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1 year ago

Which expression is equivalent to 3^0x3^-3?

Mathematics

1 answer:

Ray Of Light [21]1 year ago

4 0

Step-by-step explanation:

$= {3}^{0} \times {3}^{ - 3}$

$= 1 \times \frac{1}{ {3}^{3} }$

$= \frac{1}{3 \times 3 \times 3}$

$= \frac{1}{27}$

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The answer is b) 1/2

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3 years ago

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Samara ate 1/3 of a pizza and Vyolet ate 1/5 of the pizza. How much of the pizza did they eat in all?

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All together, the two girls ate 8/15 of a pizza. you mulitply your fractions out of equal denominaters and get that.

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3 years ago

Based on data collected 5 years ago, a hotel expects that 24% of all guests will request smoking rooms. The hotel suspects that

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Answer:

The calculated value Z = 2.3084 > 1.96 at 5% level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

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Step-by-step explanation:

Step(i):-

Given the hotel takes a random sample of 223 guests. Out of this sample, 39 guests requested smoking rooms.

Sample proportion

p = x/n = 39/223 = 0.174

Given Population proportion 'P' = 0.24

Given random sample size 'n' = 223

Level of significance ∝ =0.05

The critical value Z₀.₀₅ = 1.96

Null Hypothesis (H₀) : P=0.24

Alternative Hypothesis (H₁) : P≠ 0.24

Step(ii):-

Test statistic

$Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }$

$Z = \frac{0.174-0.24}{\sqrt{\frac{0.24 X 0.76}{223} } }$

|Z| = | -2.3084|= 2.3084

The calculated value Z = 2.3084 > 1.96 at 5% level of significance

Null hypothesis is rejected

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2 years ago

a segment has and endpoint at (-6, 8). The midpoint is at (-6, 2). What are the coordinates of the other endpoint?

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Answer:

(-6,-4)

Step-by-step explanation:

The first endpoint of the line is (-6,8), we can call

x_1 = -6

and

y_1 = 8

Let the last endpoint have coordinates (x_2,y_2)

Also, the midpoint formula is:

(x_1+x_2)/2 , (y_1+y_2)/2

Now, plugging these values is the formula, we get:

(-6+x_2)/2 = -6

-6+x_2=-12

x_2=-12+6 = -6

x_2 = -6

Also

(8+y_2)/2=2

8+y_2=4

y_2=4-8=-4

y_2 = -4

The coordinates of the other endpoint is (-6,-4)

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2 years ago

A public health official is planning for the supplyof influenza vaccine needed for the upcoming flu season. She wants to estimat

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Answer:

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And rounded up we have that n=421

Step-by-step explanation:

We know that the sample proportion have the following distribution:

$\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

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The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We assume that a prior estimation for p would be $\hat p =0.5$ since we don't have any other info provided. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.64})^2}=420.25$

And rounded up we have that n=421

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3 years ago