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3 years ago

There are 99 males and 121 females participating in a marathon. What percent of the participants are female?

Mathematics

1 answer:

ioda3 years ago

8 0

To do this, we first want to see how many participants there are in total by adding both males and females.

$99+121=220$

Now we know that there were 220 total participants, but only 121 were females.

This allows us to set up the fraction 121/220= the percent female.

$\frac{121}{220} =0.55$

or 55%

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What is the smallest integer $n$, greater than $1$, such that $n^{-1}\pmod{130}$ and $n^{-1}\pmod{231}$ are both defined?

olasank [31]

First of all, the modular inverse of n modulo k can only exist if GCD(n, k) = 1.

We have

130 = 2 • 5 • 13

231 = 3 • 7 • 11

so n must be free of 2, 3, 5, 7, 11, and 13, which are the first six primes. It follows that n = 17 must the least integer that satisfies the conditions.

To verify the claim, we try to solve the system of congruences

$\begin{cases} 17x \equiv 1 \pmod{130} \\ 17y \equiv 1 \pmod{231} \end{cases}$

Use the Euclidean algorithm to express 1 as a linear combination of 130 and 17:

130 = 7 • 17 + 11

17 = 1 • 11 + 6

11 = 1 • 6 + 5

6 = 1 • 5 + 1

⇒ 1 = 23 • 17 - 3 • 130

Then

23 • 17 - 3 • 130 ≡ 23 • 17 ≡ 1 (mod 130)

so that x = 23.

Repeat for 231 and 17:

231 = 13 • 17 + 10

17 = 1 • 10 + 7

10 = 1 • 7 + 3

7 = 2 • 3 + 1

⇒ 1 = 68 • 17 - 5 • 231

Then

68 • 17 - 5 • 231 ≡ = 68 • 17 ≡ 1 (mod 231)

so that y = 68.

3 0

3 years ago

I need help with this question ASAP!!!!!!!!!!!!!

Mazyrski [523]

The height of the flag pole is 51 ft.

Solution:

Paul creates the smaller triangle and flag pole creates the larger triangle.

Base of smaller triangle = 10 ft

Height of smaller triangle = 6 ft

Base of the larger triangle = 85 ft

Let the height of the flagpole be h.

$$\Rightarrow \frac{6}{10} =\frac{h}{85}$

Multiply by 85 on both sides.

$$\Rightarrow 85 \times \frac{6}{10} =\frac{h}{85} \times85$

$$\Rightarrow \frac{510}{10} =h$

⇒ 51 = h

The height of the flag pole is 51 ft.

7 0

3 years ago

15. Jessica is trying to hire a babysitter that charges less than $10 per hour (not including any extra fees).

tresset_1 [31]

Answer:

A. and B.

Step-by-step explanation:

A. $34 - $10= $24 hourly fee divided by 3= $8 per hour.

B. $66 - $12= $54 hourly fee divided by 6= $9 per hour.

C.$92-$8= $84 hourly fee divided by 7= $12 per hour.

D. $52.5-$0= $52.5 hourly fee divided by 3.5= $15 per hour.

E. $112-$2=$110 hourly fee divided by 5.5= $20 per hour.

So Mia and Alex are the cheapest .

7 0

3 years ago

Which pipe configuration can deliver more water to

Stels [109]

Answer: One 8-cm pipe (Its is greater than the total area of of two 4-cm pipes)

Step-by-step explanation:

The area of a circle can be calculate with this formula:

$A=\pi r^2$

Where "r" is the radius of the circle.

We need to calculate the area of 8-cm pipe. In this case:

$r=8cm$

Then, substituting the radius into the formula, we get:

$A=\pi (8cm)^2\\\\A=201.06cm^2$

Now we must calculate the area of the two 4-cm pipes.

Since they are two pipes, the formula is:

$A=2\pi r^2$

In this case:

$r=4cm$

Then, substituting into the formula, we get:

$A=2\pi (4cm)^2\\\\A=100.53cm^2$

Therefore, since the area of one 8-cm pipe is greater than the total area of of two 4-cm pipes, we conclude that the pipe configuration that can deliver more water to residents is:

One 8-cm pipe

4 0

3 years ago

There are 47 students in a class and 35 of these students passed their Geometry test.

Dafna11 [192]

Answer:

74.47%

Step-by-step explanation:

Divide the total number of students by the number who passed

passed/total

35/47

0.74468085

As a percent:

0.74468085*100=74.4680851

Rounded to the nearest hundreth:

74.4680851

74.47%

So, 74.47% passed the geometry test

Hope this helps! :)

5 0

3 years ago

There are 99 males and 121 females participating in a marathon. What percent of the participants are female?​

There are 99 males and 121 females participating in a marathon. What percent of the participants are female?