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3 years ago

Simplify the square root of five times the quantity ten minus four square root of two.

Mathematics

2 answers:

yuradex [85]3 years ago

6 0

Answer:

D. ten square root of five end root minus four square root of ten

Step-by-step explanation:

I got it right on the test

lbvjy [14]3 years ago

4 0

Answer:

I need Image but I thinck is D

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Rachel has 30 pounds of a mixture of candy that sells for $1.00/lb. If lollipops sell for $0.95/lb and caramel candies sell for

dimulka [17.4K]

L = pounds of lollipop
c = pounds of caramel candies

0.95l + 1.10c = 30 ($0.95/lb & $1.10/lb)
l + c = 30 (mixture sells for $1/lb)
c = 30 - l

0.95l + 1.10(30 - l) = 30 (Substitution)
0.95l + 33 - 1.10l = 30
-0.15l = -3 (move terms)
l = 20lbs

Hope this helps.

4 0

4 years ago

The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer ra

Snezhnost [94]

Let $X$ denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by $X_1,\ldots,X_{36}$ , each independently and identically distributed with distribution $X_i\sim\mathcal N(26,7.2)$ .

You want to find

$\mathbb P(X_1+\cdots+X_{36}>1000)=\mathbb P\left(\displaystyle\sum_{i=1}^{36}X_i>1000\right)$

Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to

$\mathbb P\left(36\displaystyle\sum_{i=1}^{36}\frac{X_i}{36}>1000\right)=\mathbb P\left(\overline X>\dfrac{1000}{36}\right)$

Recall that if $X\sim\mathcal N(\mu,\sigma)$ , then the sampling distribution $\overline X=\displaystyle\sum_{i=1}^n\frac{X_i}n\sim\mathcal N\left(\mu,\dfrac\sigma{\sqrt n}\right)$ with $n$ being the size of the sample.

Transforming to the standard normal distribution, you have

$Z=\dfrac{\overline X-\mu_{\overline X}}{\sigma_{\overline X}}=\sqrt n\dfrac{\overline X-\mu}{\sigma}$

so that in this case,

$Z=6\dfrac{\overline X-26}{7.2}$

and the probability is equivalent to

$\mathbb P\left(\overline X>\dfrac{1000}{36}\right)=\mathbb P\left(6\dfrac{\overline X-26}{7.2}>6\dfrac{\frac{1000}{36}-26}{7.2}\right)$
$=\mathbb P(Z>1.481)\approx0.0693$

5 0

3 years ago

Linda wants to determine the average salary for her employees for her Bakery business. Recorded below are the salaries for each

taurus [48]

The mean salary for Linda's employees is in thousands, is: 34,800.

Mean of a data set is the average of the data set.
To calculated the mean of a data set, use the formula: Mean = (∑fx)/∑f).

Thus:

∑fx = 974

∑f = 28

Therefore:

Mean = 974/28

Mean = 34.8

In thousands, the mean salary for Linda's employees is 34,800.

Learn more about mean of a data set on:

brainly.com/question/11015069

7 0

3 years ago

An old bone contains 80% of its original carbon-14. Use the half-life model to find the age of the bone

swat32

Answer:

This is an exponential decay problem. These problems are of the form:

y = c * ekt

y = amount of substance left

c = original amount of substance (Here, set this to 100%, or 1.)

e = exponential constant (~2.718)

k = rate of decay constant (We need to figure this out.)

t = time, in years (When t = 0, y = 1 (all of the carbon-14). When t = 5730, y = 0.5 (one half-life has passed). When t = the answer we're trying to find, y = 0.98 (98% of the carbon-14).)

First, we must find the value of k, the rate of decay constant. We know that after 5730 years (t = 5730), one-half of the carbon-14 will remain (y = 0.5).

y = c * ekt

0.5 = 1 * ek * 5730

0.5 = e5730k

To get rid of the e, take the natural logarithm (ln) of both sides:

ln(0.5) = ln(e5730k)

ln(0.5) = 5730k

ln(0.5)/5730 = k

ln(0.5) is a negative number, so our rate of decay constant will be negative. This is a little "sanity check", because radioactive decay means the amount of substance goes down over time. If you get a positive value of k, then you made a mistake somewhere.

Now that we have the rate of decay constant, we can find the value of t (in years) that will yield 98% of the carbon-14 remaining.

y = c * ekt

0.98 = 1 * e[ln(0.5)/5730]t

0.98 = e[ln(0.5)/5730]t

To get rid of the e, take the natural logarithm (ln) of both sides:

ln(0.98) = ln(e[ln(0.5)/5730]t)

ln(0.98) = [ln(0.5)/5730]t

ln(0.98) = ln(0.5)t / 5730

Solve for t:

5730 * ln(0.98) = ln(0.5)t

5730 * ln(0.98) / ln(0.5) = t

Put that into your calculator, to get t ~ 167 years. Both ln(0.98) and ln(0.5) are negative, so the negatives will cancel out to yield a positive number (another "sanity check").

Step-by-step explanation:

7 0

3 years ago

A campsite is 12.88 miles from a point directly below Mt. Adams. If the angle of elevation is 15.5° from the camp to the top of

nata0808 [166]

Answer:

3.57 miles

Step-by-step explanation:

Please consider the attachment.

We have been given that a campsite is 12.88 miles from a point directly below Mt. Adams. The angle of elevation is 15.5° from the camp to the top of the mountain. We are asked to find the height of the mountain.

We can see from the attachment that h is opposite side to angle 15.5 degrees and 12.88 miles in adjacent side.

We know that tangent relates opposite side of right triangle with its adjacent side.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$