(a) A survey of the adults in a town shows that 8% have liver problems. Of these, it is also found that 25% are heavy drinkers, 35% are social drinkers and 40% are non-drinkers. Of those that did not suffer from liver problems, 5% are heavy drinkers, 65% are social drinkers and 30% do not drink at all. An adult is chosen at random, what is the probability that this person i. Has a liver problems?

Answer:

C. Independent

Step-by-step explanation:

Independent events are events that have no impact on each other.

So, if the occurrence of an event doesn't influence the outcome of another, this means that they are independent because they do not impact each other.

This must mean C is correct because the two events have to be independent.

Answer:

(A) 0.11

(B) 0.0526

(C) Related

(D) 0.28

Step-by-step explanation:

The data provided is:

DC = event that a randomly selected driver is using a cell phone

TA = event that a randomly selected driver has a traffic accident

(A)

From the provided data:

P (DC) = 0.11

(B)

From the provided data:

P (TA) = 0.0526

(C)

To determine whether the events DC and TA are dependent, we need to show that:

[tex]P(DC\cap TA)\neq P(DC)\times P(TA)[/tex]

The value of P (DC ∩ TA) is,

[tex]P(DC\cap TA)=P(DC|TA)\time P(TA)[/tex]

                     [tex]=0.28\times 0.0526\\=0.014728[/tex]

Now compute the value of P (DC) × P (TA) as follows:

[tex]P (DC) \times P (TA)=0.11\times 0.0526=0.005786[/tex]

So, [tex]P(DC\cap TA)\neq P(DC)\times P(TA)[/tex]

Thus, cell phone use while driving and traffic accidents are related.

(D)

The probability that the driver was distracted by a cell phone given that the driver has an accident is:

P (DC | TA) = 0.28

Answer:

Step-by-step explanation:

Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.

- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.

∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]

- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.

∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]

- Angles having the same relative positions at the point of intersection are the corresponding angles.

∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]

- Co interior angles are the angles between the parallel lines located on the same side of the transversal.

∠4 and ∠5, ∠3 and ∠6 [Co interior angles]

- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.

∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]

Answer:

Below

Step-by-step explanation:

● 1 + 3^2 × 2 -5

Start by calculating 3^2 wich is 9

● 1 + 9 × 2 -5

Multiply 2 by 9 (9×2=18)

● 1 + 18 -5

Add 1 to 18 (1+18 = 19)

● 19 -5

Substract 5 from 19 (19-5 = 14 )

● 14

Answer: 22 quarters

Step-by-step explanation:

Let N be the number of nickels.

Then the number of quarters is (55-N)

The nickels  contribute 5N cents to the total.

The quarters contribute 25*(55-N) cents to the total.

5N + 25*(55-N) = 715

5N + 1375 - 25N = 715

-20N = 715 - 1375 = -660

[tex]N=\frac{-660}{-20}[/tex]

[tex]=33[/tex]

[tex]55-33=22[/tex]

So there is 22 quarters inside the jar.

Check to see if my answer is correct-

33*5 + 22*25 = 715 cents

Answer:

  60°

Step-by-step explanation:

You have the rotation matrix ...

  [tex]\left[\begin{array}{cc}\cos{\theta}&-\sin{\theta}\\\sin{\theta}&\cos{\theta}\end{array}\right]=\left[\begin{array}{cc}\dfrac{1}{2}&-\dfrac{\sqrt{3}}{2}\\\dfrac{\sqrt{3}}{2}&\dfrac{1}{2}\end{array}\right][/tex]

This tells you the angle of rotation is ...

  [tex]\tan{\theta}=\dfrac{\sin{\theta}}{\cos{\theta}}=\dfrac{\left(\dfrac{\sqrt{3}}{2}\right)}{\left(\dfrac{1}{2}\right)}=\sqrt{3}\\\\\theta=\arctan{\sqrt{3}}=60^{\circ}[/tex]

The angle of rotation is 60°.

Answer:

B----- 60

Step-by-step explanation:

Answer:

  1/7^2

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  a^-b = 1/a^b

__

Then your expression simplifies to ...

  [tex]7^3\cdot 7^{-5}=7^{3-5}=7^{-2}=\boxed{\dfrac{1}{7^2}}[/tex]

Answer:

The answer is 1/7^2

Step-by-step explanation:

I took the test lol

Answer:

the answers are below:

Step-by-step explanation:

a. null hypothesis:

H0: Pw - Pm = 0 (so Pw = Pm)

alternate hypothesis:

H1: Pw - Pm > 0 (so Pw > Pm)

where Pw is the proportion of women

Pm is the proportion of men

b.) proportion of women = o.40

proportion of men =  0.32

sample size of women = 20

sample size of men = 25

[tex]z = 0.4 - 0.32/ \sqrt{((0.4 *0.6)/20) * (0.32 * 0.68)/25)}[/tex]

[tex]z = 0.56[/tex]

c.) p value =

p(z>0.56)

= 0.7123

= 1 - 0.7123

= o.2877 which can be approximated to be 0.288

d. alpha value was set at 0.05

the p value is greater than alpha.

therefore it is not statistically significant.

we conclude that the proportion of roman catholic women is not greater than men.

Answer:

Tom:

initial money = $ 39000

% increased per annum = 2.9%

money gained per annum = 39000 * 2.9/100 = $1131

Allen:

initial money = $ 39000

% increased per annum = 5.7 %

money gained per annum = 39000 * 5.7/100 = $2223

Allen has $ (2223 - 1131) = $ 1192 more than Tom

The easy thing to do is notice that 1^4 = 1, 2^4 = 16, 3^4 = 81, and so on, so the sequence follows the rule [tex]n^4+1[/tex]. The next number would then be fourth power of 7 plus 1, or 2402.

And the harder way: Denote the n-th term in this sequence by [tex]a_n[/tex], and denote the given sequence by [tex]\{a_n\}_{n\ge1}[/tex].

Let [tex]b_n[/tex] denote the n-th term in the sequence of forward differences of [tex]\{a_n\}[/tex], defined by

[tex]b_n=a_{n+1}-a_n[/tex]

for n ≥ 1. That is, [tex]\{b_n\}[/tex] is the sequence with

[tex]b_1=a_2-a_1=17-2=15[/tex]

[tex]b_2=a_3-a_2=82-17=65[/tex]

[tex]b_3=a_4-a_3=175[/tex]

[tex]b_4=a_5-a_4=369[/tex]

[tex]b_5=a_6-a_5=671[/tex]

and so on.

Next, let [tex]c_n[/tex] denote the n-th term of the differences of [tex]\{b_n\}[/tex], i.e. for n ≥ 1,

[tex]c_n=b_{n+1}-b_n[/tex]

so that

[tex]c_1=b_2-b_1=65-15=50[/tex]

[tex]c_2=110[/tex]

[tex]c_3=194[/tex]

[tex]c_4=302[/tex]

etc.

Again: let [tex]d_n[/tex] denote the n-th difference of [tex]\{c_n\}[/tex]:

[tex]d_n=c_{n+1}-c_n[/tex]

[tex]d_1=c_2-c_1=60[/tex]

[tex]d_2=84[/tex]

[tex]d_3=108[/tex]

etc.

One more time: let [tex]e_n[/tex] denote the n-th difference of [tex]\{d_n\}[/tex]:

[tex]e_n=d_{n+1}-d_n[/tex]

[tex]e_1=d_2-d_1=24[/tex]

[tex]e_2=24[/tex]

etc.

The fact that these last differences are constant is a good sign that [tex]e_n=24[/tex] for all n ≥ 1. Assuming this, we would see that [tex]\{d_n\}[/tex] is an arithmetic sequence given recursively by

[tex]\begin{cases}d_1=60\\d_{n+1}=d_n+24&\text{for }n>1\end{cases}[/tex]

and we can easily find the explicit rule:

[tex]d_2=d_1+24[/tex]

[tex]d_3=d_2+24=d_1+24\cdot2[/tex]

[tex]d_4=d_3+24=d_1+24\cdot3[/tex]

and so on, up to

[tex]d_n=d_1+24(n-1)[/tex]

[tex]d_n=24n+36[/tex]

Use the same strategy to find a closed form for [tex]\{c_n\}[/tex], then for [tex]\{b_n\}[/tex], and finally [tex]\{a_n\}[/tex].

[tex]\begin{cases}c_1=50\\c_{n+1}=c_n+24n+36&\text{for }n>1\end{cases}[/tex]

[tex]c_2=c_1+24\cdot1+36[/tex]

[tex]c_3=c_2+24\cdot2+36=c_1+24(1+2)+36\cdot2[/tex]

[tex]c_4=c_3+24\cdot3+36=c_1+24(1+2+3)+36\cdot3[/tex]

and so on, up to

[tex]c_n=c_1+24(1+2+3+\cdots+(n-1))+36(n-1)[/tex]

Recall the formula for the sum of consecutive integers:

[tex]1+2+3+\cdots+n=\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}2[/tex]

[tex]\implies c_n=c_1+\dfrac{24(n-1)n}2+36(n-1)[/tex]

[tex]\implies c_n=12n^2+24n+14[/tex]

[tex]\begin{cases}b_1=15\\b_{n+1}=b_n+12n^2+24n+14&\text{for }n>1\end{cases}[/tex]

[tex]b_2=b_1+12\cdot1^2+24\cdot1+14[/tex]

[tex]b_3=b_2+12\cdot2^2+24\cdot2+14=b_1+12(1^2+2^2)+24(1+2)+14\cdot2[/tex]

[tex]b_4=b_3+12\cdot3^2+24\cdot3+14=b_1+12(1^2+2^2+3^2)+24(1+2+3)+14\cdot3[/tex]

and so on, up to

[tex]b_n=b_1+12(1^2+2^2+3^2+\cdots+(n-1)^2)+24(1+2+3+\cdots+(n-1))+14(n-1)[/tex]

Recall the formula for the sum of squares of consecutive integers:

[tex]1^2+2^2+3^2+\cdots+n^2=\displaystyle\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}6[/tex]

[tex]\implies b_n=15+\dfrac{12(n-1)n(2(n-1)+1)}6+\dfrac{24(n-1)n}2+14(n-1)[/tex]

[tex]\implies b_n=4n^3+6n^2+4n+1[/tex]

[tex]\begin{cases}a_1=2\\a_{n+1}=a_n+4n^3+6n^2+4n+1&\text{for }n>1\end{cases}[/tex]

[tex]a_2=a_1+4\cdot1^3+6\cdot1^2+4\cdot1+1[/tex]

[tex]a_3=a_2+4(1^3+2^3)+6(1^2+2^2)+4(1+2)+1\cdot2[/tex]

[tex]a_4=a_3+4(1^3+2^3+3^3)+6(1^2+2^2+3^2)+4(1+2+3)+1\cdot3[/tex]

[tex]\implies a_n=a_1+4\displaystyle\sum_{k=1}^3k^3+6\sum_{k=1}^3k^2+4\sum_{k=1}^3k+\sum_{k=1}^{n-1}1[/tex]

[tex]\displaystyle\sum_{k=1}^nk^3=\frac{n^2(n+1)^2}4[/tex]

[tex]\implies a_n=2+\dfrac{4(n-1)^2n^2}4+\dfrac{6(n-1)n(2n)}6+\dfrac{4(n-1)n}2+(n-1)[/tex]

[tex]\implies a_n=n^4+1[/tex]

Answer:

4, 7, 10, 13

Step-by-step explanation:

Hey there!

Well in the given pattern,

-11, -8, -5, -2, 1

we can conclude that the pattern is +3 every time.

-11 + 3 = -8

-8 + 3 = -5

-5 + 3 = -2

-2 + 3 = 1

And so on

Hope this helps :)

Answer:

P-value = 0.0455

Step-by-step explanation:

In this question, we are concerned with calculating the P- value in a test.

Mathematically we know that;

P-value = 2 * P(Z > |z|)

Please check attachment for complete solution and by step explanation

Answer:

[tex]\boxed{41.25}[/tex]

Step-by-step explanation:

Hey there!

Well we know the constant of proportionality is 16.5 because on the table it states 1 minute is 16.5 gallons.

So we can set up the following,

W = 2.5*16.5

W = 41.25

Hope this helps :)

Answer:

The amount of water in the bathtub after 1 minute is 16.5 gallons. So, the amount of water in the tub after 2.5 minutes of filling will be

2.5 minutes × 16.5 gallons per minute = 41.25 gallons.

There will be 41.25 gallons of water in the bathtub after 2.5 minutes.

Step-by-step explanation:

Answer:

maybe it's 10.because c is 10,b is 10,and so as s.

hence s is 10 also.

Answer:

6

Step-by-step explanation:

36 - 20 - 32 x 1/4

=> 36 - 20 - 32/4

=> 36 - 20 - 8

=> 36 - 28

=> 6

Answer:

hi Ghana how are you doing I am fine here. I really miss u and my friends in the old.U know what in Nigeria this school is really awesome and fantastic we have a swimming pool here and we can go to trip and we can have many things here I really loved this school.

at starting I was not have any friends and know I have many friends. But I really miss u this is what about our . Come to my house I can show you my school it is very near to my house .

Ur friend

writ ur name

Step-by-step explanation:

f(x) = integral (-8x) dx = -4x^2 + C

f(1) = -3 = -4 + C

C = 1

f(x) = -4x^2 + 1

The particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is: f(x) = -4x² + 1.

Here, we have,

To find the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3,

we can integrate the equation and use the initial condition to determine the constant of integration.

First, integrate both sides of the equation with respect to x:

∫ f'(x) dx = ∫ -8x dx

Integrating, we get:

f(x) = -4x² + C

Now, we can use the initial condition f(1) = -3 to find the value of the constant C.

Substituting x = 1 and f(x) = -3 into the equation, we have:

-3 = -4(1)² + C

-3 = -4 + C

C = -3 + 4

C = 1

Therefore, the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is:

f(x) = -4x² + 1

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Answer:

Attachment 1 : 5x + 6y = 5, Attachment 2 : 4cotθcscθ

Step-by-step explanation:

Remember that we have three key points in solving these types of problems,

• x = r cos(θ)

• y = r sin(θ)

• x² + y² = r²

a ) For this first problem we need not apply the third equation.

( Multiply either side by 5 cos(θ) + 6 sin(θ) )

r [tex]*[/tex] ( 5 cos(θ) + 6 sin(θ) ) = 5,

( Distribute r )

5r cos(θ) + 6r sin(θ) = 5

( Substitute )

5x + 6y = 5 - the correct solution is option c

b ) We know that y² = 4x ⇒

r²sin²(θ) = 4r cos(θ),

r = 4cos(θ) / sin²(θ) = 4 cot(θ) csc(θ) = 4cotθcscθ - again the correct solution is option c

Answer:

b

Step-by-step explanation:

because its right dummy

Answer:

Solution : 8i

Step-by-step explanation:

We can use the trivial identities cos(π / 2) = 0, and sin(π / 2) = 1 to solve this problem. Let's substitute,

[tex]8\left[cos\left(\frac{\pi }{2}\right)+isin\left(\frac{\pi \:}{2}\right)\right][/tex] = [tex]8\left(0+1i\right)[/tex]

And of course 1i = i, so we have the expression 8(0 + i ). Distributing the " 8, " 8( 0 ) = 0, and 8(i) = 8i, making the fourth answer the correct solution.

Answer:

[tex]\boxed{50}[/tex]

Step-by-step explanation:

Because the initial temperature is 40 degrees and it increases by 10, add the two values together to get the final temperature.

40 + 10 = 50

Therefore, the final answer is 50 degrees.

Answer:

50

Step-by-step explanation:

If it starts at 40 degrees and increases 10 degrees, it is going to be 50 degrees.  Increases means adding, so it is asking you to add 10 to 40 which is 50.  If it asks decreases in the future you will have to subtract.

Answer:

Example: solve √(2x−5) − √(x−1) = 1

isolate one of the square roots:√(2x−5) = 1 + √(x−1) square both sides:2x−5 = (1 + √(x−1))2 ...

expand right hand side:2x−5 = 1 + 2√(x−1) + (x−1) ...

isolate the square root:√(x−1) = (x−5)/2. ...

Expand right hand side:x−1 = (x2 − 10x + 25)/4. ...

Multiply by 4 to remove division:4x−4 = x2 − 10x + 25.

Answer:

Step-by-step explanation:

ewrerewrwrwerrwer

Answer:

B) same side interior

Step-by-step explanation:

Supplementary angles are angles that can add up to the sum of angles on a straight line, [tex]180^{0}[/tex]. While a transversal in a line that passes through two parallel lines at two points.

If two lines are parallel to each other and a transversal through the lines, the sum of either same side interior angles would be supplementary.

The correct option for the given question is B, same side interior.

Answer:

B

Step-by-step explanation:

Answer:

1. 1/6

2. 1/6

Step-by-step explanation:

Let A be the event that the sum of the two die is 6 and B be an event that the green die is either 4 or 1.

The conditional probability will be given by P (A/B) = P (A∩B)/ P (B).

Now the total sample space consists of 36 outcomes .

And to find (A∩B) we need to find the outcomes in which green die is either 4 or 1 and the sum of the two die is 6.

So when green is 1 red must be 5

So when green is 4 red must be 2

So there are two ways in which green die is either 4 or 1 and the sum of the two die is 6.

Therefore the probability of (A∩B)= P (A∩B)= 2/36= 1/18

Now we find the probability of green die having 4 or 1

So when green is 4 red can have all the numbers from 1- 6

And when green is 1 red can have all the numbers from 1- 6

The total number would be 12 .

So probability of green die having 1 or 4 is given by = P (B)= 12/36

Now the conditional probability = P (A/B) = P (A∩B)/ P (B)=1/18/ 1/3

= 3/18= 1/6

2. Similarly we find the conditional probability of the two die when the red one is 6, given that the sum is 11.

When red is 6 the green must be 5 to get 11. So the probability

=P (A∩B)=  1/36

Now we find the probability of red die having 6 =P(B)= 6/36

Now the conditional probability = P (A∩B)/P(B) =  1/36/ 6/36= 1/6

Answer 1:

Conditional probability Formula :

P (A/B) = P (A∩B)/ P (B).

Total sample space=36 outcomes

Conditions are :

The probability of (A∩B)= P (A∩B)= 2/36= 1/18

Now we find the probability of green die having 4 or 1

When green is 4 red can have all the numbers from 1- 6

And when green is 1 red can have all the numbers from 1- 6

Total number = 12

 P (B)= 12/36

Therefore, conditional probability = P (A/B)

The conditional probability of the indicated event when two fair dice  are rolled will be 1/6.

Answer 2:

Condition :

When red is 6 the green must be 5 to get 11.

P (A∩B)=  1/36

The probability of red die having 6 =P(B)= 6/36

The conditional probability= P (A∩B)/P(B)

The conditional probability of the indicated event when two fair dice are 1/6.

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Answer: The percentage change is 56.67%.

Step-by-step explanation:

From 120 meals to 52 meals, change in meals = ( 120- 52) meals

= 68 meals

The percentage change = [tex]\dfrac{\text{change in meals}}{\text{Original quantity of meals}}\times100[/tex]

[tex]=\dfrac{68}{120}\times100\\\\=56.67\%[/tex]

Hence, the percentage change is 56.67%.

Answer:

Mean = 1.6

Variance = 0.84

Standard deviation = 0.916

Step-by-step explanation:

We are given the following probability distribution below;

            X                         P(X)              [tex]X \times P(X)[/tex]         [tex]X^{2} \times P(X)[/tex]

            0                          0.1                     0                        0

            1                           0.4                   0.4                     0.4

            2                          0.3                   0.6                     1.2

            3                          0.2                  0.6                    1.8      

         Total                                               1.6                    3.4    

Now, the mean of the probability distribution is given by;

         Mean, E(X) =  [tex]\sum X \times P(X)[/tex]  = 1.6

Also, the variance of the probability distribution is given by;

        Variance, V(X) =  [tex]\sum X^{2} \times P(X) - (\sum X \times P(X))^{2}[/tex]

                                 =  [tex]3.4 - (1.6)^{2}[/tex]

                                 =  3.4 - 2.56 = 0.84

And the standard deviation of the probability distribution is given by;

          Standard deviation, S.D. (X) =  [tex]\sqrt{Variance}[/tex]

                                                         =  [tex]\sqrt{0.84}[/tex]  = 0.916.

Answer:

The answer is

A. True

Step-by-step explanation:

In linear regression, Linear models make a prediction using a linear function of the input features, with one being

For regression, the general prediction formula for a linear model looks as follows:

ŷ = w[0] * x[0] + w[1] * x[1] + ... + w[p] * x[p] + b

Here, x[0] to x[p] denotes the features (in this example, the number of features is p)

of a single data point, w and b are parameters of the model that are learned, and ŷ is

the prediction the model makes. For a dataset with a single feature, this is

ŷ = w[0] * x[0] + b

which you might remember from high school mathematics as the equation for a line.

Here, w[0] is the slope and b is the y-axis offset. For more features, w contains the

slopes along each feature axis. Alternatively, you can think of the predicted response

as being a weighted sum of the input features, with weights (which can be negative)

given by the entries of w.

[tex]x-1=\dfrac{6}{x}\qquad(x\not=0)\\\\x^2-x=6\\x^2-x-6=0\\x^2+2x-3x-6=0\\x(x+2)-3(x+2)=0\\(x-3)(x+2)=0\\x=3 \vee x=-2[/tex]

Answer:

8

Step-by-step explanation:

Math Word Problem: Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the number.?

Let the two numbers be x and y

As per statement twice one number added to another number is 18.

2x + y = 18

y = 18 - 2x…Eq..1

Four times the first number minus the other number is 12.

4x - y = 12…Eq..2

Now substituting the value of y from Eq..1 to Eq..2

4x - y = 12

4x - (18 - 2x) = 12

4x - 18 + 2x = 12

4x + 2x = 12 + 18

6x = 30

x = 30 / 6

x = 5

Thus one number is 5. Now calculating the other number by putting the value of x in Eq. 1

y = 18 - 2x

y = 18 - 2×5

y = 18 - 10

y = 8

Other number is 8

Answer the two numbers are 5 and 8

Let us check the correctness of answer by putting the value of x and y in Eq. 1

y = 18 - 2x

8 = 18 - 2 × 5

8 = 18 - 10

8 = 8

Means answer is correct