List the sides of DEF in order from shortest to longest.

ABCD is a quadrilateral inscribed in a circle, as shown below:

german

Answer:

A. (x + 16) + (6x − 4) = 180

Step-by-step explanation:

Inscribed quadrilateral has opposite angles supplementary.

m∠A + m∠C = 180°

or

m∠B + m∠D = 180°.

<u>Since</u>

m∠A = x + 16,
m∠B = x,
m∠C = 6x - 4,
m∠D = 2x + 16

we can use either pair of angle measures to work out the value of x and then find the value of each angle.

<u>We can verify the first option is the only correct one.</u>

m∠A + m∠C = 180°
(x + 16) + (6x − 4) = 180

3 0

2 years ago

A bank says you can double your money in 10 years if you put $1,000 in a simple interest account. What annual interest rate does

katrin2010 [14]

The simple interest formula allows us to calculate I, which is the interest earned or charged on a loan. According to this formula, the amount of interest is given by I = Prt, where P is the principal, r is the annual interest rate in decimal form, and t is the loan period expressed in years. The rate r must be converted from a percentage into decimal form.

Then, 2,000 = 1,000 * r * 10 ;

Finally, r = 2 ÷ 10 = 20 ÷ 100 = 0.2

hope this helps you

8 0

2 years ago

Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pens, and 3 green pens. If X is the number

Flauer [41]

Answer:

a) f(x,y) = $\frac{\binom{3}{x}\binom{2}{y}\binom{3}{2-x-y}}{\binom{8}{2}}$ ; x = 0, 1 , 2; y = 0, 1 , 2; 0 ≤ x+y ≥ 2

b) = $\frac{9}{14}$

Step-by-step explanation:

joint probability is a function that characterizes the distribution of a random variable. If X and Y be two random variables then the joint probability will be P(X = x, Y=y)

Given Data,

X = The number of blue Pens

Y = The number of red Pens

a)

possible outcomes(X, Y) are (0, 0), (0, 1), (1, 0), (1, 1), (0, 2), (2,0)

Please refer fig. also

total number ways of selecting any 2 pens = $\binom{8}{2}$ = $\frac{8!}{2! 6!}$ =28

f(x,y) = $\frac{\binom{3}{x}\binom{2}{y}\binom{3}{2-x-y}}{\binom{8}{2}}$ ; x = 0, 1 , 2; y = 0, 1 , 2; 0 ≤ x+y ≥ 2

b)

P(X,Y)∈A = P(X + Y ≤ 1)

= P(0,0) + P(1,0) + P(0,1)

= $\frac{3}{28}$ + $\frac{3}{14}$ + $\frac{9}{28}$

= $\frac{9}{14}$

4 0

3 years ago

I will mark brainliest

Brilliant_brown [7]

Answer:

the first answer is correct answer

8 0

2 years ago

A teacher wants to investigate whether listening to music while taking a math test increases scores. He instructs half

uysha [10]

<h2>D. This is an experiment with blocking </h2><h2 />

For your question: "A teacher wants to investigate whether listening to music while taking a math test increases scores. He instructs half

of his 36 students to listen to music while taking a test and the other half to not listen to music during the test. To

determine who listens and who does not, the teacher identifies the two students who scored highest on the last test

and randomly instructs one to listen to music and one to not. The teacher does the same for the next two highest-

scoring students and continues in this manner until each student has their instructions. Which of the following best

describes this plan?"

The answer is D

4 0

2 years ago