Please help. I’ll mark you as brainliest if correct!

Answer:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.

Answer:

Events are independent if the outcome of one effect does not effect the outcome

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

The Freeman family barbecued veggie burgers, corn cobs, and mushroom caps. 3/8 of the items barbecued are veggie burgers, and 1/3 of the items barbecued are corn cobs.

Let the total number of berbecued items be x. Therefore:

x = barbecued veggie burgers + barbecued corn cobs + barbecued mushroom caps

Barbecued veggie burgers = (3/8)x, barbecued corn cobs = (1/3)x, Let barbecued mushroom caps be y

Substituting:

x = (3/8)x + (1/3)x + y

Multiply through by 24

24x = 9x + 8x + 24y

24x = 17x + 24y

24y = 24x - 17x

24y = 7x

y = (7/24)x

barbecued mushroom caps = (7/24) of items

7/24 of the items barbecued are mushroom caps

Using fractions, it is found that the fraction of barbecued items that are mushroom caps is of [tex]\frac{7}{24}[/tex].

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

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

Thus:

[tex]\frac{3}{8} + \frac{1}{3} + x = 1[/tex]

Then:

[tex]\frac{3\times3 + 8\times1 + 24x}{24} = 1[/tex]

[tex]\frac{17 + 24x}{24} = 1[/tex]

[tex]17 + 24x = 24[/tex]

[tex]24x = 7[/tex]

[tex]x = \frac{7}{24}[/tex]

The fraction of barbecued items that are mushroom caps is of [tex]\frac{7}{24}[/tex].

A similar problem is given at https://brainly.com/question/4231000

Answer:

64

Step-by-step explanation:

Let us consider E_abc to be the event that a, b and c appear on the first, second and third slot of the spin machine.

Now, we are told that each slot has 4 possibilities which are a cherry, a lemon, a star, or a bar when spun.

Thus, from mn rule in probability, the total number of simple events in the sample space is = 4³ = 64

Answer:

see below

Step-by-step explanation:

4,7,12,19

We are adding 3,5,7,9..... each time

The sequence is not arithmetic because we are not adding a constant.  It is not geometric since we are not multiplying by a constant term each time

There is no common difference  or common ratio.

The explicit formula is

an =n^2 +3

The recursive formula is

(n+1)^2 +3 - (n^2 +3)

    n^2 +2n+1+3 - ( n^2+3)

      2n+1

a sub(n+1) = a sub( n) + 2n+1

The 10th term

an      = n^2 +3

Let n=10

an = 10^2+3

    = 100+3

    = 103

summation

see image

since the numbers are increasing and greater than 1 the sum does not exist

Answer:

  subtracting 56 instead of adding (or adding wrong)

Step-by-step explanation:

She wrote ...

  x - 56 = 230

  x - 56 - 56 = 230 -56 . . . . correct application of the addition property*

  x = 230 -56 . . . . . . . . . . . . incorrect simplification

Correctly done, the third line would be ...

  x -112 = 174

This would have made Sherina realize that the error was in subtracting 56 instead of adding it. The correct solution would be ...

  x - 56 + 56 = 230 + 56 . . . using the addition property of equality

  x = 286 . . . . . . . . . . . . . . . . correct simplification on both sides

__

There were two errors:

  1) incorrect strategy --- subtracting 56 instead of adding

  2) incorrect simplification --- simplifying -56 -56 to zero instead of -112

We don't know whether you want to count the error in thinking as the first error, or the error in execution where the mechanics of addition were incorrectly done.

_____

* The addition property of equality requires the same number be added to both sides of the equation. Sherina did that correctly. However, the number chosen to be added was the opposite of the number that would usefully work toward a solution.

Answer:

D: Sherina should have added 56 to both sides of the equation.

Step-by-step explanation:

I got a 100% on my test.

I hope this helps.

Answer:

5443

Step-by-step explanation:

Order of Operations: BPEMDAS

Always left to right.

Step 1: Add 68 and 5042

68 + 5042 = 5110

Step 2: Add 5110 and 333

5110 + 333 = 5443

And we have our answer!

Answer:

see below

Step-by-step explanation:

Difference is subtract

(8-2)

Then add this to x

(8-2) +x

6+x

Answer:

Hey there!

We can write the equation:

0.65x=39

x=60

The dress originally sold for 60 dollars.

Hope this helps :)

Answer:

[tex]\pi[/tex] radian

Step-by-step explanation:

We know that angle for a full circle is 2[tex]\pi[/tex]

In the given figure shape is semicircle

hence,

angle for semicircle will be half of angle of full circle

thus, angle for given figure = half of  angle for a full circle = 1/2 * 2[tex]\pi[/tex] = [tex]\pi[/tex]

Thus, answer is [tex]\pi[/tex] radian

alternatively, we also know that angle for a straight line is 180 degrees

and 180 degrees is same as [tex]\pi[/tex] radian.

Answer:

The mean age is 48

The standard deviation is 4

Step-by-step explanation:

The answer is, (a) mean age is 48.

                          (b)  standard deviation is 4.

Learn more about mean age and standard deviation here:

https://brainly.com/question/475676

#SPJ2

Answer:

0.000014

Step-by-step explanation:

The chart is not provided so i will use an example chart to explain the answer. Here is a sample chart:

City X's Population by Age

0-24 years old 33%

25-44 years old 22%

45-64 years old 21%

65 or older 24%

In order to find probability of independent events we find the probability of each event occurring separately and then multiply the calculated probabilities together in the following way:

P(A and B) = P(A) * P(B)

probability that the first 2 are 65 or older

Let A be the event that the first 2 are 65 or older

The probability of 65 or older 24% i.e. 0.24

So the probability that first 2 are 65 or older is:

0.24(select resident 1) * 0.24(select resident 2)

P(A) = 0.24 * 0.24

       = 0.0576

P(A) = 0.0576

probability that the next 3 are 25-44 years old

Let B be the event that the next 3 are 25-44 years old

25-44 years old 22%  i.e. 0.22

So the probability that the next 3 are 25-44 years old is:

0.22 * 0.22* 0.22

P(B) = 0.22 * 0.22 * 0.22

      = 0.010648

P(B) = 0.010648

probability that next 2 are 24 or younger

Let C be the event that the next 2 are 24 or younger

0-24 years old 33% i.e. 0.33

So the probability that the next 2 are 24 or younger is:

0.33 * 0.33

P(C) = 0.33 * 0.33

       = 0.1089

P(C) = 0.1089

probability that last is 45-64 years old

Let D be the event that last is 45-64 years old

45-64 years old 21%  i.e. 0.21

So the probability that last is 45-64 years old is:

0.21

P(D) = 0.21

So probability of these independent events is computed as:

P(A and B and C and D) = P(A) * P(B) * P(C) * P(C)

                                        = 0.0576 * 0.010648  * 0.1089  * 0.21

                                        = 0.000014

Answer:

9.488

Step-by-step explanation:

The critical value is found by first assessing which statistical test should be used.

We are interested in investigating relationship between social activity and education so chi-square test would be appropriate.

We have 3 rows and 3 columns. The degree of freedom for chi-square critical value is (r-1)(c-1)=(3-1)(3-1)=2*2=4

Chi-square critical value(0.05,4)= 9.488

Answer:

[tex] {x}^{2} + 7x + \frac{49}{4} = {(x + \frac{7}{2}) }^{2} [/tex]

Explanation:

[tex] {x}^{2} + 7x + a = {(x + b)}^{2} [/tex]

[tex] {x}^{2} + 7x + a = {x}^{2} + 2bx + {b}^{2} [/tex]

compare the x co-efficient

[tex] 7 = 2b[/tex]

[tex] b = \frac{7}{2} [/tex]

compare the constants

[tex]a = {b}^{2} [/tex]

[tex]a = {( \frac{7}{2}) }^{2} [/tex]

[tex]a = \frac{49}{4} [/tex]

HOPE IT HELPS....

The complete equation will be x^2+7x+49/4=(x+7/2)2

Given the quadratic function x^2 + 7x + ?

In order to complete the square using the completing the square method, we will add the square of the half of coefficient of x to both sides of the expression.

Coefficient of x = 7

Half of the coefficient = 7/2

Taking the square of the result = (7/2)² = 49/4

The constant that will complete the equation is 49/9. The equation becomes x^2 + 7x + (7/2)² = (x+7/2)²

Hence the complete equation will be x^2+7x+49/4=(x+7/2)2

Learn more here: https://brainly.com/question/13981588

Answer:

3/11

Step-by-step explanation:

From the above question, we have the following information

Total number of balls = 12

Number of white balls = 4

Number of blue balls = 3

Number of red balls = 5

We solve this question using combination formula

C(n, r) = nCr = n!/r!(n - r)!

We are told that 3 balls are drawn out at random.

The chance/probability of drawing out 3 balls = 12C3 = 12!/3! × (12 - 3)! = 12!/3! × 9!

= 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/(3 × 2 × 1) × (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)

= 220 ways

The chance of selecting 3 balls at random = 220

To find the chance that all the three balls are selected,

= [Chance of selecting (white ball) × Chance of selecting(blue ball) × Chance of selecting(red balls)]/ The chance/probability of drawing out 3 balls

Chance of selecting (white ball)= 4C1

Chance of selecting(blue ball) = 3C1 Chance of selecting(red balls) = 5C1

Hence,

= [4C1 × 3C1 × 5C1]/ 220

= 60/220

= 6/22

= 3/11

The chance that all three are selected is = 3/11

Answer:

D. [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]

Step-by-step explanation:

Any parabola is modelled by a second-order polynomial, whose standard form is:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex]

Where:

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients, dimensionless.

In addition, a system of three linear equations is constructed by using all known inputs:

(-2, 0)

[tex]4\cdot a -2\cdot b + c = 0[/tex] (Eq. 1)

(4, 0)

[tex]16\cdot a + 4\cdot b +c = 0[/tex] (Eq. 2)

(0,-16)

[tex]c = -16[/tex] (Eq. 3)

Then,

[tex]4\cdot a - 2\cdot b = 16[/tex] (Eq. 4)

[tex]16\cdot a + 4\cdot b = 16[/tex] (Eq. 5)

(Eq. 3 in Eqs. 1 - 2)

[tex]a - 0.5\cdot b = 4[/tex] By Eq. 4 (Eq. 4b)

[tex]a = 4 + 0.5\cdot b[/tex]

Then,

[tex]16\cdot (4+0.5\cdot b) + 4\cdot b = 16[/tex] (Eq. 4b in Eq. 5)

[tex]64 + 12\cdot b = 16[/tex]

[tex]12\cdot b = -48[/tex]

[tex]b = -4[/tex]

The remaining coeffcient is:

[tex]a = 4 + 0.5\cdot b[/tex]

[tex]a = 4 + 0.5\cdot (-4)[/tex]

[tex]a = 2[/tex]

The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]. Thus, the right answer is D.

Answer:

D ƒ(x) = 2x2 – 4x – 16

Step-by-step explanation:

Answer:

x = 2 and x = -2

Step-by-step explanation:

To find the vertical asymptotes, set the denominator equal to zero and solve for x:

vertical asymptotes are x = 2 and x = -2

Answer:

-50

Step-by-step explanation:

Basically get two slopes -50(1)+100 will get you 1,50 (1 is x and 50 is y since its the answer)

-50(0)+100 (0,100)  Y₂-Y₁/X₂-X₁ 50-100/1-0

Rate of change per month = -$50

Answer:

B

Step-by-step explanation:

x can not be greater than (1,325-270)/26 because $270 is fixed for the rental

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

First find the critical points of f :

[tex]f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7[/tex]

[tex]\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1[/tex]

[tex]\dfrac{\partial f}{\partial y}=6y=0\implies y=0[/tex]

so the point (1, 0) is the only critical point, at which we have

[tex]f(1,0)=-7[/tex]

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

[tex]f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t[/tex]

Find the critical points of g :

[tex]\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0[/tex]

[tex]\implies\sin t=0\text{ OR }1+5\cos t=0[/tex]

[tex]\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi[/tex]

where n is any integer. We get 4 critical points in the interval [0, 2π) at

[tex]t=0\implies f(10,0)=155[/tex]

[tex]t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299[/tex]

[tex]t=\pi\implies f(-10,0)=235[/tex]

[tex]t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299[/tex]

So f has a minimum of -7 and a maximum of 299.

Answer:

(A) A 95% confidence for the population mean is [$332.16, $447.84] .

(B) If the confidence level in part (a) changed from 95% to 99%, then the margin of error for the confidence interval would increase.

(C) If the sample size in part (a) changed from 19 to 22, then the margin of error for the confidence interval would decrease.

(D) A 99% confidence interval for the proportion of students who purchase used textbooks is [0.363, 0.477]  .

Step-by-step explanation:

We are given that 19 students are randomly selected the sample mean was $390 and the standard deviation was $120.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = $390

            s = sample standard deviation = $120

            n = sample of students = 19

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

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.101 < [tex]t_1_8[/tex] < 2.101) = 0.95  {As the critical value of t at 18 degrees of

                                               freedom are -2.101 & 2.101 with P = 2.5%}  

P(-2.101 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.101) = 0.95

P( [tex]-2.101 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.101 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.101 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.101 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.101 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.101 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                        = [ [tex]\$390-2.101 \times {\frac{\$120}{\sqrt{19} } }[/tex] , [tex]\$390+2.101 \times {\frac{\$120}{\sqrt{19} } }[/tex] ]

                        = [$332.16, $447.84]

(A)  Therefore, a 95% confidence for the population mean is [$332.16, $447.84] .

(B) If the confidence level in part (a) changed from 95% to 99%, then the margin of error for the confidence interval which is [tex]Z_(_\frac{\alpha}{2}_) \times \frac{s}{\sqrt{n} }[/tex] would increase because of an increase in the z value.

(C) If the sample size in part (a) changed from 19 to 22, then the margin of error for the confidence interval which is [tex]Z_(_\frac{\alpha}{2}_) \times \frac{s}{\sqrt{n} }[/tex]  would decrease because as denominator increases; the whole fraction decreases.

(D) We are given that to estimate the proportion of students who purchase their textbooks used, 500 students were sampled. 210 of these students purchased used textbooks.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                             P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion students who purchase their used textbooks = [tex]\frac{210}{500}[/tex] = 0.42    

            n = sample of students = 500

            p = population proportion

Here for constructing a 99% confidence interval we have used a One-sample z-test statistics for proportions

So, 99% confidence interval for the population proportion, p is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5%

                                               level of significance are -2.58 & 2.58}  

P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99

P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

99% confidence interval for p = [ [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

= [ [tex]0.42 -2.58 \times {\sqrt{\frac{0.42(1-0.42)}{500} } }[/tex] , [tex]0.42 +2.58 \times {\sqrt{\frac{0.42(1-0.42)}{500} } }[/tex] ]

= [0.363, 0.477]

Therefore, a 99% confidence interval for the proportion of students who purchase used textbooks is [0.363, 0.477]  .

Answer:

11.422

Step-by-step explanation:

[tex]78.2 - 66.778 \\ = 11.422[/tex]

Answer:

Step-by-step explanation:

First we start with 12 pounds

On Monday, she and her friends eat 4 pounds. So we have 8 now.

On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.

On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15

On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.

On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.

On Saturday, her mom gives her one more pound. 2 + 1 = 3.

On Sunday, she finally has 3 pounds.

Answer:

nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Step-by-step explanation:

Step-by-step explanation:

Just sub 4 into where n is

Answer:

at least one solution

Step-by-step explanation:

Consistent solutions have at least one solution, but may have more than one solution.  Intersecting lines and  Lines that are the same are consistent solutions

Answer:

[tex]\boxed{Atleast\ one \ Solution}[/tex]

Step-by-step explanation:

A consistent system of equations have at least one solution. It can be more than that. There are no compulsions.

Answer:

The answer is 36

Step-by-step explanation:

Let the number be x

7 less than the quotient of a number and 3 is written as

The result is 5

So we have

Move - 7 to the right side of the equation

That's

Multiply both sides by 3 to make x stand alone

We have

We have the final answer as

Hope this helps you

Step-by-step explanation:

Hello,

I hope you mean to cancel the common factor that exists in numerator and denominator,right.

so, Let's look for the common factor,

here, the expression is,

=4(x-2)/ (x+5)(x-2)

so, here we find the common factor is (x-2)

now, we have to cancel it. And after cancelling we get,

=4/(x+5)

Note:{ we cancel the common factor if the common factors are in multiply form.}

Hope it helps

Answer:

The standard error of the sample mean is [tex]\sigma_{\= x } = 0.40[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 5.30 \ hours[/tex]

     The population standard deviation is [tex]\sigma = 3.20 \ hours[/tex]

      The sample size is  [tex]n = 64[/tex]

Generally the standard error of the sample mean is mathematically represented as

               [tex]\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }[/tex]

substituting values

                [tex]\sigma_{\= x } = \frac{3.20}{\sqrt{64} }[/tex]

                [tex]\sigma_{\= x } = 0.40[/tex]

Answer:

The standard error decreases and the width of the confidence interval also decreases.

Step-by-step explanation:

The standard error of a distribution (E) is given as:

[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }[/tex]

Where n is the sample size, [tex]z_{\frac{\alpha}{2} }[/tex] is the z score of he confidence and [tex]\sigma[/tex] is the standard deviation.

The sample size is inversely proportional to the standard error. If the sample size is increased and everything else is constant, the standard would decrease since they are inversely proportional to each other. The confidence interval = μ ± E = (μ - E, μ + E). μ is the mean

The width of the confidence interval = μ + E - (μ - E) = μ + E - μ + E = 2E

The width of the confidence interval is 2E, therefore as the sample size increase, the margin of error decrease and since the width of the confidence interval is directly proportional to the margin of error, the width of the confidence interval also decreases.

Answer:

the nearest hundred is 50