Mathematics High School

Find the 31st term of the following sequence.

9, 15, 21, ...

Answers

Answer 1

Notice that the above sequence is arithmetic because the common difference: d is constant.

d = second term - first term.

= 15 - 9

= 6

The general term of an arithmetic sequence is,

a_{n} =a_{1} +(n-1)d

Where , nth term = [tex] a_{n} [/tex]

[tex] a_{1} [/tex] = First term

and d = common difference.

The given sequence is: 9, 15, 21, ...

Here a_{1} = 9,

d = 6

We need to find the 31st term. So, n = 31.

Next step is to plug in these values in the above formula. Therefore,

[tex] a_{31} =9 +(31-1)*6 [/tex]

= 9 + 30* 6

= 9 + 180

= 189

So, 31st term of this sequence is 189.

Hope this helps you.

Answer 2

Answer:

189

Step-by-step explanation:

Related Questions

While catching fireflies, you and a friend decide to have a competition. After mm minutes, you have (3m+13)(3m+13) fireflies and your friend has (4m+6)(4m+6) fireflies.
a. How many fireflies are caught each minute during the competition?1m+7 fireflies are caught per minute.
b. How many fireflies are caught before the competition starts? fireflies are caught before the competition starts.

Answers

a. 7 fireflies are caught per minute. b. 19 fireflies were already caught prior to the contest starting. a. Looking at the equations (3m + 13) and (4m + 6) where m is equal to the number of minutes since the contest began, it's obvious that there are 3+4 = 7 fireflies caught per minute. b. One again, look at the two equations. Or for that matter, calculate them both and add the results for m=0 (the moment the contest began). And upon doing so, you'll see that 13 + 6 = 19 fireflies were caught prior to the competition starting.

Answer: the equation is 7m + 19

Step-by-step explanation:

Is an equation that has 0 for a solution the same as an equation with no solution?

Answers

the solution exists and has the value of zero and is not in any manner the same as no solution value exists at all.

HELP ASAP 115 points please hurry...
help asap please hurry...15 points.

Clara estimates that the length of a hiking trail is 10 km. She later learns that its actual length is 12 km.

What is the percent error in Clara's estimate?

.002%

8.0%

0.2%

11.5%

Answers

Experimental value = 10 km
accepted value = 12 km

Step 1: Deduct the accepted value from the experimental value.

10 km – 12km = -2 km

Step 2: Take the absolute value of step 1

|--2km| = 2km

Step 3: Divide that answer by the accepted value. 2km/10km = 0.2%

 

Keith's florists has 15 delivery trucks, used mainly to deliver flowers and flower arrangements in the greenville, south carolina, area. of these 15 trucks, 5 have brake problems. a sample of 4 trucks is randomly selected. what is the probability that 2 of those tested have defective brakes?

Answers

Given the fact that 5 out of the 15 trucks have brake problems, we can find the probability that a delivery truck has brake problems as 5/15 = 0.3333. In the sample of 4 trucks, the number of trucks that have defective brackets is a binomially distributed random variable with n = 4 and p = 0.3333. Using the formula for binomial distribution, we get P(X = 2) = 4C2 * 0.3333² * (1–0.3333)² = 0.2963.
The answer is 0.2963. 
 

Answer:

Hence, the probability is:

0.296

Step-by-step explanation:

This can be solved with the help of the binomial probability as:

[tex]P(x=r)=n_C_rp^r(1-p)^{n-r}[/tex]

where n denote the quantity which are chosen.

r denote the quantity whose probability is to be determined or success.

and p denote the probability of success.

with n=4 since 4 trucks are randomly selected.

p=5/15=1/3 ( As 5 have brake problems out of total 15 trucks)

1-p=10/15=2/3

r=2 ( since we are asked to find the probability that 2 of those tested have defective brakes)

Hence, the probability is:

[tex]P(x=2)=4_C_2(\dfrac{1}{3})^2(\dfrac{2}{3})^2\\\\\\P(x=2)=\dfrac{4!}{2!\times (4-2)!}\times \dfrac{1}{9}\times \dfrac{4}{9}\\\\\\P(x=2)=0.296[/tex]

Hence, the probability is:

0.296

Patrick is making 8 pizzas. he has 15 2/3 cups of mozzarella cheese that he wants to divide evenly among the pizzas.

how many cups of cheese should he put on the pizzas?

Answers

Since Patrick has 15 2/3 cups of mozzarella to distribute among 8 pizzas; take 15 2/3 and divide it by 8. 15 2/3 must be converted to a mixed number (take denominator 3 times the whole number 15 = 45 and add the numerator 2 which give you 47/3 (denominator remains the same) so you have  47/3). Take
47/3 and divide it by 8 but you have to convert the division in to multiplication and use the reciprocal of 8 which would be 8 = its reciprocal 1/8. We are now left with 47/3 x 1/8 = 47/24; take 47/24 and simplify by taking 47 divided by 24 and we would have 1 23/24 cups per pizza.


Which ordered pairs are a solution to the equation?

y = 3x

Select all that apply.

(-1,3)


(2,5)


(1,3)


(-2,-6)

Answers

(1,3) and (-2,-6) are the only ones that apply. 
All you do is substitute all four of the coordinates back into the equation:
A. 3=3(-1)    3=-3    So the first choice does not work.
B. 5=3(2)     5=6     So the second choice doesn't work
C. 3=3(1)     3=3     So the third choice works
D. -6=3(-2)  -6=-6   So the fourth choice works

Please help thank you!

Answers

1 is D, an angle bisector only cuts the original angle in half.

2 is 
9x - 18 = 3x
6x - 18 = 0
6x = 18
x = 3

3 is 9(3) - 18 = 27 - 18 = 9

Which statement correctly describes the relationship between △RST and △R’S’T?

Answers

The answer is the third statement. "The triangles are congruent because triangle  R'S'T' is a rotation of triangle RST and rotation in a rigid motion" The triangles are congruent because the image is a rotation (There is a rotation of 180 degrees) of the original and a rotation is a rigid motion. The best way to test it out is to assign values to the points for points R, S, and T and then apply the rule to see where the new image will be. 

Help pleaseeeeeee!!!!!

Answers

Take a look at the tree diagram. The first branching shows the probabilities of there being oil, or not being oil.

Then, for each case we consider the probabilities of the kit being accurate or not.

we are interested in the branch Oil---Kit accurate---

Since P(Oil)=0.45, and P(Kit accurate)=0.8, the probability of there being oil and the Kit showing it correctly is:

0.45*0.8=0.36.

Answer: C) 0.36
The answer is C 0.36

A video game arcade offers a yearly membership with reduced rates for game play. A single membership costs $60 per year. Game tokens can be purchased by members at the reduced rate of $1.00 per 10 tokens. Which statements represent the function of the yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Check all that apply. The slope of the function is $1.00. The y-intercept of the function is $60. The function can be represented by the equation y = 1/10x + 60. The domain is all real numbers. The range is {y| y ≥ 60}.

Answers

The y-intercept of the function is $60
The function can be represented by the equation y=1/10x+60
The range is {y| y ≥ 60}
The range is (Y) y>60

Um navio esta situado exatamente a 10 milhas a leste de um ponto A. Um observador, situado exatamente a sul do navio, ve o ponto A sob um angulo de 40°. Qual a distância entre o observador e o navio?

Answers

1) Considerando o ponto A, um vertice; o ponto O  onde o observador está e por ultimo, o ponto N que é onde o navio está.
Com estes 3 pontos formamos um triangulo. 
O angulo OAN vale 40º
O lado AN vale 10 milhas
O que queremos saber é a distância entre o observador e o navio: lado NO

2) Para isso calculamos a tangente deste angulo: tg 40º= angulo oposto/ angulo adjacente.
angulo oposto é o NO e o lado adjacente ao angulo é o AN que vale 10

Se fores à calculadora vês que tg40º é 0,83.
0,83= angulo oposto/ 10
ang oposto= 8,3 milhas
o observador e o navio estao a  8,3 milhas de distancia

Find three consecutive even integers such that the sum of twice the smallest number and three times the largest is 42.

Answers

let x be the first 
the second x +2 
the third x+ 4


twice the smallest  2x

three times the largest  3(x+4 )
 
2x + 3(x+4 )=42

2x +3x +12 = 42

5x= 30

x=6        the second is 8   the third is 10

Given that BC = 7, AB = 17.89, and C is between A and B, what is the length of ?

Answers

*assuming that ABC is a straight line** 
then you have 
AB = 17.89 ..... this is the length of the whole line 

BC is a part of the line = 7 

therefore the length of the other part = 17.89 - 7 

= 10.89
17.89-7=10.89
You know that the distance from A to b is 17.89 and the distance from b to c is 7.  So the length from a to c is the whole distance(a to b) subtracted by a portion of the distance(b to c) giving us 10.89

What is Henry's speed

Answers

60 miles per hour; if you look at where x= 1 on the graph (one hour) y is equal to 60(which is the distance)
Therefore, for every hour henry travels 60 miles

What is the value of x?



Enter your answer in the box.
x =
°
Triangle A B C with angle A measuring thirty degrees, angle B measuring seventy degrees and angle C marked x

Answers

Since triangles always have a total amount of 180 degrees, adding the amounts we already know and subtracting that amount from 180, we get the value x. So the answer would be 80 degrees.

Answer: In a triangle, the sum of the 3 angles is always equal to 180°

Then if the angle A is equal to 30°, the angle B is equal to 70°, what is the angle C?

if x is the angle C, and using the first statement, we got:

30° + 70° + x = 180°

100° + x = 180°

x = 180° - 100° = 80°

So the angle of C is equal to 80°.

Write an equation for a rational function that has a vertical asymptote at x=1 and a hole at x=3

Answers

(x-3)
--------
(x-3)(x-1) aka x^2 - 4x+ 3

A car travels 252 miles in 5 hours and 15 minutes. how many miles does it travel per hour?

Answers

Answer:

48 miles per hour

Step-by-step explanation:

5hrs and 15minutes = 315minutes

If 252 = 315

       x = 60

By cross multiplication

315x = 60 * 252

315x = 15,120

x = 15120/315

x = 48 miles per hour

Solve these Multi-Step Equations (include work): 6-8, 9 & 10 (is the equation right? if not please help)

Answers

6. 8(t+2)-3(t-4)=6(t-7)+8
8t+16-3t+12=6t-42+8
8t-6t=-42+8-16-12
2t=-62
t=-62/2
t=-31

How many times larger is a 10-pound dog than a hamster weighing 5/8 pound?

Answers

To determine how many times larger is a 10-pound dog compared to a 5/8-pound hamster, we divide the mass of the dog by the mass of the hamster. This is as shown below,
               n = mass of the dog / mass of the hamster

Substituting the known value,
              n = 10 lb/ 5/8 lb
              n = 16

ANSWER: 16 times

Write the expression in algebraic form. [hint: sketch a right triangle.] tan(arcsec(x/3))

Answers

Sketch  a right triangle having adjacent side(A) is given as “3”, hypotenuse side (H) is “x” and assigning angle “a” as the angle between A and H. Using Pythagorean theorem, you will get “square root of x-squared minus 9” as the opposite side (O). Using SOH CAH TOA function, and since secant is the reciprocal of cosine, sec(a) = x/3. Thus, a = arcsec(x/3). The remaining expression tan(a) is Opposite side over Adjacent side which is equal to “square root of x^2 - 9” over "3". Therefore, the algebraic expression would be: tan(arcsec(x/3)) = “sqrt (x^2 -9)” /3. Different answers can be made depending on which side you consider the “3” and “x”.

The area of a rectangle is 45 square inches. The rectangle is 9 inches long. How wide is the rectangle?

A. 5 inches

B. 36 inches

C. 27 inches

D. 3 inches

Answers

the answer is definitely 5 :)

Final answer:

To find the width of a rectangle with an area of 45 square inches and a length of 9 inches, divide the area by the length, resulting in a width of 5 inches (Option A).

Explanation:

The area of a rectangle can be calculated by multiplying its length by its width. In this case, we know the area is 45 square inches and the length is 9 inches. To find the width, we divide the area by the length.

Width = Area ÷ Length = 45 sq in ÷ 9 in = 5 in

Therefore, the width of the rectangle is 5 inches, which corresponds to option A.

Which equation could be used to solve the problem?



Mr. Guzman drove his car 1080 miles in 6 weeks.



If he drove the same distance every week, which equation shows how far he drove each week (d)?



A.


d = 6 ÷ 1080



B.


d = 1080 – 6


C.


d = 1080 • 6


D.


d = 1080 ÷ 6

Answers

The answer is d :)

All you have to do is take the distance she drove and divide it by how many weeks it took.

Mr. Guzman drove 1080 miles in 6 weeks. To find the distance driven each week, use the equation d = 1080 ÷ 6, which equals 180 miles per week. Therefore, the correct equation is option D.

Mr. Guzman drove 1080 miles in 6 weeks. We need to find out how far he drove each week if he drove the same distance every week.

Identify the Total Distance Driven: 1080 milesIdentify the Total Time Period: 6 weeks

Set Up the Equation: Since Mr. Guzman drove the same distance every week, we use the formula:

d = Total Distance / Total Time.

Substitute Known Values:

d = 1080 ÷ 6

Calculate the Result:

d = 180 miles per week

The correct equation that shows how far Mr. Guzman drove each week is d = 1080 ÷ 6, which corresponds to option D.

The point slope of a line that has a slope of -2 and passes through point (5,-2) is shown below. Which equation is in slope intercept form?

Answers

y + 2 = -2(x - 5)

Simplify.

y + 2 = -2x + 10

Subtract 2 from both sides.

y = -2x + 10 - 2

Simplify.

y = -2x + 8 → Slope-intercept form

Our answer is the second option : y=-2x+8

~Hope I helped!~
 

Answer:

B. y=-2x+8

Step-by-step explanation:

edge

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 75 miles per hour. The westbound train travels at 65 miles per hour. How long will it take for the two trains to be 196 miles apart?

Answers

75+65=140
196/140=1.4 hrs, or 84 minutes
☺☺☺☺

What is the length of side AB

Answers

The length of AB is 90. You add 45 + 45 to get 90.

Erin had $35 more than Angie who had 3 times as as money as Jacob. If they had $196 altogether, how much money did Jacob have?

Answers

let j be Jacob's money. Then Angie is 3j, and Erin is 3j+35. So:
j+3j+3j+35=196
7j=161
j=23
Jacob had $23
☺☺☺☺

I need help with 13 please ASAP

Answers

338.50 - 45 = 293.50 was spent on tolls

293.50 / 14 = 20.96

 so 21 tolls

How to turn a fraction into a percentage?

Answers

Convert the fraction to a decimal number. The fraction bar between the top number (numerator) and the bottom number (denominator) means "divided by." So converting a fraction such as 1/4 to a decimal means you need to solve the math: 1 divided by 4.

i hope i helped

A firework exploded 1,360 meters away and the sound of the firework took 4 seconds to reach you. At what speed did the sound travel?

Answers

The answer is 340 meters per second. You divide the distance by the time to get the answer.

Answer:

Speed of sound, v = 340 m/s

Step-by-step explanation:

It is given that,

A exploded 1360 meters away, d = 1360 meters

time taken, t = 4 seconds

We need to find the speed of the travelled sound. Speed of sound is equal to the distance covered divided by total time taken i.e.

[tex]v=\dfrac{d}{t}[/tex]

[tex]v=\dfrac{1360\ m}{4\ s}[/tex]

v = 340 m/s

So, the speed with which sound is travelled is 340 m/s. Hence, this is the required solution.

find the perimeter of a ruler that measures 12 inches by 7/8 inch.

Answers

I'm pretty sure that the answer is 10.5 I hope this helps
12+12+7/8+7/8
24+7/8+7/8
24+1+6/8
25+3/4
25 3/4 inches
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