Find a linear equation whose graph has the indicated slope and passes through the given point. slope 3, point (−5,2) The equation of the line is y= (Simplify your answer. Type an expression using x as the variable.)

Using the slope formula, we can conclude that the slope of the line is m = 2.

So, the slope of the line is:

Now, put the values and solve for the slope as follows:

Therefore, using the slope formula, we can conclude that the slope of the line is m = 2.

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See this attachment

In the experiment, the independent variable is the amount of sunlight received by the clover plants.

The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.

The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.

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Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

From a class of 20 students, there are 6,840 ways to select a committee consisting of a president, vice-president, and secretary. This calculation is based on the concept of permutations, where the number of choices at each step is multiplied to find the total number of possibilities.

To determine the number of ways to select a committee consisting of a president, vice-president, and secretary from a class of 20 students, we can use the concept of permutations.

The president position can be filled by selecting one student from the 20 available. After the president is selected, the vice-president position can be filled by choosing one student from the remaining 19 students. Finally, the secretary position can be filled by selecting one student from the remaining 18 students.

The number of ways to make these selections is calculated by multiplying the number of choices at each step:

Number of ways = 20 * 19 * 18 = 6,840

Therefore, there are 6,840 ways to form the committee with a president, vice-president, and secretary from a class of 20 students.

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The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

so 3 guys can do the whole work in 8 days, that means that for one day the same 3 guys are doing (1/8)th of the whole work, let's divide that 1/8 by 3 to see how much each guy does rate wise

\(\stackrel{ \begin{array}{llll} \textit{fraction of}\\ \textit{the whole done}\\ \textit{by all 3} \end{array} }{\cfrac{1}{8}} \div \stackrel{ workers }{3}\implies \cfrac{1}{8}\cdot \cfrac{1}{3}\implies \cfrac{1}{24}\impliedby \begin{array}{llll} \textit{fraction done}\\ \textit{by just 1 worker} \end{array}\)

now, we know is 1/8 th because the whole thing took 8 days, so for 1 day is just 1/8 of 8, and now we know each worker is really doing 1/24 th per day of the whole thing.

now, let's add another worker, who is going to be going at the same speed as the other 3 guys, or 1/24 of the work, so the work will take "t" days total, so in 1 day all those 4 guys will be doing only (1/t)th of the whole thing, so

\(\stackrel{ \textit{rate for 4 workers} }{\cfrac{1}{24}+\cfrac{1}{24}+\cfrac{1}{24}+\cfrac{1}{24}}~~ = ~~\stackrel{ \textit{fraction of total} }{\cfrac{1}{t}} \\\\\\ \cfrac{4}{24}=\cfrac{1}{t}\implies \cfrac{1}{6}=\cfrac{1}{t}\implies t=6 ~~ days\)

Answer:

6

Step-by-step explanation:

Entry Q23 is the value in the second row, third column, 6

The equation in point slope form is y - 6 = 2(x + 3)

This is from the general point slope template of \(y - y_1 = m(x - x_1)\)

The m is the slope, which in this case is m = 2. The \((x_1,y_1)\) is the point the line goes through. In this case, \(x_1 = -3 \text{ and } y_1 = 6\)

If you were to solve that equation in bold for y, then you should get y = 2x+12 which is now in y = mx+b form, aka slope intercept form.

Answer:

7y+r+8x+94

Explanation

Given the algebraic expression 7(y+2) + (8+r) + 8(x + 9)

Given A, B and C. According to distributive law;

A(B+C) = AB + AC

A is distributed over C. In the same vein

On expanding the expression;

7(y+2) + (8+r) + 8(x + 9)

7y+7(2) + 8 + r + 8(x)+ 8(9)

7y+14+8+r+8x+72

Bringing the variables and constants together

7y+r+8x+14+8+72

7y+r+8x+94

The graph of the equation x^2/49 + (y + 1)^2/4 = 1 is added as an attachment

The expression that represents the function in words is given as

StartFraction x squared Over 49 EndFraction + StartFraction (y + 1) squared Over 4 EndFraction = 1

Express the equation properly

So, we have

x^2/49 + (y + 1)^2/4 = 1

The above equation is an ellipse

Next, we plot the graph on a coordinate plane using a graphing tool

See attachment for the graph of the equation

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Answer:

he needs 9 cans

Step-by-step explanation:

first,

43L/5L

= 8.6 cans

8.6 cans is not logical therefore u need to round up to 9 cans

1. R= {(2, 2), (3, 5), (4, 10), (4, 17)}

2. Domain = {1, 2, 3, 4}

3.  Range = {2, 3, 4, 5, 10, 17}

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

Given:

R = { ( 1 + x , 1 + x^2 ) ∶ x≤ 4, ∈ }

1) R= {(2, 2), (3, 5), (4, 10), (4, 17)}

2) Domain = {1, 2, 3, 4}

3) Range = {2, 3, 4, 5, 10, 17}

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The evaluated result of the given number is 1/625 and not the 840 Thus the evaluated value of the Rashad is not correct, because he multiplied the exponent by the base.

Power rule of exponents states that, when the two numbers with same base are multiplied then the exponents of both the numbers added.

Positive power of the negative number gives the positive result.

Given information-

The number which is evaluated by the Rashad is,

\((\dfrac{-2}{10})^4\)

Let the evaluated result of the number is n. Thus,

\(n=(\dfrac{-2}{10})^4\)

As the power is out of the bracket. This indicates that the power is for both numerator and denominator. Thus,

\(n=\dfrac{(-2)^4}{10^4}\)

Positive power of the negative number gives the positive result. Thus the above equation can be written as,

\(n=\dfrac{2\times2\times2\times2}{10\times10\times10\times10}\)

\(n=\dfrac{1}{625}\)

As the evaluated result of the given number is 1/625 and not the 840 Thus the evaluated value of the Rashad is not correct, because he multiplied the exponent by the base.

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Answer:

No, he multiplied the exponent by the base.

Step-by-step explanation:

Answer:

A: Adjacent and vertical.

Step-by-step explanation:

When two lines intersect, vertical angles are the angles that are opposite (you can see the draw at the end) such that these two angles are only connected by the intersection point.

And two angles are adjacent if these angles are separated by one of the lines.

Then two angles can't be adjacent and vertical at the same time.

Because if two angles are adjacent, then these angles are separated by one of the lines, thus these angles can't be opposite, concluding that these angles can't be vertical angles.

And if two angles are vertical, the only "contact" point between these angles is the intersection point, then these angles can't be divided by one of the lines, then these angles can't be adjacent angles.

Then the correct option is A: adjacent and vertical.

Answer: yes

Step-by-step explanation:

It is because for every x value there is a y and the x value does not repeat to any y values.

Answer:

No because the slope isnt constant, the y changes higher and higher while the x stays constant

Step-by-step explanation:

Hope this helps!:)

The conjecture "A square number is either measurable by 4 or will be after the removal of a unit" is true. If a number is a perfect square, it can be expressed as either 4k or 4k+1 for some integer k.

However, if 4 is replaced by 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3.

To prove the conjecture that a square number is either divisible by 4 or will be after subtracting 1, we can consider two cases:

Case 1: Let's assume the square number is of the form 4k. In this case, the number is divisible by 4.

Case 2: Let's assume the square number is of the form 4k+1. In this case, if we subtract 1, we get 4k, which is divisible by 4.

Therefore, in both cases, the conjecture holds true.

However, if we replace 4 with 3 in the conjecture, it is no longer valid. Counterexamples can be found where square numbers are not necessarily divisible by 3. For example, consider the square of 5, which is 25. This number is not divisible by 3. Similarly, the square of 2 is 4, which is also not divisible by 3. Hence, the conjecture does not hold when 4 is replaced by 3.

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The table of values that represents exponential decay is (c)

From the question, we have the following parameters that can be used in our computation:

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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Answer:

C is the correct answer

\(f(x) = 4tan(8\pi) + 4sec^2(8\pi)(x - 8\pi) + 8sec^2(8\pi)tan(8\pi)(x - 8\pi)^2/2!\)

This expression represents the first three nonzero terms of the Taylor series expansion for f(x) = 4tan(x) centered at c = 8π.

What is the trigonometric ratio?

the trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

To find the first three nonzero terms of the Taylor series for the function f(x) = 4tan(x) centered at c = 8π, we can use the definition of the Taylor series expansion.

The general formula for the Taylor series expansion of a function f(x) centered at c is:

\(f(x) = f(c) + f'(c)(x - c)/1! + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...\)

Let's begin by calculating the first three nonzero terms for the given function.

Step 1: Evaluate f(c):

f(8π) = 4tan(8π)

Step 2: Calculate f'(x):

f'(x) = d/dx(4tan(x))

= 4sec²(x)

Step 3: Evaluate f'(c):

f'(8π) = 4sec²(8π)

Step 4: Calculate f''(x):

f''(x) = d/dx(4sec²(x))

= 8sec²(x)tan(x)

Step 5: Evaluate f''(c):

f''(8π) = 8sec²(8π)tan(8π)

Step 6: Calculate f'''(x):

f'''(x) = d/dx(8sec²(x)tan(x))

= 8sec⁴(x) + 16sec²(x)tan²(x)

Step 7: Evaluate f'''(c):

f'''(8π) = 8sec⁴(8π) + 16sec²(8π)tan²(8π)

Now we can write the first three nonzero terms of the Taylor series expansion for f(x) centered at c = 8π:

f(x) ≈ f(8π) + f'(8π)(x - 8π)/1! + f''(8π)(x - 8π)²/2!

Simplifying further,

Hence, \(f(x) = 4tan(8\pi) + 4sec^2(8\pi)(x - 8\pi) + 8sec^2(8\pi)tan(8\pi)(x - 8\pi)^2/2!\)

This expression represents the first three nonzero terms of the Taylor series expansion for f(x) = 4tan(x) centered at c = 8π.

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Answer:

Independence and Exclusiveness are two topics which are important to probability and often confused. Discuss the difference between two events being independent and two events being mutually exclusive. Use examples to demonstrate the difference. Remember to explain as if you are talking to someone who knows nothing about the topic.

[my response: talk to them in formal language about the topic.]

Step-by-step explanation:

Answer:

x = 10

Explanation:

Using Pythagoras Theorem:

Solve:

8² + 6² = x²

x² = 64 + 36

x² = 100

x = √100

x = 10

10

Pythagoras theorem

(a² + b² = c²)

Let ,

a = 8

b = 6

c = x

Using Pythagoras theorem,

=> 8² + 6² = x²

=> x² = 64 + 36

=> x² = 100

=> x = √100

=> x = 10

Hence, the length of x is 10.

No, there is significant difference in the use of e readers by different age groups.

Given sample 1 ( 29 years old) \(n_{1}\)=628, \(p_{1}\)=7%, sample 2( 30 years old)\(n_{2}\)=2309, \(p_{2}\)=0.11.

We have to first form hypothesis one null hypothesis and other alternate hypothesis.

\(H_{0}:\)π1-π2=0

\(H_{1}:\)π1-π2≠0

α=0.05

Difference between proportions \(p_{1}-p_{2} =-0.04\)

\(p_{d}=0.07-0.11=-0.04\)

The pooled proportion needed to calculate standard error is:

\(p=(X_{1} -X_{2} )/(n_{1} +n_{2} )\)

=(44+254)/(628+2309)

=0.10146

The estimated standard error of difference between means is computed using the formula:

\(S_{p_{1} -p_{2} }=\sqrt{p(1-p)/m_{1}+p(1-p)/n_{2} }\)

=\(\sqrt{0.101*0.899/628+0.101*0.899/2309}\)

=\(\sqrt{0.000143+0.00003}\)

=\(\sqrt{0.000173}\)

=0.01315

Z= Pd-(π1-π2)/\(S_{p_{1} -p_{2} }\)

=-0.04-0/0.013

=-3.0769

This test is a two tailed test so the p value for this test is calculated as (using z table)

p value:2 P(Z<-3.0769)

=2*0.002092

=0.004189

P value< significance level of 5%.

Hence there is enough evidence to show the claim that there is a significant difference in the use of e readers by different age groups.

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Question is incomplete as it also includes:

Significance level of 5%.

The Reagan doctrine of American activism in the Third World was most particularly exercised in Nicaragua and Grenada. These countries became focal points of U.S. involvement and intervention.

The Reagan doctrine, implemented during the presidency of Ronald Reagan in the 1980s, aimed to counter Soviet influence and promote American interests in the Third World. This doctrine was characterized by a strong anti-communist stance and support for anti-communist governments and movements. Among the various countries where the Reagan doctrine was applied, Nicaragua and Grenada stand out as prime examples.

In Nicaragua, the Reagan administration actively supported the Contras, a rebel group fighting against the Sandinista government. The Contras were seen as a counterforce to the left-wing Sandinistas, who were aligned with the Soviet Union and Cuba. The United States provided financial and military assistance to the Contras, including covert operations, in an effort to undermine the Sandinista regime.

Grenada, a small island nation in the Caribbean, also witnessed American intervention under the Reagan doctrine. The United States launched Operation Urgent Fury, invading Grenada and overthrowing the government, with the stated objective of protecting American citizens and restoring democracy.

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The investment of $100 made today and an additional $100 invested at the end of 5 years, with an annual simple interest rate of 6%, will be worth $172 at the end of 10 years.

To calculate the worth of the investment at the end of 10 years, we can break it down into two periods: the initial investment from year 0 to year 5 and the subsequent investment from year 5 to year 10.

For the initial investment of $100, it will grow at a simple interest rate of 6% per year for 5 years. The formula for calculating the future value of a simple interest investment is FV = PV * (1 + r * t), where FV is the future value, PV is the present value, r is the interest rate, and t is the time in years. Applying this formula, we have FV = $100 * (1 + 0.06 * 5) = $130.

For the additional investment of $100 made at the end of 5 years, it will also grow at a simple interest rate of 6% per year for the remaining 5 years. Using the same formula, we have FV = $100 * (1 + 0.06 * 5) = $130.

Adding the two future values together, we get $130 + $130 = $260. Therefore, the investment will be worth $260 at the end of 10 years.

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:\(\implies\) perimeter (∆HFM) = HM+FM+HF

:\(\implies\) 51 = 2x+5+x+8+3x+2

:\(\implies\) 51 = 6x+15

:\(\implies\) 36 = 6x

:\(\implies\) x = 6 units.

in ∆HFM,

in ∆KFM,

Since, all the sides of one triangle does not correspond to the other, these traingles are not congruent.

Using Complete the Square method, we find out that \(x^{2} -5x+8\) can be expressed in the form of \((x-a)^{2}+b\) as \((x-\frac{5}{2}) ^{2} +\frac{7}{4}\) where a and b are top-heavy fractions.

It is given to us that the expression is -

\(x^{2} -5x+8\) ----(1)

We have to express it in the form of\((x-a)^{2}+b\) where a and b are top-heavy fractions.

In order to achieve the required expression in the form of  \((x-a)^{2}+b\) we have to use "Completing the Square" method.

The given expression from (1) is -

\(x^{2} -5x+8\)

This expression is in the form of \(ax^{2} +bx+c\)

Adding and subtracting \((b/2)^{2}\) terms into the expression, we get

\(x^{2} -5x+[\frac{5}{2}] ^{2}-[\frac{5}{2}] ^{2}+8\) -----(2)

Equation (2) can also be represented as -

\((x-\frac{5}{2}) ^{2} -[\frac{5}{2}] ^{2} +8\)

\(= > (x-\frac{5}{2}) ^{2} -\frac{25}{4} +8\\= > (x-\frac{5}{2}) ^{2} +\frac{7}{4}\)------- (3)

We see that equation (3) is in the form of \((x-a)^{2}+b\).

So, we can derive that -

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

and, \(b=\frac{7}{4}\).

Thus, \(x^{2} -5x+8\) can be expressed in the form of \((x-a)^{2}+b\) through "Complete the Square" method as \((x-\frac{5}{2}) ^{2} +\frac{7}{4}\) where a and b are top-heavy fractions.

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Answer:

b = 79°

Step-by-step explanation:

∠ b and 79° are alternate exterior angles and are congruent, thus

∠ b = 79°