Final answer:
To find the simplest form of the expression 2a^2b^2/4a, you divide both the numerator and the denominator by the common factor 2a. The resulting simplest form of the expression is ab^2/2.
Explanation:
The student has asked: What is the simplest form of the expression 2a^2b^2/4a? The simplest form is achieved by simplifying the expression through division since there are common factors in the numerator and the denominator. Here, we can divide both the numerator and the denominator by 2a, which is a common factor. This simplification process will give us the simplest form of the expression.
To simply the expression 2a2b2/4a, we can follow these steps:
Divide the numerator and denominator by the common factor 2a.This results in a2b2/2a becoming ab2/2 after reduction.Therefore, the simplest form of the expression is ab2/2.
A tunnel is in the shape of a parabola. The maximum height is 31 m and it is 13 m wide at the base as shown below.
A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 31 meters and its width from left to right is 13 meters.
What is the vertical clearance 2 m from the edge of the tunnel?
Answer:
previous is correct
Step-by-step explanation:
Anna has put her money into various investments. Which of the three Cs of credit do these investments fall into?
A. Capital
B. Character
C. Capacity
The correct answer is:
A) Capital.
Explanation:
Capital is any valuable assets that you have such as real estate, personal property, or savings and investments that you could possibly use to repay credit debts if necessary.
Anna has put her money into various investments. These are Anna's capital.
A capital amount is the money that is needed to start any business venture or investment. Capital is also an asset of any person. Apart from personal money, capital also include funds in ones deposit accounts, tangible things like machinery used for production purposes etc.
Given f(x)=2x-8, find f(3)
The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given by the function D(h)=111.7 times square root of h. Find the height that would allow a person to see 50 kilometers.
To find the height that allows a person to see 50 kilometers, we set the given function equal to 50 and solve for h. This calculation gives us the height as approximately 0.2 kilometers.
Explanation:The question requires us to find the height h that would allow a person to see 50 kilometers, given the function D(h)=111.7 * sqrt(h).
We can solve this by setting the function equal to 50 and then solving for h. Like so: 50 = 111.7 * sqrt(h).
To isolate sqrt(h), we divide both sides of the equation by 111.7: sqrt(h) = 50 / 111.7.
Then we square both sides of the equation to solve for h: h = (50 / 111.7)^2.
Upon calculating the right side of this equation, we find that the height is approximately 0.2 kilometers.
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The answer for this question is 0.2 Kilometers or 200 meters(approx.)
The detailed explanation is as follows :
The maximum distance D(h) in kilometers that a person can see from a height h kilometers above the ground is given by the function D(h)=111.7 times square root of h. We need to find the height that would allow a person to see 50 kilometers.
To solve this problem, we need to find the height h that allows a person to see a distance of 50 kilometers. We start with the given function:
D(h) = 111.7 * sqrt(h)
We set D(h) to 50 kilometers:
50 = 111.7 * sqrt(h)
To isolate sqrt(h), we divide both sides by 111.7:
sqrt(h) = 50 / 111.7
Next, we calculate the division:
sqrt(h) ≈ 0.4475
Now we square both sides to find h:
h = (0.4475)^2 ≈ 0.2002
Therefore, the height that allows a person to see 50 kilometers is approximately 0.2002 kilometers, or 200.2 meters above the ground.
Hence the required answer is 0.2 kilometers or 200 meters(approximately)
Which best describes the meaning of the term theorem? A.A statement that is easily deduced from a proven theorem B.A conclusion proved by deductive reasoning C.A conjecture based on inductive reasoning D.A statement explaining the meaning of a geometric term
find the x-intercept of the parabola with vertex (4,-1) and y- intercept (0,15). write answer in (x1,y1) (x2,y2) form :D ...?
Answer:
(3,0),(5,0)
Step-by-step explanation:
Add the comma in the middle or Plato will mark it wrong
Harriet is comparing the costs of calling cards. To use card A, the cost is $1.00 to connect and then $0.04 per minute. To use card B, it costs $0.65 to connect and then $0.06 per minute. For what number of minutes does it cost the same amount to use each card for a single call?
Answer: There are 17.5 minutes for which it costs the same amount to use each card for a single call.
Step-by-step explanation:
Let the number of minutes be x
To use card A, the cost is $1.00 to connect and then $0.04 per minute.
So, our expression becomes,
[tex]1+0.04x[/tex]
To use card B, the cost is $0.65 to connect and then $0.06 per minute.
So, our expression becomes,
[tex]0.65+0.06x[/tex]
According to question, if it cost the same amount to use each card for a single call, then it will be
[tex]1+0.04x=0.65+0.06x\\\\1-0.65=0.06x-0.04x\\\\0.35=0.02x\\\\\frac{0.35}{0.02}=x\\\\17.5=x[/tex]
Hence, there are 17.5 minutes for which it costs the same amount to use each card for a single call.
90 in fraction form show your work
Which statement is true for the set of natural numbers?
A. The set is closed under addition and closed under subtraction
B. The set is closed under addition and not closed under subtraction
C. The set is not closed under addition and closed under subtraction
D. The set is not closed under addition and not closed under subtraction
The set of natural numbers is closed under addition but not under subtraction.
Explanation:The statement that is true for the set of natural numbers is B. The set is closed under addition and not closed under subtraction.
In mathematics, a set is considered closed under an operation if applying that operation to any two elements in the set always produces an element that is also in the set.
For the set of natural numbers, adding two natural numbers will always result in another natural number, so it is closed under addition. However, subtracting two natural numbers may result in a negative number, which is not a natural number, so it is not closed under subtraction.
You have a part time job. You work for 3 hours on Friday and 6 hours on Saturday. You also receive an allowance of $20 per week. You earn $92 per week. How much do you earn per hour at your part time job?
f(x)=128(0.5)^x
(0, 1)
(1, 64)
(3, 16)
(8, 0.5)
What is the expression for "the difference of five times a number and twice that number"?
5(2 - N)
5N - 2N
2N - 5N
5(N - 2)
The angle of depression from the top of a 150 m high cliff to a boat at sea is 7 degrees. How much closer to the cliff must the boat move for the angle of depression to become 19 degrees ...?
HELPPP!!
Find the dimensions of a box with a square base with
(a) volume 12 and the minimal surface area
(b) surface area 20 and minimal volume ...?
The dimensions of the box for minimal surface area when volume is 12 are both the cube root of 3. When surface area is 20 for minimal volume, the dimensions are sqrt(5) for the base and (15 / (4*sqrt(5))) for the height.
Explanation:The concept in this problem is about minimizing surface area and volume with relation to the dimensions of a box.
Let's consider a box with a square base of side 'x' and height 'h'. For part (a), the volume V of a box is given by V = x^2 * h which implies h = V / (x^2).
Substituting V = 12, we get h = 12/x^2. The surface area S of a box is given by S = x^2 + 4xh.
Substituting the value of h in the surface area equation, we have S = x^2 + 48/x.
To find the minimum surface area, we differentiate the above with respect to 'x' and set it equal to 0, which gives the dimensions of the box to be x = h = cube root of 3.
For part (b), the surface area S is given to be 20. So, S = x^2 + 4xh implies 4xh = 20 - x^2. The volume of the box is V = x^2 * h = (20 - x^2) / 4.
To minimize the volume, we differentiate V with respect to 'x' and set it to 0. That gives us the value of 'x' to be sqrt(5), and 'h' to be (20 - 5) / (4*sqrt(5))
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How many window coverings are necessary to span 50 windows if each window covering is 15 windows long?
To find out how many 15-window coverings are needed for 50 windows, divide 50 by 15, which gives approximately 3.33. Rounding up because we can't have partial window coverings, we will need 4 coverings.
Explanation:The question asks: How many window coverings are necessary to span 50 windows if each window covering is 15 windows long?
To answer this question, we can do a simple division. We divide the total number of windows (50) by the length of each window covering (15).
So, we have 50 ÷ 15 which equals approximately 3.33. However, since we cannot have a fraction of a window covering, we need to round this number up. Therefore, we would need 4 window coverings to span 50 windows.
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During renovation, a pillar is supported by two braces as shown in the diagram. Based on the diagram, at what height should the short brace touch the pillar to ensure that the short brace is parallel to the long brace?
10 feet
12 feet
15 feet
17 feet
The answer is A. 10 feet, on Plato.
What is 1 third of 48?
Solve for b2 in A = 1/2 h(b1+b2), if A = 16, h = 4, and b1 = 3. 16= 1/2* 4(3+b2) =6+2b2 or, b2= [16-6]/2= 5
There are 4 different French books and 4 different Spanish books. How many ways are there to arrange them on a shelf if
(a) Books of the same language must be grouped together, French on the left, Spanish on the right?
(b) French and Spanish books must alternate in the grouping, beginning with a French book? ...?
Tickets for a school play cost $7 and $10 for the adults. The equation 7x+10y=80 represents the number of students(x) and the number of adults(y) who can attend the play for $80. If no students attend, how many adults can see the play for $80?
If no students attend the play, then 8 adults can see the play for $80.
Explanation:The subject of this question is Mathematics, specifically linear equations. The scenario presented involves ticket sales for a school play with different ticket prices for students and adults. $7 is the price for a student ticket and $10 is for an adult ticket. The given equation 7x+10y=80 represents the total sum of $80 that needs to be reached with a combination of student tickets (x) and adult tickets (y).
If no students attend, x in the equation is 0, so we have 10y = 80. To find the number of adults (y) that can attend the play for $80, we need to solve this equation for y. So, y = 80 / 10. Therefore, y = 8, meaning 8 adults can attend the play for $80 when no students attend.
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Numbers 1 - 10 are written on cards and placed in a bag. Find the probability of choosing a number greater than 5 or choosing an odd number. ...?
The probability of selecting a card greater than 5 or an odd number from a bag of cards numbered 1 to 10 is 0.8 or 80%.
Explanation:The question asks for the probability of choosing a number greater than 5 or an odd number from a bag containing numbered cards from 1 to 10. To solve this, we should consider that numbers greater than 5 are 6, 7, 8, 9, and 10. There are 5 odd numbers in the set: 1, 3, 5, 7, and 9. The number 7 and 9 are both greater than 5 and odd, so they are counted only once when combining the two groups.
First, let's count the total unique outcomes that either meet the criterion of being greater than 5 or being odd: 6, 7, 8, 9, 10, 1, 3, 5 (7 and 9 are already counted). There are 8 such numbers.
The total number of possible outcomes is 10, as there are 10 cards. The probability is the number of favorable outcomes divided by the total number of possible outcomes: P = favorable outcomes / total outcomes = 8/10 = 0.8 or 80%.
a bowling ball is dropped from a height of 24 feet. write a function that gives the height h (in feet) of the bowling ball after t seconds
Answer:
[tex]h=16t^2[/tex]
Step-by-step explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 32 ft/s²
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow h=ut+\frac{1}{2}32\times t^2\\\Rightarrow h=ut+16t^2[/tex]
Here, u = 0 so,
[tex]h=0t+16t^2\\\Rightarrow h=16t^2[/tex]
The equation is [tex]h=16t^2[/tex]
[tex]24=16t^2\\\Rightarrow t=\sqrt{\frac{24}{16}}\\\Rightarrow t=1.22\ s[/tex]
Time taken by the ball to hit the ground is 1.22 seconds
(4n^2 3n) (2n^3-4) (3n^2-2n) ?
The Florida tourism board surveyed people on their favorite vacation cities. Half of the people said Orlando, 1/4 said Miami, 1/8 said Kissimmee, 1/16 said Fort Lauderdale, 1/32 said Key West, and the rest said Tampa. If 22 people said Tampa, how many people responded Orlando?
To find out how many people responded Orlando, we need to add up the fractions for Miami, Kissimmee, Fort Lauderdale, Key West, and Tampa and then set up a proportion to find the number of people who said Orlando. The answer is approximately 47 people.
Explanation:To find out how many people responded Orlando, we need to add up the fractions for Miami, Kissimmee, Fort Lauderdale, Key West, and Tampa since the rest said Tampa. The fractions we need to add are 1/4, 1/8, 1/16, and 1/32. Let's calculate each fraction to get a common denominator.
1/4 = 8/32, 1/8 = 4/32, 1/16 = 2/32, 1/32 = 1/32.
Now we can add them up: 8/32 + 4/32 + 2/32 + 1/32 = 15/32.
Since the remaining fraction is Tampa, which corresponds to 22 people, we can set up a proportion: 15/32 = 22/x to find out how many people said Orlando. Cross-multiply and solve for x: 32 * 22 = 15x, 704 = 15x, x = 704/15, x ≈ 46.93.
Therefore, approximately 47 people responded Orlando.
HELPPPPPP
A person can order a new car with a choice of 10 possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?
Final answer:
To find the number of different ways a new car can be ordered with various options, multiply the number of choices for each option.
Explanation:
To find the number of different ways a new car can be ordered with regard to the given options, we need to multiply the number of choices for each option. There are 10 possible colors, 2 choices for air conditioning (with or without), 2 choices for automatic transmission, 2 choices for power windows (with or without), and 2 choices for a CD player (with or without).
Therefore, the total number of different ways a new car can be ordered is:
10 colors × 2 choices for air conditioning × 2 choices for automatic transmission × 2 choices for power windows × 2 choices for a CD player = 10 × 2 × 2 × 2 × 2 = 160
Lane is 10 times Mel's age. If the difference in their age is 27, how old is Mel? A. 26 B. 4 C. 3 D. 30
The soccer team voted on what they wanted to eat. there are 20 members on the team. six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs. which ratio represents the number of votes for hot dogs to chicken
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
The ratio is hot dogs to chicken the chicken isten tho to find the hot dogs first you do
10+6=16
So it says 20 members so then you needa see how much would equal the amont 20 obviously 4 so the hot dogs equal to 4 so the ratio is 4:10
Answer:
2/5
Step-by-step explanation:
just did it and it is correct
prove tan3A= (cos(2A)-cos(4A))/ (sin(4A)- Sin(2A)) ...?
Which of the following at the three cs of credit
The three Cs of credit are character, capacity, and capital, which represent the creditworthiness of an individual or business as assessed by lenders based on reputation, ability to repay, and assets for collateral respectively.
Explanation:The three Cs of credit refer to character, capacity, and capital. These are the main criteria that lenders consider when assessing the creditworthiness of an individual or business. Character refers to the borrower's reputation and track record for repaying debts. Capacity is the borrower's ability to repay the loan, determined by their income and existing debt levels. And capital relates to the wealth or assets the borrower can offer as collateral. When banks conduct credit checks or require a co-signer, they are evaluating these aspects to decide on lending money.
mulitply (x + 5)(2x - 6)
Answer
2x^2+4x-30
Step-by-step explanation:
Foil
First
Outside
Inside
Last