Malik is buying a guinea pig. The guinea pig comes with a cage and food bowls for $ 125.00 . The expenses for feeding and caring for the guinea pig are $ 18.00 each month. How much will it cost Malik to buy and care for the guinea pig for one year?

Answers

Answer 1
Answer:

Answer:

$341.00

Step-by-step explanation:

"$ 18.00 each month."

$18.00*$12.00=$216.00

$216.00+$125.00=$341.00

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A fruit juice box contains 6% juice how is this percent rent as a decimal

Answers

Answer:

0.06

Step-by-step explanation:

6% = 0.06

0.06  as a decimal Hope this helped!

seal had a balance of negative $4 in his saving account after making a deposit he has $25 in his account what is the overall change in his account

Answers

He deposited $29, so a $29 dollar difference

On a recent trip to the convenience store, you picked up 3 gallons of milk, 4 bottles of water, and 7 snack-size bags ofchips. Your total bill (before tax) was $23.40. If a bottle of water costs twice as much as a bag of chips, and a gallon of
milk costs $2.20 more than a bottle of water, how much does each item cost?

Answers

Answer:

bottle of water: $1.60

gallon of milk: $3.80

bag of chips: $0.80

Step-by-step explanation:

First, the amount of groceries bought can be represented as:

3m + 4w + 7c = \$ 23.40

where m represents the cost of one gallon of milk, w represents the cost of a bottle of water, c represents the cost of one bag of chips.

We can form a system of equation by constructing another equation to substitute into the first using the other pieces of information given.

"a bottle of water costs twice as much as a bag of chips"

w = 2c  →  c = (w)/(2)

"milk costs $2.20 more than a bottle of water"

m = w + \$ 2.20

Now, substitute these into the first equation and solve for w in terms of c.

3(w + 2.20) + 4w + 7\cdot (w)/(2) = 23.40

3w + 6.60 + 4w + (7)/(2) \, w = 23.40

(21)/(2) \, w = 16.80

21w = 33.60

w = 1.60

So, one bottle of water costs $1.60.

To solve for the other items, plug the solved value into the 2-variable equations.

m = 1.60 + 2.20

m = 3.80

So, one gallon of milk costs $3.80.

c = (1.60)/(2)

c = 0.80

So, one bag of chips costs $0.80.

Evaluate the indefinite integral as a power series f(x) = 1 tan-1(x7) dx n=0 What is the radius of convergence R? R= -/0.77 points
Evaluate the indefinite integral as a power series x7 In(1 x) dx f(x) = C + n=0
What is the radius of convergence R?

Answers

Answer:

A.

\mathbf{f(x)=C +  \sum \limits ^(\infty)_(n=0) ((-1)^n \ x^(14n +8))/((2n+1)(14n+8))}

For convergence  since |x| > 1

The radius of convergence R = 1

B.

\mathbf{f(x) = C + \sum \limits ^(\infty)_(n =0)  \frac{(-1)^n \ x^(n+9)} {(n+1) (x^(n+9))}}

For convergence  since |x| < 1

The radius of convergence R = 1

Step-by-step explanation:

A.

Given that:

f(x) = \int tan^(-1) (x^7) \ dx

Let recall that for Power series of tan⁻¹ (x)

tan^(-1) (x) = \sum \limits ^(\infty)_(n=0) ((-1)^n x^(2n+1))/((2n+1))

Then tan^(-1) (x^7) = \sum \limits ^(\infty)_(n=0) ((-1)^n (x^7)^(2n+1))/((2n+1))

tan^(-1) (x^7) = \sum \limits ^(\infty)_(n=0) ((-1)^n  \ x^(14n+7))/((2n+1))

Thus;

f(x) =\int  tan^(-1) (x^7) \ dx = \int \sum \limits ^(\infty)_(n=0) ((-1)^n  \ x^(14n+7))/((2n+1))

\implies  \sum \limits ^(\infty)_(n=0) ((-1)^n )/((2n+1)) \int  x^(14n+7) \ dx

\mathbf{f(x)=C +  \sum \limits ^(\infty)_(n=0) ((-1)^n \ x^(14n +8))/((2n+1)(14n+8))}

For convergence  since |x| > 1

The radius of convergence R = 1

B.

\int x^7 \ In (1 + x) \ dx

Recall that for power series of,

In(1+x) = \sum \limits ^(\infty)_(n = 0) ((-1)^n \ x^(n+1))/(n +1)

Thus;

x^7 \ In (1+x) = x^7 \sum \limits ^(\infty)_(n =0)  ((-1)^n \ x^(n+1) )/(n+1)

\implies  \sum \limits ^(\infty)_(n =0)  ((-1)^n \ x^(n+8) )/(n+1)

f(x) = \int x^7 \ In (1+x) \ dx =  \int  \sum \limits ^(\infty)_(n =0)  ((-1)^n \ x^(n+8) )/(n+1) \ dx

=\sum \limits ^(\infty)_(n =0)  ((-1)^n)/(n+1)  \int  \ x^(n+8) \ dx

\mathbf{f(x) = C + \sum \limits ^(\infty)_(n =0)  \frac{(-1)^n \ x^(n+9)} {(n+1) (x^(n+9))}}

For convergence  since |x| < 1

The radius of convergence R = 1

Final answer:

To evaluate the indefinite integral as a power series for the given equations, we use the power series expansions of the functions involved. The radius of convergence, R, is the distance from the center of the power series to the nearest point where the power series diverges.

Explanation:

To evaluate the indefinite integral f(x) = 1/tan-1(x7) dx as a power series, we can use the power series expansion of tan-1(x). The power series expansion of tan-1(x) is x - (x3/3) + (x5/5) - (x7/7) + .... We substitute x7 for x in the power series expansion and integrate term by term. The radius of convergence, R, is the distance from the center of the power series to the nearest point where the power series diverges.

To evaluate the indefinite integral f(x) = x7ln(1-x) dx as a power series, we can use the power series expansion of ln(1-x). The power series expansion of ln(1-x) is -x - (x2/2) - (x3/3) - (x4/4) - .... We substitute x7 for x in the power series expansion and integrate term by term. The radius of convergence, R, is the distance from the center of the power series to the nearest point where the power series diverges.

Learn more about Integration using power series here:

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PLEASE HELP?Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted.

The table below shows the soft drinks preferences of people in three age groups.

If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age.

Answers

The required probability of that the person is of over 40 years of age. Option D is correct.

Given that,
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age is to be determined.

What is probability?

Probability can be defined as the ratio of favorable outcomes to the totalnumber of events.

Here,
Let the total number of people that has age of more than 40 years,
= 20 + 30 + 35
= 85
Now,
According to the question,
Probability is given as,
= 85 / 255
= 1/3


Thus, the required probability of that the person is of over 40 years of age. Option D is correct.

Learn more about probability here:

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Answer:

1/3

Step-by-step explanation:

The number of people over 40 is 20 + 30 + 35 = 85.

So the probability is 85/255, which reduces to 1/3.

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If the graph of the second equation in the system passes through (-12, 20) and (4,12), which statement is true?

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I don’t any idea for this