A diagnostic test has a 95% probability of giving a positive result when given to a person who has a certain disease. It has a 10% probability of giving a (false) positive result when given to a person who doesn’t have the disease. It is estimated that 15% of the population suffers from this disease.
(a) What is the probability that a test result is positive?
(b) A person recieves a positive test result. What is the probability that this person actually has the disease? (probability of a true positive)
(c) A person recieves a positive test result. What is the probability that this person doesn’t actually have the disease? (probability of a false negative)

Answer:

72√3

Step-by-step explanation:

30 60 90 triangles are what you start out with.

Step 1: 30-60-90

x = 12

WZ = 12√3

Step 2: Area formula

A = 1/2(12)(12√3)

*Since the 2 30-60-90 triangles are congruent, both segments of the base are 12

Plug it into the calc and you should get A = 72√3 as your final answer!

Answer:

Step-by-step explanation:

max can be found by the formula:

t=-b/2a

t=-9.8/2*(-4.9)

t=-9.8/-9.8

t=1

1 sec

to find maximum height obtained we find the vertex:

plug in 1 for t and simply solve:

h(t)= -4.9t^2 + 9.8t + 1

h(t)= -4.9*1^2 + 9.8*1 + 1

h(t)= -4.9*1 + 9.8 + 1

h(t)= -4.9 + 10.8

h(t)= 5.9

height is 5.9

Answer:

the correct answer is

Step-by-step explanation:

So, the probability is:P(greater than 4)=26=13. This is a theoretical probability, which is the observed number of favorable outcomes out of a certain number of trials. For instance, suppose you rolled the six-sided die five times, and got the following results:2,6,4,5,6

hope this help you!!!!!

Answer:

1/5 chance.

Step-by-step explanation:

There is only one number, 5, that is greater than 4 and there are 5 total numbers so there is a 1/5 chance selecting that number.

Answer:

Yes, the sample has a bias

Step-by-step explanation:

Bias is the term used in statistics to describe a systematic distortion in the samples obtained for the parameter being estimated. It is evident by obtaining values higher or lower than that of the average population for the parameter being measured. As such the data is a misrepresentation of the population and cannot be trusted to give a good indices of things.

This sample has a bias because the concerned citizen opted to use a convenience sampling instead of using random sampling. In random sampling, every individual has an equal chance of being chosen which is unlike the convenience sampling when only a specific group of individuals can be chosen. In this case, the bias was introduced when the citizen went to stand outside the courthouse with his petition, the citizen should have taken samples across diverse geographical locations and professional institutions. The implication of this sampling is that a significant percentage of the population has been sidelined (considering they would not be in or around the courthouse) from the sampling and the sampling has been restricted to only those who have business around the courthouse. The result is that whatever samples he/she obtains will not be an accurate representation of the parameter being measure from the population.

As such, the sampling technique is biased

Answer:

US

World

Step-by-step explanation:

It depends on where you are. A "trapezium" outside the US is the same as a "trapezoid" in the US, and vice versa.

A trapezium (World; trapezoid in the US) is characterized by exactly one pair of parallel lines. One of the lines that are not parallel may be perpendicular to the parallel lines, but that will only be true for the specific case of a "right" trapezium.

__

A trapezium (US; trapezoid in the World) is characterized by no parallel lines. It may have one angle or opposite angles that are right angles (one or two sets of perpendicular lines), but neither diagonal may bisect the other.

In the US, "trapezium" is rarely used. The term "quadrilateral" is generally applied to a 4-sided figure with no sides parallel.

Answer: The distance of the shortest route of return is 400

Step-by-step explanation:

The direction of travel of the plane forms a right angle triangle ABC as shown in the attached photo. C represents the starting point of the plane. To determine the distance of the shortest by which the plane can return to its starting point, BC, we would apply the Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

BC² = 320² + 240²

BC² = 160000

BC = √160000

BC = 400

Answer:

[tex]n=(\frac{2.58(0.34)}{0.05})^2 =307.79 \approx 308[/tex]

So the answer for this case would be n=308 rounded up to the nearest integer

Step-by-step explanation:

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =0.1/2 =0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution since the sample size is large enough to assume the estimation of the standard deviation as the population deviation. The critical value for this case is [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(0.34)}{0.05})^2 =307.79 \approx 308[/tex]

So the answer for this case would be n=308 rounded up to the nearest integer

Answer:

C

Step-by-step explanation:

3x+2-x>8

2x+2>8

2x>8-2

2x>6

x>3

Answer:

C

Step-by-step explanation:

Answer: Undefined

Step-by-step explanation:

For this problem, we know that 3ˣ=-9. All we have to do is figure out what x is.

We know that any integer raised to the power cannot be negative. The closest answer we can get is x=2 because 3²=9. Unfortunately, we are looking for -9. Therefore, this x is undefined.

Answer:

25/88

Step-by-step explanation:

25 red marbles, 27 blue marbles, and 36 yellow marbles. = 88 marbles

P(red) = number of red/total

          = 25/88

Answer:

Dear user,

Answer to your query is provided below

Probability of choosing a red marble is 0.28 or (25/88)

Step-by-step explanation:

Total number of marbles = 88

Number of red marbles = 25

Probability = 25/88

Answer:

-4*4^7

Step-by-step explanation:

Answer:

-65536

Step-by-step explanation:

I do not think I understand the question but -4*4*4*4*4*4*4*4=-65536

I think there may be missing information like if the question is multiple choice.

Hope that helps

Answer:

9

Step-by-step explanation:

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

Let x=2

f(2) = (2 + 1)^2

     = 3^2

     = 9

Answer:

Step-by-step explanation:

Area of the circular zone = [tex]\pi[/tex]r^2

= 3.14 × 40^2 = 3.14 × 1600 = 5024 m^2

Area of the basketball court = l × b

= 30 × 15 = 450 m^2

Area of the trapezium shaped park =  ( 6 + 4 ) 3.5 / 2

= 35/2 = 17.5 m^2

∴ Area left in the circular zone = Area of the circular zone - ( Area of the basketball court + Area of the trapezium shaped park )

= 5024 - ( 450 + 17.5 )

= 5024 - 467.5

= 4556.5 m^2

hope this helps

plz mark it as brainliest!!!!!!!

Answer:

The lowest score eligible for an award is 92.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 82.2, \sigma = 5[/tex]

If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award

The lowest score is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975. So X when Z = 1.96. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.96 = \frac{X - 82.2}{5}[/tex]

[tex]X - 82.2 = 5*1.96[/tex]

[tex]X = 92[/tex]

The lowest score eligible for an award is 92.

Answer:

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

The answer is nothing duh

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

12+20+22+22+23=99

new mean=23

23*6=138

138-99=39

Answer:

Step-by-step explanation:

Hi,

the function is defined for all reals so the domain is [tex]]-\infty;+\infty[[/tex]

for x real

|x| >= 0

so f(x) >= 4

so the range is [tex][4;+\infty[[/tex]

do not hesitate if you need any further explanation

hope this helps

Answer:

Domain: (-∞,∞) Range: (4,∞)

Answer:

The future value of the annuity due to the nearest cent is $2956.

Step-by-step explanation:

Consider the provided information:

It is provided that monthly payment is $175, interest is 7% and time is 11 years.

The formula for the future value of the annuity due is:

Now, substitute P = 175, r = 0.07 and t = 11 in above formula.

Hence, the future value of the annuity due to the nearest cent is $2956.

Step-by-step explanation:

Answer:

(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b) The expected number of available places when the limousine departs is 0.338.

Step-by-step explanation:

Let the random variable Y represent the number of passenger reserving the trip shows up.

The probability of the random variable Y is, p = 0.70.

The success in this case an be defined as the number of passengers who show up for the trip.

The random variable Y follows a Binomial distribution with probability of success as 0.70.

(a)

It is provided that n = 6 reservations are made.

Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:

P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)

[tex]={6 \choose 5}\ (0.70)^{5}\ (1-0.70)^{6-5}+{6 \choose 6}\ (0.70)^{6}\ (1-0.70)^{6-6}\\\\=0.302526+0.117649\\\\=0.420175\\\\\approx 0.4202[/tex]

Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b)

The formula to compute the expected value is:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

[tex]P (X=0)={6 \choose 0}\ (0.70)^{0}\ (1-0.70)^{6-0}=0.000729\\\\P (X=1)={6 \choose 1}\ (0.70)^{1}\ (1-0.70)^{6-1}=0.010206\\\\P (X=2)={6 \choose 2}\ (0.70)^{2}\ (1-0.70)^{6-2}=0.059535\\\\P (X=3)={6 \choose 3}\ (0.70)^{3}\ (1-0.70)^{6-3}=0.18522\\\\P (X=4)={6 \choose 4}\ (0.70)^{4}\ (1-0.70)^{6-4}=0.324135[/tex]

Compute the expected number of available places when the limousine departs as follows:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

         [tex]=(4\cdot 0.000729)+(3\cdot 0.010206)+(2\cdot 0.059535)+(1\cdot 0.18522)\\+(0\cdot 0.324135)\\\\=0.002916+0.030618+0.11907+0.18522+0\\\\=0.337824\\\\\approx 0.338[/tex]

Thus, the expected number of available places when the limousine departs is 0.338.

Answer:

He served as Assistant Secretary of the Navy under President William McKinley

hope i helped

-lvr

Answer:

216-343

Step-by-step explanation:

the number 312 lies between 125 and 330

Answer:

a.) 8x + 6y

b.) 4x + 2y

Step-by-step explanation:

Simply add like terms together (x with x and y with y).

Answer:

2

Step-by-step explanation:

Scale Factor = [tex]\frac{AnySideOfDiagram}{AnySideOfMP3Player}[/tex]

So,

Scale Factor = [tex]\frac{8}{4} = \frac{14}{7}[/tex] = 2

So,

The scale factor is 2

Answer:

P(33) = 0.0826

Step-by-step explanation:

The binomial distribution in this case has parameters n=55 and p=0.55.

The probability that k successes happen with these parameters can be calculated as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{55}{k} 0.55^{k} 0.45^{55-k}\\\\\\[/tex]

We have to calculate the probability fo X=33 succesess.

This can be calculated using the formula above as:

[tex]P(x=33) = \dbinom{55}{33} p^{33}(1-p)^{22}\\\\\\P(x=33) =1300853625660220*0.0000000027*0.0000000235\\\\\\P(x=33) =0.0826\\\\\\[/tex]

Answer:

[tex]y = -\frac{7x}{3} - 24[/tex]

Step-by-step explanation:

We can model this function using the equation of a line:

[tex]y = ax + b[/tex]

Where a is the slope of the line and b is the y-intercept.

To find the values of a and b, we can use the two points given:

(-9, -3):

[tex]-3 = a * (-9) + b[/tex]

[tex]-9a + b = -3[/tex]

(-12, 4):

[tex]4 = a * (-12) + b[/tex]

[tex]-12a + b = 4[/tex]

If we subtract the second equation from the first one, we have:

[tex]-12a + b - (-9a + b) = 4 - (-3)[/tex]

[tex]-12a + 9a = 4 + 3[/tex]

[tex]-3a = 7[/tex]

[tex]a = -7/3[/tex]

Then, finding the value of b, we have:

[tex]-12a + b = 4[/tex]

[tex]28 + b = 4[/tex]

[tex]b = -24[/tex]

So the equation is:

[tex]y = -\frac{7x}{3} - 24[/tex]

Answer:

Step-by-step explanation:

We shall find the solution of this problem with the help of vector notation of i , j , which show east and  north direction .

The first displacement can be represented by the following

D₁ = - 3 cos 45 i + 3 sin45 j = - 3 / √2 i + 3 / √2 j

The second  displacement can be represented by the following

D₂ = - 5 cos 45 i - 5 sin45 j = - 5 /√2 i - 5 /√2 j

The third  displacement can be represented by the following

D₃ =  4 cos 45 i + 4 sin45 j =  4 /√2 i + 4 /√2 j

Total displacement D =

D₁ +D₂ + D₃

= i ( -3 -5 + 4 ) / √2 + j ( 3 - 5 + 4 ) / √2 j

= - 4  / √2 i + 2 / √2 j

D = - 2.8288 i + 1.414 j

Magnitude of D

= √ ( 2.8288² + 1.414² )

= 3.16 miles

For direction we calculate angle with X axis

Tanθ = 1.414 / 2.8288

θ = 26 °

As x is negative and Y is positive ,

the direction will be north of west .

Answer:

Nothing can be further done to this equation. It has been simplified all the way.

Answer:

Your correct answer is 31/50 + -4/25 i

Step-by-step explanation:

5+4i/6+8i = 31/50 + -4/25 i