A couple has 2 children. what is the probability that both are girls if the older of the two is a girl?

Answer:

The complex number 4-i has distance  [tex]\sqrt{17}[/tex] from origin.

D is correct

Step-by-step explanation:

We are given the absolute value of complex plane.

If complex number is a+ib then absolute value [tex]\sqrt{a^2+b^2}[/tex]

We have to check the absolute value of each option and check which is equal to [tex]\sqrt{17}[/tex]

Option A:  2+15i

[tex]d=\sqrt{2^2+15^2}=\sqrt{4+225}=\sqrt{229}\neq \sqrt{17}[/tex]

Option B:  17+i

[tex]d=\sqrt{17^2+1^2}=\sqrt{289+1}=\sqrt{290}\neq \sqrt{17}[/tex]

Option C:  20-3i

[tex]d=\sqrt{20^2+3^2}=\sqrt{400+9}=\sqrt{409}\neq \sqrt{17}[/tex]

Option D:  4-i

[tex]d=\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}= \sqrt{17}[/tex]

Hence, The complex number 4-i has distance  [tex]\sqrt{17}[/tex] from origin.

Z= k/x

when x is 6, Z= 2

2=k/6

k=2*6

k=12

Z=12/X

when x = 13

Z=12/13

Z=0.923

Answer:

If two angles are equal in measure then each of the two angles has a measure of 28 degrees.

Step-by-step explanation:

The converse of a statement is found by switching the hypothesis and conclusion of a conditional statement.

The hypothesis is the part that comes after "if" and the conclusion is the part that comes after "then."

This means the hypothesis is "each of two angles has a measure of 28 degrees" and the conclusion is "the two angles are equal in measure."

This gives us the converse "If two angles are equal in measure then each of the two angles has a measure of 28 degrees."

Answer:

-14

Step-by-step explanation:

khan academy

Answer:

six divided by the square root of thirteen

Step-by-step explanation:

hey there,

< sin θ = [tex]\frac{O}{H}[/tex]

So that means O = 2 and H = 3. In order to find cot θ, first let's find tan θ.

tan θ = [tex]\frac{O}{B}[/tex]

We only know what O is equal to, not B. So let's draw out a triangle.

7  

◢   6

 B

As you can see (sorry for the poor triangle), this is a right triangle. In order to find an unknown part, use [tex]a^2 + b^2 = c^2[/tex]!

[tex]6^2 + B^2 = 7^2[/tex]

B = ±√13

Obviously, a side of a triangle can't be negative, so it stays positive. Now we can find tangent!

tanθ =  [tex]\frac{6}{\sqrt{13} }[/tex]

But, we're not done here. We're trying to find cotθ.

cotθ = [tex]\frac{1}{tan}[/tex]θ

[tex]\frac{1}{\frac{6}{\sqrt{13} } }[/tex] = [tex]\frac{\sqrt{13} }{6}[/tex]

That's your final answer! >

Hope this helped! Feel free to ask anything else.

5+8 = 13 total marbles

5 are green

 so you would have a 5/13 probability of picking a green one

Coordinate geometry is the use of a 2D plane to represent the location of points. The position or location of the distress is in the first quadrant.

The coordinates of ship A and B are not given. So, I will give a general explanation.

On the four cardinal points,

So, if ship A receives a distress from the northeast, then it means that the distress is coming from a location at the top right of A. i.e. the first quadrant.

Also, ship B receives distress from the west. This means that ship B is at the right-hand side of the distress.

So, we can conclude that the position or location of the distress is at the first quadrant.

It is impossible to determine the actual coordinates of the distress because the coordinates are not given (see attachment possible illustration)

Read more about coordinate geometry at:

https://brainly.com/question/18269861

There are 30,240 codes that are possible which consist of five digits (0 through 9).

A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.

There are 10 options for each of the 5 digits in the personal identification code (0 through 9). Since the order of the digits matters, we can use the formula for the number of permutations of n items taken r at a time, which is:

n!/(n-r)!

In this case, n is the number of options (10) and r is the number of items (5). Plugging these values into the formula gives us:

10!/(10-5)! = 10!/(5!) = 109876 = 30,240

Therefore, the correct answer is (d) 30,240.

Learn more about permutation here:

brainly.com/question/1216161

#SPJ5

To drive 500 miles, taking into account both driving time and oil stop time, it would take 11 hours and 15 minutes.

The expression -3(6.3x + 7y - 2.5) expands to -18.9x - 21y + 7.5 using the distributive property by multiplying each term inside the parentheses by -3.

To use the distributive property to expand the expression -3(6.3x + 7y - 2.5), you multiply each term inside the parentheses by -3. The distributive property lets you reverse the distributive law and turn it into factors (multiples).

-3 × 6.3x = -18.9x
-3 × 7y = -21y
-3 ×-2.5 = 7.5

Once each term is multiplied, the expanded expression is:   -18.9x - 21y + 7.5

Answer:

t=30      f=10

Step-by-step explanation:

t= 100*1 - 40*4      = 30

       2*1 - 1*4

f= 2*40 - 1*100      = 10

     2*1  - 1*4

t=30         f=10

Answer:

x= -6 is the point of discontinuity.

Step-by-step explanation:

We have been given the expression

[tex]\frac{x^2-16}{4x+24}[/tex]

The first thing to find the discontinuity is to factorize the given rational function:

After factorization  we get:

We will use [tex]a^2-b^2=(a+b)(a-b)[/tex]

[tex]here, a=x\text{and}b=4[/tex] we will get:

[tex](x+4)(x-4)=x^2-4^2[/tex]

we will get:

[tex]\frac{(x+4)(x-4)}{4(x+6)}[/tex]

Discontinuity is the point where value of the function becomes not defined

Here, the point of discontinuity is -6 because when denominator becomes zero. function becomes not defined.

It has vertical asymptote but function is not defined.

Hence it is the point of discontinuity.

Final answer:

To calculate the amount of cardboard used for each box, we need to find the surface area of the hexagonal base and the lateral surface area. We can use the formula for the surface area of a hexagon to find the base area. Then, we multiply it by the height of the box and add the two areas together.

Explanation:

To find the amount of cardboard used for each box, we need to calculate the surface area of the hexagonal base and the lateral surface area. The surface area of a hexagon can be found using the formula:

Surface Area = 3 x √3 x s^2

where s is the length of the side of the hexagon. Given that the side length is 39 cm, we can substitute this into the formula to find the surface area of the hexagonal base. Once we have the surface area, we can calculate the lateral surface area by multiplying it by the height of the box, which is 4.7 cm. Adding the two areas together will give us the total amount of cardboard used for each box.