Find the first five terms of the sequence: an = 5an – 1 + 2; a1 = 3.


a) {3, 17, 87, 437, 2187}

b) {3, 15, 75, 375, 1875}

c) {3, 12, 17, 22, 27}

d) {3, 11, 27, 59, 123}

The slope of the line is 2/3

To find the slope of the line, first choose two points that are on the line. For this example we'll use (0, -4) and (6, 0). Now use the slope formula with these two points to find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (0 - -4)/(6 - 0)

m = (0 + 4)/(6 - 0)

m = 4/6

m = 2/3

A number cube is rolled 120 times. The number 4 comes up 47 times.

We have to determine the experimental probability of rolling a 4.

The formula to evaluate probability of an event is given by:

Probability  = [tex] \frac{Favourable outcomes}{Total outcomes} [/tex]

So, Probability of rolling a 4 = [tex] \frac{ Total number of times when 4 appears}{Total number of times number cube rolled} [/tex]

= [tex] \frac{47}{120} [/tex]

Now, we have to find the theoretical probability of rolling a 4.

Total number of outcomes of number cube = {1,2,3,4,5,6}

Probability of rolling a 4 = [tex] \frac{1}{6} [/tex]

So, Option B is the correct answer.

The digit 4 in 6,296.04 is in the hundredths place, representing four hundredths or 4/100. This can also be expressed in scientific notation as 4 x 10⁻².

The place value of the digit 4 in 6,296.04 is in the hundredths position. This is because the digit 4 is two places to the right of the decimal point. In a decimal number, the first place to the right of the decimal point is the tenths place, the second is the hundredths place, and it continues with thousandths, ten-thousandths, and so on. Therefore, in the number 6,296.04, the 4 represents four hundredths, or 4/100, which can also be written in scientific notation as 4 × 10⁻².

[tex]Given \ function : \ f(x) = 2x^6-2x^2-5[/tex]

In order to find the end behavior of the graph, we need to find the degree of the given function and the leading coefficent.

Degree of the given function is the highest power of the variable.

We have variable x there.

Highest power of x is 6.

So, we can say:

Degree = 6 ( an even degree)

And leading coefficent is the coefficent of highest power term.

We have highest power term is 2x^6.

So, the leading coefficent is : 2 (Positive number)

For even degree and positive leading coefficent, end behaviour is

x --> ∞  f(x) = +∞

x-->-∞   f(x) = +∞

Answer:

The answer is A on edg

Step-by-step explanation:

just took the test

The graphs of sine and cosine functions have similarities with the swinging motion such as repeating patterns at equal time intervals and smoothness.

The graphs of sine and cosine functions have several similarities with the swinging motion you observe:

These similarities are because simple harmonic motion, which includes swinging, is closely related to sine and cosine waves.

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Answer:

Number is 23.

Step-by-step explanation:

We have been given the information when a number is divided by 22 the remainder is 1.

And when it is added to 5  it will give us an even number.

So, the number 23 if we take when divided by 22 it will give the remainder 1.

And when added to 5 it will give 23+5=28 which is an even number.

So, the number is 23.

Answer:
The shorter side is 5 inches and the longer side is 8 inches.

Explanation:
We start by listing formulas for solving for the area and perimeter of a rectangle, which will then determine how we find the dimensions we are looking for.

The area of a rectangle is length (l) times width (w), often represented as:
A = l(w), or A = lw

The perimeter of a rectangle is the sum of twice the length and twice the width, often represented as:
P = 2l + 2w

If product of length and width is 40 inches per the rectangle's given area, then a factor pair of 40 must be the dimensions of the rectangle. These values can then be checked to see if they also satisfy the perimeter of the rectangle.

So first, list factors of 40:
1, 40; 2, 20; 4, 10; 5, 8

Now, we plug these pairs into the perimeter equation.
2(1) + 2(40) = 2 + 80 = 82
82 > 26

2(2) + 2(20) = 4 + 40 = 44
44 > 26

2(4) + 2(10) = 8 + 20 = 28
28 > 26

2(5) + 2(8) = 10 + 16 = 26
26 = 26
Therefore, the factors 5 and 8 are what we use. 5 inches by 8 inches are the dimensions.

Answer:  [tex]1.6202[/tex]

Step-by-step explanation:

The given confidence level : c= 89.48%.

⇒ c= 0.8948   [ in decimal]

Then, the significance level = [tex]\alpha= 1-c[/tex]

[tex]=\alpha= 1-0.8948=0.1052[/tex]

Now, to find the value of [tex]z_{\alpha/2}[/tex] , we need to find the two -tailed z-value using z-table for [tex]\alpha=0.1052[/tex] or we can also find the one-tailed z-value for  for [tex]\alpha/2=0.1052/2=0.0526[/tex]

Using z-value table , the value is [tex]1.6202[/tex]

Hence , [tex]z_{\alpha/2}=1.6202[/tex] that corresponds to a confidence level of 89.48%.

Using confidence interval concepts, it is found that the critical value is [tex]z_{\frac{\alpha}{2}} = 1.62[/tex]

For a confidence level of [tex]\alpha[/tex], the critical value of z is z with a p-value of:

[tex]\frac{1 + \alpha}{2}[/tex]

In this problem, confidence level of 89.48%, thus [tex]\alpha = 0.8948[/tex] the p-value of the z-score is:

[tex]\frac{1 + 0.8948}{2} = 0.9474[/tex]

Looking at the z-table, this value is [tex]z_{\frac{\alpha}{2}} = 1.62[/tex].

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Final Answer:

The probability that at least one of the four randomly selected people has been vaccinated is approximately 0.9606.

Explanation:

To find the probability that at least one of the four randomly selected people has been vaccinated, we can use the complement rule. The complement of "at least one person vaccinated" is "none of the people vaccinated." Then, we subtract the probability of none of them being vaccinated from 1.

Given that 61% of the population has been vaccinated, the probability that a randomly selected person has been vaccinated is [tex](P(\text{vaccinated}) = 0.61\)[/tex].

So, the probability that a randomly selected person has not been vaccinated is [tex]\(P(\text{not vaccinated}) = 1 - P(\text{vaccinated}) = 1 - 0.61 = 0.39\).[/tex]

Now, we can find the probability that none of the four randomly selected people has been vaccinated:

[tex]\[P(\text{none vaccinated}) = (0.39)^4\][/tex]

And the probability that at least one of them has been vaccinated is the complement of this:

[tex]\[P(\text{at least one vaccinated}) = 1 - P(\text{none vaccinated}) = 1 - (0.39)^4\][/tex]

Let's calculate it:

[tex]\[P(\text{at least one vaccinated}) = 1 - (0.39)^4\][/tex]

[tex]\[P(\text{at least one vaccinated}) \approx 1 - 0.0394179 \][/tex]

[tex]\[P(\text{at least one vaccinated}) \approx 0.9605821\][/tex]

So, the probability that at least one of the four randomly selected people has been vaccinated is approximately 0.9606.

The probability that at least one of the 4 randomly selected people has been vaccinated is calculated using the complement rule and is found to be 0.9769.

To determine the probability that at least one of the 4 randomly selected people has been vaccinated, we can use the complement rule. The probability of an individual not being vaccinated is 1 - 0.61 = 0.39.

We need to calculate the probability that none of the 4 selected people are vaccinated and subtract this from 1:

Thus, the probability that at least one of them is vaccinated is:

1 - 0.0231 = 0.9769

Therefore, the probability that at least one of the 4 randomly selected people has been vaccinated is 0.9769.

The number of  students enrolled this year are 17,360.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, the number of students enrolled at a community college increase by 12% from last year to this.

The enrollment last year to this year was 15,500.

Increased number of students are

12% of 15500

= 12/100 ×15500

= 12×155

= 1860

Number of students enrolled this year are 15,500+1860

= 17360

Therefore, the number of  students enrolled this year are 17,360.

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To find the balance after 10 years when $20,000 is invested at 5% interest compounded annually, we can use the formula for compound interest:

A = P(1+r)ⁿ

Where:

*A is the complete volume of money obtained after

*n years, including interest.

*P embodies the initial investment, or the principle amount.

*The yearly interest rate, calculated by decimal, is r.

*n is the number of periods the money has been put into investments for.

Given:

*P = $20,000

*r = 5% = 0.05

*n = 10 years

Taking appropriate values to carry out the calculation:

A = 20000(1 + 0.05)¹⁰

A = 20000(1.05)¹⁰

Now, let's calculate:

A ≈ 20000 × (1.05)¹⁰

A ≈ 20000 × 1.62889462677744

A ≈ 32577.89

So, the balance after 10 years will be approximately $32,577.89.

After 10 years, the balance of the investment can be calculated using the formula for compound interest: A = P(1+r)ⁿ

Where:

*A is the amount of money accumulated after

*n years, including interest.

*P is the principal amount (the initial investment).

*r is the annual interest rate (in decimal).

*n is the number of times the interest is compounded per year.

In this case, the principal (P) is $20,000, the annual interest rate (r) is 5%, and the investment is compounded annually. Substituting these values into the formula:

A = 20000(1.05)¹⁰

A ≈ 20000 × (1.05)¹⁰

After computation, the balance after 10 years is approximately $32,577.89. This represents the accumulated amount including the initial investment and the interest earned over the 10-year period.

Complete Question:

Suppose your friend’s parents invest $20,000 in an account paying 5% interest compounded annually. What will the balance be after 10yr?

volume of the rectangular prism = base area * height

base area = length * breadth

volume of the rectangular prism = length * breadth * height

volume of the rectangular prism = 5*8*2 = 80 inches ^3

volume of taken up by the eraser = 5.5 inches^3

volume that is not take-up by the eraser = 80-5.5 = 74.5 inches^3