A bicycle rider increases his speed from 5 m/s to 15 m/s in 10 seconds

A - the sum of two dice is 7

B - the first die is 2

[tex] P(A|B)=\dfrac{P(A \cap B)}{P(B)}\\\\
|\Omega|=6^2=36\\
|A\cap B|=1\\
|B|=1\cdot6=6\\\\
P(A\cap B)=\dfrac{1}{36}\\
P(B)=\dfrac{6}{36}=\dfrac{1}{6}\\\\
P(A|B)=\dfrac{\dfrac{1}{36}}{\dfrac{1}{6}}=\dfrac{1}{36}\cdot6=\dfrac{1}{6} [/tex]

Cesar purchased a total of 10 quarts of juice after converting [tex]1\frac{1}{2}[/tex] gallons to quarts and adding it to the quarts from the two bottles.

Cesar bought 2 bottles of juice that each hold 2 quarts and another bottle that holds [tex]1\frac{1}{2}[/tex] gallons of juice. To find out how many quarts of juice he bought in total, we need to convert gallons to quarts.

We know that there are 4 quarts in 1 gallon, so [tex]1\frac{1}{2}[/tex] gallons equal 6 quarts ( [tex]1\frac{1}{2}[/tex] × 4 quarts/gallon).

Adding the quarts from the two bottles, we have 2 × 2 quarts which equal 4 quarts. Now, add the quarts from the single bottle to the total:

4 quarts (from two bottles) + 6 quarts (from  [tex]1\frac{1}{2}[/tex] gallon bottle) = 10 quarts

So, Cesar bought a total of 10 quarts of juice.

Answer:

(-7,13)

Step-by-step explanation:

The equation of a circle is ​ (x+7)to the second power+(y−13)to the second power=196 ​

(x+7)^2 +(y-13)^2 = 196

To find the center of the circle we use the center radius form of the circle

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

where (h,k) is the verted and r is the radius of the circle

now we compare with the given equation

h= -7  and k =13

So center of the circle is (-7,13)

Final answer:

Mark paid $3162.50 in interest on a $5500 loan at 11.5% over five years using the simple interest formula Interest = Principal × rate × time.

Explanation:

To calculate the total amount of interest Mark paid on a $5500 loan at 11.5% for five years, we can use the formula for simple interest, which is:

Interest = Principal × rate × time

In Mark's case, the principal is $5500, the rate is 11.5% or 0.115 when converted to a decimal, and the time is 5 years. Plugging these values into the formula yields:

Interest = $5500 × 0.115 × 5 = $3162.50

So Mark will have paid $3162.50 in interest over the five years of the loan.

44+72=116

180-116=64

3rd angle=64

64+44+72=180

44+72=116

180-116=64

3rd angle=64

Answer:

Step-by-stPart A

Answer: 7/36

This is in fraction form

The decimal version of this number is roughly 0.1944

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To get this answer, we multiply the fractions 7/9 and 2/8

The fraction 7/9 is the probability of selecting purple on the first draw. There are 7 purple out of 9 total (2+7 = 9)

The fraction 2/8 is the probability of selecting white on the second draw. This is assuming we don't put the first selection back in the bag. There are 2 white out of 8 marbles over

Multiply the fractions to get:

(7/9)*(2/8) = (7/9)*(1/4) = (7*1)/(9*4) = 7/36

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Part B

Answer in fraction form: 1/36

Answer in decimal form: 0.0278 (which is approximate)

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We have 2 white out of 9 total. So the probability of getting white the first time is 2/9

After we select and don't put that first selection back, we have 1 white out of 8 left over. The probability of getting white a second time is 1/8

Multiply the fractions:

(2/9)*(1/8) = (2*1)/(9*8) = 2/72 = 1/36

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Part C

Answer: There is a greater chance to get two purple in a row

Without doing any math, you can tell that purple is more likely simply because there are more purple than white. We have 7 purple and 2 white. For any given single selection, we have a greater chance of picking purple over white.

If you want do to the math, then the probability of selecting two white marbles in a row is 1/36 = 0.0278 which was found in part B above. 

The probability of selecting two purple is (7/9)*(6/8) = (7/9)*(3/4) = (7*3)/(9*4) = 21/36 = 7/12 = 0.5833

In summary, 

the probability of selecting two white marbles in a row is 0.0278

the probability of selecting two purple marbles in a row is  0.5833

we see that the probability for the two purple marbles is much greater

Answer:

Domain (-∞,4)U(4,∞)

Step-by-step explanation:

Inmagine functions as little machines that turn one number into another, the domain would the numbers that we can enter to the machine so we would have a real number on the output of it.

In this specific case we can use all the numbers but 4 because if we make [tex]x=4[/tex]  we would have [tex]\frac{12}{4-4}=\frac{12}{0}[/tex] and this is an indeterminate form which won't be solution to the problem.

According to the explanation our domain would be all the numbers but 4 like this:

Domain (-∞,4)U(4,∞)

Answer:

The line parallel to this one and through the given point would be y = -3.

Step-by-step explanation:

In order to find a parallel line, we first have to accept that this is a horizontal line. This is because there is no x value in the equation. That means in order to make it horizontal as well, we need it to have no x value again.

Given the ordered pair, this means our new equation is y = -3

Answer:

b

Step-by-step explanation:

Final answer:

The correct statement is that the lengths AB and AC are equal.

Explanation:

The correct statement is that the lengths AB and AC are equal. When Amy walks from point A to point B along the segment AB, and Fraser walks from point A to point C along the segment AC, the statement is correct because both points are on the circumference of the same circle with B as the center.

Answer:

No picture so i cannot answer the question but i can guide you to support.

Step-by-step explanation:

The way you would do a rectangle is: The area of a rectangle is A = l × w and the way you would do the triangle is The area of a triangle is A = one half × b × h...

Hope this helps...

:)