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3 years ago

Or is it c. 10.96 or d 13.0 (sorry the rest couldn’t fit in the picture) please help me I don’t get it.

Mathematics

1 answer:

solong [7]3 years ago

6 0

We have a right triangle with legs of 6 and 8. The hypotenuse is unknown so let it be x for now

Plug these three values
a = 6
b = 8
c = x
into the Pythagorean Theorem below. Then solve for x

a^2 + b^2 = c^2
6^2 + 8^2 = x^2
36+64 = x^2
100 = x^2
x^2 = 100
sqrt(x^2) = sqrt(100) ... apply the square root to both sides
x = 10

The final answer is 10 ft. This option isn't listed which makes me think your teacher made a typo somewhere.

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Number 8 only please

givi [52]

Answer:

Should be roughly 79.76% if I'm doing this right.

Step-by-step explanation:

Looking at the problem, you're given 3 things:

1) 6.8 million tonnes are recycled;

2) 6.8 million tonnes is 27% of the total household waste;

3) 20.1 million tonnes could be recycled.

Since they're asking for what percentage of total household waste could be recycled, you're looking at a multi-step cross multiplication problem.

It's not very difficult though, don't worry.

So I'm gonna start by telling you to just forget that the word "million" exists for the moment. You only need 6.8, 20.1, and 27%.

Setting up the first part of the problem requires you to convert 27% into a fraction. That's $\frac{27}{100}$ .

6.8 is 27% of some mysterious number that we need to figure out what percent of household waste could be recycled, so that'll be set up on the opposite side of the equal sign as the equivalent to 27.

So we're starting out with this: $\frac{6.8}{?} =\frac{27}{100}$

Since you're trying to initially find the total household waste, we're setting x as the variable to solve for.

$\frac{6.8}{x} =\frac{27}{100}$

Cross-multiplying** means you multiply the numerator of one side of the equal sign to the denominator of the other side of the equal sign, and vice versa (denominator of one side to numerator of other). So multiply 6.8 to 100, and 27 to x.

$680=27x$

Now that you have this, you have to isolate x. Divide both sides by 27 to do this.

$25.185185...=x$

I'm gonna round that for simplicity's sake, because 185 repeats.

$25.2=x$

So we have 25.2 million tonnes of total household waste. Great! Now we can find the percentage of household waste that could be recycled.

Since we have how much could be recycled and the total, we just need to solve for the percent this time. So this is what the set-up will look like:

$\frac{20.1}{25.2} =\frac{x}{100}$

x being the percent we're solving for.

Cross-multiply again:

$2010=25.2x$

Divide both sides by 25.2:

$79.761904761904...=x$

Then round for simplicity's sake:

$79.76=x$

And you get 79.76% of household waste could be recycled.

Hope this helped!

**Be careful with cross-multiplying when you get to higher level math though. Not every situation allows for cross-multiplying. In fact, you can only cross-multiply when there's an equal sign.

6 0

2 years ago

Subtract. (6x + 5) - (x+3)

Roman55 [17]

(6x+5)-(x+3).

6x+5-x-3.

Add the like terms.

6x-x+5-3.

We get.

5x+2.

6 0

2 years ago

Read 2 more answers

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Anettt [7]

Answer:

Choice C: approximately 121 green beans will be 13 centimeters or shorter.

Step-by-step explanation:

What's the probability that a green bean from this sale is shorter than 13 centimeters?

Let the length of a green bean be $X$ centimeters.

$X$ follows a normal distribution with

mean $\mu = 11.2$ and
standard deviation $\sigma = 2.1$ .

In other words,

$X\sim \text{N}(11.2, 2.1^{2})$ ,

and the probability in question is $X \le 13$ .

Z-score table approach:

Find the z-score of this measurement:

$\displaystyle z= \frac{x-\mu}{\sigma} = \frac{13-11.2}{2.1} = 0.857143$ . Closest to 0.86.

Look up the z-score in a table. Keep in mind that entries on a typical z-score table gives the probability of the left tail, which is the chance that $Z$ will be less than or equal to the z-score in question. (In case the question is asking for the probability that $Z$ is greater than the z-score, subtract the value from table from 1.)

$P(X\le 13) = P(Z \le 0.857143) \approx 0.8051$ .

"Technology" Approach

Depending on the manufacturer, the steps generally include:

Locate the cumulative probability function (cdf) for normal distributions.
Enter the lower and upper bound. The lower bound shall be a very negative number such as $-10^{9}$ . For the upper bound, enter $13$
Enter the mean and standard deviation (or variance if required).
Evaluate.

For example, on a Texas Instruments TI-84, evaluating $\text{normalcdf})(-1\text{E}99,\;13,\;11.2,\;2.1 )$ gives $0.804317$ .

As a result,

$P(X\le 13) = 0.804317$ .

Number of green beans that are shorter than 13 centimeters:

Assume that the length of green beans for sale are independent of each other. The probability that each green bean is shorter than 13 centimeters is constant. As a result, the number of green beans out of 150 that are shorter than 13 centimeters follow a binomial distribution.

Number of trials $n$ : 150.
Probability of success $p$ : 0.804317.

Let $Y$ be the number of green beans out of this 150 that are shorter than 13 centimeters. $Y\sim\text{B}(150,0.804317)$ .

The expected value of a binomial random variable is the product of the number of trials and the probability of success on each trial. In other words,

$E(Y) = n\cdot p = 150 \times 0.804317 = 120.648\approx 121$