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Ierofanga [76]
2 years ago
13

The table below shows the medal count of four countries at the 2012 Summer Olympics. Use the data to complete the statement.

Mathematics
1 answer:
n200080 [17]2 years ago
6 0

Answer:

2:1

Step-by-step explanation:

The U.S. has twice as many gold medals as the Russian Federation.

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What is the smallest prime number p such that
Ne4ueva [31]

The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.

<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>

The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.

i.e.

  • p^3 + 4p^2 + 4p

By factorization, we have:

  • = p(p+2)²

Now, to get exactly 30 divisor.

  • (p+2)² requires to give us 15 factors.

Therefore, we can have an equation p + 2 = p₁ × p₂²

where:

  • p₁ and  p₂ relate to different values of odd prime numbers.

So, for the least values of p + 2, Let us assume that:

  • p₁ = 5 and p₂ = 3

p + 2 = 5 × 3²

p + 2 = 5 × 9

p + 2 = 45

p = 45 - 2

p = 43

Therefore, we can conclude that the smallest prime number p such that

p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.

Learn more about prime numbers here:

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8 0
1 year ago
There are 64 students in a speech contest. Yesterday, Ā of them gave their speeches. Today, 7 of the remaining students gave the
Alexxx [7]

Answer:

23

Step-by-step explanation:

Ā means the average

So it means the average of 64 gave their speech which should be 64/2 = 32

So 32 gave their speeches yesterday,

7 gave today

Total number that has given is

32 + 7 = 39

Therefore the number remaining are

62 - 39 = 23

8 0
2 years ago
Solve the following equation simultaneously 1/x-5/y=7, 2/x+1/y=3​
maria [59]

Answer:

  (x, y) = (1/2, -1)

Step-by-step explanation:

Subtracting twice the first equation from the second gives ...

  (2/x +1/y) -2(1/x -5/y) = (3) -2(7)

  11/y = -11 . . . . simplify

  y = -1 . . . . . . . multiply by y/-11

Using the second equation, we can find x:

  2/x +1/-1 = 3

  2/x = 4 . . . . . . . add 1

  x = 1/2 . . . . . . . multiply by x/4

The solution is (x, y) = (1/2, -1).

_____

<em>Additional comment</em>

If you clear fractions by multiplying each equation by xy, the problem becomes one of solving simultaneous 2nd-degree equations. It is much easier to consider this a system of linear equations, where the variable is 1/x or 1/y. Solving for the values of those gives you the values of x and y.

A graph of the original equations gives you an extraneous solution of (x, y) = (0, 0) along with the real solution (x, y) = (0.5, -1).

6 0
2 years ago
Help me please quickly
Akimi4 [234]

Answer:

x ≥ 1

Step-by-step explanation:

→ As it is a shaded circle you know it ≤ or ≥

x ≥ 1

6 0
2 years ago
Using a spreadsheet program, create an amortization schedule for a 30-year mortgage of $500,000 at an annual interest rate of 4.
madreJ [45]

This exercise requires the ability to create Amortization Schedules Using a Spreadsheet program. Based on the information given about the Amortization of the loan, the principal payable per month became greater than the interest payable per month on the 159th month (given that the loan amount is $500,000.

<h3>In which month does the amount of principal in a monthly payment first exceed the amount of interest?</h3>

The amount of principal in a monthly payment first exceeds the interest payment In 159th Month. The interest on this month is $1, 248.39 while the principal on this month is $1, 205.46.

It is to be noted that when a loan is taken, the constituents of the amounts being paid back is the Principal and part of the interest on the loan.

<h3>How do you Calculate Amortization of Loans?</h3>

The yearly interest rate must be divided by 12.

Your monthly interest rate, for instance, will be 0.3525 percent if your annual interest rate is 4.23 percent (0.0423 annual interest rate x 12 months).

Additionally, you'll add 12 to the number of years remaining on your loan term.

<h3>How much interest is repaid for the term of the loan?</h3>

The total amount of interest that is paid for the term loan is $383,385.54

<h3>If the loan amount was $750,000 instead of $500,000, would the month in which the amount of principal in a monthly payment first exceeded the amount of interest change?</h3>

Yes it would change. It would change to the 165th month. In this month, the interest paid is $1, 834.00 while the principal paid back is $1,846.77. See the attached image for answer C.

Learn more about Amortization at;
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3 0
1 year ago
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