If P(n) and Q(n) are polynomials of degree j and k, respectively, then the series
Infinite
Σ P(n)/Q(n)
n=1
converges if j < k − 1 and diverges if j ≥ k – 1.
Use the polynomial test given above to determine whether the series converges or diverges.
Infinite
Σ 1/(n)^8 +7
n=1
O converges
Odiverges

Answer:

V = 9 in^3

Step-by-step explanation

Comment

The formula for a Pyramid of any B is V = B * h / 3. You have to be able to calculate the Base or just be given in it.

In this case the Base is a triangle. So the first thing needed is the area of the base.

Base

Area_triangle = base length * height / 2

Neither the Base length nor the height need to be the same as the B and h used for the volume of the Pyramid

Givens

b = 4 inches

h = 1.5 inches

Area_triangle = 4 * 1.5 / 2

Area_triangle = 2 * 1.5

Area_triangle = 3 inches^2

Solution

Base (triangle) Area = 3

h = 9

V = B * h / 3  

V = 3 * 9 / 3

V = 9 cubic inches

Answer V = 9 in^3

The pair of equations (c) y = (1 / 6) x + 8 and y = 6x + 4 are not parallel

A linear equation is represented as:

y = mx + b

Where m is the slope of the line

Two lines are said to be parallel if their slopes are the same

i.e. y = mx + b and y = mx + c

Using the above as a guide, the option (c) represents lines that are not parallel, because they do not have the same slope

Hence, y = (1 / 6) x + 8 and y = 6x + 4 are not parallel

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The converse of the statement will be : if x^2 = 100 then x = -10, which is not true.

In order to write a converse of a conditional statement "p then q",  will be "q then p" the hypothesis and conclusion interchanges.

Then the converse of the statement will be :

if x^2 = 100 then x = -10,

which is not true.

Since , x = +10, then x^2 = 100

Therefore, if x^2 = 100 then x = -10, which is not true.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

Correct Expression :

[tex]\qquad \tt \rightarrow \: |10| + | - 6| [/tex]

[tex]\qquad \tt \rightarrow \: distance = 16\:\: units\degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \textsf{Using distance formula -} [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{( - 6 - 10) {}^{2} + (4 - 4) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{( - 16) {}^{2} + 0} [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{256} [/tex]

[tex]\qquad \tt \rightarrow \: 16 \: \: units[/tex]

For short it can be expressed as :

[tex]\qquad \tt \rightarrow \: |10| + | - 6| = 10 + 6 = 16[/tex]

[ y - coordinate of both the points are same ]

Correct option - D

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

The Answer is [B]

Step-by-step explanation:
i actually dont have one

Answer:

∠MOP ≅ ∠NOQ

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent.

Therefore:

∠MON ≅ POQ  and  ∠MOP ≅ ∠NOQ

We have an odd number of consecutive integers, therefore the middle one is equal to the average of all of them. And since the average is equal to the sum of the numbers divided by their number, the middle integer in this problem is equal to 369 divided by 9, which is equal to 41.

Answer:

Domain = x ≥ 0

Range = y ≥ 20

Step-by-step explanation:

The equation in slope-intercept form would look like this:

y = 4x + 20

The slope is $4 because that is the money that can be made depending on the week. Because he received a random $20 at the beginning, this is just an additional income.

                     ---------------------------------------------------------------------------

In this scenario, the domain (x-values) represent the number of weeks. The range (y-values) represent the total money made.

So the domain is asking, what is the lowest/highest amount of weeks he can save for? We know the number of weeks cannot be negative because he can't save for negative weeks. However, he could save for zero weeks. He can be saving for theoretically infinite weeks. Therefore, the domain is x ≥ 0.

The range is asking, how much money can he save? Since he starts out with a baseline of $20, this is the lowest amount of money he can have. If he were to save for an infinite amount of weeks, he could make an infinite amount of money. Therefore the range is y ≥ 20.

The question is incomplete. Below you will find the missing contents.

The correct match of events with order are,

When two events A and B are independent then,

P(A and B)=P(A).P(B)

when A and B are dependent events then,

P(A and B) = P(A) . P(B|A)

When two events A and B are mutually exclusive events then,

P(A and B)=0

So, P(A or B) = P(A) + P(B) - P(A and B) = P(A) + P(B)

P(A) + P(B) = P(A or B)

When events are not mutually exclusive then the general relation is,

P(A or B) = P(A) + P(B) - P(A and B)

If the probability of the event B conditioned by A is given by,

[tex]\mathrm{P(B|A)=\frac{P(A~and~B)}{P(A)}}[/tex]

Hence the correct match are -

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Answer:

$4

Step-by-step explanation:

Company $0.50

Store. $ 4.50

Price up $ X

4.50

- 0.50

------------

4.00

X= $4.00

If the function is reflected over the y-axis and then translated down 2 units. the resulting function will be -∛x - 2

Transformation is a technique used to change the position of an object on an xy-plane.

Given the function y = ∛x

If the function is reflected over the y-axis and then translated down 2 units to form f(x), the resulting function f(x) will be:

f(x) = -∛x - 2

The graph of the resulting function is attached

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Answer:

B

Edge 2023

The other answer is incorrect!!!

lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol

The sample size required is 2938.645

Probability is the likeliness of an event to happen.

It is given that

p = .37

∈ = 0.025

∝ = 1 - 0.995 = 0.005

∝[tex]\rm z_{\alpha/2} = z_{0.005/2} = 2.807[/tex]  (From z table)

Sample size n is given by

[tex]\rm n = (\dfrac{z_{\alpha/2}}{\epsilon})^2 p (1-p)\\\\n = (\dfrac{2.807}{.025})^2 *0.37*(1-0.37)\\\\n = 2938.645\\[/tex]

Therefore the sample size required is 2938.645

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Given that [tex]f(x) = x[/tex] and [tex]g(x) = 2x^3[/tex], we have

[tex]f(g(x)) = f(2x^3) = 2x^3[/tex]

and

[tex]g(f(x)) = g(x) = 2x^3[/tex]

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The length of the tree is 23.66 meters.

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

Let the height of the tree be represented by x.

The length of the shadow when the angle of elevation is 45°.

Length of shadow = x/ Tan(45°)

The length of the shadow when the angle of elevation is 60°.

Length of shadow = x/ Tan(60°)

Now, since the difference between shadows is 10 meters. Therefore, we can write,

x/ Tan(45°) - x/ Tan(60°) = 10m

x[1/ Tan(45°) - 1/ Tan(60°) ] = 10 m

x (0.42265) = 10 m

x = 23.66 m

Hence, the length of the tree is 23.66 meters.

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Since the product of variables in inverse proportion is constant, the equation is [tex]\boxed{xy=-1300}[/tex]

Answer: A. 6, 18, 54, 162

Step-by-step explanation:

Each term is 3 times the last, meaning the common ratio is 3.

Multiply by 9/25 to make the coefficient of the variable 1 the answer is 9/25.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a given linear equation.

After solving the linear equation we get:

[tex]\rm \dfrac{25}{9}x = 25[/tex]

To make the coefficient of the variable 1

Multiply by 9/25 on both sides.

[tex]\rm \dfrac{9}{25}\times\dfrac{25}{9}x = 25\times \dfrac{9}{25}[/tex]

x = 9

Thus, multiply by 9/25 to make the coefficient of the variable 1 the answer is 9/25.

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Answer: the answer is 9/25

Step-by-step explanation: Multiplying both sides of the equation by 9/25 isolates x

Answer:

D

Step-by-step explanation:

To find angle B, you should subtract 62 from 90 since because a right angle is 90 degrees.

The vertex of the graph is at (-2, 3).

This means the equation is of the form [tex]f(x)=a|x+2|+3[/tex].

Substituting in the coordinates of one of the other points on the graph that is not the vertex, such as (-1, -1),

[tex]-1=a|-1+2|+3\\\\-1=a+3\\\\a=-4[/tex]

So, the equation is [tex]\boxed{f(x)=-4|x+2|+3}[/tex]

Answer:

You cannot solve this problem with only one given equation

Step-by-step explanation:

You need at least 2 equations to solve for two variables.

Answer:

Slope: 10

Y-intercept: +9

Step-by-step explanation:

An equation written in slope-intercept form is y=mx+b. "m" is your slope and b is your y-intercept.

It looks like you're talking about the indefinite integral

[tex]\displaystyle \int t^2 e^{-10t} \, dt[/tex]

Integrate by parts:

[tex]\displaystyle u\,dv = uv - \int v\,du[/tex]

Let

[tex]u = t^2 \implies du = 2t \, dt[/tex]

[tex]dv = e^{-10t} \, dt \implies v = -\dfrac1{10} e^{-10t}[/tex]

Then

[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \int t e^{-10t} \, dt[/tex]

Integrate by parts again, this time with

[tex]u = t \implies du = dt[/tex]

[tex]dv = e^{-10t} \, dt \implies v = -\dfrac1{10} e^{-10t}[/tex]

Then

[tex]\displaystyle \int t e^{-10t} \, dt = -\frac1{10} t e^{-10t} + \frac1{10} \int e^{-10t} \, dt[/tex]

Putting everything together, we get

[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \int t e^{-10t} \, dt[/tex]

[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \left(-\frac1{10} t e^{-10t} + \frac1{10} \int e^{-10t} \, dt\right)[/tex]

[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} + \frac1{50} \int e^{-10t} \, dt[/tex]

[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} + \frac1{50} \left(-\frac1{10} e^{-10t}\right) + C[/tex]

[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} - \frac1{500} e^{-10t} + C[/tex]

[tex]\displaystyle \int t^2 e^{-10t} \, dt = \boxed{-\frac{e^{-10t}}{500} \left(50t^2 + 10t + 1\right) + C}[/tex]

Answer:

2 and 1/4 cups

Step-by-step explanation:

4 cups-5 cups

5 cups-?

(5×5)÷4=6 cups and 1/4

6 and 1/4-4=2 cups and 1/4

Answer:

Step-by-step explanation:

The initial vale is when x = 0

-  That is 75,

The growth factor is 2%.

A function assigns the values. The value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function f(x)=-x²-4x+5, therefore, the value of f(x) when the value of x is -3 is,

f(-3) = -(-3)² - 4(-3) + 5

f(-3) = -9 + 12 + 5

f(-3) = 8

Now, the value of f(x) when the value of x is 3 is,

f(3) = -(3)²-4(3)+5

f(3) = - 9 - 12 + 5

f(3) = -16

further, the value of f(3) + f(-3) is,

f(3) + f(-3) = -16 + 8

f(3) + f(-3) = -8

Hence, the value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.

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Answer:

9.05

Step-by-step explanation:

make gallons into quarts

quar prefix in many languages means 4

1 gallon is 4 quarts

3 gallons is 4 times 3 -> 12 quarts

just by seeing 108 and 12 the answer will be around 9

108.90 ÷ 12 = 9.05