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3 years ago

k is a an integer for which 1/2^1-k, 1/8. What is the value of k? 1/2^1-k must be equal to 1/8 if i read the question right.

Mathematics

1 answer:

svetlana [45]3 years ago

3 0

Answer:

k = -2

Step-by-step explanation:

If $\frac12^{1-k}=\frac18$

Then

$\frac1{2^{1-k}}=\frac18=\frac1{2^3}$

$1-k = 3$

From this follows k = -2

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What is the length of the radius? startfraction 6 over 85 endfraction startfraction 85 over 12 endfraction startfraction 121 ove

melomori [17]

The length of the radius will be 22 units.

<h3>What is the radius?</h3>

The radius of a circle is defined as the distance of the center of the circle to its outer layer. It is a locus of a point present at some distance from the center point.

Now from the question, we have an expression:

$r=(\dfrac{6}{85} )\times(\dfrac{85}{12} )\times (\dfrac{121}{36} )\times (\dfrac{157}{12} )$

By solving the above equation we get

$r=(\dfrac{18997}{864} )$

$r=22$

Hence the length of the radius will be 22 units.

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6 0

1 year ago

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The American Management Association is studying the income of store managers in the retail industry. A random sample of 49 manag

VashaNatasha [74]

Answer:

a) The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.

b) The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.

Step-by-step explanation:

Question a:

We have to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a p-value of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{2050}{\sqrt{49}} = 574$

The lower end of the interval is the sample mean subtracted by M. So it is 45420 - 574 = $44,846.

The upper end of the interval is the sample mean added to M. So it is 45420 + 574 = $45,994.

The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.

Question b:

The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.

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2 years ago

O.45 is equals to what in a fraction

Deffense [45]

It’s equal to 45/100 which equals 9/20

3 0

2 years ago

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Find the coordinates for the midpoint of the segment with endpoints give (3,5) and (-2,0)

Leto [7]

Answer:

The coordinates of the mid-point are :

$(\frac{1}{2}, \frac{5}{2})$

Step-by-step explanation:

We know that, the coordinates of the mid-point (x, y) of a line segment joining the points (x₁, y₁) and (x₂, y₂) is given by

$(x, y) = (\frac{x_{1} +x_{2} }{2},\frac{y_{1}+y_{2} }{2} )$

Now, we have the given points as (3, 5) and (-2, 0).

By using the above formula, coordinates of the mid-point (x, y) of the line-segment joining the points (3, 5) and (-2, 0) is given by,

$x = \frac{3+(-2)}{2} = \frac{3-2}{2} = \frac{1}{2}$

$y = \frac{5+0}{2} = \frac{5}{2}$

∴ coordinates of the mid-point of the line-segment joining the points (3,5) and (-2,0) is $(\frac{1}{2}, \frac{5}{2})$ .

8 0

2 years ago

2. Solve for x: 2(x - 5) = x + 3(x + 2)

MrMuchimi

Answer:

x=-8

Step-by-step explanation:

5 0

2 years ago

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