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3 years ago

List 2 common multiples of 2 , 5

Mathematics

2 answers:

elena55 [62]3 years ago

5 0

Answer:10 and 20

Step-by-step explanation:

2 times 5 is 10 and 2 times 10 is 20 and 5 times 4 is 20

neonofarm [45]3 years ago

3 0

Answer:

2: 2, 4, 6, 8, 10

5: 5, 10

lcm: 10

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How do I get (tan^2(x)-sin^2(x))/tan(x) equal to (sin^2(x))/cot(x)

shepuryov [24]

$LHS\\ \\ =\frac { \tan ^{ 2 }{ x-\sin ^{ 2 }{ x } } }{ \tan { x } } \\ \\ =\frac { 1 }{ \tan { x } } \left( \tan ^{ 2 }{ x-\sin ^{ 2 }{ x } } \right)$

$\\ \\ =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^{ 2 }{ x } }{ \cos ^{ 2 }{ x } } -\frac { \sin ^{ 2 }{ x\cos ^{ 2 }{ x } } }{ \cos ^{ 2 }{ x } } \right) \\ \\ =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^{ 2 }{ x-\sin ^{ 2 }{ x\cos ^{ 2 }{ x } } } }{ \cos ^{ 2 }{ x } } \right)$

$\\ \\ =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^{ 2 }{ x\left( 1-\cos ^{ 2 }{ x } \right) } }{ \cos ^{ 2 }{ x } } \\ \\ =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^{ 2 }{ x\cdot \sin ^{ 2 }{ x } } }{ \cos ^{ 2 }{ x } } \\ \\ =\frac { \cos { x } \sin ^{ 4 }{ x } }{ \sin { x\cos ^{ 2 }{ x } } } \\ \\ =\frac { \sin ^{ 3 }{ x } }{ \cos { x } }$

$\\ \\ =\sin ^{ 2 }{ x } \cdot \frac { \sin { x } }{ \cos { x } } \\ \\ =\sin ^{ 2 }{ x } \cdot \frac { 1 }{ \frac { \cos { x } }{ \sin { x } } } \\ \\ =\sin ^{ 2 }{ x } \cdot \frac { 1 }{ \cot { x } } \\ \\ =\frac { \sin ^{ 2 }{ x } }{ \cot { x } } \\ \\ =RHS$

8 0

2 years ago

What is the area of this trapezoid?

kolezko [41]

Answer:

are of trapezoid =1/2×height(a+b)

Step-by-step explanation:

A=1/2×8(10+20)

=4×30

=120cm*

5 0

3 years ago

In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces

nadya68 [22]

Answer:

a) 0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less

b) 0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c) 0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours

d) 86 should have a battery life of at least 9 hours.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

The probability of being higher than x is:

$P(X > x) = \frac{b - x}{b-a}$

The probability of being between c and d is:

$P(c \leq X \leq d) = \frac{d-c}{b-a}$

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

This means that $a = 8.5, b = 12$

a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

$P(X \leq x) = \frac{x - a}{b-a}$

$P(X \leq 10) = \frac{10 - 8.5}{12 - 8.5} = 0.4286$

0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less.

b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

$P(X > x) = \frac{b - x}{b-a}$

$P(X > 11) = \frac{12 - 11}{12 - 8.5} = 0.2857$

0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(c \leq X \leq d) = \frac{d-c}{b-a}$

$P(9.5 \leq X \leq 11.5) = \frac{11.5 - 9.5}{12 - 8.5} = 0.5714$

0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours.

d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

Proportion of iPad Minis with a battery life of at least 9 hours.

$P(X > 11) = \frac{12 - 9}{12 - 8.5} = 0.8571$

Out of 100:

0.8571*100 = 85.71

To the nearest whole number

86 should have a battery life of at least 9 hours.

5 0

3 years ago

I need the smaller and larger angle

SSSSS [86.1K]

Answer:

x=11

Step-by-step explanation:

(4x)+(3x+13)=90

if you look at the beam, it includes a 90 degree angle.

7x+13=90

distributive property

7x=77

subtracted both sides by 13

x=11

divided both sides by 7 to isolate x

4(11) 3(11)+13

44 33+13

4(x) is the larger angle

6 0

3 years ago

Solve the absolute value inequality

Anvisha [2.4K]

Absolute value= opposite. (positive turns into negative)(negative turns into positive)

4 0

3 years ago