All categories

3 years ago

Can someone please help me solve this?

Mathematics

1 answer:

ra1l [238]3 years ago

4 0

AC is congruent to itself
AC bisects angle BAD, so that angles BAC and DAC are congruent
Both angles B and D are right angles, so they are congruent

This means triangles BAC and DAC are a pair of angle-angle-side triangles, so they are congruent to one another. Corresponding parts of congruent triangles are congruent, so the line segments BC and DC are congruent and have the same length.

Then

$8n+2=2n+20\implies6n=18\implies n=3$

You might be interested in

Type the correct answer in each box. find the cofactors of each entry in the first row of the matrix . ac11 = ac12 = ac13 =

natima [27]

The cofactors of each entry in the first row of the matrix are

Ac_11 = -13

Ac_12 = 44

Ac_13 = 27

We have to determine the cofactors of each entry in the first row of the matrix.

Therefore the cofactors of each entry in the first row of the matrix are

Ac_11 = -13

Ac_12 = 44

Ac_13 = 27.

A set of numbers is arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.

Machines had to find a way to cut themselves off from the truth in order to understand humans. Neo's sole purpose in the Matrix is to prevent machines from evolving into dinosaurs.

Learn more about the matrix at

brainly.com/question/1821869

#SPJ4

4 0

2 years ago

Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls. Find the probability that (a)

UNO [17]

Answer:

a) P=0.226

b) P=0.6

c) P=0.0008

d) P=0.74

Step-by-step explanation:

We know that the seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and 18 green balls. Therefore, we have 46 balls.

a) We calculate the probability that are 3 red, 2 blue, and 2 green balls.

We calculate the number of possible combinations:

$C_7^{46}=\frac{46!}{7!(46-7)!}=53524680$

We calculate the number of favorable combinations:

$C_3^{12}\cdot C_2^{16}\cdot C_2^{18}=660\cdot 120\cdot 153=12117600$

Therefore, the probability is

$P=\frac{12117600}{53524680}\\\\P=0.226$

b) We calculate the probability that are at least 2 red balls.

We calculate the probability withdrawn of 1 or none of the red balls.

We calculate the number of possible combinations:

$C_7^{46}=\frac{46!}{7!(46-7)!}=53524680$

We calculate the number of favorable combinations: for 1 red balls

$C_1^{12}\cdot C_7^{34}=12\cdot 1344904=16138848$

Therefore, the probability is

$P_1=\frac{16138848}{53524680}\\\\P_1=0.3$

We calculate the number of favorable combinations: for none red balls

$C_7^{34}=5379616$

Therefore, the probability is

$P_0=\frac{5379616}{53524680}\\\\P_0=0.1$

Therefore, the the probability that are at least 2 red balls is

$P=1-P_1-P_0\\\\P=1-0.3-0.1\\\\P=0.6$

c) We calculate the probability that are all withdrawn balls are the same color.

We calculate the number of possible combinations:

$C_7^{46}=\frac{46!}{7!(46-7)!}=53524680$

We calculate the number of favorable combinations:

$C_7^{12}+C_7^{16}+C_7^{18}=792+11440+31824=44056$

Therefore, the probability is

$P=\frac{44056}{53524680}\\\\P=0.0008$

d) We calculate the probability that are either exactly 3 red balls or exactly 3 blue balls are withdrawn.

Let X, event that exactly 3 red balls selected.

$P(X)=\frac{C_3^{12}\cdot C_4^{34}}{53524680}=0.57\\$

Let Y, event that exactly 3 blue balls selected.

$P(Y)=\frac{C_3^{16}\cdot C_4^{30}}{53524680}=0.29\\$

We have

$P(X\cap Y)=\frac{18\cdot C_3^{12} C_3^{16}}{53524680}=0.12$

Therefore, we get

$P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)\\\\P(X\cup Y)=0.57+0.29-0.12\\\\P(X\cup Y)=0.74$

8 0

4 years ago

A student is given the rectangle and square. The student states that the two figures have the same perimeter. Is the student per

Karolina [17]

The student is correct. Due to the meaning of perimeter which is all sides added up to make a number total, it is possible for a square and a rectangle to have the same perimeter if the numbers add up.

7 0

3 years ago

Read 2 more answers

Convert 7 kilometers into miles

ladessa [460]

4.3496 miles.

HTH (Hope This Helps)

6 0

4 years ago

What is the volume of a cone with a diameter of 16 centimeters and a height of 15 centimeters?

AleksAgata [21]

Answer:

The correct answer is 8cm.

Step-by-step explanation:

Vol. Of cone= 1/3pi r²h

= 1/3×3.14× 8²×15

= 8×8×5×3.14

64× 5×3.14

= 320×314/100

=16×314=5024 cm³

Hope this helps:) Goodluck!

7 0

2 years ago

Read 2 more answers