3.How tall is the goal post?

larisa [96]

Answer:

-2, 8/3

Step-by-step explanation:

You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...

A = (1/2)(f(a) +f(4))(4 -a)

= (1/2)((3a -1) +(3·4 -1))(4 -a)

= (1/2)(3a +10)(4 -a)

We want this area to be 12, so we can substitute that value for A and solve for "a".

12 = (1/2)(3a +10)(4 -a)

24 = (3a +10)(4 -a) = -3a² +2a +40

3a² -2a -16 = 0 . . . . . . subtract the right side

(3a -8)(a +2) = 0 . . . . . factor

Values of "a" that make these factors zero are ...

a = 8/3, a = -2

The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.

_____

<em>Alternate solution</em>

The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.

5 0

3 years ago

A 2007 survey of 980 American drivers concluded that 38% of the driving population would be willing to pay higher gas prices to

Oksana_A [137]

Answer:

The correct answer to the question is

e. If is likely that between 35% and 41% percent of the driving population would be willing to pay higher gas prices to protect the environment.

Step-by-step explanation:

The margin of error expresses the number of percentage points of error is contained within survey result. A large error margin therefore reduces the level of dependence on a given statistic. The margin of error describes the expected variation between the statistic sample and the real population value.

In the question, the option

e. If is likely that between 35% and 41% percent of the driving population would be willing to pay higher gas prices to protect the environment , clearly depicts the definition of margin of error as it shows the expected variance from te real population

8 0

3 years ago

In 2010, the population of a town was 8500. The population decreased by 4.5% each year.

Soloha48 [4]

Answer:

This is a problem in exponential decay.

a) If a town's population decreases by 4.5% every year that also means that the town's population decreases by a factor of .955 each year. (1 - .045 = .955)

So, after 5 years, the town's population is:

8,500 * .955^5 which equals 6,752.

So, basically, after t years, the town's population equals

8,500 * .955^t where t is the number of years that have passed since the year 2010.

b) population = 8,500 * .955 ^ (number of years since 2010)

7,000 / 8,500 = .955 ^ (number of years since 2010)

0.8235294118 = .955 ^ (number of years since 2010)

To solve for (number of years since 2010) we take logs of both sides

log (0.8235294118 ) = number of years since 2010 * log(.955)

-0.0843208857 = number of years since 2010 * -0.0199966284

-0.0843208857 / -0.0199966284 = number of years since 2010

4.2167551422 = number of years since 2010

So, population = 7,000 when the year is 2014.2167551422

Or about 2.6 months into 2014

(YES, it's just that "easy") LOL

Step-by-step explanation:

6 0

3 years ago

Which represents the solution set to the inequality

Art [367]

$5.1(3 + 2.2x) \ \textgreater \ -14.25 - 6(1.7x + 4)$
Lets expand both multiplications first.
$15.3 + 11.22x \ \textgreater \ -14.25 - 10.2x - 24$
Simplify down the right side.
$15.3 + 11.22x \ \textgreater \ -38.25 - 10.2x$
Add 38.25 to both sides.
$53.55 + 11.22x \ \textgreater \ -10.2x$
Subtract 11.22x from both sides.
$53.55 \ \textgreater \ -21.42x$
Divide by -21.42 on both sides. Because we're dividing by a negative, we need to change the inequality direction.
$-2.5 \ \textless \ x$
This means, out of the options available, (-2.5, ∞) is the correct answer.

3 0

3 years ago

[6 points] Prove Bayes’ Theorem. Briefly explain why it is useful for machine learning problems, i.e., by converting posterior p

djverab [1.8K]

Answer: Mathematically Bayes’ theorem is defined as

P(A\B)=P(B\A) ×P(A)

P(B)

Bayes theorem is defined as where A and B are events, P(A|B) is the conditional probability that event A occurs given that event B has already occurred (P(B|A) has the same meaning but with the roles of A and B reversed) and P(A) and P(B) are the marginal probabilities of event A and event B occurring respectively.

Step-by-step explanation: for example, picking a card from a pack of traditional playing cards. There are 52 cards in the pack, 26 of them are red and 26 are black. What is the probability of the card being a 4 given that we know the card is red?

To convert this into the math symbols that we see above we can say that event A is the event that the card picked is a 4 and event B is the card being red. Hence, P(A|B) in the equation above is P(4|red) in our example, and this is what we want to calculate. We previously worked out that this probability is equal to 1/13 (there 26 red cards and 2 of those are 4's) but let’s calculate this using Bayes’ theorem.

We need to find the probabilities for the terms on the right-hand side. They are:

P(B|A) = P(red|4) = 1/2

P(A) = P(4) = 4/52 = 1/13

P(B) = P(red) = 1/2

When we substitute these numbers into the equation for Bayes’ theorem above we get 1/13, which is the answer that we were expecting.

7 0

3 years ago