Toby found their mean was \bar x=7
x
ˉ
=7x, with, \bar, on top, equals, 7 years. He thinks the standard deviation is
Answers
The standard deviation is approximately 1.825
The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values. A low standard deviation means that the values tend to be near to the established mean, whereas a large standard deviation shows that the values are distributed throughout a broader range.
The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is equal to the square root of that variable's variance. It is more algebraically straightforward than the average absolute deviation, but being less reliable in actual use.
The standard deviation is calculated by the formula :
\({\displaystyle \sigma={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\mu }\right)^{2}}}}\)
where N= n-1(n=size of sample) , \(\mu\)= mean of the data , \(x_i\)= each data value.
Now the given data for the question are {6,5,9,8}
mean of the data (\(\mu\))=(6+5+9+8)÷4=28÷4=7
Standard deviation:
\({\displaystyle \sigma ={\sqrt{{\frac {(6-7 )^{2}+(5-7 )^{2}+(9-7 )^{2}+(8-7 )^{2}}{N}}}}\)
\({\displaystyle \sigma ={\sqrt{{\frac {(-1 )^{2}+(-2)^{2}+(2)^{2}+(1 )^{2}}{N}}}}\\\)
\({\displaystyle \sigma =\sqrt{\frac{1+4+4+1}{4-1}}\\\)
\({\displaystyle \sigma =\sqrt{\frac{10}{3}}\\\)
\({\displaystyle \sigma =\sqrt{1.333}\)
\({\displaystyle \sigma =1.825\)
The standard deviation is approximately 1.825.
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Related Questions
The length of a rectangle is 12 less than four times the width. The perimeter of the rectangle is 176 cm. What are the dimensions of the rectangle?
Answers
35
28
36
Are the dimensions
Mason bought 16 tickets to a baseball game. The group rate saved him $5.75 per ticket. He paid a total of $296.00 for the tickets. What was the regular price of a ticket to the game
Answers
The regular price of a ticket to the game was $204.00.
We can use algebra to solve the problem. Let x be the regular price of a ticket to the game.
We know that the group rate saved Mason $5.75 per ticket, so the regular price of a ticket is x + $5.75.
We know that Mason bought 16 tickets and paid a total of $296.00, so we can set up the following equation:
x + $5.75 = (x + $5.75) * 16 = 16x + $92
So the regular price of a ticket is x = $296.00 - $92 = $204.00
Therefore, the regular price of a ticket to the game was $204.00.
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0.5 =
Enter your answer in the form of 1/2.
Answers
Answer:
0.5 as a fraction is written as 1/2.
Step-by-step explanation:
PLS HELP!!! 20 POINTS!!!!!
Which of the following is the correct value and interpretation of P(F|B)?
A) P(F|B) = 0.51; given that the student prefers brand B, there is a 0.51 probability that their strongest stroke is freestyle.
B) P(F|B) = 0.51; given that the student’s strongest stroke is freestyle, there is a 0.51 probability that they prefer brand B.
C) P(F|B) = 0.58; given that the student prefers brand B, there is a 0.57 probability that their strongest stroke is freestyle.
D) P(F|B) = 0.58; given that the student’s strongest stroke is freestyle, there is a 0.57 probability that they prefer brand B.
Answers
Answer:
I believe it is: P(F|B) = 0.51; given that the student prefers brand B, there is a 0.51 probability that their strongest stroke is freestyle.
Step-by-step explanation:
26/51=0.509
Round up to 0.51
The conditional order P(A|B) means that given that A is occurring, what's the probability that B occurs. Thus giving me answer A. Given that B is the preferred brand, what's the probability of freestyle being the strongest stroke. 0.51
P(F|B) = 0.51 Given that the student prefers brand B, there is a 0.51 probability that their strongest stroke is freestyle.
What is "applied statics"?In order to create scientific investigations, sample surveys, medical clinical trials, and environmental research, applied statistics uses mathematical principles and techniques. In many businesses, analysis and forecasting are made possible by the application of mathematical models of variation.
In this problem, there are two different values of P(F|B) 0.51 and 0.58 as per the option given below. we will solve both and find the most preferable. Since the Strongest stroke is directly proportional to the P(F|B) so the value of stoke when P(F|B) is 0.58 will be lesser than the value of stoke at 0.51. Hence we will solve this for 0.51
26/51=0.509
Round up to 0.51
Therefore, The conditional order P(A|B) means that given that A is occurring. Thus giving me answer A. Given that B is the preferred brand. the probability of freestyle being the strongest stroke is 0.51.
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100
o
o7
9
In a sale everything is reduced by 15%.
A week later the prices are reduced by another 20%.
The shopkeeper says that all the prices have been reduced by 35%.
5
Show that the
shopkeeper is wrong. Reduce b
educe by ist
by !5
Answers
HELP ME PLZZ I NEED HELP WITH THIS AND MAKE SURE YOU EXPLAIN!!!!!!!!!!!!!!!!
Answers
Answer:
C. 7/9 and 0.7 (with bar notation)
Step-by-step explanation:
The division keeps going with the remainder as 7 and 9 can only go into 70 with a 63 so to show the 7 keeps going you would have to use bar notation above 7.
Which of the following statements about the changing features of the family is not true of todays Commonwealth Caribbean societies?
A) men and women choose their own partners
B) husband and wives usually treat each other as equals
C) parents are becoming more autocratic
D) generally, families have fewer children
Answers
The statement about the changing features of the family that is not true of todays Commonwealth Caribbean societies is C. parents are becoming more autocratic.
How to illustrate the information?It should be noted that nowadays, men and women choose their own partners, husband and wives usually treat each other as equals and generally, families have fewer children
While role changes are often difficult, many positive things can occur as a result. Families may learn to work better together and support one another. Learning new tasks can help children gain confidence. Families may discover that, despite the changes, life can still be enjoyable.
In conclusion, the correct option is C.
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Expand 3(2x-7) - 2(3x+5)
Answers
Answer:
-31
Step-by-step explanation:
Expand 3(2x-7) - 2(3x+5)
Distribute:
3(2x-7)
6x - 21
-2(3x+5)
-6x - 10
Add:
6x - 21
- 6x - 10
- 31
Hope this helps!
Answer:
\(\boxed{\sf{-31}}\)
Step-by-step explanation:
If you want to solve this, you must expand by a distributive property.
Distributive property:
A(B+C)=AB+AC3(2x-7)-2(3x+5)
3(2x-7)
3*2=6
3*7=21
Rewrite the problem.
6x-21
6x-21-2(3x+5)
-2(3x+5)
-2*3=-6
-2*5=10
-6x-10
Rewrite the problem down.
6x-21-6x-10
Combine like terms.
6x-6x-21-10
Add similar into their elements.
6x-6x=0
-21-10
Solve.
Subtract the numbers from left to right.
-21-10=-31
-31
Therefore, the correct answer is -31.I hope this helps you! Let me know if my answer is wrong or not.
Sorry about the last question i forgot to put the picture but i need help cause i don't get it
Answers
Answer:
21:8
Step-by-step explanation:
Given information:
Lori (x) is 8 years old.
In 5 years (x + 5), Philip will be twice Lori's age (y + 5 = 2(x + 5))
The missing value, y, is needed to find the ratio for Lori's and Philip's ages in the present. To find y, solve this equation:
y + 5 = 2(x + 5) First, distribute the 2 into x + 5.
y + 5 = 2x + 10 Next, isolate the variable y by subtracting 5 from both sides.
y = 2x + 5 After that, add in the value of x, 8.
y = 2(8) + 5 Finally, simplify the right side to find Philip's age.
y = 16 + 5
y = 21
Now for the easiest part: The ratio of Philip's age now to Lori's age now.
because 21 is not divisible by any of 8's factors, the current ratio of 21:8 cannot be simplified further.
So, the ratio is 21:8
1. The table shows the relationship between y, the cost to rent a bicycle, and x, the amount of time the bicycle is
rented in hours.
Bicycle Rental Costs
Write a linear equation in slope-intercept form to represent the data shown in this table. Show your work.
Answers
The linear equation in slope-intercept form is y = 10x.
Important information:The table shows the relationship between y, the cost to rent a bicycle, and x, the amount of time the bicycle is rented in hours.Calculation:The linear equation is
\(\frac{x-20}{x-2} = \frac{20-10}{2-1}\)
y = 10x
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the yellow cab company charges a flat fee of $3.50 and an additional $2.50 per mile. the relaxicab company charge $2.30 per mile and a $4.54 fee. at how many miles do the two companies charege the same amount? write a system of equations that computes the cost of the cabs. use for the miles, and for the cost.
Answers
Step-by-step explanation:
Since the initial fee is fixed, we can assume it is a constant and the succeeding mile fee is the variable as it changes for every mile covered.
Let x = distance (mile)
let y = total charge (dollars)
Yellowcab company equation for cost calculation; 3.50 + 2.5x = y
laxicab company equation for cost calculation; 4.54+2.3x = z
the two companies charge the same amount when y = z
; 3.50 + 2.5x = 4.54+2.3x
x = 5.2 miles
COST CALCULATION
;3.50 + 2.5x = ?
if x = 5.2;
; 3.50 + 2.5(5.2) =$16.50
OR
; 4.54+2.3x = ?
; 4.54 + 2.3(5.2) = $16.50
There are
150
150150 students in an eleventh grade high school class. There are
45
4545 students in the soccer team and
35
3535 students in the basketball team. Out of these students, there are
20
2020 who play on both teams.
Let
A
AA be the event that a randomly selected student in the class plays soccer and
B
BB be the event that the student plays basketball. Based on this information, answer the following questions.
What is
P
(
A
)
P(A)P, left parenthesis, A, right parenthesis, the probability that the student plays soccer?
What is
P
(
B
)
P(B)P, left parenthesis, B, right parenthesis, the probability that the student plays basketball?
What is
P
(
A
and
B
)
P(A and B)P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, the probability that the student plays soccer and basketball?
What is
P
(
A
|
B
)
P(A | B)P, left parenthesis, A, start text, space, vertical bar, space, end text, B, right parenthesis, the conditional probability that the student plays soccer given that he or she plays basketball?
Answers
Answer:
P(a)=0.3
P(b)=0.23
P(a&b)=0.13
P(a|b)=0.57
Step-by-step explanation:
Girl can I say this was very hard to read try better next time
By using a venn diagram we can figure out that out of the 150, 45 play soccer, 35 play basketball, 20 play both, 25 play exclusively soccer and 15 play exclusively basketball and 60 students in total play either
Let A be the probability of a student playing soccer and B be the probability of a student playing basketball
P(A)= 45/150
P(B)=35/150
P(A&B)=20/150
P(A|B)= 20/35
Find the equation of the tangent to the curve at the point where x = 1. f(x)=x√1+3x²
Answers
the equation of the tangent to the curve at the point where x = 1 is:
y = 8x - 6
To find the equation of the tangent to the curve at the point where x = 1, we need to determine the slope of the tangent at that point and then use the point-slope form of a line to find the equation.
First, let's find the slope of the tangent. We can do this by finding the derivative of the function f(x) = x√(1 + 3x²) and evaluating it at x = 1.
f(x) = x√(1 + 3x²)
Taking the derivative of f(x) with respect to x:
f'(x) = √(1 + 3x²) + x * (1/2√(1 + 3x²)) * (6x)
Now, we can evaluate f'(x) at x = 1:
f'(1) = √(1 + 3(1)²) + 1 * (1/2√(1 + 3(1)²)) * (6(1))
Simplifying this expression:
f'(1) = √(1 + 3) + (1/2√(1 + 3)) * 6
f'(1) = √4 + (1/2√(4))* 6
f'(1) = 2 + (1/2)(2) * 6
f'(1) = 2 + 1 * 6
f'(1) = 2 + 6
f'(1) = 8
So, the slope of the tangent at x = 1 is 8.
Now that we have the slope, we can use the point-slope form of a line, which is:
y - y₁ = m(x - x₁)
Where:
m is the slope
(x₁, y₁) is the point on the line (x = 1, f(1))
Using the point-slope form, we can write the equation of the tangent:
y - f(1) = 8(x - 1)
Now, substitute the value of f(1) into the equation:
y - f(1) = 8(x - 1)
y - f(1) = 8x - 8
Since we know that f(1) = 1√(1 + 3(1)²), we can substitute it into the equation:
y - √(1 + 3(1)²) = 8x - 8
y - 2 = 8x - 8
y = 8x - 6
Therefore, the equation of the tangent to the curve at the point where x = 1 is:
y = 8x - 6
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The number of bacteria in a refrigerated food product is given by N(T) = 307² - 112T+75,
3
When the food is removed from the refrigerator, the temperature is given by T(t) = 3t+1.7, where t is
the time in hours.
Find the composite function N(T(t)):
N(T(t)) =
Find the time when the bacteria count reaches 20082.
Time Needed ==
hours
Answers
The composite function N(T(t)) = 20082.The time when the bacteria count reaches 20082 is approximately 30.28 hours.
To find the composite function N(T(t)), we need to substitute the expression for T(t) into the function N(T).
Given:
N(T) = 307² - 112T + 75
T(t) = 3t + 1.7
Substituting T(t) into N(T), we get:
N(T(t)) = 307² - 112(3t + 1.7) + 75
Simplifying:
N(T(t)) = 307² - 336t - 190.4 + 75
N(T(t)) = 307² - 336t - 115.4
Now let's find the time when the bacteria count reaches 20082.
N(T(t)) = 20082
307² - 336t - 115.4 = 20082
Taking 115.4 to the other side:
\(307^2\) - 336t = 20082 + 115.4
307² - 336t = 20197.4
336t = 307² - 20197.4
Dividing by 336:
t = (307² - 20197.4) / 336
Calculating the value of t:
t ≈ 30.28
Therefore, the time when the bacteria count reaches 20082 is approximately 30.28 hours.
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which expression is equal to 5√2/√13
1. √65/2
2.√26/13
3.5√25/13
4.5√26/√13
Answers
Answer:
5√26/13
Step-by-step explanation:
5√2/√13 multiply the nominator and denominator by √13 to rationalize the denominator
5√2√13/√13√13 ( √13×√13=13)
5√26/13
there is answer in multiple choice but this is the correct one
Marhall and Vickie are alepeople who earned the ame amount thi week, although Vickie made 6 more ale than Marhall. Marhall earn a bae of $186 plu $15 per ale. Vickie earn a bae of $48 plu $18 per ale. How many ale did Marhall make thi week?
Answers
Marhall made 9 ales this week, earning a base of $186 plus $15 per ale. Vickie earned a base of $48 plus $18 per ale. Since both of them earned the same amount, we can set up the equations
Marhall made 9 ales this week.
Step by explanation
We can use an equation to solve this problem.
Let x = number of ales Marhall made
Marhall's Earnings = 186 + (15 x)
Vickie's Earnings = 48 + (18 x)
Since both of them earned the same amount, we can set up the equations and solve for x:
186 + (15 x) = 48 + (18 x)
15x = 138
x = 9
Therefore, Marhall made 9 ales this week.
Marhall made 9 ales this week, earning a base of $186 plus $15 per ale. Vickie earned a base of $48 plus $18 per ale.
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What is the y-intercept of 10?
Answers
Answer:The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Add 10 10 to both sides of the equation. Using the slope-intercept form, the y-intercept is 10 .
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all fractions. y - 3x = -1
Answers
Answer:
y=3x-1
Step-by-step explanation:
y-3x=-1
y-3x+3x=-1+3x
y=3x-1
Answer:
y=3x-1
Step-by-step explanation:
y-3x=-1
y=3x+(-1)
y=3x-1
The probability distribution for the number of defective items in a random sample is as follows: x: 0 1 2 3 4 p(x) : 1 0.15 13 07 0.55
calculate:
expected value of X = ____
Answers
From the probability distribution for the number of defective items in a random sample, the expected value of X is 2.82.
To calculate the expected value of X, we need to multiply each possible value of X by its corresponding probability and sum them up.
The expected value of X, denoted as E(X) or μ, is calculated using the formula:
E(X) = ∑ (x * p(x))
where x represents each possible value of X and p(x) represents the corresponding probability.
In this case, the probability distribution for X is given as follows:
x: 0 1 2 3 4
p(x): 0.1 0.15 0.13 0.07 0.55
To calculate the expected value, we perform the following calculations:
E(X) = (0 * 0.1) + (1 * 0.15) + (2 * 0.13) + (3 * 0.07) + (4 * 0.55)
E(X) = 0 + 0.15 + 0.26 + 0.21 + 2.2
E(X) = 2.82
The expected value represents the average value or mean of the probability distribution. In this case, it represents the average number of defective items we expect to find in a random sample based on the given probabilities.
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Rectangle ABCD has a width of 8 yards and a length of 20 yards. Rectangle QRST, which is similar to rectangle ABCD, has a length of 40 yards.
Find the scale factor of ABCD to QRST and the perimeter of each rectangle.
Answers
Answer: 16 yards would be your answer
The scale factor of ABCD to QRST is 1:2
The perimeter of rectangles ABCD and QRST are 56 yards and 112 yards respectively.
Rectangle ABCD has a width of 8 yards and a length of 20 yards.
Rectangle QRST is similar to rectangle ABCD.
Rectangle QRST has a length of 40 yards.
Scale factor:Therefore, the scale factor of ABCD to QRST can be calculated as follows:
let
x = width of rectangle QRST
8 / x = 20 / 40
8 / x = 1 / 2
x = 16
The scale factor of ABCD to QRST is 1:2
Perimetersperimeter ABCD = 2(8 + 20) = 56 yards
perimeter QRST = 2(16 + 40) = 112 yards.
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Mr. and Mrs. Steele, deposited $8,000 to open a college savings account for their granddaughter on the day she was born. The account pays 5% simple interest annually. If they made no other deposits or withdrawals since then, how much money would be in the account after 18 years?
Answers
Answer:
see my explantion!!
Step-by-step explanation:
8000*0.05=400
400*18=7200$
Use each of the five digits $2, 4, 6, 7$ and $9$ only once to form a three-digit integer and a two-digit integer which will be multiplied together. What is the three-digit integer that results in the greatest product
Answers
Answer:
The 3 digit number 642 when multiplied 97 gives the greater product.
Step-by-step explanation:
The greatest product will result by multiplying the smaller 3 digit number with the greater two digit number.
The greater three digit number will be 976 and smaller 2 digit number would be 42
Multiplying
976*42 = 40992 ( descending order number)
679 *24= 16,296 ( ascending order number)
If we take the 2 digit number as 97 and 3digit number 642
Then multiplying
642* 97= 62,274 ( descending order number)
246 * 79=19434 ( ascending order number)
The 3 digit number 642 when multiplied 97 gives the greater product.
What is the reciprocal of 5/16
Answers
Answer:
16/5
Step-by-step explanation:
Answer:
16/5
Step-by-step explanation:
When you move the numerator and denominator. (aka. flip)
How can you use the distributive property to rewrite a quadratic expression in order to reveal its factors and zeros
Answers
Answer:
(x-rooot1)(x-root2)
Step-by-step explanation:
a quadratic ax²+bx+c=0 can be factor as those 2 pharanthesis
(x-rooot1) (x-root2)=0
and you can find the roots by making each parenthesis equal to 0 because of the zero product rule
x-root1 = 0, x=root1
x-root2 =0, x=root2
At a grocery store, the price of a watermelon is determined by how many pounds the watermelon weighs. The price of a watermelon that weights 9.3 pounds is $6.51. Write an equation that can be used to determine the price, p, in dollars, of any watermelon based on the number of pounds, w, the watermelon weighs. Explain the process you used to determine the equation.
Answers
The equation that can be used to determine the price, in dollars, of any watermelon based on the number of pounds is p = 0.7w
What is the equation that can be used to determine the price?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the price of a watermelon that weights 9.3 pounds is $6.51, the cost per pound of watermelon will be:
= $6.51 / 9.3
= $0.7
Therefore, the equation is p = (0.7 × w) = 0.7w
where P = price
w = pound of watermelon
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no clue how to do this, someone pls help
Answers
Answer:
6π
Step-by-step explanation:
First we need to find the circumference of the circle. We know that the radius is 4 and the formula is πd or 2πr
Leaving it in terms of pi, the circumference is 8π
Now we need to find the length of the arc.
Since the missing part of the circle is labeled with a right angle, we know that it's exactly 1/4 of the whole circle. That means the arc we need to find is 3/4 of the circumference.
3/4 of 8π is 6π
1. If R = 32 - 11 (OC+2y). then find R when: x=2 and y=4
Answers
The correct equation says to find R = 32 - 11 (X+2y). This gives us the value of -78.
How to solve for the equation belowWe have this
R = 32 - 11 (X+2y)
we have the following values for x and y as 2 and 4 respectively.
What we have to do would be to find the value of R after we have put in these values in the equation.
To do this, we would then have:
R = 32 - 11(2 + 2*4)
R = 32 -11(2+8)
R = 32 - 11 * 10
R = 32 - 110
This would give us the value that says
R = -78
Hence the value of R is given as -78
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1) Find the distance between -49.75 and 31.5 on a number line.
Answers
Answer:
81.25
Step-by-step explanation:
Because you want to know the total distance, calculate how many digits -49.75 is away from 0. It is 49.75 digits away from 0.
Now calculate how many digits 31.5 is away from 0. It is 31.5 digits away from 0.
Finally, add those two distances together so that you know the total distance:
49.75+31.5 = 81.25
Answer:
in the picture
HOPE ITS HELP
hi so the question is, The Expression
\( \frac{4 x}{5} - \frac{2x}{3}\)
is equivalent to which other expression?
A.
\( \frac{x}{2} \)
B.
\( \frac{x}{5} \)
C.
\( \frac{x}{15} \)
D.
\( \frac{2x}{15} \)
Answers
There are some bacteria in a dish. Every hour, each bacterium splits into 3 bacteria.
1. This diagram shows a bacterium in hour 0 and then hour 1. Draw what happens in
hours 2 and 3.
Answers
There are some bacteria in a dish. Every hour, each bacterium splits into 3 bacteria. Hence, in total after 3 hours, we have 27 bacteria.
Bacteria are ubiquitous, largely free-living creatures that frequently only have one biological cell. They make up a significant portion of the prokaryotic microbial kingdom. Bacteria, which tend to be a few micrometres long and were among the initial organisms that appeared on Earth, are found in the majority of its habitats.
n = the number of bacteria at a given hour
at zero hour=1 bacteria.
1 bacteria after an hour is split in to 3 bacteria.
n(1) = 3
n(2) = 3 x 3 = 9 bacteria
n(3) = 9 x 3 = 27 bacteria
Hence, in total after 3 hours, we have 27 bacteria
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