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4 years ago

6²/6⁴ A)66 B)36 C)1/36 D)1/12

1 answer:

5 0

When you divide the same numbers with powers, you subtract the powers to simplify it.

So with 6² / $6^{4}$ the powers are subtract:
(² ⁻ ⁴ = ⁻²)

6⁻² / 6⁴ = 6⁻²

6⁻² as a fraction is 1/36

So the answer is C

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3x + 15 = -45 what does x equal

Alekssandra [29.7K]

Answer: x = -20

Step-by-step explanation:

Here is the step-by step solution

3x + 15 = -45

3x = -60

x = -20

4 0

3 years ago

Read 2 more answers

Solve the problem. Type the number in the box that correctly completes the sentence.

motikmotik

Answer:

5 miles

Step-by-step explanation:

Think of this like a triangle. From the bottom of the tower, to the top of the tower, to the point 3 miles away, and back to the bottom of the tower.

So we already have 2 side lengths. The height of the tower, 3 miles, and the base, 4 miles. In order to find the 3rd length, the distance from the top of the tower to the point 4 miles away from the bottom, we need to apply the formula A squared + B squared = C squared.

We have A and B, (3 and 4) and we need C.

A squared (3 squared) is 9

B squared (4 squared) is 16

so 9 + 16 = C squared

9 + 16 = 25

C squared = 25

square root of 25 is 5

C = 5

The distance from the top of the tower to the point 4 miles away is 5.

3 0

3 years ago

According to a bridal magazine, the average cost of a wedding reception for an American wedding is $8213. Assume that this avera

Thepotemich [5.8K]

Answer:

a. The point estimate of the corresponding population mean is of $8213.

b. The margin of error is of $103.

c. The 98% confidence interval for the corresponding population mean is between $7973.5 and $8452.5, which means that for all weedings, we are 98% sure that the true population mean is in this interval.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. What is the point estimate of the corresponding population mean?

The sample mean is of $8213. So, by the Central Limit Theorem, the point estimate of the corresponding population mean is of $8213.

b. What is the margin of error for this estimate (use2 standard deviations (divided by Vn) to either side of the mean is used when no specific confidence level is stated).

Sample of 450, standard deviation of $2185. So

$M = \frac{2185}{\sqrt{450}} = 103$

The margin of error is of $103.

c. Create and interpret a 98% confidence interval for the corresponding population mean.

The confidence interval is given by:

$\mu \pm M*z$

In which $\mu$ is the sample mean and z is the value related to the confidence level.

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a pvalue of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.325$ .

Then

$\mu - M*z = 8213 - 2.325*103 = 7973.5$

$\mu + M*z = 8213 + 2.325*103 = 8452.5$

The 98% confidence interval for the corresponding population mean is between $7973.5 and $8452.5, which means that for all weedings, we are 98% sure that the true population mean is in this interval.

4 0

3 years ago

Suppose that the population P(t) of a country satisfies the differential equation dP/dt = kP (600 - P) with k constant. Its pop

jeka94

Answer:

The country's population for the year 2030 is 368.8 million.

Step-by-step explanation:

The differential equation is:

$\frac{dP}{dt}=kP(600 - P)\\\frac{dP}{P(600 - P)} =kdt$

Integrate the differential equation to determine the equation of P in terms of t as follows:

$\int\limits {\frac{1}{P(600-P)} } \, dP =k\int\limits {1} \, dt \\(\frac{1}{600} )[(\int\limits {\frac{1}{P} } \, dP) - (\int\limits {\frac{}{600-P} } \, dP)]=k\int\limits {1} \, dt\\\ln P-\ln (600-P)=600kt+C\\\ln (\frac{P}{600-P} )=600kt+C\\\frac{P}{600-P} = Ce^{600kt}$

At t = 0 the value of P is 300 million.

Determine the value of constant C as follows:

$\frac{P}{600-P} = Ce^{600kt}\\\frac{300}{600-300}=Ce^{600\times0\times k}\\\frac{1}{300} =C\times1\\C=\frac{1}{300}$

It is provided that the population growth rate is 1 million per year.

Then for the year 1961, the population is: P (1) = 301

Then $\frac{dP}{dt}=1$ .

Determine k as follows:

$\frac{dP}{dt}=kP(600 - P)\\1=k\times300(600-300)\\k=\frac{1}{90000}$

For the year 2030, P (2030) = P (70).

Determine the value of P (70) as follows:

$\frac{P(70)}{600-P(70)} = \frac{1}{300} e^{\frac{600\times 70}{90000}}\\\frac{P(70)}{600-P(70)} =1.595\\P(70)=957-1.595P(70)\\2.595P(70)=957\\P(70)=368.786$

Thus, the country's population for the year 2030 is 368.8 million.

3 0

4 years ago

No links pls help!

serg [7]

Answer:

18 in.

Step-by-step explanation:

ycvjnyucfcgvjnjbhuftytghuhvgycyccvgv

6 0

3 years ago