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3 years ago

7^16/7^12=7^-18/? what is the missing denominator

1 answer:

4 0

$\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\
-------------------------------\\\\$

$\bf \cfrac{7^{16}}{7^{12}}=\cfrac{7^{-18}}{x}\implies x\cdot 7^{16}=7^{12}\cdot 7^{-18}\implies x\cdot 7^{16}=7^{12-18}
\\\\\\
x\cdot 7^{16}=7^{-6}\implies x=\cfrac{7^{-6}}{7^{16}}\implies x=\cfrac{7^{-6}\cdot 7^{-16}}{1}\implies x=7^{-6-16}
\\\\\\
\boxed{x=7^{-22}}\implies x=\cfrac{1}{7^{22}}$

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Answer:

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Step-by-step explanation:

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2 years ago

Read 2 more answers

A manufacturer of sprinkler systems designed for fire protection claims that the average activating temperature is at least 135°

nirvana33 [79]

Answer:

$z=\frac{133-135}{\frac{3.3}{\sqrt{32}}}=-3.428$

$p_v =P(z$

If we compare the p value and the significance level given for example $\alpha=0.1$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the true mean is significantly lower than 135 so the claim not makes sense

Step-by-step explanation:

Data given and notation

$\bar X=133$ represent the sample mean

$\sigma=3.3$ represent the standard deviation for the population

$n=32$ sample size

$\mu_o =135$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the true mena is at least 135, the system of hypothesis would be:

Null hypothesis: $\mu \geq 135$

Alternative hypothesis: $\mu < 135$

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{133-135}{\frac{3.3}{\sqrt{32}}}=-3.428$

Calculate the P-value

Since is a one-side lower test the p value would be:

$p_v =P(z$

Conclusion

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3 years ago

the ratio of cars to trucks at an auto dealer is 3/2. if there are 144 cars at the dealership, how many trucks are there?

lana [24]

Answer:

Step-by-step explanation:

for every 3 cars there is 2 trucks

If you have 144 cars then we divide 144 by 3 to get 48

That is not the answer though because that would be a 3/1 ratio

We then multiply 48 by 2 to get 96

5 0

3 years ago

Please help with 11c!?

Contact [7]

Answer:

"To the nearest year, it would be about 9 years"

Step-by-step explanation:

11c)

This is compound growth problem. It goes by the formula:

$F=P(1+r)^t$

Where

F is the future amount

P is the present (initial) amount

r is the rate of growth, in decimal

t is the time in years

Given,

P = 20,000

r = 8% = 8/100 = 0.08

F = double of initial amount = 2 * 20,000 = 40,000

We need to find t:

$F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t$

To solve exponentials, we can take Natural Log (Ln) of both sides:

$2=(1.08)^t\\Ln(2)=Ln((1.08)^t)$

Using the rule shown below we can simplify and solve:

$Ln(a^b)=bLn(a)$

We can write:

$Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064$

To the nearest year, that would be about 9 years

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3 years ago

Which of the following fractions does not represent a repeating decimal? 2/3, 4/5, 9/11, 8/9

Misha Larkins [42]

Answer:

the answer is 4/5. The decimal does not repeat

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3 years ago