Randy is installing PVC tiles to cover his garage floor. The width of the garage is 6 feet more than half the length, l . The perimeter of the garage is 313 times the length. If the PVC tiles cost $2.75 per square foot, what is the total cost of the materials? Enter your answer in standard form.

Answer:

a) [tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20}{V_{\text out}\ln 10}}[/tex]

b) [tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = -\dfrac{20}{V_\text{out}^2\ln 10}}[/tex]

Step-by-step explanation:

From the given equations to find, we are differentiating function G with respect to V out. Therefore, we will be only using the equation (6):

[tex]\displaystyle{G=20\log (10V_{\text out})}[/tex]

Here’s a fresh-up reminders for logarithmic differentiation formula:

[tex]\displaystyle{f(V)=a\log_b V \to f'(x)=\dfrac{a\cdot V'}{V\ln b}}[/tex]

Note that V' means to derive or differentiate the V-term

Therefore, in this scenario, our values of term are:

Therefore, we can apply differentiation formula:

[tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20\cdot \dfrac{d(10V_{\text out})}{dV_{\text out}}}{10V_{\text out}\ln 10}}[/tex]

Simplify:

[tex]\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20\cdot 10}{10V_{\text out}\ln 10}}\\\\\displaystyle{\dfrac{dG}{dV_{\text out}}=\dfrac{20}{V_{\text out}\ln 10}}[/tex]

And we have finished the part a. On part b, we just differentiate the answer from part a again, the second part is to obtain the second derivative which is to derive the first derivative. Therefore:

[tex]\displaystyle{\dfrac{d^2G}{dV_{\text out}^2} = \dfrac{d\left(\dfrac{20}{V_{\text out}\ln 10}\right)}{dV_{\text out}}}[/tex]

First, separate the constant every time when you have to differentiate a function:

[tex]\displaystyle{\dfrac{20}{\ln 10}\cdot \dfrac{1}{V_{\text out}}}[/tex]

Differentiate 1/V out: recall the formula of fraction:

[tex]\displaystyle{f(V)=\dfrac{1}{V} =V^{-1} \to f'(x)=-V^{-2} = -\dfrac{1}{V^2}[/tex]

The formula above is derived from power rules formula where:

[tex]\displaystyle{f(V)=V^n = nV^{n-1}}[/tex]

Therefore, from the function of V out:

[tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot \left(\dfrac{1}{V_\text{out}}\right)'}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot (V_\text{out})^{-1}}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot (-V_\text{out})^{-2}}\\\\\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = \dfrac{20}{\ln 10} \cdot \left(-\dfrac{1}{V_\text{out}^2}\right)}[/tex]

Simplify to latest as we get:

[tex]\displaystyle{\dfrac{d^2G}{dV_\text{out}^2} = -\dfrac{20}{V_\text{out}^2\ln 10}}[/tex]

Please let me know if you have any questions!

Answer:

1) 112°

3) 55°

4) 51°, complementary angles

Step-by-step explanation (question one):

3x +10 +2x = 180

3x +10 +2x -10 = 180 -10

3x + 2x = 170

5x = 170

x = 34

3(x)+10 = angle ABD

3(34)+10 = angle ABD

102+10 = angle ABD

angle ABD = 112°

Step-by-step explanation (question two):

180 -70 = 2x

110 = 2x

55 = x

angle SQT = 55°

Step-by-step explanation (question three):

Since it's a right angle, we can simply subtract.

90 -39 = 51

angle b = 51°

I wish you luck on your homework!

A linear function in slope-intercept form that only corresponds with this table is y = 2x + 8.

Mathematically, the slope-intercept form of a straight line is given by;

y = mx + b

Where:

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided, we have the following parameters:

Point (x, y) = (-1, 6)

Point (x, y) =  (0, 8)

Substituting the given points into the formula, we have;

Slope, m = (8 - 6)/(0 - (-1))

Slope, m = (2)/(0 + 1)

Slope, m = 2/1

Slope, m = 2.

In Mathematics, the y-intercept of a graph occurs at the point where the x-value is equal to zero (0), which is 8 in the table shown above.

Therefore, the slope-intercept form is given by:

y = mx + b

y = 2x + 8

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Answer: 8

[tex]m^{2} = 9+55\\m^{2} = 64\\m=8[/tex]

Answer: m = 8

9 + 55 = 64

[tex]\sqrt{64}[/tex] = 8

[tex]8^{2}[/tex] = 64

The conditional relative frequency that a female prefers running is 0.36

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data

The specific number (females prefer cycling = 0.15) and the fitting total. There are 2 possibilities for that total :

all females

all people preferring cycling

the way it was phrased I would say the reference is all females.

the conditional relative frequency is then

0.15 / 0.46 = 0.326

Hence the conditional relative frequency that a female prefers running is 0.36

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Answer:

Step-by-step explanation:

Dont listen to the above the answer is acually 58

Using the theories of archaeology, we got that date on the coin represents

a terminus post quem if a coin with a date on it is found in a sealed archaeological deposit.

Potassium-argon dating: This absolute dating method was actually developed by the A.E. Douglass, an American astronomer, chiefly from work he conducted at the Pueblos of American Southwest tree-ring dating Layers of the sediments resulting from the melting of ice sheets and deposited in the lakes on an annual basis are known as varves

Hence, if a coin with a date on it is found in a sealed archaeological deposit, and we know that the deposit can be no older than the date on the coin. in that situation the date on the coin represents a terminus post quem.

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Answer:

Step-by-step explanation:

First solve the equation:

-11y-9=2

-11y=11

y=-1.

We then take this and plug it back into the original equation:

8(-1)+3

-8+3

-5.

So your answer is -5.

The representation of equation y = 3x + 1 is as shown below.

The correct answer is option (D)

In this question, we have been given an equation y = 3x + 1

We need to find the correct representation  of given equation.

For x = 0,

y = 3(0) + 1

y = 1

For x = 2,

y = 3(2) + 1

y = 7

for x = -1,

y = 3(-1) + 1

y = -2

This means, the options A, B and C are incorrect.

Therefore, the representation of equation y = 3x + 1 is as shown below.

The correct answer is option (D)

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Answer:

 (a)

  [tex]\left[\begin{array}{cc}20&80\\32&3\end{array}\right][/tex]

Step-by-step explanation:

You want the product of the given 2×2 matrices.

The value at any given (row, column) of the result matrix is the dot product of the corresponding row of the first matrix with the corresponding column of the second matrix.

For example, row 2 column 1 of the result will be the dot product of row 2 of the left matrix with column 1 of the right matrix:

  [-2, 3]·[-4, 8] = (-2)(-4) +(3)(8) = 8 +24  = 32

This is sufficient to identify the first answer choice as the correct one.

__

Additional comment

A suitable calculator can compute the entire product for you, as in the attachment.

{(1, 4), (-2, 8), (2, 2), (4, 9)} it is a function as every input has a unique output. Therefore, option B is not a function.

The given coordinate points are {(1, 2), (-2, 2), (5, 2), (4, 2)}.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

A) {(1, 2), (-2, 2), (5, 2), (4, 2)}

It is a function as every input has a single output.

So, 1, -2, 5 and 4 are the elements of the domain of the given relation.

Here domain ={1, -2, 5, 4} and range ={2}

B) {(7, 8), (7, 9), (7, 10), (7, 11)}

Since the element 7 corresponds to four different images i.e., 8, 9, 10 and 11. So, this relation is not a function.

C) {(0,0)}

It is a function as every input has a single output.

So, 0 is the element of the domain of the given relation.

Here domain ={0} and range ={0}

D) {(1, 4), (-2, 8), (2, 2), (4, 9)}

It is a function as every input has a unique output.

So, 1, -2, 2 and 4 are the elements of the domain of the given relation.

Here domain ={1, -2, 2, 4} and range ={4, 8, 2, 9}

{(1, 4), (-2, 8), (2, 2), (4, 9)} it is a function as every input has a unique output. Therefore, option B is not a function.

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From the given data, total number of hamburgers of (1/4) pounds each using 2 1/2 pounds of ground beef is equal to 10.

As given in the question,

Total pounds of hamburger need to be made = 1 / 4 pounds

Total pounds of ground beef is used to make hamburger = 2 1 / 2 pounds

Let us consider 'n' be the total number of hamburger to be made each of

1 / 4 pound .

Required equation to show the given relation is given by:

n × ( 1 / 4) = 2  1/ 2

Convert mixed fraction into proper fraction we get,

⇒ n × ( 1 / 4) = 5 /2

⇒ n = ( 5/ 2) × ( 4 /1)

⇒ n = 5 × 2

⇒ n = 10 hamburgers

Therefore, from the given data, total number of hamburgers of (1/4) pounds each using 2 1/2 pounds of ground beef is equal to 10.

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The equation of the exponential function represented by the table y = 0.12x + 0.01

From the table choose two points

The first point = (1, 0.04)

The second point = (2, 0.16)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation

The slope of the line = (0.16 - 0.04) / (2-1)

= 0.12/1

= 0.12

From the table we can see that at x = 0 the value of y = 0.01, then the value of y intercept is 0.01

The slope intercept form is

y = mx + b

Substitute the values in the equation

y = 0.12x + 0.01

Hence, the equation of the exponential function represented by the table y = 0.12x + 0.01

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Based on the calculations, the distance between points (-5, -5) and (-9, -2) on a coordinate plane is equal to: A. 5 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Given the following points:

Substituting the given points into the formula, we have;

Distance = √[(-2 - (-5))² + (-9 - (-5))²]

Distance = √[(-2 + 5)² + (-9 + 5)²]

Distance = √[3² + 4²]

Distance = √[9 + 16]

Distance = √25

Distance = 5 units.

In conclusion, we can logically deduce that the distance between the given points on a coordinate plane is 5 units.

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Complete Question:

What is the distance between (-5, -5) and (-9, -2?

Choose 1 answer:

A. 5

B. 7

C. √12

D. √29

Answer:

Step-by-step explanation:

The amount of yogurt that Karolina used when making 800 ml of salad is 300 ml.

A salad dressing is made by mixing yoghurt and mayonnaise in the ratio

3:5. For 800 ml of salad:

Amount of yoghurt = (3 / (3 + 5)) * 800 ml = 300 ml

The amount of yoghurt that Karolina used when making 800 ml of salad is 300 ml.

Answer:

Step-by-step explanation:

one over the six raised to the third power = 0.00462962962

Answer:

1/216 ≅ 0.00462963

Step-by-step explanation:

Don't know if you need decimal or fraction so I put both

1/6 X 1/6 X 1/6 = 1/216

The measure of one of its angle is 150°

A Polygon is a two-dimensional closed figure made up of line segments (not curves). Polygon is a combination of two words, poly (which means many) and gon (which means shape) (means sides). To create a closed figure, at least three line segments must be connected end to end.

Given that

12 sided regular polygon

We can use the following formula to calculate the total number of degrees in any shape:

(n−2)⋅180

[Where n = number of sides]

(12−2)⋅180

(10)⋅180

=1800

So a 12-sided polygon has 1800 degrees. To calculate the measure of one angle, divide the total number of degrees (1800) by the number of sides, n.

(1800/12) = 150°

Therefore the measure of one of its angle is 150°

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Answer: B

Step-by-step explanation:

Answer:

Your answer is B

Step-by-step explanation:

Answer: $56.25

Step-by-step explanation:

First, I'm going to assume that she makes 25% profit on the selling price.

Set the cost of the shirt as x. Profit is calculated as selling price - cost. Profit is stated to be 25% or [tex]\frac{1}{4}[/tex], so an equation can be set up as:

[tex]\frac{1}{4} *75=75-cost\\\\cost = 75-\frac{1}{4} *75=56.25[/tex]

Answer:y=mxb

Step-by-step explanation:

Answer:

The equation is: y = 5x - 268

The linear equation is equal to

y = -3x + 8

m = slope

x = input variable

c = 8

The given equation is linear function or linear equation

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

Definition of variables to suit the problem to be solved

y = output variable

m = slope

x = input variable

c = y intercept

In comparison, to the linear equation given as equal to

y = -3x + 8

m = -3

x = input variable

c = 8

putting the input variables gives out put accordingly

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Answer:

the answer is c, 6 3/4.

Step-by-step explanation:

An algebraic representation which best describes this transformation is: C. (x, y) → (5x/2, 5y/2).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

By critically observing the graph, we can logically deduce the following vertices:

In this scenario, the transformation rule is given by this algebraic representation:

Q (x, y)                      →               Q' (x, y)

Coordinate Q = (2, 0)   →  Coordinate Q' = ((5/2 × 2), (5/2 × 0)) = Coordinate Q' = (5, 0).

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Answer:

900,000

Step-by-step explanation:

From the given table, we are told that the honeybee beats its wings at a rate of:

There are 60 seconds in a minute, and 60 minutes in an hour.

Therefore, there are:

To find how many times a honeybee can beat its wings in an hour, multiply the number of times it beats its wings per second by 3600:

⇒ 250 × 3600 = 900,000

Therefore, a honeybee beats its wings 900,000 beat per hour.

The probability of a type I error is 0.022.

Given,

In the question;

It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested receive an incorrectly positive response because they do not have the condition.

The null hypothesis is given as "the individual does not have the disease".

We have to find the probability of type l error if the new blood test is used;

Here,

A: The individual does not have the disease

B: The individual does have the disease

We know that,

Type I Error is rejecting the true null hypothesis

Then, probability;

P (Type I Error) = P(Positive reaction to an individual who does not have the disease)  = 0.022

Hence, The probability of a type I error is 0.022.

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The coordinates (4, 0) and (3, -1) represents the solution of the function f(x).

According to the question -

y = f(x) = x - 4

Case 1 : P(4, 0)

0 = 4 - 4 = 0

P (4, 0) represents a solution

Case 2: P (3, -1)

-1 = 3 - 4 = -1

P (3, -1) represents a solution

Answer:

4p-5/7=a

Step-by-step explanation:

4p=12a+5-5a

4p-5=12-5a

4p-5=7a

4p-5/7=a

If  they were 70 more cheeseburgers sold than hamburgers. The number of hamburgers  that were sold on Tuesday​ is 225.

Total of 603 hamburgers and cheeseburgers = x+y= 520

70 more cheeseburgers than hamburgers = y=x+70

Hence,

x+y= 502

y=x+70

Substitution

x+(x+70)= 520

2x+70 = 520

  -70    -70

2x= 450

2    2

x=225 hamburgers

Number of cheeseburgers

Substitute  x in either equation.

y=x+ 70

y=225 +70

y=295 cheeseburgers

Therefore 225  hamburgers was sold.

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Explanation:

gradient = slope

Pick any two points on the diagonal line and use the slope formula.

I'll pick the two points (0,4) and (4,10)

[tex](x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (4,10)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{10 - 4}{4 - 0}\\\\m = \frac{6}{4}\\\\m = \frac{3}{2}\\\\[/tex]

The slope is 3/2.

Meaning we go up 3 and to the right 2.

Answer:

24

Step-by-step explanation:

let the starting number be x

she sold 1/2 x and has 1/2 x remaining with her

she bought 13 and has 25 now

so, 1/2x + 13 = 25

1/2 x= 25-13 = 12

hence x= 24

Answer:

    24

Step-by-step explanation:

now Mei has 25 stamp collections after adding 13 more to what she remained with after selling; this means that after selling she was left with (25_13)=12

this is the half of what she had initially

this means that she initially had (12*2)=24

this gives means that she started with 24 as a stamp of her collection