if you flip a coin ten times, how many diffrent sequences of heads and tails are possible

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.

If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width

Solution:

Let the length of rectangle=x

Width of rectangle=x/10

Perimeter is 2(Length+Width)

= 2(x+x/10)

Area of Rectangle= Length* Width=x*x/10

As, Perimeter=2(Area)

So,2(x+x/10)=2(x*x/10)

Multiplying the equation with 10, we get,

2(10x+x)=2x²

Adding Like terms, 10x+x=11x

2(11x)=2x^2

22x=2x²

2x²-22x=0

2x(x-11)=0

By Zero Product property, either x=0

or, x-11=0

or, x=11

So, Width=x/10=11/10=1.1

Checking:

So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2

Area=Length*Width=11*1.1=12.1

Hence, Perimeter= 2 Area

As,24.2=2*12.1=24.2

So, Perimeter=2 Area

So, Answer:Length of Rectangle=11 units

Width of Rectangle=1.1 units

we have

[tex]f(x)=\sqrt{4x+9} +2[/tex]

we know that

The radicand must be greater than or equal to zero

so

[tex]4x+9 \geq0 \\ 4x\geq -9 \\x\geq -\frac{9}{4} \\ x\geq -2.25[/tex]

the domain is is the interval--------> [-2.25,∞)

therefore

the answer is

[tex]4x+9 \geq0[/tex]

Final answer:

The probability that Talia will pull a red ball out of the bag is 2/7, given she has 2 red, 1 blue, and 4 green balls in the bag making a total of 7 balls.

Explanation:

The question you have asked is related to the subject of probability in mathematics. Specifically, it is about the probability of drawing a red ball from a bag containing red, blue, and green balls. To calculate this probability, you need to know the total number of balls and the number of red balls in the bag. Then, you use the formula for probability which is the number of favorable outcomes divided by the total number of possible outcomes.

In Talia's bag, there are 2 red, 1 blue, and 4 green balls, making a total of 2+1+4=7 balls. The probability of pulling a red ball out of the bag is the number of red balls divided by the total number of balls, which gives:

Probability of red ball = Number of red balls / Total number of balls = 2/7.

So, the correct answer to the probability that Talia will pull a red ball out of the bag is 2/7.

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...

:)  

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)

Step-by-step explanation:

                                                     MEAN

First, add all the values together and divide by the number of values in the set. Imagine 3 people donated money to red cross. Their names are Allisa, John, and Thomas. Allisa gave 20 dollars, John gave 35, and Thomas gave 20. Next, you add the amount of money they donated, which is 70. Then you divide 70, the amount of money, by 3, because thats the amount of people that donated. Then you get a mean of 23.

To put it simpler,

add the values.

then, add the amount of whatever carries that value, such as people.

after, you devide the value and the amount of people or etc.

when you finish, your mean will be what you have divided.

Another example would be this.

There are several whales out in the ocean. One is the Cuvier's beaked whales, which can swim as deep as 2,992 m. Another whale, named the sperm whale, can swim down to at least  1,000 m.

So, what is the mean?

Once again, first, we add the value, which in this case, is how deep the whales can dive. We then get 3992 m.

Next, we add the amount of whatever carries that value, which in this case are whales.

after, you devide the value by the amount of whales.

when you finish, you will get 1996

                                                     MEDIAN

Arrange your numbers in numerical order. If they were scrambled like this, 9, 7, 3, 9, 6, 1, 5, rearrange them like this. 1, 3, 5, 6, 7, 9, 9.  

When you do this, check how many numbers are in that row. In this case, the amount is 7, which is odd.

If you have an odd number like in the example above, select the number in the middle, which in our case, its 6. ( 1, 3, 5, 6, 7, 9, 9 )  So your median would be six, since median means "the middle number"

If you have an even number, add them together then divide by 2. Heres an example. 1, 3, 5, 6, 7, 9, 9. (1, 3, 5, 8, 12, 9, 9, 12) You would add 8 and 12. Your answer would be 20. So now, you divide 20 by 2. 20 divided by 2 is 10, so your median would be 10.

I did not plagerise this, I made these example up myself and solved them the way they are supposed to be and used these examples on another question similar to this.

Answer:

The value of x is 12

Step-by-step explanation:

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

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:

Step-by-stPart A

Answer: 7/36

This is in fraction form

The decimal version of this number is roughly 0.1944

-----------------------------------

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

============================================================

Part B

Answer in fraction form: 1/36

Answer in decimal form: 0.0278 (which is approximate)

------------------

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

============================================================

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

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.

Answer:

b

Step-by-step explanation: