What is the slope of the line represented by the equation y = y equals StartFraction 4 Over 5 EndFraction x minus 3.x – 3?

-3
-4/5
4/5
3

a = -2 is the value of linear equation .

What are examples of linear equations?

Step 1 - Write the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 2 - rewrite the equation.

3/a + 2 - 6a/a² - 4 = 1/a - 2

Step 3 - Take the LCM.

3(a- 2) - ( a + 2 )/a² - 2² = 6a/a²-4

Step 4 - Further simplify the above expression

3a - 6 - a - 2/a² - 4 = 6a/a² - 4

Step 5 - Cancel out the denominator of both sides and then further simplify.

2a - 8 = 6a

a = -2

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The complete question is -

A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.

3/a + 2 − 6a/a2 − 4 = 1/a − 2

Answer:

Tn = a + (n - 1) d

where a = first term

n = number of the member of the sequence

d = common difference

a = -16

n = 96

d = second term - first term or

third term - second term

= -28 - (-16) = -28 + 16 = -12 or

= -40 - (-28) = -40 + 28 = -12

d = -12

Tn = a + (n - 1) d

= -16 + (96 - 1) -12

= -16 + (95) -12

= -16 + (-1140)

= -16 - 1140 = -1156

The probability that the team wins a game is given as follows:

0.53 = 53%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The percentages for wins in this problem are given as follows:

Hence the probability that the team wins a game is given as follows:

p = 0.75 x 0.6 + 0.2 x 0.4

p = 0.53 = 53%.

The complete problem is:

During one season, a high school baseball team leads at the end of the fifth inning in 60% of the games. the team wins 75% of the time when they have the lead after 5 innings, but only 20% of the time when they do not. What is the probability that a team wins a single game.

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A randomized experiment would be the best design for determining the relationship between cell phone use and brain cancer.

In a randomized experiment, individuals are randomly assigned to either a cell phone use group or a non-cell phone use group, and then the incidence of brain cancer is compared between the two groups.

This type of study can establish causality because it eliminates the possibility of confounding variables and ensures that any observed difference in brain cancer incidence is truly due to cell phone use and not some other factor.

Additionally, randomized experiments provide more robust results than observational studies, as they reduce the potential for selection bias and allow for control over extraneous variables.

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Answer:

I believe the answer is 12

Answer:

the correct answer would be 12

Step-by-step explanation:

10 1/3 + 1 2/3

31/3 + 1 2/3

31/3 + 5/3

=12

Hope this helps, happy holidays!!

First we have to find the increase in water

400 is 80% of 500 meaning there was an increase of 20%

Now we just have to find and add 20% of all the other ingredients.

560g flour --> 672g

12g salt --> 14g (rounded) Exact: 14.4g

8g yeast --> 10g (rounded) Exact 9.6g

40ml oil --> 48g

He would make about 14 bread rolls

If Eli is baking bread with 500mL water, then he would be using 700g of flour, 15g of salt, 10g of yeast, and 50 mL of water to make 15 bread rolls.

Using simple cross multiplication,

If 400mL→12 bread rolls, then,

⇒ 500mL would yield,

(500*12)÷400 = 15

Thus, 15 bread rolls are being made.

The same follows for the ingredients:

If 400mL→560g flour, then,

⇒ 500mL would yield,

(500*560)÷400 = 700

Thus, 700g of flour is needed.

The other ingredients are calculated similarly.

Thus, Eli would be using 700g of flour, 15g of salt, 10g of yeast, and 50 mL of water to make 15 bread rolls.

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The sum of the exterior angle of the pentagon is 360 degrees.

The polygon above is a pentagon. A pentagon is a polygon with 5 sides.

If the side of a polygon is extended, the angle formed outside the polygon is the exterior angle. The sum of the exterior angles of a polygon is 360°.

Therefore, the sum of the measure of the exterior angles of the pentagon as shown is 360 degrees.

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The patterns of tiles do not follow an arithmetic sequence or geometric sequence

When the pattern number is odd, the total number of tiles (SQUARE & CIRCULAR) needed to make the pattern will always be odd

From the question, we have the following pattern:

The number of square tiles is calculated using:

Tn= n²

So, we have:

T₇ = 7²

T₇ = 49

Hence, 49 square tiles are needed in pattern 7

The number of circular tiles is calculated using:

Tn= 4n + 4

So, we have:

T₂₀= 4 * 20 + 4

T₂₀= 84

Hence, 84 circular tiles are needed in pattern 20

Using the computations in (a) and (b), we have:

The total number of tiles in odd pattern number is always odd

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The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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In such a situation, I would choose not to endorse the athlete.

From a Christian worldview perspective, moral, ethical, and character standards hold significant importance. Athlete endorsers, as role models, should strive to uphold positive character traits and high moral standards. However, it is evident that in recent years, some athletes have challenged this notion.

When faced with the decision to sign an athlete endorser with questionable character or conflicting moral and ethical values, it is crucial to prioritize one's own values and beliefs. As a Christian, I would consider the impact of endorsing such an athlete on my personal integrity, as well as the message it sends to others.

It is essential to remain true to one's own moral compass and avoid promoting behavior that goes against Christian values. By doing so, I would be staying consistent with my beliefs and upholding the standards I hold dear.

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Given that all sides are equal it mean it's a equilateral triangle which means all angles are equal.

by angle sum property

2x+2x+2x = 180

6x=180

x=30

We could expect $30.00 to gain after 20 tosses.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

The probability of all the events occurring need to be 1.

if the toss of a coin comes down heads, you win a dollar. if it comes down tails, you lose fifty cents.

We need to find out How much would you expect to gain after 20 tosses (in $ dollars).

Because if you think about it, you will see that about half of them are going to be heads and the other half are going to be tails.

Therefore, We could expect $30.00 to gain after 20 tosses.

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The salesperson's commission as a percent of the total monthly sales is approximately 5.74%.

To find the commission as a percent of the total monthly sales, first we need to calculate the total sales for both April and May:

Total sales = April sales + May sales = $84,784 + $107,270 = $192,054

Next, we can calculate the commission as a percent of the total sales:

Commission as percent of total sales = (Commission / Total sales) x 100%

Commission as percent of total sales = ($4,865 / $192,054) x 100% = 0.025 x 100% = 2.5%

Therefore, the salesperson's commission as a percent of the total monthly sales is approximately 5.74% (rounded to two decimal places).

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Answer:

I think it is 2/12

Answer:

x = 1

Step-by-step explanation:

Both equations can be set equal to each other since they are both equal to y:

\(x-10=-4x-5\\5x-10=-5\\5x=5\\x=1\)

equate both equations !

x - 10 = -4x - 5

5x - 10 = -5

5x = 5

x = 1

therefore x = 1

The inequality relating −2\(e^{(-n/n^2)}\) to 121/\(n^2\) for n ≥ 1 is -2\(e^{(-n/n^2)}\) ≤ 121/\(n^2\).

To derive the inequality, we start by comparing the expressions −2\(e^{(-n/n^2)}\)  and 121/\(n^2\).

Since we want to express the numbers in exact form, we keep them as they are.

The inequality states that −2\(e^{(-n/n^2)}\)  is less than or equal to 121/\(n^2\).

This means that the left-hand side is either less than or equal to the right-hand side.

The exponential function e^x is always positive, so −2\(e^{(-n/n^2)}\)  is negative or zero.

On the other hand, 121/\(n^2\) is positive for n ≥ 1.

Therefore, the inequality −2\(e^{(-n/n^2)}\)  ≤ 121/\(n^2\) holds true for n ≥ 1.

The negative or zero value of −2\(e^{(-n/n^2)}\)  ensures that it will be less than or equal to the positive value of 121/\(n^2\).

In symbolic notation, the inequality can be written as −2\(e^{(-n/n^2)}\)  ≤ 121/\(n^2\) for n ≥ 1.

This representation captures the relationship between the two expressions and establishes the condition that must be satisfied for the inequality to hold.

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Answer:

160 newspapers (400 × .4 = 160)

The number of men using the gun is 8, using the given ratio of men to women as 2:1.

In the question, we are given that the ratio of men to women using a gun is 2:1, and a total of 24 people use a gun.

We are asked to find the number of men using the gun.

By the given ratio, we take the number of men using a gun to be 2x, whereas the number of women using a gun is x.

Thus, the total number of people using the gun = the number of men using a gun + the number of women using the gun,

or, the total number of people using the gun = 2x + x = 3x.

But, the total number of people using the gun is given to be 24.

Thus, we get an equation 3x = 24.

On solving this, we get:

3x = 24,

or, 3x/3 = 24/3,

or, x = 8.

Now, the number of men using a gun = 2x = 2*8 = 16.

The number of women using a gun = x = 8.

Thus, the number of men using the gun is 8, using the given ratio of men to women as 2:1.

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The derivative of g(x) = cosh(ln(x)) is: g'(x) = (x^2 - 1)/(2x^2).  To find the derivative of g(x) = cosh(ln(x)).

We can use the chain rule of differentiation.

Recall that the chain rule states that the derivative of a composite function f(g(x)) is given by:

(f(g(x)))' = f'(g(x)) * g'(x)

In this case, we have:

g(x) = cosh(ln(x))

So we need to find g'(x). To do this, we will first use the chain rule to find the derivative of the inner function ln(x), which is:

(ln(x))' = 1/x

Next, we can find the derivative of cosh(u) where u = ln(x) as follows:

cosh(u) = (e^u + e^(-u))/2

cosh'(u) = (e^u - e^(-u))/2

So we have:

g'(x) = cosh'(ln(x)) * (ln(x))'

g'(x) = (e^(ln(x)) - e^(-ln(x)))/2x

g'(x) = (x - 1/x)/2x

g'(x) = (x^2 - 1)/(2x^2)

Therefore, the derivative of g(x) = cosh(ln(x)) is:

g'(x) = (x^2 - 1)/(2x^2)

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Answer:

"The expression will always equal m" is true about the quotient of \(\frac{m}{n}\) ÷ \(\frac{1}{n}\)

Step-by-step explanation:

Let us solve the question

∵ The expression is \(\frac{m}{n}\) ÷ \(\frac{1}{n}\)

→ In the division of fractions, we change the division to multiplication

   and reciprocal the fraction after the division sign

∵ The reciprocal of  \(\frac{1}{n}\) is \(\frac{n}{1}\)

∴  \(\frac{m}{n}\) ÷ \(\frac{1}{n}\) =  \(\frac{m}{n}\) × \(\frac{n}{1}\)

→ In the multiplication of fractions, we can simplify the terms in

    the numerators by the terms in the denominators

∵ There is n in the numerator and denominator

∴ Cancel n up and down

∴  \(\frac{m}{n}\) × \(\frac{n}{1}\) = \(\frac{m}{1}\)

∴  \(\frac{m}{n}\) × \(\frac{n}{1}\) = m

∴  \(\frac{m}{n}\) ÷ \(\frac{1}{n}\) = m

∴ The quotient is m

∴ The expression will always equal m

The distance between the sailboat and the dock is approximately 21.006 km

To find the distance between the sailboat and the dock, we can use trigonometry.

Given:

Distance between the lighthouse and dock (north-south direction) = 30 km

Viewing angle between the lighthouse and dock = 35 degrees

We can consider the right triangle formed by the sailboat, the lighthouse, and the dock.

The distance between the sailboat and the dock is the adjacent side of the triangle, while the distance between the lighthouse and the dock is the opposite side.

Using the trigonometric function tangent (tan), we have:

tan(angle) = opposite / adjacent

tan(35 degrees) = opposite / 30 km

Solving for the opposite side (distance between sailboat and dock):

opposite = tan(35 degrees) * 30 km

opposite ≈ 0.7002 * 30 km

opposite ≈ 21.006 km

Therefore, the sailboat is approximately 21.006 km away from the dock.

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a)The radius of convergence is R = |-2 - (-πi)| = |-2 + πi| = √(2^2 + π^2) ≈ 3.146.b)The radius of convergence is R = |1 + i - i| = |1| = 1. c)The radius of convergence is R = |1 + i - i| = |1| = 1.

The radius of convergence of a Taylor series centered at a point z0 is the distance from z0 to the nearest singularity of the function.

(a) The function sinz/e^z has singularities at z = kπi for any integer k, and the nearest singularity to z0 = -2 is at z = -πi. Therefore, the radius of convergence is R = |-2 - (-πi)| = |-2 + πi| = √(2^2 + π^2) ≈ 3.146.

(b) The function 1/cosz' has singularities at z = (k + 1/2)π for any integer k, which are equidistant from z0 = 0. Therefore, the radius of convergence is R = π/2.

(c) The function z^2+1/(z−i) has a singularity at z = i, which is the nearest singularity to z0 = 1 + i. Therefore, the radius of convergence is R = |1 + i - i| = |1| = 1.

Note that these radii of convergence only guarantee convergence within the radius; the series may converge or diverge at the boundary.

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Answer:

2x+3y

Step-by-step explanation:

you add up the known sides: (x-y)+(x+y) = 2x

Then you subtract the answer from the perimiter: 4x+3y-2x=2x+3y

Answer:

x = 4

Step-by-step explanation:

Given

\(\frac{1}{x+5}\) = \(\frac{1}{4x-7}\) ( cross- multiply )

4x - 7 = x + 5 ( subtract x from both sides )

3x - 7 = 5 ( add 7 to both sides )

3x = 12 ( divide both sides by 3 )

x = 4

Answer:

The triangles are similar due to AAA

Step-by-step explanation:

'The triangles ABC and DBE are similar because they have a common angle < B, and also angle < E is marked as congruent to angle < A. Then the third angle <C is going to be congruent to angle D as well due to the property of addition of internal angles of a triangle must add to 180 degrees.

Then the triangles are similar due to AAA

Answer:

$57.84

Step-by-step explanation:

Balloons needed = 168

Cost of 36 balloons per pack = $11.88

Cost of 12 balloons per pack = $5.16

cost per balloon

36 per pack = $11.88 / 36

= $0.33

12 per pack = $5.16 / 12

= $0.43

In order to minimize cost, she should buy as many packs of 36 per pack balloon

36 per pack × 1 pack = 36

36 per pack × 2 packs = 72

36 per pack × 3 packs = 108

36 per pack × 4 packs = 144

36 per pack × 5 packs = 180

The required number of balloons is 168

So, the number of possible 36 packs to buy is 4, that is, 144 balloons

Balloons remaining = 168 - 144

= 24

Possible packs of 12 balloons per pack possible is

12 per pack × 1 pack = 12

12 per pack × 2 packs = 24

Therefore, Megan needs to buy 4 packs of 36 balloons per pack and 2 packs of 12 balloons per pack

Cost of 4 packs of 36 balloons per pack = 4 × $11.88

= $47.52

Cost of 2 packs of 12 balloons per pack = 2 × $5.16

= $10.32

Total cost = $47.52 + $10.32

= $57.84

The half life period is the time in which only half of the given population remains. It can be represented through this equation:

\(f(t)=a\times(1/2)^{\frac{t}{h}}\)

We're given:

For most questions like this, we would have to plug these values into the equation mentioned above. However, this question asks for the time elapsed after 3 half-lives.

This can be calculated simply by multiplying the given half-life by 3:

28 million years x 3

= 84 million years

84 million years