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3 years ago

Consider the following experiment:

Mathematics

1 answer:

aleksklad [387]3 years ago

3 0

Answer:

The sample space is 52.

P(Red Card) = 1/2

Step-by-step explanation:

The sample space is simply all of the possible outcomes of an experiment;

In this case, the experiment is picking a card from a deck of 52, so there are 52 possible outcomes as you can pick any one of the 52 cards.

The probability of a red card is found by taking the number of outcomes that are picking a red card and dividing this by the sample space, so, since there are 26 red cards, there are 26 outcomes which are picking a red card and the sample space is 52;

So, we divide 52 by 26, which gives a 1/2.

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What is the answer to 2 3/4 ÷ 1 5/8

alex41 [277]

Exact form:
22/13

Mixed number:
1 9/13

6 0

3 years ago

PLEASE HELP ME If 0 < z ≤ 90 and sin(9z − 1) = cos(6z + 1), what is the value of z? z = 3 z = 4 z = 5 z = 6

Burka [1]

Answer:

z = 6

Step-by-step explanation:

We know that ...

sin(x) = cos(90 -x)

Substituting (9z-1) for x, this is ...

sin(9z -1) = cos(90 -(9z -1))

But we also are given ...

sin(9z -1) = cos(6z +1)

Equating the arguments of the cosine function, we have ...

90 -(9z -1) = 6z +1

90 = 15z . . . . . . . . . add (9z-1) to both sides

6 = z . . . . . . . . . . . . divide by 15

_____

<em>Comment on the graph</em>

The attached graph shows 5 solutions in the domain of interest. These come from the fact that the relation we used is actually ...

sin(x) = cos(90 +360k -x) . . . . . for any integer k

Then the above equation becomes ...

90 +360k = 15z

6 +24k = z . . . . . . . . . for any integer k

The sine and cosine functions also enjoy the relation ...

sin(x) = cos(x -90)

sin(9z -1) = cos(9z -1 -90) = cos(6z +1)

3z = 92 . . . . . equating arguments of cos( ) and adding 91-6z

z = 30 2/3

6 0

3 years ago

A boy purchased (bought) a party-length sandwich 56 in. long. He wants to cut it into three pieces so that the middle piece is

erik [133]

The shortest piece is 14 inches, middle piece is 19 inches and longest piece is 23 inches long.

Step-by-step explanation:

Let,

x be the shortest piece.

Therefore,

Middle piece = x+5

As shortest piece is 9 in shorter than longer piece;

Shortest piece = longest piece - 9

x = longest piece - 9

longest piece = x+9

Length of sandwich = 56 in

According to given statement;

Shortest piece + middle piece + longest piece = 56

$x+(x+5)+(x+9)=56\\x+x+5+x+9=56\\3x+14=56\\3x=56-14\\3x=42$

Dividing both sides by 3;

$\frac{3x}{3}=\frac{42}{3}\\x=14$

Shortest piece = 14 in

Middle piece = 14+5 = 19 in

Longest piece = 14+9 = 23 in

The shortest piece is 14 inches, middle piece is 19 inches and longest piece is 23 inches long.

Keywords: Addition, linear equation

Learn more about addition at:

#LearnwithBrainly

5 0

3 years ago

E^y*cos x = 1 + sin(xy)

lys-0071 [83]

I assume you are studying implicit differentiation. Solving for dy/dx.
For the Left side use product rule. For Right side, use chain rule. Remember any time you take derivative of "y-term" you must multiply it by dy/dx.

---> $\frac{dy}{dx} e^y cos (x) - e^y sin(x) = (y + x \frac{dy}{dx}) cos (xy)$

Get dy/dx terms on one side:
$\frac{dy}{dx} e^y cos (x) - \frac{dy}{dx} x cos(xy) = e^y sin(x) + y cos (xy)$

Factor out dy/dx and solve:
$\frac{dy}{dx} (e^y cos (x) - x cos(xy)) = e^y sin(x) + y cos (xy) \\.......\\ \frac{dy}{dx} = \frac{e^y sin(x) + y cos (xy) }{e^y cos (x) - x cos(xy)}$

8 0

3 years ago

Definition of mean In mathe

d1i1m1o1n [39]

An average of values added up then divided by their number.

8 0

3 years ago