Calculate the expected value of X, E(X), for the given probability distribution. E(X):_________

x 0 1 2 3
P(x) 0.5 0.1 0.1 0.3

Answer:

2.4

Step-by-step explanation:

Answer:

Step-by-step explanation:

The complete question is given thus:

Suppose that computer literacy among people ages 40 and older is being studied and that the accompanying tables describes the probability distribution for four randomly selected people, where x is the number that are computer literate. Is it unusual to find four computer literates among four randomly selected people?

x      P(x)

0     0.16

1      0.25

2     0.36

3      0.15

4      0.08

ANSWER:

The odds that this will occur according to the chart are 0.08, or 8%, so although this is unlikely, it's not terribly unusual.

⇒ NO

So from the following we can say it is not unusual to find four (4) computer literates among four randomly selected people.

ok, so P(1) + P(2) + P(3) + P(4) + P(0)  = 0.16+0.25+0.36+0.15+0.08 = 1

Whereas the chance of finding four (4) out of four (4) computer iteration is low when compared to other factors.

cheers i hope this helped  !!

Answer:

a) true

Step-by-step explanation:

Empirical hypothesis is the type of hypothesis used to try and explain a  phenomenon which leads to a theory been developed and put to the test, using observation and experiment.

Radium was discovered due to a discrepancy in pitchblende's radiation. It was noted by the Curies that Polonium alone could not suffice for that amount of radiation, leading to the theory that another element could be present. After further testing, Radium was discovered as the culprit element.

Also, the presence pf another planet, later discovered to be Neptune was theorized to explain the phenomenon that could cause the irregularities in the motion pattern of the planet Uranus. After much experimentation, observations and calculations, Neptune was discovered.

Answer:

x = -2 +/- √8 or 0.828.... and -4.828....

Step-by-step explanation:

x² + 4x + 4 = 4 + 4

(x + 2)² = 8

x + 2 = +/-√8

x = -2 +/- √8

Answer:

72

Step-by-step explanation:

120% × 60 =

(120 ÷ 100) × 60 =

(120 × 60) ÷ 100 =

7,200 ÷ 100 =

hopefully this helped

Answer:

All you have to do to identify the number of terms in a polynomial is to count the number of separate parts in the polynomial separated by a plus or minus (terms)

Step-by-step explanation:

Answer:

18 millimeters

Step-by-step explanation:

The perimeter of any shape is the sum of the sides.  A trapezoid has four sides, so the perimeter is found by adding the four side lengths together.

The trapezoid in this problem has side lengths of 5 mm, 2 mm, 5 mm, and 6 mm.

Add the sides together.

5 mm + 2 mm + 5 mm + 6 mm

7 mm + 5 mm + 6mm

12 mm + 6 mm

18 mm

The perimeter of the trapezoid is 18 millimeters.

Answer:

B. 16

Step-by-step explanation:

F(3) means we must plug the number "3" into the equation for each x.

(3)^2 + 3(3) -2

9 + 9 - 2

16

Answer:

16

Step-by-step explanation:

F(x) = x² + 3x - 2

Let x=3

F(3)= 3^2 +3*3 -2

     = 9+9-2

    = 18-2

     =16

Answer:

Step-by-step explanation:

Given:

Sample 1.71 , 2.05

Find:

Margin of error

Sample mean

Computation:

1. Margin of error = (2.05 - 1.71) / 2

Margin of error = 0.34 / 2

Margin of error = 0.17

2. Sample mean = (2.05 + 1.71) / 2

Sample mean = 3.76 / 2

Sample mean = 1.88

Answer:

72

32 x

________

 144

2160  +

________

2304

Step-by-step explanation:

Answer: $384

Step-by-step explanation:

1000- 1000=0

900-500=400

20-36=-16

400+-16=384

Answer:

(1) 0.75

(2) 30

(3) 56

Step-by-step explanation:

Let X represent the time for service call.

It is provided that: [tex]X\sim Uni(20, 60)[/tex]

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b[/tex]

(1)

Compute the probability that the service call takes longer than 30 minutes as follows:

[tex]P(X>30)=\int\limits^{60}_{30} {\frac{1}{60-20}} \, dx[/tex]

                 [tex]=\frac{1}{40}\times |x|^{60}_{30}\\\\=\frac{60-30}{40}\\\\=\frac{3}{4}\\\\=0.75[/tex]

Thus, the probability that the service call takes longer than 30 minutes is 0.75.

(2)

The Inter quartile range is the difference between the 75th and 25th percentile.

From part (1), we know that P (X > 30) = 0.75.

⇒ 1 - P (X > 30) = 0.75

⇒ P (X < 30) = 0.25

The 25th percentile is 30.

Compute the 75th percentile as follows:

[tex]P(X<x)=0.75\\\\\int\limits^{x}_{20} {\frac{1}{60-20}} \, dx=0.75\\\\\frac{1}{40}\times |x|^{x}_{20}=0.75\\\\x-20=40\times 0.75\\\\x=30+20\\\\x=50[/tex]

The 75th percentile is 50.

Then the inter quartile range is:

[tex]IQR=P_{75}-P_{25}[/tex]

        [tex]=50-20\\=30[/tex]

Thus, the inter quartile range is 30.

(3)

Compute the 90th percentile as follows:

[tex]P(X<x)=0.90\\\\\int\limits^{x}_{20} {\frac{1}{60-20}} \, dx=0.90\\\\\frac{1}{40}\times |x|^{x}_{20}=0.90\\\\x-20=40\times 0.90\\\\x=36+20\\\\x=56[/tex]

The 90th percentile is 56.

Answer:

r^2 = 1

Step-by-step explanation:

The computation of the  coefficient of determination for the two variables is shown below:

here the perfect positive linear correlation is r = 1

And, the negative linear correlation is r = -1

Based on this, the coefficient of determination is equivalent to the linear correlation coefficient square

[tex]r^2 = (\pm)^2 \\\\ = 1[/tex]

This above describes that variation that lies between the variables as explained by the linear regression line

The coefficient of determination for two variables that have perfect positive linear correlation or perfect negative linear correlation is denoted by; r² = (±1)² = 1

The mathematical computation of the coefficient of determination for two variables that have perfect positive linear correlation can be in two forms and is as follows;

In lieu of this, the coefficient of determination is equivalent to the square of linear correlation coefficient.

The computation above describes that variation that lies between the variables as explained by the linear regression line.

Read more:

https://brainly.com/question/20038665

Answer:

The left over wood in foot is 2.34  foot

or 2 foot 4 inch

Step-by-step explanation:

This problem desires to test our unit conversion skills

Step one:  let us work with foot and convert inches to foot.

The total wood is 8 foot, and we are expected to subtract 5 foot 8 inches from it.

converting 8 inches to foot we have

1 inch -----0.0833333 foot

8 inch-----x foot

cross multiplying we have

x= 8*0.0833333

x= 0.66 foot

Hence the total number of wood to be subtracted in foot is 5.66 foot

i.e 8-5.66= 2.34  foot

The left over wood in foot is 2.34  foot

or 2 foot 4 inch

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)[/tex]

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

[tex]4^n+17[/tex] is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so [tex]4^k+17[/tex] is divisible by 3

and we check what happens for k+1

[tex]4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17[/tex]

[tex]3\cdot 4^k[/tex] is divisible by 3 and

[tex]4^k+17[/tex] is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that [tex]4^n+17[/tex] is divisible by 3 for all positive integers n.

Thanks

Answer:

10; -3

Step-by-step explanation:

Let's represent the first number with x, and the second number with y.  Now let's write these two equations to find the numbers.

x + 2y = 4

2x + y = 17

We can solve using the substitution method:

x = 4 - 2y

2x + y = 17

2 (4 - 2y) + y = 17

8 - 4y + y = 17

-3y = 9

y = -3

Now plug the value of y in to find x:

x + 2y = 4

x + 2(-3) = 4

x + -6 = 4

x = 10

So, the first number is 10, and the second number is -3.

Cheers.

Answer:

39

Step-by-step explanation:

difference=28

other number=11

so:

11+28=39

39 is your other number

Answer:

Just simply add the given two numbers and you ll get the answer 39 now to check whether its right or wrong subtract 11 from 39 and you ll get 28 which proves that its correct

Step-by-step explanation:

Answer:

A histogram is a graph that organizes a group of data points. A histogram graphically summarize the distribution of a univariate data set.

The answers are:

18 to 24 =  [tex]\frac{18}{24} = \frac{3}{4}[/tex]

5 to 15 =  [tex]\frac{5}{15} = \frac{1}{3}[/tex]

14:42 =  [tex]\frac{14}{42} = \frac{1}{3}[/tex]

15 cents to 18 cents = [tex]\frac{15}{18} = \frac{5}{6}[/tex]

Explanation:

To write a fraction using a ratio, simply use the first number as the numerator (top number), in this case, the numbers 18, 5, 14, and 15, and the second or biggest number as a denominator (bottom number), in this case, the numbers 24, 15, 42 and 18. This means the fractions are  [tex]\frac{18}{24}[/tex],  [tex]\frac{5}{15}[/tex], [tex]\frac{14}{42}[/tex] , and  [tex]\frac{15}{18}[/tex].

The second step is to reduce or simplify the fractions, which means the numbers in a fraction are divided by the same factor (a number that divides another without a remainder). Additionally, to do this, it is important to reduce the fraction to its minimum.

[tex]\frac{18}{24}[/tex] divide this by 6, which is equivalent to [tex]\frac{3}{4}[/tex]

[tex]\frac{5}{15}[/tex] divide this by 5, which is equivalent to [tex]\frac{1}{3}[/tex]

[tex]\frac{14}{42}[/tex] divide this by 14. which is equivalent to [tex]\frac{1}{3}[/tex]

[tex]\frac{15}{18}[/tex] divide this by 3, which is equivalent to [tex]\frac{5}{6}[/tex]

I hope this helps you

false

cause two negative numbers multiple must be positive

(-1).(-49)

+49

The statement is false.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1.

RULE 1: The product of a positive integer and a negative integer is negative.

RULE 2: The product of two positive integers is positive.

RULE 3: The product of two negative integers is positive.

Given:

−(−49) = −49

Is we use the properties of integer

(+).(+)= (+)

(-).(-)=(+)

(-).(+)=(-)

(+).(-)= (-)

So, the statement −(−49) = −49 is false because (-).(-)= (+)

Then, −(−49) = +49

Learn more about integers here:

https://brainly.com/question/15276410

#SPJ2

Answer:

The slope is

[tex] - \frac{4}{3} [/tex]

Step-by-step explanation:

To find the slope given two points we use the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

where

m is the slope

(x1 , y1) and (x2 , y2) are the points

From the question

The points are (3,14) and (6,10)

The slope of the line (3,14) and (6,10) is

[tex]m = \frac{10 - 14}{6 - 3} = \frac{ - 4}{ 3} [/tex]

[tex]m = - \frac{4}{3} [/tex]

Hope this helps you

Answer:

The answer is

Step-by-step explanation:

Send 5 to the right side of the equation

That's

Multiply both sides of the equation by 3

We have

x = 20 × 3

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

This problem can be solved by applying Pythagoras theorem, since the segment AB is tangent to the circle(meaning that the point A is at 90 degree to the circle)

According to Pythagoras theorem "It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides".

given (as seen from the diagram)

x, hypotenuse= ?

opposite= 12

adjacent= 35

Applying Pythagoras theorem

[tex]hyp^2= opp^2+adj^2\\\\hpy=\sqrt{opp^2+adj^2}[/tex]

Substituting our given data and solving for hpy we have

[tex]hyp=\sqrt{12^2+35^2} \\\\hyp=\sqrt{144+1225}\\\\hyp=\sqrt{1369}\\\\hyp= 37[/tex]

hence x= 37

Answer:   B

Step-by-step explanation:

ax² + bx + c = 0 is rewritten as  x² + (b/a)x + (b/2a)² = -c/a + (b/2a)²

A) 4x² + 9x + 5 = 0    -->    x² + (9/4)x + (9/8)² = -5/4 + (9/8)²

                                        = x² + (9/4)x + 81/64 = -5/4 + 81/64

B) 4x² + 12x + 7 = 0    -->    x² + (12/4)x + (12/8)² = -7/4 + (12/8)²

                                         = x² + 3x + 9/4 = -7/4 + 9/4             <---- this works!

C) 3x² - 6x - 4 = 0    -->    x² + (-6/3)x + (-6/6)² = 4/3 + (-6/6)²

                                         = x² - 2x + 1 = 4/3 + 1

D) 2x² - 8x - 9 = 0    -->    x² + (-8/2)x + (-8/4)² = 9/2 + (-8/4)²

                                         = x² - 4x + 4 = 9/2 + 4

Answer:

B

Step-by-step explanation:

its the correct answer :)

Answer:

0.0857

Step-by-step explanation:

What we need is, B R -G, successively. We do not add each probability, but multiply them.

P(1st marble is B) = 6 / 16

P(2nd marble is R) = 4 / 15

*your sample space decreases because you took one marble already before, the Blue one

P(3rd marble is not Green) = 12/14

** it's 12 because you took 2 non-Green marbles before

*** it's 14 because you took 2 marbles before

To arrive at the final answer, just multiply all probability.

Expanding the first expression gives

[tex](x+y)^2=x^2+2xy+y^2=1[/tex]

Since [tex]xy=-4[/tex], we have

[tex]x^2+2(-4)+y^2=1\implies\boxed{x^2+y^2=9}[/tex]

Answer:

the Dead Sea has the least elevation.

Answer:

0.982 * [tex]\pi[/tex]  = 3.085 cubic units

Step-by-step explanation:

To find the volume of the solid generated by a region that is bounded by lines where x = 0 , x (b) = 2 we apply the formula given in the attachment below  

the required region boundaries are

y = e^-x2 , y = 0 ,  x = 0,  x = b ( b >0)

attached below is a detailed solution of the problem

Answer:

0.4

Step-by-step explanation:

The number of ways to select 3 points out of 5 points:

N1 = 5C3 =  (5 x 4 x 3)/(1 x 2 x3) = 10

The number of ways to select 3 points out of 4 points that are already collinear:

N2 = 4C3 = (4 x 3 x 2)/(1 x 2 x 3) = 4

=> The probability of selecting 3 points that are collinear:

P = N2/N1 = 4/10 = 0.4

Good day, Harry!