14#A corporation that maintains a large fleet of company cars for the use of its sales staff is interested in the mean distance driven monthly per salesperson. The following list gives the monthly distances in miles driven by a random sample of 11 salespeople.2482, 2300, 2640, 2085, 2425, 1851, 2346, 1876, 2444, 2153, 2290Send data to calculatorBased on this sample, find a 95% confidence interval for the mean number of miles driven monthly by members of the sales staff, assuming that monthly driving distances are normally distributed. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.
Solution
Given the data set 2482, 2300, 2640, 2085, 2425, 1851, 2346, 1876, 2444, 2153, 2290
The confidence interval formula is
Calculate the standard deviation of the data
The standard deviation is
237.67
Calculate the sample mean
The mean is 2262.91
[tex]\begin{gathered} s=237.67 \\ n=11 \\ mean=2262.909 \\ z=1.96 \end{gathered}[/tex][tex]\begin{gathered} CI=2262.909\pm1.96(\frac{237.67}{\sqrt{11}}) \\ CI=2262.909\pm1.96(71.6602) \\ CI=2262.909\pm140.453992 \\ CI\text{ = 2122.455008 to 2403.362992 to} \end{gathered}[/tex]Thus, the lower limit is
2122.455 ( 3 decimal places)
The Higher limit is 2403.363 ( 3 decimal places)
A 21-foot beam is to be cut into three pieces so that the second and third piece are each 3 times the length of the first piece. If X represents represents the length of the first piece find the length of each piece.
The length of the first piece is 3 inches, and the second and third pieces are each 9 inches
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Given that a 21-foot beam is to be cut into three pieces so that the second and third pieces are each 3 times the length of the first piece.
We have to determine the length of each piece.
Let x represents the length of the first piece
As per the given condition,
x + 3x + 3x = 21
7x = 21
x = 21 / 7
x = 3
Thus, the first piece is 3 inch
So 2nd piece is 3×3 = 9 inches ( 3 times to first piece )
And 3rd piece is 3×3 = 9 inches ( 3 times to first piece )
Therefore, the length of the first piece is 3 inches, and the second and third pieces are each 9 inches
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Solve for x.
3.5x=31.5
Answer:
x = 9
Step-by-step explanation:
x = 31.5 / 3.5
x = 9
Answer:
x = 9
Step-by-step explanation:
since 3.5 is being multiplied by x to get 31.5 to get rid of it and leave x by itself you have to divide both sides by 3.5
(3.5x)/(3.5)= (31.5)/(3.5)
x=9
PLEASE HELP QUICK!!!!!!!
Answer:
D
Step-by-step explanation:
Translation 4 units right and 1 unit up
5. Caleb earns points on his credit card that he can use towards future purchases. He earns four
points per dollar spent on flights, two points per dollar spent at hotels, and one voint per
dollar spent on all other purchases. Last year, he charged a total of $9.480 and earned
14,660 points. The amount of money spent on flights was $140 more than twice the amount
of money spent on hotels. Find the amount of money spent on each type of purchase.
By the concept of linear equation :
$1,500 was spent on flights,
$680 was spent on hotels,
$7,300 was spent on other purchases.
What are linear equations?An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y). For the purpose of resolving systems involving two linear equations, this form is also highly helpful.
Given:
Flights: 4 points per dollar
Hotels: 2 points per dollar
Other: 1 point per dollar.
Total spent = $9,480
Points earned = 14,660
Let
x = money spent on flights
y = money spent on hotels
z = money spent on other purchases.
Because the money spent on flights was $140 more than twice the money spent on hotels, therefore
x = 2y + 140 (1)
Total charges were $9,480, therefore
x + y + z = 9480 (2)
Total points earned was 14,660. Therefore
4x + 2y + z = 14660 (3)
Subtract (2) from (3).
4x + 2y + z - (x + y + z)
= 14660 - 9480
3x + y = 5180 (4)
Substitute (1) into (4).
3(2y + 140) + y = 5180
7y + 420 = 5180
7y = 4760
y = 680
From (1), obtain
x = 2y + 140
= 2(680) + 140
= 1500
From (2), obtain
z = 9480 - (x + y)
= 9480 - (1500 + 680)
= 7300
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Pls help i domt get this
Answer:
[tex]5^{15}[/tex] × 120 = 30,517,578,125 × 120
Step-by-step explanation:
given the following expressions1. -5/8+3/52. 1/2+ √23. (√5)×(√5)4. 3×(√49)which expression(s) will result in an irrational number.(1) only 2(2) only 3(3) 1,3,4(4) 2,3,4
1) Only 2
1) Examining the expressions we have
1. -5/8+3/5 =-1/40 Rational Expression
2. 1/2+ √2 Irrational Expression
3.(√5)×(√5)= 5 Rational Expression
4. 3×(√49) = 21 Rational Expression
2) Since √2 is an irrational number √2 = 1.4142.... non-periodic and infinite number, and number added to it will yield an irrational number.
3) So the answer is 1) Only 2
stack of mail consists of 8 bills, 10 letters, and 6 advertisements. One piece of mail is drawn at random and put aside. Then a second piece of mail is drawn. Find P (both are letters)
INFORMATION:
We know that:
- stack of mail consists of 8 bills, 10 letters, and 6 advertisements.
- One piece of mail is drawn at random and put aside. Then a second piece of mail is drawn.
And we must find P (both are letters)
STEP BY STEP EXPLANATION:
To find the probability, we need to know that we have two events. First, when one piece of mail is drawn at random and put aside and, second, when a second piece of mail is drawn.
These two events are dependent. If A and B are dependent events, P(A and B) = P(A) • P(B after A) where P(B after A) is the probability that B occurs after A has occurred.
So, first
- Probability of A (the first piece is letter)
[tex]P(A)=\frac{favorable\text{ }cases}{total\text{ cases}}=\frac{10}{24}[/tex]- Probability of B after A
Since A already occurred and one piece of the mail was drawn (a letter), now in total we would have 9 letter and 23 total pieces
[tex]P(B\text{ after }A)=\frac{9}{23}[/tex]Finally, replacing in the initial formula
[tex]P(A\text{ and }B)=\frac{10}{24}\cdot\frac{9}{23}=\frac{90}{552}=0.1630[/tex]Finally, the probability would be 0.1630
ANSWER:
P (both are letters) = 0.1630
A software company in Burlington used to bill clients $214.79 per hour for work done by its consultants. The company recently adjusted its rates and now charges the same amount. What was the percent of decrease in the billing rate?
The percent of decrease in the billing rate is 2.37%.
How to calculate the percentage?It should be noted that a percentage decrease is calculated as
= Decrease in value / Initial value × 100
Let's assume the following:
Initial amount = $220
New amount = $214.79
Decrease in amount = $220 - $214.79 = $5.21
The percentage decrease will be:
= 5.21 / 220 × 100
= 2.37%
The question is incomplete and the values were assumptions.
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Each gallon of paint covers 200 square feet. I have to paint one side of a wall that is 12 meters tall and 80 meters long. If a foot is approximately 0.3084 meters, then what is the smallest whole number of gallons I can buy and have enough paint to cover the whole wall
Answer:
1 ft ≈ 0.3048 m
1 ft2 ≈ 0.09290304 m2
200 ft2 ≈ 18.580608 m2
Step-by-step explanation:
The total surface area to paint = 12 m * 80 m = 960 square meters
1 ft ≈ 0.3048 m
1 ft2 ≈ 0.09290304 m2
200 ft2 ≈ 18.580608 m2
And so one gallon of paint covers about 18.581 square meters.
960 m2 / ( 18.581 m2 per gallon) ≈ 51.67 gallons
So 51 gallons would not be enough... it would take 52 gallons of paint to cover the wall.
5/b= 3/b-6
first i cross multiplied as i’m supposed to go and got the answer
5b-30=3b
what steps are next?
Given the equation 12.75y = 38.25, determine the value of y.
Answer:
y = 3
Step-by-step explanation:
12.75y = 38.25
To find the value of y, divide each side by 12.75
12.75y/12.75 = 38.25/12.75
y = 3
Experimental and theoretical see pic
1) Wrong statement:
The difference between the experimental and theoretical probability is 1/10
Correct statement:
The difference between the experimental and theoretical probability is 3/200
2) Wrong statement:
The difference between the experimental and theoretical probability is 1/10
Correct statement:
The difference between the experimental and theoretical probability is 3/200
Explanation:N(Pennies) = 6
N(Nickels) = 8
N(Dimes) = 4
N(quarters) = 7
N(total) = 6 + 8 + 4 + 7
N(total) = 25
1) The theoretical probability of selecting a dime = 4/25
The experimental probability of selecting a dime = 30/150 = 1/5
B is wrong because theoretical probability is 4/25, not 9/50
Wrong statement:
The theoretical probability of selecting a dime is
Correct statement:
The theoretical probability of selecting a dime is 4/25
2) The experimental probability of selecting a penny = 45/200 = 9/40
The theoretical probability of selecting a penny = 6/25
Difference between experimental and theoretical probability = 6/25 - 9/40
Difference between experimental and theoretical probability = 3/200
Wrong statement:
The difference between the experimental and theoretical probability is 1/10
Correct statement:
The difference between the experimental and theoretical probability is 3/200
7x+12=x-6 please answer
Answer:
x=-3
Step-by-step explanation:
Miss Young is bringing cookies and brownies in for one of her classes. She has to bring
a total of 26 desserts. She pays $0.65 for each cookie and $0.90 for each brownie.
Using a system of equations, supposing that she spent $19.65, the amounts are as follows:
Cookies: 15.Brownies: 11.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of this problem.
For this problem, the variables are defined as follows:
Variable x: number of cookies purchased.Variable y: number of brownies purchased.She brought a total of 26 desserts, hence:
x + y = 26.
She spent a total of $19.65, hence, considering the price of each item:
0.65x + 0.9y = 19.65.
From the first equation, we have the following relation:
y = 26 - x.
Hence, replacing in the second, we can solve for x as follows:
0.65x + 0.9(26 - x) = 19.65
0.25x = 3.75
x = 3.75/0.25
x = 15 cookies.
Then the number of brownies is found as follows:
y = 26 - 15 = 11 brownies.
Missing informationWe suppose that she spent $19.65, and that the problems asks for the amounts of cookies and brownies purchased.
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suppose you sell hats for 10 dollars each and sunglasses for 5 dollars each. you know the expected number of hats sold in a day is 10 with standard deviation 1; you know the expected number of sunglasses sold in a day is 20 with standard deviation 2; you know the sale of hats and sunglasses are independent. what is the standard deviation of your revenues in a day? (round to closest dollar)
Answer:
2
Step-by-step explanation:
because average of 1 and 2 is 1.5 rounded is 2
The standard deviation of your revenues in a day is 14.
What is a standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.
Let x be the revenue from hats.
And let y be the revenue from sunglasses.
And z be the total revenue.
Then according to the question:
z = 10x + 5y
You know the expected number of hats sold in a day is 10 with standard deviation 1.
σₓ = 1
σy = 2
Taking squares of both of the equation.
σₓ² = 1² = 1
σy² = 2² = 4
To find the standard deviation of your revenues in a day:
V(z) = (10)²σₓ² + 5²σy²
V(z) = (100)(1) + (25)(4)
V(z) = 200
Standard deviation,
σz² = √(200)
σz² = 10√(2)
σz² = 14.14
σz² ≈ 14
Therefore, the required standard deviation is 14.
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What is the transformation of both y=-√-4x, and y=√-4x? I've looked everywhere to try and find it, but the internet is not helping!
The transformation that relates the two functions:
f(x) = y = -√(-4x)
g(x) = y = √(-4x)
Is a reflection across the x-axis.
What is the transformation applied?
We define a reflection across the x-axis as a transformation that does a "vertical reflection" along the line y = 0 (which is the x-axis).
For a function f(x), a reflection across the x-axis generaste the new function g(x) that can be written as:
g(x) = -f(x).
In this case the original function is:
f(x) = y = -√(-4x)
And the transformed function is:
g(x) = y = √(-4x)
You can see that the only difference is the sign, such that we can write:
g(x) = -f(x) = -(-√(-4x)) = √(-4x)
So we conclude that the transformation is a reflection across the x-axis.
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How do you solve this
Answer: wut
Step-by-step explanation: wut
the volume of a rectangular box with a square base remains constant at 1100 cm3 as the area of the base increases at a rate of 10 2/sec. find the rate at which the height of the box is decreasing when each side of the base is 15 cm long. (do not round your answer.)
The height of the box is decreasing at a rate of 2/45 cm/sec.
The volume of a box remains constant at 1100m³ but the area of the base is increasing at a rate of 10 m²/sec.
Since the base of the box is a square, let the sides of the box be a, a, and h. The area of the base can be written as,
A = a²
Differentiate the above equation with respect to t.
dA/dt = 2a(da/dt)
Substitute 10 for dA/dt and 15 for a, to find the rate of change of side of base.
10 = 2(15)(da/dt)
da/dt = 1/3
The volume of the box can be written as,
V = (a)(a)(h) = a²h
Differentiate the above equation with respect to t.
0 = 2a(da/dt) + a² (dh/dt)
dh/dt = -2/a (da/dt)
Substitute 15 for a and 1/3 for da/dt in the above equation, to find the rate of change of height of the box.
dh/dt = -2/15 (1/3)
= -2/45
Thus, the height of the box is decreasing at a rate of 2/45 cm/sec.
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what is the answer to 2y=3x+4
Answer:
y = (3/2)x + 2
assuming that the question is to find y in its simplest form.
Step-by-step explanation:
2y=3x+4
(1/2)*(2y)= (1/2)*(3x+4)
y = (3/2)x + 2
What is the answer to the following calculation, rounded to the correct number of significant figures?100.000 g+ 75.0 g
Answer:
175g
Step-by-step explanation:
100.000g+75.0g= 175g
ps. pls give brainliest answer :)
The sum of the numbers 100.000g and 75.0g in expression is 175g.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
The given numbers are,
100.000g and 75.0g
The zeros can be neglected after decimal points,
So the numbers can be written as,
100g and 75g.
To find the required expression, add 100g and 75g.
100g + 75g = 175g.
The required sum of the numbers is 175g.
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The point where the graphs of two equations intersect has y-coordinate 2. One equation is y = -3 = 5. Find the other equation if its graph has a slope of 1.
The equation of the line for the given slope 1 is y= x + 2
Equation of the line:
An equation of the line refers the algebraic form of representing the set of points, which together form a line in a coordinate system.
Given,
The point where the graphs of two equations intersect has y-coordinate 2. One equation is y = -3x + 5.
Here we need to find the other equation if its graph has a slope of 1.
We know that, the general representation of equation of line is y= ax + b
where a is the slope and b is the y intercept.
Through the given details we know that the slope of the line is 1 and why is point where two lines intersect hence, it is the intercept.
And the intercept value is 2.
Therefore, the equation of the other line is y= x + 2
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The weight f a stack of standard 8.5*11 copier paper vs. number of sheets of paper
A. The weight of the copies and the quantity of papers are proportional.
B. There is no proportion between the number of books and their weight.
Given,
A. All versions of the document are 8.5 by 11 inches in size.
We can readily determine the quantity of papers using direct proportion because all the paper has the same dimensions and weight.
As a result, the weight of the copies and the quantity of papers are proportional.
B. Each book has a distinct weight, as we know.
Since each book varies in weight, it is difficult to calculate the quantity of papers using a direct percentage.
Therefore, there is no proportion between the number of books and their weight.
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Solve 4- 3x = 6 - 5x
X =
Answer:
Step-by-step explanation:
4 - 3 x = 6 - 5 xx
[tex]-3x+4=6-5xx^{2}[/tex]
x = 1
x = - [tex]\frac {2}{5}[/tex]
Answer:
x=1
Step-by-step explanation:
sense x's are on both sides you need to bring one of them over, add 3x to both sides to get 4=6-2x , then subtract 6 from each side to get -2=-2x , then to get x by itself divide both sides by -2 to get 1=x
Express 35 as a fraction of 95. Give your answer in its simplest form.
Answer:
=35/95
=(5 x7)/95
=5 x 7/5 x 19
=7/19
Hemework -13 .
Express the ratio 20cm to 15m in the form 1:n
Answer:
1: 75
Step-by-step explanation:
20cm : 15m
Convert meters to cm
1 meter = 100 cm
15m = 15 x 100 = 1500 cm
20cm:1500cm
Divide both sides of the ratio by 20
=> 1 : 1500/20 = 1: 75
The ratio of 20cm to 15m in the form 1:n is 1:75.
What is a ratio?A ratio is a mathematical comparison of two or more quantities expressed in terms of the number of times one quantity contains another quantity.
It is used to express the relationship between two or more numbers or variables and is usually written as a fraction or with a colon between the two numbers.
We have,
First, we need to convert both measurements to the same unit.
Let's convert 20cm to meters:
20 cm = 20/100 m = 0.2 m
Now we can express the ratio of 20cm to 15m as:
0.2m : 15m
To simplify this ratio, we can divide both sides by the greatest common factor of the two numbers, which is 0.1m:
0.2m/0.1m : 15m/0.1m
2 : 150
Finally, we can simplify the ratio by dividing both sides by 2:
1 : 75
Therefore,
The ratio of 20cm to 15m in the form 1:n is 1:75.
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If f (x) = 4x2 + 3x − 5, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following?
4 times the quantity x plus h end quantity squared plus 3 times the quantity x plus h end quantity minus 5 minus 4 times x squared plus 3 times x minus 5 all over h
4 times the quantity x squared plus 2 times x times h plus h squared end quantity plus 3 times the quantity x plus h end quantity minus 5 minus the quantity 4 times x squared plus 3 times x minus 5 end quantity all over h
the quantity 4 times x plus 4 times h end quantity squared plus the quantity 3 times x plus 3 times h end quantity minus 5 minus the quantity 4 times x squared plus 3 times x minus 5 end quantity all over h
4 times the quantity x plus h end quantity squared plus 3 times x minus 5 minus 4 times x squared minus 3 times x plus 5 all over h
The difference quotient of f(x) is:[ f(x + h) - f(x)]/h = 8x + 4h + 3
How to get the difference quotient?Here we have the function:f(x) =4x^2 +3x - 5
And we want to get the difference quotient that can be written as:
[f(x + h) - f(x)]/h
Replacing the function we get:
[f(x + h) - f(x)]/h = [4*(x + h)^2 + 3*(x + h) - 5 - 4*x^2 - 3x + 5]/h
Solving further (open the brackets), we have
[f(x + h) - f(x)]/h = [4x^2 + 8*x*h + 4h^2 + 3x + 3h -5 - 4x^2 - 3x + 5]/h
Evaluate the like terms
So, we have
[f(x + h) - f(x)]/h = [8*x*h + 4h^2 + 3h]/h
Evaluate the quotients
[f(x + h) - f(x)]/h = 8x + 4h + 3
That is the difference quotient.
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Find the value of x.
(8x - 11)
5x°
(2x+6)°
Answer: x=37/3
Step-by-step explanation:
8x-11+5x+2x+6=180 ==> three angles of a triangle add up to 180 degrees
8x+5x+2x-11+6=180
13x+2x-5=180
15x-5=180
15x=185
x=185/15
x=37/3
someone please help me please
Graph
[tex]-2x+y\ge-2[/tex]
Procedure
y = 2x + 3
when x = -1, y =
Answer: y = 1
Step-by-step explanation:
y = 2(-1) +3
y = -2 + 3
y = 1