Which of the following statements about shapes of histograms is true?

a. A histogram is said to be symmetric if, when we draw a vertical line down the center of the histogram, the two sides are identical in shape and size.
b. A negatively skewed histogram is one with a long tail extending to the left.
c. A positively skewed histogram is one with a long tail extending to the right.
d. All of these choices are true

Answers

Answer 1

Answer:

d. all of these choices are true

Step-by-step explanation:

Histograms have 3 outstanding shapes:

1. they are syymetric:

this is to say that from the middle of the histogram if you cut it into two or half, each side is an exact close representation of the other side.

2. they are positively skewed to the right:

That is it has a long tail that goes off towards the right.

3. they are negativly skewed to the left:

They have a long tail that goes off to the left.

therefore from the question option d is the best answer since a, b, c describes the shape of a histogram.


Related Questions

Please give me the answer ASAP The average of 5 numbers is 7. If one of the five numbers is removed, the average of the four remaining numbers is 6. What is the value of the number that was removed Show Your Work

Answers

Answer:

The removed number is 11.

Step-by-step explanation:

Given that the average of 5 numbers is 7. So you have to find the total values of 5 numbers :

[tex]let \: x = total \: values[/tex]

[tex] \frac{x}{5} = 7[/tex]

[tex]x = 7 \times 5[/tex]

[tex]x = 35[/tex]

Assuming that the total values of 5 numbers is 35. Next, we have to find the removed number :

[tex]let \: y = removed \: number[/tex]

[tex] \frac{35 - y}{4} = 6[/tex]

[tex]35 - y = 6 \times 4[/tex]

[tex]35 - y = 24[/tex]

[tex]35 - 24 = y[/tex]

[tex]y = 11[/tex]

Okay, let's slightly generalize this

Average of [tex]n[/tex] numbers is [tex]a[/tex]

and then [tex]r[/tex] numbers are removed, and you're asked to find the sum of these [tex]r[/tex] numbers.

Solution:

If average of [tex]n[/tex] numbers is [tex]a[/tex] then the sum of all these numbers is [tex]n\cdot a[/tex]

Now we remove [tex]r[/tex] numbers, so we're left with [tex](n-r)[/tex] numbers. and their. average will be [tex]{\text{sum of these } (n-r) \text{ numbers} \over (n-r)}[/tex] let's call this new average [tex] a^{\prime}[/tex]

For simplicity, say, sum of these [tex]r[/tex] numbers, which are removed is denoted by [tex]x[/tex] .

so the new average is [tex]\frac{\text{Sum of } n \text{ numbers} - x}{n-r}=a^{\prime}[/tex]

or, [tex] \frac{n\cdot a -x}{n-r}=a^{\prime}[/tex]

Simplify the equation, and solve for [tex]x[/tex] to get,

[tex] x= n\cdot a -a^{\prime}(n-r)=n(a-a^{\prime})+ra^{\prime}[/tex]

Hope you understand it :)

solve the system with elimination 4x+3y=1 -3x-6y=3

Answers

Answer:

x = 1, y = -1

Step-by-step explanation:

If we have the two equations:

[tex]4x+3y=1[/tex] and [tex]-3x - 6y = 3[/tex], we can look at which variable will be easiest to eliminate.

[tex]y[/tex] looks like it might be easy to get rid of, we just have to multiply [tex]4x+3y=1[/tex]  by 2 and y is gone (as -6y + 6y = 0).

So let's multiply the equation [tex]4x+3y=1[/tex]  by 2.

[tex]2(4x + 3y = 1)\\8x + 6y = 2[/tex]

Now we can add these equations

[tex]8x + 6y = 2\\-3x-6y=3\\[/tex]

------------------------

[tex]5x = 5[/tex]

Dividing both sides by 5, we get [tex]x = 1[/tex].

Now we can substitute x into an equation to find y.

[tex]4(1) + 3y = 1\\4 + 3y = 1\\3y = -3\\y = -1[/tex]

Hope this helped!

The area of a rectangular garden if 6045 ft2. If the length of the garden is 93 feet, what is its width?

Answers

Answer:

65 ft

Step-by-step explanation:

The area of a rectangle is

A = lw

6045 = 93*w

Divide each side by 93

6045/93 = 93w/93

65 =w

Answer:

[tex]\huge \boxed{\mathrm{65 \ feet}}[/tex]

Step-by-step explanation:

The area of a rectangle formula is given as,

[tex]\mathrm{area = length \times width}[/tex]

The area and length are given.

[tex]6045=93 \times w[/tex]

Solve for w.

Divide both sides by 93.

[tex]65=w[/tex]

The width of the rectangular garden is 65 feet.

Transform the given parametric equations into rectangular form. Then identify the conic. x= -3cos(t) y= 4sin(t)

Answers

Answer:

Solution : Option D

Step-by-step explanation:

The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )

x = - 3cos(t) ⇒ x / - 3 = cos(t)

y = 4sin(t) ⇒ y / 4 = sin(t)

Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )

( x / - 3 )² = cos²(t)

+ ( y / 4 )² = sin²(t)

_____________

x² / 9 + y² / 16 = 1

Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.

It is known that 80% of all brand A external hard drives work in a satisfactory manner throughout the warranty period (are "successes"). Suppose that n= 15 drives are randomly selected. Let X = the number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. Obtain the sampling distribution of this statistic.

Answers

Answer:

P (x= 5) =  0.0001

P(x=3) =  0.008699

Step-by-step explanation:

This is a binomial distribution .

Here p = 0.8  q= 1-p = 1-0.8 = 0.2

n= 15

So we find the probability for x taking different values from 0 - 15.

The formula used will be

n Cx p^x q^n-x

Suppose we want  to find the value of x= 5

P (x= 5) = 15C5*(0.2)^10*(0.8)^5 = 0.0001

P(x=3) = 15C3*(0.2)^12*(0.8)^3 =  9.54 e ^-7= 0.008699

Similarly we can find the values for all the trials from 0 -15  by substituting the values of x =0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15.

The value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.

It is given that the 80% of all brand A external hard drives work in a satisfactory manner throughout the warranty period.

It is required to find the sampling distribution if n =15 samples.

What is sampling distribution?

It is defined as the probability distribution for the definite sample size the sample is the random data.

We have p =80% = 0.8 and q = 1 - p1 -0.8 ⇒ 0.2

n = 15

We can find the probability for the given x by taking different values from 0 to 15

the formula can be used:

[tex]\rm _{n}^{}\textrm{C}_x p^xq^{n-x}[/tex]

If we find the value for p(x = 5)

[tex]\rm _{15}^{}\textrm{C}_5 p^5q^{15-5}\\\\\rm _{15}^{}\textrm{C}_5 0.8^50.2^{10}[/tex]⇒ 0.0001

If we find the value for p(x = 3)

[tex]\rm _{15}^{}\textrm{C}_3 0.8^30.2^{12}\\[/tex] ⇒  

Similarly, we can find the values for all the trials from 0 to 15 by putting the values of x = 0 to 15.

Thus, the value for p(x = 5) is 0.0001 and the value for p(x = 3) is 0.008699.

Learn more about the sampling distribution here:

https://brainly.com/question/10554762

given point (-6, -3) and a slope of 4, write an equation in point-slope form

Answers

Answer:

y = 4x + 21

Step-by-step explanation:

Hello!

Point-slope form is y - y1 = m(x - x1)

y1 is the y point

x1 is the x point

m is the slope

Put in what you know

y - -3 = 4(x - -6)

Subtracting a negative is the same as adding

y + 3 = 4(x + 6)

Distribute the 4

y + 3 = 4x + 24

Subtract 3 from both sides

y = 4x + 21

The answer is y = 4x + 21

Hope this helps!

S varies inversely as G. If S is 8 when G is 1.5​, find S when G is 3. ​a) Write the variation. ​b) Find S when G is 3.

Answers

Step-by-step explanation:

a.

[tex]s \: = \frac{k}{g} [/tex]

[tex]8 = \frac{k}{1.5} [/tex]

[tex]k \: = 1.5 \times 8 = 12[/tex]

[tex]s = \frac{12}{g} [/tex]

b.

[tex]s = \frac{12}{3} [/tex]

s = 4

Find the missing coordinate

Answers

Answer:

(0, -10a)

Step-by-step explanation:

From the picture attached,

Coordinates of a point have been given as (-10a, 0)

x-coordinate → distance of the point from the origin on x-axis

y-coordinate → distance of the point from the origin on y-axis

Therefore, distance of the given point on x-axis = -10a [(-) sign denotes the negative side of the x-axis]

Distance of the other point with unknown coordinates (x, y) (on y-axis) from the origin = y

And y = 10a

Therefore, coordinates of the unknown point will be (0, -10a).

[Here (-) sign denotes the negative side of the y-axis]

Suppose that $2000 is invested at a rate of 2.6% , compounded semiannually. Assuming that no withdrawals are made, find the total amount after 10 years.

Answers

Answer:

$2,589.52

Step-by-step explanation:

[tex] A = P(1 + \dfrac{r}{n})^{nt} [/tex]

We start with the compound interest formula above, where

A = future value

P = principal amount invested

r = annual rate of interest written as a decimal

n = number of times interest is compound per year

t = number of years

For this problem, we have

P = 2000

r = 0.026

n = 2

t = 10,

and we find A.

[tex] A = $2000(1 + \dfrac{0.026}{2})^{2 \times 10} [/tex]

[tex] A = $2589.52 [/tex]

Compound interest formula:

Total = principal x ( 1 + interest rate/compound) ^ (compounds x years)

Total = 2000 x 1+ 0.026/2^20

Total = $2,589.52

how would you write six times the square of a number

Answers

6 to the power of whatever number you are going by

Answer:

[tex]\huge \boxed{6x^2 }[/tex]

Step-by-step explanation:

6 times a number squared.

Let the number be [tex]x[/tex].

6 is multiplied to [tex]x[/tex] squared.

[tex]6 \times x^2[/tex]

Find X so that m is parallel to n. Identify the postulate or theorem you used. Please help with these 3 problems, I don’t understand it at all

Answers

the corresponding angles should be equal

so, [tex] 5x+15=90 \implies 5x=75\implies x=15^{\circ}[/tex]

HELP ASAP PLS :Find all the missing elements:

Answers

Answer:

a ≈ 1.59

b ≈ 6.69

Step-by-step explanation:

Law of Sines: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

Step 1: Find c using Law of Sines

[tex]\frac{6}{sin58} =\frac{c}{sin13}[/tex]

[tex]c = sin13(\frac{6}{sin58})[/tex]

c = 1.59154

Step 2: Find a using Law of Sines

[tex]\frac{6}{sin58} =\frac{a}{sin109}[/tex]

[tex]a = sin109(\frac{6}{sin58} )[/tex]

a = 6.68961

A blue die and a red die are thrown. B is the event that the blue comes up with a 6. E is the event that both dice come up even. Write the sizes of the sets |E ∩ B| and |B|a. |E ∩ B| = ___b. |B| = ____

Answers

Answer:

Size of |E n B| = 2

Size of |B| = 1

Step-by-step explanation:

I'll assume both die are 6 sides

Given

Blue die and Red Die

Required

Sizes of sets

- [tex]|E\ n\ B|[/tex]

- [tex]|B|[/tex]

The question stated the following;

B = Event that blue die comes up with 6

E = Event that both dice come even

So first; we'll list out the sample space of both events

[tex]B = \{6\}[/tex]

[tex]E = \{2,4,6\}[/tex]

Calculating the size of |E n B|

[tex]|E n B| = \{2,4,6\}\ n\ \{6\}[/tex]

[tex]|E n B| = \{2,4,6\}[/tex]

The size = 3 because it contains 3 possible outcomes

Calculating the size of |B|

[tex]B = \{6\}[/tex]

The size = 1 because it contains 1 possible outcome

A political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. If the candidate wants a 10% margin of error at a 95% confidence level, what size of sample is needed

Answers

Answer:

The desired sample size is 97.

Step-by-step explanation:

Assume that 50% people in the community that supports the political candidate.

It is provided that the candidate wants a 10% margin of error (MOE) at a 95% confidence level.

The confidence interval for the population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

Then the margin of error is:

[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

Compute the critical value of z as follows:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]

*Use a z-table.

Compute the sample size as follows:

[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

       [tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)} }{MOE}]^{2}[/tex]

          [tex]=[\frac{1.96\times \sqrt{0.50(1-0.50)} }{0.10}^{2}\\\\=[9.8]^{2}\\\\=96.04\\\\\approx 97[/tex]

Thus, the desired sample size is 97.

I need help on this question :(​

Answers

Answer: 40 degree

Explanation:

FT bisect angle EFD dividing it into 2 equal angles (EFT and DFT)

And EFD = 80

We get :
EFT = 80/2
EFT = 40

And EFT + DFT = EFD = 80 degree

Therefore EFT = 40 degrees

A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure:
A: The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
B: The hypothesis µ1 = µ2 would be rejected at the 10% level of significance.
C: The hypothesis µ1 = µ2 would be rejected at the 1% level of significance.
A) A and B
B) A and C
C) A only
D) A, B, and C

Answers

Answer:

C) A only

Step-by-step explanation:

In statistics, the null hypothesis is the default hypothesis and the alternative hypothesis is  the research hypothesis. The alternative hypothesis usually comes in place to challenge the null hypothesis in order to determine if the test is statistically significant or not.

Similarly,

In hypothesis testing, the confidence interval consist of all reasonable value of the population mean. Values for which the null hypothesis will be rejected [tex]H_o[/tex] .

Given that:

At 95% confidence interval for the  difference between the population means is (1.4, 8.7).

The level of significance = 1 - 0.95 = 0.05  = 5%

So , If the hypothesis test is based on the same samples, The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.

Which of the following graphs accurately displays a parabola with its directrix and focus?

Answers

Answer:

Hey there!

The first graph is the correct answer. A point on the parabola is equally far from the focus as it is to the directrix.

Let me know if this helps :)

The graph that  accurately displays a parabola with its directrix and focus is the first graph.

How do we make graph of a function?

Suppose the considered function whose graph is to be made is  f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values  f(x) are plotted on the vertical axis.

They are together plotted on the point  (x,y) = (x, f(x))

This is why we usually write the functions as:  y = f(x)

A point shown in the graphs on the parabola is equally far from the focus as it is to the directrix.

Therefore, The first graph is the correct answer.

Learn more about graphing functions here:

https://brainly.com/question/14455421

#SPJ2

Which choice shows the product of 22 and 49 ?

Answers

Answer:

1078

Step-by-step explanation:

The product of 22 and 49 is 1078.

Answer:

1078 is the product

Step-by-step explanation:

can anyone show me this in verbal form?

Answers

Answer:

2 * (x + 2) = 50

Step-by-step explanation:

Let's call the unknown number x. "A number and 2" means that we need to add the numbers, therefore it would be x + 2. "Twice" means 2 times a quantity so "twice a number and 2" would be 2 * (x + 2). "Is" denotes that we need to use the "=" sign and because 50 comes after "is", we know that 50 goes on the right side of the "=" so the final answer is 2 * (x + 2) = 50.


An apartment building is infested with 6.2 X 10 ratsOn average, each of these rats
produces 5.5 X 10' offspring each year. Assuming no rats leave or die, how many additional
rats will live in this building one year from now? Write your answer in standard form.

Answers

Answer: 3.41x10^3

Step-by-step explanation:

At the beginning of the year, we have:

R = 6.2x10 rats.

And we know that, in one year, each rat produces:

O = 5.5x10 offsprins.

Then each one of the 6.2x10 initial rats will produce 5.5x10 offsprings in one year, then after one year we have a total of:

(6.2x10)*(5.5x10) = (6.2*5.5)x(10*10) = 34.1x10^2

and we can write:

34.1 = 3.41x10

then: 34.1x10^2 = 3.41x10^3

So after one year, the average number of rats is:  3.41x10^3

The weight of an object on moon is 1/6 of its weight on Earth. If an object weighs 1535 kg on Earth. How much would it weigh on the moon?

Answers

Answer:

255.8

Step-by-step explanation:

first

1/6*1535

=255.8

Identifying the Property of Equality

Quick

Check

Identify the correct property of equality to solve each equation.

3+x= 27

X/6 = 5

Answers

Answer:

a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication

Step-by-step explanation:

a) This expression can be solved by using the Compatibility of Equality with Addition, that is:

1) [tex]3+x = 27[/tex] Given

2) [tex]x+3 = 27[/tex] Commutative property

3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition

4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property

5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction

6) [tex]x=24[/tex] Modulative property/Subtraction/Result.

b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:

1) [tex]\frac{x}{6} = 5[/tex] Given

2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division

3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication

4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property

5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse

6) [tex]x = 30[/tex] Modulative property/Result

Answer:

3 + x = 27

✔ subtraction property of equality with 3

x over 6  = 5

✔ multiplication property of equality with 6

What is the error in this problem

Answers

Answer:

10). m∠x = 47°

11). x = 30.96

Step-by-step explanation:

10). By applying Sine rule in the given triangle DEF,

   [tex]\frac{\text{SinF}}{\text{DE}}=\frac{\text{SinD}}{\text{EF}}[/tex]

   [tex]\frac{\text{Sinx}}{7}=\frac{\text{Sin110}}{9}[/tex]

   Sin(x) = [tex]\frac{7\times (\text{Sin110})}{9}[/tex]

   Sin(x) = 0.7309

   m∠x = [tex]\text{Sin}^{-1}(0.7309)[/tex]

   m∠x = 46.96°

   m∠x ≈ 47°

11). By applying Sine rule in ΔRST,

   [tex]\frac{\text{SinR}}{\text{ST}}=\frac{\text{SinT}}{\text{RS}}[/tex]

   [tex]\frac{\text{Sin120}}{35}=\frac{\text{Sin50}}{x}[/tex]

   x = [tex]\frac{35\times (\text{Sin50})}{\text{Sin120}}[/tex]

   x = 30.96   

Find the value of the expression: −mb −m^2 for m=3.48 and b=96.52

Answers

Answer:

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

Step-by-step explanation:

Let be [tex]f(m, b) = m\cdot b - m^{2}[/tex], if [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex], the value of the expression:

[tex]f(3.48,96.52) = (3.48)\cdot (96.52)-3.48^{2}[/tex]

[tex]f(3.48,96.52) = 323.779[/tex]

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

There are 30 colored marbles inside a bag. Six marbles are yellow, 9 are red, 7 are white, and 8 are blue. One is drawn at random. Which color is most likely to be chosen? A. white B. red C. blue D. yellow Include ALL work please!

Answers

Answer:

red

Step-by-step explanation:

Since the bag contains more red marbles than any other color, you are most likely to pick a red marble

The top speed of this coaster is
128 mph. What is the tallest peak
of this coaster?
** Hint... convert mph into m/s.*​

Answers

To convert miles per hour to meters per second divide by 2.237

128 miles per hour / 2.237 = 57.22 meters per second.

Using the first equation:

57.22 = sqrt(2 x 9.81 x h)

Remove the sqrt by raising both sides to the second power:

57.22^2 = (2 x 9.81 x h)

Simplify Both sides:

3274.1284 = 19.62h

Divide both sides by 19.62:

H = 3274.1284/ 19.62

H = 166.88 meters

A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 140 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month? Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents 8 15 9 8 13 6 17 15 10 9 18 12

Answers

Answer:

There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.

There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.

Step-by-step explanation:

Month       No. of              Mean       Squared

           Fatal Accidents  Deviation   Difference

Jan          8                       -4                  16

Feb        15                        3                   9

Mar         9                       -3                   9

Apr         8                       -4                  16

May       13                        1                    1

Jun         6                      -6                 36

Jul         17                       5                 25

Aug       15                       3                   9

Sep       10                      -2                   4

Oct        9                       -3                   9

Nov    18                          6                 36

Dec    12                          0                   0

Total 140                                         170

Mean = 140/12 = 12    Mean of squared deviation (Variance) = 170/12 = 14.16667

Standard deviation = square root of variance = 3.76386 = 4

The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set.  It also shows how variable the data varies from the mean of approximately 12.

The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.

The angles of a quadrilateral are (3x + 2), (x-3), (2x+1), and 2(2x+5). Find x.

Answers

Answer:

3x+2+x-3+2x+1+2(2x+5)=360

10x+10=360

x=35

Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.1. Compute the values below.

(a) P(E ∪ F) =



(b) P(Ec) =



(c) P(Fc ) =



(d) P(Ec ∩ F) =

Answers

Answer:

(a) P(E∪F)= 0.8

(b) P(Ec)= 0.4

(c) P(Fc)= 0.7

(d) P(Ec∩F)= 0.8

Step-by-step explanation:

(a) It is called a union of two events A and B, and A ∪ B (read as "A union B") is designated to the event formed by all the elements of A and all of B. The event A∪B occurs when they do A or B or both.

If the events are not mutually exclusive, the union of A and B is the sum of the probabilities of the events together, from which the probability of the intersection of the events will be subtracted:

P(A∪B) = P(A) + P(B) - P(A∩B)

In this case:

P(E∪F)= P(E) + P(F) - P(E∩F)

Being P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.1

P(E∪F)= 0.6 + 0.3 - 0.1

P(E∪F)= 0.8

(b)  The complement of an event A is defined as the set that contains all the elements of the sample space that do not belong to A.  The Complementary Rule establishes that the sum of the probabilities of an event and its complement must be equal to 1. So, if P (A) is the probability that an event A occurs, then the probability that A does NOT occur is  P (Ac) = 1- P (A)

In this case: P(Ec)= 1 - P(E)

Then: P(Ec)= 1 - 0.6

P(Ec)= 0.4

(c) In this case: P(Fc)= 1 - P(F)

Then: P(Fc)= 1 - 0.3

P(Fc)= 0.7

(d)  The intersection of two events A and B, designated as A ∩ B (read as "A intersection B") is the event formed by the elements that belong simultaneously to A and B. The event A ∩ B occurs when A and B do at once.

As mentioned, the complementary rule states that the sum of the probabilities of an event and its complement must equal 1. Then:

P(Ec intersection F) + P(E intersection F) = P(F)

P(Ec intersection F) + 0.1 = 0.3

P(Ec intersection F)= 0.2

Being:

P(Ec∪F)= P(Ec) + P(F) - P(Ec∩F)

you get:

P(Ec∩F)= P(Ec) + P(F) - P(Ec∪F)

So:

P(Ec∩F)= 0.4 + 0.3 - 0.2

P(Ec∩F)= 0.8

Question: The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Which equation can be used to find the length of the remaining side?

Answers

Answer:

The hypotenuse is the longest side in a triangle.

a^2=b^2+c^2.

14^2=9^2+c^2.

c^2=196-81.

c^2=115.

c=√115.

c=10.72~11cm

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