Answer:
[tex]\sigma = 12.5[/tex] ---- sample standard deviation
[tex]\sigma^2 = 157.2[/tex] ---- sample variance
Step-by-step explanation:
Solving (a): The sample variance
First, we calculate the midpoint of each class (this is the average of the limits)
So, we have:
[tex]x_1 = \frac{56 + 64}{2} = 60[/tex]
[tex]x_2 = \frac{65 + 73}{2} = 69[/tex]
And so on
So, the table becomes:
[tex]\begin{array}{cc}{x} & {f} & {60} & {11} & {69} & {15} & {78} & {14} & {87} & {4} & {96} & 11 \ \end{array}[/tex]
Calculate the mean
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \frac{60*11+69*15+78*14+87*4+96*11}{11+15+14+4+11}[/tex]
[tex]\bar x = \frac{4191}{55}[/tex]
[tex]\bar x = 76.2[/tex]
The variance is:
[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]
So, we have:
[tex]\sigma^2 = \frac{(60 - 76.2)^2*11+(69 - 76.2)^2*15+(78 - 76.2)^2 *14+(87 - 76.2)^2*4+(96 - 76.2)^2*11}{11+15+14+4+11-1}[/tex]
[tex]\sigma^2 = \frac{8488.8}{54}[/tex]
[tex]\sigma^2 = 157.2[/tex]
The sample standard deviation is:
[tex]\sigma = \sqrt{\sigma^2[/tex]
[tex]\sigma = \sqrt{157.2[/tex]
[tex]\sigma = 12.5[/tex]
Solving (b): The sample variance
In (a), we calculate the sample variance to be:
[tex]\sigma^2 = 157.2[/tex]
What is the axis of symmetry for the function f(x)=7−4x+x2?
x = –3
x = –2
x = 2
x = 3
Answer:
x = 2
Step-by-step explanation:
[tex]y = {x}^{2} - 4x + 7 \\ y = (x - 2) {}^{2} - 4 + 7 \\ y = {(x - 2)}^{2} + 3[/tex]
Therefore, axis of symmetry is x = 2
The solution is: x=2, is the axis of symmetry for the function f(x)=7−4x+x2.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, we have,
f(x)=7−4x+x^2
Rewriting as
f(x) = x^2 -4x+7
a =1 b -4 c=7
The axis of symmetry is:
h = -b/2a
= -(-4)/ 2(1)
= 4/2(1)
= 4/2
=a
The axis of symmetry is x=2.
Hence, The solution is: x=2, is the axis of symmetry for the function f(x)=7−4x+x2.
To learn more on function click:
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identify the 3D shape
Answer and Step-by-step explanation:
The 3D shape shown is a rectangle. This is the net-form of a rectangle.
#teamtrees #PAW (Plant And Water)
Answer:
rectangular prism
Step-by-step explanation:
a rectangle is not 3d. a rectangle is 2d. the correct answer is a rectangular prism.
A certain game consists of rolling a single fair die and pays off as follows: $10 for a 6, $7 for a 5, $4 for a 4, and no payoff otherwise,
Find the expected winnings for this game.
The expected winnings for this game are
(Round to the nearest hundredth.)
1
m
21
m
se
?
Enter your answer in the answer box.
Answer:
$3.50
Step-by-step explanation:
Given:
$10 for a 6, $7 for a 5, $4 for a 4, and no payoff otherwise
P(6) = 1/6 ; p(5) = 1/6 ; p(4) = 1/6 ; p(1,2or3) = 3/6 = 1/2
P(x) ____ 1/6 _____ 1/6 _____1/6 _____1/2
x______ 10 _______ 7 _____ 4 _______ 0
Expectwd value ; E(x)
Σx*p(x) = (1/6 * 10) + (1/6 * 7) + (1/6 * 4) + (1/2 * 0)
E(x) = 3.50
calculate the value of A in the statement
please edit your question man
Let m Z1=(3x)º, m 22=(5x-7)", m 23=(4x+15), and m ZAFD=128º. Find m44 and m ZBFD.
Answer:
m<4 = 52°
m<BFD = 98°
Step-by-step explanation:
m<1 = (3x)°
m<2 = (5x - 7)°
m<3 = (4x + 15)°
m<AFD = 128°
✔️Find m<4:
m<4 = 180° - m<AFD (angles on a straight line)
Substitute
m<4 = 180° - 128°
m<4 = 52°
✔️m<BFD = m<2 + m<3
Substitute
m<BFD = (5x - 7)° + (4x + 15)°
We need to find the value of x.
Create an equation to find x.
m<1 + m<2 + m<3 = m<AFD (angle addition postulate)
Substitute
3x + 5x - 7 + 4x + 15 = 128°
Add like terms and solve for x
12x + 8 = 128
12x + 8 - 8 = 128 - 8
12x = 120
12x/12 = 120/12
x = 10
m<BFD = (5x - 7)° + (4x + 15)°
Plug in the value of x
m<BFD = 5(10) - 7 + 4(10) + 15
m<BFD = 50 - 7 + 40 + 15
m<BFD = 98°
Helen is taking part in a quiz on tv. The Probability she answers the questions correctly is 4/5. Helen is asked two questions. Calculate the probability she answered both questions correctly
Answer:
16/25
Step-by-step explanation:
To find the probability that she gets both questions right, multiply the probabilities together:
4/5 x 4/5
= 16/25
So, the probability that she answers both correctly is 16/25
Find the value for the side marked below.
Round your answer to the nearest tenth.
47
у
74°
y = [?]
Answer:
y ≈ 13.5
Step-by-step explanation:
In the given right triangle we have to find the measure of unknown side 'y'.
Since, measure of opposite side and adjacent side of the angle measuring 74° have been given,
We will use tangent ratio for the given angle.
tan(74°) = [tex]\frac{\text{Measure of opposite side}}{\text{Measure of adjacent side}}[/tex]
tan(74°) = [tex]\frac{47}{y}[/tex]
y = [tex]\frac{47}{\text{tan}(74^{\circ})}[/tex]
y = 13.48
y ≈ 13.5 units
Tony wants to save 10,000 in 6 years. Assuming interest rate what is the minimum he must save month to goal?
Answer:
Tony wants to save $10000 in 6 years. which is approx $123. Hence final answer is C) $123.
Answer:
c
Step-by-step explanation:
We have been given that Tony wants to save $10000 in 6 years.
That means future value S = $10000
Time t= 6 years
Interest rate = 4% yearly = 0.04 yearly
n=12 months per year
Now we have to find monthly payment to recieve $10000 in 6 years. so we need to apply monthly payment formula which is
which is approx $123.
Hence final answer is C) $123.
If F(x)= 3x-2 and G(x)= x^2+8, what is G(F(x))?
Answer:
(3x-2)^2+8= 9x^2-12x+12
According to the National Beer Wholesalers Association, U.S. consumers 21 years and older consumed 26.9 gallons of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers 21 years and older in Milwaukee will be taken, and the sample mean 2017 beer and cider consumption will be used to test the following null and alternative hypotheses:
H, :μ< 26.9
Ha : μ> 26.9
a. Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?b. What is the Type I error in this situation? What are the consequences of making this error?c. What is the Type II error in this situation? What are the consequences of making this error?
Answer:
Kindly check explanation
Step-by-step explanation:
If the null is rejected, then we conclude that the average Consumption of beer and cider by customers who are 21 years and above is greater than 26.1
A type 1 error is committed if the null hypothesis is incorrectly rejected ; this means we will be concluding that customers who are 21 years and older have higher average Consumption when they actually do not. This may lead to a restriction on beer consumption in the city when there actually isn't a need for it.
For type 2 error, a false null is incorrectly accepted, in this scenario, we are saying that the consumption of beer and cider is not beyond the mean value when in actual sense it is.
using the digits 0-9 at most one time each fill in the boxes so that the fraction equals the decimal
Step-by-step explanation:
Z 00m
336"083"2553
(wZE2XQ) are
if y=8, evaluate the following expression: 40-5y
1, Find the interior angle of a regular polygon with 20 sides. What is the size of exterior angle?
2, Calculate the
(I) exterior angle
(ii) the number of sides of a regular polygon with an interior angle of
(a) 60° (b) 72° (c) 165°
Answer:
Step-by-step explanation:
1) (20 -2) * 180 = 3240 (sum of the inner angles)
3240 : 20 = 162 degrees
2) (I) 180 - 162 = 18 degrees
(ii)
a = 3 (it is an equilateral triangle)
b = 5 (it is a pentagon)
c = 24
Answer:
1. 180(n-2) gives you the angle sum
devide by n to get the value of one interior angle
n are the number of sides, or corners
180(20-2)/20 = 162° is the interior angle.
the exterior angle is just 360°-162° = 198°
2i) seems to be included in 1), pls clarify if that's not the case.
remember
180(n-2)/n = int.angle
let's do this with (a) 60°
180(n-2)/n = 60
(180n-360)/n = 60 |*n
180n-360 = 60n |-180n
-360 = -120n |/(-120)
3 = n
2iia) 3 sides / triangle
2iib) 5 sides / pentagon
2iic) 24 sides
2,45,250 students appeared for an entrance examination. If 94,750 students did not get admission, find how many students got admission.
can i please get the answer
Answer:
2.45.250- 94.750
= 92. 2975. this is the learners who got the admission
Answer:
1,50,500 students
Step-by-step explanation:
Hope this helps... vote as brainliest
Select all that apply.
Which of the following name a line segment in the drawing?
Answer:
lineAF, CE, EF
Step-by-step explanation:
Because a line does not curve. And AB curves.
Assuming I got the correct question, this is the answer.
So, take this as an advice, and next time u post such questions, give a pick, so we know which question u are talking about
Thank You
Hope u understood
Please mark as brainliest
Question 1 of 10
Simplify this algebraic expression completely.
5y-3(y + 2)
Answer:
2y -6
Step-by-step explanation:
5y-3(y + 2)
Distribute
5y -3y - 6
Combine like terms
2y -6
Ali wants to attend more group exercise classes at his gym. This week, he plans to attend 1 cardio class and 5 weightlifting classes, which will last a total of 237 minutes. Next week, he hopes to attend 5 cardio classes and 5 weightlifting classes, which will last a total of 465 minutes.
a) Write a system of equations that represents the above situation.
b) Use the elimination method to show the length of the cardio class and the length of the weightlifting class.
Answer:
x + 5y = 237
5x + 5y = 465
Step-by-step explanation:
Let
x = length of cardio class
y = length of weightlifting class
x + 5y = 237 (1)
5x + 5y = 465 (2)
Using elimination method
Subtract (1) from (2) to eliminate y
5x - x = 465 - 237
4x = 228
x = 228/4
x = 57 minutes
Substitute x = 57 into (1)
x + 5y = 237 (1)
57 + 5y = 237
5y = 237 - 57
5y = 180
y = 180/5
y = 36 minutes
x = length of cardio class = 57 minutes
y = length of weightlifting class = 36 minutes
Given the set of vectors , decide which of the following statements is true:
A: Set is linearly independent and spans ℛ 3. Set is a basis for ℛ 3.
B: Set is linearly independent but does not span ℛ 3. Set is not a basis for ℛ 3.
C: Set spans ℛ 3 but is not linearly independent. Set is not a basis for ℛ 3.
D: Set is not linearly independent and does not span ℛ 3. Set is not a basis for ℛ 3.
(1,0,0),(0,1,2)
plz answer this very important
Answer:
16
Step-by-step explanation:
From the question given above, the following data were obtained:
1 = 1
2 = 4
3 = 9
4 =?
Observing the data, we can see that the numbers on the right side are simple the squares of the numbers on the left side. This is illustrated below:
1 = 1² = 1
2 = 2² = 4
3 = 3² = 9
Thus, we shall use the same logic to obtain that of 4. This is illustrated below:
4 = 4² = 16
Thus the answer to the question is 16.
Your job in a company is to fill quart sized bottles of oil from a full 50-gallon oil drum
Step-by-step explanation:
....
I Dont Known........
Answer:
16 full cases
Step-by-step explanation:
4 quarts to a gallon
50 gallons is 200 quarts (50 x 4)
200 quarts / 12 quarts per case = 16.66667 (.66667 isn't a full case)
so, it's 16
I WILL MAKE YOUR ANSWER THE BRAINLIST MAKE SURE YOU ARE RIGHT
FIND THE VOLUME OF THE CONE
Answer:
301.59
Step-by-step explanation:
V=1/3hπr²
sorry in advance if its wrong, this is my 1st time answering this type of question. that's what i got for the answer
Translate the phrase into an algebraic expression.
3 more than b
Answer:
b+3 or 3+b
Step-by-step explanation:
There are four white socks and six black socks in a drawer what is the probability of selecting a white sock not replacing it and then selecting another white sock
Answer:
Step-by-step explanation:
Add all the socks in the drawer to get a denominator
12
blue socks can be picked out of the
36
total socks, so
12
36
Then you take away one sock from the top and bottom, so you now have
11
35
Multiply the two numerators (
12
and
11
), then multiply the denominators (
36
and
35
), then divide the numerator by the denominator,
132
1260
, to get your answer.
Answer:
6/10
Step-by-step explanation:
1st step: 4+6=10
Stevens College plans to have 20 computers for every 100 students. How many computers are needed for 1,500 students?
Answer:
300 computers
Step-by-step explanation:
So I divided 1500 out of a 100 and got 15, then I multiply 15 to 20 and got 300.
(I am a high schooler so I hope this is 3rd grade math because I notice you are a college student and I hope this not some college tricky math, if you get this wrong I am truly sorry)
CAN YOU SOLVE THIS MATH PROBLEM 20 POINTS
Ahmad made $114 for 12 hours of work. At the same rate, how many hours would he have to work to make $108?
Answer:6
Step-by-step explanation:
If you help me I’ll mark brainliest
Answer:
∠2=92°
Step-by-step explanation:
Using an angle formula, -8x+144=2x+74
Simplification:
-8x+144=2x+74
-8x+70=2x
70=10x
x=7
Therefore, each angle is 88°
Now, because ∠2 is adjacent to one of 88°, they add up to 180°
Therefore,
180°=88°+∠2
∠2=92°
Hi if you have a 65% grade can a 80% bring it up to a C 70%
Answer:
Not a 70%, but a 72.5% (or a 73%)
Step-by-step explanation:
Assuming that the 65% is the first grade and the 80% is your second, adding both numbers and dividing by 2 will get you 72.5%.
The best possible grade you can get from that 65% is an 82.5%, or 83% if you round the grade up. 100+65=165÷2 will get you 82.5.
One day, a café sells 3 more than twice the number of cappuccinos as they do lattes. They sold a total of 33 cappuccinos and lattes together.
Which equation could be used to find the number of lattes, x, sold at café
Answer:
x=6
Step-by-step explanation:
What is the standard form of y - 8 = 2(x + 3)
Answer:
y=2x+14
Step-by-step explanation:
y=2x+2.3+8=2x+14