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3 years ago

Please help for #10 both parts will give 30 points!!!!!

Mathematics

1 answer:

Andreas93 [3]3 years ago

5 0

8x6= 48 (not necessary to divide by 8 since you'd have to multiply it by 2 anyway because there are 2 triangles)
6x12=72
10x12=120
12x8=96

48+72+120+96=336

336cm^2 is the answer

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What is the C of a circle that has a radius of 4.5

Jlenok [28]

Step-by-step explanation:

$C = 2\pi \: r \\ = 2 \times 3.14 \times 4.5 \\ = 3.14 \times 9 \\ =28.26 \: units$

5 0

3 years ago

Which of the following geometric series converges?

Artist 52 [7]

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is

$S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}$

Multiply both sides by r :

$rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n$

Subtract the latter sum from the first, which eliminates all but the first and last terms:

$S_n-rS_n=a-ar^n$

Solve for $S_n$ :

$(1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}$

Then as gets arbitrarily large, the term $r^n$ will converge to 0, leaving us with

$S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}$

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

8 0

2 years ago

If f(x) = 3 ^ x - 4 what is f(- 2) ?

Karolina [17]

Answer:

-35/9

Step-by-step explanation:

(3^-2)-4

1/9-4

-35/9

8 0

2 years ago

When Brooklyn runs the 400 meter dash, her finishing times are normally distributed with a mean of 76 seconds and a standard dev

KonstantinChe [14]

Using the Empirical Rule, it is found that her finishing time will be between 70 and 82 seconds in 95% of her races.

<h3>What does the Empirical Rule state?</h3>

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, the mean is of 76 seconds and the standard deviation is of 3 seconds, then:

76 - 2 x 3 = 70.

76 + 2 x 3 = 82.

Which means that values between 70 and 82 seconds are within 2 standard deviations of the mean, hence the percentage is of 95%.

More can be learned about the Empirical Rule at brainly.com/question/24537145

3 0

2 years ago

Marisol is being paid $792 to provide nutrition counseling, It took her 8 hours more than she expected, so

olchik [2.2K]

Answer: 44 hours.

Step-by-step explanation:

Marisol is being paid $792.

We know that the job took her 8 hours more than she expected, so if we define T as the time she expected, this job took her:

T + 8 hours.

The amount of money per hour that she expected is calculated as:

$792/T = X

And for those 8 extra hours, she won $4 less per hour, then we have:

$792/(T + 8hs) = X - $4

Then we have a system of equations:

$792/T = X

$792/(T + 8hs) = X - $4

To solve this, we can notice that in the first equation X is isolated, then we could replace that in the second equation to get:

$792/(T + 8hs) = $792/T - $4

Now we can solve this for T.

$792 = ($792/T - $4)*(T + 8hs) = $792 + $792*(8hs/T) - $4*T + $32*hs

0 = $792*(8hs/T) - $4*T + $32*hs

Let´s multiply this both sides by T

0*T = ($792*(8hs/T) - $4*T + $32*hs)*T

0 = $792*8hs - $4*T^2 +$32*T*hs

This is a quadratic equation, where i will write this witout units so it is easier to read and follow:

0 = -4*T^2 + 32*T + 792*8

The solutions cab be found by using the Bhaskara´s formula, these are:

$T = \frac{-32 +- \sqrt[2]{(32^2 - 4*(-4)*(792*8)} }{2*-4} = \frac{-32 +-320}{-8}$

Then the solutions are:

T = (-32 + 320)/-8 = -36 hours (This is a negative time, and it does not really have a meaning in this problem, so we can discard this option)

The other solution is:

T = (-32 - 320)/-8 = 44 hours.

Then we can conclude that she expected the job would take 44 hours in total.

5 0

2 years ago