12^5 times 12^7 over -12^4

A truck's varying distance from the warehouse, d , measured in miles is modeled by the formula d=t2+50t where t is the varying n

Dafna1 [17]

Answer:

7.596 hours
57.596 mph

Step-by-step explanation:

a) The distance is given as ...

d = t^2 +50t

We want to find the value of t for which this distance is 437.5 miles. That means we want to solve the equation ...

437.7 = t^2 +50t

We can complete the square by adding the square of half the t coefficient, (50/2)^2 = 625

437.5 +625 = t^2 +50t +625

1062.5 = (t +25)^2

√1062.5 -25 = t ≈ 7.596 . . . . hours

It will take the truck about 7.596 hours to reach its destination.

__

b) Average speed is total distance divided by total time. Here, we can find the average speed as ...

d/t = (t^2 +50t)/t = t +50

That is, the average speed over the 437.5-mile trip is ...

7.596 +50 = 57.596 . . . . miles per hour

The car must maintain a constant speed of 57.596 mph to reach the destination at the same time.

_____

When solving equations using a graphing calculator, I like to put them into a form such that the solution is the x-intercept. Here, that means the equation we're solving is ...

x^2 +50x -437.5 = 0 . . . . x is hours to destination

8 0

3 years ago

47/10 as a mixed number

Alenkasestr [34]

First, 10 goes into 47, 4 times.

4 is your whole number.

10 x 4 = 40

47 - 40 = 7

then put 7/10

Put them together and your answer will be (4 7/10)

3 0

3 years ago

Read 2 more answers

63

Rudiy27

854 and 13 x this statment is true

7 0

3 years ago

Assuming there are no reflections or dilations explain how you would write the equation of the function whose graph is sketched

Fantom [35]

Answer:4

Step-by-step explanation:

6 1

3 years ago

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5

masya89 [10]

Answer:

$z= \frac{3.44-2.54}{0.45}=2$

$P(X>3.44) = P(Z>2) = 0.025$

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the grade points avergae of a population, and for this case we know the following properties

Where $\mu=2.54$ and $\sigma=0.45$

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

So we can find the z score for the value of X=3.44 in order to see how many deviations above or belowe we are from the mean like this:

$z= \frac{3.44-2.54}{0.45}=2$

So the value of 3.44 is 2 deviations above from the mean, so then we know that the percentage between two deviations from the mean is 95% and on each tail we need to have (100-95)/2 = 2.5% , because the distribution is symmetrical, so based on this we can conclude that:

$P(X>3.44) = P(Z>2) = 0.025$

5 0

4 years ago