Compare 5.87 and 5.087 which greatest

The quotient of 5/31 divided by 15/23, reduced to the lowest fraction, is

Nataliya [291]

If you would like to solve 5/31 / 15/23, you can calculate this using the following steps:

5/31 / 15/23 = 5/31 * 23/15 = 23/93

The correct result would be C. 23/93.

6 0

4 years ago

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Misty surveyed 200 students and asked their favorite type of music. The results

NemiM [27]

Answer:

The answer is 9%

Step-by-step explanation:

18

200

x 100% = 9%

I turned 200 into 100% and if you divide 18 by 2 you can get 9

Hope this helped if you need more info let me know!!

8 0

2 years ago

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Which of the following represents the polar equation r = (cot 2θ)(csc θ) as a rectangular equation?

STALIN [3.7K]

The option that depicts the polar equation r = (cot 2θ)(csc θ) as an equation that is rectangular is: y² = 2x.

<h3>What is a polar equation?</h3>

A polar expression is any equation that describes the correlation between r and θ, where r signifies the anticlockwise angle formed by a point on a curve, the pole, and the positive x-axis, and means the breadth between the origin and a location on a curve.

<h3>What is the solution to the equation above?</h3>

Step 1 - expand the polar equation

r = 2cosθ * cscθ

Step 2 - convert csc and cos to their equivalents in tan and sin

r = 2 * (1/tanθ) * (1/sinθ) * sinθ

r = 2 * (1/tanθ) * sinθ/sinθ

r = 2 * 1/tanθ

r = 2/tanθ, making 2 the subject of the formula, we have

rtanθ = 2

Note that rectangular coordinates of a point will be depicted as (x,y) and it's plolar coordinate will be (r, θ).

This mean

x = r cos θ; and

y = r sinθ

From the above, we can state that:

Since y = r sinθ
⇒ tanθ = y/x

⇒ (rsinθ/y) * tanθ = 2

Thus y * (y/x) = 2

Therefore,

y²/x = 2

y² = 2x

Learn more about polar equation at:

brainly.com/question/9363127
#SPJ1

5 0

2 years ago

Suppose the method of tree ring dating gave the following dates A.D. for an archaeological excavation site. Please show your wor

natita [175]

Answer:

a) $\bar X=\frac{1245+1245+1321+1191+1295+1330+1239+1250+1228}{9}= 1260.444$

b) $s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And if we replace we got:

$s = 45.580$

c) For this case since the sampel size is n=9 <30 we can use the t distribution in order to find the confidence interval.

d) $1260.444-2.306 \frac{45.580}{\sqrt{9}}= 1225.408$

$1260.444+2.306 \frac{45.580}{\sqrt{9}}= 1295.480$

Step-by-step explanation:

For this case we ave the following data:

1245 1245 1321 1191 1295 1330 1239 1250 1228

Part a

We can calculate the sample mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And if we replace we got:

$\bar X= \frac{1245+1245+1321+1191+1295+1330+1239+1250+1228}{9}= 1260.444$

Part b

For this case we can use the following formula in order to find the sample standard deviation:

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And if we replace we got:

$s = 45.580$

Part c

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

For this case since the sampel size is n=9 <30 we can use the t distribution in order to find the confidence interval.

Part d

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

We need to find the degrees of freedom given by:

$df = n-1 = 9-1=8$

Since the Confidence is 0.95 or 95%, the value of $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that $t_{\alpha/2}=2.306$

Now we have everything in order to replace into formula (1):

$1260.444-2.306 \frac{45.580}{\sqrt{9}}= 1225.408$

$1260.444+2.306 \frac{45.580}{\sqrt{9}}= 1295.480$

8 0

4 years ago

Which group contains elements that are most likely to have similar properties?

astraxan [27]

<span>- lithium, beryllium, and boron - nitrogen, arsenic, and antimony - potassium, calcium, and gallium - cesium, platinum, and radon</span>

3 0

3 years ago

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