The fuel efficiency in miles per gallon of all bmw 320i's is (approximately) normally distributed with a mean of 25 and a standard deviation of 2. a dealer receives a shipment of a random sample of 320i's (random with respect to m.p.g., that is) from the factory. find the probability that average fuel efficiency for this shipment is less than 24 miles per gallon if the dealer receives (i) one car, (ii) four cars and (iii) sixteen cars. explain briefly why these three answers differ.
Given that the points (-1, 6), (3, 6), (3, 1), and (-1, 1) are vertices of a rectangle, how much shorter is the width than the length?
Answer:
1 unit shorter
Step-by-step explanation:
By plotting the given points in the coordinate plane,
We get a rectangle ABCD having vertices,
A(-1,6), B (3,6), C (3,1), D (-1,1)
By the distance formula,
Shorter side or width of the rectangle,
[tex]AB=\sqrt{(3-(-1))^2+(6-6)^2}=\sqrt{4^2+0}=4\text{ unit}[/tex]
Longer side or length of the rectangle,
[tex]BC=\sqrt{(3-3)^2+(1-6)^2}=\sqrt{5^2}=5\text{ unit}[/tex]
The difference between length and width,
[tex]BC - AB = 5 - 4 = 1\text{ unit}[/tex]
Hence, the width of rectangle is 1 unit less than the length.
which is longer 84 inches or 12 feet
Madeline bought 30 hotdogs and burgers altogether. 2/5 of the food bought were burgers. How many hotdogs did she buy?
How many faces has an icosahedron?
An icosahedron is a symmetrical, solid shape with 20 triangular faces and 12 corners.
Explanation:An icosahedron is a symmetrical, solid shape that has 20 faces. Each of these faces is an equilateral triangle. The structure of an icosahedron also includes 12 corners, where the faces meet. This geometric shape is an example of a regular polyhedron, one of the five Platonic solids, which are convex polyhedra with faces made of congruent regular polygons.
QUESTION 2
A $5000 investment earns $550 annual simple interest in one year. What is the annual interest rate?
11.5%
11%
12%
10.5%
QUESTION 5
Marie mixes 16 liters of 18% acid solution with a 27% acid solution to make a 21% acid solution.
How many liters of 27% solution did she use?
8 liters
12 liters
13.7 liters
16 liters
Question 2 is 11 i am sure
what is the greatest common factor of 27 and 36
Find the solution to the linear system of differential equations {x′y′==−5x+3y−18x+10y satisfying the initial conditions x(0)=4 and y(0)=11
The problem given is a linear system of differential equations with initial conditions, but the system is not properly defined and appears to have a typo. Normally, such a system would be in the form x' = ax + by and y' = cx + dy, with initial conditions that would determine the particular solution.
Explanation:This question is about solving a linear system of differential equations with initial conditions, specifically the system {x′y′==−5x+3y−18x+10y with the initial conditions x(0)=4 and y(0)=11. However, there seems to be a typo, as the system is not properly defined and doesn't make sense as written. Under normal conditions, such a system would be in the form x' = ax + by and y' = cx + dy, where a,b,c,d are constants and x' and y' are the derivatives of x and y respectively.
Additionally, the initial conditions x(0)=4 and y(0)=11 would serve to define the particular solution for the system of differential equations. Correcting and resolving such typos would be the first step in progressing towards a solution.
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Kwan's parents bought a home for $50,000 in 1997 just as real estate values in the area started to rise quickly. Each year, their house was worth more until they sold the home for $309,587. Model the growth of the home's value from 1997 to 2007 with both linear and an exponential equation. Graph the two models below.
A. First let us start with the linear model.
The equation is in the form of y = m x + b
Calculating for the slope m:
m = (309,587 – 50,000) / (2007 – 1997)
m = 25,958.7
Subsituting:
y = 25,958.7 x + b
Taking x = 1997, y = 50,000. Solve for b:
50,000 = 25,958.7 (1997) + b
b = -51,789,523.9
The complete equation is therefore:
y = 25,958.7 x - 51,789,523.9
B. The exponential model has the following form:
y = a b^x
where a and b are constants
Taking x1= 1997, y1 = 50,000; x2 = 2007, y2 = 309,587
50,000 = a b^1997
309,587 = a b^2007
Combining in terms of a:
50,000 / b^1997 = 309,587 / b^2007
b^2007 / b^1997 = 309,587 / 50,000
b^10 = 6.19174
b = 1.2
Substituting:
y = a 1.2^x
Solving for a:
50,000 = a 1.2^1997
a = 3.75 x 10^-154
The complete equation is:
y = 3.75 x 10^-154 * 1.2^x
What is 3 tenths + 1 hundredths as a decimal
Evaluate the line integral ∫cf⋅dr∫cf⋅dr, where f(x,y,z)=−5xi+yj+zkf(x,y,z)=−5xi+yj+zk and c is given by the vector function r(t)=⟨sint,cost,t⟩, 0≤t≤3π/2.
If we put five math, six biology, eight history, and three literature books on a bookshelf at random, what is the probability that all the math books are together?
The probability that all the math books are together can be calculated by considering the number of ways the math books can be arranged together and dividing it by the total number of ways all the books can be arranged.
Explanation:The probability that all the math books are together can be calculated by considering the number of ways the math books can be arranged together and dividing it by the total number of ways all the books can be arranged.
First, calculate the total number of ways the books can be arranged on the bookshelf. Since there are 22 books in total, the number of arrangements is 22!.
Next, calculate the number of ways the math books can be arranged together. Since there are 5 math books, the number of arrangements is 5!.
Finally, divide the number of arrangements of the math books by the total number of arrangements to find the probability. So the probability is 5! / 22!.
there are 4 bears. some are black and some are brown. there are fewer than 2 black bears. how many bears are Brown?
There are either three or four brown bears, and brown bear > 2 is the inequality that best describes the circumstance.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
given, there are 4 bears. some are black and some are brown. there are fewer than 2 black bears.
Since,
Black bear < 2
mathematically it can be 0 or 1
the inequality that represents the number of brown bears> 4 - 2
brown bear > 2
theoretically, it could be 3 or 4
therefore, there are either 3 or 4 brown bears, and the inequality that represents the situation is brown bear > 2.
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Arleen has a gift card for a local lawn and garden store. She uses the gift card to rent a tiller for 4 days. It cost $35 per day to rent the tiller. She also buys a rake for $9.
A. Find the change to the value on the gift card. (Question #1)
B. The original amount on the gift card was $200. Does Arleen have enough to buy a Wheelbarrow for $50? (Question #2)
Answer:
Step-by-step explanation:
Arleen has a gift card of the amount = $200
The total cost to rent the tiller for 4 days and a rake for $9
= ($35 × 4) + $9
= 140 + 9 = $149
A. Now the balance on the gift card = $200 - $149
= $51
B. Arleen have $51 in her gift card so she has enough to buy a wheelbarrow for $50.00.
Can you help me on #5
Show how to multiply 6 x 298 using friendly numbers and then using properties and mental math.Write about which method you like better and why
Final answer:
To multiply 6 x 298 using friendly numbers, you multiply 6 by 300 and then subtract 12, getting 1788. Using properties and mental math, you break 298 into 200 + 90 + 8, multiply each by 6, and add the results together to get the same answer, 1788. The second method is preferred for its accuracy and reinforcement of the associative property.
Explanation:
To multiply 6 x 298 using friendly numbers, we can adjust 298 to a number that is easier to multiply, such as 300. This method involves approximation for ease of calculation. Here's how it would look:
First, multiply 6 by 300 to get 1800 (since 6 x 3 = 18, and then we add two zeros because we're multiplying by 300).Since we multiplied by 2 more than the original number (298 + 2 = 300), we subtract 2 times 6 from the result (which is 12) to correct for our approximation.Therefore, the final result is 1800 - 12 = 1788.Using properties and mental math, we can use the distributive property to break 298 into more manageable numbers. Here's the step-by-step process:
Break 298 into 200 + 90 + 8.Multiply each part by 6: (6 x 200) + (6 x 90) + (6 x 8).Calculate each multiplication separately: 1200 + 540 + 48.Add the results together: 1200 + 540 + 48 = 1788.I prefer the second method because it guarantees accuracy and still takes advantage of the associative property to simplify calculations without approximations. Additionally, this type of mental math helps to reinforce an understanding of multiplication as a series of simpler, added-together parts.
What are the solutions of the following system?
To solve the system of equations, set the demand and supply equation equal to each other and solve for the unknown. Substitute Qd with Qs and solve for P.
Explanation:We now have a system of three equations and three unknowns (Qd, Qs, and P), which we can solve with algebra. Since Qd = Qs, we can set the demand and supply equation equal to each other:
By substituting Qd with Qs, we get:
16 - 2P = 2 + 5P
From here, we can solve for P to find the value of the unknown.
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You have a map where indy and fort wayne are 13 centimeter apart. kokomo and indy are 6.5 cm apart on the map. if you know that indy and fort wayne are actually 120 miles apart, how far apart would indy and kokomo be in real life? express your answer rounded to the nearest tenth of a mile
The distance between Indy and Kokomo be in real life is given by the proportion A = 60 miles
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
Let the distance between Indy and Fort Wayne in map = 13 cm
Let the distance between Indy and Fort Wayne in real = 120 miles
And , let the distance between Kokomo and Indy map = 6.5 cm
So , the proportion is
120 / 13 = A / 6.5
Multiply by 6.5 on both sides , we get
A = 120 / 2
A = 60 miles
Hence , the distance is 60 miles
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A digit thermometer reports a temperature of 32*F as being 32.02*F. Which of the followings true?
A. The thermometer is both accurate and precise.
B. The thermometer is neither accurate nor precise.
C. The thermometer is precise, but not accurate.
D. The thermometer is accurate, but not precise.
Answer: The thermometer is both accurate and precise
Step-by-step explanation: Hope this helped!!
How do I solve for x?
A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 4 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 31 days.
one pumpkin vine produce 5pumpkins I harvest 30 how many vines do I have
Help Please.
1 inch=2.54 centimeters
68 centimeters= ..... inches
(round the answer to two decimal places)
Find the second of two consecutive integers if the second is 13 less than twice the first.
It takes 40 min for a bus to travel the 36 miles from Framingham to Worcester. A car traveling from Worcester to Framingham moves 1.5 times as fast as the bus. If the car and the bus start moving towards each other simultaneously, after how many minutes will they meet?
The velocity of the bus is:
velocity (bus) = 36 miles / 40 min
velocity (bus) = 0.9 miles / min
Since the car is 1.5 times faster, so the velocity of the car is:
velocity (car) = 1.5 * 0.9 miles / min
velocity (car) = 1.35 miles / min
At the meeting point, the sum of the distance is equal to 36 miles. Therefore:
1.35 t + 0.9 t = 36
2.25 t = 36
t = 16 min
So they will meet after 16 minutes.
Twice the difference between a number and 10 is equal to 6 times the number plus 16. What is the number?
Jay is cutting a roll of biscuit dough into slices that are 3/8 inch thick. If the roll is 10 1/2 inches long, how many slices
can he cut?
The number of slices that Jay could make is equal to 28
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given here: Dimension of the roll= 10¹/₂ inches and length of each slice=3/8 inch
Thus the number of slices that Jay could make is = 10+ 1/2 /3/8
=21/2 × 8/3
=28
Hence The number of slices that Jay could make is equal to 28
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please can you help me!
z-² as a fraction
Recycling Center A processes aluminum at a rate of 100 pounds per hour, while Recycling Center B processes aluminum at a rate of 2 tons per week. Assuming that both centers operate all day every day, which center processes aluminum faster, and why?
A:Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 12 pounds per hour.
B:Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 24 pounds per hour.
C:Recycling Center B processes aluminum faster; its rate is about 120 pounds per hour.
D:Recycling Center B processes aluminum faster; its rate is about 240 pounds per hour.
Josh is twenty-five years older than his son Carlos. In ten years Josh will be twice as old as Carlos. How old is Carlos now?