A sample of 50 students is taken from a local college and it is found that the

Likurg_2 [28]

.7766 approximately

8 0

3 years ago

A recipe calls for 3/4 lb of cream cheese. A small tub of cream cheese at the grocery store weighs 12oz. Is this enough cream ch

Vsevolod [243]

Yes this is enough cream cheese

4 0

4 years ago

Can someone tell me how

gulaghasi [49]

the way I get the subsequent term, nevermind the exponents, the exponents part is easy, since one is decreasing and another is increasing, but the coefficient, to get it, what I usually do is.

multiply the current coefficient by the exponent of the first-term, and divide that by the exponent of the second-term + 1.

so if my current expanded term is say 7a³b⁴, to get the next coefficient, what I do is (7*3)/5 <----- notice, current coefficient times 3 divided by 4+1.

anyhow, with that out of the way, lemme proceed in this one.

$\bf ~~~~~~~~\textit{binomial theorem expansion} \\\\ \qquad \qquad (1+ax)^n\implies \begin{array}{llll} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(1)^n(ax)^0\\\\ 2&+\frac{(1)(n)}{1}\to n&(1)^{n-1}(ax)^1\\\\ 3&+\frac{n\cdot (n-1)}{2}&(1)^{n-2}(ax)^2 \end{array}$

so, following that to get the next coefficient, we get those equivalents as you see there for the 2nd and 3rd terms.

so then, we know that the expanded 2nd term is 24x therefore

$\bf n(1)^{n-1}(ax)1 = 24x\implies n(1)(ax)=24x\implies nax=24x\implies n=\cfrac{24}{a}$

we also know that the expanded 3rd term is 240x², therefore we can say that

$\bf \cfrac{n(n-1)}{2}~~(1)^{n-2}(ax)^2 = 240x^2\implies \cfrac{n(n-1)}{2}(1)(a^2x^2) = 240x^2 \\\\\\ \cfrac{(n^2-n)(a^2x^2)}{2}=240x^2\implies \cfrac{(n^2-n)(a^2)}{2}=\cfrac{240x^2}{x^2}\implies \cfrac{a^2n^2-a^2n}{2}=240 \\\\\\ a^2n^2-a^2n=480$

but but but, we know what "n" equals to, recall above, so let's do some quick substitution

$\bf a^2n^2-a^2n=480\qquad \boxed{n=\cfrac{24}{a}}\qquad a^2\left( \cfrac{24}{a} \right)^2-a^2\left( \cfrac{24}{a} \right)=480 \\\\\\ a^2\cdot \cfrac{24^2}{a^2}-24a=480\implies 24^2-24a=480\implies 576-24a=480 \\\\\\ -24a=-96\implies a=\cfrac{-96}{-24}\implies \blacktriangleright a = 4\blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ n=\cfrac{24}{a}\implies n=\cfrac{24}{4}\implies \blacktriangleright n=6 \blacktriangleleft$

7 0

4 years ago

Given that 1 inch=2.54cm how many centimeters are there in 4 feet

telo118 [61]

Answer: The answer is 121.92

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

When completing an online shopping transaction, a typical shopper takes 5 seconds to select each product and another 28 seconds

JulijaS [17]

Answer:

a) 4 products

b) 10 products

Step-by-step explanation:

When completing an online shopping transaction, a typical shopper takes 5 seconds to select each product and another 28 seconds to complete the check-out process.

For 1 product, the total time =

5 seconds + 28 seconds = 33 second.

We can derive an equation

Total time of transaction = 5x + 28

Where x is the number of products you are selecting

a) If it takes 48 seconds to complete a transaction, how many products are being purchased?

Total time = 5x + 28

48s = 5x + 28

5x = 48 - 28

5x = 20

x = 20/5

x = 4 items

b) If it takes 80 seconds to complete a transaction, how many products are being purchased?

Total time = 5x + 28

80s = 5x + 28

5x = 80 - 28

5x = 52

x = 52/5

x = 10 items

In whole number = 10 items

5 0

3 years ago