what are the first four terms if a1=2 and an= an-1 +3?

Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.

What is answer parallel line?

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.

Parallel lines are two lines in the same plane that are equal distance apart and never intersect.

Real-world parallel line examples include railroad tracks, sidewalk edges, street markings, zebra crossings, the surface of pineapple and strawberry fruit, staircases and railings, and so on.

Parallel lines are lines in a plane that never meet, no matter how far they are extended. The distance between the parallel lines is constant because they never meet.

Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.

these are 8 parallel lines

2x+3y = 6

2x+3y = 4

2x+3y = 1

2x+3y = 2

2x+3y = 3

2x+3y = 8

2x+3y = 7

2x+3y = 5

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Let's see

\(\\ \rm\rightarrowtail (fog)(x)=f(g(x))\)

\(\\ \rm\rightarrowtail f(5x-4)=20x+p\)

\(\\ \rm\rightarrowtail 4(5x-4)+3=20x+p\)

\(\\ \rm\rightarrowtail 20x-16+3=20x+p\)

\(\\ \rm\rightarrowtail -13=p\)

Answer:

\(\sf p = -13\)

Step-by-step explanation:

Given functions:

\(\sf f(x)=4x+3\)

\(\sf g(x)=5x-4\)

\(\sf fg(x)=20x+p\)

\(\sf fg(x)=f[g(x)]\)

This means g(x) is substituted for x in f(x).

\(\sf \implies f[g(x)]=4[g(x)]+3\)

                 \(\sf =4(5x-4)+3\)

                  \(\sf= 20x-16+3\)

                  \(\sf =20x-13\)

\(\sf f[g(x)]=f[g(x)]\)

\(\sf \implies 20x+p=20x-13\)

\(\sf \implies p=-13\)

Answer:

2.8 years

Step-by-step explanation:

Answer: x+ 2x -3 = 12

Step-by-step explanation:

x represents Michael's laps. 2x -3 represents Braden's laps. Added together for a total of 12

One step further would be to combine the x terms, so the equation becomes 3x - 3 = 12

Answer:

explanation

Step-by-step explanation:

it drives 18 miles?

I'm not sure.

if I am right plz give brainliest

Let the number be n, then -1<3n+5<38 or -1≤3n+5≤38 depending on what is meant by “between”. We’ll assume the former.

-1<3n+5<38, subtract 5 throughout: -6<3n<33, divide through by 3: -2<n<11, shows the number to be in the range (-2,11) or possibly [-2,11].

For f(1) = 0 the statement is true that (x - 1) is the factor of the function.

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given a function,

f(x) = x⁶ - x⁴ + 2x² - 2

and f(1) = 0

substitute the values,

f(x) = x⁶ - x⁴ + 2x² - 2

f(1) = 1⁶ - 1⁴ + 2(1)² - 2

f(1) = 0

so when x = 1 function is zero,

so x - 1 = 0 and (x - 1) is one of the factor of function f(x).

Hence the statement is true.

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Answer:

\(\large \boxed{\sf \ \ 70\% \ \ }\)

Step-by-step explanation:

Hello,

We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :

   \(1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})\)

For the second week

   \(1000\cdot (1+\dfrac{r}{5200})^2\)

After 52 weeks

   \(1000\cdot (1+\dfrac{r}{5200})^{52}\)

and we want to be equal to 2000 so we need to solve:

\(1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...\)

Rounded to the nearest percent, the solution is 70%.

If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

4%

Step-by-step explanation:

The answer to this question requires the use of the Poisson distribution and the cumulative distribution function.

(a) We are asked to find the probability that the fourth person weighed is the first person to be overweight. Since 63% of Americans are overweight, this means that the probability of a randomly selected American being overweight is 0.63. The probability of the first overweight person being the fourth person weighed is given by P(X=3) where X is the number of overweight people in the first 4 people weighed. Using the binomial distribution formula, we have:

\(P(X=3) = (4 choose 3) * (0.63)^3 * (0.37)^1\\\\ = 4 * (0.63)^3 * (0.37)\)

(b) We are asked to find the probability that it takes more than 4 people to observe the first overweight person. This is equivalent to finding the probability that none of the first 4 people weighed are overweight. Using the complement rule, we have:

\(P(X=0) = 1 - P(X > 0)\\\\ = 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4)]\\\\ = 1 - [ (4 choose 1) * (0.63)^1 * (0.37)^3 + (4 choose 2) * (0.63)^2 * (0.37)^2 + P(X=3) ]\)

(c)  The expected value (mean) of a binomial distribution is given by μ = np, where n is the number of trials and p is the probability of success in each trial. In this case, n=4 and p=0.63. Thus, the mean number of overweight people in 4 trials is 4 * 0.63 = 2.52. The variance of a binomial distribution is given by σ^2 = np(1-p), so in this case the variance is 4 * 0.63 * 0.37 = 1.41. The standard deviation is the square root of the variance, so the standard deviation is approximately \(\sqrt{(1.41) } = 1.19\). This means that the number of overweight people in 4 trials is expected to be around 2.52, with a standard deviation of 1.19.

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Answer:

  75 seconds

Step-by-step explanation:

You want to know how long it took Sean to drink his slushy, given a graph of amount remaining versus time.

Sean will have finished his slushy when the amount remaining is zero. That point on the graph occurs when the time is 75 seconds.

It takes 75 seconds for Sean to finish the slushy.

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Complete question:

A wheel of radius 10 cm is turning at a rate of 5 revolutions per minute.

Calculate  the angle subtended at the centre by the minor arc after 1 second.

Answer:

the angle subtended at the centre by the minor arc is 30⁰

Step-by-step explanation:

Given;

radius of the wheel, r = 10 cm = 0.1 m

angular speed of the when, ω = 5 rev/min

duration of the motion, t = 1 second

Determine the angular speed in radian per second,

\(\omega = 5\ \frac{rev}{\min} \times \frac{2\pi \ rad}{1 \ rev} \ \times \frac{1 \min}{60 \ s} = \frac{10\pi \ rad}{60 \ s} = \frac{\pi }{6} rad/s\)

After 1 second, the angular distance turned by the wheel is calculated as;

\(\theta = \omega t\\\\\theta = \frac{\pi \ rad} {6 \ s} \times 1 \ s\\\\\theta = \frac{\pi } {6 } \ rad\\\\in \ degrees; \theta = \frac{\pi \ rad}{6} \times \frac{180^0}{\pi \ rad} = \frac{180^0}{6} = 30^0\)

Therefore, the angle subtended at the centre by the minor arc is 30⁰

The null hypothesis is formulated as a statement of equality to represent the assumption of no effect, no difference, or no relationship between variables in hypothesis testing.

The null hypothesis is typically formulated as a statement of equality because it represents the assumption or claim of no effect, no difference, or no relationship between variables in the context of statistical hypothesis testing.

When conducting hypothesis tests, we start with the assumption that there is no significant difference or relationship between variables, and any observed differences or relationships are merely due to random chance or sampling variability. The null hypothesis serves as a benchmark or reference point against which we compare the observed data.

Formulating the null hypothesis as a statement of equality allows for a clear and specific claim to be tested statistically. It sets the baseline or default position that is assumed to be true unless there is sufficient evidence to reject it in favor of an alternative hypothesis.

For example, in a study comparing the mean scores of two groups, the null hypothesis might state that the population means are equal (μ1 = μ2). This implies that any observed difference in sample means is due to chance, rather than a true difference in the population means.

By specifying the null hypothesis as a statement of equality, statistical tests provide a framework to assess the likelihood of observing the obtained data under the assumption of no effect or no difference, allowing us to make inference and draw conclusions about the population parameters based on the evidence from the sample.

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The student council sold $273$ t-shirts were sold at $\$10$ per shirt.

Let $x$ be the number of shirts sold at $\$10$

Let $y$ be the number of shirts sold at $\$12$

$x+y=661$

$10x+12y=3780$

$x=y+101$

$10y+12y=3780$

$22y=3780$

$y=172$

$x=172+101$

$x=273$

Hence $273$ t-shirts were sold at $\$10$ per shirt.

If they sold $661$ t-shirts in total, and they made a mistake when recording the amount of t-shirts sold at each price, then they actually sold more t-shirts at $\$10$ than they thought. This means that they thought they sold fewer t-shirts at $\$10$ than they actually did.

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Answer:

10^-9

Step-by-step explanation:

Answer:

45 * 100 / 330 = amount in 100 ml of solution

13.6363636364  grams

Step-by-step explanation:

Answer:

Cost of ties and pants = $52.5

Step-by-step explanation:

Total cost of ties = $19.99

cost of dress pants = $64, discountted by 30%

discount on dress pants = 30% of 64 = 0.3 × 64 = $19.2

∴ Discounted price of dress pants = 64 - 19.2 = $44.8

Total cost of ties and dress pants = 19.99 + 44.8 = $64.79

Now, let us apply the coupon

coupon = $10 off every purchase of $50 or more

Purchase amount = $64.79 ;  therefore coupon applies.

Applying coupon

Purchase amount = 64.79 - 10 = $54.79

sale tax = 6% or purchase price

sale tax = 6% × 54.79

sale tax = 0.06 × 54.79 = $3.29

∴ Final cost of ties and dress pants = 54.79 - 3.29 = $52.5

Answer:

f(1) = 8

Common ratio: 0.5

Step-by-step explanation:

f(1) is the first term, which is 8.

The common ratio = 4/8 = 2/4 = 1/2   etc

Rounding a percentage to the nearest whole number can be done by considering the decimal part of the percentage. For the percentages provided, 11.969 would round to 12%, 39.9804 would round to 40%, and 11.61+32 would equal 43.

To round a percentage to the nearest whole number, we examine the decimal part. If the decimal is 0.5 or greater, we round up to the next whole number. If the decimal is less than 0.5, we round down to the previous whole number. In the given examples, 11.969 has a decimal of 0.969, which is closer to 1 than to 0, so it rounds up to 12. Similarly, 39.9804 has a decimal of 0.9804, which is closer to 1, resulting in rounding up to 40. Lastly, the expression 11.61 + 32 equals 43, as it is a straightforward addition calculation.

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Answer:

A. vertex B

B. Side BC and BD

C. Angle EBD

Step-by-step explanation:

An angle is an undefined term in plane geometry.

Vertex of \(\angle 4\)

The vertex of an angle is the point where the rays that form the angle meet.

From the diagram, rays BE and BA meet at point B to form \(\angle 4\).

Hence, the name of the vertex is B

Sides of \(\angle 1\)

The sides of an angle are the rays or sides that form the angle

\(\angle 1\) is formed by rays BC and BD

Hence, the sides are BC and BD

Another name for \(\angle 5\)

An angle can be named by combining the sides and the vertex.

The sides of \(\angle 5\) are DB and BE, while the vertex is B

This means that rays DB and BE meet at point B

Hence, another name is \(\angle DBE\)

Classify the angles

Angles are classified based on the measure

\(\angle FBC\) is a right angle, because \(\angle FBC = 90^o\)

\(\angle EBF\) is an obtuse angle because \(\angle EBF\) is greater than \(90^o\) but less than \(180^o\)

\(\angle ABC\) is a straight angle, because \(\angle ABC= 180^o\)

Angle bisector

The line or ray that divides an angle into equal halves is an angle bisector.

Ray BE is an angle bisector, because it divides \(\angle DBA\) into two equal halves.

Find \(\angle EBC\)

We have:

\(\angle EBD = 36\)

\(\angle DBC = 108\)

\(\angle EBC\) is calculated using:

\(\angle EBC = \angle EBD +\angle DBC\)

\(\angle EBC = 108+36\)

\(\angle EBC = 144\)

Find \(\angle ABE\)

We have:

\(\angle EBF = 117\)

\(\angle DBC = 108\)

\(\angle ABE\) is calculated using:

\(\angle EBF = \angle ABE +\angle EBD + \angle ABF\)

Where

\(\angle ABF = 90\)

\(\angle ABE = \angle EBD\)

So, we have:

\(117 = \angle ABE +\angle ABE + \angle 90\)

\(117 = 2\angle ABE + 90\)

Collect like terms

\(2\angle ABE =117 - 90\)

\(2\angle ABE =27\)

Divide both sides by 2

\(\angle ABE =13.5\)

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Answer:

95

Step-by-step explanation:

The length of the y of the triangle is y = 96 inches

The Law of Cosines is a mathematical formula used to find an unknown side or angle of a triangle, given the lengths of the other two sides and the angle opposite the unknown side. It is also known as the Cosine Rule.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite side c, the following equation is true:

c² = a² + b² - 2ab cos(C)

where cos(C) is the cosine of angle C. This formula can be rearranged to solve for any of the variables, depending on which values are known.

Given data ,

Let the triangle be represented as ΔXYZ

And , the measures of the sides of the triangle are

z = 75 inches

x = 26 inches

And , the measure of ∠Y = 135°

We can use the Law of Cosines to find the length of y, since we know two sides and the included angle of the triangle.

The Law of Cosines states that:

c² = a² + b² - 2ab cos(C)

where c is the side opposite angle C, and a and b are the other two sides.

In this case, we want to find the length of side y, which is opposite angle Y. So we can write:

y² = x² + z² - 2xz cos(Y)

Substituting in the given values, we get:

y² = 26² + 75² + 2(26)(75) cos(135°)

Simplifying, we get:

y² = 676 + 5625 - 2925√2

y² ≈ 9163

Taking the square root of both sides, we get:

y ≈ 95.76

Rounding to the nearest inch, we get:

y ≈ 96 inches

Hence , the length of y, to the nearest inch, is 96 inches

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margin of error = z* * sqrt(pq/n) = 1.55 * sqrt(0.150.85/280) ≈ 0.056

Rounded to 3 decimals, the margin of error is 0.056.

The 88% confidence interval for the percent of men in the general population who are color blind is:

p ± margin of error = 0.15 ± 0.056

Lower Bound: 0.15 - 0.056 = 0.094

Upper Bound: 0.15 + 0.056 = 0.206

Rounded to 3 decimals, the 88% confidence interval is (0.094, 0.206).

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In this case the answer is very simple. .

Step 01:

Data

side a = 8m

side b = 15m

c = hypotenuse = ?

Step 02:

Pythagoras Theorem Formula

Hypotenuse² = Perpendicular² + Base²

c² = a² + b²

c ² = (8m)² + (15m)²

c ² = 64m² + 225m²

c ² = 289m²

Answer:

The answers for this question are 1 and 0

Answer:

the correct answers are 1 and 0

Answer:

A - Sales associate

B - Summer Camp Counselor

Step-by-step explanation:

First, lets look at how much Joseph would averagely earn from each job.

Cashier in bookstore: in 6 weeks he will earn 900

Summer camp counselor: in 4 weeks 700

Sales associate: in 4 weeks he will earn 850

Overall, becoming a Sales associate will allow Joseph to earn his $850 quicker.

B - the Summer Camp Counselor job will not allow Joseph to make $850 because Summer Camp only lasts 4 weeks.

Step-by-step explanation:

so sorry

don't know but please mark me as brainliest please

Answer:

At least be nice about it bruh.

In this study on road rage, a random sample of 596 men and 523 women were surveyed about their driving behavior.

Based on their responses, each individual was assigned a road rage score on a scale of .

The road rage score scale should be selected according to the researcher's preference, and it should be explained.The researcher should clarify how the data was collected in order to improve the study's transparency and reliability.

ll of these aspects should be explained to make the research findings more reliable.The study's results should be presented in tabular or graphical format to better comprehend the data.

The researcher can use bar charts, pie charts, or histograms, among other things. The researcher should also utilize statistical tools such as mean, median, and mode to present the data's central tendency.

Based on the road rage score results, the study's conclusions and implications should be drawn.

The researcher should emphasize the gender-based findings of the study and discuss whether there is a difference between male and female road rage. Furthermore, the study should propose measures to reduce road rage among motorists.

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The plane travels 2500 miles in 5 hours. The solution has been obtained by using unitary method.

What is the unitary method?

Using the unitary technique, the value of each individual unit is first calculated, and then the value of the necessary number of units is determined.

We are given that an airplane travels 125 miles in 1/4 hour. It travels the same number of miles each hour.

Using unitary method,

The miles traveled in 1 hour = 125 * 4 = 500 miles

So, the miles traveled in 5 hours = 500 * 5 = 2500 miles

Hence, the plane travels 2500 miles in 5 hours.

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Question:  An airplane travels 125 miles in 1/4 hour. It travels the same number of miles each hour. How many miles does the plane travel in 5 hours?

Given:

A number is 400.

To find:

The additive inverse of 400.

Solution:

We know that the sum of a number and its additive inverse is 0.

If "a" is number and "b" is its additive inverse, then

\(a+b=0\)

Let x be the additive inverse of 400. Then,

\(400+x=0\)

Subtract both sides by 400.

\(400+x-400=0-400\)

\(x=-400\)

Therefore, the additive inverse of 400 is \(-400\).