onfirm that the integral test can be applied to the series. then use the integral test to determine the convergence or divergence of the series. [infinity] 2 3n 9 n = 1 [infinity] 2 3x 9 dx =

Answer:

C

Step-by-step explanation:

The function is nonlinear because the slope is not constant.

Answer:

T-statistic

Step-by-step explanation:

As the sample size is less than 30, the t-statistic is the more appropriate test statistic. If it were greater than 30, then the t-statistic distribution and normal distribution would be indistinguishable, making the z-statistic a more preferable choice.

Answer:

13/5+(-12/7)÷ -31/7×1/-2.

13/5-12/7=31/35.

-31/7×1/-2=31/14.

31/35÷31/14=14/35.

Step-by-step explanation:

We can solve the given equation for y in terms of x by treating it as a quadratic equation in y. To do so, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, we can rearrange the equation to get:

9x^2y^2 - 12xy + 4 = 0

which can be written as:

(3xy)^2 - 2(3xy)(2) + 2^2 - 2^2 = 0

This is a quadratic equation in 3xy, which can be solved using the quadratic formula:

3xy = [2 ± sqrt(2^2 - 4(1)(-2^2))]/(2*1)

3xy = [2 ± sqrt(4 + 32)]/2

3xy = [2 ± 2sqrt(9)]/2

3xy = 1 ± 3

Therefore, we have two possible solutions:

3xy = 1 + 3 = 4 or 3xy = 1 - 3 = -2

Solving for y in terms of x, we get:

3xy = 4 => y = 4/(3x)

or

3xy = -2 => y = -2/(3x)

Therefore, the solutions to the given equation are:

y = 4/(3x) or y = -2/(3x)

To find the volume of the solid generated by revolving the region between y = x^2 and y = 12 - x about the line y = -2, we can use the disk/washer method by integrating the difference between the functions squared over the interval of intersection.

To find the volume of the solid generated by revolving the region bounded by y = x^2 and y = 12 - x about the horizontal line y = -2, we can use the disk/washer method.

First, let's find the points of intersection between the two curves:

x^2 = 12 - x

Rearranging the equation:

x^2 + x - 12 = 0

Factoring the quadratic equation:

(x - 3)(x + 4) = 0

So, the points of intersection are x = 3 and x = -4.

To use the disk/washer method, we need to integrate over the interval [-4, 3].

The radius of each disk or washer is given by the difference between the functions:

r = (12 - x) - x^2

The volume element can be expressed as:

dV = πr^2 dx

Integrating the volume element over the interval [-4, 3]:

V = ∫[-4,3] π((12 - x) - x^2)^2 dx

Evaluating this integral will give us the volume of the solid.

Note: The washer method is used when the region between the curves is revolved around a horizontal or vertical axis, and the disk method is used when the region below the curve is revolved around a horizontal or vertical axis. In this case, we are revolving the region between the curves, so we use the washer method.

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These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

To solve the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0, we need to simplify and rearrange the equation to its standard form and then solve for p.

Combining like terms, the equation becomes:

3p^2 - 10p + 5 = 0

Now, we can use the quadratic formula to solve for p. The quadratic formula states:

p = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -10, and c = 5. Substituting these values into the quadratic formula, we have:

p = (-(-10) ± √((-10)^2 - 4 * 3 * 5)) / (2 * 3)

Simplifying further:

p = (10 ± √(100 - 60)) / 6

p = (10 ± √40) / 6

p = (10 ± 2√10) / 6

Now, we can simplify and find the two possible values of p:

p₁ = (10 + 2√10) / 6

p₂ = (10 - 2√10) / 6

These are the solutions to the quadratic equation p^2 + 2p^2 - 5 * 2p + 5 = 0.

In simplified form, the solutions are:

p₁ = (5 + √10) / 3

p₂ = (5 - √10) / 3

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Answer: -1-1i and -1+1i

Step-by-step explanation:

Answer:

1. 44 GB

2. 12 ft

3a. 49

3b. -155

3c. 6

3d. -53

Answer:

1)44 GB

2)24 FT

3)

A. 49

B. -115

C.6

D.-53

Step-by-step explanation:

For 2 she went down then up to the second floow meaning she is 12x2 ft up the ground, the basement doesnt count

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

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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The computation shows that 1756.18595945 to the nearest hundred-thousandth will be 1756.18596.

After being rounded, the value of the hundred thousandth place, which is five places to the right of the decimal point, determines the value of the nearest ten thousandth of a decimal number, which is the value four places to the right of the decimal point.

The thousandth digit should be rounded down if the digit is less than 5. If that number is five or more, round it up to the nearest thousand. We must round up the thousandth digit because in the example given above, the digit following the thousandth digit (i.e., 9) is more than 5. This will give a value of 1756.18596.

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a. Yes Juan is correct.

b. The given quadratic equation can be solve by using quadratic formula.

What is a quadratic equation?

A quadratic equation is a polynomial equation with a maximum degree of two. Where a ≠ 0, the equation is given by ax² + bx + c = 0.

Given equation is x² + 7x + 3.

The given equation can't factorized by using middle term or splitting method.

Factorization of quadratic equations can be done in different methods. They are:

Splitting the middle term

Using formula

Using Quadratic formula

Using algebraic identities

Assume that x² + 7x + 3 = 0

x = [-7 ± √(7² - 4 × 1 × 3)]/ 2 × 1

x = [-7 ± √37]/ 2

The factors of quadratic polynomial is ( x - [-7 ± √37]/ 2).

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Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

Step-by-step explanation:

i guess it helps..if yuh need step by step explanation.comment i try to explain in worda

The exact percentage of roses purchased on Valentine's Day that are red are 60% to 80% or even higher.

can vary depending on various factors such as location, personal preferences, and cultural traditions. However, it is generally observed that red roses are the most popular and commonly associated with Valentine's Day, symbolizing love and romance.

It is estimated that a significant majority of roses purchased on Valentine's Day are red, often ranging from 60% to 80% or even higher. This high percentage is due to the traditional symbolism and cultural significance attached to red roses as a romantic gift.

However, it's important to note that individual preferences may vary, and some people may choose different colored roses or alternative flowers to express their feelings on Valentine's Day.

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It is a true statement that; "understanding the effect of any confounding variables on the dependent variable is important to the outcome of an experiment. "

A confounding variable is a variable that is not directly involved in the study but has an impact on the results of the experiment. It is a sort of a third variable but it is able to affect the results that we obtain from the experiment.

Thus, it is a true statement that; "understanding the effect of any confounding variables on the dependent variable is important to the outcome of an experiment. "

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Answer:

946 miles

Step-by-step explanation:

\(\frac{301}{7} = \frac{x}{22} \\301(22)=7x\\6622=7x\\x=\frac{6622}{7} \\x=946\)

1.9/10. 2.22 3.64. 4.3.15. 5.160. 6.81

10 meters away is the bus from the bus stop after 10 seconds.

A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.

A bus moves away from bus stop in a straight line. After 1 second it was 10 meters away, after 2 seconds it was 20 meters and after 3 seconds it was 30 meters away.

In this way bus forms an arithmetic sequence

10, 20, 30, 40........up to 10 terms.

nth term of an arithmetic sequence is represented by

\(T_{n}\) = a+ (n - 1)d

Here a = 10 and d = common difference = 10

Therefore 10th term = 10 + (10-1)10

                                  = 10 + 90

                                  = 100

Therefore after 10 seconds bus will be 10 meters away from the bus stop.

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Answer:

Probably how much you want this job, if you say 0, than they are prob gonna assume you dont want to do this job, and you wont do your best. If you say 5, then you do want this job and your excited and youll give your all

Step-by-step explanation:

Questions regarding the level of excitement or happiness of one's self are called mental health or happiness test.

Hence, the type of test on this context is Happiness test.

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Answer:

x=32°

Step-by-step explanation:

3x-2=2x+30

x-2=30

x=32°

Answer:

no

Step-by-step explanation:

because even going back to back it would take you about one or two days

Answer:

18.

Domain: X E \{-3,2}

Y-Intercept: 1/2

X-Intercept: 3

19.

Domain: (I think it's none)

Y-Intercept: -2

X-Intercept: 2

20.

Domain: X E R\ {-3,1}

y-INTERCEPT: 2/3

x-INTERCEPT: -1

Step-by-step explanation:

Evaluating p(4) using Horner's algorithm:

1. To use Horner's algorithm, we write the polynomial in nested form as follows:

p(z) = ((3z - 7)z - 5)z^2 + (z - 8)z + 2

Now, we can evaluate p(4) by starting from the inside and working our way out:

p(4) = ((3(4) - 7)4 - 5)4^2 + (4 - 8)4 + 2

= (5)4^2 - 4 + 2

= 78

Therefore, p(4) = 78.

2. Finding the Taylor series expansion of p(z) about z0 = 4:

To find the Taylor series expansion of p(z) about z0 = 4, we need to compute the derivatives of p(z) at z0 = 4. First, we compute p'(z) = 6z^2 - 28z^3 - 10z^2 + 2z - 8, then p''(z) = 12z - 84z^2 - 20z + 2, p'''(z) = 12 - 168z - 20, and so on.

Using these derivatives, we can write the Taylor series expansion of p(z) about z0 = 4 as follows:

p(z) = p(4) + p'(4)(z - 4) + p''(4)(z - 4)^2/2! + p'''(4)(z - 4)^3/3! + ...

Substituting in the values we computed, we get:

p(z) = 78 + 10(z - 4) - 41(z - 4)^2/2! - 14(z - 4)^3/3! + ...

Therefore, the Taylor series expansion of p(z) about z0 = 4 is:

p(z) = 78 + 10(z - 4) - 20.5(z - 4)^2 - 2.333(z - 4)^3 + ...

3. Using Newton's method to find a root of p(z):

To use Newton's method to find a root of p(z), we start with an initial guess z0 = 4 and iterate the formula z1 = z0 - p(z0)/p'(z0) until we reach a desired level of accuracy.

4. We already computed p'(z) in part 2, so we can use the formula to compute z1 as follows:

z1 = z0 - p(z0)/p'(z0)

= 4 - (78 + 10(4) - 20.5(4 - 4)^2 - 2.333(4 - 4)^3)/[6(4)^2 - 28(4)^3 - 10(4)^2 + 2(4) - 8]

= 3.9167

We can continue to iterate using this formula to get better approximations for the root of p(z).

Horner's algorithm is a fast and efficient way to evaluate a polynomial at a particular point. It involves using the distributive property of multiplication to rewrite a polynomial in a nested form, then evaluating the polynomial from the inside out.

In this problem, we will use Horner's algorithm to evaluate p(4) for a given polynomial, find its Taylor series expansion about the point z0 = 4, and then use Newton's method to find an approximation for a root of the polynomial.

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Answer:

2 root 17

Step-by-step explanation:

The square root of 68 in simplest radical form is 2√17

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

The square root of 68

Mathematically, we have

The square root of 68 = √68

Expand 68

So, we have

The square root of 68 = √(4 * 17)

So, we have

The square root of 68 = √4 * √17

Evaluate

The square root of 68 = 2 * √17

Evaluate the products

The square root of 68 = 2√17

Hence, the square root of 68 is 2√17

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Answer:

5 inches for 100 yards

Step-by-step explanation:

add 20 till u get 100 the add 1 for every time u add 20

Answer:

10

Step-by-step explanation:

3 x 3 + 5 - 6 + 2=

PEMDAS states we do multiplication first.

9 + 5 - 6 + 2

Since it's just addition and subtraction, we calculate left to right

14 - 6 + 2

8 + 2

10

Answer:

a)0.11

b) 3.75

Step-by-step explanation:

a) take 4 away from 15

B) do 15 divided by 4

hope this helps bye if right mark brainlest PLEASE