in bowling you get a spare when you knock down the ten pins in two throws. how many possible ways are there to get a spare?

Given the following information:

\(\displaystyle\sf n(U) = 50\)

\(\displaystyle\sf n(P) = 28\)

\(\displaystyle\sf n(Q) = 35\)

\(\displaystyle\sf n(P'\cap Q') = x\)

Let's express the requested values in terms of x:

1. \(\displaystyle\sf P'\cap Q\):

Using the principle of complements, we know that \(\displaystyle\sf P'\cap Q = U \setminus (P \cup Q) = U - (P \cup Q)\).

Since the universal set U has 50 elements, and we are given that \(\displaystyle\sf n(P) = 28\) and \(\displaystyle\sf n(Q) = 35\), we can calculate the value of \(\displaystyle\sf n(P \cup Q)\):

\(\displaystyle\sf n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)\).

Since we don't have the value of \(\displaystyle\sf n(P \cap Q)\), we cannot calculate the exact value of \(\displaystyle\sf n(P \cup Q)\). Therefore, we cannot express \(\displaystyle\sf P'\cap Q\) in terms of x.

2. \(\displaystyle\sf P \cap Q\):

Using the same principle of complements, we know that \(\displaystyle\sf P \cap Q = U \setminus (P' \cup Q') = U - (P' \cup Q')\).

Similarly, we cannot calculate the exact value of \(\displaystyle\sf n(P' \cup Q')\) since we don't know \(\displaystyle\sf x\). Thus, we cannot express \(\displaystyle\sf P \cap Q\) in terms of x.

3. \(\displaystyle\sf n(P \cap Q')\):

Using De Morgan's laws, we know that \(\displaystyle\sf n(P \cap Q') = n(P) - n(P \cap Q)\).

Since we are given that \(\displaystyle\sf n(P) = 28\), we need to calculate \(\displaystyle\sf n(P \cap Q)\). Unfortunately, we don't have enough information to find the exact value of \(\displaystyle\sf n(P \cap Q)\) in terms of x. Therefore, we cannot express \(\displaystyle\sf n(P \cap Q')\) in terms of x.

Regarding the greatest and smallest possible values of x, without additional information or constraints, we cannot determine those values. We would need more details or conditions related to the intersection of sets P and Q or other relevant factors to determine the range or limitations of x.

This is a question related to set theory, a branch of mathematics that deals with the properties of well-defined collections of objects1. Here are some formulas that might help you solve the question2:

The complement of a set A is denoted by A’ and it contains all the elements that are not in A.

The union of two sets A and B is denoted by A ∪ B and it contains all the elements that are in either A or B or both.

The intersection of two sets A and B is denoted by A ∩ B and it contains all the elements that are in both A and B.

The difference of two sets A and B is denoted by A - B and it contains all the elements that are in A but not in B.

The cardinality of a set A is denoted by n(A) and it represents the number of elements in A.

Using these formulas, we can express the sets (P’nQ), (PnQ), and n(PnQ’) in terms of x as follows:

(P’nQ) = (P ∪ Q)’ = U - (P ∪ Q) = U - P - Q + P ∩ Q

(PnQ) = P ∩ Q

n(PnQ’) = n(P) + n(Q’) - n(P ∩ Q’) = n(P) + n(U) - n(Q) - n(P ∩ Q)

To find the greatest and smallest possible values of x, we need to use the following formula2:

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

Applying this formula to P and Q, we get:

n(P ∪ Q) = n(P) + n(Q) - n(P ∩ Q)

50 - x = 28 + 35 - n(P ∩ Q)

x + n(P ∩ Q) = 13

Since x and n(P ∩ Q) are both non-negative integers, the greatest possible value of x is 13 when n(P ∩ Q) is 0, and the smallest possible value of x is 0 when n(P ∩ Q) is 13.

I hope this helps you understand the question better.

Answer:

A rectangular prism has six faces, commonly referred to as the base, top and four sides. The base and top always have the same area as do pairs of opposite sides

Step-by-step explanation:

Answer:

the base and the top, along with the opposite sides

Step-by-step explanation:

A rectangular prism has six faces, commonly referred to as the base, top, and four sides. The base and top always have the same area as do pairs of opposite sides.

just get the area for all of them and add legth time width

Answer:

30%

Step-by-step explanation:

Percentage- 9/30×100%

=30%

Step-by-step explanation:

There were 9 sunny days out of 30 days in September

% of sunny days in September= 9/30× 100

= 30%

Answer:

Step-by-step explanation:

123456789101112131415161718192021222324252627282930

Answer:

A. Square

B. Squares

C. They have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors.

Step-by-step explanation:

A. Since a cube has its faces shaped in square and all the edges of the cube are equal in length. Therefore, when we cut the cube by a plane, we get a square shape.

B. A vertical cut is an up and down cut. This shape is a cube, which has a base and sides in the shape of squares; thus, the two dimensional shape is a square.

Answer:

-4 degrees Celsius

Step-by-step explanation:

start at 8

subtract 12 from 8

8-12=-4

Answer:

90

Step-by-step explanation:

900 in groups of 10 would need 90 groups to equal 900.

Answer:

90

Step-by-step explanation:

We also have 9 tens, which means we can say 9×10=90. And we have 24 ones, which means we can say 24×1=24.

Answer:

The total interest earned in both accounts after 6 years would be $2,100 + $1,560 = $3,660.

Step-by-step explanation:

After 6 years, the total interest earned on account A would be:

Interest = Principal x Rate x Time

Interest = $10,000 x 0.035 x 6

Interest = $2,100

The total interest earned on account B would be:

Interest = Principal x Rate x Time

Interest = $10,000 x 0.026 x 6

Interest = $1,560

Therefore, the total interest earned in both accounts after 6 years would be $2,100 + $1,560 = $3,660.

Answer:

2430m^3

Step-by-step explanation:

6*21*9=1134

6*24*9=1296
1296+1134=2430

Answer:

because they all have the smae #'s in the numerator and denominater. I amswered, so MAKE ME BRAINLEST

Step-by-step explanation:

Answer:

05/3

Step-by-step explanation:

5/3 = 1.66

Answer:

5/3

Step-by-step explanation:

a= 3 and b= 5

b/a

5/3

Explanation:

The data from the stem-and-leaf plot is:

10,

24,25,26,

30,30,32,33,

40,45,46

Add up those values

10+24+25+26+30+30+32+33+40+45+46 = 341

Then divide over n = 11 which is the sample size.

341/11 = 31 is the arithmetic mean.

Answer:

341/11 = 31 is the arithmetic mean.

Step-by-step explanation:

Answer:

The radius is: 3.5

The diameter is: 7

Step-by-step explanation:

The radius is always half of the diameter!

Good luck!

Answer:

The radius is 3.5 cm and the diameter is 7 cm

Step-by-step explanation:

The diameter is the line that is already drawn. And the radius is just half of the diameter which means it is 3.5 cm.

Answer:

416

Step-by-step explanation:

ummmmmmmm yeah

Answer:

416

Step-by-step explanation:

i geuss.

Answer:

Step-by-step explanation:

reason 1:

opening of brackets to solve the expression

reason 2:

in multiplication order is followed i.e. the number always lead the variable in the expression

reason 3:

for clarification brackets are added to multiply like terms i.e. numbers with numbers and variable with the variable

reason 4:

the solved and simplified expression is delivered as a result

Answer:

I got the answer!!

Step-by-step explanation:

\(\frac{1}{w^{6} }\) i hope this helps!!

Answer:

The simplified expression is 1/w^6.

Step-by-step explanation:

Using the product of powers exponent rule, we have

w^3 * w^(-9) = w^(3 + (-9)) = w^(-6).

However, the problem says to write the expression using only positive exponents. Here's an example of how to interpret negative exponents as positive exponents:

3^2 = 9

3^1 = 3

3^0 = 1

3^(-1) = 1/3

(and keeps on dividing by three onward)

Here, we see that 3^(-1) = 1/3^1.

Applying the same logic here, we have

w^(-6) = 1/w^6.

I hope this helps!

Answer:

1. 45 + 18

2. 77 - 35

3. 22 - 7

4. 94 + 56

5. 88 + 41

6. 43 - 29

7. 68 - 55

8. 1 + 67

9. 27 + 72

10. 97 - 93

11. 34 - 2

12. 42 + 80

hope this helps

Answer:

1. 45 + 18

2. 77 - 35

3. 22 - 7

4. 94 + 56

5. 88 + 41

6. 43 - 29

7. 68 - 55

8. 1 + 67

9. 27 + 72

10. 97 - 93

11. 34 - 2

12. 42 + 80

Step-by-step explanation:

Answer:

Second option is correct one (9,3/2)

Value of x=9

Value of y

2y=x-6

By substituteing value of x

2 y=9-6

2y=3

Y =3/2

(x,y)

(9,3/2)

request :- If you are helped with my answer pls tag me brianliest I really want it... Plzz

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Answer:

9 3/2

Step-by-step explanation:

substitute the given value of X into the equation 2y=X-6

2y=9-6

solve for y

y=3/2

The possible ordered pair of the system is the ordered pair (x,y)

(x,y)=(9, 3/2)

check the given ordered given pair is the system of equations

2 ×3/2=9-6

simplify the equality

9=9

3=3

since all the equalities are true,the ordered pair is the solution of the system

(x,y) =(9 3/2)

Answer:

The answer is 3

y=4x-3❌

Step-by-step explanation:

1)y=3x=3(1)=3✅

2)y=x+2=1+2=3✅

3)y=4x-3=4-3=1❌

4)y=4x-1=4-1=3✅

Answer:

Step-by-step explanation:

QUESTION 7:

We are trying to find angles 1 and 2.

Known angle: 107˚.

In this question, we have 2 parallel lines with a transversal. A transversal is a line that passes through 2 parallel lines making it so that the angles on both sides are exactly the same.

Step 1: Find the measures of all the angles using the one we already know.

I will start with the angle adjacent (right next to) the angle that measures 107˚. As you can see, it is a supplementary angle because both of them form a straight line, or 180˚.

Therefore,

107+x= 180

x= 180-107

x= 73˚

Next, I will find the measure of the angle that is vertical to the one that measures 107˚. Note that angles that are vertical to each other are always identical, or in other words they have the same measure. Hence, the angle "vertical", or opposite to the one that measures 107˚ has to measure 107˚ as well.  You can also tell this is true because they look the same.

Now I'll find the measure of the angle vertical to the one that measures 73˚. As we know, vertical angles are identical, so the one vertical to it is 73˚.  

Here, I'll solve for angles 1 and 2. Like I said earlier, when a transversal crosses through 2 parallel lines, there will be 2 sets of angles that all have the same measurements.  

To solve for angle 1, simply know what angle is right below it, and that is the one that measures 107˚. (If you look at the 2 lines, you will see that both angle sets are essentially duplicates of each other.) Likewise, angle 2 has to be 73˚ because the one under it is also 73˚.

Angle 1: 107˚

Angle 2: 73˚

QUESTION 8:

Again, we have a transversal that passes through 2 parallel lines. One angle measures 95˚.  When there are 3 seperate angles along a straight line,  the one next to the one with the given measurement will be the same as that one.

So angle 3 is 95˚. To find angle 4, find the angle measurement that's vertical to angle 3, which is 95˚. Now, since that angle and angle 4 are supplementary (both form a straight line which is always 180˚), 95+x= 180.

(x stands for angle 4)

x+95= 180

x= 180-95

x= 85

Angle 4= 85˚.

QUESTION 9:

ANGLE 5: 49˚

When there is a transversal, there are 2 identical pairs of angles. Therefore, angle 5 must be 49˚.

ANGLE 6: 131˚

angle 5 and angle 6 form a straight line which means they are supplementary angles. Therefore, both angles must add up to 180˚. So 49+x= 180

x= 180-49= 131

(x stands for angle 6)

Hope this helps!! Also I worked pretty hard on this so brainliest would be appreciated :D

Practice problems if it helps :) : https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_1