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2 years ago

A8=21 a10=27 find nth term arthemetic sequence

Mathematics

1 answer:

Contact [7]2 years ago

8 0

Answer:

an = 3n - 3

Step-by-step explanation:

The nth term of an arithmetic progression is expressed as;

an = a + (n-1)d

a is the first term

n is the number of terms

d is the common difference

a8 = a + (8-1)d

a8 = a + 7d = 21 ....1

a10 = a+9d = 27 ....2

Subtract 1 from 2

7d - 9d = 21 - 27

-2d = -6

d = -6/-2

d = 3

Since a + 7d = 21

a + 7(3) = 31

a + 21 = 21

a = 21 - 21

a = 0

Get the nth term

Recall that an = a + (n-1)d

an = 0 + (n-1)*3

an = 3n - 3

Hence the nth term of the sequence is 3n - 3

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A box is filled with 2 brown cards,8 yellow cards, and 8 green cards. A card is chosen at random from the box. What is the proba

IgorLugansk [536]

2 brown, 8 yellow, 8 green, thus our sample space is 2+8+8 = 18.

What is the probability that the card is NOT yellow? How many non-yellow are there? well 2 + 8 = 10, favorable outcomes.

$\bf \cfrac{\stackrel{\textit{favorable outcomes}}{10}}{\underset{\textit{sample space}}{18}}\implies \cfrac{5}{9}\implies 0.\overline{555}\qquad \approx \qquad 55.6\%$

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3 years ago

Plz help and explain

Westkost [7]

Answer: B

Step-by-step explanation:

In order to get the best representative sample, you should choose the widest range of students, which is from a random sample of all students.

(A) Choosing from only the 6th graders, eliminates the choices the other grade-level students would choose.

(C) Choosing only from students who participate in after-school activities, eliminates the choices the other students would choose.

(D) Chhosing only from students not participating in the fundraiser is silly since you want to know what the students participating in the fundraiser would choose.

The only possible option is B - students from all grades, regardless of whether or not they participate in after-school activities.

5 0

3 years ago

How do I find the inverse of this problem?

raketka [301]

$\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}$

Actually Welcome to the Concept of the Inverse of real function.

Let's consider here, g(n) = y ,

so we get as,

$y = \sqrt[3]{ \frac{n - 1}{2} }$

no, cubing the power both side we get as,

${y}^{3} = \frac{n - 1}{2}$

now,

$2 {y}^{3} = n - 1$

so finally, we get as,

$n = 2 {y}^{3} + 1$

hence,here, n = inverse of the g(n) function.

so,

g^-1 (n) = 2y^3+1.

7 0

2 years ago

Suppose we have a right triangle with legs of length a and b and hypotenuse of length c. Suppose b=3 and c=5. Then a= , For the

ANTONII [103]

Answer:

Length of right-angle triangle 'a' = 4

$sin(A) = \frac{opposite side}{Hypotenuse} = \frac{a}{c} = \frac{4}{5}$

$cos(A) = \frac{Adjacent side}{Hypotenuse} = \frac{b}{c} = \frac{3}{5}$

$tan(A) = \frac{opposite side}{Adjacent side} = \frac{a}{b} = \frac{4}{3}$

Step-by-step explanation:

Step(i):-

Given b = 3 and hypotenuse c = 5

Given ΔABC is a right angle triangle

By using pythagoras theorem

c² = a² + b²

⇒ a² = c² - b²

⇒ a² = 5²-3²

=25 - 9

a² = 16

⇒ a = √16 = 4

The sides of right angle triangle a = 4 ,b = 3 and c = 5

Step(ii):-

$sin(A) = \frac{opposite side}{Hypotenuse} = \frac{a}{c} = \frac{4}{5}$

$cos(A) = \frac{Adjacent side}{Hypotenuse} = \frac{b}{c} = \frac{3}{5}$

$tan(A) = \frac{opposite side}{Adjacent side} = \frac{a}{b} = \frac{4}{3}$

7 0

2 years ago

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

yan [13]

Answer:

138.16 in²

Step-by-step explanation:

The surface area SA of the cone is the sum of the base area B and the lateral area LA. The lateral area is half the product of the circumference and the slant height. The radius is half the diameter, so is 4 inches.

SA = B + LA

= πr² + (1/2)(2πrh) . . . . where h is the slant height

= (πr)(r +h)

Filling in the numbers, you have ...

SA = (3.14)(4 in)(4 in + 7 in) = 3.14×(44 in²) = 138.16 in²

7 0

3 years ago