which right triangle’s unknown leg measures is 43 square root units ? Assume the given length are in the same unit of measure.

Micah rows his boat on a river 4.48 miles downstream, with the current, in 0.32 hours. He rows back upstream the same distance,

Molodets [167]

Let the speed of the current be y and the speed of Micah's sailing speed be x. Then 4.48/(x + y) = 0.32
4.48/(x - y) = 0.56

0.32x + 0.32y = 4.48 . . . (1)
0.56x - 0.56y = 4.48 . . . (2)
(1) x 7 => 2.24x + 2.24y = 31.36 . . . (3)
(2) x 4 => 2.24x - 2.24y = 17.92 . . . (4)
(3) - (4) => 4.48y = 13.44
y = 3
From (1), 0.32x + 0.32(3) = 4.48
0.32x = 4.48 - 0.96 = 3.52
x = 3.52/0.32 = 11

Therefore, the speed of the current is 3 miles per hour.

3 0

2 years ago

Read 2 more answers

There were 8,651 deaths and 14,662 births reported in Hillsborough County in the year 2000. If there were 998,948 people living

alexdok [17]

Crude birth rate is all the time reported per 1000 living people.

To compute for this, the formula is number of births x 1000 divided by the estimated population at midyear. So plugging in the values given:

14,662 x 1000 divided by 994,948

= 14662000 / 994948

= 14.68 per 1000 living people.

7 0

2 years ago

Read 2 more answers

Prove the following using a proof by contradiction:The average of four real numbers is greater than or equal to at least one of

skelet666 [1.2K]

Answer:

By contradiction it can be proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

Step-by-step explanation:

Method of contradiction means we assume opposite to the facts to be proved and then we contradict our assumption.

As a result, we prove the fact.

Here, let the four number be:

$p, q, r, s$

The average will be Sum of all numbers divided by count of numbers.

$\dfrac{p+ q+ r+ s}4$

Now, let us assume the opposite that the average is less than all the numbers.

i.e.

$\dfrac{p+ q+ r+ s}4$

Now, let us add all of them:

$\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 +\dfrac{p+ q+ r+ s}4 < p+q+r+s\\\Rightarrow \dfrac{4(p+q+r+s)}4$

Which can never be possible hence, our assumption is contradicted.

our assumption is wrong.

Therefore, by contradiction it is proved that:

Average of four real numbers will be greater than or equal to at least one of the four real numbers.

8 0

2 years ago

What is the future value of $845 a year for seven years at an interest rate of 11.3 percent? $6,683.95 $6,075.69 $8,343.51 $8,00

k0ka [10]

The future value of cash whose initial value is $845, at the rate of 11.3% for 7 years will be calculated using the compound interest rate, that is:
A=p(1+r/100)^n
where:
A=future amount
r=rate=11.3%=0.113
time=7 years
thus the future value of our cash will be:
A=845(1+0.113)^7
A=845(1.113)^7
A=$1,787.82

7 0

2 years ago

Read 2 more answers

A survey of 2690 musicians showed that 368 of them are left-handed. Find a point estimate for p, the population proportion of mu

makkiz [27]

Answer: 0.137.

Step-by-step explanation:

Let p be the population proportion of musicians that are left-handed.

Given: Sample size : n= 2690 [subset of population]

Number of musicians that are left-handed: x= 368

Then the sample proportion: $\hat{p}=\dfrac{368}{2690}\approx0.137$

Since sample proportion is the best point estimate of the population proportion.

Hence, a point estimate for p, the population proportion of musicians that are left-handed is 0.137.

7 0

2 years ago