Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were allergic to penicillin, Nathan has a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The test is 98% accurate. What is the probability that Nathan is not allergic to penicillin and the test predicts it?

A.
0.005

B.
0.015

C.
0.245

D.
0.735

Answer:

B

Step-by-step explanation:

Remark

I'm hesitant to get an exact answer. You could do that with the cos law for distance. To get an approximate answer you could use the Pythagorean Theorem.

I'll try the cos law first.

Formula

c^2 = a^2 + b^2 - 2abcos(C)

Givens

c = 24

a = 18

b = ?

Solution

24^2 = 18^2 + b^2 - 2*18*b*cos(94)

576 = 324 + b^2 - 36*b*(-0.0698)

0 = 324 - 576 + b^2 + 2.511b

0 = b^2 + 2.511 - 252

Using the quadratic formula, the roots are

b1 = 14.66

b2 = - 17.11

The second one has no meaning in the real world.

Answer

the distance is 14.66 miles from Chaplin to Asherville

Note: using the Pythagorean theorem gives 15.87 which I would count as a good approximation.

Answer:

14.7

Step-by-step explanation:

got 100% on plato

Answer:

0.0367 = 3.67% probability that exactly 6 patients will die

Step-by-step explanation:

The patients are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question, we have that:

20 patients means that [tex]N = 20[/tex]

Sample of 8 means that [tex]n = 8[/tex]

9 have the heart problem, so [tex]k = 9[/tex]

What is the probability that exactly 6 patients will die?

This is P(X = 6).

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 6) = h(6,20,8,9) = \frac{C_{9,6}*C_{11,2}}{C_{20,8}} = 0.0367[/tex]

0.0367 = 3.67% probability that exactly 6 patients will die

The answer is A the y=2.25

The equation of the exponential regression that fits these data,

y = 2.25 [tex](1.75)^x[/tex]

It is a model that explains processes that increase at twice the rate. It is employed in circumstances where growth starts slowly but quickly accelerates without bounds, or decay starts quickly but slows down to zero.

The formula for expressing Exponential Regression is

y = a[tex]b^x[/tex]

We have given that,

The table below represents The closing prices of stock at TUV for the last five days

Days      Value

1           3.938

2          6.891

3          12.059

4          21.103

5          36.929

First we have to find r as

r= 6.891/ 3.938

r = 1.749

As, the standard form of Exponential function

y = a[tex]b^x[/tex]

So, y = 2.25 [tex](1.75)^x[/tex]

learn more about linear regression here:

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Answer is in a photo. I can only upload[tex]^{}[/tex] it to a file hosting service. link below!

bit.[tex]^{}[/tex]ly/3tZxaCQ

Answer:

If 34.54 is the diameter then 17.27 is the radius

Step-by-step explanation:

34.54 ÷ 2 = 17.27

Answer:

1. right

2. acute

3. obtuse

4. obtuse

5. acute

6. acute

7. scalene

8. scalene

9. isosceles

10. equilateral

11. scalene

12. isosceles

Step-by-step explanation:

Answer:

9 hours

Step-by-step explanation:

$247/13hours=$19 per hour

$171/$19=9 hours

Answer:

x=y-75x-5y=-35

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Before graphing this equation we first need to isolate y on one side like so...

y + 2 = 3(x+1)   ... distribute the 3 to both values inside the parenthesis

y + 2 = 3x + 3   ... subtract 2 on both sides

y = 3x + 1

Now that we have the y variable isolated we see that the slope of the function is 3, meaning that for every 1 unit right the line needs to move 3 units up. We also have the value where the line needs to cross the y-axis and that is 1. Using this information we see that the correct graph is C.

Answer:

That's false

Step-by-step explanation:

6000(1.02)³⁶​ = 2.1 × 10¹³⁶

Answer:

the steady-state percentage of residents who are uninvolved is 0.5

Step-by-step explanation:

 Given the data in the question;

let N represent total number of people in the dormitory

I represent  people involved in a relationship

and U represent people uninvolved in a relationship.

so

N = I + U

I = N - U ------ let this be equation 1

Rate of Uninvolved = U/N

now, given that rate of break ups B = 15% every month = 0.15

rate of entering into relationship  R = 15% every month = 0.15

Now, the steady state condition is;

RU = BI ------- let this be equation 2

such that uninvolved rate is constant.

we input equation 1 into 2;

RU = B( N - U  )

we divide both sides by N

RU/N = B( N/N - U/N  )

RU/N = B( 1 - U/N  )

U/N = B / (B + R)

so we substitute

U/N = 0.15 / (0.15 + 0.15)

U/N = 0.15 / 0.3

U/N = 0.5

Therefore, the steady-state percentage of residents who are uninvolved is 0.5

Answer:

y = 0, -2

Step-by-step explanation:

Factor out the common term 3y.

[tex]3y( {y}^{2} + 4y + 4) = 0[/tex]

Rewrite y² + 4y + 4 in the form of a² + 2ab + b², where a = y and b = 2.

[tex]3y( {y}^{2} + 2(y)(2) + {2}^{2} ) = 0[/tex]

Use square sum: (a + b)² = a² + 2ab + b².

[tex]3y(y + 2) ^{2} = 0[/tex]

solve for y.

y = 0, -2.

therefor, the answer for this equation is 0, - 2.

Answer:

B

Step-by-step explanation:

Marcus can expect to have red chip 20 times.

Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen.

Given that, Marcus has a bag of 10 red chips, 15 blue chips, and 5 black chips.

He did an experiment 60 times and we need to find that how many times would he expect to pick a red chip,

So,

Here the favorable outcomes = red chips (10)

Total outcomes = all the chips = 15+5+10 = 20

So, the probability of finding a red chips for the 60 times = 10/20 x 60

= 30

Hence, Marcus can expect to have red chip 20 times.

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Answer:

no

Step-by-step explanation:

Zero is Soo's miserly number. It won't give the number four

Answer:

$258.75

Step-by-step explanation:

225 * 0.15

Let last weeks pay = x

This week she earned 15% more so she earned 100% + 15% more for 115% total.

Setup an equation:

115% times x = $225

115% as a decimal = 1.15

So the equation is:

1.15x = 225

Solve for x by dividing both sides by 1.15:

X = 225/1.15

X = 195.65

Last week she earned $195.65

Answer: B. 12.7

Step-by-step explanation:

Answer:

D.8.5

Step-by-step explanation:

38.4/2=

19.2 L

19.2-10.7=

8.5

hope this helps ; )

9514 1404 393

Answer:

  e(w) = -40w^2 +400w +20

Step-by-step explanation:

A graphing calculator or spreadsheet can do the quadratic regression and help you find the formula. Here earnings (e) as a function of weeks (w) can be expressed by ...

  e(w) = -40w^2 +400w +20

__

Further development

There are a couple of other ways you can go at this. One is to write equations for a, b, c using the standard form quadratic.

  aw^2 +bw +c = e

  a +b +c = 380 . . . . . . for week 1

  4a +2b +c = 660 . . . for week 2

  9a +3b +c = 860 . . . for week 3

The solution of this system of equations will give the coefficients of the quadratic. Your graphing calculator or any of several web sites can solve these equations for you.

__

Consider the differences between quadratic values for w = 1, 2, 3.

  e2 -e1 = (4a +2b +c) -(a +b +c) = 3a +b

  e3 -e2 = (9a +3b +c) -(4a +2b +c) = 5a +b

Then the second differences are ...

  (e3 -e2) -(e2 -e1) = (5a +b) -(3a +b) = 2a

In the given set of numbers, the first differences are ...

  660 -380 = 280 . . . . . . . call this d1

  860 -660 = 200

And the second difference is ...

  200 -280 = -80 . . . . . . . call this d2

From the above, we know that 2a = -80  ⇒  a = -40

and 3a +b = 280 = 3(-40) +b  ⇒  b = 400

Finally, a+b+c = 380 = -40 +400 +c  ⇒  c = 20

Then the generic solution is ...

  a = d2/2

  b = d1 -3a

  c = e1 -a -b . . . . . where e1 is the first-week's earnings

Answer:

We know that:

Sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)

Then if we use this property in our expression:

sin(a-30)-sin(a+30)

We get:

sin(a)*cos(-30°) + sin(-30°)*cos(a) - sin(a)*cos(30°) - sin(30°)*cos(a)

Now remember that:

sin(-x) = -sin(x)

and

cos(-x) = cos(x)

Then we can rewrite our expression as:

sin(a)*cos(30°) - sin(30°)*cos(a) - sin(a)*cos(30°) - sin(30°)*cos(a)

= -2*sin(30°)*cos(a)

and sin(30°) = 0.5

Then:

-2*sin(30°)*cos(a) = -2*0.5*cos(a) = -cos(a)

So we get:

sin(a-30)-sin(a+30)= - cos(a)

Answer:

Heyyyyy! Help with what?

Step-by-step explanation:

Let me know :)

Have a nice day <3

Answer:

the answer is 1 because the power of any no. 0 is always 1

Answer:

y diles que yo me se tu pose favorita, que te hablo mal y que eso te U-U

Step-by-step explanation:

Answer:

59

Step-by-step explanation:

360 - ( 156 + 86 ) = 118

118 / 2 = 59

Answer:

third side = 7

Step-by-step explanation:

x² = 9² - (4√2)² = 81 - 32 = 49

x = √49 = 7

Answer:

4

Step-by-step explanation:

Another way to write this is 8/1 x 1/2. Then the answer would be 8/2. Simplify to get 4.

8 × 1/2 = 4!

Calculation steps:

8 ×

1

2

= 8 ×

1

2

=

8 × 1

1 × 2

=

8

2

=

8 ÷ 2

2 ÷ 2

= 4

Answer:

A: save $250 per month for the next 3 years

Step-by-step explanation:

Melinda has three more years in high school as stated in the question.

One year private university tuition = $22,500

Support from family = $13,500

Amount that Melinda has to pay = $22,500 - $13,500 = $9000

Number of months in three years = 3 * 12 = 36 months

If she must save $9000 in 36 months

Then $x  must be saved in 1 month

x = $9000/36

x = $250

Answer:

16+12i

Step-by-step explanation:

Answer:

Step-by-step explanation:

what are the options