Suppose that the functions f and g are defined for all real numbers x as follows.
f(x)=4 x
g(x)=2 x-5

Answer:

His rate is a whopping $231.47 per hour.

:)

Step-by-step explanation:

We can conclude that.

[tex]r*t_1=p_{reg}[/tex]   is the gross pay from his regular hours.

[tex]1.5r*t_2=p_{ovt}[/tex] is the gross pay from his overtime hours.

So all together we can say

[tex](r*t_1)+(1.5r*t_2)=p[/tex]

We are looking for his hourly rate.

Lets solve for [tex]r[/tex].

Multiply the terms in the parenthesis.

[tex]rt_1+1.5rt_2=p[/tex]

Factor [tex]r[/tex] out of [tex]rt_1[/tex].

[tex]r(t_1)+1.5rt_2=p[/tex]

Factor [tex]r[/tex] out of [tex]1.5rt_2[/tex].

[tex]r(t_1)+r(1.5t_2)=p[/tex]

Factor [tex]r[/tex] out of [tex]r(t_1)+r(1.5t_2)[/tex].

[tex]r(t_1+1.5t_2)=p[/tex]

Divide each term in [tex]r(t_1+1.5t_2)=p[/tex] by [tex]t_1+1.5t_2[/tex] and simplify.

[tex]\frac{r(t_1+1.5t_2)}{t_1+1.5t_2} =\frac{p}{t_1+1.5t_2}[/tex]

Simplify the left side.                                                                              Cancel the common factor of [tex]t_1+1.5t_2[/tex]

[tex]r=\frac{p}{t_1+1.5t_2}[/tex]

Now we have an equation to find his regular hourly rate.

We are given

[tex]p=16203[/tex]

[tex]t_1=40[/tex]

[tex]t_2=20[/tex]

Lets plug these numbers into our equation for [tex]r[/tex].

[tex]r=\frac{16203}{40+1.5*20}[/tex]

[tex]r=\frac{16203}{70}[/tex]

[tex]r=231.47[/tex]

1) The differential equation is: dP/dt=kP

2) P(t)=8000[tex]e^{-0.28t}[/tex]

3)  The solution at the specified value of the independent variable is 1490.991

In practical contexts, derivatives frequently represent the rates of change of physical quantities, and the differential equation establishes a relationship between the two. As a result of the frequent occurrence of these correlations, differential equations are widely employed in a wide range of disciplines, including engineering, physics, economics, and biology.

Only the simplest differential equations can be resolved explicitly, but many aspects of a given differential equation's solutions can be determined without doing an exact calculation.

1) The differential equation is: dP/dt=kP

Here k is the proportionality constant

2) Now, we have to solve the differential equation on dP/dt=kP

∫dP/P=∫kdt+lnP₀

lnP₀=kt+lnP₀

lnP/P₀=kt

P=P₀[tex]e^{kt}[/tex]

Here P₀ is the constant of integration.

P(t)=P₀[tex]e^{kt}[/tex]

And they have given that,

P(0)=8000=P₀e⁰

P₀=8000

P(1)=5200

5200=8000[tex]e^{k}[/tex]

k=-2log(2)+log(3)≈ -0.28

Therefore, the required function is:

P(t)=8000[tex]e^{-0.28t}[/tex]

3) Now, we have to put t=6 in the above equation:

P(6)=8000[tex]e^{-0.28*6}[/tex]

P(6)=1490.991

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Answer: $60.00

Step-by-step explanation: If we want to find how much money she makes in 12 hours, we must use the information we got for how much she makes in 1 hr, and apply that to make a proportional relationship. So, it would look like this:

[tex]\frac{5}{1}[/tex] = [tex]\frac{?}{12}[/tex]

Now, using cross multiplying, we multiply 1 x 12 and 5 x 12 to get $60. I hope this helped.

By using the concept of stretch, it can be concluded that -

When 0 < b < 1, the graph of y = [tex](bx)^2[/tex] is stretched horizontally by a factor of b

What is stretch?

Stretch is a mathematical transformation in which an object enlarges in one direction only.

y = [tex](\frac{1}{2}x)^2[/tex] is a horizontal stretch of y = [tex]x^2[/tex] by a factor of 2

y = [tex](\frac{1}{3}x)^2[/tex] is a horizontal stretch of y = [tex]x^2[/tex] by a factor of 3

y = [tex](\frac{1}{4}x)^2[/tex] is a horizontal stretch of y = [tex]x^2[/tex] by a factor of 4

So when 0 < b < 1, the graph of y = [tex](bx)^2[/tex] is stretched horizontally by a factor of b

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Number of years it will take for the amount to double is 23 years

The principal amount = $900

The interest rate = 3%

The interest is compounded monthly

The given equation is

S = 900(1.0025)^12t

Where S is the final amount

t is the time period in years

The final amount is the double of principal amount

Final amount = 2 × 900

= $1800

Substitute the values in the equation

1800 = 900(1.0025)^12t

1.0025^12t = 1800/900

1.0025^12t = 2

Then value of t = ln(2) / 12ln (1.0025)

Divide the numbers

= 23.13b years

Therefore, the time period is 23 years

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Hello,

I hope you and your family are doing well!

To solve this problem, you need to set up a proportion using the information given in the problem. Let x represent the number of miles the family will travel during the next 4 hours. The proportion will look like this:

318 miles / 6 hours = x miles / 4 hours

To solve for x, you can cross-multiply and solve the equation:

318 miles / 6 hours = x miles / 4 hours

6 hours * 318 miles = 4 hours * x miles

1848 miles = 4x miles

x = 462 miles

Therefore, if the family continues at the same rate, they will travel a total of 462 miles during the next 4 hours.

---

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Happy Holidays!

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-6}{2 +1} \implies \cfrac{ -6 }{ 3 } \implies \text{\LARGE -2}[/tex]

Answer:

The slope is 2

Step-by-step explanation:

To find the slope you divide the rise by the run. Rise being how many units it goes up or down) (run being how many units it goes to the side).

In this case the rise is -2 and the run is -1.

See in the picture, for every 2 units the line goes down, it moves one unit to the right.

so, -2/-1= 2

Answer:

Area = 28.27 in²

Step-by-step explanation:

Now we have to,

→ find the area of the circle.

Formula we use,

→ π × r²

Now the required area will be,

→ π × r²

→ 3.14 × 3²

→ 3.14 × 9

→ 28.27 in²

Hence, the area is 28.27 in².

Answer:

AA similarity theorem.

Step-by-step explanation:

The probability of choosing a random number that starts with 6 from this group is 1/5 Or 0.2.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, All three-digit numbers that can be created from the digits 0-9.

So, The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 total of 10 digits.

No. of even digits is 4 and the number of odd digits is 5.

The total number of 3 digits that can be formed where the first and last digits must be even and no digit can repeat and can start with 0 is,

= 5×10×4.

= 200.

The number of digits starts with 6 in this group is,

= 1×10×4.

= 40.

∴ The probability of choosing a random number that starts with 6 from this group is (40/200) = 1/5 Or 0.2

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Answer:

5.89 green jelly beans or we would round down to the nearest whole jellybean, 5.

Step-by-step explanation:

I am assuming that the ration is 36:32 pink:green so we need 7:?

36/32

7/ (36/32) =5.8947

The linear function g(x) = 3 · x + 6 has the following features:

Domain: - ∞ < x < + ∞

Range: - ∞ < y < + ∞

x-Intercept: (- 2, 0)

In this problem we must determine the domain, the range and the x-intercept of a linear function, that is, a polynomial of the form y = m · x + b, where m is the slope and b is the x-intercept. We must find the information by understanding the following features:

If we know that the function is g(x) = 3 · x + 6, then its domain and range are - ∞ < x < ∞ and - ∞ < y < ∞ and its x-intercept is:

0 = 3 · x + 6

- 3 · x = 6

x = - 2

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Step-by-step explanation:

The given function is g(x) = 3x + 6.

Domain: The domain of a function is the set of all possible input values (x) for which the function is defined. Since the function is a linear equation, it is defined for all real values of x. Therefore, the domain of the function is: Domain: -∞ < x < ∞ Range: The range of a function is the set of all possible output values (y) that the function can produce. The slope of the given function is positive (3), so the function increases without bound as x increases.

Therefore, the range of the function is: Range: -∞ < y < ∞ x-intercept: The x-intercept of a function is the point at which the graph of the function intersects the x-axis. To find the x-intercept, we set y = 0 and solve for x. 0 = 3x + 6 -6 = 3x -2 = x Therefore, the x-intercept is (-2, 0).

So, the correct option is: Domain: -∞ < x < ∞; Range: -∞ < y < ∞; x-intercept (-2, 0).

Answer:

(-5, 0)

|z| = 5

Step-by-step explanation:

Complex numbers can be represented on an Argand diagram.

The x-axis is called the real axis and the y-axis is called the imaginary axis.

The complex number  z = x + iy  is represented on the diagram by the point  P(x ,y), where x and y are Cartesian coordinates.

Therefore, the complex number z = -5 can be represented on the Argand diagram by the point:

The absolute value of a complex number is the magnitude of its corresponding vector.

For a complex number  z = x + iy,  the absolute value is given by:

[tex]|z|=\sqrt{x^2+y^2}[/tex]

Therefore, the absolute value of complex number z = -5 is:

[tex]\implies |z|=\sqrt{(-5)^2+(0)^2}[/tex]

[tex]\implies |z|=\sqrt{25+0}[/tex]

[tex]\implies |z|=\sqrt{25}[/tex]

[tex]\implies |z|=5[/tex]

Answer:

x = In(26)/In(27)

Step-by-step explanation:

26=27^(x)

take the logarithm of both sides

x = In(26)/In(27)

Answer:

This is a bit late but I believe the answer is

Step-by-step explanation:

x = In (26)/3In (3).

Im very sorry if this turns out to be wrong.

For the given function, f(x)=0.48 ln (x+2)+27. The distance is 6.004 from the eye is the pressure of 28 inches of mercury.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that the function is, f(x)=0.48 ln (x+2)+27

f(x)=28

28 = 0.48 ln (x+2)+27

0.48 ln(x+2)=28-27

ln(x+2)=1/0.48

ln(x+2)=2.08

[tex]\rm x+2 = e^{2.08}[/tex]

x+2 = 8.004

x=8.004 - 2

x=6.004

Thus, for the given function, f(x)=0.48 ln (x+2)+27. The distance is 6.004 from the eye is the pressure of 28 inches of mercury.

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A farmer needs to pack 2,903 apples into crates to ship to supermarkets. Each crate can hold only 30 apples. Choose true or false for each statement.

A. The farmer needs 96 crates to ship out all apples. False

B. The farmer needs 97 crates to ship out all the apples. True

C. At least one of the crates will not be filled to capacity. True

D. To determine the number of crates needed, divide 30 by 2,903. False

Answer:

A. False, you will need another crate in order for all of the apples to be shipped to the supermarkets.

B. True, this will hold all of the apples with some extra space left in the last crate.

C. True, 2,903 divided by 30 is 96.76666666666667. Meaning that one of them won't have exactly 30 apples.

D. False, you divide 2,903 by 30.

The two column proof in completed as follows

Statement                                                 Reason

1 line UV ≅ line ST                                  Given

2 line QR ≅ line PQ                                Given

3 line OT ≅ line OU                                Given

4 line PV ≅ line RS                                 Given

5 PT = PQ + QT                                      Additive Property of Length

6 RU = QR + QU                                     Additive Property of Length

7 PY = QR + QU                                      Substitution

8 PT = RU                                               Transitive Property of Equality

9 TV = UV + TU                                      Additive Property of Length

10 SU = ST + TU                                     Additive Property of Length

11 TV = ST + TU                                      Substitution

12 SU = TV                                             Transitive Property of Equality

13 ΔSUR ≅ ΔVTP                                   SSS

14 ∠V ≅ ∠S                                            CPCTC

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

The problem requires the prove by Side - Side - Side = SSS rules to ensure that the the triangles are congruent

The SSS have it that the two triangles being compared should have their three sides being are equal then the triangles are congruent

Achieving the SSS rules then by Corresponding Parts of Congruent Triangles are Congruent CPCTC theorem ∠V ≅ ∠S

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Answer:

Look at images

Step-by-step explanation:

it doesn't let me put the full image

The value of ∠ A = 40°,∠C = 70° and AC = 12

What is value ?

Value in mathematics can refer to a number of closely related ideas. A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42.

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value. Consider the number 45, for example. Here, the fourth digit is in the tens column.

If triangle is isosceles it means the two sides and angles are equal

∴ BC = AC

 AC = 8 cm

A + B + C = 180

A = 180 - 70 -70

∠A = 40°

∠C = 70°

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According to the given statement the greatest common factor is -1(x+10).

Examples involving linear equations are 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3. The concept of linear equations, the including that for linear equations involving one parameter, two independent variables, or three variables, and examples of each will all be explored in detail in this article.

A linear equation has the slope-intercept form y = mx + b. When x is 0, the integers m and b provide the line's slope (m) and also the value of y. (b). It y-intercept is indeed the value that y has when x is 0 because (0,y) is the point at which the line crosses the y-axis.

= -x – 10

= -1(x+10)

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Answer:

Step-by-step explanation:

Sue is older than Ria, but Ria is younger than Jill. Ria is the middle of the three. Paula is the youngest. So the order would be Paula, Ria, Michelle, Jill, and Sue. Hope this was correct and hoped it helped. :)

Answer:

z = -8

Step-by-step explanation:

6(z-1) + 14 = -40

6z - 6 + 14 = -40   Distribute the 6

6z + 8 = -40   Combine Like Terms

6z = -48   Subtract 8 on Both Sides

z = -8   Divide by 6 on Both Sides

The value of the test statistic rounded to two decimal places is equal to 5.05.

In Mathematics, a sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.

For a claim that most adults would erase all of their personal information online if they could, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:

H₀: p ≤ 0.5.

Ha: p > 0.5.

Mathematically, the test statistic for the z-test of a population proportion can be calculated by using this mathematical expression;

[tex]z=\frac{\hat{p} \;- p}{\sqrt{\frac{p(1\;-p)}{n } } }[/tex]

Where:

Substituting the given parameters into the formula, we have;

z = (0.61 - 0.5)/√(0.5(1 - 0.5)/526)

z = (0.11)/√(0.5(0.5)/526)

z = (0.11)/√(0.25/526)

z = 0.11/0.0218

z = 5.05.

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The number of servings of juice in the bottles on the shelf is 135

From the question, we have the following parameters that can be used in our computation:

Bottles = 9

Serving of juice per bottle = 15

This means that

The number of servings of juice in the bottles on the shelf = Bottles x Serving of juice per bottle

So, we have

The number of servings of juice in the bottles on the shelf = 9 * 15

Evaluate

The number of servings of juice in the bottles on the shelf = 135

Hence, the servings is 135

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Complete question

There are 9 bottles of juice on a shelf. Each serving of juice is 15 of a bottle.

How many servings of juice are there in the bottles on the shelf?

The first numSelected of the selected elements to an array selectedData is assigned in the programme.

The program for the given condition is-

function selectedData = SelectLogicalN( dataMatrix, logicalSelect, numSelected )

% SelectLogicalN: Return the first numSelected values of input 2D

% array dataMatrix indexed by localSelect indexing array.

%Inputs: dataMatrix - input data matrix (2D array)

%logiccalSelect - logical indexing array, can be 2D or linear

%numSelected - number of indexed elements to return in selectedData%

%Outputs: selectedData - column vector of logically indexed elements to return

dataMatrix = dataMatrix(logical(logicalSelect));

% assign tempSelected with logically indexed elements of dataMatrixtemp

Selected = dataMatrix

% find the size of tempSelected

s=size(tempSelected);

% remove the last element from the temp

SelectedselectedData =tempSelected

(1:s-1)end

Thus, the first numSelected of the selected elements to an array selectedData is assigned in the programme.

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The elevation needs to be smaller than the decrease of the elevation like this.

What is the elevation on the number line?

The elevation of a location describes its height above or below the sea level, which has an elevation of 0. Elevations below the sea level are represented by negative numbers, and elevations above the sea level are represented by positive numbers.

Whatever number is larger than the number of the elevation of the bottom of the harbor

the elevation needs to be smaller than the decrease of the elevation like this.

e.g.

The temperature elevated by 28 degrees and then decreased by 30 degrees.

Hence, the elevation needs to be smaller than the decrease of the elevation like this.

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There would be 52 atoms after 25 years and it would take 13 years for half the number of atoms to remain.

We know that the term radioactive decay has to do with the break down of a substance to form the daughter nuclei of the particular element. In this case, we have the decay function of the element to be; A(t) =200e^-0.054t.

t is the time taken for decay.

Now in 25 years we would have;

A(t) =200e^-0.054(25)

A(t) = 52 atoms

The time that it would take for half of the original number to remain is obtained from;

100 = 200e^-0.054t

100/200 = e^-0.054t

0.5 = e^-0.054t

ln(0.5) = -0.054t

t = ln(0.5)/-0.054

t = 13 years

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Answer:

a) 23,1 milions

b) en 2013 - 2014

Answer:

the chance to pull a blue marble is 3/20

the chance to pull a yellow marble is 5/20

Answer:

Step-by-step explanation:

It will lie in quadrant 3

Step-by-step explanation:

Here, we want to know where the resulting image will lie after the rotation

After the rotation, it is expected that the resulting image will lie in quadrant 3

First 90 to quadrant 1

second 90 to quadrant 2

Third 90 to quadrant 3

Answer:

B is the correct answer

Step-by-step explanation:

i think:)