Find a possible formula for the general nth term of the sequence that begins as follows. Please simplify your solution. 1/8, 1/27, 1/64, 1/125

The given equation 6x+2y=13 is a linear equation in two variables. In this equation, x and y are variables while 6 and 2 are their respective coefficients, and 13 is a constant term. The equation can be represented as a straight line on a graph. The slope of this line is -3, and it intersects the y-axis at the point (0, 13/2).

In this equation, if we substitute x=0, then y=13/2, and if we substitute y=0, then x=13/6. These are the two points that the line passes through the x and y-axis.

A linear equation is a polynomial equation that is of the first degree, meaning the variables in the equation are not raised to any powers other than one. This equation is in the standard form where the variables are in the first degree. 6x + 2y = 13 is the form of the given linear equation. x and y are the two variables, and 6 and 2 are their respective coefficients. The equation can be represented as a straight line on a graph. The slope-intercept form of this equation is y = -3x + 13/2. The equation is also in standard form.

When x = 0, the equation becomes 2y = 13. This means that the point of intersection is (0, 13/2) when y = 0, the equation becomes 6x = 13, and the point of intersection is (13/6, 0). The slope of the line is -3. When x increases by 1, y decreases by 3.

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Answer:

-8ab-6+26

Step-by-step explanation:

-2(4ab+3-4c)

-2(4ab) = -8ab

-2(3) = -6

-2(-4c)= 2c

Combine:

-8ab-6+26

Answer: 26 and 30

Step-by-step explanation: The pattern is adding 4, so 10 + 4 is 14, 14 + 4 is 18, and 18 + 4 is 22.

So you add 4.

22 + 4 is 26.

26 + 4 is 30.

Answer:

26, 30 are the next two terms

Step-by-step explanation:

Step 1

Let the length in minutes of Tika's class be m

His class had lasted already for 18 minutes

His class had 37 more minutes to end.

Step 2

Get the equation

Hence the answer is option B ------ ( m - 37 = 18)

Using the perimeter concept, the measures are given as follows:

a) Perimeter when the missing box is of -7: -6x² + 8x + 4.

b) Coefficient missing when the perimeter is of 5x² + 8x + 4: a = 4.

c) Perimeter from part B when x = 3: 73 inches.

The perimeter of a figure is obtained by the sum of their outer side lengths.

For this shape, these lengths are given as follows:

With a missing coefficient of a = -7, we have that:

ax² + x = -7x² + x.

Hence the perimeter is:

3x + x² + 5 - 7x² + x + 4x - 1 = -6x² + 8x + 4.

In symbolic terms, the perimeter is:

(1 + a)x² + 8x + 4.

When the perimeter is of 5x²+8x + 4, the coefficient is:

1 + a = 5

a = 5 - 1

a = 4.

When x = 3 and a = 4, the perimeter is given as follows:

P = 5(3)² + 8(3) + 4 = 73 inches.

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Answer:

9 feet

Step-by-step explanation:

3X3=9 feet therefore 3 yards is equal to 9 feet

Answer:

24/5 or 4.8

Step-by-step explanation:

This would be 6/10 multiplied by 8 making it 48/10 and if you simplify that you will get 24/5.

Answer:

4.8

Step-by-step explanation:

6 tenths can be written like this: 0.6

If you were to pretend the 0.6 was a six..

6*8=48

There actually is a decimal point and you must move it back to the left one place because there was one before the six

4.8

Boom.

\(5 \div 3 \frac{1}{3} \\ = 5 \div \frac{10}{3} \\ = 5 \times \frac{3}{10} \\ = \frac{3}{2} \\ = 1 \frac{1}{2} \)

Hope you could understand.

If you have any query, feel free to ask.

Answer:

1.5 or 1  1/2

Step-by-step explanation:

5 divided by 3 1/3 is 1.5

The minimum distance you can park from a driveway leading from a fire department can vary depending on the local laws and regulations in your area.

However, it is important to keep in mind that fire departments need clear and unobstructed access to their driveways at all times, in case of an emergency.
In many areas, the law requires a minimum distance of 20 feet from the edge of a fire department driveway to the nearest parked vehicle. This distance allows fire trucks and emergency vehicles enough space to turn, enter, and exit the driveway without any obstruction or delay.
It is also important to note that blocking a fire department driveway can result in a hefty fine or even a vehicle being towed away. This is because obstructing the entrance and exit to a fire department can cause unnecessary delay, which can be dangerous or even fatal in emergency situations.
Overall, it is important to always be aware of your surroundings and the laws in your area when parking near a fire department or any other emergency service. By doing so, you can ensure the safety and accessibility of these essential services at all times.

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If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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Answer:

Data set A

Step-by-step explanation:

Data set A is the one that is more spread out.

The mean is the same as the average of a given sample. It is usually a measure of the central tendency of a data set.

Standard deviation is a measure of the spread of a given set of data.

Since data set A has a standard deviation of 35, it the most spread out.

In a right triangle with cos0 = 4/5, the exact value of cot(0) is 4/3.

In a right triangle, if cos0 = 4/5, then the exact value of cot(0) can be found using the Pythagorean Theorem and the definition of cotangent.

First, let's use the Pythagorean Theorem to find the third side of the right triangle.

If cos0 = 4/5, then the adjacent side is 4 and the hypotenuse is 5. The Pythagorean Theorem states that a^2 + b^2 = c^2, where a and b are the legs of the right triangle and c is the hypotenuse. Plugging in the known values, we get:

4² + b² = 5²
16 + b² = 25
b² = 9
b = 3

Now that we know the third side of the right triangle, we can use the definition of cotangent to find the exact value of cot(0).

Cotangent is defined as the ratio of the adjacent side to the opposite side. In this case, the adjacent side is 4 and the opposite side is 3, so:
cot(0) = 4/3

Therefore, the exact value of cot(0) is 4/3.

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The marginal cost for the given average cost function is

�

�

=

10

�

−

1

,

000

�

2

MC=10q−

q

2

1,000

​

.

To find the marginal cost, we need to take the derivative of the average cost function with respect to quantity (q). Let's calculate step by step:

�

ˉ

=

5

�

2

+

2

�

+

10

,

000

+

1

,

000

�

c

ˉ

=5q

2

+2q+10,000+

q

1,000

​

Differentiating the average cost function with respect to q:

�

�

ˉ

�

�

=

�

�

�

(

5

�

2

+

2

�

+

10

,

000

)

+

�

�

�

(

1

,

000

�

)

dq

d

c

ˉ

​

=

dq

d

​

(5q

2

+2q+10,000)+

dq

d

​

(

q

1,000

​

)

Simplifying:

�

�

ˉ

�

�

=

10

�

+

2

−

1

,

000

�

2

dq

d

c

ˉ

​

=10q+2−

q

2

1,000

​

The resulting expression is the marginal cost function:

�

�

=

10

�

−

1

,

000

�

2

MC=10q−

q

2

1,000

​

The marginal cost function for the given average cost function is

�

�

=

10

�

−

1

,

000

�

2

MC=10q−

q

2

1,000

​

. Marginal cost represents the change in total cost incurred by producing one additional unit of output. It consists of the change in variable costs as quantity changes. In this case, the marginal cost is determined by the linear term

10

�

10q and the inverse square term

−

1

,

000

�

2

−

q

2

1,000

​

. The linear term represents the variable cost component that increases linearly with the quantity produced. The inverse square term represents the diminishing returns, indicating that as quantity increases, the cost of producing additional units decreases. Understanding the marginal cost is crucial for companies to make informed decisions regarding production levels and pricing strategies.

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The probability that every even number appears at least once before the first occurrence of an odd is 1/20.

Given:

A fair 6-sided die is repeatedly rolled until an odd number appears.

There are 6! ways to order the 6 numbers and 3!(3!) ways to order the evens in the first three spots and the odds in the next three spots.

so the probability = 3!*3! / 6!

= 3!*3! / 6*5*4*3!

= 3*2*1 / 6*5*4

= 6*1 / 30*4

= 6/120

= 1/20

Therefore the probability that every even number appears at least once before the first occurrence of an odd is 1/20.

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Answer:

B.

Step-by-step explanation:

So to make it look simpler, rewrite it as this:

\(\frac{4^{5} 7^{3} }{4^27^4}\)

Now, you can cross out the 4^2 and 7^3

You're left with:

\(\frac{4^3}{7}\)

Based on the results of the chi-square test, at a significance level of 0.01, there is insufficient evidence to suggest that people prefer different food rewards in general.

A chi-square test of independence can be used to see if the results suggest that people prefer different food rewards in general. The steps for testing a hypothesis are as follows:

Step 1: Create the alternative and null hypotheses:

H0 is the null hypothesis: The participants' preference for food rewards is unrelated.

A different hypothesis (Ha): The participants' preference for food rewards is contingent.

Step 2: Set the level of significance (): In the question, the significance level is stated to be 0.01.

Step 3: Make the tables of the observed and expected frequency:

The following frequencies have been observed:

Cupcakes: 16 bars of candy: 26 Dry fruits: 18 We must assume that the null hypothesis holds true, indicating that the preferences are independent, in order to calculate the expected frequencies. Based on the proportions specified in the question, we can determine the anticipated frequencies.

Frequencies to anticipate:

Cupcakes: Six candy bars: 60 x 0.10 Dried fruit: 60 x 0.70 = 42 60 * 0.20 = 12

Step 4: Determine the chi-square test statistic as follows:

The following formula can be used to calculate the chi-square test statistic:

The chi-square test statistic can be calculated by using the observed and expected frequencies. 2 = [(Observed - Expected)2 / Expected]

χ^2 = [(16 - 6)^2 / 6] + [(26 - 42)^2 / 42] + [(18 - 12)^2 / 12]

Step 5: Find out the crucial value:

A chi-square test with two degrees of freedom and a significance level of 0.01 has a critical value of 9.21.

Step 6: The critical value and the chi-square test statistic can be compared:

We reject the null hypothesis if the chi-square test statistic is greater than the critical value. We fail to reject the null hypothesis otherwise.

Because the calculated chi-square test statistic falls below the critical value (2  9.21), we are unable to reject the null hypothesis in this instance.

At a significance level of 0.01, the results of the chi-square test indicate that there is insufficient evidence to suggest that people generally prefer different food rewards.

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A: To determine when the lizard is back on the water, we need to find the time when the height (h) is equal to 0. So we set the equation -12t^2 + 6t = 0 and solve for t.

-12t^2 + 6t = 0

Factor out common terms:

-6t(2t - 1) = 0

Set each factor equal to 0:

-6t = 0 or 2t - 1 = 0

Solving each equation:

-6t = 0 --> t = 0

2t - 1 = 0 --> 2t = 1 --> t = 1/2

So the lizard is back on the water at t = 0 seconds and t = 1/2 seconds.

B: The height of each jump can be determined by substituting the time (t) values into the equation h = -12t^2 + 6t.

For t = 0 seconds:

h = -12(0)^2 + 6(0)

h = 0

For t = 1/2 seconds:

h = -12(1/2)^2 + 6(1/2)

h = -12(1/4) + 6/2

h = -3 + 3

h = 0

So each jump has a height of 0 feet.

C: To find the time it takes to reach the highest point, we need to find the vertex of the parabolic equation -12t^2 + 6t. The time at the vertex represents the highest point.

The formula for the x-coordinate of the vertex of a quadratic equation in the form ax^2 + bx + c is given by -b/(2a). In this case, a = -12 and b = 6.

t = -6/(2(-12))

t = -6/(-24)

t = 1/4

So it takes 1/4 seconds to reach the highest point.

Therefore, the answers are:

A: The lizard is back on the water at t = 0 seconds and t = 1/2 seconds.

B: Each jump has a height of 0 feet.

C: It takes 1/4 seconds to reach the highest point.

The value of  zα for the following is :

(a)  α = 0.0089 is 2.37

(b) α = 0.09 is 1.34

(c)  α = 0.707 is -0.545

zα is the inverse function of the standard normal CDF.

(a) Central limit c= 1-α

for α = 0.0089 , c=1-0.0089

∴ c=0.9911

Hence confidence level in percentage= 99.5%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.9911)

zα =2.37

(b) Central limit c= 1-α

for α = 0.09 , c=1-0.09

∴ c=0.91

Hence confidence level in percentage= 91%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.91)

zα=1.34

(c) Central limit c= 1-α

for α = 0.707 , c=1-0.707

∴ c=0.293

Hence confidence level in percentage= 29.3%

Now,  the value of zα will be calculated with the help of an excel sheet function normsinv(c).

∴zα = normsinv(c)

where c is central limit

zα = normsinv(0.707)

zα= -0.545

Therefore zα value for 0.0089 is 2.37, for 0.09 is 1.34 and for 0.707 it is -0.545.

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Answer: 0.04536

Step-by-step explanation:

Answer:

1671.58

Step-by-step explanation:

V=1/3(3.14)(9.75)squared(16.8)

A group contains n men and n women. 2n! number of ways are there to arrange these people in a row if the men and women alternate. Arrangement is known as permutation.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

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Option B is the correct answer Multiply both sides by -2 and reverse the inequality symbol.

To isolate the variable, we should multiply both sides by -2 and reverse the inequality symbol.

Isolating variables in inequality. Isolation of variables is defined by making the variable the subject of the formula from the given expression.

Given the inequality expression -1/2 w < 12

To make w the subject of the formula, we should have to multiply -2 on both sides and we get

-1/2 w × -2 > 12 × -2

w > -24

So, to isolate the variable, we have to multiply both sides by -2 and reverse the inequality symbol.

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Full question:

Mei wants to solve the inequality -1/2W < 12. How can she isolate the variable?

A) Multiply both sides by -2 and reverse the inequality symbol.

B) Multiply both sides by -2 and do not reverse the inequality symbol.

C) Divide both sides by 12 and reverse the inequality symbol.

D) Divide both sides by 12 and do not reverse the inequality symbol.

Answer:

y - 4= -3(x - 2)

I'm 101% sure

The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)

The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.

First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.

Now we'll apply the chain rule. We have:

f'(x) = (derivative of outer function) * (derivative of inner function)

f'(x) = (-1/√(1-u^2)) * (2x)

Since u = x^2, we'll substitute that back into our equation:

f'(x) = (-1/√(1-x^4)) * (2x)

So, the derivative of f(x) = arccos(x^2) is:

f'(x) = -2x / √(1-x^4)

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Answer:

Step-by-step explanation:

Given

Solving for x

Answer:

y is -16

Step-by-step explanation:

Fory =3x -1

Substitute x= -5

y=3(-5) -1

3(-5) -1= -16

y= -16