The age of accountant is more variable than salary.
What is standard deviation ?Standard deviation is the square of difference between the sets of data and mean.
Comparison for variation of data can be determined by coefficient of variation (C.V).
We know C.V = [tex]\frac{\sigma}{|\overline{x|}}[/tex] × 100.
First we are determining C.V for ages.
Where [tex]\sigma[/tex] = standard deviation and [tex]|\overline{x}|[/tex] = arithmetic mean or average.
∴ C.V for ages, where [tex]\sigma[/tex] = 4 and [tex]|\overline{x}|[/tex] = 25 years is
C.V = [tex]\frac{4}{25}[/tex] × 100.
C.V = 16.
[tex]C.V_a_g_e[/tex] = 16%.
Now C.V for salary,
where [tex]\sigma[/tex] = 4500 and [tex]|\overline{x}|[/tex] = 30500.
C.V = [tex]\frac{4500}{30500}[/tex] × 100.
C.V = [tex]\frac{4500}{305}[/tex].
[tex]C.V_s_a_l_a_r_y =[/tex] 14.75 %.
So, the coefficient of variation of age is more than that of salary.
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Solve 2|x| = 3
{-3/2, 3/2}
{-1, 1}
{-2/3, 2/3}
Answer:
{-3/2, 3/2}
Step-by-step explanation:
Let's solve your equation step-by-step.
2(|x|)=3
Step 1: Divide both sides by 2.
2(|x|)/2 = 3/2
|x|= 3/2
Step 2: Solve Absolute Value.
|x|= 3/2
We know either x= 3/2 or x=−3/2
x=3/2
(Possibility 1)
x=−3/2
(Possibility 2)
a cheetah that is running 90 feet per second is running 120 feet behind an antelope that is running 60 feet per second. How long does it take for the cheetah to run up to the antelope? PLS FINISH ASAP
Answer: 4 seconds
Step-by-step explanation:
c=cheetah. a=antelope
a=c+120
c/90=a/60
c/90=(c+120)/60
60*c/90=60*(c+120)/60
6*c/9=c+120
2c/3=c+120
(2c/3=c+120)*3 ==> multiply the equation by 3 to get rid of fractions
2c=3c+360
2c-3c=3c-3c+360
-c=360
c=-360 feet==> position of cheetah before catching up to the antelope. This means that the cheetah needs to travel 360 feet before reaching 0 ft when it catches the antelope.
360 feet * 1 second/90 feet=
360*1/90=
360/90=4 seconds
Y² = 64 ? What is the solution of this equation it could possibly be more that one answer
Answer: Y = -8 or Y = 8
Step-by-step explanation:
Y² = 64
Y = -8 or Y = 8 ==> yes there is more than one answer
A baseball coach spent $118.25 on 11 pizzas. Estimate ate the cost of each pizza using numbers with one nonzero digit. Then find the exact cost per pizza. Show all work
The baseball coach bought each pizza at an approximate cost of $ 10 or an exact cost of $ 10.75.
What is are the approximate and exact cost of each pizza bought by a baseball coach?
In this problem we know that a baseball coach spends a total of $ 118.25 on buying 11 pizzas. First, we need to estimate the amount of money spent per each pizza bought, which is found by means of multiplication tables and the supposition of truncation, that is, finding the maximum integer less than or equal to the real total cost.
By direct inspection we find that 10 times the 11 pizzas is equal to $ 110, which is the maximum integer less than or equal to the real total cost. Then, we estimate a cost of $ 10 per each pizza bought. Second, the exact unit cost is found by dividing the total by the number of pizzas:
c = $ 118.25 / 11
c = $ 10.75
In a nutshell, the baseball coach bought each pizza at an approximate cost of $ 10 or an exact cost of $ 10.75.
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simplify (7-1 over 4 square root of 16) ^2 +2-5^2 and REALLY ANSWER IT YOU WILL GET BRAINLEST
Answer:
13
Step-by-step explanation:
Simplify the following:
(7 - (sqrt(16))/4)^2 + 2 - 5^2
sqrt(16) = sqrt(2^4) = 2^2:
(7 - (2^2)/4)^2 + 2 - 5^2
2^2 = 4:
(7 - 4/4)^2 + 2 - 5^2
(-4)/4 = 4/4×-1 = -1:
(-1 + 7)^2 + 2 - 5^2
7 - 1 = 6:
6^2 + 2 - 5^2
5^2 = 25:
6^2 + 2 - 25
6^2 = 36:
36 + 2 - 25
36 + 2 - 25 = 13:
Answer: 13
Factor x^4y^2+x^3y^3
Answer: x^3y^2(x+y)
Step-by-step explanation:
x^4y^2+x^3y^3=
x*(x^3y^2)+(x^3y^2)*y=x^3y^2(x+y)
For a single randomly selected steel rod, find the probability that the length is between 213.3-cm and 213.7-cm.
Answer: probably like 1.8%
Step-by-step explanation:
mars has a maximum temperature of "-7°c" at the equator and a minimum temperature of "-133" °c at the winter pole. write an inequality that describes the possible temperatures on mars.
The inequality that describes the possible temperatures on Mars is
-133°c ≤T≤ -7°c .
What is inequality ?Inequality compares two values by if they are less than or greater than each other.
According to the given question Mars has a maximum temperature of -7°c at the equator and a minimum temperature of -133°c at the winter pole.
We have to write an inequality that describes the possible temperatures on Mars.
Let us denote all the possible range of temperatures by T,
∴ T is less or equal to the maximum temperature and T is greater than or equal to the minimum temperature.
So, -133°c ≤T≤ -7°c .
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On which interval(s) is the function f(x) = x^3+3x^2−4x−12 increasing?
The interval at which the function x³ + 3x² - 4x - 12 increases is
x ∈ (- ∞, - 2.5) ∪ (0.5, ∞).
We have,
x³ + 3x² - 4x - 12
We need to draw a graph to see at which interval the graph is increasing.
The graph is given below.
We see that the graph is increasing from x = -∞ to x = -2.5 and from x = -2.5 it decreases till x = 0.5 and again from x = 0.5 it increases to x = ∞.
So we can write the interval as:
x ∈ (- ∞, - 2.5) and x ∈ (0.5, ∞)
We can write it as one single interval as:
S = (- ∞, - 2.5) ∪ (0.5, ∞)
Thus the interval at which the function x³ + 3x² - 4x - 12 increases is
x ∈ (- ∞, - 2.5) ∪ (0.5, ∞).
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22647 inches to miles, please show work
Answer: 0.3574 miles
Step-by-step explanation:
22647 inches = 0.3574 miles
() Listen
Which expressions of the division of integers will result in a rational number?
Select all that apply.
-5/7
0/6
4/0
-2/0
Reason:
A rational number is a fraction of any two integers, as long as the denominator is nonzero. This applies to the first two answer choices.
Choices C and D are undefined because of the 0 in the denominator. You cannot divide by zero. This rules out the last two choices.
How can you find the reciprocal of 0.375? Select all the correct methods.
A Solve the equation 0.375x=1
B. Solve the equation 0.375+X=1,
C. Divide 1 by 0.375.
D. Solve the equation 0.375x=-1.
OE. Divide 0.375 by (1-0.375)
The reciprocal of 0.375 is gotten by Dividing 1 by 0.375 and Solving the equation 0.375x = 1
What is reciprocal?The reciprocal of a number is the multiplicative inverse of that number. For a number x, the reciprocal is x⁻¹
Hence, the reciprocal of 0.375 is:
a) Dividing 1 by 0.375
b) Solving the equation 0.375x = 1
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5. Kerry McCarthy is a news traffic reporter with an annual gross
pay of $44,500. He is single and is paid on a monthly basis.
How much is withheld monthly for state taxes?
$3,708.33 is withheld monthly for state taxes.
Some states have a graduated income tax that involves a different tax rate for each of several levels of income. The tax rate increases as income increases.
Tax Withheld per Pay Period = Annual Tax Withheld/ Number of Pay Periods per Year
Here, we are given that Kerry McCarthy is a news traffic reporter with an annual gross pay of $44,500.
Thus, the Annual Tax Withheld = $44,500.
He is paid on a monthly basis ⇒ Number of Pay Periods per Year = 12
Hence, we get-
Tax Withheld per Pay Period = 44,500/ 12
= 3,708.33
Thus $3,708.33 is withheld monthly for state taxes.
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Taylor and Alex are looking for a daycare for their child. They want to make sure the daycare is midway between their jobs. Taylor works at the Rogers Middle School located at (4, -5), and Alex works at St. Philip's located at (2, 5). Where should the daycare be located?
Step-by-step explanation:
(5 ,_4) it the location this is the answer
7x 1 3/5
simplest formm
Answer:
56/5 or 11 1/5
Step-by-step explanation:
Convert 1 3/5 to an improper fraction
1 3/5 = (1 x 5 + 3)/5 = (5 + 3)/5 = 8/5
7 x 1 3/5 = 7 x 8/5 = 56/5
In mixed fraction, 56/5 = 11 1/5
Find the average rate of change of
g(x)=-2x^3+5 from z=-4 to x=3
The average rate of change of the function from x == -4 to x = 3 is calculated as: -26.
How to Determine the Average Rate of Change of a Function?The formula for determining the average rate of change across a given interval of a function is expressed as:
Average rate of change = g(b) - g(a)/b - a.
Given the function, g(x) = -2x³ + 5 to find the average rate of change from x = -4 to x = 3, do the following:
a = -4
g(a) = g(-4) = -2(-4)³ + 5 = -2(-64) + 5 = 128 + 5 = 133
b = 3
g(b) = g(3) = -2(3)³ + 5 = -2(27) + 5 = -54 + 5 = -49
Substitute the values into g(b) - g(a)/b - a:
Average rate of change = (-49 - 133)/(3 - (-4))
Average rate of change = -182/7
Average rate of change = -26
Thus, the average rate of change of the function from x == -4 to x = 3 is calculated as: -26.
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Jakob received a $1,000-a-year raise in January, sold stocks in March for $6,000 that were originally purchased for $4,000, and in July had a $100 monthly
increase in mortgage payments on his adjustable rate mortgage. The increased mortgage payment started in July and was in effect for the remainder of the year.
What was the total impact on Jakob's cash flow for the year?
|
A. $5,400
B. $7,600
C. $6,400
D. $1,000
The total impact on Jakob's cash flow for the year is C. $6,400.
How to calculate the value?It should be noted that Jakob received a $1,000-a-year raise in January, sold stocks in March for $6,000 that were originally purchased for $4,000.
The impact will be:
= Raise + Sale of stock - Mortgage
= 1000 + 6000 - 600
= 6400
Therefore, the correct option is C
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branlyueer099799893
3 minutes ago
Mathematics
College
ANSWER RIGHT AWAY PLEASE!
question one: simply the exponents. (show your work)
- 21^0 = ?
- (2/3)^-2 = ?
question two: Solve the problem. (leave your answer as a base number with an exponent and show your work)
- 4^6 / 4^2 = ?
question three: Convert the number into numerical form. (show your work)
- 8.723 x 10^-10 = ?
question four: Solve the problem. (leave your answer in scientific notion and show your work)
- 5.1 x 10^8 - 2.3 x 10^3 = ?
- 6 x 10^5 x 1.1 x 10^7 = ?
PLEASE ANSWER I WILL GIVE 50 POINTS TO ANYONE WHO ANSWERS AND MARK BRAINLIEST AT LEAST ANSWER THE ONES YOU KNOW
Avery is renting a car and needs to compare the prices of the two car rental companies. Hertz charges $42 per day and an additional $32 in service charges. Enterprise charges $46 per day and an additional $24 in service changes.
Part A: Write an equations for EACH company that represents the total charges for renting a car for a certain number of days. For both questions (one for Hertz and one for Enterprise), define the variable used.
Part B: Use the equations you made in Part A. Which company charges more for renting a car for 6 days? Show your work and justify your answer.
Part C: If Avery decides to rent the car for only 4 days, which company is less expensive? How much money will Avery save? Show your work and explain your reasoning.
The total cost functions are:
total charges for Hertz=32+42x
total charges for Enterprise=24+46x
What does the total rental cost of each company entails?
The total rental cost of each company consists the fixed service charges and the daily charge which can be multiplied by the total of number of days of rental to determine total charges overall.
Hertz:
total charges=32+42x
when x=6 days
total charges=32+(42*6)
total charges=$284
Enterprise:
total charges=24+46x
when x=6 days
total charges=24+(46*6)
total charges=$300
Renting for 4 days:
total charges(Hertz)=32+(42*4)
total charges(Hertz)=$200
total charges(Enterprise)=24+(46*4)
total charges(Enterprise)=$208
savings=$208-$200
savings=$8
The company that charges less when Avery decides to rent car for only 4 days is Hertz and Avery can $8 as result of choosing Hertz
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A certain race is a distance of 24 furlongs. How far is the race in (a) miles? (b) yards?
A coffee company surveyed 40 potential customers to see where they would like the company's new organic coffee sold. Respondents were given the following four locations and asked to choose as many as they liked: grocery stores, drugstores, health food stores, and big box stores. The results are summarized in the bar graph below, with the number of times each location was chosen noted above the corresponding bar.
As per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.
As given,
Total number of potential customers =40
Number of respondents from bar graph
At grocery stores= 40
At drugstores respondents =32
At health food stores =8
At big box stores =20
Average number=(40 +32+8+20)/40
= 100 /40
=2.5
Therefore, as per given data of respondents of four locations in the bar graph per40 potential customers , the average number of location chosen per potential customer is equal to 2.5.
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Solve.
2x+y+z=−4
3x+2y−z=6
x+2y−3z=2
Enter your answer, in the form (x, y, z), in the boxes in simplest terms.
Solution of 2x+y+z=−4, 3x+2y−z=6, x+2y−3z=2 value of
(x , y, z) =(10,-16,-8) in the simplest terms.
As given,
2x+y+z=−4 __(1)
3x+2y−z=6 __(2)
x+2y−3z=2 __(3)
Add (1) and (2)
2x+y+z=−4
3x+2y−z=6
5x + 3y=2 __(4)
Multiply 3 to (1) add it to (3)
6x+3y+3z=-12
x+2y−3z=2
7x + 5y = -10 __(5)
Now [5× (4)] subtract [3×(5)] from it
25x + 15y=10
21x+15y=-30
4x= 40
⇒x=10
Substitute in (4)
y=[2-5(10)]/3
=-16
Substitute value of x and y in (1)
z=-4 -2(10)-(-16)
=-8
Therefore, solution of 2x+y+z=−4, 3x+2y−z=6, x+2y−3z=2 value of
(x , y, z)=(10,-16,-8) in the simplest terms.
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PLEASE HELP!! 50 points
I’m confused on how to solve this for gross pay :(
Ted worked 40 hours last week and earned $1200. 40% of his pay is from commission. How much did Ted earn in commission? What is his hourly wage?
The value of the 7 in 7.8 is. then the 7 in 23.97. 10 times greater 100 times greater 10 times last 100 times less
7 in 7.8 is 100 times greater than 7 in 23.97.
What is place value ?As the name suggests place value is where the digit is being placed in decimal number system.
We can multiply both these numbers by 100 in that way we'll get rid of the decimal and it doesn't effect our answer.
Now 7.8 and 23.97 multiplied by 100 becomes 780 and 2397.
We can observe that 7 in 780 is in hundreds place and 7 in 2397 is in ones place.
∴ If we divide (100/1) = 100.
So, it is 100 times greater.
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The capacities at which U.S. nuclear power plants are working are shown in table for various years.
Year Percent
1975 56
1980 59
1985 58
1990 70
1995 76
2000 88
2004 89
Let
f
(
t
)
be the capacity (in percent) at which U.S. nuclear power plants are working at t years since 1970. A model of the situation is
f
(
t
)
=
0.027
t
2
+
0.216
t
+
53.296
.
Use a graphing calculator to draw the graph of the model and, in the same viewing window, the scattergram of the data. Does the model fit the data well?
The function is not a good model for the data
The function is a good model for the data.
Estimate at what capacity U. S. nuclear power plants were working in 2014.
% Round to the nearest whole percent.
Predict when U. S. nuclear power plants will be working at full (100%) capacity.
Enter the year this occurs.
The function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.
Given that the table which shows the capacities at which U.S. nuclear power plants are working and a model of the situation is f(t)=0.027t²+0.216t+53.296.
The Scatter plot for our function and points is shown in attached image and the point are highly related to the curve .
So the function is good model.
The year 2014 means t=2014-1970=44
So to get the population,put t=44 in equation
f(t)=0.027(44)²+0.216(44)+53.296
f(t)=0.027(1936)+0.216(44)+53.296
f(t)=52.272+9.504+53.296
f(t)=115.072
And on rounding it we get 115%.
Now, to find year at which capacity is 100% ,put f(t)=100 and solve for t
f(t)=0.027t²+0.216t+53.296=100
0.027t²+0.216t+53.296=100
0.027t²+0.216t+53.296-100=0
0.027t²+0.216t-46.704=0
Now, we will solve this using quadratic formula for f(x) =ax²+bx+c=0
[tex]\begin{aligned}x&=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\end[/tex]
for our function a= 0.027 , b=0.216 ,c=-46.704 substitute this value and we get
[tex]\begin{aligned}t&=\frac{-0.216\pm \sqrt{(0.216)^2-4\times 0.027\times (-46.704)}}{2\times 0.027}\\ &=\frac{-0.216\pm \sqrt{0.046656+5.044032}}{0.054}\\ &=\frac{-0.216\pm \sqrt{5.090688}}{0.054}\\ &=\frac{-0.216\pm 2.256}{0.54}\\ &=37.78, -45.78\end[/tex]
As we all know time cannot be negative so t=-45.78 will be rejected.
So, t=37.78=38
Now, we will find the corresponding year
1970+38=2008
Hence, from the given table the function is a good model for the data, capacity U. S. nuclear power plants were working in 2014 is 115% and the year when nuclear power plant working with full capacity is 2008.
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One hall can accommodate 65 people. How many halls are required to accommodate 520 people?
8 halls would be required to accommodate 520 people in the hall.
As we know that a hall can accommodate 65 people.
To determine the number of hall required for 520 people,
first we need to find that how many halls would be required for one person,
So, we will divide the 1 by 6 to find :
The number of one person accommodate = 1/65 Hall
Then, 520 people required to accommodate = 1/65 × 520
= 8 Halls.
[Accommodate: to have enough space for somebody/something, especially for a certain number of people]
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Evaluate
P/2 -
5 when p =14
Answer:2
Step-by-step explanation:
[tex]\frac{14}{5} -5[/tex]
Divide 14 by 2 to get 7.
7−5
Subtract 5 from 7 to get 2.
Answer=2
Solve the equation below for p:
14p-3=25
Answer:
p=2
Step-by-step explanation:
How can I do this -5/8 x 10/9
Maddie's Boutique paid the members of its staff $20 per hour. Then the boutique merged with another store, and the staff members started making $24 per hour. What was the percent increase in pay?
Enter your answer to the following equation below. You must include a percent sign.
The percent increase in pay was 20%
Maddie's Boutique paid the members of its staff $20 per hour.
and, the boutique merged with another store, and the staff members started making $24 per hour.
To find the what percent increase in pay ?
Now, According to the question:
Based on the given conditions,
= (24 - 20) ÷ 20
= [tex]\frac{24-20}{20}[/tex]
= 1/5
and, Covert to percentage
= 1/5 x 100
= 20%
Hence, The percent increase in pay was 20%
What is Percentage?
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is :
(value/ total value) x 100%
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