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3 years ago

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 Arithmetic Sequence the difference between one term and the next is a constant called the common difference

we have

$5,8,11,14$

$a1=5$

$a2=8$

$a3=11$

$a4=14$

$a2-a1=8-5=3$

$a3-a2=11-8=3$

$a4-a3=14-11=3$

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:

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%.

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%.

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:

Problem 1:

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

Problem 2:

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

Step-by-step explanation:

Problem 1

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)

Problem 2

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