What is the solution for |2x-3|<5

A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Five marbles are drawn from the bag. wha

Charra [1.4K]

To determine the probability that exactly two of the five marbles are blue, we will use the rule of multiplication.

Let event A = the event that the first marble drawn is blue; and let B = the event that the second marble drawn is blue.
To start, it is given that there are 50 marbles, 20 of them are blue. Therefore, P(A) = 20/50
After the first selection, there are 49 marbles left, 19 of them are blue. Therefore, P(A|B) = 19/49
Based on the rule of multiplication:P(A ∩ B) = P(A)*P(A|B)P(A ∩ B) = (20/50) (19/49)P(A ∩ B) = 380/2450P(A ∩ B) = 38/245 or 15.51%

The probability that there will be two blue marbles among the five drawn marbles is 38/245 or 15.51%

We got the 15.51% by dividing 38 by 245. The quotient will be 0.1551. We then multiplied it by 100% resulting to 15.51%

7 0

3 years ago

A force of 50 pounds acts on an object at an angle of 45 degrees. A second force of 75 pounds acts on the object at an angle of

Contact [7]

Answer:

The magnitude of the resultant force is:

$R=100.3 \:pound$

The direction is:

$\theta=1.2^{\circ}$

Step-by-step explanation:

Let's find the components of each vector is x and y-directions first.

<u>Sum of x-component vector forces.</u>

$F_{tot-x}=F_{1}cos(45)+F_{2}cos(30)$

$F_{tot-x}=50cos(45)+75cos(30)$

$F_{tot-x}=100.3 \: pound$

<u>Sum of y-component vector forces.</u>

$F_{tot-y}=-F_{1}sin(45)+F_{2}sin(30)$

$F_{tot-y}=-50sin(45)+75sin(30)$

$F_{tot-y}=2.1 \: pound$

The magnitude of the resultant force is:

$R=\sqrt{100.3^{2}+2.1^{2}}$

$R=100.3 \:pound$

The direction is:

$tan(\theta)=\frac{2.1}{100.3}$

$\theta=arctan(\frac{2.1}{100.3})$

$\theta=1.2^{\circ}$

I hope it helps you!

4 0

3 years ago

I’m begging you help me!!! 1. The table below shows 3 recipes for a fruit punch

wariber [46]

Answer:

The answer to this question is given below in the explanation section.

Step-by-step explanation:

The table shows three different recipes. In this question, it is asked that will all the recipes taste same. To obtain the answer to this question, first, we measure the taste of each recipe in terms of calculating the ratio.

Water ............................. Cups

1 ............................. 3

4 ............................. 12

6 ............................. 18

1. The fraction of the first recipe is 1/3 so the ratio is 1:3(water to cup)

2. The fraction of the second recipe is 4/12

which can be simplified as 4/12=1/3 so the ratio is 1:3(water to cup)

3. The fraction of the third recipe is 6/18

which can be simplified as 6/18 = 3/9 = 1/3 so the ratio is 1:3(water to cup).

So based on the above answer, all recipes taste the same.

Answer 2:

No recipe taste different, all the recipe taste the same. Because all the recipe ratios are equivalent.

5 0

2 years ago

Simplify: sec(θ) sin(θ) cot(θ)

krek1111 [17]

We have to simplify

sec(θ) sin(θ) cot(θ)

Now first of all let's simplify these separately , using reciprocal identities.

Sec(θ) = 1/cos(θ)

Sin(θ) is already simplified

Cot(θ)= cos(θ) / sin(θ) ,

Let's plug these values in the expression

sec(θ) sin(θ) cot(θ)

= ( 1/cos(θ) ) * ( sin(θ) ) * ( cos(θ) / sin(θ) )

= ( sin(θ) /cos(θ) ) * ( cos(θ) /sin(θ) )

sin cancels out with sin and cos cancels out with cos

So , answer comes out to be

=( sin(θ) /cos(θ) ) * ( cos(θ) /sin(θ) )

= 1

4 0

3 years ago

Read 2 more answers

Which arrangement shows 318 , 3.7, 334 , and 3.89 in order from least to greatest?

Stolb23 [73]

Answer: OPTION D.

Step-by-step explanation:

<h3> The complete exercise is: "Which arrangement shows $3\frac{1}{8}$ , 3.7, $3\frac{3}{4}$ , and 3.89 in order from least to greatest?"</h3><h3> </h3>

Convert from mixed numbers to decimal numbers.

The steps to do this, are the following:

1. You must divide the numerator of the fraction by the denominator.

2. Then you must add the quotient obtained to the whole number part.

Applying this procedure, you get that:

$3\frac{1}{8}=3+0.125=3.125$