1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ghella [55]
3 years ago
5

The third term in an arithmetic sequence is 9 and the fifth term is 21 . If the first term if a1, which is an equation for the n

th term of this sequence?
A:an=6n-9
B:an=14n+6
C:an=6n+14
D:an=9n-6
Mathematics
1 answer:
tino4ka555 [31]3 years ago
3 0

Answer:

A: an = 6n - 9

Step-by-step explanation:

third term in an arithmetic sequence is 9

a3 = a + 2d

a + 2d = 9

the fifth term is 21

a5 = a + 4d

a + 4d = 21

a + 2d = 9 (1)

a + 4d = 21 (2)

Subtract (1) from (2) to eliminate a

4d - 2d = 21 - 9

2d = 12

d = 12/2

d = 6

Substitute d = 6 into (1)

a + 2d = 9 (1)

a + 2(6) = 9

a + 12 = 9

a = 9 - 12

a = -3

nth term of this sequence = a + (n - 1)d

= -3 + (n - 1)6

= -3 + 6n - 6

= 6n - 9

an = 6n - 9

You might be interested in
Professor Halen teaches a College Mathematics class. The scores on the midterm exam are normally distributed with a mean of 72.3
lbvjy [14]

Answer:

14.63% probability that a student scores between 82 and 90

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 72.3, \sigma = 8.9

What is the probability that a student scores between 82 and 90?

This is the pvalue of Z when X = 90 subtracted by the pvalue of Z when X = 82. So

X = 90

Z = \frac{X - \mu}{\sigma}

Z = \frac{90 - 73.9}{8.9}

Z = 1.81

Z = 1.81 has a pvalue of 0.9649

X = 82

Z = \frac{X - \mu}{\sigma}

Z = \frac{82 - 73.9}{8.9}

Z = 0.91

Z = 0.91 has a pvalue of 0.8186

0.9649 - 0.8186 = 0.1463

14.63% probability that a student scores between 82 and 90

3 0
3 years ago
What is 15/4 as a mixed number?
max2010maxim [7]
It would be: 15/4 = 3 3/4

In short, Your Answer would be 3 3/4

Hope this helps!
8 0
3 years ago
The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere. Wh
viktelen [127]

Answer:

Radius of sphere is 3 units.

Step-by-step explanation:

Volume of sphere is given by 4/3 \pi r^3

surface area of sphere is given by 4 \pi r^2

where r is the radius of the sphere.

Given that

The number of cubic units in the volume of a sphere is equal to the number of square units in the surface area of the sphere.

we equate formula of Volume of sphere  and surface area of sphere

assuming r as the radius.

thus,

4/3 \pi r^3 = 4 \pi r^2\\\\4/3 \pi r^3/ 4 \pi r^2 = 1\\=>r/3 = 1\\=> r = 3

Thus, radius of sphere is 3 units.

5 0
3 years ago
A scale model of a tower is 24 inches tall and 18 inches wide. If the height of the actual tower is 60 feet, what is its width?
alex41 [277]

Answer:

45 feet

Step-by-step explanation:

To find the width of the model, we need to find the scale of the model to the actual tower.

Since we know the height of both towers, we can use that as the basis.

24 inches : 60 feet

12 inches : 30 feet

6 inches : 15 feet

So the width of the tower is 18 inches wide.

18 inches will then be equal to 12 + 7 inches : 30 + 15 feet

18 inches : 45 feet

6 0
3 years ago
A store is having a sale on jellybeans in trail mix. For 2 pounds of jellybeans and 12 pounds of trail mix, the total cost is $2
Tresset [83]

Answer:

The jelly beans cost $2.25 / pound

The trail mix costs $1.25 / pound

Step-by-step explanation:

Let +a+ = cost/pound of jelly beans

Let +b+ = cost/pound of trail mix

(1) 6a + 2b =16

(2) 3a + 5b =13

Multiply both sides by 2  

and subtract (1) from (2)

(2) 6a -2b = -16

(1) -6a -2b = -16

8b=10

b=1.25

and

(1) 6a+2b=16

(1) +3a+b=8

(1) 3a+1.25=8

(1) +3a=6.75

(1) a=2.25

4 0
3 years ago
Other questions:
  • Simplify the expression 2x - 4 + 3
    12·2 answers
  • One tea bag can brew two or three cups of tea. Anastasia and Elizabeth shared the box of tea bags equally. Anastasia made 57 cup
    15·2 answers
  • Let p and q be rational. Prove that p+q is rational
    9·1 answer
  • Create a scenario for y=3x+4 will mark brainliest
    5·1 answer
  • Which one ????????????
    6·1 answer
  • A person might accidentally overdraw because they did not reconcile their statement. True False
    13·2 answers
  • PLEASE HELP ASAP :)))))))) Rachelle is watching a bug crawl toward her on a sidewalk. As the bug gets closer to her, she stomps
    5·1 answer
  • James and Cameron are watching a film. They pause it with one fifth left to watch. What is the ratio of how much they have watch
    11·1 answer
  • Which BEST describes the construction of a triangle if given one side length of 10 cm and one right angle?
    6·1 answer
  • What is the difference between-2 and -8
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!