Slips of paper are numbered 1 through 10. If one slip is drawn and replaced 40 times, how many times should the slip with number 10 appear?

Slope=  

2.000

0.667

​  

=0.333

x−intercept=  

−1

9

​  

=−9.00000

y−intercept=  

3

9

​  

=3

The required graph that represents the equation 3y - x - 9 = 0 is graph B. Option B is correct.

Which graph represents the solution set of the equation 3y - x - 9 = 0 is to determine.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Given equation,
3y - x - 9 = 0
Rearranging the equation,
y = x/3 + 3

Since the slope of the equation is m = 1/3 and the intercept is  positive
So graph A and C can be omitted because the intercept is negative.
Now, x intercepet,
put Y = 0
0 = x/3 + 3
-3 = x/3
x = -3 * 3
x = -9

So graph D is also omitted because the x-intercept is -1 which is wrong, So graph B is a correct option which has the x-intercept at x = -9.

Thus, the required graph that represents the equation 3y - x - 9 = 0 is graph B. Option B is correct.

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Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

The exact values of the given trigonometric functions are

\(sin(A) = \frac{80}{89}\)

\(cos(A) = \frac{39}{89}\)

\(tan(A) = \frac{80}{39}\)

\(sec(A) =\frac{89}{39}\)

\(csc(A) =\frac{89}{80}\)

\(cot(A) =\frac{39}{80}\)

From the question, we are to determine the values of the trigonometric functions

First, we will determine the length of side c

By the Pythagorean theorem, we have that

c² = a² + b²

c² = 80² + 39²

c² = 6400 + 1521

c² = 7921

c = √7921

c = 89

Now, Using SOH CAH TOA

That is,

\(sin(A) = \frac{opposite}{hypotenuse}\)

\(cos(A) = \frac{adjacent}{hypotenuse}\)

\(tan(A) = \frac{opposite}{adjacent}\)

In the triangle,

opposite = a = 80

adjacent = b = 39

hypotenuse = c = 89

Thus,

\(sin(A) = \frac{80}{89}\)

\(cos(A) = \frac{39}{89}\)

\(tan(A) = \frac{80}{39}\)

\(sec(A) =\frac{1}{cos(A)} =\frac{89}{39}\)

\(csc(A) =\frac{1}{sin(A)} =\frac{89}{80}\)

\(cot(A) =\frac{1}{tan(A)} =\frac{39}{80}\)

Hence, the exact values of the given trigonometric functions are

\(sin(A) = \frac{80}{89}\)

\(cos(A) = \frac{39}{89}\)

\(tan(A) = \frac{80}{39}\)

\(sec(A) =\frac{89}{39}\)

\(csc(A) =\frac{89}{80}\)

\(cot(A) =\frac{39}{80}\)

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First, let's find Maura's running speed by using the information that Carlos runs at a rate that is 25% slower than Maura's rate. If Carlos runs at a rate of 6 miles per hour, then Maura runs at a rate of 6 * 1.25 = 7.5 miles per hour.

Next, let's calculate how long it takes for Carlos to finish the marathon. We know that Carlos runs at a rate of 6 miles per hour and the marathon is 26 miles long. So we can use the formula:

time = distance/rate

time = 26/6

time = 4.33 hours

Now let's find how long it takes for Maura to finish the marathon. We know that Maura runs at a rate of 7.5 miles per hour and the marathon is 26 miles long. So we can use the formula again:

time = 26/7.5

time = 3.47 hours

Finally, let's convert Jacob's time of 2 hours and 36 minutes to hours. We can use the formula:

time = 2 + (36/60)

time = 2 + 0.6

time = 2.6 hours

In conclusion, Carlos takes 4.33 hours, Maura takes 3.47 hours and Jacob takes 2.6 hours to finish the marathon.

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Answer:

The correct features are;

2, 3, and 4

Step-by-step explanation:

2) Information carried by digital communication can be stored as digital information on electronic media such that they can be accessed with the aid of electronics and can be stored in a wide variety of recording formats including magnetic and optical media

3) Digital communication can be made over very long distance using serial communication. Fiber optics cables are used for transmitting information across continents using square waves which is a digital signal

4) Digital signals are less likely to be subjected to interference, distortion, and generation loss which is prone to analog signals, and therefore, there is less chance of signal loss when using digital communication.

Answer:

WR ≈ 13.862

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

WR² + RT² = WT²

WR² + 12.1² = 18.4²

WR² + 146.41 = 338.56 ( subtract 146.41 from both sides )

WR² = 192.15 ( take the square root of both sides )

WR = \(\sqrt{192.15}\) ≈ 13.862 ( to the nearest thousandth )

Answer:

because it never changes.

The solution by using the quadratic formula is,

x = 4 + 2√6 i / 4   and x = 4 - 2√6 i / 4

What is Quadratic formula?

To solve a quadratic equation ax²+ bx + c = 0 , we use the quadratic formula,

x = - b ± √b² - 4ac / 2a

The given expression is;

- 2x² + 4x = 5

Now, The given equation is solve by using Quadratic formula as;

- 2x² + 4x = 5

Move terms to the left side

- 2x² + 4x - 5 = 0

- ( 2x² - 4x + 5 ) = 0

2x² - 4x + 5 = 0

Compare with quadratic equation ax²+ bx + c = 0 we get;

a = 2, b = -4, c = 5

Since, Quadratic formula is,

x = - b ± √b² - 4ac / 2a

Hence, Substituting all the values of a, b and c in quadratic formula we get;

x = - (-4) ± √(-4)² - 4*2*5 / 2*2

x = 4 ± √16 - 40 / 4

x = 4 ± √-24 / 4

x = 4 ± 2√-6 / 4             ( Since, i = √-1  )

x = 4 + 2√6 i / 4   and x = 4 - 2√6 i / 4

So, The solution by using the quadratic formula is,

x = 4 + 2√6 i / 4   and x = 4 - 2√6 i / 4

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After solving the equation the jet is descending vertically at 12 mph.

The Pythagorean Theorem is a mathematical statement that states that in a right triangle the sum of the squares of the lengths of the two sides that make up the right angle are equal to the square of the length of the hypotenuse. This theorem is named after the ancient Greek mathematician, Pythagoras. It can be expressed as the equation: a2 + b2 = c2, where 'a' and 'b' are the lengths of the two sides adjacent to the right angle and 'c' is the length of the hypotenuse. The Pythagorean Theorem is a fundamental tool used in geometry and trigonometry, and it is used to calculate the lengths of the sides of a right triangle. It can also be used to calculate the distances between two points or to calculate the area of a triangle.

The jet is descending at 12 mph. This can be calculated by using the Pythagorean Theorem. Since the jet is approaching the oil depot horizontally at 738 mph and descending diagonally at a constant speed of 750 mph, we can use the Pythagorean Theorem to calculate the vertical component of the jet's descent.
750^2 = 738^2 + x^2
x = √(750^2 - 738^2)
x = 12 mph
Therefore, the jet is descending vertically at 12 mph.

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The subscriber needs to use 363 minutes in a month in order for the second plan to be preferable

What should be sign between the equations for the second option to be better?

The sign between the equation of the first cell phone plan and the second phone plan must less  than for the second option to yield more value

Let x be number of minutes of call

Total cost of first option=0.20x

Total cost of second option=39.95+0.09x

For the second option to be better, its value must be less than that of first option

39.95+0.09x<0.20x

39.95<0.20x-0.09x

39.95<0.11x

39.95/0.11<x

x>363

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Answer:2.2%

Step-by-step explanation: I took the test

The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.

In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.

The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.

According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms

Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.

Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

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\( \frac{1}{3} b = \frac{4}{5} \\ \)

Multiply sides by 3

\( 3 \times \frac{1}{3} b =3 \times \frac{4}{5} \\ \)

\(b = \frac{12}{5} \\ \)

\(b = \frac{10 + 2}{5} \\ \)

\(b = 2 \frac{2}{5} \\ \)

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Thus the correct answer is (( A )) .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

your answer should be A. 2 2/5

Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

Explanation:

The paragraph explains how TERFs have alienated many feminists from radical feminism and why TERF is a harmful and anti-trans movement.

Some other possible sentences are:

Answer:

Step-by-step explanation:

Hydrogen

Answer:

Hydrogen

Step-by-step explanation:

Look at the periodic table.

Also, has the lowest attomic number.

Hey there! I'm happy to help!

To turn 12.5% into a decimal, you simply take off the percent sign and move the decimal to the left two places, giving us 0.125.

To make it a fraction, you put the percent out of 100 and you see if it simplifies. We see that the numerator and denominator are both divisible by 12.5, giving us 1/8.

DECIMAL: 0.125

FRACTION: 1/8

Have a wonderful day! :D

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

(i) \(80-x\)

(ii) \(S(x) = 40 - 0.10x\)

(iii) $36.5

Step-by-step explanation:

Given that:

1. Total Number of fruits = 80

2. Number of mangoes = x

3. Both mangoes and oranges are there in the basket.

Solution (i):

Only mangoes and oranges are there in the basket and the basket is full.

so, Number of mangoes + Number of oranges = Total number of fruits

x + Number of oranges = 80

Number of oranges = \(80 -x\)

Solution (ii):

Given:

Cost of an orange = 50 cents = $0.50

Cost of a mango = 40 cents = $0.40

Cost for x mangoes = \(\$ 0.40x\)

Cost for (\(80-x\)) oranges = \(\$ 0.50 \times (80-x)\)

\(\Rightarrow S(x) = 0.50 (80-x) + 0.40x\\\Rightarrow S(x) = 40 -0.50x + 0.40x\\\Rightarrow S(x) = 40 - 0.10x\)

Solution (iii):

Put value of x = 35 in S(x)

\(S(35) = 40 - 0.10 (35)\\\Rightarrow S(35) = 40 - 0.35\\\Rightarrow S(35) =\$ 36.5\)

Hence, answers are:

(i) \(80-x\)

(ii) \(S(x) = 40 - 0.10x\)

(iii) $36.5

The decimal equivalent of 1/18 is 0.125

Answer:  (1) 26   (2) 1, 3, 25

Step-by-step explanation:

Let a, b, and c represent the three discs.

a + b + c + 12 + 9 = 50

a + b + c = 29

1) Since a, b, and c are all different numbers then the one possibility is:

a = 1, b = 2, --> c = 26

2) There are many different possibilities for creating a sum of three numbers whose total is 29.

One example is provided above in #1.

Here are few other examples:

1, 3, 25               2, 3, 24            3, 4, 19               4, 5, 20

1, 4, 24               2, 4, 23            3, 5, 18               4, 6, 19

1, 5, 23               2, 5, 22            3, 6, 17               4, 7, 18

Using a system of equations, it is found that:

\(x + y + z = 29\)

---------------------

\(x + y + z + t + w = 50\)

\(x + y + z + 9 + 12 = 50\)

\(x + y + z + 21 = 50\)

\(x + y + z = 29\)

\(x + y + z = 29\)

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Answer:

Step-by-step explanation:

Given

5x : 8 = 7 : 2

\(\frac{5x}{8} =\frac{7}{2}\\cross , multiply\\\\10x = 56\\x = \frac{56}{10}\\x =\frac{28}{5}\)

hope it helps :)

Answer:

2 ; -2

Step-by-step explanation:

Both numbers squared equal 4

The solved inverse matrices.

(9x - 2y = 12

3x + 4y = 18

([2],[3 ])

To solve a system of linear equations using inverse matrices, we can express the system in matrix form as follows:

[9 -2] [x] = [12]

[3 4] [y] [18]

Then we can find the inverse of the coefficient matrix, which is the matrix containing the coefficients of the variables in the system:

[9 -2]^⁻¹ = 1/((9)(4) - (-2)(3)) * [ 4 2]

[3 4] [ -3 9]

= 1/14 * [ 4 2] = [2/7  1/7]

[ -3 9] [-3/7  2/7]

We can then multiply both sides of the equation by the inverse matrix to obtain the solution:

[2/7   1/7] [9 -2] [x] = [2/7   1/7] [12]

[-3/7   2/7] [3 4] [y] [-3/7   2/7] [18]

[x] = [2/7   1/7]^-1 [2/7   1/7] [9  -2] [x]

[y] [-3/7   2/7] [-3/7    2/7] [3   4] [y]

[x] = [1  0] [9  -2] [x]

[y] [0  1] [3  4] [y]

This simplifies to the following system of equations:

9x - 2y = 12

3x + 4y = 18

Therefore in solving this system, we find that x = 2 and y = 3. So, the solution to the original system is (x, y) = (2, 3).

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The biomass a year later is \(& \ y \approx 3.23 \times 10^7 \mathrm{~kg}\)  and t=1.58 years to reach 4 times 107 kg of biomass.

The following differential equation: \(& \Rightarrow \frac{d y}{d t}=k y\left(1-\frac{y}{M}\right) \\\)

\(& \Rightarrow \frac{d y}{d t}=k y\left(\frac{M-y}{M}\right)\)

Using variable separable method:

\($$\Rightarrow \frac{d y}{y(M-y)}=\left(\frac{k}{M}\right) d t$$\)

Integrate both sides:

\($$\begin{gathered}\Rightarrow-\int \frac{d y}{y(y-M)}=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int \frac{M}{y(y-M)} d y=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int \frac{y-(y-M)}{y(y-M)} d y=\int\left(\frac{k}{M}\right) d t \\\\\Rightarrow-\frac{1}{M} \int\left(\frac{1}{y-M}-\frac{1}{y}\right) d y=\int\left(\frac{k}{M}\right) d t\end{gathered}$$\)

\(\Rightarrow-\frac{1}{M}(\ln (y-M)-\ln y)=\frac{k t}{M}+C \\\)

Let C1 be a constant such that C1 = MC, therefore,

\($$\begin{gathered}\Rightarrow-\ln (y-M)+\ln y=k t+C_1 \\\Rightarrow \ln \frac{y}{y-M}=k t+C_1 \\\Rightarrow \frac{y}{y-M}=e^{k t+C_1} \\\\\Rightarrow y=y e^{k t+C_1}-M e^{k t+C_1} \\\\\Rightarrow y e^{k t+C_1}-y=M e^{k t+C_1} \\\\\Rightarrow y=\frac{M e^{k t+C_1}}{e^{k t+C_1}-1} \\\\\Rightarrow y=\frac{M}{1-e^{-k t-C_1}} \\\Rightarrow y=\frac{M}{1-e^{-k t} e^{C_1}}\end{gathered}$$\)

Let A be a new constant such that:

\(\Rightarrow y=\frac{M}{1-A e^{-k t}}\)

Substitute the values of M and k, we'll get:

\(\Rightarrow y=\frac{7 \times 10^7}{1-A e^{-0.76 t}}\)

Substituting the given initial condition:\(\Rightarrow y(0)=2 \times 10^7\)

\(\Rightarrow 2 \times 10^7=\frac{7 \times 10^7}{1-A e^{-0.76(0)}} \\\\\\Rightarrow 2=\frac{7}{1-A} \\\)

=2-2A=7

=A=-2.5

Therefore, \(\Rightarrow y=\frac{7 \times 10^7}{1+2.5 e^{-0.76 t}}\)

On simplification, we'll get:

\($$\begin{aligned}& \Rightarrow y \approx 32270466.08 \mathrm{~kg} \\& \Rightarrow y \approx 3.23 \times 10^7 \mathrm{~kg}\end{aligned}$$\)

(b). Substitute the given value in the equation

\($$\begin{gathered}\Rightarrow 4 \times 10^7=\frac{7 \times 10^7}{1+2.5 e^{-0.76 t}} \\\Rightarrow 4=\frac{7}{1+2.5 e^{-0.76 t}} \\\Rightarrow 4+10 e^{-0.76 t}=7\end{gathered}$$\)

On simplification, we'll get t=1.58 years

Therefore, it will take for the biomass to reach 4 times 107 kg is 1.58 years.

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Answer:

x = - 3, x = 0, x = 3

Step-by-step explanation:

Given

4x³ = 36x ( subtract 35x from both sides )

4x³ - 36x = 0 ← factor out 4x from each term

4x(x² - 9) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

x² - 9 = 0 ⇒ x² = 9 ⇒ x = ± \(\sqrt{9}\) = ± 3

Answer:

4x^3=36x.

4x^3-36x=0.

4x^3=36x.

4x(x^2-9)=0.

4x=0,x^2-9=0.

x=0,x^2=9.

x=0,√9=+3 or -3.

x=0,+3,-3.

Thank you for the question

Answers:  2700 and 5300 in that order

Katie invested $2700 at a rate of 3% and $5300 at a rate of 4%

===============================================================

Explanation:

Those two amounts must add to 8000 because this is how much she invests total. So x+y = 8000 is the first equation to set up.

The formula we'll be using is the simple interest formula, which is,

i = p*r*t

where p is the amount deposited or principal, r is the interest rate, and t is the number of years. Luckily, we don't have to worry about the time value t because t = 1 so it effectively goes away. We just need to worry about p and r.

The variable p will be tied directly to the values of x and y, as these are deposit amounts. The r values are decimal forms of the percentages (eg: 3% converts to 0.03)

In short, Katie will earn

In total, she earns 0.03x+0.04y dollars combined. This is set equal to 293 as this is the stated interest she earns over the entire year.

So another equation to set up is 0.03x+0.04y = 293

This only works for simple interest. Compound interest may likely be a different story.

----------------------------------------------------

To summarize so far, we found these two equations:

We have a number of options on how to solve this system. I'll use substitution.

Solve the first equation for y

x+y = 8000

y = 8000-x

Then we'll plug this into the other equation to solve for x like so,

0.03x+0.04y = 293

0.03x+0.04( y ) = 293

0.03x+0.04( 8000-x ) = 293

0.03x+0.04(8000)+0.04(-x) = 293

0.03x+320-0.04x = 293

-0.01x+320 = 293

-0.01x = 293-320

-0.01x = -27

x = -27/(-0.01)

x = 2700

This tells us that Katie invested $2700 at 3%

Use this x value to find y

y = 8000-x

y = 8000-2700

y = 5300

She also invested $5300 at 4%

----------------------------

As a quick check,

so that works out

Also,

which also works out. The answers are fully confirmed.

Answer:

Yes, if you want to graduate yes