Solve for x. 2х+25 3х + 1 69° 420 5x

Troy is building a rectangular garden that is 10 feet by 6 feet. what should be the length of the diagolas to ensure a 90 degree

Maksim231197 [3]

To find the length of the diagonals, Troy should use the Pythagorean Theorem. The diagonal is going to be the hypotenuse of the triangle (the side directly across from the 90 degree angle).

a^2 + b^2 = c^2
6^2 + 10 ^2 = c^2
136 = c^2; find the square root of 136
c = 11.66 feet

Troy's diagonals are approximately 11.66 feet.

5 0

4 years ago

$800 is invested at a rate of 7%. What will be the total amount of the investment after 3 1/2 years?

torisob [31]

Answer:

A = $996.00

Step-by-step explanation:

(I = A - P = $196.00)

Equation:

A = P(1 + rt)

Where:

A = Total Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

r = Rate of Interest per year in decimal; r = R/100

R = Rate of Interest per year as a percent; R = r * 100

t = Time Period involved in months or years

From the base formula, A = P(1 + rt) derived from A = P + I and I = Prt so A = P + I = P + Prt = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 7%/100 = 0.07 per year.

Solving our equation:

A = 800(1 + (0.07 × 3.5)) = 996

A = $996.00

The total amount accrued, principal plus interest, from simple interest on a principal of $800.00 at a rate of 7% per year for 3.5 years is $996.00.

4 0

3 years ago

If f(x) = x and g(x) = 2, what is (f*g)(x)?

gayaneshka [121]

Answer:

I think this question is askingg fofr f(g(x)), in which case you are simply inserting g(x) into the f(x) solution, in this case 2 for x. This is because (f*g)(x)=f(g(x)).

Step-by-step explanation:

6 0

3 years ago

A professor at a university wants to estimate the average number of hours of sleep students get during exam week. The professor

kotegsom [21]

Answer:

$n=(\frac{1.64(6.995)}{1.939})^2 =35.003 \approx 36$

So the answer for this case would be n=36 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =6.995$ represent the population standard deviation

n represent the sample size

Solution to the problem

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =1.939 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

If we replace we have this:

$n=(\frac{1.64(6.995)}{1.939})^2 =35.003 \approx 36$

So the answer for this case would be n=36 rounded up to the nearest integer

4 0

4 years ago

Is the length of the hypotenuse of a right triangle with legs that mea-

icang [17]

Answer:
Irrational Number

Step-by-step explanation:
So, since it's a right triangle, you can use Pythagorean Theorem to calculate the measure of the hypotenuse.

Pythagorean Theorem says the hypotenuse squared = the sum of the sides squared.

5² + 6² = 25 + 36 = 61

And the square root of 61 is 7.8102496.... and the decimal continues in no distinguishable pattern. Therefore, the length of the hypotenuse is an irrational number.

4 0

3 years ago

Solve for x. 2х+25 3х + 1 69° 420 5x - 2​

Solve for x. 2х+25 3х + 1 69° 420 5x - 2