The length of a rectangle is given by the function l(x)=2x+1, and the width of the rectangle is given by the function w(x)=x+4.Which function defines the area of the rectangle?Hint: A=l⋅w

We have to write the facts..

It's a little bit easy to understand if you put that numbers in a table.. like this

Now, they ask you an integer that represents a change per hour, and they say you that assume a constant change... then we complement the table with different values per hour until arrive at midnight..

now, you can see that you have two points.. with two coordinates, and you can find a line equation assuming that you have a constant change like this case...

that you place in the cartesian axes.. like this..

You know that you put x values in the horizontal line and y values in the vertical line..

for example, we're gonna place the point (2,1) that means that 2 in x axe and 1 in y axe..

We are asked to evaluate cot 120,

Answer:

-5

Step-by-step explanation:

To find the standard deviation of this set of numbers, we will use the formula

let us explain the parts of this formula, as follows:

We will proceed by parts, the first thing to do is find the mean of the data

Calculating the mean

To find the mean, we will sum all the numbers and divide by the total quantity of numbers, as follows:

That is, the mean of the set is 43. Now we proceed to find the difference between the data and the mean, and the add them to the power of two, in symbols we have:

Now we introduce this result into the formula for the standard deviation, we find:

That is, after approximate to the nearest tenth, we found that the standard deviation of the set of numbers is 2.8

The given function is expressed as

y = (6x + 12)/2

In order to determine the inverse of the given function, we would substitute x for y and y for x. Then we would solve for y. It becomes

x = (6y + 12)/2

x = 3y + 6

3y = x - 6

y = (x - 6)/3

y = x/3 - 2

The inverse is

y = x/3 - 2

Answer:

2m(-4.2m)

-4.2[tex]m^{2}[/tex] + - (4.2[tex]m^{2}[/tex])

-8.4[tex]m^{2}[/tex]

Step-by-step explanation:

2m(-4.2m) = -8.4 [tex]m^{2}[/tex]

-4.2 [tex]m^{2}[/tex] + (-4.2 [tex]m^{2}[/tex]) = 8.4[tex]m^{2}[/tex]

Answer:

B

Step-by-step explanation:

Because i used a calculator

Answer:

C 700

Step-by-step explanation:

7271 is close to 7000

12 is close to 10

So 7000/10 = 700

The percent of change from Week 1 to Week 2 is 10%.

The percent of change from Week 2 to Week 3 is  6.8%

Percentage is the ratio of an amount that is expressed as a number out of 100. Percentage is a measure of frequency. The sign that is used to represent percentage is %.

The percent of change from Week 1 to Week 2 = (number of sit ups in week 2 / number of sit ups in week 1) - 1

(44 / 40) - 1 = 0.1 = 10%

The percent of change from Week 2 to Week 3 = (number of sit ups in week 3 / number of sit ups in week 2) - 1

(47 / 44) - 1 = 0.068 = 6.8%

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We go from degrees to radians:

Now, the length of arc CE is:

Where CD = 6 units. Using the angle in radians:

The width of the combined three panels when installed next to each other is  [tex]37\frac{7}{8}[/tex] inches.

In order to determine the width of the three combined panels, multiply the width of one fluorescent lighting panel by the total number of panels.

Multiplication is the mathematical operation that is used to calculate the product of two or more numbers. The sign that represents multiplication panel is ×.

Width of the combined panels = width of one panel x number of panels

[tex]12\frac{5}{8}[/tex] × 3

[tex]\frac{101}{8}[/tex] x 3 = [tex]\frac{303}{8}[/tex] = [tex]37\frac{7}{8}[/tex] inches

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Answer:

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Equation of 'm'

(y - 6) = - ³/₅ (x - 2)     [point-slope form]

y = - ³/₅ x + ³⁶/₅    [slope-intercept form]

Equation of 'q'

(y - 6) = ⁵/₃ (x - 2)         [point-slope form]

y = ⁵/₃ x + ⁸/₃         [slope-intercept form]

To find the equation for both 'm' and 'q' requires a bit of work. Because neither  'm' nor 'q' has two points to find the slopes of the line, we have to get creative.

The Line 'n' has two points [ (4, 4) & (1, -1) ], and as such we can find the slope of that line. The line 'n' is parallel with 'q' and perpendicular with m.

For finding the slope of 'n'

The slope of the 'n'    =  (y₂ - y₁) ÷ (x₂ - x₁)      

=  (4 - (- 1)) ÷ (4 - 1)  

=  5 ÷ 3

=  ⁵/₃

To estimate the slope of 'q' and 'm'

When two lines exists parallel, they contain the exact slope.

Since 'n' and 'q' exists parallel,

then the slope of q = ⁵/₃

When two lines exists perpendicular, the product of their slopes exists -1. This means that the slopes exists negative-reciprocals of each other.  

Since 'n' and 'm' exists perpendicular

then the slope of m = - ³/₅

Write the equation for 'q' and 'm'

We can now utilize the point-slope form (y - y₁) = m(x - x₁)) to write the equation for the lines

For both 'q' and 'm' let (x₁, y₁) be (2, 6)

Equation of 'm'

(y - 6) = - ³/₅ (x - 2)     [point-slope form]

y = - ³/₅ x + ³⁶/₅    [slope-intercept form]

Equation of 'q'

(y - 6) = ⁵/₃ (x - 2)         [point-slope form]

y = ⁵/₃ x + ⁸/₃         [slope-intercept form]

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The coefficient of the GCF of a set of algebraic terms, wil be the GCF of the coefficients of the terms.

Notice that the coefficients in this case, are 30 and 60.

The greatest comon factor of this set, is 30, since:

On the other hand, the variable x appears with an exponent of 5 in one case and an exponent of 3 in the other case. The greatest common factor for the variable x will be the lowest power, in this case, 3. Notice that:

Then, we can factor out the following:

Notice that each term can be written as a product of this factor:

Therefore, the greatest common factor (GCF) is:

Answer:

4.6

Explanation:

The diagram shown is a right triangle having the following sides;

Opposite = 17

Adjacent = x

Angle of elevation = 75 degrees

Using SOH CAH TOA identity

Tan theta = opposite/adjacent

Tan 75 = 17/x

x = 17/tan 75

x = 17/3.73205

x = 4.6

Hence the value of x to the nearest tenth is 4.6

Answer:

7 day

Step-by-step explanation:

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Answer: 8 days

Step-by-step explanation:

1) Set up an equation. Let x be the day

3,500 >= 2(816) + x(100+95)

The 816 is just two times (Plane ticket back and forth) so it doesn't go into the x. 100 and 95 do as it is one day.

2) Solve the equation

3,500 >= 2(816) + x(100+95)

1868 >= 195x

9.57 >= x

3) Rounding

Since the x has to be less than 9.57, our next option is 8

Explanation

For the given data, we will have the following:

We are given grouped data, from which we will obtain the mean and standard deviation

Thus, we will have

From the above,

We have the mean to be approximately 44.68.

For the standard deviation

We will have

Thus, we have the standard deviation to be 10.22

Conversion of Degrees Celsius to Degrees Fehrenheit.

Substitute 12 for t in eqn(1), we get

When t =24,

C(24) = 0 , ( does not exist since the graph did not touch the graph)

Hence, the correct answer are:

t =12, C(12) = 104 degrees Fehrenheit, and

t =24, C(24) = 32 degrees Fehrenheit

The values of x and y will be 100° and 10° when two parallel lines are being cut by a transversal line.

According to the question,

We have a figure where two parallel lines are being cut by a transversal line.

Now, we know that the angles formed on a straight line is 180° and vertically opposite angles are equal.

The sum of consecutive interior angles is 180°.

Now, we will use these three statements in finding the values of x and y.

Now, adding (2x-70)° and (5y)° will give 180° because the angles made are on a straight line.

(2x-70)°+(5y)° = 180°

2x+5y = (180+70)°

2x+5y = 250° .... (1)

Now, (x+30)° will be the interior angle consecutive to 5y° because they are vertically opposite angles.

So, we have:

(x+30)°+5y° = 180°

x+5y = (180-30)°

x+5y = 150°

5y = 150-x

Now, putting this value of 5y in equation 1:

2x+5y = 250

2x+150-x = 250

x+150 = 250

x = (250-150)°

x = 100°

Now, we will find the value of y:

5y = 150-x

5y = 150-100

5y = 50

y = 50/5

y = 10°

(Note that the values of x and y will be in ° because angles are measured in degree.)

Hence, the value of x is 100° and the value of y is 10°.

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The linear equation parallel to y = 3x - 2 that passes through the point (4, 6) is:

y = 3*x - 6

Here we want to find a linear equation parallel to:

y = 3x - 2

Now, a general linear equation is:

y = m*x + b

Where m is the slope and b is the y-intercept.

Remember that two lines are parallel if and only if the lines have the same slope and different y-intercept.

So our linear equation will be something like:

y = 3*x + c

Now we also want our line to pass through the point (4, 6), then we can replace these values:

6 = 3*4 + c

6 = 12 + c

6 - 12 = c

-6 = c

So the linear equation is:

y = 3*x - 6

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Solution

For this case we have the following random variable:

X= amount spend on average for groceries by one person

And we have the following properties:

mean= 52

sd= 14

The distribution of the variable is normal

We can find the middle 50% using a graph like this one:

We can find two quantiles from the normal distribution that accumulates 25% of the area on each tail of the distribution and we have:

Z= -0.674 and 0.674

Now we can use the z score formula given by:

So then we have:

Minimum= 52 - 0.674*14 = 42.56

Minimum= 52 + 0.674*14 = 61.44

the given equation is,

and

now the expression is,

2y + z

put the values,

thus, the correct answer is option C

The number of tiles required to cover the floor is 2880 tiles.

To solve this problem, we can find the number of tiles by calculating the area of a rectangle:

We have to convert the dimensions from feet to inches will be

1 feet = 12 inches

12 feet = 12 * 12  = 144in

15 feet = 12 * 15  = 180in

The area of the rectangle can be calculated as:

A = l * w

A = 180 * 144

A = 25920in²

The tiles are 9 squared inches, we can divide the area by 9 to find the number of tiles needed:

25920/9=  2880

Hence, The number of tiles needed will be 2880 tiles

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The elements of the set given by A∩B is {12,18} .

Set theory, a branch of mathematical logic, studies sets, which are essentially collections of objects.

Despite the fact that every form of object may be turned into a set, set theory is a branch of mathematics that primarily deals with issues that are relevant to mathematics as a whole.

The foundation of set theory is a straightforward binary link between an object o and a set A.

If o is a component (or member) of A, it is expressed as o A. When listing members of a set, commas are used to indicate their separation, or brackets are used to surround a property of those parts.

Since sets are objects, they can be connected by the membership relation.

Given set U = {11,12,13,14,15,16,17,18,19,20}

A = {12,14,16,18,20}

B = {12,15,18}

A∩B = {12,18}

A∪B = {12,14,15,16,18,20}

A' = {11,13,15,17,19}

Therefore the elements of the set given by A∩B is {12,18} .

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Answer:

B

Step-by-step explanation:

the treaty for defeated Germany was Article 231, commonly known as the "War Guilt Clause," which forced the German nation to accept complete responsibility for initiating World War I. Germany was required to make enormous reparation payments

The expression given as -8+19+8 has a value of 19

From the question, the expression is given as

-8+19+8

Rewrite the expression properly

This is rewritten as follows

-8 + 19 + 8

Collect the like terms in the above expression

So, we have the following equation

-8 + 19 + 8 = 8 - 8 + 19

Evaluate the like terms in the above expression

So, we have the following equation

-8 + 19 + 8 = 0 + 19

Finally. we add 0 and 19

So, we have the following equation

-8 + 19 + 8 =  19

Hence, the valye of the expression is 19

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The obtained value of the given expression -8 + 19 + 8 would be 19 which is determined by using the arithmetic operation.

In mathematics, the addition, subtraction, division, and multiplication of built-in expressions can also be used to specify arithmetic operations.

The expression which is given in the question is below

⇒ -8 + 19 + 8

Rearrange similar terms in the above expression,

⇒ 8 - 8 + 19

Apply the subtraction operation,

⇒ 0 + 19

Apply the addition operation to get the answer,

⇒ 19

Hence, the obtained value of the given expression -8 + 19 + 8 would be 19 which is determined by using the arithmetic operation.

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Solution

Total numbers of Doctors = 7

Number of female doctors = 4

Number of male doctors = 3

The probability that the patient is assigned to a female doctor is given as

To express as a percentage

Answer: 5.67> 1.93

Step-by-step explanation:

Let's think of it this way, if you have five apples and another person has one apple. Do you think you have a greater amount of apples?

Of course because 5.67 is a larger number than 1.93. You can always make a number line.

We will find the quotient and remainder as follows:

The quotient is 749 and the remainder is 2.