The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the standard deviation. Round your answer to one decimal place. Waiting Time (Minutes) Number of Customer 0-3 13 4-7 13 8-11 10 12-15 11 16-19 0 20-23 3
Answers
The standard deviation of the frequency distribution is 5.54
How to determine standard deviation?The table of values is given as:
x f(x)
0-3 13
4-7 13
8-11 10
12-15 11
16-19 0
20-23 3
Rewrite the table by calculating the class midpoints:
x f(x)
1.5 13
5.5 13
9.5 10
13.5 11
17.5 0
21.5 3
Start by calculating the mean using:
\(\bar x = \frac{\sum fx}{\sum f}\)
This gives
\(\bar x = \frac{1.5 * 13 + 5.5 * 13 + 9.5 * 10 + 13.5 * 11 + 17.5 * 0 + 21.5 * 3}{13 + 13 + 10 + 11 + 0 +3}\)
Evaluate
\(\bar x = 7.98\)
The standard deviation is then calculated as:
\(\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f }}\)
So, we have:
\(\sigma= \sqrt{\frac{13 * (1.5 - 7.98)^2 + 13 * (5.5 - 7.98)^2 + (9.5 - 7.98)^2 * 10 + (13.5 - 7.98)^2 * 11 + (17.5 - 7.98)^2 * 0 + (21.5 - 7.98)^2 * 3}{13 + 13 + 10 + 11 + 0 +3}}\)
Evaluate
\(\sigma= \sqrt{30.6496}\)
Solve
\(\sigma= 5.54\)
Hence, the standard deviation is 5.54
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Related Questions
48% as its simplest fraction
Answers
Answer:
12/25
Step-by-step explanation:
Percent means out of 100
48% means 48/100
Divide top and bottom by 4
12/25
48/4=12 and 100/4=25, so 12/25.
g the volume of a cube is increase at a rate of 5 cm^3/min. how fast is the surface area increasing when the lenght of an edge is 16 cm
Answers
Step-by-step explanation:
the volume of the cube at the beginning is
edge³ = 16³ = 4096 cm³
after 1 minute it is 4101 cm³
that means the edge is then
cubic root(4101) = 16.00650777... cm
the surface area of a cube is
6×edge²
at the beginning it was
6×16² = 1536 cm²
after 1 minute (and the increased volume) it is
6×16.00650777...² = 1,537.249746... cm²
at that moment the surface area is increasing at
1.249745825... cm²/ minute
For a trip to the beach Kelly drove for 5/6 hour and Joshua drove 2/5 hour estimate how much longer Kelly drove than Joshua.
Answers
Step-by-step explanation: You would get them to the same denominator first which is 30. 5/6 becomes 25/30 and 2/5 becomes 12/30. 25 minus 12 is 13 over 30.
which go's to which.................................
Answers
the matches are
-2(2x+5) ≤ -7(x+4) x<=-6
4x-3x-1 x<=-1
5(x-3)9(x+1) x>=-6
3(x-4)+5 2x-9 x>=-2
What is inequality?Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.
Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.
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The correct matching of the inequalities can be shown from the calculations below
What is inequality?
Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.
Using the principle of inequalities we have;
1) -2(2x + 5) ≤ - 7(x + 4)
-4x -10 ≤ -7x -28
-4x +7x ≤ -28 + 10
3x ≤ -18
x ≤ -6
2) 4x - 6/2 ≥ 3x - 1
4x - 6 ≥ 6x - 2
4x - 6x ≥ -2 + 6
-2x ≥ 4
x ≤ -2
3) 5(x - 3) ≤ 9(x + 1)
5x - 15 ≤ 9x + 9
5x - 9x ≤ 9 + 15
-4x ≤ 24
x ≥ -6
4) 3(x - 4) + 5 ≥ 2x - 9
3x - 12 + 5≥ 2x - 9
3x - 2x ≥ -9 + 12 -5
x ≥ -2
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Twenty people are put into an insurance pool. Of these twenty people, • 12 people each have expected payouts of $4,500 per year. 5 people each have expected payout of $12,300 per year. • 2 people each have expected payouts of $20,800 per year. • 1 person has an expected payout of $30,900 per year. How much is the average expected payout for each member of the group of twenty? Average Expected Payout is $
Answers
Answer:
the average payout should be $157,100
hope this helps <3
write an equation of the given line that passes through the given point and has the given slope m
(5,1);m=2
Answers
Answer:
y = 2x - 9
Step-by-step explanation:
Use slope intercept form, y = mx + b
Plug in the slope, x, and y, then solve for b:
y = mx + b
1 = 2(5) + b
1 = 10 + b
-9 = b
Then, plug in b and the slope into y = mx + b
y = mx + b
y = 2x - 9
So, the equation of the line is y = 2x - 9
Answer:
Step-by-step explanation:
y=mx+b, m=2
y=2x+b, using point (5,1)
1=2(5)+b
b=-9
y=2x-9
Is the relation in the problem in the image a function? explain i will mar you brainliest
Answers
Because it has a domain and range
HELP ASAP!!!!!!!
Which expression is equivalent to −5 + 8 − 6x − 8x?
1.) 14x + 13
2.)-14x - 3
3.)-14x + 3
4.)-14x + 13
Answers
The expression 3-14x is equivalent to -5+8-6x-8x.
The phrase has the same meaning as,
=-5+8-6x-8x
=(3)-(14x)
=3-14x
Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known variable expression. Let's use the equation 5x + 7 as an example. Thus, 5x + 7 is an illustration of an algebraic expression.
There are three primary categories of algebraic expressions, including: Numeral Expression. Binary Expression of a polynomial.
Properties:
Equivalence Property.Associative Quality.Discretionary PropertyProperty of identity.Contrary Property.Hence, the expression 3-14x is equivalent to -5+8-6x-8x.
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Answer: -14x + 13
Step-by-step explanation:
the drawing below shows an above ground swimming pool in the shape of a cylinder with a radius of r feet and a height of 1/3 feet. of the water level is x feet from the top of the pool, which expression best represents the volume of water in this pool in cubic feet?
Answers
The expression that best represents the volume of water in this pool in cubic feet is V = πr^2(1/3 - x), where V represents the volume in cubic feet, r represents the radius in feet, x represents the distance in feet from the top of the pool to the water level, and π is the mathematical constant pi.
Based on the information provided, we can determine the volume of the water in the above-ground swimming pool.
First, we know that the pool is in the shape of a cylinder with a radius of r feet and a height of 1/3 feet. To find the volume of the cylinder, we use the formula:
Volume = π * r^2 * h
In this case, h is the actual height of the water, which is (1/3 - x) feet, as the water level is x feet from the top of the pool.
Now, we can plug in the values into the formula:
Volume = π * r^2 * (1/3 - x)
This expression represents the volume of water in the swimming pool in cubic feet.
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The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 5 cm and the width is 4 cm, how fast is the area of the rectangle increasing
Answers
Let us set up the following variables:
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
l
Length of Rectangle (cm)
w
Width of Rectangle (cm)
A
Area of Rectangle (
c
m
2
)
t
Time (s)
We are told that:
d
l
d
t
=
8
cm/s (const), and,
d
w
d
t
=
3
cm/s (const)
The Area of the rectangle is:
A
=
l
w
Differentiating wrt
t
(using the product rule) we get;
d
A
d
t
=
(
l
)
(
d
w
d
t
)
+
(
d
l
d
t
)
(
w
)
∴
d
A
d
t
=
3
l
+
8
w
So when
l
=
20
and
w
=
10
⇒
d
A
d
t
=
3
⋅
20
+
8
⋅
10
∴
d
A
d
t
=
60
+
80
∴
d
A
d
t
=
140
cm
2
/
s
Given that f(x)=3x-6 and h(x)=x^2-3x-4 . Evaluate the following .
f(h(2))
Answers
Answer:
Step-by-step explanation:
The way I understand (remember) the problem is....
you want to evaluate h(x) by substituting 2 in for x's
then substitute the value for h(2) into f(x) to get the answer
evalute f(h(2)) by following the parentheses
h(x) = x² - 3x - 4 evaluate when x = 2
h(2) = 2² - 3(2) - 4
= 4 - 6 - 4
h(2) = -6 so now -6 is the new x in the f(x) equation
f(x) = 3x - 6
f(-6) = 3(-6) - 6
= -18 - 6
= -24
so f(h(2)) = -24
In a survey of 2,800 people who owned a certain type of car, 840 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answers
Answer:
30% of people surveyed were satisfied with the car.
Step-by-step explanation:
We are given:
Total participants in survey= 2800
People satisfied with car = 840
We need to find percent of the people surveyed were satisfied with the car.
The formula used is: \(\frac{People \ satisfied \ with \ car}{Total \ participants \ in \ survey} \times 100\)
\(=\frac{840}{2800}\times 100\\=30\%\)
So, 30% of people surveyed were satisfied with the car.
One positive integer is 1 greater than 3 times another positive integer. If the product of the two integers is 154, then what is the sum of the two integers?
Answers
Answer:
29
Step-by-step explanation:
Let the smaller integer be x.
The other integer is 1 greater than 3 times x, or 3x + 1.
The product is 154.
x(3x + 1) = 154
3x^2 + x - 154 = 0
157 = 2 * 7 * 11
14 * 11 = 154
22 * 7 = 154
(3x + 22)(x - 7) = 0
3x + 22 = 0 or x - 7 = 0
3x = -22 or x = 7
x = -22/3 or x = 7
-22/3 is not a positive integer, so we discard that solution.
The smaller integer is 7.
3x + 1 = 3(7) + 1 = 22
The greater integer is 22.
The sum of the integers is 7 + 22 = 29
Answer: 29
Step-by-step explanation:
Stars and Strikes offers a Sunday special to bow. Each game costs $2.50, and the
shoe rental is $2. You spent $14.50 total. How many games did you bowi?"
Your answer
Answers
Answer:
5 games :)
. .
Answer:
4 games
Step-by-step explanation:
You take the two given numbers and add them together, which is 4.50.
Then you take 10 and divide it by 2.50 which gets you 4
4 GAMES
Lindsey is working really hard to improve her grade. on her first quiz she scored 67 point, on her second she scored 71, and on her third she scored 75. her scores continue to increase at the same rate. write a recursive and explicit formula for this geometric sequence.
Answers
The recursive formula for Lindsey's scores is aₙ = aₙ₋₁ \(\times\) r, and the explicit formula is aₙ \(= 67 \times r^{(n-1).\)
To find the recursive and explicit formulas for the given geometric sequence, let's analyze the pattern of Lindsey's scores.
From the given information, we can observe that Lindsey's scores are increasing at the same rate.
This suggests that the scores form a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio.
Let's denote the first term as a₁ = 67 and the common ratio as r.
Recursive Formula:
In a geometric sequence, the recursive formula is used to find each term based on the previous term. In this case, we can write the recursive formula as:
aₙ = aₙ₋₁ \(\times\) r
For Lindsey's scores, the recursive formula would be:
aₙ = aₙ₋₁ \(\times\) r
Explicit Formula:
The explicit formula is used to directly calculate any term of a geometric sequence without the need to calculate the previous terms.
The explicit formula for a geometric sequence is:
aₙ = a₁ \(\times r^{(n-1)\)
For Lindsey's scores, the explicit formula would be:
aₙ \(= 67 \times r^{(n-1)\)
In both formulas, 'aₙ' represents the nth term of the sequence, 'aₙ₋₁' represents the previous term, 'a₁' represents the first term, 'r' represents the common ratio, and 'n' represents the term number.
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Right triangle JKL is shown below.
What is the measure of
nearest degree.
Answers
Answer:
Step-by-step explanation:
Hypotenus=6
Adjacent=4
H and A
Cos x degrees= A divided by H
4 divided by 6=0.666666666
cos inverse(0.6666666666666666)
=48.2
=48
Raul sells fancy new TVs. They cost $600. He sells the TV for $900. What is his percent markup? show your work
Answers
Answer:
His percent markup is 150%
Step-by-step explanation:
Solve the equation for x
√√x+5-3-4
Ox=2
Ox=12
Ox=44
Ox=53
help!!
Answers
Hence, OPTION (C) is your answer: X = 44
Step-by-step explanation:
SOLVE FOR X:√x + 5 - 3 = 4
Isolate√x + 5 = 3 + 4
√x + 5 = 7
Squared Both Sides:(√x + 5)2 = (7)2
x + 5 = 49
Rearranged:x - 44 = 0
+44 = 44
X = 44
Add 44 on both sides:Now we conclude!Hence, X = 44
Draw The conclusion: CheckEquation: √x + 5 = 7
Now we Plug in 44 for x√(44) + 5 = 7
Now Simplify√49 = 7
Conclusion checks Solution is:Hence, x = 44
I hope this helps!
Use interval notation to represent the set of numbers-7 ≤x≤ 3.
Answers
Answer:
[ - 7, 3 ]
Step-by-step explanation:
note that the ≤ symbol means that x can equal the end values, thus use a bracket [ ] to show this
- 7 ≤ x ≤ 3 is { - 7, 3 ] in interval notation
the country of transylvania contains 2.3 million people (vampires not included) and covers 800,000 square miles. in the year after the last census, the crude birth rate was 48 out of 1000 and the crude death rate was 47 out of 1000. 1. what is the population growth rate (r)? 2. in how many years will the population of transylvania double?
Answers
In 700 years the population of Transylvania will double
What is growth rate ?
the typical annual rate of population change during a particular period for a certain nation, region, or geographic area. In most cases, a factor of 100 is used to describe the ratio between the annual growth in population size and the total population for the year.
Growth rate equals Absolute Change divided by Previous Value. Calculate the percentage of change: Percent of change = Growth rate x 100 is the formula that may be used to calculate the percent of change.
To calculate in how many years the population of Transylvania double
= 70 / 0.1
= 700 years
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Can someone please help me out with these two problems
Answers
The solution of the functions are as follows;
6. f(-9) = 31
7. g(-7) = 15
8. p(5) = 72
9. t = 8
How to solve functions?A function relates an input to an output. Function relates independent variables and dependent variables.
Therefore, let's solve the following function.
f(x) = -5x - 14
g(x) = -x² - 9x + 1
Hence,
6.
f(-9) = -5(-9) - 14
f(-9) = 45 - 14
f(-9) = 31
7.
g(-7) = -(-7)² - 9(-7) + 1
g(-7) = - 49 + 63 + 1
g(-7) = 14 + 1
g(-7) = 15
p(t) = 97 - t²
Hence,
8.
p(5) = 97 - 5²
p(5) = 97 - 25
p(5) = 72
9.
p(t) = 33
let's find t
33 = 97 - t²
33 - 97 = - t²
-64 = - t²
t² = 64
t = √64
t = 8
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= f(x) g(x) { x + 5 g x + 7 = 8 6 4 2 -8 -6 -4 -2 1-24 Clear All Draw: For what value of x is f(x) = g(x)?
Answers
The quetion provides two functions, that is f(x) and g(x).
For what value of x is f(x) = g(x)
We can solve this by simply equating both functions, as shown below;
\(\begin{gathered} f(x)=\frac{2}{3}x+5 \\ g(x)=\frac{4}{3}x+7 \\ f(x)=g(x)\text{ now becomes;} \\ \frac{2}{3}x+5=\frac{4}{3}x+7 \\ \text{Collect all like terms and we'll have} \\ \frac{2}{3}x-\frac{4}{3}x=7-5 \\ \frac{2x-4x}{3}=2 \\ -\frac{2x}{3}=2 \\ \text{Cross multiply and we'll have} \\ -x=\frac{2\times3}{2} \\ -x=3 \\ \text{Multiply both sides by -1 and we'll have} \\ -x(-1)=3(-1) \\ x=-3 \end{gathered}\)The answer is, when x = 3
**Note**
Thi can also be solved graphically and at the point where the graph of both function intersect, we'll have our answer. The graphs of f(x) and g(x) is shown below;
Note that the blue line represents
\(f(x)=\frac{2}{3}x+5\)The green line represents
\(g(x)=\frac{4}{3}x+7\)Observe carefully that both graphs intersect at the point -3.
Therefore, the value of x that makes f(x) = g(x) is -3
Massa says that 540 ÷ 6 = 9. Is he right? Explain how you know using an equation.
Answers
Both sides of the equation are not equal, therefore, Massa was wrong.
How to Evaluate an Equation?For an equation to be correct, the values on both sides of the equation must be equal and balance.
Given the expression, 540 ÷ 6 = 9, 540 divided by 6 is 90. 90 is not equal to 9.
Thus, the value on the both sides are not balanced, therefore, Massa is incorrect.
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Sarah loves to skateboard. She currently has 10 state boards. Write an equation to represent the number of skateboards, y, she will have in x years if she gets 3 new skateboards each year.
Answers
Answer:
Step-by-step explanation:
y = 10+3x
2/5 of a kiddy pool was filled with water. After pouring out 5/7
of the amount of water in the pool 62 liters of water was needed to fill the pool completely. Find
the amount of water needed to fill up the empty
pool.
Answers
Answer:
The question is asking what is the volume of water in the full pool. It is 70 liters.
Step-by-step explanation:
Let P represent the volume of a full pool.
"2/5 of a kiddy pool was filled with water" can be written as:
(2/5)P.
"After pouring out 5/7 of the amount of [I assume from the 2/5P] water in the pool" can be written as:
(2/7)(2/5)P, or (4/35)P [This represents the amount of water remaining in the pool after the above shenanigans.]
The we are told that when 62 liters are added back to the pool, it is full. That can be written as:
62 + (4/35)P = P [Add 62 liters to what was remaining. ((4/35)P), and we'll have P, a full pool, for a cool fool. [sorry]
62 = (31/35)P
P = 62(35/31)
P = 70 liters
The possible number of ways a vector can be decomposed into components from W and W perpendicular is ... a. none. b. one. c. infinitely many
Answers
C). Infinitely many. option is correct answer.
The possible number of ways a vector can be decomposed into components from W and W perpendicular is Infinitely many ways.
The possible number of ways a vector can be decomposed into components from W and W perpendicular depends on the dimensions of the vector space. In a two-dimensional vector space, there is only one way to decompose a vector into components from W and W perpendicular. This is because any vector in the plane can be uniquely represented as the sum of a vector in W and a vector in W perpendicular.
However, in a three-dimensional vector space, there are infinitely many ways to decompose a vector into components from W and W perpendicular. This is because W and W perpendicular are orthogonal complements of each other, meaning that any vector in the space can be expressed as the sum of a vector in W and a vector in W perpendicular in infinitely many ways.
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22.
Makes s the subject
\( \sqrt{p} \: is \: equals \: to \: \sqrt[r]{w \: - as ^{2}}\)
Answers
Step-by-step explanation:
\( \sqrt{p} = \sqrt[r]{w - {as}^{2} } \)
Find raise each side of the expression to the power of r
That's
\(( \sqrt{p} )^{r} = (\sqrt[r]{w - {as}^{2} } ) ^{r} \)we have
\(( \sqrt{p} )^{r} = w - {as}^{2} \)Send w to the left of the equation
\(( \sqrt{p} )^{r} - w = -{as}^{2} \)Divide both sides by - a
We have
\( {s}^{2} = -\frac{( \sqrt{p} )^{r} - w}{a} \)Find the square root of both sides
We have the final answer as
\(s = \sqrt{ -\frac{( \sqrt{p} )^{r} - w }{a} } \)Hope this helps you
Graph the function.
h(x) = -1/5x^2+2x
Answers
Answer:
Hello there I would love to assist but could you give me a little more info I think I know the answer but I want to make sure I got it 100% correct unless you cant give me more info ill just tell you what I think it is but if u can give me more info before I give u the answer to make sure its correct would be appreciated
Step-by-step explanation:
A bond yleided a real rate... A bond yieded a real rite of return of 3.87 percent for o time period when the infition rate was 2.75 percent. What was the actuai nominal rate of return?
8.28%
87.58%
7.77%
36%
6.77%
Answers
The actual nominal rate of return is approximately 6.68%. None of the provided answer options exactly match this value, but the closest option is 6.77%.
To calculate the actual nominal rate of return, we use the Fisher equation:
Nominal Rate = (1 + Real Rate) * (1 + Inflation Rate) - 1
Given:
Real Rate = 3.87% (0.0387 as a decimal)
Inflation Rate = 2.75% (0.0275 as a decimal)
Now, let's plug in the values:
Nominal Rate = (1 + 0.0387) * (1 + 0.0275) - 1
Nominal Rate = 1.0387 * 1.0275 - 1
Nominal Rate = 1.0668 - 1
Nominal Rate = 0.0668 or 6.68% (rounded to two decimal places)
So, the actual nominal rate of return is approximately 6.68%. None of the provided answer options exactly match this value, but the closest option is 6.77%.
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pls answer i need help
Answers
Answer:
the first one is 2/4 and 3/6
the second one is 4/6 and 6/8 and the equation is
3/4 times 4/6 = .5
Step-by-step explanation: