MATHEMATICS HIGH SCHOOL

Which would be appropriate compatible numbers to use to estimate (19 4/5)(4/6)

Answers

Answer 1

Answer:

Answer:

Approximately 10

Step-by-step explanation:

19 / 5 Approximately 4

4 * 4 = 16

16 * 4 / 64

64 / 6 * = Approximately 10 / 10.6 ish

Actual Answer is 10.133

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The population of the country of Oz was 600,000 in the year 2010. The population is expected to grow by a factorof 5% annually. The annual food supply of Oz is currently sufficient for a population of 700,000 people and isincreasing at a rate that will supply food for an additional 10,000 people per year.c. At what point does the population exceed the food supply? Justify your response.
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Fraction: least to greatest... 2/3, 9/16, 0.52
Plz halp i need to get this right.

a square wrestling mat has a perimeter of (12x - 32) feet. Write an expression in simplest form that represents the side length of mat.

Answers

In a square, all four sides are equal, so you would take the perimeter and divide by 4.

(12x - 32)/4 = 3x - 8 feet

Plz help me!!The data below represents the number of medals won by the top ten countries in the 2014

Winter Olympics. If the mean is 20.4 and the standard deviation is 7.9, circle all values that

fall within one standard deviation of the mean.

6, 11, 15, 17, 19, 24, 25, 26, 28, 33

Answers

Answer:

You should circle:

15, 17, 19, 24, 25, 26, 28

Step-by-step explanation:

The values x that falls within 1 standard deviation of the mean are those which.

$|x - 20.4| \leq 7.9$

|6 - 20.4| = 14.4 > 7.9

6 is not within 1 standard deviation of the mean.

|11 - 20.4| = 9.4 > 7.9

11 is not within 1 standard deviation of the mean.

|15 - 20.4| = 5.4 < 7.9

15 is within 1 standard deviation of the mean.

|17 - 20.4| = 3.4 < 7.9

17 is within 1 standard deviation of the mean.

|19 - 20.4| = 1.4 < 7.9

19 is within 1 standard deviation of the mean.

|24 - 20.4| = 3.6 < 7.9

24 is within 1 standard deviation of the mean.

|25 - 20.4| = 4.6 < 7.9

25 is within 1 standard deviation of the mean.

|26 - 20.4| = 5.6 < 7.9

26 is within 1 standard deviation of the mean.

|28 - 20.4| = 7.6 < 7.9

28 is within 1 standard deviation of the mean.

|33 - 20.4| = 12.6 > 7.9

33 is not within 1 standard deviation of the mean.

Solve the inequality:

4|x+5| -2 <10

Answers

4 |x + 5| - 2 < 10 4 |x + 5| - 2 < 10
4 |x + 5| < 12 4(x + 5) - 2 < 10
------------ ----- 4x + 20 - 2 < 10
4 4 4x + 18 < 10
|x + 5| < 3 4x < -8
-x - 5 < 3 ---- ------
-x < 8 4 4
---- --- X < -2
-1 -1
X > -8

-8 < x < -2

A circle has a radius of 11 cm. What is the approximate area of the circle? Use 3.14 to approximate pi. Write the answer to the nearest hundredth.

Answers

area of a circle is pi x r x r
then you substitute the numbers in
therefore you would get 3.14 x 11 x 11 = 379.994
to the nearest hundredth degree would to 379 cm squared because you are finding the area so you put a small 2 above the cm
the person above has done it wrong as they have halved the radius but you only have the diameter to get the radius and they have used the wrong equation

For the love of God help me !! I'm desperate for it tomorrow

Answers

Try to relax. Your desperation has surely progressed to the point where
you're unable to think clearly, and to agonize over it any further would only
cause you more pain and frustration.
I've never seen this kind of problem before. But I arrived here in a calm state,
having just finished my dinner and spent a few minutes rubbing my dogs, and
I believe I've been able to crack the case.

Consider this: (2)^a negative power = (1/2)^the same power but positive.

So:
Whatever power (2) must be raised to, in order to reach some number 'N',
the same number 'N' can be reached by raising (1/2) to the same power
but negative.

What I just said in that paragraph was: log₂ of(N) = - log(base 1/2) of (N) .
I think that's the big breakthrough here.
The rest is just turning the crank.

Now let's look at the problem:

log₂(x-1) + log(base 1/2) (x-2) = log₂(x)

Subtract log₂(x) from each side:

log₂(x-1) - log₂(x) + log(base 1/2) (x-2) = 0

Subtract log(base 1/2) (x-2) from each side:

log₂(x-1) - log₂(x) = - log(base 1/2) (x-2) Notice the negative on the right.

The left side is the same as log₂[ (x-1)/x ]

==> The right side is the same as +log₂(x-2)

Now you have: log₂[ (x-1)/x ] = +log₂(x-2)

And that ugly [ log to the base of 1/2 ] is gone.

Take the antilog of each side:

(x-1)/x = x-2

Multiply each side by 'x' : x - 1 = x² - 2x

Subtract (x-1) from each side:

x² - 2x - (x-1) = 0

x² - 3x + 1 = 0

Using the quadratic equation, the solutions to that are
x = 2.618
and
x = 0.382 .

I think you have to say that x=2.618 is the solution to the original
log problem, and 0.382 has to be discarded, because there's an
(x-2) in the original problem, and (0.382 - 2) is negative, and
there's no such thing as the log of a negative number.

There,now. Doesn't that feel better.

Nth term question help please

Answers

Answer:

$\displaystyle{a.) \ \ a_n = -2n+14}\n\n\displaystyle{b.) \ \ a_n = -5n+30}$

Step-by-step explanation:

Part A

The common difference is -2 as the sequence decreases down to 2 each. Thus, the sequence is an arithmetic sequence. To find the nth term of an arithmetic sequence, we can follow the formula:

$\displaystyle{a_n = a_1+\left(n-1\right)d}$

Where $a_n$ is the nth term, $a_1$ is the first term, and $d$ is the common difference which we know that it is -2. By substitution of values we know, we will have:

$\displaystyle{a_n = 12+\left(n-1\right)\left(-2\right)}\n\n\displaystyle{a_n = 12-2n+2}\n\n\displaystyle{a_n = -2n+14}$

Hence, the nth term of the sequence is $\displaystyle{\bold{a_n = -2n+14}}$

Part B

The common difference is -5 as the sequence decreases by 5 each. This also makes the sequence an arithmetic sequence. Thus, we can apply the same formula as we did previously. By substitution of known values, we will have:

$\displaystyle{a_n = 25+\left(n-1\right)\left(-5\right)}\n\n\displaystyle{a_n = 25-5n+5}\n\n\displaystyle{a_n = -5n+30}$

Hence, the nth term of the sequence is $\displaystyle{\bold{a_n = -5n+30}}$

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