Solve: x ÷ 0.6 = 8.9 5.34 9.5 8.3 0.07

What is the answer to > solve 4cos (theta/3) -2 = 0, over [0, 4pi)

Vesna [10]

Hello from MrBillDoesMath!

Answer:

@ = pi/3 (or 60 degrees) or @ = 7 pi/3 (or 420 degrees)

Discussion:

Let "@' denote the angle "theta". We are asked to find @ in the interval [0, 4 pi)

where

4cos(@) - 2 = 0. Adding 2 to both sides

4 cos(@) - 2 +2 = 2 =>

4 cos(@) = 2 Divide both sides by 4

cos(@) = 2/4 = 0.5

This implies that @ = pi/3 (or 60 degrees) or @ = (pi/3 + 2pi) = 7 pi/3 (or 420 degrees)

Thank you,

MrB

5 0

3 years ago

A rectangular prism is made of 81 unit cubes. The prism is 9 unit cubes long.

dimaraw [331]

Answer:

A width: 3 unit cubes

height 3 unit cubes

Step-by-step explanation:

Volume of rectangular prism = 81 unit cubes

$l$ = Length of rectangular prism = 9 unit cubes

$w$ = Width of rectangular prism

$h$ = Height of rectangular prism

Volume of a rectangular prism is given by

$V=lwh\\\Rightarrow 81=9wh\\\Rightarrow wh=\dfrac{81}{9}\\\Rightarrow wh=9$

The product of width and height must be 9 so from the options this is only possible when width and height both are 3 units.

So, the width is 3 unit cubes and the height is 3 unit cubes.

4 0

2 years ago

Your friend says 8,705 divided by 1000 is equivalent to 8705 times 0.001. Is your friend correct? Explain

irakobra [83]

Answer:

yes

Step-by-step explanation:

8705/1000 = 8705*0.001

8.705 = 8.705

3 0

3 years ago

Suppose that the sample standard deviation was s = 5.1. Compute a 98% confidence interval for μ, the mean time spent volunteerin

NISA [10]

Answer:

The 95% confidence interval would be given by (5.139;5.861)

Step-by-step explanation:

1) Previous concepts

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

2) Confidence interval

Assuming that $\bar X =5.5$ and the ranfom sample n=1086.

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=1086-1=1085$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that $t_{\alpha/2}=2.33$

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

$5.5-2.33\frac{5.1}{\sqrt{1086}}=5.139$

$5.5+2.333\frac{5.1}{\sqrt{1086}}=5.861$

So on this case the 95% confidence interval would be given by (5.139;5.861) We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.

5 0

3 years ago

An angelfish was 1 1/2 inches long when it was bought. Now it is 2 1/3 inches long.

____ [38]

A)

Earlier, The length of the angelfish = $1 \frac{1}{2}$ inches