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Correction:

Because F is not present in the statement, instead of working on​P(E)P(F) = P(E∩F), I worked on

P(E∩E') = P(E)P(E').

Answer:

The case is not always true.

Step-by-step explanation:

Given that the odds for E equals the odds against E', then it is correct to say that the E and E' do not intersect.

And for any two mutually exclusive events, E and E',

P(E∩E') = 0

Suppose P(E) is not equal to zero, and P(E') is not equal to zero, then

P(E)P(E') cannot be equal to zero.

So

P(E)P(E') ≠ 0

This makes P(E∩E') different from P(E)P(E')

Therefore,

P(E∩E') ≠ P(E)P(E') in this case.

Answer:

10 km

Step-by-step explanation:

Distance = 5 cm

4 cm = 8 km

In km, how far apart is school and home?

Cross Multiply

[tex]\frac{4cm}{8km}[/tex] · [tex]\frac{5cm}{1}[/tex]

Cancel centimeters

[tex]\frac{40(km)(cm)}{4cm}[/tex]

Divide

= [tex]\frac{40km}{4}[/tex]

= 10 km

Answer:

They will need 160 cans to make 5 lbs

32 cans for 1 lbs

Step-by-step explanation:

We can use ratios to solve

8 cans             x cans

--------------- = ---------------

1/4 lbs             5 lbs

Using cross products

8 * 5 = 1/4x

40 = 1/4 x

Multiply each side by 4

4 * 40 = 1/4 x * 4

160 =x

They will need 160 cans to make 5 lbs

8 cans             x cans

--------------- = ---------------

1/4 lbs             1 lbs

Using cross products

8 * 1 = 1/4x

Multiply each side by 4

8*4 = x

32 cans for 1 lbs

Answer:

32 cans per pound of aluminum

160 cans per 5 pounds of aluminum

Step-by-step explanation:

will make it short and simple.

8 empty cans can make 1/4 pound of aluminum.

therefore... 8 x 4 = 32 cans per pound of aluminum.

Number of cans to make 5 pounds of aluminum = 32 x 5

= 160 cans per 5 pounds of aluminum

Answer:

60 pounds

Step-by-step explanation:

Let x = number of pounds of grass seeds A

The number of pounds of grass seed B = 140 pounds

Total pounds of the resulting mixture = (140 + x) pounds

Rye grass A = 60% = 0.6

Rye grass B = 80% = 0.8

Total percent of mixture formed = 74% = 0.74

Hence, we have the equation:

0.6x + 0.8 × 140 = 0.74 ( 140 + x)

0.6x + 112 = 103.6 + 0.74x

Collect like terms

112 - 103.6 = 0.74x - 0.6x

8.4 = 0.14x

x = 60 pounds

Therefore, the quantity of the 60% mixture used is 60 pounds.

The manager of a garden shop mixes grass seed that is 60% rye grass with 140 pound of grass seed that is 80% rye grass to make a mixture that is 74% rye grass. How much of the 60% mixture is used?

Answer: Expected value

Step-by-step explanation: The expected value of a random variable refers to a predicted variable which is obtained from the summation of the product of all possible values and the probability of occurrence of each value. The expected values gives the mean or average possible value over the cause of a certain experiment or scenario. It is thus the probability weighted average of all possible values or outcomes of an experiment.

The expected value could be represented mathematically as thus;

E(x) = [Σ(x * p(x)]

Where x = all possible values or outcomes of x;

p(x) = corresponding probability of each x value.

Answer:

37°

This is because the square indicates a right angle.

53 - 90 = 37

We have,

Now,

AOB + ∠BOC = ∠A0C

⇒ 53° + x° = 90°

⇒ x° = 90° - 53°

⇒ x° = 37°

Answer:

288

Step-by-step explanation:

Area of two triangles=2(½bh)

=bh

=8×6

=48

For the rectangles=lb + lb +lb

l(b+b+b)

=12(8+6+6)

=12×20

=240

Total area=240 +48=288

Let assume that the mean is 184 and the standard deviation is 6

Heights of men on a baseball team have a​ bell-shaped distribution with a mean 184 of and a standard deviation of 6 . Using the empirical​ rule, what is the approximate percentage of the men between the following​ values? a.166 cm and 202 cm b. 172 cm and 196cm

Answer:

P(156<X<202) =  99.7%

P(172<X<196) =  95.5%

Step-by-step explanation:

Given that :

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of and a standard deviation of . Using the empirical​ rule, what is the approximate percentage of the men between the following​ values? a.166 cm and 202 cm b. 172 cm and 196cm

For a.

Using the empirical​ rule, what is the approximate percentage of the men between the following​ values 166 cm and 202 cm.

the z score can be determined by using the formula:

[tex]z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]z(166) = \dfrac{166-184}{6}[/tex]

[tex]z(166) = \dfrac{-18}{6}[/tex]

z(166) = -3

[tex]z(202) = \dfrac{202-184}{6}[/tex]

[tex]z(202) = \dfrac{18}{6}[/tex]

z(202) = 3

P(156<X<202) = P( μ - 3σ < X < μ + 3σ )

P(156<X<202) = P( - 3 < Z < 3)

P(156<X<202) = P( Z <  3) - P(Z < -3)

P(156<X<202) = 0.99865-  0.001349

P(156<X<202) =  0.997301

P(156<X<202) =  99.7%

For b.

b. 172 cm and 196cm

[tex]z = \dfrac{X - \mu}{\sigma}[/tex]

[tex]z(172) = \dfrac{172-184}{6}[/tex]

[tex]z(172) = \dfrac{-12}{6}[/tex]

z(172) = -2

[tex]z(196) = \dfrac{196-184}{6}[/tex]

[tex]z(196) = \dfrac{12}{6}[/tex]

z(196) = 2

P(172<X<196) = P( μ - 2σ < X < μ + 2σ )

P(172<X<196) = P( - 2 < Z < 2)

P(172<X<196) = P( Z <  2) - P(Z < -2)

P(172<X<196) = 0.9772 -  0.02275

P(172<X<196) =  0.95445

P(172<X<196) =  95.5%

Answer:

The probability that a particular firm selected has $1 million or more in income after taxes is 49%.

Step-by-step explanation:

We are given a study of 200 computer service firms revealed these incomes after taxes below;

         Income After Taxes                  Number of Firms

           Under $1 million                              102

      $1 million up to $20 million                    61

           $20 million or more                          37      

                 Total                                           200    

Now, the probability that a particular firm selected has $1 million or more in income after taxes is given by;

Total number of firms = 102 + 61 + 37 = 200

Number of firms having $1 million or more in income after taxes = 61 + 37 = 98  {here under $1 million data is not include}

So, the required probability =  [tex]\frac{\text{Firms with \$1 million or more in income after taxes}}{\text{Total number of firms}}[/tex]

                                           =  [tex]\frac{98}{200}[/tex]

                                           =  0.49 or 49%

The probability that a particular firm selected has $1 million or more in income after taxes is 0.49 or 49%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

A study of 200 computer service firms revealed these incomes after taxes:

Income After Taxes Number of Firms Under

$1 million 102

$1 million up to $20 million 61

$20 million or more 37.

Then the total event will be

Total event = 102 + 37 +61 = 200

The probability that a particular firm selected has $1 million or more in income after taxes will be

Favorable event = 37 + 61 = 98

Then the probability will be

[tex]\rm P = \dfrac{98}{200} \\\\P = 0.49 \ or \ 49 \%[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

Answer:

When a shape is congruent they are equal in shape, size, and measure. Although if a shape is similar they will be the same shape, but not the same size, instead they will be proportionate.

Step-by-step explanation:

Answer:

CongruentCongruent figures are identical in size, shape and measure. SimilarTwo figures are similar if they have the same shape, but not necessarily the same size.

Step-by-step explanation:

Answer:

There is a positive correlation between these two variables.

Step-by-step explanation:

Positive correlation is an association amid two variables in which both variables change in the same direction.  

A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.

As the distance covered by the vehicle increases the amount of gas consumed also increases. Thus, the weekly cost of gas will also increase.

Thus, there is a positive correlation between these two variables.

Answer:

Step-by-step explanation:

Since the above figure is a right angled triangle we can use trigonometric ratios to find y

To find y we use tan

tan∅ = opposite/ adjacent

From the question

the opposite is y

the adjacent is 350 ft

Substitute the values into the above formula

That's

[tex] \tan(27) = \frac{y}{350} [/tex]

y = 350 tan 27

y = 178.3339

We have the final answer as

Hope this helps you

Answer:

0

Step-by-step explanation:

[tex]\lim_{x \to 0} (csc(x)-cot(x))\\= \lim_{x \to 0}(\frac{1}{sin x}-\frac{cos(x)}{sin (x)} )\\=\lim_{x \to 0}(\frac{1-cos x}{sin x} )\\=\lim_{x \to 0}(\frac {2 sin ^2 \frac{x}{2}}{2sin \frac{x}{2} cos\frac{x}{2} } )\\=\lim_{x \to 0}(tan \frac{x}{2} )\\=\lim_{x \to 0}\frac{tan \frac{x}{2} }{\frac{x}{2} } \times \frac{x}{2} \\=1 \times 0\\=0[/tex]

Answer:

75%

Step-by-step explanation:

75% of possibility to have gold coin

Answer: 6

Step-by-step explanation:

Answer:

Hey there!

Using the foil method: (3x+2)(5x-7)

15x^2+10x-21x-14

15x^2-11x-14

Let me know if this helps :)

Answer:

[tex]p = 2[/tex] if given vectors must be linearly independent.

Step-by-step explanation:

A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If [tex]\vec u = (1,1,2)[/tex], [tex]\vec v = (1,p,5)[/tex] and [tex]\vec w = (5,3,4)[/tex], the linear combination is:

[tex]\alpha_{1}\cdot (1,1,2)+\alpha_{2}\cdot (1,p,5)+\alpha_{3}\cdot (5,3,4) =(0,0,0)[/tex]

In other words, the following system of equations must be satisfied:

[tex]\alpha_{1}+\alpha_{2}+5\cdot \alpha_{3}=0[/tex] (Eq. 1)

[tex]\alpha_{1}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex] (Eq. 2)

[tex]2\cdot \alpha_{1}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex] (Eq. 3)

By Eq. 1:

[tex]\alpha_{1} = -\alpha_{2}-5\cdot \alpha_{3}[/tex]

Eq. 1 in Eqs. 2-3:

[tex]-\alpha_{2}-5\cdot \alpha_{3}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex]

[tex]-2\cdot \alpha_{2}-10\cdot \alpha_{3}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex]

[tex](p-1)\cdot \alpha_{2}-2\cdot \alpha_{3}=0[/tex] (Eq. 2b)

[tex]3\cdot \alpha_{2}-6\cdot \alpha_{3} = 0[/tex] (Eq. 3b)

By Eq. 3b:

[tex]\alpha_{3} = \frac{1}{2}\cdot \alpha_{2}[/tex]

Eq. 3b in Eq. 2b:

[tex](p-2)\cdot \alpha_{2} = 0[/tex]

If [tex]p = 2[/tex] if given vectors must be linearly independent.

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

Answer:

Step-by-step explanation:

To find the missing side in the question, we use the cosine rule

That's

Since we are finding a we use the formula

From the question

b = 2

c = 4

A = 78°

Substitute the values into the above formula

We have

a² = 2² + 4² - 2(2)(4) cos 78

a² = 4 + 16 - 16 cos 78

a² = 20 - 16cos 78

a² = 16.67341

Find the square root of both sides

a = 4.0833

We have the final answer as

Hope this helps you

let the numbers be a and b, a>b

a+b=6(a-b)

we need to find reciprocal of ratio of larger to smaller , which will be same as ratio of smaller to larger or b/a, let's call it x

divide the equation by a.

1+x=6(1-x)

on solving, x=5/7

Answer:

After solving the power:

[tex]\bold{2(cos60^\circ+isin60^\circ)}[/tex]

Rectangular form:

[tex]\bold{1+i\sqrt3}[/tex]

Step-by-step explanation:

Given the complex number:

[tex]2(cos20^\circ+isin20^\circ)^3[/tex]

To find:

The indicated power by using De Moivre's theorem.

The complex number in rectangular form.

Rectangular form of a complex number is given as [tex]a+ib[/tex] where a and b are real numbers.

Solution:

First of all, let us have a look at the De Moivre's theorem:

[tex](cos\theta+isin\theta )^n=cos(n\theta)+isin(n\theta )[/tex]

First of all, let us solve:

[tex](cos20^\circ+isin20^\circ)^3[/tex]

Let us apply the De Moivre's Theorem:

Here, n = 3

[tex](cos20^\circ+isin20^\circ)^3 = cos(3 \times 20)^\circ+isin(3 \times 20)^\circ\\\Rightarrow cos60^\circ+isin60^\circ[/tex]

Now, the given complex number becomes:

[tex]2(cos60^\circ+isin60^\circ)[/tex]

Let us put the values of [tex]cos60^\circ = \frac{1}{2}[/tex] and [tex]sin60^\circ = \frac{\sqrt3}{2}[/tex]

[tex]2(\dfrac{1}{2}+i\dfrac{\sqrt3}2)\\\Rightarrow (2 \times \dfrac{1}{2}+i\dfrac{\sqrt3}2\times 2)\\\Rightarrow \bold{1 +i\sqrt3 }[/tex]

So, the rectangular form of the given complex number is:

[tex]\bold{1+i\sqrt3}[/tex]

Answer:

Step-by-step explanation:

The summary of the statistics given include:

population mean [tex]\mu[/tex] = 15

sample mean [tex]\oerline x[/tex] = 13.5

sample size n = 16

standard deviation s = 6

The level of significance ∝ = 0.10

The  null and the alternative hypothesis can be computed as follows:

[tex]\mathtt{H_o: \mu = 15} \\ \\ \mathtt{H_1 : \mu \neq 15}[/tex]

Since this test is two tailed, the t- test can be calculated by using the formula:

[tex]t = \dfrac{\overline x - \mu}{\dfrac{\sigma }{\sqrt{n}}}[/tex]

[tex]t = \dfrac{13.5 - 15}{\dfrac{6}{\sqrt{16}}}[/tex]

[tex]t = \dfrac{- 1.5}{\dfrac{6}{4}}[/tex]

[tex]t = \dfrac{- 1.5\times 4}{6}}[/tex]

[tex]t = \dfrac{- 6.0}{6}}[/tex]

t = - 1

degree of freedom = n - 1

degree of freedom = 16 - 1

degree of freedom = 15

From the standard normal t probability distribution table, the p value when t = -1 at  0.10 level of significance, the p - value = 0.3332

Decision Rule: We fail to reject the null hypothesis since the p-value is greater than the level of significance at 0.10

Conclusion: Therefore, we can conclude that  there is insufficient evidence at the 0.10 level of significance to conclude that the population  mean μ is different than 15.

Answer:

 At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

Step-by-step explanation:

From the question we are told that

   The  population mean is [tex]\mu = 60 \ hr[/tex]

    The sample size is  [tex]n = 16[/tex]

    The  sample mean is  [tex]\= x = 68 \ hr[/tex]

     The  standard deviation is  [tex]\sigma = 20 \ hr[/tex]

The  null hypothesis is  [tex]H_o : \mu = 60[/tex]

The  alternative [tex]H_a : \mu > 60[/tex]

Here we would assume the level of significance of this test to be  

         [tex]\alpha = 5\% = 0.05[/tex]

Next we will obtain the critical value of the level of significance from the normal distribution table, the value is    [tex]Z_{0.05} = 1.645[/tex]

  Generally the test statistics  is mathematically represented as

           [tex]t = \frac{ \= x - \mu}{ \frac{ \sigma }{\sqrt{n} } }[/tex]

substituting values

           [tex]t = \frac{ 68 - 60 }{ \frac{ 20 }{\sqrt{16} } }[/tex]

          [tex]t = 1.6[/tex]

Looking at the value of t and  [tex]Z_{\alpha }[/tex] we see that [tex]t< Z_{\alpha }[/tex] hence we fail to reject the null hypothesis

   This means that there no sufficient evidence to conclude that it takes more than 60 hours to complete the course

So

   At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.

Answer:

That would be written as $16,800.00, or as $19,811.90 if you convert it at the current rate of exchange.

Step-by-step explanation:

Periods are used in European numbers to split up each third placed number while commas are used in the U.S.

Answer:

= 19824 us dollars

Step-by-step explanation:

Today august 09 2020:

1€ = 1.18 us dollars

then:

16800€ = 16800*1.18 = 19824 us dollars

Answer: There are 75 books.

Price of each book = $4.

Step-by-step explanation:

Let x = Number of books in the box.

Then as per given,

Cost of x books = $300

Cost of one book = [tex]\$(\dfrac{300}x)[/tex]

Books left after giving 15 of them = x-15

Selling price of (x-15) books=  $330

Selling price of one book = [tex]\$(\dfrac{330}{x-15})[/tex]

Profit on each book= $1.50

Profit = selling price - cost price

[tex]\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}][/tex]

[tex]\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75[/tex]

Number of books cannot be negative.

So, there are 75 books.

Price of each book = [tex]\dfrac{300}{75}=\$4[/tex]

So price of each book = $4.

Answer:

20 times.

Step-by-step explanation:

To find out how many times larger a number is than another number, simply divide the two numbers, with the larger number being in the numerator.

For example, how many times larger is 6 than 2? The answer would be 6/2 or 3 times larger.

So, divide 8*(10^3) and 4*(10^2):

[tex]\frac{8\times10^3}{4\times10^2}[/tex]

Expand the expressions. This is the same as saying:

[tex]\frac{8\times10\times10\times10}{4\times10\times10}[/tex]

We can cancel two of the 10s since they are in both the numerator and the denominator. Thus, only one 10 is left in the numerator:

[tex]\frac{8\times10}{4}[/tex]

Simplify:

[tex]=\frac{80}{4} =20[/tex]

Therefore, 8*(10^3) (or 8000) is 20 times larger than 4*(10^2) (or 400).

Answer:

20 times

Step-by-step explanation:

hey,

so lets solve 8*10^3  first

so we use the order of operations

P

= Parentheses first

E

= Exponents (ie Powers and Square Roots, etc.)

MD

= Multiplication and Division (left-to-right)

AS

= Addition and Subtraction (left-to-right)

so  after doing the exponents part 8*1000

we do the multiplication

=8000

SO THE FIRST NUMBER IS 8000

now lets solve 4*10^2

so we use the order of operations

P

= Parentheses first

E

= Exponents (ie Powers and Square Roots, etc.)

MD

= Multiplication and Division (left-to-right)

AS

= Addition and Subtraction (left-to-right)

so we do exponents first 4*100

then multiplication

=400

SO THE SECOND NUMBER IS 400

To find out how many times larger a number is than another number, simply divide the two numbers, with the larger number being in the numerator.

now we divide  8000 by 400

=20

so 8*10^3 is 20 times larger than  4*10^2

HOPE I HELPED

PLS MARK BRAINLIEST  

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                    PEACE!

Answer:

$69,361.23

Step-by-step explanation:

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

[tex] A = 10000(1 + \dfrac{0.09}{2})^{2 \times 22} [/tex]

[tex]A = 10000(1.045)^{44}[/tex]

[tex] A = 69361.23 [/tex]

Answer: $69,361.23

Answer:

Step-by-step explanation:

Hello, please consider the following.

P(a) = 7 * a - 6

P(-x)= 7 *(-x) - 6 = -7x - 6

P(x+h) = 7 * (x+h) - 6 = 7x + 7h - 6

Hope this helps.

Thank you.

The values of the polynomial for the given expressions are:

P(a) = 7a - 6

P(-x) = -7x - 6

P(x + h) = 7x + 7h - 6

To find P(a), P(-x), and P(x + h) for the given polynomial P(x) = 7x - 6, we need to substitute the respective values of x into the polynomial expression.

1. P(a):

P(a) = 7a - 6

2. P(-x):

P(-x) = 7(-x) - 6

P(-x) = -7x - 6

3. P(x + h):

P(x + h) = 7(x + h) - 6

P(x + h) = 7x + 7h - 6

To know more about polynomial:

https://brainly.com/question/2928026

#SPJ2

Answer:

1. C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistics.

2. B. 10

3. A. 12

Step-by-step explanation:

The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution.

Answer:

A:$2478

B:$728

Total:$3206

Step-by-step explanation:

2.95x3000=8850

1.30x2000=2600

8850x0.28=2478

2600x0.28=728

2478+728=3206