All categories

3 years ago

Analyze the table below and answer the question that follows.

Mathematics

1 answer:

lora16 [44]3 years ago

8 0

Answer:

C. Events E and A are independent

Step-by-step explanation:

we will verify each options

(a)

We can use independent events formula

P(B∩C)=P(B)*P(C)

we are given

P(B)=0.4

P(C)=0.25

P(B∩C)=0.05

now, we can plug these values into formula

and we get

0.05=0.4*0.25

0.05=0.1

we can see that left side is not equal to right side

so, this is FALSE

(b)

We can use independent events formula

P(D∩A)=P(D)*P(A)

we are given

P(D)=0.25

P(A)=0.6

P(D∩A)=0.1

now, we can plug these values into formula

and we get

0.1=0.25*0.6

0.1=0.15

we can see that left side is not equal to right side

so, this is FALSE

(c)

We can use independent events formula

P(E∩A)=P(E)*P(A)

we are given

P(E)=0.5

P(A)=0.6

P(E∩A)=0.3

now, we can plug these values into formula

and we get

0.3=0.5*0.6

0.3=0.3

we can see that both sides are equal

so, this is TRUE

(d)

We can use independent events formula

P(D∩B)=P(D)*P(B)

we are given

P(D)=0.25

P(B)=0.4

P(D∩A)=0.15

now, we can plug these values into formula

and we get

0.15=0.25*0.4

0.15=0.1

we can see that left side is not equal to right side

so, this is FALSE

You might be interested in

Can you help me with the bottom three please?

nika2105 [10]

Answer:

6= 66.67%

7=25%

8=70%

6 0

3 years ago

Which of the following is not a valid conversion factor?

inessss [21]

Answer:

Out of the 3 that were listed, the "conversion" that is invalid is 1 meter = 10 millimeters.

Step-by-step explanation:

First: Well, for something like this, you don't really need steps, you just need to know how to do process of elimination and also your conversions:

We know that 1 meter is 100 centimeters

We know 1 kilometer is 1000 meters

We know that 1 meter is 10 millim....... Wait. Do we know that?

No! 1 meter is not 10 millimeters, it's 1000 millimeters. So 1 meter = 10 millimeters is invalid.

If you ever need a converter, use this link: https://www.google.com/search?q=centimeters+to+inches&rlz=1CAFQZI_enCA835&oq=centim&aqs=chrome.2.69i57j0l5.9328j0j7&sourceid=chrome&ie=UTF-8

Thank you for reading

Topic: Metric Conversions

4 0

3 years ago

Read 2 more answers

What are the solutions of the equation x4 – 5x2 – 36 = 0? Use factoring to solve.

pentagon [3]

Answer:

x=+/-3

Step-by-step explanation:

x^4-5x^2-36=0

factor

(x^2-9)(x^2+4)=0

split into 2 equations because one of these terms will need to equal zero for the eqation to be true

x^2-9=0 x^2+4=0

x^2=9 x^2=-4

x=+/-3 no real numbers

7 0

3 years ago

In which of the options below will the number 3 correctly fill in the blank. Select all that apply. A) ___ : 4 = 12 : 16 B) 1 :

aniked [119]

Answer:

A and B

Step-by-step explanation:

Given

List of given options

Required

Which will correctly take 3 to fill the blank

Represent the blanks with x

Option A:

$x : 4 = 12 : 16$

Convert to fractions

$\frac{x}{4} = \frac{12}{16}$

Multiply through by 4

$4 * \frac{x}{4} = 4 * \frac{12}{16}$

$x = \frac{48}{16}$

$x = 3$

Option B:

$1 : 5= x : 15$

Convert to fraction;

$\frac{1}{5} = \frac{x}{15}$

Multiply through by 15

$15 * \frac{1}{5} = \frac{x}{15} * 15$

$15 * \frac{1}{5} = x$

$3 = x$

$x = 3$

Option C:

$x : 1 = 12 : 3$

Convert to fraction

$\frac{x}{1} = \frac{12}{3}$

$x = 4$

Option D

$15:x = 3:1$

Convert to fraction

$\frac{15}{x} = \frac{3}{1}$

Cross Multiply

$3 * x = 15 * 1$

$3 * x = 15$

Divide through by 3

$x = 5$

From the above calculations.

<em>Option A and B can be filled with 3</em>

5 0

3 years ago

100 points! simplify write as a product compute

Rom4ik [11]

Answer:

a) $\sqrt{61 - 24 \sqrt{5} } = - 4 + 3 \sqrt{5}$

b) $( \sqrt{ ( {c}^{2} - 1) ({b}^{2} - 1) } - {2 \sqrt{bc} }) (\sqrt{ ( {c}^{2} - 1) ({b}^{2} - 1) } + {2 \sqrt{bc} } )$

c) $\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 - \sqrt{5} } = - 1$

Step-by-step explanation:

We want to simplify

$\sqrt{61 - 24 \sqrt{5} }$

Let :

$\sqrt{61 - 24 \sqrt{5} } = a - b \sqrt{5}$

Square both sides of the equation:

$(\sqrt{61 - 24 \sqrt{5} } )^{2} = ({a - b \sqrt{5} })^{2}$

Expand the RHS;

$61 - 24 \sqrt{5} = {a}^{2} - 2ab \sqrt{5} + 5 {b}^{2}$

Compare coefficients on both sides:

${a}^{2} + 5 {b}^{2} = 61 - - - (1)$

$- 24 = - 2ab \\ ab = 12 \\ b = \frac{12}{b} - - -( 2)$

Solve the equations simultaneously,

$\frac{144}{ {b}^{2} } + 5 {b}^{2} = 61$

$5 {b}^{4} - 61 {b}^{2} + 144 = 0$

Solve the quadratic equation in b²

${b}^{2} = 9 \: or \: {b}^{2} = \frac{16}{5}$

This implies that:

$b = \pm3 \: or \: b = \pm \frac{4 \sqrt{5} }{5}$

When b=-3,

$a = - 4$

Therefore

$\sqrt{61 - 24 \sqrt{5} } = - 4 + 3 \sqrt{5}$

We want to rewrite as a product:

${b}^{2} {c}^{2} - 4bc - {b}^{2} - {c}^{2} + 1$

as a product:

We rearrange to get:

${b}^{2} {c}^{2} - {b}^{2} - {c}^{2} + 1- 4bc$

We factor to get:

${b}^{2} ( {c}^{2} - 1) - ({c}^{2} - 1)- 4bc$

Factor again to get;

$( {c}^{2} - 1) ({b}^{2} - 1)- 4bc$

We rewrite as difference of two squares:

$(\sqrt{( {c}^{2} - 1) ({b}^{2} - 1) })^{2} - ( {2 \sqrt{bc} })^{2}$

We factor the difference of square further to get;

$( \sqrt{ ( {c}^{2} - 1) ({b}^{2} - 1) } - {2 \sqrt{bc} }) (\sqrt{ ( {c}^{2} - 1) ({b}^{2} - 1) } + {2 \sqrt{bc} } )$

c) We want to compute:

$\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 - \sqrt{5} }$

Let the numerator,

$\sqrt{9 - 4 \sqrt{5} } = a - b \sqrt{5}$

Square both sides of the equation;

$9 - 4 \sqrt{5} = {a}^{2} - 2ab \sqrt{5} + 5 {b}^{2}$

Compare coefficients in both equations;

${a}^{2} + 5 {b}^{2} = 9 - - - (1)$

and

$- 2ab = - 4 \\ ab = 2 \\ a = \frac{2}{b} - - - - (2)$

Put equation (2) in (1) and solve;

$\frac{4}{ {b}^{2} } + 5 {b}^{2} = 9$

$5 {b}^{4} - 9 {b}^{2} + 4 = 0$

$b = \pm1$

When b=-1, a=-2

This means that:

$\sqrt{9 - 4 \sqrt{5} } = - 2 + \sqrt{5}$

This implies that:

$\frac{ \sqrt{9 - 4 \sqrt{5} } }{2 - \sqrt{5} } = \frac{ - 2 + \sqrt{5} }{2 - \sqrt{5} } = \frac{ - (2 - \sqrt{5)} }{2 - \sqrt{5} } = - 1$

3 0

3 years ago

Read 2 more answers