(3 pt) Which shows the dimensions of two rectangular prisms that have volumes of 320 mm3 but different surface areas? A. 16 mm by 5 mm by 4 mm; 5 mm by 4 mm by 16 mm B. 10 mm by 4 mm by 6 mm; 6 mm by 10 mm by 4 mm C. 8 mm by 10 mm by 4 mm; 10 mm by 8 mm by 4 mm D. 8 mm by 10 mm by 4 mm; 20 mm by 8 mm by 2 mm

Using equations, the two numbers are 27 and 13, with the first number being 14 less than the second number, and their sum is 40.

How to use equations to find the two numbers?

Let's represent the two numbers as x (the second number) and y (the first number).

According to the given information:

The first number is 14 less than the second number: y = x - 14

When she adds them, she gets 40: x + y = 40

Now, we can use these two equations to find the values of x and y.

Substitute the value of y from the first equation into the second equation:

x + (x - 14) = 40

Now, solve for x:

2x - 14 = 40

2x = 54

x = 27

Now that we have the value of x, we can find y using the first equation:

y = x - 14

y = 27 - 14

y = 13

So, the two numbers are 27 and 13.

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Answer:

34 and 6 =40

Step-by-step explanation:

40 divided by 2=20 20-14=6 14+20=34

Answer:

40%

Step-by-step explanation:

From the given statements:

The probability that it rains on Saturday is 25%.

P(Sunday)=25%=0.25

Given that it rains on Saturday, the probability that it rains on Sunday is 50%.

P(Sunday|Saturday)=50%=0.5

Given that it does not rain on Saturday, the probability that it rains on Sunday is 25%.

P(Sunday|No Rain on Saturday)=25%=0.25

We are to determine the probability that it rained on Saturday given that it rained on Sunday, P(Saturday|Sunday).

P(No rain on Saturday)=1-P(Saturday)=1-0.25=0.75

Using Bayes Theorem for conditional probability:

P(Saturday|Sunday)=[TeX]\frac{P(Sunday|Saturday)P(Saturday)}{P(Sunday|Saturday)P(Saturday)+P(Sunday|No Rain on Saturday)P(No Rain on Saturday)}[/TeX]

=[TeX]\frac{0.5*0.25}{0.5*0.25+0.25*0.75}[/TeX]

=0.4

There is a 40% probability that it rained on Saturday given that it rains on Sunday.

Final answer:

To find the probability that it rained on Saturday given that it rained on Sunday, we can use Bayes' theorem. We are given the probabilities of rain on Saturday and Sunday, and we can use the law of total probability to calculate the probability of rain on Sunday. Then, using Bayes' theorem, we can determine the probability of rain on Saturday given that it rained on Sunday.

Explanation:

We need to use Bayes' theorem to find the probability that it rained on Saturday given that it rained on Sunday. Let's denote R1 as the event that it rains on Saturday and R2 as the event that it rains on Sunday. We are given P(R1) = 0.25, P(R2|R1) = 0.50, and P(R2|~R1) = 0.25, where ~R1 represents the event that it does not rain on Saturday. We want to find P(R1|R2), which is the probability that it rained on Saturday given that it rained on Sunday.

1. First, let's find P(R2).
2. Using the law of total probability, we can express P(R2) as P(R2|R1)P(R1) + P(R2|~R1)P(~R1).
3. Since P(R2|R1) = 0.50, P(R1) = 0.25, P(R2|~R1) = 0.25, and P(~R1) = 1 - P(R1) = 0.75, we can substitute these values into the equation and calculate P(R2).
4. Next, we can use Bayes' theorem to find P(R1|R2).
5. Bayes' theorem states that P(R1|R2) = (P(R2|R1)P(R1))/P(R2).
6. Substituting the values we know, we get P(R1|R2) = (0.50*0.25)/P(R2).
7. We can use the value we calculated for P(R2) in the previous step to find P(R1|R2).

Calculating these values will give us the probability that it rained on Saturday given that it rained on Sunday.

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Answer:

f(3) = 7

Step-by-step explanation:

Using the recursive formula and f(1) = - 3 , then

f(2) = f(1) + 5 = - 3 + 5 = 2

f(3) = f(2) + 5 = 2 + 5 = 7

Final answer:

The equation of the line that passes through the points (2,1) and (6,-5) is y = -3/2x + 4. This is calculated using the formula for a line y - y1 = m(x - x1) and the formula for slope.

Explanation:

In order to find the equation of the line passing through the points (2,1) and (6,-5), we can use the formula for a line y - y1 = m(x - x1). Here, m is the slope of the line. We can calculate the slope using the formula (y2 - y1) / (x2 - x1). Thus, for the points (2,1) and (6,-5), the slope m is (-5 - 1) / (6 - 2) = -6/4 = -3/2. We can substitute one pair of points and the slope into the line equation. Let's use (2,1). The equation of this line is then y - 1 = -3/2 * (x - 2). Simplifying, we get the equation of the line to be y = -3/2x + 4.

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