Colby left out reasons from his proof. Which reason best supports the statement
<1 ≅<2
PHOTO ABOVE

PLEASE HELPPP
NEED TO PASS

Answer:

3

Step-by-step explanation:

18 divided by 6 is 3

Answer:1.333

Step-by-step explanation:

Answer: −717x−7

Step-by-step explanation: Add −846 and 129 to get −717. −717x−7

Answer:

x=-1.29

Step-by-step explanation:

-717x-7=916

-717x=923

X=-1.29

NOTICE: THIS IS ROUNDED

The solution of the differential equation for the given initial conditions is x = e^-2t (-1/2 cos(3t) + sin(3t))

The equation of motion of the spring-mass-damper system is given by2x'' + 8x' + 26x = 0

            where x is the displacement of the mass from its equilibrium position, x' is the velocity of the mass, and x'' is the acceleration of the mass.

The characteristic equation for this differential equation is:

                          2r² + 8r + 26 = 0

Dividing by 2 gives:r² + 4r + 13 = 0

Solving this quadratic equation, we get the roots: r = -2 ± 3i

The general solution of the differential equation is:

                    x = e^-2t (c₁ cos(3t) + c₂ sin(3t))

where c₁ and c₂ are constants determined by the initial conditions.

Using the initial conditions x(0) = -1 m and x'(0) = 2 m/s,

we get:-1 = c₁cos(0) + c₂

              sin(0) = c₁c₁ + 3c₂ = -2c₁

              sin(0) + 3c₂cos(0) = 2c₂

Solving these equations for c₁ and c₂, we get: c₁ = -1/2c₂ = 1

Substituting these values into the general solution, we get:x = e^-2t (-1/2 cos(3t) + sin(3t))

The solution of the differential equation for the given initial conditions is x = e^-2t (-1/2 cos(3t) + sin(3t))

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Answer:

Using the Pythagorean Theorem we can see that:

\(9^2+40^2=1681\\\sqrt{1681}=41\)

Thus, x is 41.

The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.

According to the statement

we have given Following are the pairs of the complex number:

(1+2i)(8i),

(1 + 2i)(2 – 5i)

(1+2i)(1-2i) and (1+2i)(4i)

We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".

So, For this purpose

we have to multiply these pairs with each other.

So,

(1+2i)(8i) = 8i +16(i)^2

And

(1 + 2i)(2 – 5i) = 2 +4i - 5i +10(i)^2

And

(1+2i)(1-2i) = 1 -4(i)^2 -2i +2i = 1+4 = 5

And

(1+2i)(4i) = 4i + 6(i)^2

From these multiplication we found that the third pair have a real number product.

So, The third pair [(1+2i)(1-2i)] have a real number product and other pairs have complex number.

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The Power e is to which a number should be raised to get the specified number is called the logarithm of that specific number. For example, the logarithm to the base of 10 of 1000 is 3 because 10 raised to the power 3 is 1000.

The logarithmic function is the reverse of the Mathematical function of the exponential function. The logarithmic function is log ax = y is equal to x = ay.

There are mainly two types of logarithms normally used in Mathematics. They are one is common logarithms and second natural logarithms.

The log number ‘e’ is an irrational Mathematical constant and is mostly used as the base of natural logarithms. The number ‘e’ is the only unique number in mathematics whose value of natural logarithm is equal to unity.

The value of log ‘e’ was calculated in 1683 by Jacob Bernoulli.

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Complete question is;

The decibel level of sound is 50 dB greater on a busy street than in a quiet room where the intensity of sound is 10^-10 watt/m2. The level of sound in the quiet room is (10,20,100) dB, and the intensity of sound in the busy street is (10^-1, 10^-5, 10^-10) watt/m2.

Use the formula , β = 10log I/I 0 where β is the sound level in decibels, I is the intensity of sound you are measuring, and Io is the smallest sound intensity that can be heard by the human ear (roughly equal to 1 x 10^-12 watts/m2).

Answer:

A) The level of sound in the quiet room will be 20 dB

B) The intensity of sound in the busy street is 10⁻⁵ W·m⁻²

Step-by-step explanation:

Formula given is; β = 10log(I/I₀)

(a) For Quiet room:

We are given;

I = 10⁻¹⁰ W·m⁻²

I₀ = 1 × 10⁻¹² W·m⁻²

Plugging these values into the given equation, we have;

β = 10log[(10⁻¹⁰/(1 × 10⁻¹²)]

β = 10log(10²)

β = 10 × 2 = 20 dB

Thus, the level of sound in the quiet room will be 20 dB.

(b) For the Street;

We are given;

β(street) - β(room) = 50 dB

Now, let's rewrite the given intensity level equation;

β = 10logI - 10 logI₀

Now, Let the intensity level for the room be β₁ and let the intensity level for the road be β₂. Thus;

β₁ = 10logI₁ - 10log I₀ - - - - (eq 1)

β₂ = 10logI₂ - 10logI₀ - - - - (eq 2)

Subtract eq 1 from eq 2 to give;

β₂ - β₁ = 10logI₂ - 10logI₁

50 = 10logI₂ - 10log(10⁻¹⁰)

Divide each term by 10 to give:

5 = logI₂ - log(10⁻¹⁰)

5 = logI₂ - (-10)

5 = logI₂ + 10

Subtract 10 from each side to give;

-5 = logI₂

Taking the antilog of both sides to give;

I₂ = 10⁻⁵ W·m⁻²

Thus, the intensity of sound in the busy street is 10⁻⁵ W·m⁻².

Answer:

10⁻⁵ W·m⁻² THE ANSWER IS CORRECT

Step-by-step explanation:

Answer:

The sum is $10

Step-by-step explanation:

Since Tony got $5 on Monday and $5 on Tuesday, we can add them together by doing 5+5. We can add 5 and 5 together to get a total of $10 that Tony has earned. This means that it isn't a sum of 0 but a sum of 10.

(hope this helped)

Joseph's purple paint will be bluer because he used 64.3% blue paint (9 cups of blue paint divided by 14 cups of paint total) while Audrey used 62.5% blue paint (5 cups of blue paint divided by 8 cups of paint total).

There is a 0.5477 probability that a randomly selected customer will arrive less than 5 minutes after the previous customer during the 3 pm to 5 pm time period. (option a)

Given that the arrival rate of cars at the bank's drive-through window during the 3 pm to 5 pm time period is 15 customers per hour, we can calculate the average time between arrivals as follows:

Average time between arrivals = 1 / arrival rate

= 1 / 15

= 0.0667 hours (since there are 60 minutes in an hour, this is equivalent to 4 minutes)

Now, we need to find the probability of a customer arriving less than 5 minutes after the previous customer. Since the time between arrivals follows the exponential distribution, we can use the cumulative distribution function (CDF) of the exponential distribution to calculate this probability. The CDF gives us the probability of an event occurring within a certain time frame.

To find the probability of a customer arriving less than 5 minutes after the previous customer, we need to calculate the probability of an arrival occurring within a 5-minute time frame, which is equivalent to 0.0833 hours. So, we can substitute λ = 15 and x = 0.0833 in the formula for the CDF and get:

F(0.0833) = 1 - e¹⁵ˣ⁽⁻⁰°⁰⁸³³⁾

= 0.5477 (rounded to four decimal places)

Therefore, the answer is option (a) 0.5477.

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Answer:

\(\mbox{\large $0.5 + 0.16 \bar {3}$ = \boxed{\dfrac{199}{300}}}\)

Step-by-step explanation:

\(0.16\bar{3} = 0.16333333333\\\)

the 3 repeats until infinity

Let's multiply this by 100 to move the non-repeating part to the left of the decimal point

0.1633333333...... x 100 = 16.333333333333333...

.333333 = 1/3

Therefore the recurring number multiplied by 100 is
\(16 + \dfrac{1}{3} = \dfrac{16 \times 3 + 1}{3}=\dfrac{49}{3}\)

Since this fraction was arrived at by multiplying by 100, divide this fraction by 100 to get back the fraction in its original decimal value of 0.163333

\(\dfrac{49}{3} \div 100\)

To divide by a number, multiply by the reciprocal of that number

Reciprocal of 100 is 1/100:

\(\dfrac{49}{3} \div 100 = \dfrac{49}{3} \times \dfrac{1}{100} = \dfrac{49}{300}\)

(You can verify this by dividing 49 by 300 in a calculator and seeing that the result is 0.163333333333333333333 i.e. 0.16333 recurring

We want to add 0.5 to this.

0.5 = \(\dfrac{1}{2}\)

so
0.5 + 0.16333333 = 0.6633333

\(= \dfrac{1}{2} + \dfrac{49}{300}\)

We can write \(\dfrac{1}{2}\) as \(\dfrac{150}{300}\)  by multiplying numerator and denominator by 150

So we get

\(0.5 + 0.1633333 = \dfrac{150}{300} + \dfrac{49}{300} = \dfrac{150+49}{300} = \dfrac{199}{300}\)

If you perform this division on a calculator you will get the answer as 0.663333 = \(0.66\bar{3}\) which is what you get when you add 0.5 and \(0.16\bar{3}\)

Step-by-step explanation:

For this problem, we need to use the fact that the circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2.

This means the equation of the circle is (x-3)^2 + (y-1)^2 = 1.

The difference between the height (h) and the slant height (L) of the pyramid is that the height measures the vertical distance from the apex to the base, while the slant height measures the length along the surface of the pyramid from the apex to any point on the base's edge.

The height (h) of a pyramid refers to the perpendicular distance between its base and its apex. It is the vertical measurement from the highest point of the pyramid to the base. In the given context, the specific value of the height (h) is not provided, so we cannot determine its exact value.

On the other hand, the slant height (L) of a pyramid refers to the length of the line segment that connects the apex of the pyramid to any point on the edge of its base. The slant height is measured along the surface of the pyramid, forming an inclined line from the apex to the base. In this case, the slant height is given as 10.50 units.

Therefore, the difference between the height (h) and the slant height (L) of the pyramid is that the height measures the vertical distance from the apex to the base, while the slant height measures the length along the surface of the pyramid from the apex to any point on the base's edge.

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

The answer is Part B I think. I'm not fully sure, but it sounds much more logical in my opinion.

Step-by-step explanation:

Answer:

hi, first question's answer B.

because if you want to draw a triangle, there is have to be some rules. like can you draw a triangle 2,2,20? that could be impossible because all the edges have to intersect. think a triangle and it has 3 edges. they are A,B,C

if you wanna write random numbers, you have to do this.

A+B>C>|A-B|

A+C>B>|A-C|

C+B>A>|C-B|

soo, 7+11= 18 and 11-7=4

second question's answer is this:

60+x+32+90=180(if you wonder where is the 90 came from, the triangle's one side has square. that mean its 90°.

182+x=180

x=-2

if you have questions about these questions, you can ask me.

good luck(:

The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.

This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.

Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:

f(x) = −7x + 5

⇒ f′(x) = d/dx (−7x + 5)

⇒ f′(x) = d/dx (−7x) + d/dx(5)

⇒ f′(x) = −7(d/dx(x)) + 0

⇒ f′(x) = −7⋅1 = −7

Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7

Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

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The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Inequalities are used for the non equal comparison of numbers and variables.

Given the inequalities:

y ≥ (1/2)x - 1     (1)

and

x - y > 1     (2)

The graph of the inequality is attached. Shannon's graph is correct.

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Answer:

A and C

Step-by-step explanation:

3:6 Divide both sides by 3 => 1:2

3:6 multiply both sides by 4 => 12:24

Hey there!

"8x = 25"

In order for you to solve for "x-value" (or the equation) we have to DIVIDE both of your sides by 8

8x/8 = 25/8

Cancel out: 8x/8 because that gives you the value of 1 and you don't need it at the moment (in that equation that is)

Keep: 25/8 Because it solves for your equation

Your x equals: 25/8 aka 1 1/8 aka 3.125 (you could choose any one of these as your answer because they are all correct)

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

The average rate of change of an exponential function can be calculated by finding the difference in function values at the endpoints of the given interval and dividing it by the difference in the corresponding x-values.

In this case, since the table represents values of an exponential function, we'll use the formula for average rate of change to determine the value. Let's assume the table contains the following values: |  x  |  y  |
| --- | --- |
|  2  |  8  |
|  4  |  32 |

To calculate the average rate of change for the interval from x=2 to x=4, we first find the difference in y-values: 32 - 8 = 24. Next, we calculate the difference in x-values: 4 - 2 = 2. Finally, we divide the difference in y-values by the difference in x-values: 24 / 2 = 12. Therefore, the average rate of change for the given exponential function over the interval from x=2 to x=4 is 12. This means that, on average, the function is increasing by 12 units for every unit increase in x within the specified interval.

The average rate of change is a measure of how the output of a function changes on average over a given interval. For an exponential function, it can be determined by calculating the difference in function values at the endpoints of the interval and dividing it by the difference in the corresponding x-values . In this case, the average rate of change for the function represented by the given table is found to be 12, indicating an average increase of 12 units in the function's output for every unit increase in the input from x=2 to x=4.

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The correct option is option a) The critical value depends on the number of categories, not the sample size.

The critical value for a chi-square test is determined by the level of significance (alpha) and the degrees of freedom (df). The degree of freedom is a function of the number of categories in the test, not the sample size. Therefore, increasing the sample size does not affect the critical value for a chi-square test.

The chi-square test is a statistical test used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. It is used to test the independence of two categorical variables.

Therefore, The correct option is option a) critical value depends on the number of categories, not the sample size.

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To find the probability that a randomly selected store does not violate the institute's scanner accuracy standard, we need to determine the number of stores that comply with the standard and divide it by the total number of stores.

Given that there are 60 company stores and 53 of them violate the standard, we can subtract the number of stores that violate the standard from the total number of stores to find the number of stores that comply:

Number of stores that comply = Total number of stores - Number of stores that violate the standard

Number of stores that comply = 60 - 53

Number of stores that comply = 7

Therefore, there are 7 stores that do not violate the institute's scanner accuracy standard.

To calculate the probability, we divide the number of stores that comply by the total number of stores:

Probability = Number of stores that comply / Total number of stores

Probability = 7 / 60

Probability ≈ 0.1167

The probability that a randomly selected store does not violate the institute's scanner accuracy standard is approximately 0.1167 or 11.67%.

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Answer:

the greatest common factor of 10 and 70 is 10

Answer:

5

Step-by-step explanation:

have a good day

Answer:

Step-by-step explanation:

-23=-3X-8

Answer:

(x+6)(x-2)

Step-by-step explanation:

The correct answer is S = {A, D, D, I, T, I, O, N}.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The sample space is the set of all possible outcomes of an experiment or event.

In this case, the experiment is choosing one card from a set of eight labeled cards.

The sample space for this experiment is the set of all possible cards that can be chosen.

In the given problem, there are eight cards labeled A, D, D, I, T, I, O, N.

The sample space is the set of all possible cards that can be chosen, which is {A, D, D, I, T, I, O, N}.

This is because each card is distinct and can be chosen independently of the others.

Therefore, the correct answer is S = {A, D, D, I, T, I, O, N}.

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Answer: A( A,D, D,I, I,N,O,T)

Step-by-step explanation:

Order does not matter!!

In a competitive market, we need to graph the market demand and supply curves and determine the equilibrium quantity. The equilibrium quantity represents the quantity at which the demand and supply curves intersect.

To sketch the supply and demand curves, we first need to gather information on the market demand and supply. The demand curve represents the quantity of ventilators that the four hospitals are willing to purchase at different prices, while the supply curve represents the quantity of ventilators that the four producers are willing to sell at different prices.

Using the multipoint drawing tool, we can plot the market demand curve based on the data provided for the hospitals. Label this line as 'Demand'. Next, using the same tool, we can plot the market supply curve based on the data provided for the producers. Label this line as 'Supply'.

The equilibrium quantity is determined at the point where the demand and supply curves intersect. It represents the quantity of ventilators that will be sold in the market. To find this point, we identify the quantity at which the demand and supply curves meet on the graph.

By following the instructions and accurately plotting the demand and supply curves, we can determine the equilibrium quantity of ventilators sold in the market.

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Answer: The answer is B

Step-by-step explanation: Round 632 to 600 and 19 to 20 divided by 600 / 20Its choice B