hi can someone help with this question

Answer:

A) Both events are not independent.

B) Both events are not mutually exclusive

C) 8.33%

D) 80%

Step-by-step explanation:

A) Both events are not independent. This is because, If B occurs it means that it is very likely that J will occur as well.

B) Both events are not mutually exclusive. This is because it is possible for both events J and B to occur at the same time.

C) we want to find the probability that Joe who is not a business student will receive the job offer.

This is;

P(J|Not B) = P(J & Not B)/P(Not B)

Now,

P(J & Not B) = P(J) – (P(B) × P(J | B))

25% of the students who attended received job offers. Thus; P(J) = 0.25

40% were from the College of Business. Thus;

P(B) = 0.4

Among the business students, 50% received job offers. Thus;

P(J|B) = 0.5

Thus;

P(J & Not B) = 0.25 - (0.4 × 0.5)

P(J & Not B) = 0.25 - 0.2

P(J & Not B) = 0.05

Since P(B) = 0.4

Then, P(Not B) = 1 - 0.4 = 0.6

Thus;

P(J|Not B) = 0.05/0.6

P(J|Not B) = 0.0833 = 8.33%

D) This probability is represented by;

P(B | J) = P(B & J)/P(J)

P(B & J) = (P(B) × P(J | B)) = (0.4 × 0.5) = 0.2

P(B | J) = 0.2/0.25

P(B | J) = 0.8 = 80%

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

a) What is the probability that we will pick a blue ball?

there is a 50% chance that urn 1 will be selected and the possibility of a blue ball is 3/4 x 0.5 = 1.5/4

there is also a 50% chance that urn 2 will be selected and the possibility of a blue ball is 2/4 x 0.5 = 1/4

the probability of choosing a blue ball = 1.5/4 + 1/4 = 2.5/4 or 5/8

b) If we picked a blue ball, what is the probability that the selected urn was urn-1?

there are 5 blue balls in total, and 3 of them come from urn 1

c) Suppose we picked a blue ball. If we randomly pick one additional ball from the same urn, what is the probability that we pick a red ball?

there is a 50% chance that urn 1 will be selected, and the possibility of a red ball after a blue ball is 1/3 x 0.5 = 0.5/3

there is also a 50% chance that urn 2 will be selected and the possibility of a red ball after a blue ball is 2/3 x 0.5 = 1/3

the possibility of choosing a red ball after a blue ball = 0.5/3 + 1/3 = 1.5/3 = 1/2

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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Answer:

False ;

False ;

False

Step-by-step explanation:

In a perfectly symmetric distribution, the mean and Median values are the same. But for skewed distributon, the median is greater than the mean (negatively skewed or left skewed data). Hence, the assertion is false.

The sign of the correlation Coefficient does not give information about how good a line fits. The sign attached to the correlation Coefficient gives information about the slope and hence, the type of relationship between the variables.

Positive (+) sign = positive relationship between variables ; negative (-) sign = negative relationship between variables.

C.)

The value of the range is not always higher Than the value of the interquartile range. The IQR might have the same value as the value of the range.

For instance :

Given the data :

1, 1, 1, 2, 2, 3, 4, 4, 4

Range = maximum - minimum

Range = 4 - 1 = 3

Interquartile range (IQR) :

IQR = Q3 - Q1

Q3 = 3/4(n+1)th term

Q3 = 3/4(10) = 7.5th term

Q3 = (7th + 8th) / 2 = (4+4)/2 = 4

Q1 = 1/4(10) = 2.5th term

Q1 = (2nd + 3rd) / 2

Q1 = (1 + 1) /2 = 1

Q3 - Q1 = 4 - 1 = 3

We have the next graph

(a) To know if g(-1) is negative we must see the graph when x = 0

We can see that when x = 0 the function takes the value of -4. Since -4 is negative, g(-1) is negative.

So, the answer to the question is: Yes

(b) To know for which values of x g(x) = 0, we must see the points where the function passes through the x-axis.

In this case we can see only one point: (1, 0)

So, the answer is

(c) To find the values of x where g(x) < 0 we must see the part in the graph that is below the x-axis.

In this case, these values go from

Answer:

12m because I am right see you in the back of the booster

17) 12

18) •12

19) -6

20) -6

21) 8

22) -6

23) -14

24) -12

25) 14

Explanation:

#CarryOnLearning

Answer:

answer is a

Step-by-step explanation:

thank me later:)

The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

From the question, we have the following parameters that can be used in our computation:

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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The line PQ of the triangle is an altitude. The correct option is A.

A line segment passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.

The extended base of the altitude is the name given to this line that contains the opposing side. The foot of the altitude is the point at where, the extended base and the height converge.

In the given triangle the line segment PQ is passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry.

Therefore, the line PQ of the triangle is an altitude. The correct option is A.

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Factor of polynomial m are 0,   6n⁴.

What is polynomial in maths?

A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.

= 30m³n⁴ - 5m⁴

= 5m³(6n⁴ - m )

let 5m³(6n⁴ - m ) = 0

       5m³ = 0

         m = 0

 6n⁴ - m = 0

      m =   6n⁴

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Answer:

Step-by-step explanation:

821

200

To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:

1. Determine the ratio between the first and last parts. In this case, it is 2:3.

2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.

3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.

4. Multiply the value of each part by the respective ratio values to obtain the individual parts:

- First part: 2 * 6 = 12

- Second part: 6

- Third part: 6

- Fourth part: 6

- Last part: 3 * 6 = 18

Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.

Answer:

\(C(t)=125\cdot 0.9^t\)

Step-by-step explanation:

Exponential Decay Function

The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

\(C(t)=C_o\cdot(1-r)^t\)

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The doctor prescribed 125 milligrams of a therapeutic drug. It decays by 10% each hour. The initial value is Co=125 and the decay rate is r=0.1 per hour. Substituting into the function:

\(C(t)=125\cdot(1-0.1)^t\)

Operating:

\(\mathbf{C(t)=125\cdot 0.9^t}\)

Where t is expressed in hours.

The value of the function when differentiated w.r.t "x" is -2 / 1+x^2.

To differentite the function \(f(x) = tan^{-1}(\frac{1-x}{1+x}) - tan^{-1}(\frac{x+2}{1-2x})\) w.r.t "x", we have to make use of chain rule and the derivative of the inverse tangent function. By applying both the methods, we have to find out the differentiated value of the function.

Chain rule is basically a fundamental rule in calculus that allows us to find the derivative of a function. The chain rule comes out to be very usefull when the functions are layered. On the other hand, inverse tangent function is a mathematical function that takes an input value and returns the angle whose tangent is equal to that value.

We know that;

\(tan^{-1}a - tan^{-1}b = tan^{-1}(\frac{a-b}{1+ab} )\)

So, by following the above method we get the function as:

\(f(x) = (tan^{-1}1 - tan^{-1}x) - (tan^{-1}x + tan^{-1}2)\)

\(f(x) = tan^{-1}1 - tan^{-1}2 - 2tan^{-1}x\)

Now, differentiating both the sides w.r.t "x":

f'(x) = 0 - 0 - 2/1+x^2

f'(x) = 2/1+x^2

Therefore, the value of the function when differentiated w.r.t "x" is

-2 / 1+x^2.

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Answer:

no

Step-by-step explanation:

In 3 weeks he rides 53 miles. In 6 weeks he rides 106 miles but since he rides 106 - 27 = 79 miles (which is less than 100) in 5 weeks the answer is no.

Answer: The area is  (800)

Step-by-step explanation: (10x 10= 100)

(100 x 8= 800)

FINAL ANSWER: 800m

~ i really hope this is correct, have a gr8 day/night my friend!~

Answer:

(a) A 95% confidence interval for the mean score of all New Jersey third graders is [56.41, 59.59] .

(b) A 90% confidence interval for the difference in mean scores between Iowa and New Jersey is [3.363, 4.637]  .

(c) Yes, we are 90% confident that the population means for Iowa and New Jersey students are different.

Step-by-step explanation:

We are given that a new standardized test is given to 100 randomly selected third-grade students in New Jersey. The sample average score Y on the test is 58 points and the sample standard deviation sY is 8 points.

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

                               P.Q.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~  \(t_n_-_1\)

where, \(\bar X\) = sample average score = 58 points

             s = sample standard deviation = 8 points

            n = sample of third-grade students = 100

             \(\mu\) = population mean score of all New Jersey third graders

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, a 95% confidence interval for the population mean, \(\mu\) is;

P(-1.987 < \(t_9_9\) < 1.987) = 0.95  {As the critical value of t at 99 degrees of

                                                 freedom are -1.987 & 1.987 with P = 2.5%}    P(-1.987 < \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\) < 1.987) = 0.95

P( \(-1.987 \times {\frac{s}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(1.987 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

P( \(\bar X-1.987 \times {\frac{s}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+1.987 \times {\frac{s}{\sqrt{n} } }\) ) = 0.95

95% confidence interval for \(\mu\) = [ \(\bar X-1.987 \times {\frac{s}{\sqrt{n} } }\) , \(\bar X+1.987 \times {\frac{s}{\sqrt{n} } }\) ]

                                       = [ \(58-1.987 \times {\frac{8}{\sqrt{100} } }\) , \(58+1.987 \times {\frac{8}{\sqrt{100} } }\) ]

                                       = [56.41, 59.59]

Therefore, a 95% confidence interval for the mean score of all New Jersey third graders is [56.41, 59.59] .

Now, the same test is given to 200 randomly selected third graders from Iowa, producing a sample average of 62 points and a sample standard deviation of 11 points.

(b) Firstly, the pivotal quantity for finding the confidence interval for the difference in population mean is given by;

                               P.Q.  =  \(\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }\)  ~  \(t__n_1_+_n_2_-_2\)

where, \(s_p = \sqrt{\frac{(n_1-1)\times s_1 + (n_2-1)\times s_2}{n_1+n_2-2} }\)

                = \(\sqrt{\frac{(200-1)\times 11 + (100-1)\times 8}{200+100-2} }\) = 3.163

Here for constructing a 90% confidence interval we have used a two-sample t-test statistics because we don't know about population standard deviations.

So, a 90% confidence interval for the difference in two population means, (\(\mu_1-\mu_2\)) is;

P(-1.645 < \(t_2_9_8\) < 1.645) = 0.90  {As the critical value of t at 298 degrees of

                                                    freedom are -1.645 & 1.645 with P = 5%}    P(-1.645 < \(\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }\) < 1.645) = 0.90

90% confidence interval for (\(\mu_1-\mu_2\)) = [ \({(\bar X_1-\bar X_2) -1.645\times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }\) , \({(\bar X_1-\bar X_2) +1.645\times {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }\) ]

= [ \({(62-58) -1.645\times {3.163 \times \sqrt{\frac{1}{200}+\frac{1}{100} } }\) , \({(62-58) +1.645\times {3.163 \times \sqrt{\frac{1}{200}+\frac{1}{100} } }\) ]

= [3.363, 4.637]

Therefore, a 90% confidence interval for the difference in mean scores between Iowa and New Jersey is [3.363, 4.637]  .

(c) Yes, we are 90% confident that the population means for Iowa and New Jersey students are different because in the above interval 0 is not included.

Answer:

3.0000

Step-by-step explanation:

Answer:

i'm assuming you mean tenth so 3

Step-by-step explanation:

you start by looking at just 2.97, the seven will round the 9 up to a ten so you will add one to the 2 and end up with 3 as your answer

When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)

First, we shall determine the value of A. Details below:

Quadratic equation is expressed as:

x² - (sum of root)x + product of root

Comparing the above with x² - 11x + 30, we have

x² - 11x + 30 = x² - (sumof root)x + product of root

Product of roots = 30

Thus,

A = 30

Next, we shall determine the value of B. details below:

f(x) = x² + 5

f(2) = 2² + 5

f(2) = 9

Thus,

B = 9

Next, we shall determine the value of C. Details below:

Let

x + 4 = 0

Thus,

x = -4

Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:

Remainder = x² - 2x - 24

Remainder = (-4)² - 2(-4) - 24

Remainder = 0

Thus,

C = 0

Finally, we shall determine value of A/5 + √(B - C). Details below:

A/5 + √(B - C) = 30/5 + √(9 - 0)

A/5 + √(B - C) = 6 + √(9

A/5 + √(B - C) = 6 + 3

A/5 + √(B - C) = 9

Thus, the value of A/5 + √(B - C) is 9 (option B)

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Answer:

The answer is 29.

Step-by-step explanation:

The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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Answer:

B. It has 2 terms and a degree of 3.

Step-by-step explanation:

There's a quizlet that has this exact question.

The degree of the polynomial after it is simplified is; B: It has 2 terms and a degree of 3

We are given the polynomial;

3x²y² - 5xy² - 3x²y² + 2x²

From the polynomial, we see that 3x²y² will cancel out to give;

- 5xy² + 2x²

Now, we can see that the polynomial has been reduced to 2 terms. However, for the degree we see that the term - 5xy² has two variables x and y. Thus, the degree of the polynomial is the sum of the power of x and y in - 5xy².

Thus, degree of polynomial = 2 + 1 = 3

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Answer:

I rhink the answer would be 273°

Step-by-step explanation:

57+180=237°

Answer:

∠ BAC = 28.5°

Step-by-step explanation:

∠ AOB = 180° - 57° = 123° ( straight angle )

OA and OB are congruent ( radii of the circle ) , then Δ AOB is isosceles with base angles congruent, that is

∠ BAC = ∠ ABO , then

∠ BAC = \(\frac{180-123}{2}\) = \(\frac{57}{2}\) = 28.5°

Answer:

B

Step-by-step explanation

B because 45 x 76 =3420

Answer:

B

Step-by-step explanation:

Because I need points