Solve the following equation using the distributive property

What is the rate of change please help asap

pav-90 [236]

The rate of change is 5

3 0

2 years ago

The Wilsons drove 324 miles in 6 hours if they drilled the same number of miles each hour how many miles did they drive in 1 hou

krok68 [10]

They would have traveled 54 miles
324/6=54

8 0

3 years ago

[need math help] Study buddies part #2

rosijanka [135]

Answer:

Part A) The distance between Whitney's house and Anh's house is 6.5 miles.

Part B) The total distance traveled by Whitney during the trip was 9.5 miles.

Step-by-step explanation:

Part A)

Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.

So, instead, we can calculate Whitney's total displacement. Total displacement is given by:

$\displaystyle \text{Displacement}=\int_a^bv(t)\, dt$

Where v(t) is the velocity function.

So, the displacement of Whitney when she traveled from her house to Anh's house will be:

$\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt$

To calculate the integral, we can split it off at t = 11, t = 16, and t = 24.

The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:

$\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt$

Now, we can calculate the area of each figure.

The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:

$\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}$

The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:

$\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}$

Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:

$\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}$

However, notice that the second figure is below the x-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.

Then the displacement will be:

$\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}$

So, the distance between Whitney's house and Anh's house is 6.5 miles.

Part B)

The total distance differs from displacement in that it includes all the distances in both directions. It is given by:

$\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt$

In other words, all of our values are now positive. We will utilize the same strategy:

$\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt$

Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:

$\displaystyle \text{Distance} =5.6+1.5+2.4=9.5$

Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.

6 0

3 years ago

What is a negative minus a negative

Rainbow [258]

Answer:

It would be a negative or positive depending on the situation.

Step-by-step explanation:

A negative minus a negative would result in either a positive or negative. For example, -8 - (-9) would be 1 while -8 - (-7) would be -1. If the negative number your subtracting is greater than the number you're subtracting from then it will be positive, vice versa.

3 0

2 years ago

Berdine's Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server p

nata0808 [166]

Answer:

The probability of the tip to be more than 200 is 0.1.

Step-by-step explanation:

As per the given data

Amount of tip Number

0-20 200

20-50 100

50-100 75

100-200 75

200+ 50

____________________

Total= 500

So what is the probability of tip to be more than 200 is given as

$P(200+)=\frac{no. \, of\,occurrence}{Total\, Number}$

From the table the value is 50 for the tip to be more than 200 where as the total occurrences are 500 so substituting values:

$P(200+)=\frac{no. \, of\,occurrence}{Total\, Number}\\P(200+)=\frac{50}{500}\\P(200+)=0.1$

So the probability of the tip to be more than 200 is 0.1.

5 0

3 years ago