Please help! Double points!!

9. Raymond and Rose were working with exponents. Part A: Raymond claims that 5^5 * 5^2 = 5^3. Rose argues that 5^5 * 5^2 = 5^7.

tamaranim1 [39]

Answer: Rose is correct 5^5*5^2=5^7

Step-by-step explanation:

when multiplying two powers that have the same base you can add the exponent s (product property’s)

6 0

3 years ago

the Function h(x)=1/2(x+3)^2+2. How is the graph of h(x) translated from the parent graph of a qaudratic function, f(x)=x^2

Kay [80]

Answer:

Translation of h(x) is 2 unit down, 3 unit right and vertical stretch by 2

Step-by-step explanation:

Given function: $h(x)=\dfrac{1}{2}(x+3)^2+2$

Parent function: $f(x)=x^2$

It is parabolic function.

$h(x)=\dfrac{1}{2}(x+3)^2+2$

Shift 2 unit down

$g(x)=\dfrac{1}{2}(x+3)^2+2-2$

$g(x)=\dfrac{1}{2}(x+3)^2$

Shift 3 unit right

$g(x)=\dfrac{1}{2}(x+3-3)^2$

$g(x)=\dfrac{1}{2}x^2$

Vertical stretch by factor 2

$g(x)=2\cdot dfrac{1}{2}x^2$

$g(x)=x^2=f(x)$

So, Translation of h(x) is 2 unit down, 3 unit right and vertical stretch by 2

6 0

3 years ago

Read 2 more answers

2 + (3 – 2 x 2) *1 What’s the answer on this Problem

Pavlova-9 [17]

The answer is 4 or 5

5 0

3 years ago

110 minutes as hours in fraction

inessss [21]

Answer:

you divide the number by 60 and get 1.83333333 then you have 1 (whole number with 83333333/100000000

Step-by-step explanation:

8 0

3 years ago

A survey of magazine subscribers showed that 45.2% rented a car during the past 12 months for business reasons, 56% rented a car

IgorLugansk [536]

Answer:

a. 0.692 or 69.2%; b. 0.308 or 30.8%.

Step-by-step explanation:

This is the case of the probability of the sum of two events, which is defined by the formula:

$\\ P(A \cup B) = P(A) + P(B) - P(A \cap B)$ (1)

Where $\\ P(A \cup B)$ represents the probability of the union of both events, that is, the probability of event A plus the probability of event B.

On the other hand, $\\ P(A \cap B)$ represents the probability that both events happen at once or the probability of event A times the probability of event B (if both events are independent).

Notice the negative symbol for the last probability. The reason behind it is that we have to subtract those common results from event A and event B to avoid count them twice when calculating $\\ P(A \cup B)$ .

We have to remember that a sample space (sometimes denoted as S) is the set of the all possible results for a random experiment.

<h3>Calculation of the probabilities</h3>

From the question, we have two events:

Event A: event subscribers rented a car during the past 12 months for business reasons.

Event B: event subscribers rented a car during the past 12 months for personal reasons.

$\\ P(A) = 45.2\%\;or\;0.452$

$\\ P(B) = 56\%\;or\;0.56$

$\\ P(A \cap B) = 32\%\;or\;0.32$

With all this information, we can proceed as follows in the next lines.

The probability that a subscriber rented a car during the past 12 months for business or personal reasons.

We have to use here the formula (1) because of the sum of two probabilities, one for event A and the other for event B.

Then

$\\ P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$\\ P(A \cup B) = 0.452 + 0.56 - 0.32$

$\\ P(A \cup B) = 0.692\;or\;69.2\%$

Thus, the probability that a subscriber rented a car during the past 12 months for business or personal reasons is 0.692 or 69.2%.

The probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons.

As we can notice, this is the probability for the complement event that a subscriber did not rent a car during the past 12 months, that is, the probability of the events that remain in the sample space. In this way, the sum of the probability for the event that a subscriber rented a car plus the event that a subscriber did not rent a car equals 1, or mathematically:

$\\ P(\overline{A \cup B}) + P(A \cup B)= 1$

$\\ P(\overline{A \cup B}) = 1 - P(A \cup B)$

$\\ P(\overline{A \cup B}) = 1 - 0.692$

$\\ P(\overline{A \cup B}) = 0.308\;or\;30.8\%$

As a result, the requested probability for a subscriber that did not rent a car during the past 12 months for either business or personal reasons is 0.308 or 30.8%.

We can also find the same result if we determine the complement for each probability in formula (1), or:

$\\ P(\overline{A}) = 1 - P(A) = 1 - 0.452 = 0.548$