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2 years ago

Match the following items.

1 answer:

4 0

This problem can be solved using probability, the equation of the probability of an event A is P(A)= favorable outcomes/possible outcomes. The interception of two probable events is P(A∩B)= P(A)P(B).

There are 12 black marbels, 10 red marbles, and 18 white marbels, all the same size. If two marbles are drawn from the jar without being replaced.

The total of the marbles is 40.

If two marbles are drawn from the jar without being replaced, what would the probability be:

1. of drawing two black marbles?

The probability of drawing one black marble is (12/40). Then, the probability of drawing another black marble after that is (11/39) due we drawing one marble before.

P(Black∩Black) = (12/40)(11/39) = 132/1560, simplifying the fraction:

P(Black∩Black) = 11/130

2. of drawing a white, then a black marble?

The probability of drawing one white marble is (18/40). Then, the probability of drawing then a black marble after that is (12/39) due we drawed one marble before.

P(White∩Black) = (18/40)(12/39) = 216/1560, simplifying the fraction:

P(White∩Black) = 9/65

3. of drawing two white marbles?

The probability of drawing one white marble is (18/40). Then, the probability of drawing another white marble after that is (17/39) due we drawed one marble before.

P(White∩White) = (18/40)(17/39) = 306/1560, simplifying the fraction:

P(White∩White) = 51/260

4. of drawing a black marble, then a red marble?

The probability of drawing one black marble is (12/40). Then, the probability of drawing then a red marble after that is (10/39) due we drawed one marble before.

P(Black∩Red) = (12/40)(10/39) = 120/1560, simplifying the fraction:

P(Black∩Red) = 1/13

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Which of the following options is an equivalent function to f(x) = 4(3)2X?

Paha777 [63]

Answer:

$f(x)=4(6x)$

Step-by-step explanation:

Given:

the given expression is.

$f(x)=4(3)2x$

Simplify the given expression.

$f(x)=4(3)2x$

$f(x)=4(3\times 2x)$

$f(x)=4(6x)$

Therefore, the option $f(x)=4(6x)$ is an equivalent function to $f(x)=4(3)2x$ .

8 0

2 years ago

Using the information given, select the correct ending balance.

klemol [59]

Step-by-step explanation:

Simple first we will add previous balance and total deposit

498.03 + 604.28

= 1102. 31

Then we will subtract it by total withdrawals

1102.31 - 599.49

= 502. 82

The ending balance is 502.82

6 0

2 years ago

salina is one-quarter of her aunts age if a represents her aunts age which expression represents her age

katovenus [111]

Answer:

s = .25a

Step-by-step explanation:

if s is Salina's age, and we know that she is 1/4 (.25) her aunt's age, then ONE QUARTER (.25) times AUNT'S AGE (a) = SALINA'S AGE (s)

7 0

2 years ago

You begin your first day as a police officer earning $30,000/yr. Assuming that you obtain a full 5% increase each year, what wil

spayn [35]

Answer:

The equation for the amount of salary after x number of years is given by:

$y = a(1+r)^x$

where

a is the initial amount

x represents the number of years and

r represents the growth rate( in decimal)

As per the statement:

You begin your first day as a police officer earning $30,000/yr

⇒ a= 30,000

It is also given that you obtain a full 5% increase each year,

⇒ $r = 5\% = 0.05$

then;

$y = 30,000(1+0.05)^x$

$y = 30,000(1.05)^x$ ....[1]

we have to find the salary in three years.

⇒ $x = 3$

Substitute this value in [1] we have

$y = 30,000(1.05)^3$

Simplify:

$y = \$ 34,4728.75$

therefore, your salary be in three years will be $34,4728.75

3 0

2 years ago

Read 2 more answers

A rectangular portrait measures 50cm by 70cm. It is surrounded by a rectangular frame of uniform width. If the area of the frame

snow_tiger [21]

Let us assume uniform width = x cm wide.

Length of rectangular portrait = 50cm and width of rectangular portrait = 70cm.

Therefore, length of rectangle made by frame = 50 + x+x = (2x+50) cm.

And width of rectangle made by frame = 70+x+x = (2x+70) cm.

We know, the area of rectangular portrait = 50 × 70 = 3500 cm^2.

Total area of the rectangle made by frame would be = (2x+50) * (2x+70)

We know,

Actual area of frame = Area of rectangle made by frame - area of rectangular portrait.

We also given "the area of the frame is the same as the area of the portrait."

We can setup an equation now,

3500 = (2x+50) * (2x+70) - 3500.

Subtracting 3500 from both sides, we get

3500-3500 = (2x+50) * (2x+70) - 3500-3500.

0 = (2x+50) * (2x+70) -7000.

FOIL (2x+50) * (2x+70), we get

0 = 2x*2x +2x*70 + 50*2x +50*70 - 7000.

0 = 4x^2 +140x +100x +3500 -7000.

4x^2 +240x -3500 = 0.

Dividing whole equation by 4, we get

x^2 +60x - 875 =0

Applying quadratic formula $=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , we get

$=\frac{-60\pm \sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}$

$x=\frac{-60+\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}=5\left(\sqrt{71}-6\right)$

$x=\frac{-60-\sqrt{60^2-4\cdot \:1\left(-875\right)}}{2\cdot \:1}:\quad -5\left(6+\sqrt{71}\right)$

We cant take negative value.

So, $x=5\left(\sqrt{71}-6\right)=12.13$

We could take approximately 12 cm.

7 0

2 years ago