write an equation that describes the sequence below. use n to represent the position of a term in the sequence

Answer:

Use dimensional analysis to answer each of the following questions. To find the distance light travels in a year for part a, convert sec to yr by using unit ratios with min, hr, and days in their denominators. Thus, a light year is approximately 5,874,589,152,000 mi

The number of miles that the light covers in a light year will be 5.89 × 10¹² miles.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

At 186282 miles per second.

We know that in one light year, the number of seconds will be 31.536 × 10⁶.

Then the distance is given as,

186282 = d / (31.536 × 10⁶)

d = 31.536 × 10⁶ × 186282

d = 5.89 × 10¹² miles

The number of miles that the light covers in a light year will be 5.89 × 10¹² miles.

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Answer:

I) coordinate of P is (11, 5.5)

II) Points are not collinear

Step-by-step explanation:

I) Let the coordinates of P be (a, b)

We are told that its x-coordinate is twice its y-coordinate. Thus, a = 2b

Now, P is equidistant from R(-2, 4) and S(6,-4). Thus;

PR = PS

Using the formula for distance between two coordinates, we have;

√((a - (-2))² + (b - 4)²) = √((a - 6)² + (b - (-4))²)

This gives;

(a + 2)² + (b - 4)² = (a - 6)² + (b + 4)²

Since a = 2b,then we have;

(2b + 2)² + (b - 4)² = (2b - 6)² + (b + 4)²

4b² + 8b + 4 + b² - 8b + 16 = 4b² - 12b + 36 + b² + 8b + 16

Simplifying this gives;

20 = 42 - 4b

42 - 20 = 4b

4b = 22

b = 22/4

b = 11/2

b = 5.5

Since a = 2b

Then a = 2 × 5.5

a = 11

Thus, coordinate of P is (11, 5.5)

II) Formula for area of triangle formed by three points is given as;

A = ½|(x1 - x2) (x2 - x3)|

|(y1 - y2) (y2 - y3)|

x1 - x2 = 11 - (-2) = 13

x2 - x3 = -2 - 6 = -8

y1 - y2 = 5.5 - 4 = 1.5

y2 - y3 = 4 - (-4) = 8

Thus;

A = ½|13 -8|

|1.5 8|

A = ½((13 × 8) - (1.5 × - 8))

A = ½(104 + 12)

A = 58

Since the area is not zero, then it means the points are not collinear.

Answer:

ab=56

Step-by-step explanation:

14 x 4 = 56

Answer:

56

Step-by-step explanation:

14*4 = 56

AB = multiplication

Answer:

\(115 \dfrac{1}{2}\:cm^3\)

Step-by-step explanation:

The volume of a rectangular prism is the product of each of the sides of the prism

Given the sides have lengths
\(3\dfrac{1}{2}, 6 \;and\; 5 \dfrac{1}{2} cm\)

the volume would be
\(3\dfrac{1}{2} \times 6 \times 5 \dfrac{1}{2}\)

To perform this multiplication, convert mixed fractions to improper fractions first

Use the rule that mixed fraction
\(a\dfrac{b}{c}=\dfrac{a\times \:c+b}{c}\)

\(3\dfrac{1}{2}=\dfrac{3\times 2+1}{2} = \dfrac{7}{2}\)

\(5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}= \dfrac{11}{2}\)

Therefore
\(3\dfrac{1}{2}\times \:6\times \:5\dfrac{1}{2}\\\\= \dfrac{7}{2}\times \:6\times \dfrac{11}{2}\\\\= \dfrac{7}{2}\times \dfrac{6}{1}\times \dfrac{11}{2} \quad(6 = \dfrac{6}{1})\)

\(=\dfrac{7\times \:6\times \:11}{2\times \:1\times \:2}\\\\= \dfrac{462}{4}\\\)

Divide numerator and denominator by 2 to get
\(\dfrac{231}{2}\\\)

Convert improper fraction \(\dfrac{231}{2}\) to mixed fraction using quotient/remainder

\(\dfrac{231}{2} \\\\\rightarrow Quotient: 115\\\\\rightarrow Remainder = 231 - 115 \times 2 = 231 - 230 = 1\)

\(\dfrac{231}{2} = 115 \dfrac{1}{2}\)

Answer:

5

Step-by-step explanation:

Q is asking how many (1/3)s are in (15/8):

(15/8) / (1/3)

(to divide fractions, flip the second fraction over and then multiply)

(15/8) * (3/1)

(15 * 3) / (8*1)

45/8

=5.625

Answer:

n=2

Step-by-step explanation:

(6n-7)+(8n+2)=23

14n-5=23

14n=28

n=2

Answer:

Step-by-step explanation:

Answer:(4,5π/4)

Step-by-step explanation:

Note that the point is on the circle whose radius is labeled 4, so r=4. The angle of the point is 5π4, so θ=5π4. Thus, the polar coordinates are (4,5π4).

Answer:

(A-c)/8 = b

Step-by-step explanation:

A = 8b +c

A - c = b

(A-c)/8 = b

Hope this helps you!

We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D

We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.

If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.

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Answer:

(L-6)(L+2)

Step-by-step explanation:

Let L be the length of the flower garden.

Then the width will be L-4.

The area of the flower garden = L*(L-4) =L²-4L

The area of the birdbath is 3*4 = 12 ft²

The area of the remaining space for planting is

= Area of flower garden - area of birdbath

We can factor the expression as follows:

taking common frome each two terms

Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.

Answer:

7

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

Answer:

–3

Step-by-step explanation:

i got 90% on my quiz also may i pleas get brainliest

Answer:

6 inches

Step-by-step explanation:

You can write this as a ratio of a length over width.

\(\frac{12}{9}=\frac{8}{x}\)

Cross Multiply:

12x=72

x=6

Answer:

The first step is to calculate the average daily balance for the billing cycle. This is done by adding up the daily balances for each day of the billing cycle and then dividing by the number of days in the billing cycle. In this case, the billing cycle is from July 7 to August 6, so there are 31 days in the billing cycle.

The daily balances are as follows:

* July 7: $216.71

* July 14: $268.75

* July 17: $284.37

* July 21: $116.71

* July 24: $260.74

The average daily balance is therefore $226.81.

The next step is to calculate the finance charge. This is done by multiplying the average daily balance by the interest rate and then by the number of days in the billing cycle. In this case, the interest rate is 1.25% and the number of days in the billing cycle is 31 days.

The finance charge is therefore $7.43.

The final step is to calculate the new balance. This is done by adding the finance charge to the previous balance. In this case, the previous balance is $216.71 and the finance charge is $7.43. The new balance is therefore $224.14.

Here is the solution in mathematical form:

* Average daily balance = (216.71 + 268.75 + 284.37 + 116.71 + 260.74) / 31 = 226.81

* Finance charge = 226.81 * 0.0125 * 31 = 7.43

* New balance = 216.71 + 7.43 = 224.14

Step-by-step explanation:

Answer: \(\frac{1}{4}\)

Step-by-step explanation:

Given

For 30 ml of orange Juice

45 ml of apple Juice is needed and

25 ml of coconut milk is required

The proportion of coconut milk in the cocktail is

\(\Rightarrow \dfrac{\text{amount of coconut milk}}{\text{total volume of mixture}}\\\\\Rightarrow \dfrac{25}{30+45+25}=\dfrac{25}{100}\\\\\Rightarrow \dfrac{1}{4}\)

Answer: Yes

Step-by-step explanation: A rational number is a number that can be described as a fraction. -92 can be a fraction, therefor it's rational.

No

A rational number is any number that can be expressed as a ratio of two integers. For example, 1.5 is rational since it can be written as 3/2, 6/4, 9/6 or another fraction or two integers. Pi is irrational since it cannot be written as a fraction.

The perimeter of the actual pool will be option C. 1100 ft.

It's the sum of the length of the sides used to make the given figure.

A scale drawing of a new pool is shown. All the corners are at right angles.

The lengths are 6 in, 2 in, 5 in and 3 in.

Perimeter = 6 + 2 + 5 + 3 + 2 + 4

                 = 22 in

We have given a scale;

1/2 in = 25 ft

So, 1 in = 50 ft

26 in will be

22 x  50 = 1100 ft

Hence, the perimeter of the actual pool will be option C. 1100 ft.

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The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

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Problem 1

Answer: C) No solution

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

Explanation:

We have z = -4 and 4z = -4 at the same time. Solving 4z = -4 leads to z = -1

So in effect we have z = -4 and z = -1 at the same time, but this is a contradiction. A variable can only hold one number at a time.

======================================================

Problem 2

Answer: C) Infinitely many solutions

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

Explanation:

The two equations are equivalent. You can prove as such by isolating 2y in the first equation.

5x = 8-2y

5x+2y = 8

2y = 8-5x

2y = -5x+8

-5x+8 = 2y

This shows the first equation is equivalent to the second, and vice versa. They both graph the same line. Any point along the line is a solution. So that's why there are infinitely many of them.

======================================================

Problem 3

Answer: Choice A) \(-6 < y \le 3\)

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

Explanation:

The range is the set of the possible y values. We're concerned with every y coordinate of each (x,y) solution. So we only focus on the shaded region.

The dashed line means we exclude the boundary. It's an electric fence we cannot touch. So y > -6 or -6 < y describes part of the range

The other part is \(y \le 3\) since y = 3 is the when the highest point occurs.

So writing \(-6 < y \le 3\) describes all possible y values of each (x,y) solution in the shaded region.

Answer:

I believe it is A or D

Step-by-step explanation:

I took this a while ago I can't remember the answer fully, but I believe it's a or d

My theorems include the Pythagoras theorem, midpoint theorem, and angle bisector theorem.

The Pythagoras theorem is used to find the length in a right angle.

The midpoint theorem states that the line segment in a triangle is parallel to the third side and is half the length.

The angle bisector theorem is concerned with the lengths of the two segments that the triangle side is divided into by a line which bisects the opposite angle.

I like them because they're important when solving triangle related problems.

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Answer:

5.58

Step-by-step explanation:

The distance of a rock after three seconds will be 144 feet.

A function is an assertion, concept, or principle that establishes an association between two variables.

Let's use the formula for direct variation, which is:

d = kt²

64 = k(2²)

64 = 4k

k = 16

Now we can use this value of k to find the distance when t = 3:

d = 16 × (3²)

d = 16(9)

d = 144

Therefore, the rock will fall 144 feet in 3 seconds.

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The complete question is given below.

The distance, d, that a rock falls when dropped from a cliff varies directly as the square of time, t, the rock is falling. If a rock falls 64 feet in 2 seconds, how far will it fall in 3 seconds?

The question is incomplete. The complete question is :

The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 24 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period.

a. Which form of the null and alternative hypotheses most appropriate for this situation.

\($H_0$\): is (greater than or equal to 24/greater than 24/less than or equal to 24/less than 24/equal to 24/not equal to 24)

\($H_a$\): is (greater than or equal to 24/greater than 24/less than or equal to 24/less than 24/equal to 24/not equal to 24)

Solution :

It is given that the current mean sales volume in one month is 24 automobiles. The automobile dealership manager wants to conducts research study to check the increase in the sales volume due to the launch of a new bonus plan. So to collect the data on plan, sample of the sales personnel is allowed to sell for one month period only according to the new bonus plan.

Therefore the null hypothesis and the alternate hypothesis that most appropriates the situation is :

Answer:

\(y=-\frac{4}{5}x-\frac{21}{5}\)

Step-by-step explanation:

The fastest way is to use point-slope form with \(m=-\frac{4}{5}\) and \((x_1,y_1)=(-4,-1)\):

\(y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}\)

To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting m = -4/5, x = -4, and y = -1, we can solve for b:

-1 = (-4/5)(-4) + b

-1 = 3.2 + b

b = -4.2

Therefore, the equation of the line is:

y = (-4/5)x - 4.2

To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:

y = (-4/5)x - 4.2

y = (-4/5)(0) - 4.2

y = -4.2

So the y-intercept is (0,-4.2).

Using this point and the given point (-4,-1), we can draw a straight line passing through both points.

Here is a rough sketch of the graph:

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     |   /

     |  /

-----*--------

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The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.