The following data set represents the ACT scores for students in Mrs. Smith's collegescience class.18 32 16 2319 21 28 2922 30 19 21What is the range for the ACT scores for the class?

Answers

Answer 1

Answer:

The range is the difference between the greatest and the smallest number, so it is 32 - 16 = 16.

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Paul owns 8 CDs, 6 of which are rock-and-roll. What percent of Paul's CDs are rock-and-roll?

Answers

Answer:

75% are rock and roll

Step-by-step explanation:

6 /8 = 3/4 = 0.75 = 75%

The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. make a system of equations to find the smallest number of busses the orchestra can rent. Let x= the number of busses and y= the number of vans make an equation representing the number of vehicles needed. __________ make an equation representing the total number of seats in vehicles for the orchestra members. __________ Solve the system of equations. How many busses does the orchestra need to rent? ____________ How many 12-passenger vans does the orchestra need to rent? ____________

Answers

Using a Systemof equations, the numberof buses and vans required are 3respectively.

Usingthesystemofequations:

Totalnumberofbuses:

b + v ≤ 6 - - - - (1)

Totalnumberofpassengers:

25b + 12v ≥ 111 - - - - (2)

From (1)

b = 6 - v - - - - - (3)

Substitute(3)into(2)

25(6-v) + 12v = 111

150 - 25v + 12v = 111

-13v = 111 - 150

-13v = - 39

v=39/13

v=3

From (3)

b = 6 - 3

b=3

Hence, the number of vans and buses required are 3and 3 respectively.

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- Make an equation representing the number of vehicles needed.

We have six drivers so

x + y ≤ 6

That's not really an equation; it's an inequality. We want to use all our drivers so we can use the small vans, so

x + y = 6

- Make an equation representing the total number of seats in vehicles for the orchestra members.

s = 25x + 12y

That's how many seats total; it has to be at least 111 so again an inequality,

25x + 12y ≥ 111

We solve it like a system of equations.

x + y = 6

y = 6 - x

111 = 25x + 12y = 25x + 12(6-x)

111 = 25x + 72 - 12x

111 - 72 = 13 x

39 = 13 x

x = 3

Look at that, it worked out exactly. It didn't have to.

y = 6 - x = 3

Answer: 3 buses, 3 vans

Barbara is 142 cm tall this is 2 cm less than 3 times her height at birth find her heaight at birth

Answers

142/3= 47.333-2 =45.333

At the end of 2019, Mark owes $250,000 on the mortgage related to the 2016 purchase of his residence. When his daughter went to college in the fall of 2019, he borrowed $20,000 through a home equity loan on his house to help pay for her education. The interest expense on the main mortgage is $15,000, and the interest expense on the home equity loan is $1,500. How much of the interest is deductible as an itemized deduction?

Answers

Answer:

$15,000

Step-by-step explanation:

The $1500 interest on a home equity loan used for purposes other than home improvement is not deductible with other home loan interest as an itemized deduction.

However, the interest on a loan for qualified educational expenses may be considered an adjustment to income, within limits.

Only the $15,000 main mortgage interest can be an itemized deduction.

Final answer:

The total possible mortgage interest deduction for Mark in this scenario is $16,500. However, the actual amount he can deduct depends on his adjusted gross income and whether his itemized deductions exceed the standard deduction.

Explanation:

Under US tax law, taxpayers can deduct the interest on home mortgages and home equity loans, subject to some limitations. The interest expense on the main mortgage ($15,000) and the interest expense on the home equity loan ($1,500) can be combined for a total interest deduction of $16,500. However, the deduction may not be the full amount if there are other factors that would limit the amount of itemized deductions that Mark can claim. This can depend on his adjusted gross income and whether the total of his itemized deductions exceeds the standard deduction. It's also worth noting that the tax benefits of home ownership, such as the mortgage interest deduction, is a key reason why many people choose to buy rather than rent, as it can lead to significant financial savings.

Learn more about Mortgage Interest Deduction here:

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Disculpen alguien sabe de algun buen curso o tutorial para saber calculo?

Answers

Puedes ver a https://es.khanacademy.org/math/calculus-home

The function f(x,y,z)equals2 x plus z squared has an absolute maximum value and absolute minimum value subject to the constraint x squared plus 2 y squared plus 3 z squaredequals16. Use Lagrange multipliers to find these values.