A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:
769 691 699 730 711 765 702 718 719 712 768 688 757
695 768 735 709 758 708 693 736 700 687 772 715
a. Find the mean, median and mode of this information. (Round your answers to 2 decimal places.)
b. What are the range and standard deviation? (Round your answers to 2 decimal places.)
c. Use the Empirical Rule to establish an interval which includes about 95 percent of the observations. (Round your answers to 2 decimal places.)
Answers
Answer:
A.
mean = 724.2
Median = 715
Mode = 768
B.
Range = 85
Standard deviation = 29.30
C.
Interval = [665.6, 782.8]
Step-by-step explanation:
Number of samples n = 25
Summation X= 769 + 691 + 699 +730+711+ 765+ 702 718 +719 +712+ 768 +688 +757+695 768 +735 +709 +758 +708+ 693 +736 700+ 687 +772 +715 = 18105
A.
1. Mean = 18105/25
= 724.2
2. Median is the middle value when arranged from the least value to the highest = 715
3. Mode is the number with the highest frequency = 768 (occured two times)
B.
1. Range = highest value - lowest value
Highest value = 772
Lowest value = 687
772-687 = 85
2. Standard deviation = √(X-barX)²/n-1
= √20604/25-1
=√858.5
= 29.30
Please check attachment for the full calculation of the standard deviation
C.
Interval
[Mean - 2(sd), mean + 2(sd)]
= [724.2-2x29.3, 724.2+2x29.3]
=[665.6, 782.8]
Related Questions
Math problem
Math problem Math problem
Answers
Answer:
93.69 Ft for fencing
Explanation:
So first find the perimeter for the rectangle (what is exposed)
SO its 17+25+25=67
Now we need to find the Circumference of the circle (perimeter of circle)
SO circumference formula is just
π*d
So in this case 17 *3.14 is 53.38
53.38 is the full Circumfrnce but divide that by 2 due to the circle being only half exposed
53.38/2=26.69
Now 26.69+67= 93.69 ft
For perimeter
Answer:
soit should angle + angle
Step-by-step explanation:
because what number they are you have to add both of the first numbers then you have too add the second two times
Logan wants to save 35% of his weekly paycheck he earns $125 a week how much does he plan to save each week enter the correct answer in the box
Answers
Answer:
35%
Step-by-step explanation:
Logan wants to save 35% of his weekly paycheck he earns $125 a week how much does he plan to save each week enter the correct answer in the box, he wants to save 35%, how much does he plan to save, 35% easy. JK its 125 - 81.25 which is $43.75.
Let y=f(x) be a twice differentiable function such that f(1)=3 and dy/dx= (4y^2+7x^2)^1/2. What is the value of d2y/dx2 at x=1?
Answers
Answer:
[tex]\displaystyle f''(1) = \frac{7}{\sqrt{43}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeCalculus
Derivatives
Derivative Notation
Taking Derivatives with respect to x
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Chain Rule: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Function: y = f(x), twice differentiable.
[tex]\displaystyle f(1) = 3\\\frac{dy}{dx} = (4y^2 + 7x^2)^{\frac{1}{2}}[/tex]
Step 2: Differentiate
Remember we are taking the derivative with respect to x.
Chain Rule [Basic Power Rule]: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{1}{2}(4y^2 + 7x^2)^{\frac{1}{2} - 1} \cdot \frac{dy}{dx} (4y^2 + 7x^2)[/tex][2nd Derivative] Simplify: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{1}{2}(4y^2 + 7x^2)^{-\frac{1}{2}} \cdot \frac{dy}{dx} (4y^2 + 7x^2)[/tex][2nd Derivative - Chain Rule] Basic Power Rule: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{1}{2}(4y^2 + 7x^2)^{-\frac{1}{2}} \cdot (0 + 2 \cdot 7x^{2 - 1})[/tex][2nd Derivative] Simplify: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{1}{2}(4y^2 + 7x^2)^{-\frac{1}{2}} \cdot 2 \cdot 7x[/tex][2nd Derivative] Simplify: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{7x}{\sqrt{7x^2 + 4y^2}}[/tex]Step 3: Evaluate
We are given x = 1 and f(1) = 3. This will tell us the instantaneous slope.
Substitute [2nd Deriv]: [tex]\displaystyle f''(1) = \frac{7(1)}{\sqrt{7(1)^2 + 4(3)^2}}[/tex][√Radical] Exponents: [tex]\displaystyle f''(1) = \frac{7(1)}{\sqrt{7(1) + 4(9)}}[/tex][Fraction] Multiply: [tex]\displaystyle f''(1) = \frac{7}{\sqrt{7 + 36}}[/tex][√Radical] Add: [tex]\displaystyle f''(1) = \frac{7}{\sqrt{43}}[/tex]This tells us that the rate of change of the slope of the tangent line is [tex]\displaystyle \frac{7}{\sqrt{43}}[/tex].
We can also write an equation for the instantaneous slope:
[Equation] [tex]\displaystyle y - 3 = \frac{7}{\sqrt{43}}(x - 1)[/tex]
Suppose y varies directly as x. If x = 27 when y = 6, find x when y = 2.
Answers
0.22
Step-by-step explanation:
y=kx
6=27k6/27=kk=0.22y=0.22*2y=0.44(-3, 0) to polar form.
Answers
9514 1404 393
Answer:
(3; 180°)
Step-by-step explanation:
The point (-3, 0) is located on the -x axis at a distance of 3 units from the origin. The -x axis is at an angle of 180° CCW from the +x axis. So, the polar coordinates are ...
r = 3
θ = 180°
This might be written as ...
(r; θ) = (3; 180°) = (3; π radians)
3/4 + 2/3 using fractions
Answers
Step-by-step explanation:
Lowest common multiple (LCM) of 4 and 3 = 12.
Therefore 3/4 + 2/3
= 9/12 + 8/12
= 17/12 or 1 5/12.
Answer:
1 5/12
Step-by-step explanation:
To do this, we need to find the LCM of 4 and 3. The LCM of 4 and 3 is 12. Now, since 4x3 is 12, we multiply 3/4 by 3/3 to get 9/12. Now, we multiply 2/3 by 4/4 (since 3x4 is 12) to get 8/12. Now, we add only the top numbers to get 17/12. To simplify this, we divide 17 by 12 (check attached screenshot). The quotient (the answer) becomes the whole number, the divisor (12) becomes the denominator, and the remainder (5) becomes the numerator. This gets us 1 5/12.
In a class of 23 students, 12 have a cat and 6 have a dog. There are 2 students who
have a cat and a dog. What is the probability that a student who has a cat also has a
dog?
Answers
Answer:
2/23
Step-by-step explanation:
I think it's because there's 2 students out of 23 students who have a cat and a dog. So, I'm assuming the answer is 2/23
Answer:
2/12
Step-by-step explanation:
describe the reflection of the figure
Answers
Answer:
Reflection across the A axis
Write an equation for the following table.
Answers
Answer:
y= 38x
Step-by-step explanation:
It is going up by 38 each time. There is no b value (y=mx + b), because if you times 6 by 38, you get 228. You don't need to add any remainders.
If
1+3= 12
2+7=27
5+6 = 90
then 3+5= ?
Answers
Answer:
8
Step-by-step explanation:
3+5=8
Find the unit rate of miles 1/5 in 1/65hour
Answers
Answer: 13 miles per hour
Step-by-step explanation:
1/5mi=1/65hr
65/5mi=hr
13mi hr
The IRS was interested in the number of individual tax forms prepared by small accounting firms. The IRS randomly sampled 50 public accounting firms with 10 or fewer employees in the Dallas-Fort Worth area. The following frequency table reports the results of the study.
Number of Clients Frequency
25 up to 40 3
40 up to 55 11
55 up to 70 24
70 up to 85 8
85 up to 100 4
Estimate the mean and the standard deviation. Round squared deviations to the nearest whole number and the final answer to 2 decimal places.
Answers
Answer:
Estimates of the number of individual tax forms prepared by small accounting firms:
1. Mean = 10
2. Standard deviation = 7.56
Step-by-step explanation:
a) Data and Calculations:
Number of Clients Frequency Mean Diff Squared Deviation
25 up to 40 3 -7 49
40 up to 55 11 1 1
55 up to 70 24 14 196
70 up to 85 8 -2 4
85 up to 100 4 -6 36
Sum 50 286
Mean of frequencies = 10 (50/5) 57.2 (286/5)
Standard deviation = square root of 57.2 = 7.56
b) The IRS can obtain the mean value of the number of individual tax forms prepared by small accounting firms by dividing the sum of the frequencies by the numbers (50/5). Similarly, the IRS can calculate the standard deviation of the number of individual tax forms prepared by small accounting firms, which measures how spread out the data is about the mean value, by working out the mean of the frequency numbers. Then subtract the mean for each number and square each result. Add up the squared differences and divide by the number to get the mean. Finally, take the square root of the mean differences.
Felipe is making goody bags for the students in his class. He has 32 cookies and 24 candies to put in the bags. He wants to put an equal number of cookies and candies in each bag. What is the greatest number of bags that he can make for his students.
Answers
Answer:
I think HCF of 32 and 24=8
Answer two questions about Equations A and B:
A. 5x = 20
B. x=4
1) How can we get Equation B from Equation A
Choose 1 answer:
A: Multiply/divide both sides by the same non-zero constant
B: Multiply/divide both sides by the same variable expression
C: Add/subtract the same quantity to/from both sides
D: Add/subtract a quantity to/from only one side
2: Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
A: Yes
B: No
PLS HELP
Answers
2) Choice A, yes.
Let’s divide both sides of the equation by 5.
5x=20
5x/5 = 20/5
x = 4
The equations have the same solution, so they are equivalent
plssssssssssssssssss help asap so am what part % of 18 is 24 it iis not 75
Answers
24
Percentage Calculator: 18 is what percent of 75? = 24.
If 1 yard=3 feet and 1 mile = 5,280 feet, how many yards are there in 5 miles
Answers
Answer:
There are 3520 yards in 2 miles
Answer:
There are 3520 yards in 2 miles
Step-by-step explanation:
6(4 - 2р) + 9p
Can any one help
Answers
Answer: p = 8
Step-by-step explanation:
6(4-2p)+9p
24 - 12p + 9p
24 - 3p
-3p = -24
3p = 24
p = 8
is y=4x+2 proportional?
Answers
Answer: yes
Step-by-step explanation:
List the factors of 95
Answers
Write two polynomials whose difference is 6x+3. Then prove it.
Answers
Answer:
One possible pair:
7 x + 4 and x + 1
Step-by-step explanation:
There are infinitely many pairs that meet this requirement.
Please mark me brainliest :D
Given a1 = 1 and an = an-1 + 2. Find a7.
A 9
B 11
C 7
D 13
Answers
Answer:
7
Step-by-step explanation:
Sorry if my answer is wrong
y=1/2-2
find the y-intercept
find the x-intercept
Answers
Y-intercept: -3/2
What is 11/4 as a mixed number
Answers
Answer:
34
Step-by-step explanation:
Answer:
2.75 round it up 3
Step-by-step explanation:
divide 11 to 4
Why is 2x 3/4 less than 2?
Answers
Answer & Step-by-step explanation:
It is less because 2 times 3/4 is the same as 2/1 times 3/4 which is 6/4 then simplify it and you get 3/2 which then is 1 1/2.
That is why 2 times 3/4 is less than 2.
Hope that helps ;)
Cheryl's famous pumpkin pie Seasoning consists of a blend of cinnamon, nutmeg and cloves. WHen cheryl mixes up a batch, she uses 200 ounces of cinnamon, 100 ounces of nutmeg, and 100 ounces of cloves. If cinnamon sells for $1.80 per ounce, nutmeg sells for $1.60 per ounce, and cloves sell for $1.40 per ounce, what should be the price per ounce of the mixture. math problem answer
Answers
Answer:
$1.65
Step-by-step explanation:
Given that:
Batch mixture :
Cinnamon - 200 ounces
Nutmeg - 100 ounces
Cloves - 100 ounces
Cost of Seasoning mix :
Cinnamon - 1.80 per ounce
Nutmeg - 1.60 per ounce
Cloves - 1.40 per ounce
Price per ounce of mixture :
Let the price per ounce of mixture = x
Total ounce of mixture = (100 + 100 + 200) = 400 ounces
Σ(ounce * cost) = total ounce * cost of mixture
(200*1.80)+(100*1.60)+(100*1.40) = 400 * x
$360 * $160 * $140 = 400x
$660 = 400x
x = $660 / 400
x = $1.65
Price per ounce of mixture = $1.65
can you answer me please
Answers
Answer: 1. 10 2. 18
Step-by-step explanation:
1.) 25% of 40 is 10 so she made 10 free throws.
2.) 150% of 12 is 18 so she made 18 free throws.
It is very blurry.. please try asking the question again for me to see.
10k+7k2+4k2–6k
simplify the expression
Answers
[tex]10k + 7k2 + 4k2 - 6k \\ 10k + 14 + 4k \\ = 14k + 14[/tex]
your welcome and give me brainlest
What type of graph is this?
Answers
Answer:
The graph of a quadratic equation, or a parabola, looks like a U, an upside down U, a C, or a backwards C. We can use the following rules to determine what the graph of a given quadratic equation looks like. If y = ax2 + bx + c, and a is positive, then the graph of the equation is the shape of a U.
Step-by-step explanation:
bc
PLS HELP PLS PLS PLS WILL MARK BRAINLIEST
select the table representing a Linear function. (graph them if necessary)
Answers
It’s going down by the same rate of change, 2.
Find x & y so that quadrilateral is a parallelogram. (Look at image)
Answers
Answer:
x = 5° y = 75
Step-by-step explanation:
Here given it is a quadrilateral
105° + y = 180° ( being co-interior angles)
y = 180° - 105°
y = 75°
Now
15x + 105° = 180° (being co-interior angles)
15x = 180° - 105°
15x = 75°
x = 75° / 15
x = 5°
Hope it will help :)❤