A box has dimensions of 4.1 inches, 5.9 inches, and 7.2 inches. Estimate the volume of the solid.

Last year, the standard deviation of the ages of the students at UA was 1.8 years. Recently, a sample of 31 students had a stand

scZoUnD [109]

Answer: $H_0: \sigma=1.8$

Step-by-step explanation:

Let $\sigma$ represents the standard deviation .

Given : Last year, the standard deviation of the ages of the students at UA was 1.8 years.

The researcher are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA.

We know that the null hypothesis always contains the equal signs, then the null and alternative hypothesis is given by :-

$H_0: \sigma=1.8\\\\ H_a:\sigma\neq1.8$

8 0

3 years ago

Riverside Elementary School is holding a school-wide election to choose a school color. Five-eighths of the votes were for blue,

Mnenie [13.5K]

Answer:

Step-by-step explanation:

Let the total number of votes to choose a color = x

Number of votes for blue = $\frac{5}{8}\times x$

Remaining votes = x - $\frac{5}{8}\times x$

= $\frac{8x-5x}{8}\times x$

= $\frac{3}{8}\times x$

Votes for green = $\frac{5}{9}\times (\text{Remaining votes})}$

= $\frac{5}{9}\times \frac{3x}{8}$

= $\frac{5}{24}\times x$

Finally remaining votes = $\frac{3x}{8}-\frac{5x}{24}$

= $\frac{9x-5x}{24}$

= $\frac{4x}{24}$

= $\frac{x}{6}$

Since these votes are for red therefore,

$\frac{x}{6}$ = 48

x = 48×6

= 288

a) Votes for blue are $\frac{5x}{8}$

Therefore, exact number for blue votes = $\frac{5\times 288}{8}$

= 5×36

= 180

b). Votes for green = $\frac{5x}{24}$

= $\frac{5\times 288}{24}$

= 60

c). Since 25 students were absent on that day of the vote, number of students at Riverside Elementary School = 288 + 25

= 313

d). Since seven tenths of the votes for blue were made by the girls.

Therefore, number of girls voted for blue = $\frac{7}{10}\times 180$

= 7×18

= 126

Since total votes made = 288

Therefore, half of the votes made = $\frac{288}{2}$

= 144

Now it's clear that number of votes made by girls is less than half of all the votes.

e). 126 girls voted for blue.

5 0

3 years ago

Solve x2 – 64 = 0. Isolate x2: x2 = 64 Apply the square root property of equality: Isolate the variable: x = x =

dybincka [34]

Solve the equation by isolating the variable you're solving for on one side of the equation and get everything on the opposite side.

$x^2 - 64 = 0$

The x variable is being square and is being subtracted by 64.
Find the inverse of all of these operations.

First, get rid of the subtraction operation. The inverse of subtraction is addition.

Add 64 to both sides of the equation.

$x^2 - 64 + 64 = 0 + 64 \\ x^2 = 64$

Now the variable x is only being squared. Reverse this operation by using the inverse of exponents.

Take the square root of both sides.

$\sqrt{x^2} = \sqrt{64} \\ x = 8$

So, x is equal to 8.

6 0

4 years ago

Read 2 more answers

Given point A (3, 8) and point B (-5, 1). Find the following: a.) The coordinates of the midpoint of segment AB. Write your answ

ss7ja [257]

Answer:

Mid point:

$= ( \frac{3 + - 5}{2} , \: \frac{1 + 8}{2} ) \\ = ( - 1, \: 4.5)$