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3 years ago

1) In the diagram, l || m. If the measure of angle 3 is 120 find the measure of the following angles

Mathematics

1 answer:

Anton [14]3 years ago

6 0

Answer:

a) 60° , b) 120° and c) 60°

Step-by-step explanation:

See the diagram attached to this question.

a) Here, ∠ 4 and ∠ 3 are supplementary angles.

So, ∠ 4 + ∠ 3 = 180° {Here, ∠ 3 is given to be 120°}

⇒ ∠ 4 = 180° - ∠ 3 = 180° - 120° = 60° (Answer)

b) Now, ∠ 3 and ∠ 6 are alternate angles and hence, ∠ 3 = ∠ 6 = 120° (Answer)

c) Here, ∠ 6 and ∠ 8 are supplementary angles.

So, ∠ 6 + ∠ 8 = 180°

⇒ ∠ 8 = 180° - ∠ 6 = 180° - 120° = 60° (Answer)

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businessText message users receive or send an average of 62.7 text messages per day. How many text messages does a text message

KiRa [710]

Answer:

(a) The probability that a text message user receives or sends three messages per hour is 0.2180.

(b) The probability that a text message user receives or sends more than three messages per hour is 0.2667.

Step-by-step explanation:

Let X = number of text messages receive or send in an hour.

The random variable X follows a Poisson distribution with parameter λ.

It is provided that users receive or send 62.7 text messages in 24 hours.

Then the average number of text messages received or sent in an hour is: $\lambda=\frac{62.7}{24}= 2.6125$ .

The probability of a random variable can be computed using the formula:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!} ;\ x=0, 1, 2, 3, ...$

(a)

Compute the probability that a text message user receives or sends three messages per hour as follows:

$P(X=3)=\frac{e^{-2.6125}(2.6125)^{3}}{3!} =0.21798\approx0.2180$

Thus, the probability that a text message user receives or sends three messages per hour is 0.2180.

(b)

Compute the probability that a text message user receives or sends more than three messages per hour as follows:

P (X > 3) = 1 - P (X ≤ 3)

= 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3)

$=1-\frac{e^{-2.6125}(2.6125)^{0}}{0!}-\frac{e^{-2.6125}(2.6125)^{1}}{1!}-\frac{e^{-2.6125}(2.6125)^{2}}{2!}-\frac{e^{-2.6125}(2.6125)^{3}}{3!}\\=1-0.0734-0.1916-0.2503-0.2180\\=0.2667$

Thus, the probability that a text message user receives or sends more than three messages per hour is 0.2667.

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3 years ago

How many liters are in 21 cups? if 1L=4.2cups i don't understand how to do it

Luda [366]

Answer:

5 L

Step-by-step explanation:

As given in question,

1 L can fill 4.2 cups.

So, 1 cup can hold $\frac{1}{4.2}$ L of fluid.

Therefore,

21 cups can hold = $\frac{1}{4.2}$ × 21

= 5 L

So, there is 5 L of fluid in 21 cups.

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3 years ago

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Write the word namefor the decimal 31.903

Alecsey [184]

Thirty-one and 903 thousandths

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2 years ago

△WPJ∼△DNJ What is PWPW ? Enter your answer in the box.

Kruka [31]

Use CPCTC and make ratios and proportionalities to find the value of segment PW:

If △WPJ∼△DNJ, then according to CPCTC, WP must be proportional to DN and PJ must be proportional to JN. Now, we can make a ratio:

$\frac{WP}{DN}= \frac{PJ}{NJ}$

Substitute the values that are given in the diagram.
DN=87.5
NJ=56
PJ=64

$\frac{WP}{87.5}= \frac{64}{56}$

Solve for x. You can do it by cross-multiplication.

$\frac{WP}{87.5}= \frac{64}{56} \\ 56*WP=64*87.5 \\ 56*WP=5600 \\ WP=100$

The measure of segment WP is 100 meters.

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3 years ago

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Crazy boy [7]

Answer:

(2,2)

Step-by-step explanation:

-3 + 5 = 2

4 - 2 = 2

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3 years ago

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