Answer:
[tex]Range = 85[/tex]
[tex]\sigma = 28.71[/tex]
[tex]Interval = [666.78, 781.62][/tex]
Step-by-step explanation:
Given
The data for 25 undergraduates
Solving (a): Range and Standard deviation
The range is:
[tex]Range = Highest - Least[/tex]
From the dataset:
[tex]Highest = 772[/tex]
[tex]Least = 687[/tex]
So:
[tex]Range = Highest - Least[/tex]
[tex]Range = 772-687[/tex]
[tex]Range = 85[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
First, calculate the mean
[tex]\bar x = \frac{769 +691 +............+715}{25}[/tex]
[tex]\bar x = \frac{18105}{25}[/tex]
[tex]\bar x = 724.2[/tex]
So, the standard deviation is:
[tex]\sigma = \sqrt{\frac{(769-724.2)^2 +(691-724.2)^2 +(699-724.2)^2 +(730-724.2)^2 +............+(715-724.2)^2}{25}}[/tex]
[tex]\sigma = \sqrt{\frac{20604}{25}}[/tex]
[tex]\sigma = \sqrt{824.16}[/tex]
[tex]\sigma = 28.71[/tex]
Solving (b): The interval of the 95% of the observation.
Using the emperical rule, we have:
[tex]Interval = [\bar x - 2*\sigma, \bar x+ 2*\sigma][/tex]
[tex]Interval = [724.2 - 2*28.71, 724.2 + 2*28.71][/tex]
[tex]Interval = [666.78, 781.62][/tex]
help please jfisaljfdlsajflsd
9514 1404 393
Answer:
108 square units
Step-by-step explanation:
The area of a trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
This trapezoid has bases 8 and 1, and a height of 24. Its area is ...
A = (1/2)(8 +1)(24) = 108 . . . square units
find the derivative
f (x ) = (x-5)^2 (3-x)^2
Given:
The function is
[tex]f(x)=(x-5)^2(3-x)^2[/tex]
To find:
The derivative of the given function.
Solution:
Chain rule of differentiation:
[tex][f(g(x))]'=f'(g(x))g'(x)[/tex]
Product rule of differentiation:
[tex][f(x)g(x)]'=f(x)g'(x)+g(x)f'(x)[/tex]
We have,
[tex]f(x)=(x-5)^2(3-x)^2[/tex]
Differentiate with respect to x.
[tex]f'(x)=(x-5)^2\dfrac{d}{dx}(3-x)^2+(3-x)^2\dfrac{d}{dx}(x-5)^2[/tex]
[tex]f'(x)=(x-5)^2[2(3-x)(0-1)]+(3-x)^2[2(x-5)(1-0)][/tex]
[tex]f'(x)=(x^2-10x+25)(-6+2x)+(9-6x+x^2)(2x-10)[/tex]
[tex]f'(x)=(x^2)(-6)+(-10x)(-6)+(25)(-6)+(x^2)(2x)-10x(2x)+25(2x)+(9)(2x)+(-6x)(2x)+x^2(2x)+9(-10)+(-6x)(-10)+x^2(-10)[/tex]
On further simplification, we get
[tex]f'(x)=-6x^2+60x-150+2x^3-20x^2+50x+18x-12x^2+2x^3-90+60x-10x^2[/tex]
[tex]f'(x)=(2x^3+2x^3)+(-6x^2-20x^2-12x^2-10x^2)+(60x+50x+18x+60x)+(-90-150)[/tex]
[tex]f'(x)=4x^3-48x^2+188x-240[/tex]
Therefore, the derivative of the given function is [tex]f'(x)=4x^3-48x^2+188x-240[/tex].
Tamara uses a coupon to save 20% off her purchase at the bookstore. The original cost of Tamara's purchase is d dollars.
Which expressions represent the cost, in dollars, of Tamara's purchase after using the coupon? Choose all that apply.
Answer:
The equation would be d - (d×0.2)
Find y if the distance between
points P and R is 25 and point R
is located in the first quadrant.
p= (3,-18) r=(10,y)
Answer:
y = 6
Step-by-step explanation:
[tex]\sqrt{(10-3)^2 + (y+18)^2} = 25 \\ 49 + y^2 + 324 + 36y = 625 \\[/tex]
y^2 + 36y - 252 = 0
(y-6)(y+42) = 0
y = 6 (accettable)
y = -42 (not accettable)
usain bolt broke the world record for the mens 100 m sprint with a time of 9.58 seconds. Florence Griffith Joyner broke the world record for the womens 100 m sprint with a time of 10.49 seconds. If florence and usain were running at their world-record speed in the same race, how many metres behind usain would florence finish?
Answer:
If Florence Griffith Joyner and Usain Bolt were running at their world-record speed in the same race, Florence Griffith Joyner would finish 8.67 m behind Usain Bolt.
Step-by-step explanation:
Step 1: Determine the speed of each athlete in m/s
Speed = distance / time
Distance = 100 m
Usain Bolt's speed: 100m / 9.58 s = 10.438 m/s
Florence Griffith Joyner's speed: 100 m/ 10.49 s = 9.533 m/s
Step 2: Determine the distance covered by Florence Griffith Joyner in 9.58 s
Distance = Speed × time
Distance covered by Florence Griffith Joyner = 100 m/ 10.49 s × 9.58 s = 91.32 m
Step 3: Determine the difference in the distance covered by Usain Bolt and Florence Griffith Joyner after 9.58 s
After 9.58 s, Usain Bolt have covered a distance of 100 m
After 9.58 s, Florence Griffith Joyner have covered a distance of 91.33 m
Difference between the distances = (100 - 91.33) m = 8.67 m
Therefore, if Florence Griffith Joyner and Usain Bolt were running at their world-record speed in the same race, Florence Griffith Joyner would finish 8.67 m behind Usain Bolt
What angle is formed by the arms of a clock when the time is 6:50 a.m
A group of students were asked if they carry a credit card. The responses are listed in the table.
If a student is selected at random, find the probability that he or she owns a credit card given that the student is a freshman. Round your answer to three decimal places.
Answer:
0.383 (3 d.p.)
Step-by-step explanation:
Probability formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Let P(A) = probability that the student owns a credit card
Let P(B) = probability that the student is a freshman
Use the given table to calculate the probability that the student is a freshman and owns a credit card:
[tex]\implies \sf P(B \cap A)=\dfrac{23}{100}=0.23[/tex]
Use the given table to calculate the probability that the student is a freshman:
[tex]\sf \implies P(B) = \dfrac{60}{100}=0.6[/tex]
To find the probability that the student owns a credit card given that they are a freshman, use the conditional probability formula:
Conditional Probability Formula
The probability of A given B is:
[tex]\sf P(A|B)=\dfrac{P(B \cap A)}{P(B)}[/tex]
Substitute the found values into the formula:
[tex]\implies \sf P(A|B)=\dfrac{0.23}{0.6}=0.383333...[/tex]
Therefore, the probability that the student owns a credit card given that they are a freshman is 0.383 (3 d.p.).
P(Freshman credit card holder)
23/1000.23P(Freshman)
60/1000.60P(Freshman credit holder|Freshman)
0.23/0.60.383The correlation coefficient for practicing violin and getting better grades in a group of people is 0.8. Analyze the following statement:
Playing violin causes students to get better grades.
Is this a reasonable conclusion?
Answer:
D No; even though there is a strong positive correlation, playing violin doesn't cause students to get better grades
HELP!! PLEASE ASAP!!!!
Wylie is renting a bicycle from a local shop that charges $5 to rent a helmet, plus an hourly rate of $8.50 for the bike. For how long can Wylie rent a bicycle if he pays a total of $47.50? Enter your answer in the box.
hours
Answer:
Wylie can rent a bike for 5 hours.
Step-by-step explanation:
Since Wylie is renting a bicycle from a local shop that charges $ 5 to rent a helmet, plus an hourly rate of $ 8.50 for the bike, to determine for how long can Wylie rent a bicycle if he pays a total of $ 47.50 the following calculation has to be done:
(47.50 - 5) / 8.50 = X
42.50 / 8.50 = X
5 = X
Therefore, Wylie can rent a bike for 5 hours.
HELP ME PLEASE!!!!!
The 2 questions is down below with the picture; please let me know.
Given:
1. 60 is the sum of 15 and Mabel's age.
2. Given equation is
[tex]-8(x+1)=-40[/tex]
To find:
1. The equation for the given situation.
2. Complete the two column proof.
Solution:
1.
60 is the sum of 15 and Mabel's age.
Let m be the Mabel's age. Then,
[tex]15+m=60[/tex]
Therefore, the required equation for the given situation is [tex]15+m=60[/tex].
2.
The complete two column proof is:
Steps Reasons
[tex]-8(x+1)=-40[/tex] Given equation
[tex]\dfrac{-8(x+1)}{-8}=\dfrac{-40}{-8}[/tex] Division Property of Equality
[tex]x+1=5[/tex] Simplifying
[tex]x+1-1=5-1[/tex] Subtraction Property of Equality
[tex]x=4[/tex] Simplifying
Which pair of diagrams best models the equation 3/4 = 6/8.
the one we barely see in the photo you took seems a good fit. on the left wich 3 blue stripes and one white. and with stripes of half the size, 6 blue and two white
Answer:
Answer is a because it has
Step-by-step explanation:
3 blue and 6 blue trust me
Find the distance between the points ( 19,-5) and ( 11, 10).
Answer:
Let the given two points be A & B. Let A ( 19 , - 5 ) be ( x₁ , y₁ ) & B ( 11 , 10 ) be ( x₂ , y₂ ) Remember : The formula to find out the distance between any two points is [tex] \tt{ \sqrt{( x_{2} -x _{1}) ^{2} + (y _{2} - y_{1}) ^{2} }} [/tex] .[tex] \large{ \tt{✺ \: SOLUTION}} : [/tex]
[tex] \large{ \boxed{ \tt{AB = \sqrt{(x_{2} - x_{1} ) ^{2} + (y_{2} - y_{1}) ^{2} } }}}[/tex]
[tex] \large{ \tt{⟶ \sqrt{(11 - 19)^{2} + (10 - ( - 5) ^{2} } }}[/tex]
[tex] \large{ \tt{⟶ \sqrt{ {8}^{2} + {15}^{2} } }}[/tex]
[tex] \large{ \tt{⟶ \: \sqrt{64 + 225} }}[/tex]
[tex] \large{ \tt{⟶ \sqrt{289}}} [/tex]
[tex] \boxed{ \large{ \tt{⟶ \: 17 \: \text{units}}}}[/tex]
And we're done! Let me know if you have any questions regarding my answer :)▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
Select the correct answer.
What is the factored form of this expression?
-12x+36
ОА.(x - 12)(x-3)
O B. (x - 6)^2
OC. (x + 6)^2
OD. (x-6)(x+6)
The answer is B
the method use to solved this is called foil
In right triangle PQR, the length of side P Q is 70, the measure of angle P is 90 degrees, and the measure of angle R is 38 degrees. How we will represents the length of side QR?
Answer:
70/sin38°
Step-by-step explanation:
According to question,we have
PQ=70 , ∠P=90° & ∠R=38°
We know, sine rule
So, Sin90° / QR = Sin38° / 70
on solving, we get
QR = 70 / Sin38°
Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y=[tex]\frac{9}{x^2} + 2[/tex]
Hope this help!!!
Have a nice day!!!
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
12x – 3y = 15
Help plsss
Answer:
y=4x-5
Step-by-step explanation:
-3y = -12x+15. y = (-12x+15)/(-3). y = (-12x/-3)+(15/-3). y = 4x-5.
1.(06.05 MC)
Albiologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. She has devised an equation to solve for which day (x) the lizard
would be able to eat the entire population. The equation is 2* - 3 = 4x + 2.
Explain to the biologist how she can solve this on a graph using a system of equations. (10 points)
What is the volume of a cube
of ice with a 3 cm edge?
Answer:
27 cm
Step-by-step explanation:
every side of a cube is equal to each other. the formula for volume is LxWxH, so 3*3*3=27
4. Damiel and Kianny are going to the Pizza Palace for dinner. Damiel orders 2 slices of pizza and 1 cola and has a bill that totals $12. Kianny orders 3 slices of pizza and 2 colas and has a bill that totals $19.
Answer:
if the question is how much does the pizza and coke cost then:
1 slice of pizza is $5 and coke is $2
Step-by-step explanation:
(2×$5)+(1×$2)=$12
(3×$5)+(2×$2)=$19
[tex]Find the missing side or angle of this equation. This is not a right triangle.[/tex]
Answer:
15.6
Step-by-step explanation:
the angle = 180-61-42=77°
x = 14.sin 77/sin 61
= 14×0.97/0.87
= 15.6
I need help with #7. Please help. I have to show all work so please explain
Answer: 2√17 A website to use for this would be "M a t h w a y"!!! Good luck, hope I helped!!!
Classify the quadrilateral.
Answer:
B Kite.
Step-by-step explanation:
It has 2 distinct pairs of equal size.
Answer:
B) kite
Step-by-step explanation:
Kite has two pairs of equal-length adjacent sides
(doesnr let me put 2 pictures) what name length describes the center of the data? (a question to the number line) (i mark brainlist)
Work it out yourself lad
Answer:
three
Step-by-step explanation:
answer might be 3... shortest name length
in induction, you look for a pattern and then form an educated guess or?
Answer:
look for a pattern then take an estimate or 'educated guess'
Step-by-step explanation:
Answer:
The answer is conjugation
Hope this helps!
What is the surface area of the solid that this net can form?
8 mm
25 mm
8 mm
5 mm
5 mm
8 mm
8 mm
5 mm
5 mm
8 mm
8 mm
25 mm
O 730 square millimeters
O 875 square millimeters
O 1,000 square millimeters
O 1,444 square millimeters
Answer:
730
Step-by-step explanation:
separate each rectangle
use the formula to calculate the area of each rectangle.
1st rectangle
area = length ×breadth
length =5, breadth =8+25+8=41
A1=5×41=205
2nd rectangle
A2=8×25=200
....
A3=5×25=125
A4=8×25=200
Add all As and you have your ans 730
Andrew walks 2000 feet from his house to his office. What distance does he cover?
A. 18,000 in.
B. 24,000 in.
C. 25,000 in.
D. 30,000 in.
What is the value of x?
O 20
(x + 40)
(3x)
R
O 35
w
O 60
S
070
Answer:
Hello! answer: 20
Step-by-step explanation:
These are vertical angles meaning they will have the same measure so... 20 + 40 = 60 20 × 3 = 60 therefore x = 20 hope that helps!
In the given scenario, the value of x is 20. The correct option is A.
What is parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. This means that opposite sides of a parallelogram are parallel and congruent, and opposite angles are congruent as well.
To find the value of x in the given diagram, we need to use the fact that the opposite sides of a parallelogram are equal in length.
Therefore, we can set the expressions for the opposite sides equal to each other and solve for x:
x + 40 = 3x
Simplifying the equation, we get:
40 = 2x
Dividing both sides by 2, we get:
x = 20
Therefore, the value of x is 20.
For more details regarding parallelogram, visit:
https://brainly.com/question/29147156
#SPJ7
The product of a and the sum of a and 34?
Roderick has an Internet service that charges by the hour. This piecewise function shows the cost of the Internet service based on the number of hours that Roderick uses
the Internet.
when x 34
10
(10 + 2.50(x-4)
when x > 4
Last month, Roderick used the Internet for 7.5 hours. What was he charged?
Helppppp Plssssssss
Answer:
18.75 is the answer
Step-by-step explanation:
since the internet usage is more than 4 hrs, the second equation will be used. that is
cost = (10 + 2.50 (x - 4)) where x is the usage hours.
thus
[tex]cost = 10 + (2.5 \times (7.5 - 4)) \\ = 10 + (2.5 \times 3.5) \\ = 10 + 8.75 \\ = 18.75[/tex]