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Oksana_A [137]
3 years ago
9

Given the sequence 8, 12, 16, 20, 24, what is the sum of the 31st and 19th terms?

Mathematics
1 answer:
erica [24]3 years ago
7 0

Answer:

First term (a) =8

Common difference (d)= t2-t1

=12-8

=4

Now, sum of first 31th term (tn31) =n/2{2a+(n-1)d}

= 31/2{2×8+(31-1)4}

=31/2{16+(30×4)

=31/2(16+120)

=31/2×126

=31×63

Step-by-step explanation:

Similarly use 19 as (n) for the 19th term

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The window in Mr. Rodriguez's attic is in two parts, each shaped like a trapezoid and each with identical dimensions.
MaRussiya [10]

Answer and Step-by-step explanation:

First, ~multiply~base~and~height.~In~our~case~the~base~is~30~inches~and the~height~is~12~inches.Then,~we 'll~take~16~inches~and~multiply~it~with~12~inches

<u><em>So, it'll be :</em></u>

<u><em></em></u>30~inches × 12~inches =360~inches

16~inches × 12~inches=192~inches

Now,~that~we've~got~ 360 ~and~ 192~ as~ our~ answers ~we ~add~ them ~up..

<u><em>Like this :</em></u>

<u><em /></u>360+192=552<u><em /></u>

<u><em /></u>

<u><em /></u>And,~that's~our~final~answer!-522~in^2<u><em /></u>

4 0
3 years ago
Read 2 more answers
The angle measures are represented by algebraic expressions.
Anuta_ua [19.1K]

Answer:

The value of x is 0.5

The value of y is 0.8

The value of z is 0.9

Step-by-step explanation:

* Lets explain how to find the values of x , y and z

- <u><em>From the attached figure</em></u>

# l_{1} and l_{2} intersect each other at a point

- When two lines intersect each other at a point they formed

 congruent vertical opposite angles

∴ The angle of measure (50z + 13)° = the angle of measure (80z - 14)°

  because thy are vertical opposite angles

∴ 50z + 13 = 80z - 14

- Add 14 to both sides

∴ 50z + 27 = 80z

- Subtract 50z from both sides

∴ 27 = 30z

- Divide both sides by 30

∴ z=\frac{27}{30}=\frac{9}{10}=0.9

* The value of z is 0.9

- <u><em>From the attached figure</em></u>

# The angles of measures (50z + 13)° and (45x + 19/2)° have sum

   of 90°

∴ 50z + 13 + 45x + 19/2 = 90

∵ z = 0.9

∴ 50(0.9) + 13 + 45x + 19/2 = 90

∴ 45 + 13 + 45x + 9.5 = 90

- Add like term in the left hand side

∴ 67.5 + 45x = 90

- Subtract 67.5 from both sides

∴ 45x = 22.5

- Divide both sides by 45

∴ x = 0.5

* The value of x is 0.5

- <u><em>From the attached figure</em></u>

# There is a ray perpendicular to line l_{1}

∴ The measure of the angle whose measure (225y/2)° is 90°

∴ \frac{225y}{2}=90

- Multiply both sides by 2

∴ 225y = 180

- Divide both sides by 225

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* The value of y is 0.8

8 0
3 years ago
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Rudik [331]

Answer:

a=1/2b, 2a=b

Step-by-step explanation:

Since angle a is 1/2 the size of angle b, a=1/2b and b=2a. In order to get a numeral answer, you need the number of one of the angles.

7 0
2 years ago
According to the National Institute of Allergy and Infectious Diseases, approximately 7% of U.S. children 4 years of age or youn
Yuliya22 [10]

Answer:

0.337 = 33.7% probability that one of the eight children has a food allergy.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they have a food allergy, or they do not. The probability of a child having food allergy is independent of any other child. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

7% of U.S. children 4 years of age or younger have a food allergy.

This means that p = 0.07

A day care program has capacity for 8 children in that age range.

This means that n = 8

What is the probability that one of the eight children has a food allergy?

This is P(X = 1).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{8,1}.(0.07)^{1}.(0.93)^{7} = 0.337

0.337 = 33.7% probability that one of the eight children has a food allergy.

6 0
3 years ago
Y=2x+3 <br> y=3x+1 <br> solve the system of equations using substitution
Lynna [10]

Answer:

(2, 7 )

Step-by-step explanation:

Given the 2 equations

y = 2x + 3 → (1)

y = 3x + 1 → (2)

Substitute y = 3x + 1 into (1)

3x + 1 = 2x + 3 ( subtract 2x from both sides )

x + 1 = 3 ( subtract 1 from both sides )

x = 2

Substitute x = 2 into either of the 2 equations for corresponding value of y

Substituting x = 2 into (1)

y = 2(2) + 3 = 4 + 3 = 7

Solution is (2, 7 )

4 0
3 years ago
Read 2 more answers
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