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4 years ago

Suppose △DEF≅△MNO. Which congruency statement is true?

Mathematics

2 answers:

Mrac [35]4 years ago

7 0

△DEF≅△MNO

answer

DE≅MN

photoshop1234 [79]4 years ago

5 0

Answer:

DE≅MN

Step-by-step explanation:

We know that corresponding parts of congruent triangles are congruent (CPCTC). Using the congruence statement we can match up the corresponding sides.

From the statement, ∠D matches ∠M, ∠E matches ∠N, and ∠F matches ∠O.

We also see that DE matches MN, EF matches NO, and DF matches MO.

Thus we have that DE≅MN.

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3 years ago

Suppose you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. If you randomly

mina [271]

Answer:

(a) The probability you pass the exam is 0.0000501.

(b) The expected number of correct guesses is 7.5.

(c) The standard deviation is 2.372.

Step-by-step explanation:

We are given that you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. And you randomly guess on all 30 questions.

Since there is an assumption of only 1 correct choice out of 4 which means the above situation can be represented through binomial distribution;

$P(X =x) = \binom{n}{r}\times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,3,......$

where, n = number of trials (samples) taken = 30

r = number of success = at least 60%

p = probbaility of success which in our question is the probability

of a correct answer, i.e; p = $\frac{1}{4}$ = 0.25

Let X = Number of questions that are correct

So, X ~ Binom(n = 30 , p = 0.25)

(a) The probability you pass the exam is given by = P(X $\geq$ 18)

Because 60% of 30 = 18

P(X $\geq$ 18) = P(X = 18) + P(X = 19) +...........+ P(X = 29) + P(X = 30)

= $\binom{30}{18}\times 0.25^{18}\times (1-0.25)^{30-18} + \binom{30}{19}\times 0.25^{19}\times (1-0.25)^{30-19} +.......+ \binom{30}{29}\times 0.25^{29}\times (1-0.25)^{30-29} + \binom{30}{30}\times 0.25^{30}\times (1-0.25)^{30-30}$

= 0.0000501

(b) The expected number of correct guesses is given by;

Mean of the binomial distribution, E(X) = $n \times p$

= $30 \times 0.25$ = 7.5

(c) The standard deviation of the binomial distribution is given by;

S.D.(X) = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{30 \times 0.25 \times (1-0.25)}$

= $\sqrt{5.625}$ = 2.372

8 0

4 years ago

Dave and Ellen are newly married and living in their first house. The yearly premium on their homeowner's insurance policy is $4

Mila [183]

Answer:

a. $27

b. $9

Step-by-step explanation:

The yearly premium on their homeowner's insurance policy is $450 for the coverage they need.

Their insurance company offers a discount of 6 percent if they install dead-bolt locks on all exterior doors.The couple can also receive a discount of 2 percent if they install smoke detectors on each floor.

a. What discount will Dave and Ellen receive if they install the dead-bolt locks?

$0.06\times450=27$ dollars