the largest perfect square possible. That way we can use the rule [tex]\sqrt{x*y} = \sqrt{x}*\sqrt{y}[/tex] to break up the root and simplify.
1 bag of grape tomatoes coast $3 how many packages can you buy for $15
Answer:
5 package
Step-by-step explanation:
1 bag = $3
X bag = $15
1 * 15/3 = 5 bags
hence : 5 bag can be bought out of $15
What is the slope of a line parallel to a line whose slope is 5/2?
Answer:
5/2
Step-by-step explanation:
Parallel lines have the same slopes
Answer:
Step-by-step explanation:
because the new line is parallel, it will have the same slope as the original equation.
slope
=
−
3
we know the slope and a point, so we can use the point slope formula:
y
−
y
1
=
m
(
x
−
x
1
)
y
1
is the y coodinate,
x
1
is the x coordinate,
and m is the slope
plug the values in
y
+
2
=
−
3
(
x
+
5
)
Which point represents the opposite of –2?
A number line going from negative 5 to positive 5. Point A is at negative 2, point B is between negative 1 and 0, point C is between 0 and 1, and point D is at 2.
A
B
C
D
Answer:
D
Step-by-step explanation:
I did this already
A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of LaTeX: 50cm^3/hr. At what rate is it's diameter decreasing
Complete question is;
A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cm/hr. At what rate is its diameter decreasing?
Answer:
Diameter is decreasing at the rate of 5/(2πr) cm/hr
Step-by-step explanation:
We are told the stone is wearing away at a rate of 50 cm/hr. This means the volume is decreasing. Thus;
dV/dt = -50 cm/hr
Now, a grindstone is in the shape of a cylinder. Thus, volume of grindstone is;
V = πr²h
dV/dr = 2πrh
Now,to find the rate at which the diameter is decreasing, we'll write;
dr/dt = (dV/dt)/(dV/dr)
dr/dt = -50/(2πrh)
We are given;
Diameter = 200 cm
Radius; r = 200/2 = 100 cm
Thickness; h = 10 cm
Thus;
dr/dt = -50/(2π × r × 10)
dr/dt = -5/(2πr) cm/hr
The rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex] and this can be determined by using the given data.
Given :
A 10 cm thick grindstone is initially 200 cm in diameter and it is wearing away at a rate of 50 [tex]\rm cm^3/hr[/tex].
The following steps can be used in order to determine the rate at which grindstone diameter decreases:
Step 1 - According to the given data, the rate at which grindstone volume decreases is:
[tex]\dfrac{dV}{dt} = 50\;{\rm cm^3/hr}[/tex] --- (1)
Step 2 - The formula of the volume of the cylinder (grindstone) is given below:
[tex]V = \pi r^2 h[/tex]
Step 3 - Differentiate the above expression with respect to 'r'.
[tex]\dfrac{dV}{dr} = 2\pi r h[/tex] --- (2)
Step 4 - So, using the expression (1) and (2) the rate at which grindstone diameter decreases is:
[tex]\dfrac{dr}{dt}=\dfrac{\frac{dV}{dt}}{\frac{dV}{dr}}[/tex]
[tex]\dfrac{dr}{dt}=\dfrac{-50}{2\pi r \times 10}\\[/tex]
[tex]\dfrac{dr}{dt} = -\dfrac{5}{2\pi r }\; {\rm cm/hr}[/tex]
So, the rate at which grindstone diameter decreases is [tex]-5/2\pi r \;{\rm cm/hr}[/tex].
For more information, refer to the link given below:
https://brainly.com/question/12748872
A pair of $72 sneakers is marked with a sign $20 OFF or 20% OFF: The $20 of final price is
Answer:
52
Step-by-step explanation:
i did the test.
Find the directional derivative of the function at the given point in the direction of the vector v. g(p, q) = p4 − p2q3, (2, 1), v = i + 3j
Answer:
-4√10 / 5 or -8√10 / 5
Step-by-step explanation:
See attachment for calculation
Choose the true statement.
Answer:
-8 < 8
Step-by-step explanation:
-8 is less than 0 so it is definitely less than 8
Hope this helped :)
what is 2(3x+4)=x-7
can u solve this please? 18x-2 = 17x +2
Answer:
Step-by-step explanation:
18x-2 = 17x +2
⇒18x-17x - 2 = 2
⇒x - 2 = 2
∴ x = 4
Answer:
x=4
Step-by-step explanation:
18x-2=17x+2
step 1: isolate the x by subtracting 17x from both sides
18x-2-17x=17x+2-17x
x-2=2
then add 2 to both sides
x-2+2 = 2+2
x=4
7. Given a right triangle as shown below, use a calculator to estimate the length of the
missing side to the nearest tenth of a centimeter
Answer:
D. 11.6 cm
Step-by-step explanation:
The missing length of the right angled triangle can be calculated using Pythagorean Theorem as shown below:
[tex] c^2 - b^2 = a^2 [/tex]
Where,
a = x cm
b = 11 cm
c = 16 cm
Thus:
[tex] 16^2 - 11^2 = x^2 [/tex]
[tex] 256 - 121 = x^2 [/tex]
[tex] 135 = x^2 [/tex]
[tex] \sqrt{135} = \sqrt{x^2} [/tex]
[tex] \sqrt{135} = x [/tex]
[tex] 11.61895 = x [/tex]
[tex] x = 11.6 cm [/tex] (nearest tenth)
Answer:
Step-by-step explanation:
11.16
Main Menu
Solve the equation
Unit 2
- 8c+7= -25
Section 3.2
Section 3.3
Section 9.3
Section 9.5
Section 9.6
Answer:
c = 4
Step-by-step explanation:
Solve for"c" in the following equation:
- 8 c + 7 = - 25
Subtract 7 from both sides:
- 8 c = - 25 - 7
combine like terms
- 8 c = -32
divide both sides by "-8" to isolate c on the left
c = - 32 / (-8)
c = 4
in the diagram of the collinear points, PT=20 QS=6 and PQ= QR= RS. find each lenght
Answer:
QR=3, PQ=3, RP=6, SP=9, RS=3, ST=11, RT=14, QR=3
Step-by-step explanation:
The Area of a rectangle is 70 cm²
What could be the perimeter of the rectangle?
Type Out The Answer.
A) 7 cm
B) 9 cm
C) 12 cm
D) 26 cm
E) 34 cm
GOOD LUCK
Answer:
D
Step-by-step explanation:
Answer:
E.
Step-by-step explanation:
Area=7*10=70
Perimeter=7+7+10+10=34
1 A hiker starts at point P and walks 2.0 kilometers due east and then 1.4 kilometers due north.
-What is the total distance traveled by the hiker?
-Draw a sketch representing the situation. Draw the resultant vector for the hiker’s displacement and label it R.
-What is the magnitude of the hiker’s displacement vector?
Answer:
Step-by-step explanation:
Distance has to do with how far an object or a body has travelled. If a hiker starts at point P and walks 2.0 kilometers due east and then 1.4 kilometers due north, the total distance covered by the hiker will be:
Distance = 2.0km + 1.4km
Total distance travelled = 3.4km
The displacement is the distance covered in a specified direction. This is expressed using the Pythagoras theorem as shown:
R² = 2.0²+1.4²
R² = 4+1.96
R² = 5.96
R = √5.96
R = 2.44km
Hence the magnitude of the hiker’s displacement vector R is 2.44km
Find the diagram attached
Viel
Eram
back
A movie theater has 4 groups of seats. The largest group
of seats, in the middle, has 21 rows, with 21 seats in each
row. There are 2 smaller groups of seats on the sides, each
with 21 rows and 7 seats in each row. A group of seats in
the back has 6 rows, with 33 seats in each row.
Step by s
How many seats are in the movie theater
Textbod
side
middle
side
Print
Part 1 out of 6
Complete the explanation for what you need to know.
of the movie theater.
You need to find the number of sections that are in each row
Check
Next
Tuin
Se
and Close
Oo
Answer:
933 seats
Step-by-step explanation:
Given that :
4 different group of seats are in a movie theater :
The middle group ; 2 side groups and the back group
Number of seats in the movie theater :
THE MIDDLE GROUP:
21 Rows and 21 seats per row
Number of seats = 21 * 21 = 441 seats
THE SIDE GROUPS:
21 rows and 7 seats per row
Number of seats = 2(21 * 7) = 294 seats
BACK GROUP:
6 rows and 33 seats per row
Number of seats = 6 * 33 = 198 seats
Total number of seats :
441 + 294 + 198 = 933 seats
Thirty-seven school buses arrived at the zoo, each carrying thirty-seven to forty-three students per bus.
Estimate the number of students visiting the museum.
A: 16,000
B: 160
C: 1,600
D: 160,000
Answer:
C 1,600
Step-by-step explanation:
because If you multiply 37*43 It will get you 1591 and it's asking for the estimated answer which is 1600
what is the sale tax on a $14,500 truck if the tax rate is 9%
Answer:
$15, 805.00
Step-by-step explanation:
Tax is based on the state you live in.
Assuming the butterflies traveled 3000 miles to reach their winter home, they averaged 60 miles per day and flew for an average of 8 hours per day.
What is there average speed per hour?
How many days would it take for them to reach their destination?
Answer:
1. 7.5 mph
2. 400
Step-by-step explanation:
1. You would just do 60/8 to find the answer.
2. You would take the answer you got from the previous question and do 3000/7.5
Hope I helped!! :)
Jada is putting a border around her rectangular garden. The garden is 12.63 meters long and 3.28 wide. Jada estimates the perimeter of her garden by rounding the length and width to the nearest whole number. What equation shows
Answer:
12.63 rounded to 13 and 3.28 rounded to 3 the perimeter is 32