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grigory [225]
3 years ago
15

What is the common difference of the arithmetic sequence 5, 8, 11, 14?

Mathematics
1 answer:
AnnZ [28]3 years ago
3 0

Answer:

The common difference is 3

Step-by-step explanation:

we know that

In an <u>Arithmetic Sequence</u> the difference between one term and the next is a constant called the common difference

we have

5,8,11,14

so

a1=5

a2=8

a3=11

a4=14

a2-a1=8-5=3

a3-a2=11-8=3

a4-a3=14-11=3

therefore

The common difference is 3

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A couple intends to have two children, and suppose that approximately 52% of births are male and 48% are female.
Pachacha [2.7K]

a) Probability of both being males is 27%

b) Probability of both being females is 23%

c) Probability of having exactly one male and one female is 50%

Step-by-step explanation:

a)

The probability that the birth is a male can be written as

p(m) = 0.52 (which corresponds to 52%)

While the probability that the birth is a female can be written as

p(f) = 0.48 (which corresponds to 48%)

Here we want to calculate the probability that over  2 births, both are male. Since the two births are two independent events (the probability of the 2nd to be a male  does not depend on the fact that the 1st one is a male), then the probability of both being males is given by the product of the individual probabilities:

p(mm)=p(m)\cdot p(m)

And substituting, we find

p(mm)=0.52\cdot 0.52 = 0.27

So, 27%.

b)

In this case, we want to find the probability that both children are female, so the probability

p(ff)

As in the previous case, the probability of the 2nd child to be a female is independent from whether the 1st one is a male or a female: therefore, we can apply the rule for independent events, and this means that the probability that both children are females is the product of the individual probability of a child being a female:

p(ff)=p(f)\cdot p(f)

And substituting

p(f)=0.48

We find:

p(ff)=0.48\cdot 0.48=0.23

Which means 23%.

c)

In this case, we want to find the probability they have exactly one male and exactly one female child. This is given by the sum of two probabilities:

- The probability that 1st child is a male and 2nd child is a female, namely p(mf)

- The probability that 1st child is a female and 2nd child is a male, namely p(fm)

So, this probability is

p(mf Ufm)=p(mf)+p(fm)

We have:

p(mf)=p(m)\cdot p(f)=0.52\cdot 0.48=0.25

p(fm)=p(f)\cdot p(m)=0.48\cdot 0.52=0.25

Therefore, this probability is

p(mfUfm)=0.25+0.25=0.50

So, 50%.

Learn more about probabilities:

brainly.com/question/5751004

brainly.com/question/6649771

brainly.com/question/8799684

brainly.com/question/7888686

#LearnwithBrainly

5 0
3 years ago
Help.. or die.. you decide.
Studentka2010 [4]

Answer:

<u>Problem 1:</u>

x = 12 unit ; y = 120 ; z = 60 ; perimeter = 58 unit

<u>Problem 2:</u>

FG = 16 unit ; EG = 2√153 unit ; y = 5 unit

Step-by-step explanation:

<u>Problem 1</u>

Since ABCD is a parallelogram. so,

∠ABC = ∠ADC  [Since opposite angles of a parallelogram are equal]

but, ∠ADC = 120° [given]------------(1)

So, ∠ ABC = y° = 120° ----------------(2)

Again, sum of two consecutive angles of a parallelogram is, 180°, so,

∠BCD + ∠ADC = 180°

So, ∠BCD =z°  =  180° - 120° = 60° [Putting the value of ∠ADC from (1)]-----(3)

Again, since opposite sides of a parallelogram are equal,

so, BC = AD

⇒ (x + 5) = 17

⇒ x = 12------------------------(4)

So, AB = 12 unit , AD = 17 unit

So, the perimeter of the parallelogram is given by,

2(AB + AD)

= 2 \times (12 + 17)  unit

= 58 unit --------------------------------------------------------------(5)

<u>Problem 2</u>

Perimeter of parallelogram EFGH = 52 unit

So, 2(EH + GH) = 52 unit

⇒ 2 ( x + x + 6) = 52

⇒ 4x = 40

⇒ x = 10

Now,  FG = EH [since opposite sides of a parallelogram are equal]

            = (x + 6) unit

            = (10 + 6) unit = 16 unit ------------------------------(1)

Again for a parallelogram, the diagonals bisect each other.

so, EG = 2 \times \sqrt{153}

           = 2√153 unit -----------------------------------------(2)

and,

3y - 10 = y

⇒ y = 5 -----------------------------------------------(3)

5 0
3 years ago
Help with number 8 please
Mrrafil [7]
The answer would be 1440 feet^2, becasue for area you have to multiply the width, length, and depth.  You bascally would draw a 3D rectangle and label the depth, height, and width. That would be your diagram. 
7 0
3 years ago
Find the fourth roots of i
antoniya [11.8K]

Answer:

  1∠22.5°, 1∠112.5°, 1∠202.5°, 1∠292.5°

Step-by-step explanation:

A root of a complex number can be found using Euler's identity.

<h3>Application</h3>

For some z = a·e^(ix), the n-th root is ...

  z = (a^(1/n))·e^(i(x/n))

Here, we have z = i, so a = 1 and z = π/2 +2kπ.

Using r∠θ notation, this is ...

  i = 1∠(90° +k·360°)

and

  i^(1/4) = (1^(1/4))∠((90° +k·360°)/4)

  i^(1/4) = 1∠(22.5° +k·90°)

For k = 0 to 3, we have ...

 for k = 0, first root = 1∠22.5°

  for k = 1, second root = 1∠112.5°

  for k = 2, third root = 1∠202.5°

  for k = 3, fourth root = 1∠292.5°

4 0
1 year ago
What is the slope and the y-intercept of -1.7x-1.9y=5.8
Julli [10]

Answer:

The slope is -0.89 and the y-intercept is (0, -3.05).

Step-by-step explanation:

To find the slope and y-intercept, convert the equation to y=mx+b where m=slope and b=y-intercept.

Convert the equation by rearranging the terms using inverse operations.

-1.7x - 1.9y = 5.8                                 Add 1.7x to both sides.

+1.7x                     +1.7x

------------------------------------

       -1.9y = 5.8 + 1.7x                         Divide both sides by -1.9.

            y= - 0.89 x - 3.05

This is now in y=mx+b and m=-0.89 and b=-3.05.

The slope is -0.89 and the y-intercept is (0, -3.05).

3 0
3 years ago
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