Simplify the expression (-3) ^4

Final answer:

There will be 36 handshakes among the nine people at the party, as determined by the combination formula 9C2.

Explanation:

Calculating Handshakes

To determine the number of handshakes that occur when nine people shake hands with each other, we can use the concept of combinations. In a handshake situation, the order in which the handshakes occur does not matter; what matters is which two people are shaking hands. Therefore, we can use the formula for combinations without repetition, which is nCk = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose at a time.

In this case, there are 9 people (n=9) and the handshake involves 2 people at a time (k=2). So, the calculation would look like this:

9C2 = 9! / (2!(9-2)!) = 9! / (2!7!) = (9 × 8) / (2 × 1) = 36 handshakes

Therefore, there would be a total of 36 handshakes among nine people at the party.

divide the number of guests by the number of spoons in a package

150/24 = 6.25 so they need to buy 7 packages

The packages of spoons will be needed to so that each guest gets 1 spoon is 7.

It is required to find the packages of spoons.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

The committee is planning a party = 150 guests

package of plastic =24 spoons.

According to given question we have

The packages of spoons will be needed to so that each guest gets 1 spoon

150/24

= 6.25 ≈7

Therefore, the packages of spoons will be needed to so that each guest gets 1 spoon is 7.

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Answer:

4.67 with the bar notation above the 67

Step-by-step explanation:

To solve this correctly you need to recall the rules repeating decimal numbers and what bar notation looks like. but i forgot my answer so its not above 6

To find out how many times more people live in Texas than in Vermont, calculate the ratio of their populations, resulting in 41.33 times more people live in Texas than in Vermont.

To find out how many times more people live in Texas than in Vermont, we can calculate the ratio of the populations of Texas and Vermont. Given that about 24.8 million people live in Texas while about 0.6 million people live in Vermont, the ratio would be 24.8 million / 0.6 million = 41.33 times as many people live in Texas than in Vermont.

Answer:-9/-2

Step-by-step explanation:

m=yz-yz/x2-x1=

-4-5/0-2=

-9/-2

(the / means over, for instance 9-2/8+4 is 9-2 over 8+4)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. 9/2  is the slope of a line passing through the points (2, 5) and (0, −4)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The given two points are (2, 5) and (0, −4)

The slope of line passing through two points (x1,y1) and (x2,y2) is

m=(y₂-y₁)/(x₂-x₁)

where m is the slope of line.

x₁=2,x₂=0, y₁=5,y₂=-4

Substitute the values of x₁, x₂, y₁ and y₂ in formula of slope

=-4-5/0-2

Minus plus minus we get plus, so add -4 and -5

=-9/-2

The minus on numerator and denominator will be cancelled.

=9/2

Hence slope of a line passing through the points (2, 5) and (0, −4) is 9/2.

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4.625 as a fraction in the simplest form can be written as 37/8.

Given is a decimal number 4.625.

Here the decimal point is 3 units to the left.

So any decimal number can be written as a fraction with powers of 10 as the denominator.

Here since the decimal point is 3 units to the left divide by 1000.

So,

4.625 = 4625 / 1000

Both 4625 and 1000 are multiples of 25.

So this can be written as  :

4625 / 1000 = 4625 ÷ 25/ 1000 ÷ 25

                    = 185 / 40

                    = 37/8

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Final answer:

The GCF of 55 and 88 is 11. Applying the distributive property, 55 + 88 is equal to 143.

Explanation:

The student is asking about the greatest common factor (GCF) and the distributive property of the expression 55 + 88.

To find the GCF, we need to break down the numbers 55 and 88 into their prime factors. The prime factorization of 55 is 5 × 11, and the prime factorization of 88 is 2² × 11. The GCF is the highest common factor between the two prime factorizations, which is 11.

The distributive property states that a × (b + c) = a × b + a × c. Applying this property to the expression 55 + 88, we get 11 × 5 + 11 × 8 = 55 + 88 = 143.

Final answer:

The GCF of 55 and 88 is 11. When we apply the distributive property to 55 and 88, the expression simplifies to 143.

Explanation:

To find the Greatest Common Factor (GCF) of 55 and 88, we can first list the factors of each number:

Factors of 55: 1, 5, 11, 55

Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88

The GCF is the largest factor that both numbers have in common, which in this case is 11.

Now, let's apply the distributive property to the numbers 55 and 88:

55 + 88 = (5 * 11) + (8 * 11)

Using the distributive property, we can simplify this to:

55 + 88 = (5 + 8) * 11

Therefore, the expression 55 + 88 is equal to 13 * 11, which is 143.

The correct answers are:

Distributive property; subtraction; addition property of equality.

Explanation:

To get from the first step to the second step, the terms inside parentheses have been multiplied by -2.  The property that allows us to multiply through parentheses, or distribute through parentheses, is the distributive property.

To get from the second step to the third step, the -6 and 4 have been subtracted; this means the reason for this is subtraction.

To get from the fourth step to the fifth step, 10 has been added to each side.  The addition property of equality allows us to do this.

Inequalities help us to compare two unequal expressions. The given inequality can be solved as shown below.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequality can be solved as shown below.

−2(x+3)−4>4x+30 → Given

−2x−6−4>4x+30 → Solving the parenthesis using the distributive property

−2x−10>4x+30 → Subtract 4x from both the sides of the inequality, Subtraction property of order

−6x−10>30 → Subtraction Property of Order

−6x>40 → Division property of order

x<−203 → Division Property of Order

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Final answer:

The prime factorization of the number 46 is 2 times 23, with 2 and 23 being prime numbers.

Explanation:

To write the number 46 as a product of prime numbers, we need to perform prime factorization. Here is the step-by-step process:

So, the prime factorization of 46 is 2 times 23. This can't be simplified any further as these are both prime numbers.

Answer:

x=6-2y

Step-by-step explanation:

Measure of ∠HNK is equals to 73°.

" Linear angles are formed when the sum of pairs of adjacent angles is equals to 180°."

According to the question,

Measure of ∠GNF = 60°

Measure of ∠MNL = 47°

As per the linear pair angles definition ,

∠GNF, ∠FNM,  ∠MNL forms linear pair angles .

Therefore,

∠GNF + ∠FNM + ∠MNL = 180°

Substitute the given values we get,

60° + ∠FNM + 47° = 180°

⇒ ∠FNM = 180° - 107

               = 73°

As given three lines intersect at 'N'

∠FNM and ∠HNK are vertically opposite angles and are congruent.

Therefore,

Measure of ∠HNK = 73°

Hence, measure of ∠HNK is equals to 73°.

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