what is the sum of three consecutive odd integers is 75?

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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Answer:

Option: d is the correct answer.

               d. 98

Step-by-step explanation:

The scores of Myra's test are as follows:

               84, 99, 88, 82, 95, 85

Let 'x' be the minimum  score that is obtained by Myra in the last test so that the average is greater than 90 marks.

i.e.

[tex]\dfrac{84+99+88+82+95+85+x}{7}>90\\\\\\i.e.\\\\\\\dfrac{533+x}{7}>90\\\\\\i.e.\\\\\\533+x=90\times 7\\\\\\533+x>630\\\\\\x>630-533\\\\\\x>97[/tex]

Hence, the minimum score has to be 98.

(   Since, the scores are in whole number )

option C: (6, 2).

The student has asked for the possible dimensions of a rectangle given that its perimeter is 16 inches. To find the dimensions that are correct, we need to remember that the perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. We must check each pair of dimensions provided and see if they satisfy this equation when the perimeter is 16 inches.

Therefore, the only possible dimensions for the rectangle given the choices provided and where both dimensions are greater than zero is option C: (6, 2).

let number of hours = x

1st equation is 15.54+0.11x

2nd equation is 16.14-0.09x

now calulate x so the 2 equations are equal:

15.54+0.11x=16.04-0.09x

mutiply evrything by 100 to get rid of the decimal points andmake the calculations a little easier

1554+11x=1604-9x

add 9 x to both sides:
1554+20x=1604

subtract 1554 from both sides:
20x=50

divide 50 by 20 for x
x=50/20 = 2.5

x = 2.5

 so they were the same after 2.5 hours

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.

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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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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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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20/8 = 2.5

multiply all the ingredients by 2.5

10 ml  * 2.5 = 25 ml of baking powder

70 *2.5 = 175 ml of butter

190 * 2.5 = 475 ml of sugar

420 * 2.5 = 1050 ml of flour

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.