In the past, joe got paid $229,390 annually. Since switching to a new career he has been making 10% less. How much does Joe make now.

Answer:

68.2°

Step-by-step explanation:

AC is the longest side which means 90° is at B

SinA = BC/AC

sinA = 5/sqrt(29)

sinA = 0.9284766909

A = 68.19859051

A = 68.2°

To find the measure of angle A, we used the tangent function, which is the ratio of the side opposite the angle to the side adjacent to it. Using a calculator, the inverse tangent of the ratio BC/AB equals approximately 68.2 degrees.

In order to solve for angle A in a right triangle, we can use the concept of trigonometry. Specifically, we'll use the tangent (tan) function, which in a right triangle is the ratio of the side opposite the angle to the side adjacent to it. Since angle A is between sides AB and AC, the tangent of A would be defined as tan(A) = opposite side/adjacent side = BC/AB = 5/2.

After calculating the ratio, typically, we would use a calculator to find the arctan or inverse tangent of this ratio, which should give the angle A in degrees. In this case, the arctan(5/2) equals about 68.2 degrees when rounded to the nearest tenth.

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Answer: [tex]7.29[/tex]

Order the numbers

[tex]Before: 8,9,5,1,3,19,6\\After: 1, 3, 5, 6, 8, 9, 19[/tex]

Add

[tex]1+3+5+6+8+9+19=51[/tex]

Divide

[tex]51/7=7.28571428571[/tex]

Round

[tex]7.28571428571=7.29[/tex]

Final Answer

[tex]7.29[/tex]

Answer: y=  −3 /10 x +  2 /5

Step-by-step explanation:

Let's solve for y.

−3(x+y)+4=7y

Step 1: Add -7y to both sides.

−3x−3y+4+−7y=7y+−7y

−3x−10y+4=0

Step 2: Add 3x to both sides.

−3x−10y+4+3x=0+3x

−10y+4=3x

Step 3: Add -4 to both sides.

−10y+4+−4=3x+−4

−10y=3x−4

Step 4: Divide both sides by -10.

−10y /−10  =  3x−4 / −10

y=  −3 /10 x+  2 /5

Answer:

Step-by-step explanation:

Answer:

There will be 50 bacteria remaining after 28 minutes.

Step-by-step explanation:

The exponential decay equation is

[tex]N=N_0e^{-rt}[/tex]

N= Number of bacteria after t minutes.

[tex]N_0[/tex] = Initial number of bacteria when t=0.

r= Rate of decay per minute

t= time is in minute.

The sample begins with 500 bacteria and after 11 minutes there are 200 bacteria.

N=200

[tex]N_0[/tex] = 500

t=11 minutes

r=?

[tex]N=N_0e^{-rt}[/tex]

[tex]\therefore 200=500e^{-11r}[/tex]

[tex]\Rightarrow e^{-11r}=\frac{200}{500}[/tex]

Taking ln both sides

[tex]\Rightarrow ln| e^{-11r}|=ln|\frac{2}{5}|[/tex]

[tex]\Rightarrow {-11r}=ln|\frac{2}{5}|[/tex]

[tex]\Rightarrow r}=\frac{ln|\frac{2}{5}|}{-11}[/tex]

To find the time when there will be 50 bacteria remaining, we plug N=50, [tex]N_0[/tex]= 500 and  [tex]r}=\frac{ln|\frac{2}{5}|}{-11}[/tex] in exponential decay equation.

[tex]50=500e^{-\frac{ln|\frac25|}{-11}.t}[/tex]

[tex]\Rightarrow \frac{50}{500}=e^{\frac{ln|\frac25|}{11}.t}[/tex]

Taking ln both sides

[tex]\Rightarrow ln|\frac{50}{500}|=ln|e^{\frac{ln|\frac25|}{11}.t}|[/tex]

[tex]\Rightarrow ln|\frac{1}{10}|={\frac{ln|\frac25|}{11}.t}[/tex]

[tex]\Rightarrow t= \frac{ln|\frac{1}{10}|}{\frac{ln|\frac25|}{11}.}[/tex]

[tex]\Rightarrow t= \frac{11\times ln|\frac{1}{10}|}{{ln|\frac25|}}[/tex]

[tex]\Rightarrow t\approx 28[/tex] minutes

There will be 50 bacteria remaining after 28 minutes.

Final answer:

To solve this problem, we use the formula for exponential decay and solve for the time when there are 50 bacteria remaining.

Explanation:

To solve this problem, we can use the formula for exponential decay: A = A0 * e^(kt), where A is the final population, A0 is the initial population, e is Euler's number (approximately 2.71828), k is the decay constant, and t is the time in minutes.

First, let's determine the value of k. We know that after 11 minutes, the population is 200 bacteria, so we can substitute these values into the formula to solve for k: 200 = 500 * e^(11k).

Divide both sides of the equation by 500: 0.4 = e^(11k).

Take the natural logarithm of both sides to solve for k: ln(0.4) = 11k.

Divide both sides by 11 to find the value of k: k ≈ -0.07761.

Now we can use the formula to solve for t when there are 50 bacteria remaining: 50 = 500 * e^(-0.07761t).

Divide both sides by 500: 0.1 = e^(-0.07761t).

Take the natural logarithm of both sides to solve for t: ln(0.1) = -0.07761t.

Divide both sides by -0.07761 to find the value of t: t ≈ 13.857 minutes.

Therefore, after approximately 14 minutes (rounded to the nearest whole number), there will be 50 bacteria remaining.

Answer:

[tex]\frac{21}{4}[/tex]

Step-by-step explanation:

So to start, you need to make 3 [tex]\frac{3}{4\\}[/tex] into an improper fraction, which will give you [tex]\frac{15}{4}[/tex]. Then to make it easier, instead of dividing it by [tex]\frac{5}{7}[/tex], multiply it by the reciprocal ( [tex]\frac{7}{5}[/tex] )

Your new expression should look like this:

    [tex]\frac{15}{4}[/tex] x [tex]\frac{7}{5}[/tex]

To make it even easier, you can simplify this expression even further. Looking at the numerators and denominators, we see that we have a 15 on top and a 5 on the bottom. Cross out the 5 and put a 1 in its place since 5 goes into 5 one time! Now we have to do it to the 15... Cross out the 15 and put a 3 since 5 goes into 15 three times!

Your simplified expression should look like this:

    [tex]\frac{3}{4}[/tex] x [tex]\frac{7}{1}[/tex]

Now, just multiply the numerators and the denominators to get your final answer of

    [tex]\frac{21}{4}[/tex]

Since you cannot simplify this anymore, that is your answer!!!

Answer:

3/28

Step-by-step explanation:

Answer:

5789 pages

Step-by-step explanation:

9+180+2700+2900=5789

Answer:

Answer: b. 20.8 ft-lb

Step-by-step explanation:

Answer:

D. 4821 years

Step-by-step explanation:

A = A0e-0.000124t

A/A0 = e^-0.000124t

0.55 = e^-0.000124t

ln(0.55) = ln(e^-0.000124t)

ln(0.55) = -0.000124t × lne

t = ln(0.55)/-0.000124

4821.266135

Answer: 5.2752

Final answer:

To calculate the mean number of push-ups Justin did each weekday, add up the total push-ups for the week and divide by 5. Justin did a mean of 186.8 push-ups per day.

Explanation:

To find the mean number of push-ups Justin did each weekday, we need to add the number of push-ups he did each day and then divide by the number of days. The steps are:

Therefore, the mean number of push-ups Justin did on a weekday is 186.8 push-ups.

Final answer:

The mean number of push-ups Justin did each weekday is calculated by adding the total push-ups for all the days and dividing by the number of days, resulting in 186.8 push-ups.

Explanation:

To find the mean number of push-ups, Justin did over the weekdays, you need to sum up the total push-ups and then divide by the number of days.

Add the number of push-ups for each day: 888 (Monday) + 14 (Tuesday) + 18 (Wednesday) + 6 (Thursday) + 8 (Friday) = 934 push-ups in total.

Divide the total number of push-ups by the number of days: 934 ÷ 5 days = 186.8 push-ups.

Therefore, the mean number of push-ups Justin did each weekday is 186.8 push-ups.

Answer:

D. There are zeros between x = 1 and x = 2, x = 0 and x = –1.

Step-by-step explanation:

A zero point is inside an interval where value of y changes from positive to negative or viceversa. The curve is evaluated in the given points hereafter:

f(-3) = - 909, f(-2) = -192, f(-1) = -9,f(0) = 18, f(1) = 3, f(2) = -204, f(3) = -1017

There two zero, one between x = -1 and x = 0 and other between x = 1 and x = 2. Hence, the answer is D.

Answer:

24/5                                               (Nothing wrong with that.)

Step-by-step explanation:

Dividing is multiplying with the second fraction flipped.

4/5 / 2/12 ----> 4/5 x 12/2

Multiply across. 4 x 12 = 48. 5 x 2 = 10.

Combine. 48/10.

Simplify (divide both sides by 2) . 24/5.

Answer:

[tex] \frac{24}{5} [/tex]

Step-by-step explanation:

To divide two fractions we turn the second fraction upside down and multiply two fractions afterwards

[tex] \frac{4}{5} \div \frac{2}{12} = \\ \frac{4}{5} \times \frac{12}{2} [/tex]

now multiply 4 by 12 and 5 by 2

[tex] \frac{48}{10} [/tex]

now simplify fraction if needed

[tex] \frac{24}{5} [/tex]

Answer:

True

Step-by-step explanation:

That is the definition of a asymptote.  It is approached but will never get to the line.

Answer: True!

Step-by-step explanation:

An asymptote for a function f(x) is a straight line which is approached but never reached by f(x)

The objective function in this scenario is minimizing the cost of shipping goods from the plant to the store.

The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.

The most likely goal function, if we were to create a linear programme for this situation, would be to reduce the cost of shipping from the plants to the stores. This is important since it can become an expensive bottleneck.

Despite the fact that there are three factories and three stores, the costs will not be minimized if the same amount of goods are produced in each plant and carried to a specific store. In fact, the likelihood that each facility generates a distinct volume of items further exacerbates the issue.

Finding the optimal distribution of shipping commodities from each facility to each retailer is important as a result.

Hence, the objective function is minimizing the cost of shipping goods from the plant to the store.

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The options are missing in the question, which are as follow:

a. minimizing the quantity of goods distributed across the stores

b. minimizing the cost of shipping goods from the plant to the store

c. decreasing the cost of their raw material sourcing

d. increasing the number of goods manufactured at the plant

Answer:

6 * [tex]\sqrt[3]{x}[/tex]

Step-by-step explanation:

6 x^1/3

The 1 means inside to the power of 1 and the 3 means to the cubed root

6 * [tex]\sqrt[3]{x}[/tex]

Answer:

0.5 meters per second

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the first one

Answer:

Step-by-step explanation:

Given that:

R(x) = [tex]\frac{17}{2x+1}[/tex] + 34x − 17

As we know that derivative of revenue function is marginal revenue function .

We will use following rules of derivative

=> dR/ dx = [tex]\frac{-17*2}{(2x+1)^{2} } + 34[/tex]

=> R' (x) =   [tex]\frac{-34}{(2x+1)^{2} } + 34[/tex]

=> R '(2000) =  [tex]\frac{-34}{(2*2000+1)^{2} } + 34[/tex] = 34

The revenue when 2000 units are sold is:

R(2000) = [tex]\frac{17}{2*2000+1}[/tex] + 34*2000 − 17 = $69,783

The marginal revenue be "34" and revenue change be "$69,783".

The increase throughout income caused by the acquisition of one more unit of production, is a Marginal revenue. Although marginal income can stay unchanged at a predetermined interval, it's indeed subject to the regulations of decreasing returns as well as will ultimately slow as outcome level grows.

According to the question,

Revenue function,

R(x) = [tex]\frac{17}{2x+1}[/tex] + 34x - 17

Units sold = 2000

(a) The marginal revenue be:

→ [tex]\frac{dR}{dx}[/tex] = [tex]-\frac{17\times 2}{(2x+1)^2}[/tex] + 34

R'(x) = [tex]- \frac{34}{(2x+1)^2}[/tex] + 34

By substituting "x = 2000",

R'(2000) = [tex]- \frac{34}{(2\times 2000+1)^2}[/tex] + 34

              = 34

(b) The revenue change be:

→ R(2000) = [tex]\frac{17}{2\times 2000+1}[/tex] + 34 × 2000 - 17

                 = 69,783 ($)

Thus the above response is appropriate.

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Answer:

The base charge = $18.5 and surcharge for each pound is = $1.75

Step-by-step explanation:

Solution:

- Denote:

     Base charge = $x   ...... For for Weight ≤ 1 lbs

     Additional charge = $y / unit pounds

- We are given that the customer is billed $29.00 for shipping a 7​-pound package. We can express this statement in terms of "x" and "y".

- The 1-pound out of 7 pounds will be charged with $x and remaining 6 additional pounds of weight will be charged "$y" for each unit of weight.

                         $x + ( 7 - 1 )*$y = $29.00    .... Eq1

- Similarly for a receipt of $64.00 for a 27​-pound package. The 1-pound out of 27 pounds will be charged with $x and remaining 26 additional pounds of weight will be charged "$y" for each unit of weight.      

                         $x + ( 27 - 1 )*$y = $64.00   .... Eq2

- Now solve the two equations simultaneously by subtracting Eq1 from Eq2:

                        (26 - 6 )*$y = $(64 - 29)

                        20*$y = $35

                         y = 1.75

                        $x = 29 - 6*1.75

                        x = 18.5    

- The base charge = $18.5 and surcharge for each pound is = $1.75

Answer:

6

Step-by-step explanation:

The outlier is 67.

The mean with the outlier is: 115

(112+ 118 + 120 +67 + 128 + 119 + 121 + 124 + 126) ÷ 9

The mean without he outlier is: 121

(112+ 118 + 120 + 128 + 119 + 121 + 124 + 126) ÷ 8

So, 121 - 115 = 6

Answer:

Step-by-step explanation:

Answer:

x=40

Step-by-step explanation:

Since a circle has a total of a 360 degree angle the equation is

(x+40)+(2x+60)+(3x+20)=360

to simplify this we can bring all the variables(x) together and the numbers together.

(x+2x+3x)+(40+60+20)=360

6x+120=360

6x=360-120

6x=240

6x/6=240/6

x=40

The sum of all the degrees in a circle is 360 degrees. Knowing this you can make a equation:

(x + 40) + (2x + 60) + (3x + 20) = 360

x + 40 + 2x + 60 + 3x + 20 = 360

(x + 2x + 3x) + (40 + 60 + 20) = 360

Now you must combine like terms  This means the numbers with the same variables must be combined...

(x + 2x + 3x) + (40 + 60 + 20) = 360

x + 2x + 3x = 6x

(6x) + (40 + 60 + 20) = 360

Now combine the terms without variables (on the left side of the equation) together

(6x) + (40 + 60 + 20) = 360

40 + 60 + 20 = 120

(6x) + 120 = 360

Now we must isolate x. To do this first bring 120 to the right side by subtracting 120 to both sides (what you do on one side you must do to the other). Since 120 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

6x + 120 - 120 = 360 - 120

6x + 0 = 240

6x = 240

To further isolate x  you must divide 6 to both sides. Since x is being multiplied by 6 you must divide 6 to both sides to make 6 one on the left side and bring it over to the right side

6x / 6 = 240 / 6

1x = 40

x = 40

Check:

(40 + 40) + (2(40) + 60) + (3(40) + 20)

(80) + (80 + 60) + (120 + 20)

80 + 140 + 140

360

Hope this helped! Let me know if you have any further questions or want anything clarified.

~Just a girl in love with Shawn Mendes

Given:

Given that the diameter of the circle is 10 kilometers.

We need to determine the area of the circle.

Radius of the circle:

The radius of the circle can be determined using the formula,

[tex]r=\frac{d}{2}[/tex]

Substituting d = 10, we get;

[tex]r=\frac{10}{2}[/tex]

[tex]r=5[/tex]

Thus, the radius of the circle is 5 kilometers.

Area of the circle:

The area of the circle can be determined using the formula,

[tex]A=\pi r^2[/tex]

Substituting r = 5, we get;

[tex]A=(3.14)(5)^2[/tex]

[tex]A=(3.14)(25)[/tex]

[tex]A=78.5[/tex]

Thus, the area of the circle is 78.5 square kilometers.

Determine the radius, which is 5 kilometers, before calculating the area of a circle with a diameter of 10 kilometers. Next, find the area, or roughly 78.54 km², using the formula Area = π × (radius)².

How to Calculate a Circle's Area

You can use the following formula to get the area of a circle with a given diameter:

π × (radius)² equals area.

Consequently, 78.54 km² is the approximate size of the circle with a diameter of 10 km.

Answer:

3.06 megawatts

Step-by-step explanation:

Firstly, we write the proportionality equation.

wind power varies directly as the square of the length r of one of the blades;

P ∝ r^2

Let’s introduce a constant of proportionality k; This means;

P = kr^2

Now let’s calculate the value of k when 1.5 megawatts and r is 35m

1.5 mw = 35^2 * k

k = 1.5/35^2 = 1.5/1225 = 0.001224489796 MW/m^2

Now we want to calculate the amount of megawatts to be produced by a turbine with 50m blades.

That would be;

P = 0.001224489796 * 50^2 = 3.06 megawatts

Answer:

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that P varies directly with r², if we introduce a constant of proportionality, k, the expression becomes

P = kr²

If P = 1.5 when r = 35, then

1.5 = k × 35²

k = 1.5/35² = 1.5/1225

Therefore, the direct variation function is

P = 1.5r²/1225

When r = 50, then

P = 1.5 × 50²/1225

P = 3.06 megawatt

Answer:

Answer is below

Step-by-step explanation:

Use 3 as the y-intercept. Factor the equation to find the solutions

(x - 1) (x - 3) so 1 and 3 are the x-intercepts. The vertex of the graph is at (2,-1).

I also graphed the equation below.

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The graph of [tex]y = x^2 - 4x + 3[/tex] is a parabola that opens upward with its vertex at (2, -1). It intersects the x-axis at x = 3 and x = 1 and the y-axis at y = 3.

The equation is [tex]y = x^2 - 4x + 3.[/tex]

Use the formula x = -b / (2a) to find the x-coordinate of the vertex. In this case, a = 1, b = -4.

x = -(-4) / (2*1)

= 4 / 2

= 2.

So, the x-coordinate of the vertex is 2.

Subtitute x = 2 into the equation:

[tex]y = (2)^2 - 4(2) + 3[/tex]

= 4 - 8 + 3

= -1.

The y-coordinate of the vertex is -1.

The vertex is at (2, -1).

The y-intercept, we will set x = 0 in the equation:

[tex]y = (0)^2 - 4(0) + 3[/tex]

= 0 - 0 + 3

= 3.

The get x-intercepts, we set y = 0 in the equation:

[tex]0 = x^2 - 4x + 3.[/tex]

(x - 3)(x - 1) = 0.

x = 3 or x = 1.

The x-intercepts are 3 and 1.

Now, we will plot the y-intercept and x-intercepts. The y-intercept is at (0, 3), and the x-intercepts are at (3, 0) and (1, 0).

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Correct Question:

John works as a tutor for $12 an hour and as a waiter for $8 an hour. This month, he worked a combined total of 86 hours at his two jobs.

Let be the number of hours John worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.

Answer:

Total hours = 86

Let t is the hours he spent on tutoring

then (86-t) is hours spent on waiting

Let Y is the total amount in dollars which is required .

Now;

y = (tutoring hours x 12$) + (waiting hours x 8$)

Y = 12t + 8(86-t)

Answer:

a) Q = 0 or 9

b) Q = 5

c) Q = 7

d) Q = 8

Step-by-step explanation:

We assume the postal money order to be of the United State. A smudged digit is calculated using the following algorithm.

1. Add first 10 digits of 11-digit number.

2. Divide the sum of the 10 numbers by 9.

3.The remainder is the smudged digit.

4.The smudged digit is appended to the end of the ID number or anywhere in the number.

It is calculated as:

[tex]x_{11} = (x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} + x_{7} + x_{8} + x_{9} + x_{10} )mod 9[/tex]

a) 493212Q0688

[tex]8 = (4 + 9 + 3 + 2 + 1 + 2 + Q + 0 + 6 + 8) mod 9\\8 = (Q + 35) mod 9\\8 = Q mod 9 + 35 mod 9\\8 = Q mod 9 + 8\\Q mod 9 = 8 - 8\\Q mod 9 = 0\\Q = 0 or 9[/tex]

Therefore, Q is either 0 or 9.

b) 850Q9103858

[tex]8 = (8 + 5 + 0 + Q + 9 + 1 + 0 + 3 + 8 + 5) mod 9\\8 = (Q + 39) mod 9\\8 = Q mod 9 + 39 mod 9\\8 = Q mod 9 + 3\\Q mod 9 = 8 - 3\\Q mod 9 = 5\\Q = 5[/tex]

Therefore, Q is 5 because from Q mod 9 = 5, we have Q = 5 mod 9.

c) 2Q941007734

[tex]4 = (2 + Q + 9 + 4 + 1 + 0 + 0 + 7 + 7 + 3) mod 9\\4 = (Q + 33) mod 9\\4 = Q mod 9 + 33 mod 9\\4 = Q mod 9 + 6\\Q mod 9 = 4 - 6\\Q mod 9 = -2\\Q = -2 mod 9\\Q = 7[/tex]

Therefore, Q is 7 because we have to cancel out the negative sign by adding the modulo base (9) to the negative number: -2 + 9 = 7.

d) 66687Q03201

[tex]1 = (6 + 6 + 6 + 8 + 7 + Q + 0 + 3 + 2 + 0) mod 9\\1 = (Q + 38) mod 9\\1 = Q mod 9 + 38 mod 9\\1 = Q mod 9 + 2\\Q mod 9 = 1 - 2\\Q mod 9 = -1\\Q = -1 mod 9\\Q = 8[/tex]

Therefore, Q is 8 because we have to cancel out the negative sign by adding the modulo base (9) to the negative number: -1 + 9 = 8.

For the given postal money order scenarios, the smudged digit, Q, is determined as follows: Scenario a - either 0 or 9, Scenario b - 5, Scenario c - 5, and Scenario d - 3.

Let's analyze the given postal money order scenarios and determine the smudged digit, Q, using the provided algorithm:

Scenario a:

ID number: 493212Q0688

Sum of the first 10 digits: 4 + 9 + 3 + 2 + 1 + 2 + 0 + 6 + 8 + 8 = 43

43 divided by 9 equals 4 with a remainder of 7.

Therefore, the smudged digit, Q, is either 0 or 9.

Scenario b:

ID number: 850Q9103858

Sum of the first 10 digits: 8 + 5 + 0 + 9 + 1 + 0 + 3 + 8 + 5 + 8 = 47

47 divided by 9 equals 5 with a remainder of 2.

Therefore, the smudged digit, Q, is 5.

Scenario c:

ID number: 2Q941007734

Sum of the first 10 digits: 2 + 7 + 9 + 4 + 1 + 0 + 0 + 7 + 7 + 3 = 40

40 divided by 9 equals 4 with a remainder of 4.

To cancel out the negative sign in the remainder, we add the modulo base (9) to the negative number: -4 + 9 = 5.

Therefore, the smudged digit, Q, is 5.

Scenario d:

ID number: 66687Q03201

Sum of the first 10 digits: 6 + 6 + 6 + 8 + 7 + 0 + 3 + 2 + 0 + 1 = 33

33 divided by 9 equals 3 with a remainder of 6.

To cancel out the negative sign in the remainder, we add the modulo base (9) to the negative number: -6 + 9 = 3.

Therefore, the smudged digit, Q, is 3.

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Answer:

The answer is 19

Step-by-step explanation:

2 + 2 = 4

3 + 5 = 8

4  + 8 = 12

12 + 7 = 19

Answer:

20.4°C

Step-by-step explanation:

Initial temperature 't1'= -4.8°C

Final temperature 't2'= 15.6°C

In order to find change in temperature, take the difference of above two temperatures. So,

Change in temperature 'ΔT' = t2 - t1

ΔT= 15.6 - (-4.8)

ΔT= 20.4 °C

Therefore, the change in temperature was 20.4°C