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3 years ago

The sum of three consecutive odd numbers is 69. What is the third number in this sequence?

Mathematics

1 answer:

Papessa [141]3 years ago

4 0

let the first odd number = x

the sum of three consecutive odd numbers is 69

(x) + (x + 2) + (x + 4) = 69

Simplify. Combine like terms

3x + 6 = 69

Isolate the x. Note the equal sign. What you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 6 from both sides

3x + 6 (-6) = 69 (-6)

3x = 63

Next, divide 3 from both sides to isolate the x.

3x/3 = 63/3

x = 63/3

x = 21

To solve for the third number, plug in 21 back into x.

(x + 4)

21 + 4 = 25

The third number is 25

hope this helps

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7/12 divided by 2/5 I need help thanks and bye

Law Incorporation [45]

hey there!

7/12 divided by 2/5 is 7/30

first you have to find the reciprocal for 2 / 5 can do that by flipping 2 / 5 you'll then get 5 / 2 now the rest is simple all you have to do is multiply 7/12 by 2/5 so you multiply 7 by 2 and you get 14 that's your numerator 10 divide 12 by 5 and you'll get 60 so now you have 14 / 60 7 / 30 now you simplify and you get

I hope I helped please mark me brainliest

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3 0

3 years ago

When a frequency distribution is exhaustive, each individual, object, or measurement from a sample or population must appear in

KiRa [710]

Answer:

a. True

Step-by-step explanation:

The frequency distribution is a summary of the gathered data set, in which the interval of values is divided into classes.

A requirement for a frequency distribution is for the classes to be mutually exclusive and exhaustive. That is, each individual, object, or measurement in the data set must belong to one and only one class.

Then, we can conclude that each individual, object, or measurement must appear in at least one (in fact, only in one) category or class.

4 0

4 years ago

A company that produces fine crystal knows from experience that 13% of its goblets have cosmetic flaws and must be classified as

Kisachek [45]

Answer:

(a) The probability that only one goblet is a second among six randomly selected goblets is 0.3888.

(b) The probability that at least two goblet is a second among six randomly selected goblets is 0.1776.

Step-by-step explanation:

Let X = number of seconds in the batch.

The probability of the random variable X is, p = 0.31.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

$P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...$

(a)

Compute the probability that only one goblet is a second among six randomly selected goblets as follows:

$P(X=1)={6\choose 1}0.13^{1}(1-0.13)^{6-1}\\=6\times 0.13\times 0.4984\\=0.3888$

Thus, the probability that only one goblet is a second among six randomly selected goblets is 0.3888.

(b)

Compute the probability that at least two goblet is a second among six randomly selected goblets as follows:

P (X ≥ 2) = 1 - P (X < 2)

$=1-{6\choose 0}0.13^{0}(1-0.13)^{6-0}-{6\choose 1}0.13^{1}(1-0.13)^{6-1}\\=1-0.4336+0.3888\\=0.1776$

Thus, the probability that at least two goblet is a second among six randomly selected goblets is 0.1776.

(c)

If goblets are examined one by one then to find four that are not seconds we need to select either 4 goblets that are not seconds or 5 goblets including only 1 second.

P (4 not seconds) = P (X = 0; n = 4) + P (X = 1; n = 5)

$={4\choose 0}0.13^{0}(1-0.13)^{4-0}+{5\choose 1}0.13^{1}(1-0.13)^{5-1}\\=0.5729+0.3724\\=0.9453$

Thus, the probability that at most five must be selected to find four that are not seconds is 0.9453.

8 0

3 years ago

A car dealership pays you 4% commission on your first $8,000 in car sales and 8% commission on additional sales over the $8,000.

Zigmanuir [339]

Answer:

Total Commission = $400

Step-by-step explanation:

Since total is $9000 (in sales) -- commision is 4% on the first $8000 and 8% in the additional part over $8000 (9000-8000=1000). So 8% on $1000.

Total commission = 4% of 8000 + 8% of 1000

= (0.04)(8000) + (0.08)(1000)

= 400

Total Commission is $400

7 0

3 years ago

Read 2 more answers

Kate has a rectangular garden that is 8 feet long by 3 feet wide. She wishes to extend the length and width by the same amount i

elena55 [62]

Let the extension of the length and width be x.
The new dimensions are: Length = 8+x
Width =3+x
Area = 104 ft squared
Area of a rectangle = Length x Width
Therefore,
(8+x)(3+x) = 104
x^2 +11x +24=104
x^2 +11x +24-104=0
x^2 +11x-80=0

Factorize using splitting the middle term method. X^2 +16x-5x-80=0 x(x+16)-5(x+16)=0 (x-5)(x+16)=0 either x-5 = 0 or x+16=0 x=5 or x=-16 length and width measure cannot be negative. Therefore, the extension of the length and width is 5 feet each.

4 0

3 years ago