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2 years ago

What functions have a range of {y £ R | -

Mathematics

1 answer:

Fudgin [204]2 years ago

4 0

Answer:

the second and the fourth have a range of real no

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I need to calculate X 2^x=200 Solve for x

antoniya [11.8K]

Remember
$log(a^z)=zlog(a)$
so

notice that 200=2*2*2*5*5, so x cannot be a whole number

take the log base 10 of both sides

$log_{10}(2^x)=log{10}(200)$
$xlog_{10}(2)=log{10}(200)$
divide both sides by $log_{10}(2)$
$x= \frac{log_{10}(200)}{log_{10}(2)}$

if we used $log_{2}$ instead of $log_{10}$ we would get
$x= log_{2}(200)$ because $log_{a}(a^b)=b$

8 0

3 years ago

find the value of an investment of $3500 for 3 years at an interest rate of 5.6% if the money is compounded weekly

sergeinik [125]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$3500\\
r=rate\to 5.6\%\to \frac{5.6}{100}\to &0.056\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{weekly, thus fifty two}
\end{array}\to &52\\
t=years\to &3
\end{cases}$

$\bf A=3500\left(1+\frac{0.056}{52}\right)^{52\cdot 3}\implies A=3500\left( \frac{6507}{6500} \right)^{156}
\\\\\\
A\approx 4139.9038869337$

3 0

3 years ago

Emily sold 66 boxes of cookies for a fundraiser. If she sold 40% of the total boxes of cookies sold for the fundraiser, how many

Kitty [74]

She sold about 40 boxes because you do 66 - 40% = 39.6 or about 40

5 0

3 years ago

What is the relationship between ∠HIK and ∠JIK?

blagie [28]

Complementary angles --- they add up to 90 degrees

4 0

3 years ago

If we sample from a small finite population without replacement, the binomial distribution should not be used because the event

seropon [69]

Answer:

5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

$\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}$

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

As we see, the situation is exactly the same, but changing the numbers. So the answer would be

$\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}$

Now compute each combination separately:

$\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700$

and now replace the values:

$\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}$

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

6 0

3 years ago