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Answer:

  4 pairs

Step-by-step explanation:

You want the number of pairs of integers (m, n) such that m > n and m² -n² = 96.

The difference of squares is factored as ...

  m² -n² = (m -n)(m +n)

In order for the difference to be 96, these factors must be factors of 96.

The prime factorization of 96 is ...

  96 = 2^5 · 3

The number of divisors of 96 is the product of the exponents of these factors, each increased by 1:

  (5+1)(1+1) = 12

That is, there are 12/2 = 6 factor pairs ab such that a<b. They are ...

   96 = 1·96 = 2·48 = 3·32 = 4·24 = 6·16 = 8·12

The values of m and n relate to the values of 'a' and 'b' by ...

  m = (a+b)/2

  n = (b-a)/2

In order for m and n to be integers, the values of 'a' and 'b' must both have the same parity. That is, they must both be even, or both be odd. This eliminates the factor pairs 1·96 and 3·32, leaving 4 (a, b) pairs, hence 4 (m, n) pairs. Possible ordered pairs are ...

  (m, n) ∈ {(25, 23), (14, 10), (11, 5), (10, 2)} . . . . . 4 pairs

The minimum number of pizzas that john must deliver to earn back the money he spent on the car he bought  is 715 pizzas   .

In the question,

it is given that ,

the amount for which John bought the used car for pizza delivery = $5000

the amount John gets for 1 pizza he delivers = $10

the amount John spend on gas for 1 pizza he delivers = $3

So , the amount that John earned for 1 pizza delivered is = 10 - 3 = $7 .

the number of pizza required to sell = (price of car)/(amount earned from 1 pizza)

Substituting the values , we get

number of pizza required to sell = 5000/7 = 714.2857

rounding the answer to  whole number ,

we get

= 715 pizzas

Therefore , The minimum number of pizzas that John must deliver to earn back the money he spent on the car he bought  is 715 pizzas   .

The given question is incomplete , the complete question is

John recently bought a used car for $5000 for his pizza delivery job. he gets $10 for each pizza he delivers, but he has to spend $3 on gas for each pizza he delivers. what is the minimum whole number of pizzas john must deliver in order to earn back the money he spent on the car he bought ?

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The order of T is 82.

Let n and e be the order and number of edges of T respectively.

Also, let a, b, c and d be the number of vertices of degree 2, 3, 4 and 5 respectively.

Then, 50+a+b+c+d = n

And by the Handshake Lemma,  the sum of the degrees of all the vertices of T is twice the number of edges, so we have

50+2a+3b+4c+5d = 2e

Since a=b=c=d then we have the following two equations,

50+4a = n

50+14a = 2e

But, T is a tree so e=n=1, then the two equations become,

50+4a = n ...............(1)

50+14a = 2(n-1) .............(2)

Solving for a in (1) we get,

a = [tex]\frac{n-50}{4}[/tex]

Plugging a into (2) we get,

50+14([tex]\frac{n-50}{4}[/tex]) = 2(n-1)

50+3.5n-175 = 2n-2

3.5n-2n = 175-50-2

1.5n = 123

n = [tex]\frac{123}{1.5}[/tex] = 82

Therefore, the order of T is 82.

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Answer:

70 dogs

Step-by-step explanation:

total animal is 98

total ratio is 5+2 = 7

calculate how much each ratio has

98/7 = 14

5 ratio are dogs, so multiply 14 with 5 to get 70 dogs

you can also do:

5/7 × 98 = 70

According to the given standard deviation, the true mean number of chocolate chips per cookie to within 2 chocolate chips with 99% confidence is 10.6

Standard deviation:

Basically, the standard deviation refers a quantity expressing by how much the members of a group differ from the mean value for the group.

Given,

It is desired to estimate the mean number of chocolate chips in a chocolate chip cookie.

Here we need to find how many cookies need to be sampled to estimate the true mean number of chocolate chips per cookie to within 2 chocolate chips with 99% confidence and assume that the population standard deviation is 3.7 chocolate chips.

From the given question we have identified the following details,

Confidence interval = 99%

Standard deviation = 3.7

So, the critical value is calculated as,

=> 1 - 0.99

=> 0.01

So, the z scores is 2.576.

Now, the formula to confidence interval is given by : -

=> 10.6 ± 2.576 (0.01)/ √3.7

=> 10.6

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Explicit formula for this sequence is (C) an= 6+ (n-1)(-4)

Given sequence,

6, 2, -2, -6.....

First term = a = 6

Difference = d = 2 - 6

                        = -4

No. of terms = n

Therefore, an = a + (n-1)d

                       = 6 + (n-1)(-4)

Hence, an= 6+ (n-1)(-4).

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Answer:

2 pound bottle

Step-by-step explanation:

convert ounce to pounds:

37/16=2.3125

find price of 1 pound of bbq sauce:

35.15/2.3125=$15.2

23.36/2=$11.68

$11.68 is more cheaper so 2 pound bottle is better to buy

The goal of a hypothesis test is to determine if the data can refuse an assumption a parameter or a population.

Statistical hypothesis test:

A statistical hypothesis test is a technique for determining whether the available data are sufficient to support a specific hypothesis. We can make probabilistic claims about population parameters through hypothesis testing.

The purpose of a hypothesis test is to ascertain whether the data can refute a parameter or population assumption.

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Answer:

False

Step-by-step explanation:

[tex]10^{-2}[/tex] id not a negative number it means

[tex]\frac{1}{10^{2} }[/tex] or [tex]\frac{1}{100}[/tex]  Which is a number with a lesser value than 1, but it is not a negative number.

The area of the smaller triangle is 18 squared units which is determined by the property of similar triangles.

The area of the larger triangle is 36.

The two triangles are similar which is given in the question

We know that the corresponding sides of similar triangles are being in the same ratio.

As per the property of similar triangles,

A₁ : S₁ = A₂ : S₂

Here A₁ is area of the larger triangle,  A₂ is area of the smaller triangle

S₁ is side of the larger triangle, and S₂ is side of the smaller triangle,

⇒ A₁ / S₁ = A₂ / S₂

⇒ 36 / 12 = A₂ / 6

⇒ 3 = A₂ / 6

⇒ A₂ = 18

Therefore, the area of the smaller triangle is 18 squared units.

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The correct interpretation of the expression "minus, 7, minus, left parenthesis, minus, 11, right parenthesis" is 8.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We have to write the correct interpretation of the expression "minus, 7, minus, left parenthesis, minus, 11, right parenthesis".

We have to subtract when two different signs appear next to each other (-+ or +-)

Similalry We have to add when two of the same signs appear next to each other (++ or --)

So:

-7 - (-11)−7−(−11)

-7 + 11 - 7 + 11

-14 + 22

8

Therefore, the correct interpretation of the expression "minus, 7, minus, left parenthesis, minus, 11, right parenthesis" is 8.

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Answer: -1.73 ft

Step-by-step explanation:

(-2.54 - 3.16 - 2.82 + 1.6) / 4 = -1.73

Answer:

50.6 ft

Step-by-step explanation:

We can use the pythagoreas theorem to solve this problem.

If the service drop is 20 ft from the ground and the insulator is 35 ft, that means that the insulator is 15 ft higher than the service drop.

a² + b² = c²

15² + 48² = c²

255 + 2304 = c²

2559 = c²

√2559 = c

50.6 ≈ c

Answer: About 140,514 ft²

Step-by-step explanation:

The area of a parallelogram is base × height. The base is already determined as 740 ft. You can find the height(h) with trigonometry:

[tex]sin(88)=\frac{h}{190}\\ \\h=190sin(88)=189.88425713[/tex]

Now, multiply the values together:

[tex]740*189.88425713=140514.350[/tex]

Answer:

28.3

Step-by-step explanation:

To solve this problem, we must follow PEMDAS, which must be used in solving all mathematical equations and expressions.

PEMDAS is the order you solve the equation/expression in. It is an acronym for:

P: Parenthesis

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

Keep in mind that multiplication and division are too be done left and right. You do not do multiplication first and division last, read left to right. Same goes with addition and subtraction.

This is the less confusing notation of PEMDAS.

P: Parenthesis

E: Exponents

M: Multiplication D: Division

A: Addition S: Subtraction

Now, lets solve the problem.

92.3 - (3.2 ÷ 0.4) × 2³

What do we do first? Well since parenthesis is first according to PEMDAS, we must solve the division in side of the parenthesis first.

3.2/0.4 = 8

Now we have:

92.3 - (8) × 2³

Remove the parenthesis as there is only one term inside and therefore not needed.

92.3 - 8 × 2³

What do we do next?

We have:

Subtraction: 92.3 - 8

Multiplication: -8 × 2³

Exponent: 2³

Because PEMDAS states exponents is to be solved in front of multiplication/division and addition/subtraction, we must do that.

What is an exponent?

2³

2 is the base, 3 is the exponent.

2³

Means multiplying 2 by itself 3 times:

2 × 2 × 2

8

Now we have:

92.3 - 8 × 8

Because PEMDAS states solving multiplication/division is prioritized over addition/ subtraction, we must solve 8 × 8

8 × 8 = 64

Now we have: 92.3 - 64

Solve.

28.3

Answer:5,149 pounds of sawdust for $1,132.78

Step-by-step explanation:

Step 1 is to convert 4 tons into pounds is:

4 tons * 2000 pounds per ton = 8000 pounds

Step 2 is to find the cost of saw dust per pound in each scenario:

Scenario 1: $1132.78 / 5149 = .22 dollars per pound

Scenario 2: $2800 / 8000 = .35 dollars per pound

Step 3 is just comparing which one is the cheapest per pound based on step 2:

.22 per pound is less than .35 per pound. So the answer is scenario 1 (5149 pounds for 1132.78) is the better buy

Answer: He is incorrect.

Step-by-step explanation:

        Since we are talking about -8.0, we can "ignore" the .0 because 0 has no value. An integer is a whole negative number, whole positive number, or zero. -8 is a whole negative number, since .0 means "nothing" here, so it is an integer.

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The sale price of the oil change after the discount can be found to be $25.50.

When given a discount, the selling price of an item is found by the formula:

= Price of item before discount - Discount

The discount on the oil change, given the price of the oil change and the coupon is:

= Price of oil change x Coupon rate

= 30 x 15%

= $4.50

The sale price after the oil change is:

= Price of oil change before discount - discount

= 30 - 4.50

= $25. 50

The first part of the question is:

An oil change at city auto is regularly $30. Mr Allen has a coupon for 15% off.

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Step-by-step explanation:

Great Meadow Loop and Jordan Pond Path

The equation of the function in slope-intercept form with slope of 2 is y = 2x+19.

According to the question,

We have the following information:

Slope = 2 (Note that slope of a line is denoted by m.)

Points through which function is passing = (-8,3)

So, we have x' = -8 and y' = 3.

We know that the following equation is used to find the equation of the function or line:

(y-y') = m(x-x')

y-3 = 2{x-(-8)}

y-3 = 2(x+8)

y-3 = 2x+16

y = 2x+16+3

y = 2x+19

Hence, the equation of the function in slope-intercept form with slope of 2 is y = 2x+19.

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Answer:

{A) X=5} {B) X=2.75}

Step-by-step explanation:

A) (2)4x-1/2=x+7(2) - multiply each side by denominator

4x-1=x+14

-x + 1 -x +1

3x=15

÷3. ÷3

x=5

B) (2)3x+2=2x+13/2(2)

6x+2=2x+13

-2x -2. -2x -2

4x=11

÷4. ÷4

x=2.75

Answer:

x = 7.5 , x = 1

Step-by-step explanation:

(a)

[tex]\frac{4x-1}{2}[/tex] = x + 7 ( multiply both sides by 2 to clear the fraction )

4x - 1 = 2(x + 7)

4x - 1 = 2x + 14 ( subtract 2x from both sides )

2x - 1 = 14 ( add 1 to both sides )

2x = 15 ( divide both sides by 2 )

x = 7.5

(b)

3x + 2 = [tex]\frac{2x+13}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

3(3x + 2) = 2x + 13

9x + 6 = 2x + 13 ( subtract 2x from both sides )

7x + 6 = 13 ( subtract 6 from both sides )

7x = 7 ( divide both sides by 7 )

x = 1

Answer:

in six years, Mo will have roughly $393090.4 in savings bonds.

Step-by-step explanation:

(This might not be the most efficient way to do it.)

year one - 290000 x 1.052 = 305080

year two - 305080 x 1.052 = 320944.16

year three - 320944.16 x 1.052 = 337633.256

year four - 337633.256 x 1.052 = 355190.185

year five - 355190.185 x 1.052 = 373660.075

year six - 373660.075 x 1.052 = 393090.399

in six years, Mo will have roughly $393090.4 in savings bonds.

B) direction ratio of any two diagonals in vector form is 60°.

C) cos²α+cos²β+cos²γ+cos²δ= [tex]\frac{4}{3}[/tex]

​In Euclidean geometry, a perspective is a parent created by rays, often referred to as the angle's perimeters, sharing a single endpoint known as the perspective's vertex. Angles created by rays are located in the plane that contains the rays. Angles can also be created by intersecting two planes. They are referred to as dihedral angles. Curves that cross may also define an angle, which is the angle formed by rays that are perpendicular to the individual curves at the point of junction.

The degree of an angle or rotation is also expressed in terms of perspective. This metric represents the relationship between a circular arc's length and radius.

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The force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.

According to the question,

We have the following information:

The force of attraction, F of a body varies directly as its mass (m) and inversely as the square of the distance (d) from the body. And when m=8kg and d=5meters then F=100 Newtons.

Now, let's take the constant for this case to be k.

We have the following expression:

F = km/[tex]d^{2}[/tex]

Putting the values in this expression to find the value of k:

100 = 8k/(5*5)

Using the cross multiplication method:

2500 = 8k

k = 2500/8

k = 312.5

Now, we have the following value of F:

F = 312.5*2/15*15

F = 625/225

F = 2.78 Newton

Hence, the force of attraction is 2.78 Newton when m = 2 kilograms and d = 15 meters.

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Large sample size gives more accurate information about population.

The main advantages of Large sample size is :

1. Large sample size provide stronger and more reliable information about parent population.

2. It will help researcher to capture outliers and sweeping out in sample.

3. Measuring large sample size allows one to divide the sample into segments .

4. Large sample size helps in obtaining a quality and precise mean .

Some disadvantages of Large sample size is :

1. Large sample size will be time consuming and more expensive to work with

2. It require higher financial involvement to complete the survey.

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Based on the information given: A. c║d; converse of alternate exterior angles theorem.

Exterior alternate angles are congruent based on the alternate exterior angles theorem. Conversely, it can also be stated that if two angles, which are exterior alternate angles, are congruent to each other, therefore the lines they lie on that is crossed by a transversal are proven to be parallel to each other based on the converse of alternate exterior angles theorem.

Given that angles 11 and 13 are congruent angles, the diagram also shows that they are alternate exterior angles. They lie on each lines, c and d, that are crossed by transversal a.

Therefore, based on the converse of alternate exterior angles theorem, lines c and d are parallel.

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Answer: 18.75%

Step-by-step explanation:

To find the percentage decrease, the formula is shown below.

Plug in the values and calculate:

[tex]\frac{8-6.5}{8} *100=18.75%[/tex]

So, the chunk of meat lost 18.75% of its initial weight.

Answer:

[tex]0 < x < 60[/tex]

Step-by-step explanation:

By the Triangle Inequality Theorem:

30 + 30 > x, so 60 > x ----> x < 60

30 + x > 30, so x > 0

x + 30 > 30, so x > 0

Putting these inequalities together, we have 0 < x < 60. So the length of the third side can be greater than 0 inches but less than 60 inches.

The product of two consecutive non-negative integers is 240 and the integers are 15,16.

What are consecutive integers?

Let the numbers be x, x+1

Product is x(x+1)=240

x² + x = 240

x² + x − 240 = 0

x² + 16x − 15x − 240 = 0

x(x+16) − 15(x+16) = 0

(x+16)(x−15)=0

x = 15,−16

So, the product of two consecutive non-negative integers is 240,then numbers are 15, 16.

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