For each situation, make a tree diagram to show the sample space. Then give the total number of outcomes.
choosing a silver, black, or red CD player and choosing a rock, country, or rap CD
a. 3
c. 9
b. 6
d. 12

Answer:

about 180

Step-by-step explanation:

(when rounding, numbers 0-4 "stay" meaning you'd round down. If the numbers are 5-9, you round up)

91 rounded to the nearest ten would be 90

94 rounded to the nearest ten would be 90 as well

So, 90 + 90 = 180

Technically though, 91+94 = 185. So rounding this to the nearest ten would be 190.

Do what you will :)

Answer:

Identities used:

Square root of it is:

The first part without root:

Its square root is:

The second part without root:

Its square root is:

Sum of the results:

Step-by-step explanation:

Question 1:

Consider the left-hand side

[tex] \sqrt{ \frac{ 1 - \sin\theta }{1 + \sin\theta} } = \sqrt{ \frac{ 1 - \sin\theta }{1 + \sin\theta} \times \frac{1 - \sin\theta }{1 - \sin\theta } }[/tex]

[tex] = \sqrt{ \frac{ {(1 - \sin\theta )}^{2} }{(1 - { \sin}^{2}\theta) } } = \frac{1 - \sin\theta }{ \cos\theta} [/tex]

[tex] = \frac{1}{ \cos\theta} - \frac{ \sin\theta}{\cos\theta } [/tex]

[tex] = \sec\theta \: - \tan\theta[/tex]

Question 2:

The left-hand side can be rewritten as

[tex] \sqrt{\frac{1+ \cos \theta}{1- \cos\theta} \times \frac{1+ \cos \theta}{1+ \cos \theta} } \: +\sqrt{\frac{1- \cos\theta}{1+ \cos \theta} \times \frac{1 - \cos \theta}{1 - \cos \theta} }[/tex]

[tex] = \frac{1 + \cos\theta}{ \sin\theta} + \frac{1 - \cos\theta}{ \sin\theta}[/tex]

[tex] = \frac{2}{ \sin\theta } = 2 \csc\theta[/tex]

If a line is drawn so that it passes through the point [tex](2,-1)[/tex] and [tex](0,5)[/tex] , then  slope of line is -3 .

What is Slope ?

The slope of a line is defined as measure of steepness and direction of  line. The slope of line in a plane help in predicting whether lines are parallel, perpendicular, or none without using a compass.

The slope of line passes through points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is calculated by formula ⇒ [tex]Slope = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] ;

the points are given as  [tex](2,-1)[/tex] and [tex](0,5)[/tex]  ;

So , on substituting the values in the slope formula ,

we get ;

[tex]Slope = \frac{5 -(-1) }{0 -2 }[/tex] ;

= [tex]\frac{6}{-2}[/tex]

= -3 .

Therefore , the required slope of the line is -3 .

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Answer:

- [tex]\frac{3}{7}[/tex]

Step-by-step explanation:

Change in y over the change in x.

(3,2)(-4,1)

The y values are 1 and 2.

The x values are -4 and 3.  

You find the change by subtracting.

[tex]\frac{1--2}{-4-3}[/tex] = [tex]\frac{1+2}{-7}[/tex] = [tex]\frac{3}{-7}[/tex]

Can be written - [tex]\frac{3}{7}[/tex]

Answer:

Step-by-step explanation:

The additive inverse of 6 /- 5 is 6/5

We know that for any real number 'a' an additive inverse is a number 'b' such that a + b = 0

i.e., b = -a

An additive inverse of 'a' is -a.

The means, an additive inverse is nothing but changing sign + to - OR - to +

Here we have been given a rational number 6/(-5)

Let m be the additive inverse of number 6/(-5)

From the definition of additive inverse,

6/(-5) + m = 0

[6/(-5) + m] - 6/(-5) = -6/(-5)            

[6/(-5) - 6/(-5)] + m= -6/(-5)       ...........(associative property of addition)

0 + m =  6/5

m = 6/5

Hence, the additive inverse is 6/5

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Answer:

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

5 x 4 x 2 = 40

length x width x height = volume

Answer:

c

Step-by-step explanation:

The circumference should equal c = 2π × 8 cm = 50.265 cm . The area should equal A = π × (8 cm)² = 201.06 cm² . To check your results, input the 8 cm diameter in the calculator. The results should also be 50.265 cm and 201.06 cm². which is closest to c

Answer:

x^2-9

Step-by-step explanation:

-3 + 3 = 0 so the x terms cancel out.  This leaves you with only x^2-9

Answer:

112 feet squared

Step-by-step explanation:

Just multiply the length and the width then you get the area which is 112 ft squared.

Answer:

Use the Pythagorean identity

tan2x+1=sec2x

to start the simplification on the left side.

Step-by-step explanation:

・ᗜ・

Answer:

Step-by-step explanation:

? = 1/2( big ∠ - small ∠)

? = 1/2(184 - 84)

? = 1/2(100)

? = 50 °

Answer:

Dylan has 5

Step-by-step explanation:

jessie 8+x

‘Dylan  x

so

8+x+x=18

2x=10

x=5

jessie has 13

dylan has 5

Answer:

C.) 13

Step-by-step explanation:

So, I'm going to break this down to the three sentences. If you look at the key words in each sentence, grammatically the last one stands out.

In the first sentence it is saying Jessie HAS 8 more pencils than Dylan

In the second sentence it is saying Together they HAVE a total of 18 pencils

In the third sentence it is asking How many pencils DID Dylan have

The word MORE implies in addition to. And this very well could mean at least. I believe the answer is 13.

Saying Dylan had 5 pencils (+ J's 8), would be 13

Saying Dylan had 8 pencils (+J's 8), would be 16

Both of which are not AT LEAST 18

Saying Dylan had 13 pencils (+J's 8), would be 21

If 10 is incorrect, your answer should be 13

The interpretation of the slope is that the cost per minute is $2

From the question, we have the following parameters that can be used in our computation:

C(m) = 2m + 15

Where

m = number of minutes

C(m) = cost function

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 2

This means that the slope is 2

And it means that the cost per minute is $2

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The equation of the magnitude of the force applied at the back of otter is F is (P+P0)A F is ( P + P 0 ) A .

The amount that encapsulates the force's power is known as its magnitude. Consider the following scenario: the force is 10 N in the east. The direction is indicated by "towards east," while the force is indicated by "10." Magnitude may be thought of as simply the "value" or "amount" of any physical quantity.

The surface area of the otter's back is A = 0.55 m2.

The fluid pressure at the depth of the otter is P = 11500 Pa.

Thus, the equation of the magnitude of the force applied at the back of otter is F=(P+P0)A F = ( P + P 0 ) A .

The complete question is

An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A = 0.55 m2. The fluid pressure at the depth of the otter is P = 11500 Pa.

Write an equation for the magnitude of the force F on the back of the otter in terms of the pressure P and the atmospheric pressure P0.

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Note: your teacher may not want you to enter "feet" and instead may just want the number only.

===================================================

Work Shown:

tan(angle) = opposite/adjacent

tan(40) = h/20

20*tan(40) = h

h = 20*tan(40)

h = 16.7819926 which is approximate

h = 16.8

The streetlamp is approximately 16.8 ft tall.

When using your calculator, make sure it's in degree mode. One way to check is to compute something like tan(45) and you should get 1 as a result.

The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.

Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D

where, A --> amplitude

B--> period in form of pi

C--> phase or horizontal shift

D --> vertical shift

We have, the depth of water in a tank oscillates sinusoidally.

The smallest depth of water in tank = 6.6 feet

The largest depth of water in tank = 9.4 feet

We have to determine the formula of depth of water in tank as a function of time in hours .

For sinusoidal function,

Amplitude , A = average depth

= ( largest depth + smallest depth)/2

= (6.6 + 9.4)/2

= 16.0/2 = 8

Now, The period of 8 hours so, B = 2π/8

=> B = 45° = π/4

Also, upward shift , D is 9.4 - 6.6 = 2.8

Horizontal shift, C = 0

So, required function is D = 2.8 + 8 sin(π t/4) .

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Answer:

C. ∠1 and ∠3 are vertical angles and congruent.

A statement 'The lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.' is True.

We know that the formula for the lateral surface area of cone:

Area = π × radius × slant height

and the formula for the lateral surface area of cylinder:

Area = 2π × (radius) × (height)

Here we have been given a cone A with radius r and slant height 2h.

Using the above formula, the lateral surface area of cone A would be:

A1 =  π × r × 2h

A1 =  2π × r × h                    ..................(1)

Also, we have been given a cylinder B with radius r and height h.

Using the above formula, the lateral surface area of cylinder A would be:  

A2 =  2π × r × h                   ..............(2)

From (1) and (2) we can observe that,

A1 = A2

Therefore, the lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.

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Answer:

31:150

Step-by-step explanation:

First of all we convert the hours into minutes:

5×60=300

which gets us 42:300, which we can simplify to:

31:150

and is 31 is prime and 150 can't be divided into it without a remainder, it is in it's simplest form and it is the answer.

Answer:

7:50

Step-by-step explanation:

The ratio:

 42 min

-------------- can be rewritten in the equivalent

  5 hours

 42 min

--------------- = 42/300 = 7/50 or 7:50

300 min

The height of the mt. Everest in miles exists 5.499 miles.

By changing the unit of measurement, a quality can be expressed differently. In contrast to distance, which can be stated in miles, kilometers, feet, or any other unit of length, time can also be expressed in minutes rather than hours.

By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. The right conversion factor to an equal value must be used when a conversion is required. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.

The height of the mt. Everest is : 29035 feet.

The unit conversion is given as :

5280 feet = 1 mile

1 feet = 1/5280 mile

So, 29035 feet =29035 × 1/5280 miles

29035 feet = 29035/5280 miles

29035 feet = 5.499 miles

So, the height of the mt. Everest in miles is 5.499 miles.

The complete question is:

In the Himalaya mountains along the border of Tibet and Nepal, mount Everest reaches a record height of 29,035 feet. how high is mt. Everest in miles? use the conversion equivalency of 1 mile = 5280 feet.

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Answer:  The height of the Mount Everest in miles is 5.499 miles

Step-by-step explanation:

1 miles = 5,280 feet

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Answer:

2x + 2

Step-by-step explanation:

Combine all the like terms:

-5x + 7x -12 + 14 = 2x + 2

Answer:

2x + 2

Step-by-step explanation:

(- 5x - 12) + (14 + 7x) ← remove parenthesis

= - 5x - 12 + 14 + 7x ← collect like terms

= (- 5x + 7x) + (- 12 + 14)

= 2x + 2

answer:

2x + 12 = c

step-by-step explanation:

2x + 12 = c

Answer:

Yolanda's answer is incorrect because the recipe calls for 1 cup of almonds, 1 cup of pecans, and 1 cup of dried fruit, which totals 3 cups of nuts. The correct ratio of nuts to fruit in this recipe is 3:1. This means that for every 3 cups of nuts, there is 1 cup of fruit.

Thus , Heat moves from a hotter object to a colder one, which accurately sums up the properties of the heat equation. Energy moves from one item to another in the form of heat.

An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate

Here,

Heat's characteristics

The direction of this transmission is always determined by the temperature differential between the bodies.

To achieve an equilibrium temperature, heat is transferred from the hotter to the cooler body.

As a result of the fact that a body and its surrounds are at different temperatures, we can infer that heat is the energy that is transferred between them.

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Answer:

25%

Step-by-step explanation:

1 out of 4 chance = 25% chance to get 2