Which is the equation of a line that has a slope of 1 and passes through point (5, 3)?
y = -2
y = x + 2
y = x + 3
y=x-5

Answer:

The quantity of salt at time t is [tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex], where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

[tex]\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}[/tex]

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

[tex](0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}[/tex]

Where:

[tex]c[/tex] - The salt concentration in the tank, as well at the exit of the tank, measured in [tex]\frac{pd}{gal}[/tex].

[tex]\frac{dc}{dt}[/tex] - Concentration rate of change in the tank, measured in [tex]\frac{pd}{min}[/tex].

[tex]V[/tex] - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

[tex]V \cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]

[tex]60\cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]

[tex]\frac{dc}{dt} + \frac{1}{10}\cdot c = 3[/tex]

This equation is solved as follows:

[tex]e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }[/tex]

[tex]\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }[/tex]

[tex]e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt[/tex]

[tex]e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C[/tex]

[tex]c = 30 + C\cdot e^{-\frac{t}{10} }[/tex]

The initial concentration in the tank is:

[tex]c_{o} = \frac{10\,pd}{60\,gal}[/tex]

[tex]c_{o} = 0.167\,\frac{pd}{gal}[/tex]

Now, the integration constant is:

[tex]0.167 = 30 + C[/tex]

[tex]C = -29.833[/tex]

The solution of the differential equation is:

[tex]c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }[/tex]

Now, the quantity of salt at time t is:

[tex]m_{salt} = V_{tank}\cdot c(t)[/tex]

[tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex]

Where t is measured in minutes.

Answer:

10 red marbles

Step-by-step explanation:

Total= 45 marbles

Probability of red= 2/9

Number of red= 45*2/9= 10

Answer:

Step-by-step explanation:

155

The number of boxes required by the school to order is 155.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.  If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We have been given that the school needs 1,860 pencils for its students. Also, the pencils are sold in boxes of 12.

We need to find the school needs to requires boxes to order.

Total number of pencil = 1,860

Number of boxes = 12

Therefore, boxes needed = 1,860 / 12

= 155

Hence, the number of boxes required by the school to order is 155.

To learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ5

Answer:

[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]

The numbers are    [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]

Step-by-step explanation:

Step(i):-

Given sum of the three numbers is 10

Let x , y , z be the three numbers is 10

x +y + z = 10  ...(i)

Given two times the second number minus the first number is equal to 12

2 × y - x = 12 ...(ii)

Given the first number minus the second number plus twice the third number equals 7

x + y + 2 z = 7 ...(iii)

Step(ii):-

Solving (i) and (iii) equations

                       x + y +   z     =    10  ...(i)

                       x + y + 2 z   =     7 ..   (iii)

                     -      -     -         -              

                     0    0    -z      =   3              

Now we know that    z = -3 ...(a)

from (ii)  equation

           2 × y - x = 12 ...(ii)

               x = 2 y -12  ...(b)

Step(iii):-

substitute equations (a) and (b) in equation (i)

                x+y+z =10

           2 y - 12 + y -3 =10

              3 y -15 =10

              3 y = 10 +15

              3 y =25

               [tex]y = \frac{25}{3}[/tex]

Substitute   [tex]y = \frac{25}{3}[/tex]  and   z = -3 in equation(i) we will get

        x+y+z =10

       [tex]x + \frac{25}{3} -3 = 10[/tex]

       [tex]x +\frac{25-9}{3} = 10[/tex]

      [tex]x +\frac{16}{3} = 10[/tex]

      [tex]x = 10 - \frac{16}{3}[/tex]

     [tex]x = \frac{30 -16}{3} = \frac{14}{3}[/tex]

Final answer :-

[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]

The numbers are  [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]

Answer:

-2, 5, 7 on Edge.

Step-by-step explanation:

I got the Answer right.

Answer:

3

Step-by-step explanation:

0 pairs mean when two "boxes" add together to make 0. For the x's we only have one because x + (-x) = x - x = 0. For the other ones we have two (the + means 1 and the - means -1) because 1 + (-1) = 1 - 1 = 0. Therefore the answer is 1 + 2 = 3.

Answer: B

Step-by-step explanation:

For this problem, to solve for x, you want to move all like terms to one side.

[tex]\frac{1}{4}x-\frac{1}{2}x=\frac{7}{8} +\frac{1}{8}[/tex]

Now that you have moved like terms to one side, you can directly add and subtract to combine like terms.

[tex]-\frac{1}{4} x=1[/tex]

x=-4

Answer:

[tex]x = - 4[/tex]

Second answer is correct

Step-by-step explanation:

[tex] \frac{1}{4} x - \frac{1}{8} = \frac{7}{8} + \frac{1}{2} x \\ \frac{1}{4} x - \frac{1}{2} x = \frac{1}{8} + \frac{7}{8} \\ \frac{1x - 2x}{4} = \frac{8}{8} \\ - \frac{1}{4} x = 1 \\ - 1x = 1 \times 4 \\ - 1x = 4 \\ x = - 4[/tex]

hope this helps you

Answer:

The solution is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex].

Step-by-step explanation:

An inequality is a mathematical relationship between two expressions and is represented using one of the following:

To find the solution of the inequality [tex]0>\:20x+2>\:-32[/tex] you must:

[tex]\mathrm{If}\:a>u>b\:\mathrm{then}\:a>u\quad \mathrm{and}\quad \:u>b\\\\0>20x+2\quad \mathrm{and}\quad \:20x+2>-32[/tex]

First, solve [tex]0>20x+2[/tex]

[tex]\mathrm{Switch\:sides}\\\\20x+2<0\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\20x+2-2<0-2\\\\\mathrm{Simplify}\\\\20x<-2\\\\\mathrm{Divide\:both\:sides\:by\:}20\\\\\frac{20x}{20}<\frac{-2}{20}\\\\\mathrm{Simplify}\\\\x<-\frac{1}{10}[/tex]

Next, solve [tex]20x+2>-32[/tex]

[tex]20x+2-2>-32-2\\\\20x>-34\\\\\frac{20x}{20}>\frac{-34}{20}\\\\x>-\frac{17}{10}[/tex]

Finally, combine the intervals

[tex]x<-\frac{1}{10}\quad \mathrm{and}\quad \:x>-\frac{17}{10}\\\\-\frac{17}{10}<x<-\frac{1}{10}[/tex]

The interval notation is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex] and the graph is:

Answer:

the elevation of base camp is 35 ft

Step-by-step explanation:

Starting at 65 feet elevation, and the descending 30 feet to reach base camp, that means that base camp is at: 65 ft - 30 ft = 35 ft elevation

Answer:

35 feet

Step-by-step explanation:

65 feet- 30 feet= 35 feet is the elevation of the base

Answer:

(x, y) → (4/5 x, 4/5 y)

Question:

The answer choices to determine the rule that represent the dilation were not given. Let's consider the following question:

A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation?

A) (x, y) → (0.5 − x, 0.5 − y)

B) (x, y) → (x − 7, y − 7)

C) (x, y) → ( 5/4 x, 5/4 y)

D) (x, y) → (4/5 x, 4/5 y)

Step-by-step explanation:

To determine the rule that could represent the dilation, we would multiply each coordinate by a dilation factor (a constant) to create a dilation. Since the dilation would be used to create a smaller polygon, the constant multiplied with the coordinates of x and y would be less than 1.

Let's check the options out.

In option (A), the coordinates is subtracted from the constant (0.5).

In option (B), the constant (7) is subtracted from the coordinates.

In option (C), the coordinates are multiplied by constant (5/4).

But 5/4 = 1.25. This is greater than 1.

In option (D), the coordinates are multiplied by constant (4/5).

4/5 = 0.8

The constant multiplied with the coordinates of x and y is less than 1 in option (D) = (x, y) → (4/5 x, 4/5 y)

4/5 = 0.8

0.8 is less than 1

Answer:

1

Step-by-step explanation:

x^2−2x=3

Take the coefficient of x

-2

Divide by 2

-2/2 =-1

Square it

(-1)^2 = 1

Add this to each side

Answer:

Step-by-step explanation:

A possible study is to compare the prices of items in a two different online auction platform: the Dutch auction and the first-priced sealed auction.

Independent variable = the two types of auction

• Condition A = Dutch auction

• Condition B = First-price sealed auction

The Dependent variable in my case study is the prices for each pair of identical items I place in each auction using a known pair sample. The depends variable is measured in the continuous scale because prices are in numbers and these numbers vary continuously, it is not fixed.

The null hypothesis for my study would be: there is no difference in the prices of identical items in the two different auction.

The alternative hypothesis for my study would be: there is a difference in the prices of identical items in the two different auction.

I would set it to the 0.05 level of significance because this is the standard level of significance normally set in a study although this varies.

Answer:

4.3 units

Step-by-step explanation:

In this question we use the Pythagorean Theorem which is shown below:

Data are given in the question

Right angle

a = 3.4

b = 2.6

These two are legs of the right triangle

Based on the above information

As we know that

Pythagorean Theorem is

[tex]a^2 + b^2 = c^2[/tex]

So,

[tex]= (3.4)^2 + (2.6)^2[/tex]

= 11.56 + 6.76

= 18.32

That means

[tex]c^2 = 18.56[/tex]

So, the c = 4.3 units

Answer:

Option (3)

Step-by-step explanation:

Given functions are f(x) = 4 - x² and g(x) = 6x

We gave to find the expression for (g - f)(3).

(g - f)(x) = g(x) - f(x)

            = 6x - (4 - x²)

            = 6x - 4 + x²

By substituting x = 3 in this expression,

(g - f)(x) = 6(3) - 4 + (3)²

Therefore, option (3) will be the answer.

Answer:

10.

A. 10240

6.

B. 2^18 = 262144

Step-by-step explanation:

Answer:

270

Step-by-step explanation:

For any arithmetic sequence

nth term is given by

nth term = a + (n-1)d

where a is first term,

d is common difference

d is given by nth term - (n-1)th term

sum of n terms given by

sum = n/2(2a + (n-1)d)

________________________________________________

Given arithmetic sequence

-2,0,2,4,6,8...

first term a = -2

lets take third term as nth term and second term as (n-1)th term to find common difference d.

d = 2 - 0 = 2

using a = -2 , d = 2, n = 18

thus, sum of first 18 terms = n/2(2a + (n-1)d)

                                           =18/2( 2*(-2) + (18-1) 2)

                                           =9 ( -4 + 34)

                                           =9 ( 30) = 270

Thus, sum of first 18 terms is 270.

Answer:

45°

Step-by-step explanation:

There is a propiety that says "The measure of the inscribed angle is half that of the arc that the two sides cut out of the circle."

So the central angle is 90, the inscribed angle will be 90/2=45°

Answer:

Dear User,

Answer to your query is provided below

(i) Total Loss = Rs.15

(ii) Loss percent = 5%

Step-by-step explanation:

Eggs purchased = 5x12 = 60

Total Cost = 60x5 = Rs 300

Eggs Broken = 10

Eggs Broken cost = 10x5= Rs. 50

Eggs sold = 60-10 = 50

Egg Sale cost = 50x5.70 = Rs 285

(i) Total Loss = C.p. - S.p. = 300 - 285 = 15

(ii) Loss Percent = (Loss/CP)x100 = (15/300)x100 = 5%

Answer:

John is 9.21 km form the school.

Step-by-step explanation:

John leaves school to go home. His bus drives 6 kilometres north and then goes 7 kilometres west. It is required to find John's distance from the school. It is equal to the shortest path covered or its displacement. So,

[tex]d=\sqrt{6^2+7^2} \\\\d=9.21\ km[/tex]

So, John is 9.21 km form the school.

Answer:

Donde didn't multiply 4(1+3i)

Answer: it’s A he did not apply distributive property yo

Step-by-step explanation:

Answer:

Step-by-step explanation:

Consider the augments matrix (the right most column is  the extra vector).

[tex]\left[\begin{matrix} 1 & 4 & -2 \\3 & h & -6\end{matrix}\right][/tex]

By multypling the first row by 3 and substracting it from the second row and saving the result in the second row we get the matrix

[tex]\left[\begin{matrix} 1 & 4 & -2 \\0 & h-12 & 0\end{matrix}\right][/tex]

Note that since the value of the third column in the second row is 0, any value of h gives us a consistent system. An inconsistent system is when we get a row of zeros that is equal to a number different from 0.

Answer:

The probability that at least one defective card appears in the sample

P(D) = 0.9644 or 96.44%

Step-by-step explanation:

Given;

Total number of cards t = 140

Number of defective cards = 20

Number of non defective cards x = 140-20 = 120

The probability that at least one defective card = 1 - The probability that none none is defective

P(D) = 1 - P(N) ........1

For 20 selections; r = 20

-- 20 cards are selected from the lot without replacement for functional testing

The probability that none none is defective is;

P(N) = (xPr)/(tPr)

P(N) = (120P20)/(140P20)

P(N) = (120!/(120-20)!)/(140!/(140-20)!)

P(N) = (120!/100!)/(140!/120!) = 0.035618370821

P(N) = 0.0356

The probability that at least one defective card appears in the sample is;

P(D) = 1 - P(N) = 1 - 0.0356 = 0.9644

P(D) = 0.9644 or 96.44%

Note: xPr = x permutation r

[tex]\text{Solve:}\\\\3x^2+7=28\\\\\text{Subtract 7 from both sides}\\\\3x^2=21\\\\\text{Divide both sides by 3}\\\\x^2=7\\\\\text{Square root both sides}\\\\\sqrt{x^2}=\sqrt7\\\\x=\pm\sqrt7\\\\\boxed{x=\sqrt7\,\,or\,\,x=-\sqrt7}[/tex]

Answer:

[tex]y=\frac{3}{2} x-4[/tex]

Step-by-step explanation:

The graph I provided shows it passes thru (4,2) and that it is parallel

Answer:

y = 3/2x -4

Step-by-step explanation:

3x - 2y = - 6

First find the slope by putting it in slope intercept form

Subtract 3x from each side

-2y = -3x-6

Divide by -2

y = -3x/-2  -6/-2

y = 3/2x +3

The slope is 3/2

Parallel lines have the same slope

We have the slope 3/2 and a point (4,2)

y = mx+b where m is the slope and b is the y intercept

y =3/2x+b

Substitute the point into the equation

2 = 3/2(4) +b

2 = 6 +b

Subtract 6

2-6 = 6-6+b

-4 =b

y = 3/2x -4

Answer:

(See explanation below for further details)

Step-by-step explanation:

The domain of the function is:

[tex]x \in \mathbb{R} - \{ \pm \pi \cdot i \}[/tex] for [tex]i \in \mathbb{N}_{O}[/tex]

The range of the function is:

[tex]f(x) \in \{-\infty, +\infty \}[/tex]

There are no absolute extrema and such function is not bounded.

Function is symmetric, whose period is π.

Lastly, the set of asymptotes is:

[tex]x = \pm \pi \cdot i[/tex], for [tex]i \in \mathbb{N}_{O}[/tex]

Answer:

Step-by-step explanation:

edge

Answer:

The integral is

∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx

x₁ = (-π/5)

x₂ = (π/5)

And the area of the surface generated by revolving = 9.71 square units

Step-by-step explanation:

When a function y = f(x) is revolved about the x-axis, the formula for the area of the surface generated is given by

A = 2π ∫ˣ²ₓ₁ f(x) √[1 + (f'(x))²] dx

A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx

For this question,

y = cos 2x

x₁ = (-π/5)

x₂ = (π/5)

y' = -2 sin 2x

1 + y'² = 1 + (-2 sin 2x)² = (1 + 4 sin² 2x)

So, the Area of the surface of revolution is

A = 2π ∫ˣ²ₓ₁ y √[1 + y'²] dx

= ∫ˣ²ₓ₁ 2πy √[1 + y'²] dx

Substituting these variables

A = ∫ˣ²ₓ₁ 2π cos 2x √[1 + 4 sin² 2x] dx

Let 2 sin 2x = t

4 cos 2x dx = dt

2 Cos 2x dx = (dt/2)

dx = (1/2cos 2x)(dt/2)

Since t = 2 sin 2x

when x = (-π/5), t = 2 sin (-2π/5) = -1.90

when x = (π/5), t = 2 sin (2π/5) = 1.90

A

= ∫¹•⁹⁰₋₁.₉₀ π (2 Cos 2x) √(1 + t²) (1/2cos 2x)(dt/2)

= ∫¹•⁹⁰₋₁.₉₀ (π/2) √(1 + t²) (dt)

= (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)

But note that

∫ √(a² + x²) dx

= (x/2) √(a² + x²) + (a²/2) In |x + √(a² + x²)| + c

where c is the constant of integration

So,

∫ √(1 + t²) dt

= (t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)| + c

∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)

= [(t/2) √(1 + t²) + (1/2) In |t + √(1 + t²)|]¹•⁹⁰₋₁.₉₀

= [(1.90/2) √(1 + 1.90²)+ 0.5In |1.90+√(1 + 1.90²)|] - [(-1.9/2) √(1 + -1.9²) + (1/2) In |-1.9 + √(1 + -1.9²)|]

= [(0.95×2.147) + 0.5 In |1.90 + 2.147|] - [(-0.95×2.147) + 0.5 In |-1.90 + 2.147|]

= [2.04 + 0.5 In 4.047] - [-2.04 + 0.5 In 0.247]

= [2.04 + 0.70] - [-2.04 - 1.4]

= 2.74 - [-3.44]

= 2.74 + 3.44

= 6.18

Area = (π/2) ∫¹•⁹⁰₋₁.₉₀ √(1 + t²) (dt)

= (π/2) × 6.18

= 9.71 square units.

Hope this Helps!!!

Answer:

The 95% confidence interval for the true mean is between $0 and $342,729

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448

The margin of error is:

M = T*s = 2.1448*81000 = 173,729.

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 169,000 - 173,729 = -4,... = $0(cannot be negative)

The upper end of the interval is the sample mean added to M. So it is 169,000 + 173,729 = $342,729

The 95% confidence interval for the true mean is between $0 and $342,729

Answer:

32

Step-by-step explanation:

if u do pythagoras, sq root of 20^2-12^2=16

16x2=32

9514 1404 393

Answer:

  32°

Step-by-step explanation:

The law of cosines can be used for this:

  h^2 = f^2 +g^2 -2fg·cos(H)

  cos(H) = (f^2 +g^2 -h^2)/(2fg)

  cos(H) = (650,500/763,600)

  H = arccos(6505/7636) ≈ 31.5826°

Angle H is about 32°.

Answer:

6.8

Step-by-step explanation:

27 / 4 = 6.75, which rounded to the nearest tenth, is 6.8.

Answer:

70 pounds

Step-by-step explanation:

3 boxes= 105 pounds

2boxes= x pounds

Cross Multiply

3*x=105 *2

3x=210

3x/3=210/3

x=70 pounds

Answer:

70

Step-by-step explanation:

105/3=35

35x2=70

So 70 is the answer