Which set of coordinates, when paired with (3, −3) and (10, −3), result in a square? (−3, −3) and (−10, −3) (3, 10) and (10, 3) (−3, 4) and (−10 , 4) (3, 4) and (10, 4)

Answer:

  (-5/2, 3/2)

Step-by-step explanation:

The midpoint is the average of the coordinates of the endpoints:

  (P +Q)/2 = ((-2, 1) +(-3, 2))/2 = (-2-3, 1+2)/2 = (-5/2, 3/2)

Answer: The probability of hitting an odd number three times is [tex]3\dfrac{3}{8}[/tex] times more than the probability of hitting an even number 3 times.

Step-by-step explanation:

From the given picture , the total total number of sections in the spinner = 5

Sections having Odd numbers = 3

Sections having Even numbers =2

We know that , [tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

So , probability of hitting an odd number = [tex]\dfrac{3}{5}[/tex]

Probability of hitting an even number = [tex]\dfrac{2}{5}[/tex]

Since all events are independent of each other ,

So , probability of hitting an odd number three times = [tex](\dfrac{3}{5})^3=\dfrac{27}{125}[/tex]

Probability of hitting an even number three times = [tex](\dfrac{2}{5})^3=\dfrac{8}{125}[/tex]

Divide  [tex]\dfrac{27}{125}[/tex] by [tex]\dfrac{8}{125}[/tex] , we get

[tex]\dfrac{27}{125}\div\dfrac{8}{125}\\\\=\dfrac{27}{125}\times\dfrac{125}{8}=\dfrac{27}{8}=3\dfrac{3}{8}[/tex]

Hence, the probability of hitting an odd number three times is [tex]3\dfrac{3}{8}[/tex] times more than the probability of hitting an even number 3 times.

Answer:

3.375

Step-by-step explanation:

To get it, combine like terms and restrain the variable. Segregating both sides by 3 gives the solution to the equation as v = -7.

To solve the condition 12 + 5v = 2v - 9, take after these steps:

Step 1: Segregate the variable terms on one side of the condition and the steady terms on the other side.

Subtract 2v from both sides to move the variable term to the cleared outside:

12 + 5v - 2v = 2v - 9 - 2v

Alter both sides of the condition:

12 + 3v = -9

Step 2: Separate the variable term by moving the reliable term to the other side.

Subtract 12 from both sides to move the dependable term to the proper side:

12 + 3v - 12 = -9 - 12

Unwind both sides of the condition:

3v = -21

Step 3: Light up for v by confining both sides of the condition by the coefficient of v, which is 3.

Portion by 3 to clarify for v:

v = -21 / 3

Streamline the division:

v = -7

The solution to the equation is v = -7.

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Answer:

7 ab ( 8 ab² - 5 ) .

Step-by-step explanation:

Given  : 56 a²b³ − 35 ab.

To find : Factor completely.

Solution : We have given 56 a²b³ − 35 ab.

Taking 7ab common form both terms .

7 ab ( 8 ab² - 5 ) .

Therefore, 7 ab ( 8 ab² - 5 ) .

We have that for the Question "each of 5 boys ate 2/3 of a pizza. what is the total amount of pizza the boys ate?" it can be said that each boy ate

From the question we are told

Generally the equation for the total amount of pizza the boys ate  is mathematically given as

Pt=N*Ratio

Therefore

Pt=5*2/3

Pt=3.333pizza

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Answer: 156 square feet of carpet would be needed to cover the floor in his room.

Step-by-step explanation:

Since we have given that

Dimensions of his room as follows :

Length of his room = 13 feet

Width of his room = 12 feet

We need to find the square feet of carpet which is used to cover the floor of his room.

so, we just need to find the area of his room.

Area of rectangle = Length × Breadth

So, Area of his room becomes

[tex]13\times 12\\\\=156\ sq.\ feet[/tex]

Hence, 156 square feet of carpet would be needed to cover the floor in his room.

The total sum of money will be $320.

Let the total sum of money be represented by x.

Based on the information given, the equation to solve the question will be:

12 1/2% × x = 40

0.125x = 40

Divide by 0.125

x = 40/0.125.

x = 320

Therefore, the total sum of money will be $320.

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Answer:72.03

Step-by-step explanation:

The sum of the series is 28.

The series 13 + 9 + 5 + 1 is an arithmetic series with a common difference of -4. To express this in summation (sigma) notation and find its sum, we first identify the first term (a1) as 13 and the common difference (d) as -4.

Next, we determine the number of terms (n). The series decreases by 4 each time, so we find the number of steps it takes to go from 13 to 1, which are 4 terms in total (13, 9, 5, 1).

We can write the summation formula for an arithmetic series as Sn = n/2 * (2a1 + (n-1)d), where Sn is the sum of the first n terms. With n = 4, a1 = 13, and d = -4, we plug these into the formula:

S4 = 4/2 * (2(13) + (4-1)(-4))

S4 = 2 * (26 - 12)

S4 = 2 * 14

S4 = 28

The sum of the series is 28.

The amount of calories that are in 6 grams of crackers is 30 grams.

Division is the mathematical operation that is used to determine the quotient of a number.  It is the process of grouping a number into equal parts using another number.

Calories in 6 grams = (150 / 30) x 6 = 30 grams

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Final answer:

To find the calories in 6 grams of Mike's crackers, divide the total calories by the total mass of one serving to get the unit rate (5 calories/gram) and then multiply by the mass in question (6 grams) to obtain 30 calories.

Explanation:

The question asks how many calories are in 6 grams of Mike's crackers, given that one serving of 30 grams has 150 calories. To find the calories in 6 grams of the crackers, we can use unit rate and proportions.

Step-by-Step Calculation

First, determine the calories per gram of the crackers by dividing the total calories by the total mass (in grams) of one serving. This gives us the unit rate: 150 calories / 30 grams = 5 calories per gram.

Next, since we're asked about the calories in 6 grams, we multiply the calories per gram (unit rate) by the mass: 5 calories/gram × 6 grams = 30 calories.

Therefore, there are 30 calories in 6 grams of Mike's crackers. This calculation illustrates the utility of understanding proportions and unit rates in everyday applications such as determining caloric intake from portions of food.