Answer:
[tex]s^2 = 0.9938[/tex] --- sample variance
[tex]s = 0.9969[/tex] --- sample standard deviation
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Heights} & {Frequency} & {116.1-120.0} & {38} & {120.1-124.0} & {24} &{124.1-128.0} & {28} & {128.1-132.0} & {43} & {132.1-136.0} & {29} \ \end{array}[/tex]
Required
Calculate the sample variance and sample standard deviation
First, we calculate the midpoint of each class:
[tex]\begin{array}{ccc}{Heights} & {Frequency} & {m} &{116.1-120.0} & {38} & {118.05}& {120.1-124.0} & {24}& {122.05} &{124.1-128.0} & {28} &{126.05}& {128.1-132.0} & {43} & {130.05} &{132.1-136.0} & {29} &{134.05}\ \end{array}[/tex]
The midpoints are calculated by taking the average of the class intervals.
For instance:
Class 116.1 to 120.0 has a midpoint of
[tex]m = \frac{1}{2}(116.1+120.0)[/tex]
[tex]m = \frac{1}{2}(236.1)[/tex]
[tex]m = 118.05[/tex]
The same approach is applied to other classes.
Next, is to calculate the mean:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
In this case, it is:
[tex]\bar x = \frac{\sum fm}{\sum f}[/tex]
Where
[tex]m = midpoint[/tex]
So, we have:
[tex]\bar x = \frac{118.05*38+122.05*24+126.05*28+130.05*43+134.05*29}{38+24+28+43+29}[/tex]
[tex]\bar x = \frac{20424.10}{162}[/tex]
[tex]\bar x = 126.07[/tex]
The sample variance (s^2) is:
[tex]s^2 = \frac{\sum(m - \bar x)^2}{\sum f -1}[/tex]
This gives:
[tex]s^2 = \frac{(118.05-126.07)^2+(122.05-126.07)^2+(126.05-126.07)^2+(130.05-126.07)^2+(134.05-126.07)^2}{38+24+28+43+29-1}[/tex]
[tex]s^2 = \frac{160.002}{161}[/tex]
[tex]s^2 = 0.9938[/tex]
The sample standard deviation (s) is:
[tex]s = \sqrt{s^2[/tex]
[tex]s = \sqrt{0.9938[/tex]
[tex]s = 0.9969[/tex]
On an American League baseball team with 15 field players and 10 pitchers, the manager must select for the starting line-up, 8 field players, 1 pitcher and 1 designated hitter. A starting line-up specifies the players for these positions and the positions in a batting order for the 8 field players and designated hitter. If the designated hitter must be chosen among all the possible field players, how many possible starting line-ups are there.
Answer:
There are 18,162,144,000 possible starting line-ups
Step-by-step explanation:
The order in which the player are chosen is important, as if two player exchange places, we have a new batting order. So we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
Batting order:
9 batters(8 field + the designated hitter) from a set of 15. So
[tex]B = P_{(15,9)} = \frac{15!}{(15-9)!} = 1816214400[/tex]
Pitcher:
1 from a set of 10. So
[tex]P = P_{(10,1)} = \frac{10!}{(10-1)!} = 10[/tex]
Total:
[tex]T = B*P = 1816214400*10 = 18162144000[/tex]
There are 18,162,144,000 possible starting line-ups
What is the area of the figure?
118 in 2
48 in 2
128 in 2
108 in 2
The answer Is D! 108 In 2.
Help anyone please
Giving out brainliest
(T & G) -> (E v D) what does this mean
Answer:
The work done by the electric field in Figure 1 to move a positive charge q from A, the positive plate, higher potential, to B, the negative plate, lower potential, is
W = −ΔPE = −qΔV.
The potential difference between points A and B is
−ΔV = −(VB − VA) = VA − VB = VAB.
Entering this into the expression for work yields W = qVAB.
Work is W = Fd cos θ; here cos θ = 1, since the path is parallel to the field, and so W = Fd. Since F = qE, we see that W = qEd. Substituting this expression for work into the previous equation gives qEd = qVAB.
The charge cancels, and so the voltage between points A and B is seen to be
{
V
AB
=
E
d
E
=
V
AB
d
(uniform E − field only)
Step-by-step explanation:
The relationship between V and E for parallel conducting plates is E=Vd E = V d. From a physicist's point of view, either ΔV or E can be used to describe any charge distribution
What is the inverse of the function f(x) = 2x + 1?
O.h(x) =
h(x) =
1 x + 2 / 2
Oh(x) =
= 5X-2
+x-2
on(x) = -x + 2
We have [tex]y=2x+1[/tex], to find inverse switch y and x then solve for y.
[tex]x=2y+1 \\ x-1=2y \\ y=\frac{x-1}{2}[/tex].
Hope this helps.
Which number in the expression is the CONSTANT?
бу — 5
Aniyah has 10 1/3 feet of ribbon. She wants to cut the ribbon into 1 2/5 size pieces. How many full pieces of ribbon can she cut? helpppp
Answer:
7
Step-by-step explanation:
Because 10 1/3 divided by 1 2/5 would be 7 and something and the question is asking how many full pieces, so just 7
Data on U.S. work-related fatalities by cause follow (The World Almanac, 2012). Cause of Fatality Number of Fatalities Transportation incidents 1795 Assaults and violent acts 837 Contact with objects and equipment 741 Falls 645 Exposure to harmful substances or environments 404 Fires and explosions 113 Assume that a fatality will be randomly chosen from this population. Round your answers to four decimal places. a. What is the probability the fatality resulted from a fall
Answer:
0.1634 = 16.34% probability the fatality resulted from a fall
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, we have that:
1795 + 837 + 741 + 645 + 404 + 113 = 4535 total fatalities.
Of those, 741 from falls.
741/4535 = 0.1634
0.1634 = 16.34% probability the fatality resulted from a fall
Dan used 942 units of electricity from July to October.
The meter reading in July was 32,347 units
Work out the meter reading in October
Answer:
89n
Step-by-step explanation:)
Answer:
33289
Step-by-step explanation:
July reading + Useage
= 32347 + 942 = 33289
what is the distance between
11 degree c and 15 degree c
Answer:
Uhm would it be 4 c?
Step-by-step explanation:
Answer:
4 degree c
Step-by-step explanation:
15-11=4
hello i need help pls
Answer:
1. 3
2. 3
3. 18
Step-by-step explanation:
Answer:
A = 3
B = 3
C = 18
have a nice day!
:)
need help plssssssssssssssssssssssssssssssss
Answer:
29
Step-by-step explanation:
PEMDAS
PARENTHESIS: [3-10]=7
EXPONENTS: 3^3= 27
MULTIPLICATION:8×7=56
DIVISION:NONE
ADDITION:NONE
SUBTRACTING: 56-27=29
ANSWER: 29
Complete the explanation of how you would shade a model to show 2 x 2/3
To model 2 ×2/3 you would shade a model to show 2/3 [Your answer here] times.
A: seven
B: two
C: four
D: Nine
Answer:
B.
Step-by-step explanation:
Help me out with this mathematic question please
Answer:
The answer is 95°!
Step-by-step explanation:
180°-60°-25°= 95°
What is the value of x in the equation 3(2x + 8) = 0? Group of answer choices −8 −4 4 8 please hurry!
Answer:
-4
Step-by-step explanation:
3(2x+8) = 0
Distribute
6x + 24 = 0
24 = -6x + 0
24/-6 = -4
Grace took one of her friends out to lunch. The lunches cost $100 and she paid 9% sales tax. If Grace left a 15% tip on the $100, how much in total did she pay?
Answer:
124
Step-by-step explanation:
100 x .09=9
100 x ,15=15
9 + 15=24
100+24=124
it takes 15 cups of water to fill 1/3 bucket. How much water is needed to fill 1 bucket?
Answer:
45 cups
Step-by-step explanation:
find the LCD for each set of rational expressions.
x/2x + 16 and -4x/3x - 27
please help!! fast!!
4. The__________ is the original figure.
A. image
B. per-image
C. enlargement
D. reduction
Answer:
he is the answer
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Three machines turn out all the products in a factory, with the first machine producing 30% of the products, the second machine 20%, and the third machine 50%. The first machine produces defective products 13% of the time, the second machine 9% of the time and the third machine 9% of the time. What is the probability that a non-defective product came from the second machine
Answer:
0.2027 = 20.27% probability that a non-defective product came from the second machine
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Non-defective product.
Event B: From the second machine.
Probability of a non-defective product:
100-13 = 87% of 30%(first machine)
100-9 = 91% of 20%(second machine)
100-9 = 91% of 50%(third machine).
So
[tex]P(A) = 0.87*0.3 + 0.91*0.2 + 0.91*0.5 = 0.898[/tex]
Non-defective and from the second machine:
91% of 20%. So
[tex]P(A \cap B) = 0.91*0.2 = 0.182[/tex]
What is the probability that a non-defective product came from the second machine
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.182}{0.898} = 0.2027[/tex]
0.2027 = 20.27% probability that a non-defective product came from the second machine
Ava is going to the county fair. The cost of admission is $5.50 and it is $1.50 for each ride. If Ava has $19.00, Write and solve an equation to determine how many rides Ava can ride.
Answer:
5.50 + 1.50x = 19
x = 9
Ava can ride 9 rides.
Step-by-step explanation:
5.50 + 1.50x = 19
-5.50 -5.50
1.50x = 13.50 (divide both sides by 1.50)
x = 9
2(x-5) + 3y + 12 - y
Answer:
2(x+y+11)
Step-by-step explanation:
2(x+5)+3y+12−y
Use the distributive property to multiply 2 by x+5.
2x+10+3y+12−y
Add 10 and 12 to get 22.
2x+22+3y−y
Combine 3y and −y to get 2y.
2x+22+2y
Answer:
2x+22 +2y
Step-by-step explanation:
If $700 is invested in an account that pays 3% compounded annually, the total amount, A(t), in the account after t years is Ant 700(1.03)^t.
Required:
a. Find the average rate of change per year of the total amount in the account for the first four years of the investment (from t= 0 to t= 4).
b. Find the average rate of change per year of the total amount in the account for the second four years of the investment (from t=4 to t=8)
c. Estimate the instantaneous rate of change for t =4.
d. The average rate of change per year of the total amount in the account for the first years of the investment â(from t= 0 to t=4â) is ___________â$
e. The average rate of change per year of the total amount in the account for the second years of the investment â(from t= 0 to t=4â) is_____________ â$
f. The instantaneous rate of change for t=4 is about â$_____________
Answer:
21.96 ; 24.72
Step-by-step explanation:
Given that :
Give the equation:
A(t) = 700(1.03)^t
A.)
Average rate of change over the first 4 years ;
(t=0 to t=4)
At t = 0
A(0) = 700(1.03)^0 = 700
A(1) = 700(1.03)^1 = 721
A(2) = 700(1.03)^2 = 742.63
A(3) = 700(1.03)^3 = 764. 9089
A(4) = 700(1.03)^4 = 787.856167
[(721 - 700) + (742.63 - 721) + (764.9089 - 742.63) + (787.856167 - 764.9089)] / 4
= 87.856167 / 4
= 21.96404175
= 21.96
Over the 2nd 4 years :
A(4) = 700(1.03)^4 = 787.856167
A(5) = 700(1.03)^5 = 811.49185201
A(6) = 700(1.03)^6 = 835.8366075703
A(7) = 700(1.03)^7 = 860.911705797409
A(8) = 700(1.03)^8 = 886.73905697133127
[(811.49185201 - 787.856167) + (835.8366075703 - 811.49185201) + (860.911705797409 - 835.8366075703) + (886.73905697133127 - 860.911705797409)] / 4
= 98.88288997133127 / 4
= 24.72
Please help quick!!
8/5 + 8 ≤ 13
Answer:
Well the answer to the first half of the question is 9.6 so.. 13 would be greater than that. :/
Step-by-step explanation:
Answer:
48/5 <= 13 is always true there are infinitely many solutions
Last year at a certain high school, there were 50 boys on the honor roll and 75 girls on the honor roll. This year, the number of boys on the honor roll increased by 8% and the number of girls on the honor roll increased by 24%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
About 15.3%!
Step-by-step explanation:
ill explain in comments, i hope this helps you out
Answer:
17.6
Step-by-step explanation:
Two students, Alice and Bob, forgot to put their names on their exam papers. The professor knows that Alice does well with probability 0.8, and Bob does well with probability 0.4, independently of each other. What is the probability that exactly one of Alice and Bob does well on the exam
Answer:
[tex]Probability = 0.56[/tex]
Step-by-step explanation:
Represent the probability that Alice does well with P(A), the probability that Bob does well with P(B).
So, we have:
[tex]P(A) = 0.8[/tex]
[tex]P(B) = 0.4[/tex]
Required
Determine the probability that only one of them do well
This event is represented as: (A and B') or (B and A')
Where B' means Bob does not perform well and A' means Alice does not perform well.
And:
[tex]P(B') = 1 - P(B)[/tex]
[tex]P(A') = 1 - P(A)[/tex]
So, the probability becomes:
[tex]Probability = P(A\ and\ B')\ or\ P(B\ and\ A')[/tex]
[tex]Probability = P(A) * P(B')\ +\ P(B)*P(A')[/tex]
[tex]Probability = P(A) * (1-P(B)) +\ P(B)*(1-P(A))[/tex]
[tex]Probability = 0.8 * (1-0.4) +\ 0.4*(1-0.8)[/tex]
[tex]Probability = 0.8 * 0.6 +\ 0.4*0.2[/tex]
[tex]Probability = 0.48 + 0.08[/tex]
[tex]Probability = 0.56[/tex]
Hence, the required probability is 0.56
Suppose 88% of all batteries from a supplier have acceptable voltages. A certain type of flashlight requires two D batteries, and the flashlight will work only if both its batteries have acceptable voltages. Treat all batteries and flashlights as independent of one another. Suppose 20 randomly selected batteries are placed into 10 flashlights. What is the probability that at least 9 of the flashlights function properly
Answer:
0.3036 = 30.36% probability that at least 9 of the flashlights function properly.
Step-by-step explanation:
For each flashlight, there are only two possible outcomes. Either it works, or it does not. Flashlights are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Flashlight works correctly if both its batteries have acceptable voltages:
Each battery has an 88% = 0.88 probability of working correctly(having acceptable voltage), so the probability of the flashlight working correctly is given by:
[tex]p = (0.88)^2 = 0.7744[/tex]
10 flashlights.
This means that [tex]n = 10[/tex]
What is the probability that at least 9 of the flashlights function properly?
This is
[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{10,9}(0.7744)^{9}.(0.2256)^{1} = 0.2260[/tex]
[tex]P(X = 10) = C_{10,10}(0.7744)^{10}.(0.2256)^{0} = 0.0776[/tex]
[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.2260 + 0.0776 = 0.3036[/tex]
0.3036 = 30.36% probability that at least 9 of the flashlights function properly.
1. A wagon wheel has a radius of 4.9 inches. Which of the following is closest to the distance the wagon
travels in two turns of the wheel?
A 31 inches
B 15 inches
C 62 inches
D 75 inches
Answer:
b.
Step-by-step explanation:
(05.05 MC) The length of a rectangle is shown below: On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. The point A is on ordered pair 1, 3, and the point B is on ordered pair negative 3, 3. A straight line joins the points A and B. If the area of the rectangle to be drawn is 20 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle? A. C(−3, −2), D(1, −2) B. C(−3, −1), D(1, −1) C. C(−3, −7), D(1, −7) D. C(−3, −5), D(1, −5)
Answer:
Your answer is C.
Step-by-step explanation:
Have a great day!
Answer:
you need 2 answers to give brainlies so here you go I guess
Help please please please ok
Answer:
6h +210
Step-by-step explanation:
6 x h = 6h
3.5 x 6 = 210