n − 10 + 9n − 3 4) −4x − 10x

The constant average rate of change is the slope of the line which can be used to write the linear function.

What is a Data Table ?

A table of data is linear if there is a constant average rate of change between all pairs of points.

Testing for Linearity

Finding a Function from a Table that is Linear

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Answer:

x=7

Step-by-step explanation:

Since these angles are complementary, they will add up to 90 degrees, so you can set up the equation like so:

8x+5+3x+8=90

First, combine like terms:

(8x+3x)+(5+8)=90

11x+13=90

Then, subtract 13 from both sides:

11x+13(-13)=90(-13)

11x=77

Then divide both sides by 11:

11x(/11)=77(/11)

x=7

7 is your answer

hope this helps!

Answer:

x=7

Step-by-step explanation:

Said it in the last question you had.

Answer: You add up 12+12+18+18 and get 60

Step-by-step explanation:

The sampling technique used to obtain the described sample is A. Systematic sampling.

In systematic sampling, the elements of the population are ordered in some way, and then a starting point is randomly selected. From that point, every nth element is selected to be part of the sample.

In the given scenario, the first 35 students leaving the library were selected. This suggests that the students were ordered in some manner, and a systematic approach was used to select every nth student. Therefore, the sampling technique used is systematic sampling.

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Answer:

3 and 2 is 40 and 4 is 140

Step-by-step explanation:

in the comments

Answer:

measure of angle 4 is 140°

measure of angle 1 is 140° (given)

measure of angle 3 is 40°

measure of angle 2 is 40°

Step-by-step explanation:

We're given that one angle is equal to the measure of 140° (we'll make this one be angle 1)

because of vertical angles theorem, which states that angles that are opposite to each other and are formed by two intersecting lines will be congruent.

So that means that measure of angle 4 will also be 140°

Because of vertical angles theorem, that means that <3 is ≅ to <2 (we can make them be x)

The sum of all the angles will equal to 360° (since it's a full angle)

Here's the equation:

140+140+x+x=360

simplify

280+2x=360

2x=80

x=40°

Which means that <3 and <2 both equal 40°

Hope this helps!

Answer:

25

Step-by-step explanation:

hope this helps :) <3

Answer:

2/-9

Step-by-step explanation:

Answer:

Amber ran 8,333 kilometers during each hour, and the equation to determine that amount is 25/3 = X.

Step-by-step explanation:

Given that Amber ran a 25 kilometer road race in 3 hours, and she ran at the same speed and covered the same distance each hour, to draw a visual model to find the distance Amber ran each hour the following calculation must be performed:

25/3 = X

8.333 = X

So Amber ran 8,333 kilometers during each hour, and the equation to determine that amount is 25/3 = X.

Answer:

Answer = D

Step-by-step explanation:

If you add all of the heights up you get 480. divide that by ten (because there were 10 students whose height was taken) then you get 48. therefore, the typical second-grade student is about 48 inches tall.

I hope this helps have a good day :)

The typical second-grade student is about 48 inches tall.

'Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.'

According to the given problem,

Given data = { 44, 45, 47, 49, 48, 48, 49, 50, 48, 52 }

Sum of the given data = 44 + 45 + 47 + 49 + 48 + 48 + 49 + 50 + 48 + 52

                                     = 480

Average of the given heights = \(\frac{480}{10}\)

                                                 = 48

Hence, we can conclude,  The typical second-grade student is about 48 inches tall since the average of the given data is 48.

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Answer:

You can find the x-intercept and y-intercept by looking at the origin (0,0). There you will see x and y point at zero.

Step-by-step explanation:

Hope this Helped

Answer:

x=22

Step-by-step explanation:

set all of your values equal to 360 (bc thats the value of the degrees in a circle) and then solve for x!

75 + 92 + ( x+57 ) + ( x+92) = 360

( x+57 ) + ( x+92 ) = 201

2 x = 44

x = 22

Her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h

Let's assume that the total distance of the round trip is d kilometers and that she drove at a constant speed of v km/h for the entire trip. The time it takes for her to travel the entire distance at speed v is given by t = d/v.

Since she drove back home using the same path she took out to the university, her average speed for the entire trip must be equal to her speed on the way out and back. Therefore, the total time it took for her to complete the round trip is 2t = 2d/v.

Since the total time it took for her to complete the round trip is 7.1 hours, we can set up an equation:

2d/v = 7.1 hours

Converting hours to seconds and solving for v, we have:

v = 2d / (7.1 * 3600) km/s

Finally, converting to km/h, we get:

v = 2d / (7.1 * 3600) * 3600 km/h

Therefore, her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h

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Answer:

40 units^2

Step-by-step explanation:

Answer:

105, C

Step-by-step explanation:

16x + 1 + 40 = 27x - 3

This is because 180 - (27x - 3) = the missing angle in the triangle shown

16x + 1 + 40 = 27x - 3

1+ 40 = 41

16x + 41 = 27x - 3

        +3            +3

16x + 44 = 27x

-16x           -16x

44 = 11x

44/11 = x

x = 4

27x - 3 is equal to 27(4) - 3 = 108 - 3 = 105

Ans = 105

Answer:

  3

Step-by-step explanation:

Given that installing 6 apps increases the Eric : Ian app ratio from 3:4 to 5:4, you want to know how many more apps Ian needs to install to have the same number as Eric.

We note that the number of apps representing Ian's apps remains at 4 in both ratios, but increasing Eric's apps by 6 changes his number of ratio units from 3 to 5, a change of 2 ratio units. That is, each ratio unit represents 3 apps.

Eric now has 1 more ratio unit (5) than Ian (4), so Ian needs to increase his number by 1 ratio unit, or 3 apps.

Ian must install 3 apps to have the same number as Eric.

__

Additional comment

To see how many actual apps we're talking about, multiply the ratios by 3. The initial Eric : Ian app ratio was 9 : 12. After Eric installed 6, it became (9+6) : 12 = 15 : 12. So, Ian needs to install 15-12 = 3 apps to have as many as Eric.

Answer:

24

Step-by-step explanation:

Okay, let's solve this step-by-step:

1) We are given: a = -8, b = 2, c = 7, d = 11

2) We are asked to solve the matrix equation: [[x + y, z], [z - x, w - y]] = [[a, b], [c, d]]

3) Matching up the elements in the matrices:

x + y = a = -8 (1)

z = b = 2 (2)

z - x = c = 7 (3)

w - y = d = 11 (4)

4) Solving the equations:

From (1): x + y = -8 => x = -8 - y

Substitute in (3): z - (-8 - y) = 7 => z - (-8) = 7 + y => z = 15 + y

Substitute (2) into the above: 2 = 15 + y => y = 13

Substitute y = 13 into (1): -8 - 13 = -21 = x

Substitute x = -21 and y = 13 into (4): w - 13 = 11 => w = 11 + 13 = 24

Therefore, the values are:

x = -21

y = 13

z = 15

w = 24

So the final value of w is:

w = 24

Answer:

magnitude = -87

direction = 53.50°

Step-by-step explanation:

magnitude is the distance between the initial point and the end point,

magnitude = -50 - 37 = -87

direction, tan ∅ = y / x

tan ∅ = -50/37

∅ = tan¬ -50 / 37

where¬ symbol stands for tan inverse

∅ = -53.50

thus direction = 53.50°

The entropy change per mole for a Joule expansion is given by ΔS° = 8.31 J/(mol K) * ln(V₂/V₁)

The formula for entropy change per mole is given by:

ΔS° = R ln(V₂/V₁)

where; R is the gas constant (8.31 J/mol K) V1 and V2 is the initial and final volume respectively.

Now, Joule expansion is a process in thermodynamics whereby a gas is allowed to expand freely without doing work on the surroundings, this is an isenthalpic process, and the enthalpy is given by

H = U + PV

where; U is the internal energy of the gas, P is the pressure, V is the volume.

For this process, ΔH = 0 (Enthalpy change is zero), and since ΔH = ΔU + PΔV,

ΔU = -PΔV

Hence, ΔU = 0, and ΔV is not equal to zero, thus ΔS° = R ln(V₂/V₁) = 8.31 J/mol K * ln(V₂/V₁)

Therefore, the entropy change per mole for a Joule expansion is given by ΔS° = 8.31 J/(mol K) * ln(V₂/V₁)

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The hydronium ion concentration (H₃O⁺) of a fruit juice with a pH of 3.4 can be calculated using the pH formula. The hydronium ion concentration is approximately 4.0 x 10⁻⁴ M.

The pH is a logarithmic scale that measures the acidity or alkalinity of a solution. It is defined as the negative logarithm (base 10) of the hydronium ion concentration. The pH formula is given by pH = -log[H₃O⁺], where [H₃O⁺] represents the hydronium ion concentration.
To find the hydronium ion concentrationThe, we can rearrange the pH formula as [H₃O⁺] = 10^(-pH). Substituting the given pH value of 3.4 into the formula, we have [H₃O⁺] = 10^(-3.4).
Evaluating this expression, we find that the hydronium ion concentration of the fruit juice is approximately 4.0 x 10⁻⁴ M. This means that in every liter of the juice, there are approximately 4.0 x 10⁻⁴ moles of hydronium ions present.

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a) Marathon Incorporated can deduct $0 of the dividend payment in determining its taxable income. b)  Guy will pay $4,070 in tax on the $11,000 dividend he received. c) Little Rock Corporation will pay $0 in tax on the $33,000 dividend it received from Marathon Incorporated.

a) Marathon Incorporated can deduct $0 of the dividend payment in determining its taxable income. This is because the dividends distributed to shareholders are not deductible expenses for the corporation. Dividends are paid out of after-tax profits and are not considered a deductible expense for the distributing corporation.

b) Guy will pay $4,070 in tax on the $11,000 dividend he received from Marathon Incorporated, including the net investment income tax. To calculate the tax, we need to consider Guy's marginal ordinary tax rate and the net investment income tax. Assuming Guy's marginal ordinary tax rate is 37 percent, the tax on the dividend would be $4,070 (0.37 * $11,000). The net investment income tax is an additional 3.8 percent tax on investment income for individuals with certain income thresholds, so it would also apply to the dividend income received by Guy.

c) Little Rock Corporation will pay $0 in tax on the $33,000 dividend it received from Marathon Incorporated. This is because C corporations are eligible for a 50 percent dividends-received deduction. The dividends-received deduction allows corporations to exclude 50 percent of the dividends received from taxable income. In this case, Little Rock Corporation would be able to exclude $16,500 (50 percent of $33,000) from its taxable income, resulting in a tax liability of $0 on the dividend income.

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4.1 The tariff for electricity consumption is R2.55 per kilowatt-hour (kWh).

4.2 The cost of electricity for 80 kWh is R204

4.3 One way of saving electricity is by ensuring energy-efficient practices such as putting off lights, electronics, and appliances when not in use and using LED or other energy-efficient light bulbs.

4.4.1 The oven uses 1.5 kilowatts of electricity per hour.

4.4.2 The amount of money left on the meter after baking for 4 hours is  R39.70.

4.2 To calculate the cost of electricity for 80 kWh, we shall use the formula:

Cost = R2,55 x number of kWh of electricity used:

Cost = R2,55 x 80

= R204

Therefore, the cost of electricity for 80 kWh is R204.

4.4.1 We calculate the kilowatts (kW) of electricity the oven uses per hour, by converting the watts to kilowatts.

1 kilowatt (kW) = 1000 watts

Oven uses 1500 watts each hour, so we convert:

1500 watts = 1500/1000 = 1.5 kilowatts (kW)

So, the oven uses 1.5 kilowatts of electricity per hour.

4.4.2 If Mary has R55,00 worth of electricity and bakes for 4 hours, we compute the cost of electricity used during baking.

Cost of electricity used for baking = Cost per kWh x number of kWh used

= R2,55 x (1.5 kW x 4 hours)

= R2,55 x 6 kWh

= R15.30

Next, we estimate the amount of money left on the meter after baking:

Amount left on meter = Initial amount - Cost of electricity used

= R55.00 - R15.30

= R39.70

Hence, Mary will have R39.70 left on the meter after baking for 4 hours.

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To find \(\( f'(x) \)\) using the definition of the derivative, we have:

\(\[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \]\)

Given that \(\( f(x) = x + \frac{1}{x} \)\) , let's substitute this into the definition:

\(\[ f'(x) = \lim_{h \to 0} \frac{(x+h) + \frac{1}{x+h} - (x + \frac{1}{x})}{h} \]\)

Simplifying the numerator, we get:

\(\[ f'(x) = \lim_{h \to 0} \frac{x + h + \frac{1}{x+h} - x - \frac{1}{x}}{h} \]\)

Combining like terms in the numerator, we have:

\(\[ f'(x) = \lim_{h \to 0} \frac{h + \frac{1}{x+h} - \frac{1}{x}}{h} \]\)

Now, let's find a common denominator for the fractions:

\(\[ f'(x) = \lim_{h \to 0} \frac{hx(x+h) + (x+h) - hx}{hx(x+h)} \]\)

Simplifying further, we get:

\(\[ f'(x) = \lim_{h \to 0} \frac{hx^2 + hx^2 + hx^2 + h^2x + x^2 + hx - hx}{hx(x+h)} \]\)

Combining like terms, we obtain:

\(\[ f'(x) = \lim_{h \to 0} \frac{2hx^2 + h^2x + x^2}{hx(x+h)} \]\)

Factoring out an \(\( h \)\) from the numerator, we have:

\(\[ f'(x) = \lim_{h \to 0} \frac{h(2x^2 + hx + x^2)}{hx(x+h)} \]\)

Canceling out the \(\( h \)\) terms, we get:

\(\[ f'(x) = \lim_{h \to 0} \frac{2x^2 + hx + x^2}{x(x+h)} \]\)

Simplifying further, we have:

\(\[ f'(x) = \lim_{h \to 0} \frac{3x^2 + hx}{x(x+h)} \]\)

Taking the limit as \(\( h \)\) approaches 0, we obtain:

\(\[ f'(x) = \frac{3x^2}{x^2} \]\)

Simplifying, we find:

\(\[ f'(x) = 3 \]\)

Therefore, the derivative of  \(\( f(x) = x + \frac{1}{x} \) is \( f'(x) = 3 \).\)

Now, let's specify the domains of \(\( f(x) \) and \( f'(x) \)\). The function \(\( f(x) = x + \frac{1}{x} \)\) is defined for all \(\( x \neq 0 \)\), since division by 0 is undefined. Therefore, the domain of \(\( f(x) \) is \( (-\infty, 0) \cup (0, \infty) \)\).

The derivative \(\( f'(x) = 3 \)\)  is a constant function, which means it is defined for all real numbers. Therefore, the domain of \(\( f'(x) \) is \( (-\infty, \infty) \).\)

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All of the given options are generally correct regarding the considerations for Maximum Time Frame calculations.

Let's break down each option:

a. If you take an Incomplete or Withdrawal, this will not be included: In most cases, if you receive an Incomplete or withdraw from a course, the units for that particular course will not be included in the calculation for Maximum Time Frame.

b. F grades won't count toward your Max Time Frame: Usually, failing grades (F) are not counted towards the Maximum Time Frame calculation since they do not contribute to earned credits.

c. When you withdraw from a class, it's taken out of the calculation for Max Time Frame: Generally, when you withdraw from a class, the units for that class are not considered in the calculation for Maximum Time Frame.

d. If you drop a class before the drop/add deadline, it will not show up as an attempted class: Typically, if you drop a class before the drop/add deadline, it will not be considered as an attempted class and therefore will not be included in the Maximum Time Frame calculation.

However, it's important to note that policies regarding Maximum Time Frame calculations may vary among educational institutions. It's always advisable to consult your institution's specific policies or contact the appropriate academic advisors for accurate information regarding Maximum Time Frame calculations at your institution.

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Check the picture below.

The orthocenter of a triangle is the point at which the perpendicular lines drawn from the vertices to the opposite sides of the triangle intersect. The coordinates of the orthocenter of ΔJKL is (5, -1).

The orthocenter of a triangle is the point at which the perpendicular lines drawn from the vertices to the opposite sides of the triangle intersect. The orthocenter of an acute angle triangle is located within the triangle. The orthocenter of the obtuse angle triangle is located outside the triangle.

The slope of JK is (6+2)/(5-3) or 4.

So, the slope of the altitude, which is perpendicular to JK is -1/4.

Now, the equation of the altitude from L to JK is:

y + 2 = -1/4 (x - 9)

y = -1/4x + 1/4

Use the same method to find the equation of the altitude from J to KL. That is, y + 2 = 1/2 (x - 3) or y = 1/2x - 7/2.

Solve the equations to find the intersection point of the altitudes.

-1/4x + 1/4 = 1/2x - 7/2

simplifying the above equation, we get

-1/4x - 1/2x = - 7/2 - 1/4

-3/4x = - 15/4

x = 5

y = -1/4(5) + (1/4)

simplifying the above equation, we get

= -4/4

y = -1

Therefore, the coordinates of the orthocenter of ΔJKL is (5, -1).

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a) The logistic equation for this problem is L dP/dt = P(1 - P/L), where L = 2000 and Po = 100.

b)  The maximum reproduction rate is 0.03465 times the current population.

a. The logistic equation for this problem is:

L dP/dt = P(1 - P/L)

where L is the carrying capacity of the lake, P is the current population, and dP/dt is the rate of change of the population over time.

We know that at t = 0, P = 100, and one year later at t = 1, P = 200. So we can use this information to find k, which is the growth rate coefficient:

P(t) = L / (1 + (L / Po - 1) * exp(-kt))

200 = L / (1 + (L / 100 - 1) * exp(-k))

200 = L / (1 + (L - 100) * exp(-k))

200 + 200L - 20000 = L * (1 + (L - 100) * exp(-k))

200L -\(L^2\) * exp(-k) + 200L * exp(-k) - 10000 * exp(-k) = 0

\(L^2\) - 400L + 5000 = (L - 200)^2 - 30000

\((L - 200)^2\) = 35000

L = 200 + sqrt(35000) ≈ 223.6

So L ≈ 223.6, and we can use this to find k:

2000 = 223.6 / (1 + (223.6 / 100 - 1) * exp(-k))

20000 + 2000L - 2236 = L * (1 + (L - 100) * exp(-k))

2236 - \(L^2\)  * exp(-k) + 2236 * exp(-k) - 100 * exp(-k) = 0

\(L^2\) - 4472L + 220000 = 0

(L - 2000)(L - 100) = 0

So either L = 2000 or L = 100. We know that L ≠ 100, since we know that the population stabilizes at 2000 after a long time. Therefore, L = 2000, and we can solve for k:

k = -ln((L / Po - 1) / (1 + (L / Po - 1))) / t

k = -ln((2000 / 100 - 1) / (1 + (2000 / 100 - 1))) / 1

k ≈ 0.0693

Therefore, the logistic equation for this problem is:

L dP/dt = P(1 - P/L)

dP/dt = 0.0693P(1 - P/2000)

b. The maximum reproduction rate occurs when the population is halfway to the carrying capacity, or P = L/2. At this point, the equation becomes:

dP/dt = 0.0693P(1 - 0.5)

dP/dt = 0.03465P

Therefore, the maximum reproduction rate is 0.03465 times the current population. For example, if the current population is 1000, the maximum reproduction rate is 34.65 fish per year.

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Full Question : Logistic Equation: L dP dt P(1-2). P() = L - Po Po 1+ 4e ki Where A 1. Fish population in a lake grows according to the logistic law. The initial population of 100 fish and year later it was 200. After a long time fish population stabilized at 2000.

a. Write down the logistic equation for this problem.

b. What is the maximum reproduction rate (fish/year)?

Answer:

80

Step-by-step explanation:

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