which equation would be used to find three consecutive even integers whose sum is 78

Using the arrangements formula, the number of ways that they can be seated for each case is given as follows:

a) No restrictions: 362,880.

b) Sam next to Sarah: 80,640.

c) Boy-girl-boy-girl: 2,880.

The number of possible arrangements of a set containing n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

For item a, we consider that 9 people will be seated with no restrictions, hence the number of ways is given as follows:

9! = 362,880

For item b, there is the restriction that Sam has to be seated next to Sarah, hence:

Hence the number of ways is:

2 x 8 x 7! = 80,640.

For item c, we can treat the boys and the girls places as independent, hence:

Hence the number of ways is:

5! x 4! = 2,880.

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Answer:

ummm i don't know....

..,....

let's put the information given in a mathematical equation:

we pass all the terms thas has w in them to the left side and left the other terms in the right side:

Answer:

Mechanical Keyboard

The type of keyboard that Shelley is most likely to use is a mechanical keyboard. The correct option is a.

Mechanical keyboards offer a considerably more comfortable typing experience, as well as a plethora of customization options in terms of style and feel, and they're also more durable and easier to repair.

Mechanical keyboards often require only a half-press of a key to transmit a signal to your computer, allowing for faster and easier typing.

Here a mechanical keyboard will be used because she is an assistant and uses a desktop computer for scheduling appointments. She would not use tablets and laptops or virtual keyboards.

Therefore, the correct option is a. Mechanical keyboard.

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8[tex]\frac{2}{9}[/tex] as improper fraction is [tex]\frac{74}{9}[/tex]

A fraction that has the numerator higher than or equal to the denominator is said to be improper. A mixed fraction is one that has both a correct fraction and a whole number portion, and whose value is consistently greater than 1. When the numerator is always higher than or equal to the denominator, the fraction is said to be inappropriate. 4/3, 7/3, 11/5, and other incorrect fractions are a few instances. In fact, using improper fractions in mathematics is simpler than using mixed fractions. However, mixed numbers are easier for individuals to understand in daily life. It is crucial that you understand how to change from one form to another.

Given,

Mixed Fraction

8[tex]\frac{2}{9}[/tex]

Improper fraction:

[tex]\frac{8(9) +2}{9}[/tex]

[tex]\frac{72 +2}{9}[/tex]

[tex]\frac{74}{9}[/tex]

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QR = QS + SR

QS = y+1/2

QS= SR

SR= y+1/2

QR= y+1/2 +y+ 1/2 = 2y + 1

QT = TP

RP = 2 TP

RP = 10

10 = 2 TP

10/2= TP

5 = TP

TP= QT

QT= 5

Since y= 5

QR = 2y + 1 = 2 (5) + 1 = 10 + 1 = 11

Answers:

QT= 5

QR= 11

The number whose 0.7 is 42 is 5.715.

What do you mean by number?

In mathematics, a number serves as both a unit of measurement and a label. The first examples are the natural numbers 1, 2, 3, 4, and so forth. Language can express numbers by the use of number terms. Numerals are symbols that are used to symbolize specific numbers; for example, the number "5" can be symbolize as number five.

Let the required number be X

As given in the question 0.7 of X is 42,

We can write it as:

(0.7)X = 42

If a number make to change its side around the equal sign then if it is in divide on one side so it will become in multiplication on the other side.

So,

X = 4/0.7

X = 5.715 (approximately)

Therefore, The number whose 0.7 is 42 is 5.715

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We can conclude that the distance traveled in 1 hour is 57 miles after doing some mathematical operations.

So, the distance traveled in 1 hour:

Then divide 238 by 4.15 as follows:

Rounding off: 57 miles

Therefore, we can conclude that the distance traveled in 1 hour is 57 miles after doing some mathematical operations.

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Answer:

It depends on what the question is.

Step-by-step explanation:

Your question is unclear.

If the question is the fraction 0/03, then that equals 0, but that is not a choice.

If the question is 0.03, then the answer is 3/100.

If the question is 0.03030303... (repeating 03, then the answer is worked out below.

Let x = 0.030303...

    100x = 3.0303030...

-         x = 0.0303030...

---------------------------------

     99x = 3

x = 3/99

x = 1/33

the ratio 6.3 g to 3.6 g​ as a fraction is:

Given the following formula given in the exercise:

You can solve for the variable "t" by following the steps shown below:

1. You must apply the Disrtributive proprerty on the right side of the equation:

2. Now you need to apply the Subtraction property of equality by subtracting "W" from both sides of the equation:

3. Finally, you can apply the Division property of equality by dividing both sides of the equation by "Wr":

The answer is:

You have the following equation:

if you divide by 6 both sides, you obtain:

the slope of the previous line is m = 1/6.

Take into accout that the relation between the slopes of two perpendicular lines is given by:

For the required perpendicular line you have:

Now, use the following general equation for a line:

where (xo,yo) is any point on the line.

Replace (xo,yo) = (3,5) and m' = -6 into the previous formula and solve for y:

Hence, the equation of the perpendicular line is, in intercept slope form:

y = -6x + 23

SOLUTION:

Step 1:

In this question, we are given the following:

Find the equation of the line through the point (10,-6) that is perpendicular to the line with equation

-11x-18y=-2070

Step 2:

The details of the solution are as follows:

CONCLUSION:

The final answer is:

Answer:

The crickets do not chirp at all below 40 degrees and at 75 degrees they chirp about 161 times per minute.

Answer:

A,B,C is the answer

e

Solution:

A boxplot is a standardized way of displaying the dataset based on a five-number summary: the minimum, the maximum, the median, the first quartile, and the third quartile.

The general representation for a box plot is given below;

Comparing this to the box plot given in the question, the following can be deduced;

Therefore, the answer as arranged is;

The interquartile range, IQR is given by;

Therefore, the interquartile range is 5.

Given data:

The first number is -4.

The second number is 4.

Positive number is always bigger than negative number.

Thus, 4 is bigger than -4.

Answer:

a=1,b=-3,c=2

Explanation:

The standard form of a quadratic equation is given as:

Comparing with the equation:

We observe that the equation is already in the standard form.

Furthermore:

Using a system of inequalities, it is found that:

The variables to the system of inequalities are given as follows:

At least 6 units of protein are needed, hence, considering the amount of protein or each snack, the inequality is:

3y ≥ 6

y ≥ 2.

At least 10 units of carbohydrates are needed, hence, considering the amount of carbohydrates of each snack, the inequality is:

3x + 2y ≥ 10.

At least 16 units of fat are needed, hence, considering the amount of fats of each snack, the inequality is:

2x + 4y ≥ 16

x + 2y ≥ 8.

Hence the system is:

Each ounce of fruit contains 40 calories, and each ounce of nuts contains 50 calories, hence the calories function is:

Calories function = 40x + 50y.

Possible solutions to the system, containing only integers, as units is an integer amount, and their calorie consumption are:

Hence the quantities with the least calories are: 2 ounces of fruit and 3 ounces of nuts, with a calorie load of 230 calories.

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The midsegment theorem states that the length of the midsegment is equal to half the length of the base. From the information given,

midsegment = CD = 22

base = XY = 4x + 1

By applying the midsegment theorem, we have

CD = 1/2XY

22 = 1/2(4x + 1)

By crossmultiplying, we have

22 * 2 = 4x + 1

44 = 4x + 1

4x = 44 - 1

4x = 43

x = 43/4

x = 10.75

Thus,

Substituting x = 10.75 into XY = 4x + 1, it becomes

XY = 4(10.75) + 1

XY = 43 + 1

XY = 44

Substituting x = 10.75 into WZ = x + 3, it becomes

WZ = 10.75 + 3

WZ = 13.75

Given:

Cost of computer without tax $1800.

Total cost including tax is $1890

Let the tax rate be x

Tax rate is 5%

(a) For an HCF of 22, the residential plan costs $44 and the business plan costs $36.

(b) $14, business plan.

To make a+b= 0

Since b is positive ( to the right of zero), a must be positive and must be have the same distance from 0.

So:

The class width for this frequency table is 5.

The class width is described as the distance between the lower class of two consecutive classes.

One can calculate class width by finding the difference between the two consecutive lower classes.

In the figure above, the first two classes are described as

0-4

5-9

So, the lower classes of these intervals are 0,5

Thus the difference between them is 5

Therefore, the class width for this frequency distribution table is 5.

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It is necessary to expand the natural numbers to rational numbers or real numbers in order for division to always result in one number rather than a quotient plus a remainder. The  answer will be 4.4.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

At a fundamental level, the process of counting how many times one number is included within another is referred to as the division of two natural numbers. This number of times need not be integer. For instance, if 20 apples are distributed equally among 4 persons, each person will get 5 apples.

When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.

It is necessary to expand the natural numbers to rational numbers or real numbers in order for division to always result in one number rather than a quotient plus a remainder. In these expanded number systems, division operates in the opposite direction as multiplication, i.e., a = c / b implies that, if b is not zero, a b = c. This is a division by zero, which is not defined, if b = 0. In the case of the twenty-one apples, there would be no leftovers because each person would get five apples and a quarter of an apple.

Different algebraic structures, or ways of defining mathematical structure, use both modes of division. These are known as Euclidean domains and contain polynomial rings in one indeterminate space where a Euclidean division (with remainder) is defined (which define multiplication and addition over single-variabled formulas). Fields and division rings are those where a division (with a single result) by all nonzero elements is defined. The elements in a ring by which division is always feasible are known as the units; in the ring of integers, this would be 1 and 1. The quotient group is another way to apply division to algebraic structures; in this case, the outcome of "division" is a group rather than a number.

Just divide 3.96 by 0.9

[tex]\frac{3.96}{0.9}[/tex]= 4.4

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Now, Now,We are given the following vectors:

We are asked to determine the following vector:

First, we will determine the vector PQ and RS. To determine PQ we use the following:

This means we need to subtract "P" from "Q". We do that by subtracting each component of the points, like this:

Solving the operations:

Now, we use a similar procedure to determine RS:

Substituting we get:

Solving the operations:

Now, we substitute the values in the vector we are looking for:

Now, we solve the product by multiplying both components of RS:

Now, we solve the addition by adding each corresponding component:

Solving the operations:

And thus we have determined the components.

Part B. We area asked to determine the magnitude of the vector. To do that we will use the following:

Given a vector of the form:

Its magnitude is:

This means that the magnitude is the square root of the sum of the square of the components. Applying the formula we get:

Now, we solve the squares:

Solving the addition:

Now, we factor the term inside the radical as follows:

Now, we distribute the radical:

Taking the left square root:

And thus we have determined the magnitude.

SOLUTION

The standard quantity of water is 2000 liters

The quantity of water in the pool is 10,000

Since 3 chlorine is added to every 2000 liters of water then the number of chlorine added to 10000 liters of water is:

Since 8 tablets is added instead of 15 then:

The park pool has less chlorine than the safety standards require

SOLUTION

From the question, we are told to distribute the multiplication across in

This means we should expand.

This becomes

The ordered pair is 4 is 7.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

Given that,

The equation is

y = 2x-1

Substitute the value of x =4

y = 2x-1

y = 2×4-1

y = 7

The value of y at x = 4 is 7.

Hence, the ordered pair of 4 is 7.

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$200-$225  interval shows the greatest change in water bills

A diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.

The interval which contains the median water bill is $200 - $225

The tabulated data  is given in the attachment.

The median class = Cummulative frequency / 2

The median class = 40 / 2

The class interval which contains the 20th frequency.

This is the 200 - 225 class

The interval which contains the median water bill is $200 - $225

Hence $200-$225  interval shows the greatest change in water bills

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Answer:

C)$200–$225

Step-by-step explanation:

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