Express the area of the entire rectangle Your answer should be a polynomial in standard form

What is the solution to 0.3(12x - 16) = 0.4(12 - 3x)?

telo118 [61]

Step-by-step explanation:

The solution is one-solution

.3(12x-16)=.4(12-3x) (you do the distributive property)

3.6x-4.8=4.8-.12x (you add 1.2 to both sides)

3.6x-3.6=4.8 (You add 3.6 to both sides)

3.6x=8.4 ( You divide 3.6 both numbers)

x=0.4285...

Its a one-solution

5 0

3 years ago

David is going to install tiles on the floor of two rooms. One of the floors is 18 feet long by 12 feet wide. The other floor is

crimeas [40]

Dimension of one of the floors of one room that David wants to install tiles is 18feet long by 12 feet wide
Then
Area of the above room = 18 * 12 square feet
   = 216 square feet
Dimension of the floor of the other room that David wants to install tiles is 24 feet long and 16 feet wide
Then
Area of the other room = 24 * 16 square feet
   = 384 square feet
Then
The total square feet of the
rooms that David wants to install tiles = 216 + 384
   = 600 square feet
Cost of the tile that covers 1 square feet = $5
Cost of the 4 tiles that cover 4 square feet = $17
Then
Area that can be covered with 4 square feet of tiles = 600/4 square feet
      = 150 square feet
Minimum cost of covering
the two rooms that David wants to install tiles = 150 * 17 dollars
      = 2550 dollars
So the minimum cost of installing the tiles on the two floors of David's two rooms is $2550. I hope the procedure is simple enough for you to understand.

8 0

3 years ago

4. Two friends, Sequoia and Raven, sold organic chap sticks at the local market.

Nina [5.8K]

Answer:

Sequoia sold 2 chap sticks while Raven sold 4.

Step-by-step explanation:

Since two friends, Sequoia and Raven, sold organic chap sticks at the local market, and Sequoia sold her chap sticks for $ 4 and Raven sold hers for $ 3 each, and in the first hour, their total combined sales were $ 20, if in the first hour, the friends sold a total of 6 chap sticks between them, to determine the number of chap sticks each of the friends sold during this time the following calculation must be performed:

6 x 4 + 0 x 3 = 24

5 x 4 + 1 x 3 = 23

2 x 4 + 4 x 3 = 20

Therefore, Sequoia sold 2 chap sticks while Raven sold 4.

7 0

3 years ago

A tank contains 100 gal of brine made by dissolving 80 Ib of salt in water. Pure water runs into the tank at the rate of 4 gal/m

ohaa [14]

Answer:

Step-by-step explanation:

Amount of brine = 100 gal

amount of salt = 80 lb

rate of water running = 4 gal / min

Let A be the amount of salt in lb in the tank at any time t.

(a) dA/dt = rate of salt in - rate of salt out

Rate of salt in = 0

rate of salt out = A x 4 / 100 = A / 25 lb/min

So, dA/dt = 0 - A/25 = - A/25 lb/min

$\frac{dA}{A}=-\frac{1}{25}dt$

$\int \frac{dA}{A}=-\frac{1}{25}\int dt$

$A(t) = C e^{-0.04t}$

When t = 0, A = 80 lb

So,

$A(t) = 80 e^{-0.04t}$

(b) Now, A = 40 lb

So,

$40 = 80 e^{-0.04t}$

$0.5 = e^{-0.04t}$

take log on both the sides

$ln 0.5 = - 0.04 t$

t = 17.3 minutes

8 0

3 years ago

The U.S. Census Bureau conducts annual surveys to obtain information on the percentage of the voting-age population that is regi

yan [13]

Answer:

We conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.

Step-by-step explanation:

We are given that 513 employed persons and 604 unemployed persons are independently and randomly selected, and that 287 of the employed persons and 280 of the unemployed persons have registered to vote.

Let $p_1$ = percentage of employed workers who have registered to vote.

$p_2$ = percentage of unemployed workers who have registered to vote.

So, Null Hypothesis, $H_0$ : $p_1\leq p_2$ {means that the percentage of employed workers who have registered to vote does not exceeds the percentage of unemployed workers who have registered to vote}

Alternate Hypothesis, $H_A$ : $p_1>p_2$ {means that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote}

The test statistics that would be used here Two-sample z test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of employed workers who have registered to vote = $\frac{287}{513}$ = 0.56

$\hat p_2$ = sample proportion of unemployed workers who have registered to vote = $\frac{280}{604}$ = 0.46

$n_1$ = sample of employed persons = 513

$n_2$ = sample of unemployed persons = 604

So, the test statistics = $\frac{(0.56-0.46)-(0)}{\sqrt{\frac{0.56(1-0.56)}{513}+\frac{0.46(1-0.46)}{604} } }$

= 3.349

The value of z test statistics is 3.349.

Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.

Since our test statistic is more than the critical value of z as 3.349 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.

5 0

3 years ago