If A ⊂ B and A ∩ B = θ then which of the following can be concluded about the sets A and B?

Set A has more elements in it than set B.
Set A is the set containing zero.
Set A is the empty set.
Both sets A and B are the empty set.

The equation can be used to find m, is [tex]m^{2} -100 = -99[/tex].

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

According to the given question.

We have two numbers.

Both are 10 m away from their midpoint, m.

Therefore,

If the first number is ( m + 10).

Then the second number will (m-10).

Also it is given that the product of these two numbers is 99.

⇒ [tex]( m + 10)( m - 10) = -99[/tex]

⇒ [tex]m^{2} -10m + 10m -100 = -99[/tex]

⇒  [tex]m^{2} - 100 = -99[/tex]

Hence, the equation can be used to find m, is [tex]m^{2} -100 = -99[/tex].

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Answer:

72 ÷ 8 is equal to 9

Step-by-step explanation:

If we want to solve 72 ÷ 8 by breaking apart and distributing, the first step is to write the number ''72'' as the sum or subtraction of two numbers that are divisible by ''8''.

We can write :

[tex]72 = 40+32[/tex]

If we replace this last expression in the original one :

72 ÷ 8 = (40 + 32) ÷ 8 (II)

Now in (II) we can use the distributive property of the division :

(40 + 32) ÷ 8 = (40 ÷ 8) + (32 ÷ 8) (III)

Finally, we need to solve the expression (III) :

(40 ÷ 8) + (32 ÷ 8) = 5 + 4 = 9

We find that 72 ÷ 8 is 9 by breaking apart and then distributing.

Answer: The fraction of pounds of fruits over total pounds of fruits and vegetables is given by

[tex]\frac{25125}{66724}[/tex]

Step-by-step explanation:

Since we have given that

Total amount of vegetables = 208 pounds

Total amount of fruits is given by

[tex]125\frac{5}{8}\text{ pounds}[/tex]

Total amount of fruits and vegetables is given by

[tex]208+125\frac{5}{8}\\\\=208+\frac{1005}{8}\\\\=\frac{1664+1005}{8}\\\\=\frac{2669}{8}\\\\=333.625\text{ pounds }[/tex]

So, we need to find the fraction of pounds of fruits over the total pounds of fruit and vegetables :

[tex]\frac{\text{Pounds of fruits }}{\text{ total pounds of fruits and vegetables}}\\\\=\frac{\frac{1005}{8}}{333.62}\\\\=\frac{1005}{8\times 333.62}\\\\=\frac{1005}{2668.96}=\frac{25125}{66724}[/tex]

The fraction of the total pounds of fruit and vegetables that fruits represent is approximately 0.377, or 37.7%.

To find out what fraction the pounds of fruits represent out of the total pounds of fruits and vegetables, we first need to calculate the total pounds of fruits and vegetables consumed. This is found by adding the pounds of vegetables (208) to the pounds of fruits (125 5/8). So, 208 + 125 5/8 = 333 5/8 pounds.

Now, to determine the fraction, we take the pounds of fruits and divide by the total. Hence, the fraction is given by 125 5/8 ÷ 333 5/8. To divide fractions, we multiply by the reciprocal of the divisor, which gives us (125 5/8) * (8/333) = 0.377 (rounded to three decimal places).

Therefore, fruits represent approximately 0.377, or 37.7% of the total pounds of fruits and vegetables consumed.

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Answer:

Option C

Step-by-step explanation:

A function is a relation that does not contain two pairs with same first component.

Option A

{(-1,2),(3,-2),(0,1),(5,2)}  is a function, since there are no two pairs with the same first component.

option B

{(-1,2),(3,2),(-2,2),(0,2)} is a function, since there are no two pairs with the same first component.

option C

{(-1,2),(3,-2),(0,1),(3,5)} is not a function, since there are two pairs with the same first component i.e, 3

OptionD

{(-1,2),(2,3),(3,-2),(-2,0)} is a function, since there are no two pairs with the same first component.

So, {(-1,2),(3,-2),(0,1),(3,5)} is the required  answer.

To rewrite 1/3 and 7/9 using the least common denominator, you need to find the smallest number that both 3 and 9 can divide evenly into. The least common denominator (LCD) of 3 and 9 is 9. Rewrite the fractions as 3/9 and 7/9, respectively.

To rewrite the fractions 1/3 and 7/9 using the least common denominator, we need to find the smallest number that both 3 and 9 can divide evenly into. The least common denominator (LCD) of 3 and 9 is 9. We can now rewrite the fractions:

So, 1/3 and 7/9 can be rewritten as 3/9 and 7/9, respectively, using the least common denominator.

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The correct Options are  B and C.

To solve y = 5x we check all options in equation by value putting.

let y = 5x .......................(1)

    Put point A ( 5, -1) in equation (1)

So,    x = 5 & y = -1

          y = 5x ⇒ -1 = 5 ×5= 25

  Put point B (1,5) in equation (1)

So,     x = 1 & y = 5

          y = 5x ⇒ 5 = 5 × 1 = 5

Put point C (0,0) in equation (1)

           x = 0 & y = 0    

                y = 5x ⇒ 0 = 5 × 0 =0

Put point D ( -3 ,2) in equation (1)

        x = -3 & y = 2

         y = 5x ⇒ 2 = -3× 2 = -6

In all these points ,  B & C points are have same value on both side.

So, we can say that b&c are the points which are shown on the line.

Therefore, The correct Options are  B and C.

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Answer:

x=8 or just x+2=10

Step-by-step explanation:

if you wanted to know this without absolute value, its still x+2=10. if you wanna know what 'x' is, its 8.

Answer:

A line that rises from left to right has a positive slope

Step-by-step explanation:

Verify each statement

case A) A horizontal line has no slope

The statement is False

Because a horizontal line has a slope equal to zero

case B) A vertical line has a slope of zero

The statement is False

Because a vertical line has a undefined slope

case C) A line that rises from left to right has a positive slope

The statement is True

case D) A line that falls right to left has a negative slope

The statement is False

Because a is a positive slope

Answer:

absolute value is 6

Part 1)

In this problem we know that

[tex]4y\°+112\°=180\°[/tex] ------> by supplementary angles

solve for y

[tex]4y\°=180\°-112\°[/tex]

[tex]y=68\°/4[/tex]

[tex]y=17\°[/tex]

Part 2)

In this problem we know that

[tex]7x+7=112\°[/tex] ------> by vertical angles

solve for x

[tex]7x=112\°-7\°[/tex]

[tex]x=105\°/7[/tex]

[tex]x=15\°[/tex]

therefore

the answer is the option A

[tex]x=15\°, y=17\°[/tex]

Answer:

5000

Step-by-step explanation:

400 ÷ 4% = 5000

The complement of set A with respect to the universal set U (A') is {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}, which contains all elements in U that are not in set A.

The student is asked to use the roster method to write the set A', which represents the complement of set A with respect to the universal set U. The set A' consists of all elements in the universal set U that are not in set A.

First, we list all the elements of the universal set U, which are {21, 22, 23, ..., 40}. Set A contains {21, 22, 23, 24, 25}. To find A', we remove the elements of A from U, resulting in A' = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}.

Final answer:

The set A' includes all numbers from 26 to 40 in the universal set U, which are not included in set A.

Explanation:

To find the set A' or the complement of set A in the universal set U, we need to list all the elements in U that are not in A. Given that the universal set U consists of the numbers 21 through 40, and the set A includes the numbers 21, 22, 23, 24, and 25, we can determine A' by subtracting these from U.

The roster method simply lists out all of the elements. Doing so for A' yields the following:

A' = {26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}

These are all the numbers in U that are not in A.

Answer:

[tex]F(64)=2[/tex]

Step-by-step explanation:

Given the funtion:

[tex]F(x)=log_8(64)[/tex]

We need to find the value of the function at x=64:

[tex]F(64)=log_8(64)= z[/tex]

Where z is the value we are trying to find. In order to find z, let's use the definition of the base of a log:

[tex]log_xy=z\Rightarrow x^z=y[/tex]

So:

[tex]8^z=64[/tex]

Express [tex]8^z[/tex] as:

[tex]2^{3z}[/tex]

And express 64 as:

[tex]2^6[/tex]

Which leads to:

[tex]2^{3z}=2^6[/tex]

Equate exponents of 2 on both sides:

[tex]3z=6[/tex]

Solving for z:

[tex]z=\frac{6}{3} =2[/tex]

Therefore:

[tex]F(64)=log_8(64)= z=2[/tex]

Troy Aikman make 6667000 and Deion Sanders makes 6200000 for the Cowboys cornerback.

Two or more expressions with an Equal sign is called as Equation.

Given,

Troy Aikman, the quarterback for the Dallas Cowboys, earned $0.467 million more than Deion Sanders

Let Deion Sanders earning is x.

Troy Aikman earning is x+467000

Together they cost the Cowboys $12.867 million

x+x+467000=12867000

2x+467000=12867000

Subtract 467000 on both sides

2x=12867000-467000

2x=12400000

Divide both sides by 2

x=6200000

So Troy Aikman make 6200000+467000=6667000 and

Deion Sanders makes 6200000

Hence Troy Aikman make 6667000 and Deion Sanders makes 6200000 for the Cowboys cornerback.

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Final answer:

By using the counting principle and multiplying the choices for ice cream flavors (3) by the choices for toppings (4), we find there are 12 possible sundae combinations.

Explanation:

To determine the number of possible sundae combinations with the given choices, we can use the counting principle. We multiply the number of options for each category. In this case, there are three choices for ice cream flavors (chocolate, vanilla, and strawberry) and four choices for toppings (chocolate syrup, sprinkles, caramel, and whipped cream).

Since a sundae consists of one ice cream flavor and one topping, we simply multiply the number of options for ice cream by the number of options for toppings.

3 ice cream flavors × 4 toppings = 12 possible combinations.

Therefore, there are 12 unique sundae combinations a customer can choose from.