Anthony is going to invest in an account paying an interest rate of 2%
compounded monthly. How much would Anthony need to invest, to
the nearest cent, for the value of the account to reach $15,000 in 10
years?

Answer:

2 times

Step-by-step explanation:

Khan Academy

You can use the formula for margin of error and the fact that the point estimates of both the samples are same to calculate the ratio of margin of errors of both the samples.

The margin of error from the smaller sample will be about double of the margin of error from the larger sample.

[tex]MOE_1 = 2 \times MOE_2[/tex]

Let the level of significance be [tex]\alpha[/tex] and the standard deviation of the population be [tex]\sigma[/tex] and the sample size be n, then we have:

[tex]\text{MOE(Margin of Error)} = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]

For first sample :

[tex]\text{Sample size} = n_1 = 1000\\\\MOE_1 = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{1000}}[/tex]

For second sample :
[tex]\text{Sample size} = n_1 = 1000\\\\MOE_2 = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{4000}}[/tex]

(since it was given that they have same point estimates, so same standard deviation)

Their ratios are given by

[tex]\dfrac{MOE_2}{MOE_1} = \dfrac{Z_{\alpha/2}\dfrac{\sigma}{\sqrt{4000}}}{Z_{\alpha/2}\dfrac{\sigma}{\sqrt{1000}}} = \sqrt{\dfrac{1000}{4000}} = \dfrac{1}{2}\\\\\\MOE_1 = 2 \times MOE_2[/tex]

Thus,

The margin of error from the smaller sample will be about double of the margin of error from the larger sample.[tex]MOE_1 = 2 \times MOE_2[/tex]

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Answer:

Diagonal length = 8.59

Step-by-step explanation:

To find the diagonal length, we need the length of the sides. We find the length of the sides by finding the square root of 36, which is 6. Then, we use this equation (see attached image)

Answer:

0.9332 = 93.32% probability that the mean of the sample will be less than 12.1 ounces.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

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

Mean of 12 ounces and a standard deviation of 0.2 ounces.

This means that [tex]\mu = 12, \sigma = 0.2[/tex]

Sample of 9:

This means that [tex]n = 9, s = \frac{0.2}{\sqrt{9}}[/tex]

Find the probability that the mean of the sample will be less than 12.1 ounces.

This is the pvalue of Z when X = 12.1. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{12.1 - 12}{\frac{0.2}{\sqrt{9}}}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a pvalue of 0.9332

0.9332 = 93.32% probability that the mean of the sample will be less than 12.1 ounces.

Answer:

Using Pythagoras Theorem, squareroot 15^2 - 5^2.

After you found the opposite length, use the cosine rule to find angle x.

9514 1404 393

Answer:

  x = {2π/3, 4π/3}

Step-by-step explanation:

The equation can be factored as ...

  (cos(x) +3)(2cos(x) +1) = 0

The solutions are the values of x where the factors are zero.

  cos(x) +3 = 0

  cos(x) = -3 . . . . . . no real solution

__

  2cos(x) +1 = 0

  cos(x) = -1/2

  x = arccos(-1/2) = 2π/3

The other solution in the desired interval is ...

  x = 2π -(2π/3) = 4π/3

The solutions are x∈ {2π/3, 4π/3}.

Answer:

The copy machine makes 32 copies per minute.

Step-by-step explanation:

Given that a copy machine makes 136 copies in 4 minutes and 15 seconds, to determine how many copies does it make per minute, the following calculation must be performed:

15 seconds = 0.25 minutes

136 / 4.25 = X

32 = X

Therefore, the copy machine makes 32 copies per minute.

The measure of other supplementary angle where one angle is 100° is 80°

In the above question, it is given that two angles are supplementary angles and,

Two angles are said to be supplementary angles if their sum is 180 degrees.

We have,

The measure of one angle is = 100°

Let the angle which needs to be find as ∠x

That means, we need to find the measure of ∠x

So, according to the supplementary angles property,

100° + ∠x = 180°

∠x = 180 - 100

∠x  = 80°

Hence,  the measure of other supplementary angle where one angle is 100° is 80°

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Answer:

​(b), (c),​ (a)

Step-by-step explanation:

The Most area in the tails of the distribution can be ordered as :

T-distribution is a continuous probability distribution that is  applied when the population is small and when the population standard deviation is not given

Answer:

Step-by-step explanation:

[tex]x=\frac{D_{1}}{D} \\y=\frac{D_{2}}{D}[/tex]

Step-by-step explanation:

Arc AD = 70

< D = 98

So

Arc BC = 2 * < D ( relation between arc and inscribed angle)

= 2 * 98

= 196

Hope it will help :)❤

Answer:

in my panies

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The expression under the radical can be written in vertex form as ...

  x^2 -12x +32 = (x -6)^2 -4

The function will be symmetrical about x=6. The minimum is at x=6 where we have ...

  F(6) = ∛(-4)

The maximum is at the end of the interval farthest from the vertex, so is ...

  F(10) = ∛((10 -6)² -4) = ∛12

The minimum is -∛4 ≈ -1.587; the maximum is ∛12 ≈ 2.289.

Answer:

B) -3x+y=1

Step-by-step explanation:

y=mx+b

b=y-intercept=1

m=slope=3/1

y=3x+1

-3x+y=1

9514 1404 393

Answer:

 46 yd

Step-by-step explanation:

The sum of horizontal lengths across the top is 8+6 = 14 yd. The length across the bottom is the same, so the total of horizontal lengths is

  14 yd +14 yd = 28 yd

The sum of vertical lengths at the right is the same as the sum of vertical lengths at the left, 9 yd, so the total of vertical lengths is ...

  9 yd + 9 yd = 18 yd

The total of all lengths around the perimeter of the figure is ...

  28 yd + 18 yd = 46 yd

Answer:

Yes, it's when the tank is out of water.  

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer: 6.1

Step-by-step explanation:

Answer:

6.1

Step-by-step explanation:

have a good day/night may i please have a branlliest

Answer:

desculpa mas eu não sei a resposta mais eu vou ver se posso te ajudar taaa

Answer:

$30

Step-by-step explanation:

The formula for interest is I = Prt

Principal = 600

Rate = 0.05 or 5%

Time: 1 year

600 x 0.05 x 1 = 30

She earned an interest of 30.

Answer:

m<1 = 137

Step-by-step explanation:

Exterior angles thm:

41 + 96 = m<1

m<1 = 137

Answer:

1.) up

2.) (-2,-5)

3.) x = -2

4.) (-2,-5)

5.) y = -5

6.) -∞ < x < ∞

7.) -5 < y < ∞

8.) (0,0)

9.) (0,0) and (-4,0)

10.) two solutions

Step-by-step explanation:

1.) because the parabola opens upward and the vertex is down

2.) the lowest point of the parabola is (-2,-5)

3.) If a line was drawn through the point x = -2, the two halves of the parabola would look symmetrical ( the same on both sides).

4.) The minimum point on the graph is ( -2,-5), because that is the lowest point on this upward parabola, and we can not determine the maximum.

5.) The minimum value of y is y = -5, because that is the lowest value of y on this graph, and we can not determine the maximum.

6.) Because the arms of the parabola continue traveling through negative infinity and positive infinity on the x-axis, the domain is -∞ < x < ∞.

7.) The arms of the parabola go from y = -5 to infinity, so the range of the parabola is -5 < y < ∞.

8.) The parabola first crosses the y-axis at the point (0,0)

9.) The parabola first crosses the x-axis at the points (0,0) and (-4,0)

10,) The solution to the parabola is the variable x. The solutions (x intercepts) of the parabola are x = 0 and x = -4.

Does this help you?

B

Step-by-step explanation:

In a year, offer B would be more. Since annually is once a year and there are 12 months in a year, multiplying B by 12 would get each to a year.

Answer:

A. 6+24p

Step-by-step explanation:

=(3)(2+8p)

=(3)(2)+(3)(8p)

=6+24p

=24p+6

Answer:

C) 2

Step-by-step explanation:

Emma: Range  = 8

Arianna: Range = 6

The difference in the range is 2 (8-6)

Answer:

C) 2

Step-by-step explanation:

Emma:

Max = 20

Min = 12

Range = 20 - 12

Range = 8

Arianna:

Max = 18

Min = 12

Range = 18 - 12

Range = 6

Difference between the 2 ranges:

8 - 6 = 2

Answer:

131

Step-by-step explanation:

Sorry but I am not conform to this answer

Answer:

20 - 6x = 4x - 15

35 - 6x = 4x

35 = 2x

x = 15.5

The solution to the equation 20 - 6x = 4x -15 is x = 3.5.

To solve the equation 20 - 6x = 4x - 15,

20 - 6x = 4x - 15

To isolate the variable terms on one side,  add 6x to both sides:

20 - 6x + 6x = 4x - 15 + 6x

20 = 10x - 15

Next, add 15 to both sides to further isolate the variable term:

20 + 15 = 10x - 15 + 15

35 = 10x

Finally, divide both sides by 10 to solve for x:

35/10 = 10x/10

3.5 = x

Therefore, the solution to the equation is x = 3.5.

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Answer:

C) 3.5 hours

Step-by-step explanation:

55h = 192.5

55h/55 = 192.5/55

h = 3.5 hours

Answer:

k = 7

Step-by-step explanation:

63 ÷ 9 = 7