In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11. What is the probability that the mixture will test positive?

Answers

Answer 1

From the information available, the mixture will test negative if all 6 samples are negative.

The probability of each is independent of the other for all 6 samples.

The probability of a sample testing positive is 0.11. That means the probability of a sample testing negative would be

[tex]\begin{gathered} P\lbrack neg\rbrack=1-P\lbrack pos\rbrack \\ P\lbrack\text{neg\rbrack}=1-0.11 \\ P\lbrack\text{neg\rbrack}=0.89 \end{gathered}[/tex]

However, for all 6 samples, the probability of having a negative result would be a product of probabilities, that is;

[tex]\begin{gathered} P\lbrack tests\text{ negative}\rbrack=0.89\times0.89\times0.89\times0.89\times0.89\times0.89 \\ P\lbrack\text{tests negative}\rbrack=0.89^6 \\ P\lbrack\text{tests negative\rbrack}=0.4969 \end{gathered}[/tex]

Therefore if we have the probability of the mixture testing negative as

[tex]P_{\text{neg}}=0.4969[/tex]

The probability of the mixture testing positive would be;

[tex]\begin{gathered} P_{\text{pos}}=1-P_{\text{neg}} \\ P_{\text{pos}}=1-0.4969 \\ P_{\text{pos}}=0.5031 \end{gathered}[/tex]

ANSWER:

The probability that the mixture will test positive is 0.5031

Rounded to 2 decimal places,

[tex]P_{\text{pos}}=0.50[/tex]

Answer 2
Okay okay if you don’t need it then I’ll let you know what I am

Related Questions

I need help to know how to solve graphing a system of inequalities2x - 3y > -12x + y ≥ -2

Answers

Answer

2x - 3y > -12 (in red ink)

x + y ≥ -2 (in black ink)

The solution region is the region that the two shaded regions have in common.

Explanation

When plotting the graph of linear inequality equations, the first step is to first plot the graph of the straight line normally, using intercepts to generate two points on the linear graph.

If the inequality sign is (< or >), then the line drawn will be a broken line.

If the inequality sign is (≤ or ≥), then the line drawn is an unbroken one.

Step 1

For this question, we easily see that the first inequality will have a broken line and the second one will have an unbroken line.

To plot each of the lines, we will use intercepts to obtain the coordinates of two points on each line

Recall, we will first plot the lines like they are equations of a straight line.

To plot the graph

2x - 3y = -12

when x = 0,

2(0) - 3y = -12

-3y = -12

Divide both sides by -3

(-3y/-3) = (-12/-3)

y = 4

First point on the line is (0, 4)

when y = 0

2x - 3(0) = -12

2x = -12

Divide both sides by 2

(2x/2) = (-12/2)

x = -6

Second point on the line is (-6, 0)

For the second line,

To plot the graph,

x + y = -2

when x = 0

0 + y = -2

y = -2

First point on the line is (0, -2)

when y = 0

x + 0 = -2

x = -2

Second point on the line is (-2, 0)

So, for the plotting, we connect the two points for each of the lines.

Step 2

The shaded region now depends on whether the inequality sign is facing y or not.

If the inequality sign is facing y, it means numbers above the line plotted are the wanted region and the upper part of the graph is shaded.

If the inequality sign is not facing y, it means numbers below the line plotted are the wanted region and the lower part of the graph is shaded.

2x - 3y > -12

Can be rewritten as

-3y > -2x - 12

Divide through by -3 (this changes the inequality sign)

y < (2x/3) + 4

Here, we see that the inequality sign is not facing y, hence the numbers below the broken line plotted are the shaded region (in red ink)

x + y ≥ -2

We can rewrite this as

y ≥ -x - 2

Here, we see that the the inequality sign is facing y, hence, the numbers above the unbroken line plotted are the shaded region (in black ink)

The graph of this system of inequalities is presented above under 'Answer'

Hope this Helps!!!

It goes from -1 to 1 on the x axis.

Answers

ANSWER :

EXPLANATION :

The area (in square inches) of a rectangle is given by the polynomial function A(b)=b^2 +9b+18. If the width of the rectangle is (b+3) inches what is the length?

Answers

As given by the question

There are given that area of rectangle and width of a rectangle

[tex]\begin{gathered} \text{Area}=A(b)=b^2+9b+18 \\ \text{Width}=(b+3) \end{gathered}[/tex]

Now,

From the formula of area of a rectangle:

[tex]\text{Area}=\text{length}\times width[/tex]

Then,

Put the value of an area and width into the above formula

So,

[tex]\begin{gathered} \text{Area}=\text{length}\times width \\ b^2+9b+18=length\times(b+3) \end{gathered}[/tex]

Then,

[tex]\begin{gathered} b^2+9b+18=length\times(b+3) \\ (b+3)(b+6)=\text{length}\times(b+3) \\ \text{length}=\frac{(b+3)(b+6)}{(b+3)} \\ \text{length}=(b+6) \end{gathered}[/tex]

Hence, the value of length is ( b + 6 ).

Rick buys a $4,500 stove with an installment plan that requires 12% down. How much
is the down payment?
O $540
O $375
O $250
O $125

Answers

Answer: 540

Step-by-step explanation: 12% of 4500 is 540

Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2–8x+2

Answers

We have to calculate the zeros of the function with the quadratic formula.

[tex]f(x)=x^2-8x+2[/tex][tex]\begin{gathered} x=\frac{-(-8)}{2\cdot1}\pm\frac{\sqrt[]{(-8)^2-4\cdot1\cdot2}}{2\cdot1}=\frac{8}{2}\pm\frac{\sqrt[]{64-8}}{2}=4\pm\frac{\sqrt[]{56}}{2}=4\pm\sqrt[]{\frac{56}{4}}=4\pm\sqrt[]{14} \\ \\ x_1=4+\sqrt[]{14}\approx4+3.742=7.742 \\ x_2=4-\sqrt[]{14}\approx4-3.742=0.258 \end{gathered}[/tex]

The roots are x1=7.742 and x2=0.258, both reals., both

I’ve been trying to figure out how to solve this and was wondering how to do this correctly!

Answers

SOLUTION

To solve this we will use the form for exponential growth to determine the formula to use.

Exponential growth has the form

[tex]\begin{gathered} P=P_0e^{rt} \\ P=\text{population after timer t} \\ P_0=\text{ initial population growth } \\ r=\text{ percent growth rate} \end{gathered}[/tex]

Now the frogs tripple in population after 9 days. Initially they were 21. So in 9 days they become

[tex]21\times3=63\text{ frogs }[/tex]

Applying the formula, we have

[tex]\begin{gathered} P=P_0e^{rt} \\ 63=21e^{9r} \\ 3=e^{9r} \\ \text{taking ln of both sides } \\ \ln 3=\ln e^{9r} \\ \ln 3=9r \\ r=\frac{\ln3}{9} \end{gathered}[/tex]

The time for the frogs to get to 290 becomes

[tex]undefined[/tex]

Question
Find the values for x and y .

Answers

Step-by-step explanation:

6x+3=75° ( being alternate angle )

6x = 72°

x=12

75+45+y= 180

y= 60°

If f (x) = 4x^3 - 25x^2 – 154x+ 40 and (x - 10) is a factor, what are the remaining factors?

Answers

[tex]f(x)=4x^3-25x^2-154x+40[/tex][tex]f(x)=4\cdot(\frac{1}{4})^3-25(\frac{1}{4})^2-154(\frac{1}{4})+40[/tex][tex]f(x)=\frac{1}{16}-\frac{25}{16}-\frac{77}{2}+40[/tex][tex]f(x)=0[/tex]

A reflection across which line(s) carries the trapezoid onto itself?

Answers

If we reflect about x =2, it is a mirror image on each side ( left and right). There is no other line where we can have a mirror image on each side.

3 A free diver can dive at a rate of -0.75 meters per second. About how long would it take to reach a depth of -145 meters?

Answers

Answer:193.33s or 3.2 mins

Step-by-step explanation:

Here the diver dives at -0.75 constant velocity. So we can use the formula s = vt

from there we can find out the time when s = -145 m and v = -0.75m/s

Sean johnson 1. The angles of a triangle are described as follows: angle A is the largest angle: its measure is twice the measure of angle B. The measure of angle C is 2 less than half the measure of angle B. Find the measures of the three angles in degrees.

Answers

Explanation

Let

angle A is the largest angle

[tex]m\measuredangle A=m\measuredangle A[/tex]

its measure is twice the measure of angle B,( in other words you have to multiply angle b by 2, to get angle A)

[tex]2(m\measuredangle B)=m\measuredangle A[/tex]

Solve for y Simplify your answer as much as possible Find by linear equation.

Answers

Given the equation:

[tex]-7=\frac{3y+7}{4}-\frac{9y-5}{2}[/tex]

We will solve the equation to find y

Multiply the equation by 4 to eliminate the denominators

[tex]\begin{gathered} 4(-7)=4\cdot\frac{3y+7}{4}-4\cdot\frac{9y-5}{2} \\ \\ -28=(3y+7)-2(9y-5) \\ -28=3y+7-18y+10 \end{gathered}[/tex]

Combine the like terms

[tex]\begin{gathered} -28=(3y-18y)+(7+10) \\ -28=-15y+17 \\ \end{gathered}[/tex]

Subtract (17) to both sides

[tex]\begin{gathered} -28-17=-15y+17-17 \\ -45=-15y \end{gathered}[/tex]

Divide both sides by (-15)

[tex]\begin{gathered} \frac{-45}{-15}=\frac{-15y}{-15} \\ \\ y=3 \end{gathered}[/tex]

So, the answer will be y = 3

Which of the following options correctly represents the complete factored form of the polynomial F(x)= x - x2 - 4x-6?

Answers

Notice that:

[tex]F(3)=3^3-3^2-4\cdot3-6=27-9-12-6=27-27=0.[/tex]

Therefore 3 is a root of the given polynomial.

Now, we can use this root to factor the polynomial:

[tex]F(x)=(x-3)\frac{x^3-x^2-4x-6}{x-3}.[/tex]

Using the synthetic division algorithm we get that:

[tex]\frac{x^3-x^2-4x-6}{x-3}=x^2+2x+2.[/tex]

The roots of the above polynomial are:

[tex]\begin{gathered} x=-1+i, \\ x=-1-i\text{.} \end{gathered}[/tex]

Therefore:

[tex]F(x)=\mleft(x-3\mright)(x+1+i)(x+1-i)\text{.}[/tex]

Answer:

[tex]F(x)=(x-3)(x+1+i)(x+1-i)\text{.}[/tex]

Which of the following best describes terms that have the same degree in the same radicand? A. like rational termsB. like fractional termsC. like radical termsD. like polynomial terms

Answers

Two radical expressions are called like terms if they have the same degree and the same radicand.

So, like radical terms, best describes terms that have the same degree and the same radicand.

Like radicals are those, that have the same root number and radicand.

So, the correct answer is option C.

Question 13 (3 points)
Intel's microprocessors have a 1.8% chance of malfunctioning. Determine the
probability that a random selected microprocessor from Intel will not malfunction.
Write the answer as a decimal.

Answers

EXPLANATION

The probability that Event A happening is the following:

[tex]P(A)[/tex]

The probability of Event A not happening is the following:

[tex]100-P(A)[/tex]

Therefore, we have:

[tex]P(Malfunctioning)+P(Non\text{ Malfunctioning\rparen=100\%}[/tex]

Plugging in the terms into the expression:

1.8 + P(Not malfunctioning) = 100%

Subtracting -1.8 to both sides:

[tex]P(Not\text{ malfunctioning\rparen=100-1.8}[/tex]

Subtracting numbers:

[tex]P(Not\text{ malfunctioning\rparen=98.2}[/tex]

In conclusion, the probability of not malfunctioning is 0.982

Determine the height of the lift, in metres, above the gym floor. show all your work algebraically. round to the nearest cm, if necessary.

Answers

Height of lift = x + x = 2x

We can find x using triangle ABC by the cosine rule

[tex]\begin{gathered} x^2=5.6^2+5.6^2-2(5.6)(5.6)\cos40^0 \\ x^2=62.72-48.04352 \\ x^2=14.67648 \\ x=\sqrt{14.67648} \\ x=3.831m \end{gathered}[/tex]

Height of lift = 2 X 3.831m = 7.662m

This will be converted to cm by multiplying by 100

Height of lift = 7.662 X 100 cm

= 766.2 cm

= 766cm ( nearest cm )

Hence the answer is 766cm

I’ve already done this problem, but I’m being told it’s wrong and I need to simplify but I don’t know how to do it with this question.

Answers

[tex]\begin{gathered} y=x^2-3 \\ For\text{ (1,2)} \\ x=1,\text{ y=2} \\ y=1^2-3 \\ y=1-3 \\ y=-2,\text{ -2}\ne2,\text{ hence} \\ \text{ this pair doesnt satisfy the equation }y=x^2-3 \\ \text{For (}4,13\text{)} \\ x=4,y=13 \\ y=4^2-3 \\ y=16-3 \\ y=13,\text{ 13=13, hence} \\ \text{This pair satisfies the equation }y=x^2-3 \\ \text{for (}-3,-9\text{)} \\ x=-3,\text{ y=-9} \\ y=(-3)^2-3 \\ y=9-3 \\ y=6,\text{ -9}\ne6,\text{ hence} \\ \text{ this pair doesnt satisfy the equation }y=x^2-3 \\ \text{For (}-5,22\text{)} \\ x=-5,\text{ y=22} \\ y=(-5)^2-3 \\ y=25-3 \\ y=22,\text{ 22=22, hence} \\ \text{This pair satisfies the equation }y=x^2-3 \end{gathered}[/tex]

Robin is saving money to buy a 720$ phone. she has 105$ saved, and each week she adds 30$ to her savings. write an equation to find the number of weeks (w) until she has enough savings to buy the phone.

Answers

Let call w the number of weeks she has been saving.

Then, we can write the expression for her saving in function of the number of weeks as:

[tex]S(w)=105+30\cdot w[/tex]

We now have to find the number of weeks it will take for her savings to reach $720.

We can find it by calculating w for S(w)=720:

[tex]\begin{gathered} S(w)-105+30w=720 \\ 105+30w=720 \\ 30w=720-105 \\ 30w=615 \\ w=\frac{615}{30} \\ w=20.5\approx21 \end{gathered}[/tex]

Answer: it will take her 21 weeks to have enough savings.

Four friends had dinner at a restaurant. The bill was $45.40, and they added a 20% tip. The 4 friends shared the total cost equally. How much money did each person pay?

Answers

Answer:

$13.62

Step-by-step explanation:

To find the tip of 20%, multiply 45.40 by 0.20, and you get 54.48.

Now, since there are 4 friends, divide the amount by 4.

54.48/4=13.62

So each person would pay $13.62.

Hope this helps! :D

Andy spent 1/3 of his money on pastries and 3/4 of his remaining money on 2 pies. Each pie costs 6 times as much as each pastry. if all pastries cost the same how many did he buy

Answers

3/4 x 2/3 = 6/12 = 1/2 so he spend 1/2 of his money on 2 pies
This means he originally had enough money to buy 4 pies or 24 pastries
1/3 of his money would buy 8 pastries

What is the greatest common factor of 9 and 72?

Answers

The Greatest Common Factor of 9 and 72 is: 9

SOLUTION

Problem Statement

The question asks us to find the greatest common factor of 9 and 72.

Method

In order to solve this question, we just need to follow these steps:

1. Write out the prime factors of 9 and 72

2. Choose the common factors from both expressions.

3. Multiply the common factors.

Implementation

1. Write out the prime factors of 9 and 72:

[tex]\begin{gathered} 9=1\times3\times3 \\ \text{The common factors of 9 are: 3 and 3} \\ \\ 72=1\times2\times2\times2\times3\times3 \\ \text{Common factors of 72 are: 1,2, 2, 2 and 3, 3} \end{gathered}[/tex]

2. Choose the common factors from both expressions.:

We need to examine the two expressions for 9 and 72 above. Choose the common values.

[tex]\begin{gathered} 3\times3\text{ is common to both 9 and 72} \\ i\mathrm{}e\text{.} \\ 9\text{ is common to both 9 and 72} \\ 3\text{ is common to both 9 and 72 as well} \\ 1\text{ is also common to both 9 and 72} \end{gathered}[/tex]

3. Multiply the common factors.:

[tex]\begin{gathered} \text{Thus, choosing the greatest values from 1,3 and 9.} \\ \therefore\text{The Greatest Common Factor = 9} \end{gathered}[/tex]

Final Answer:

The Greatest Common Factor of 9 and 72 is: 9

Ronda ate 2/5 of the pie. Connor ate .375 of the pie. How much did they eatcombined? (Express your answer either as a fraction or decimal)

Answers

[tex]\begin{gathered} \text{Ronda ate }\frac{2}{5}\text{ of the pie} \\ \text{Connor ate 0.375 of the pie} \\ We\text{ can either convert Ronda's part to a decimal or} \\ we\text{ can convert Connor's part to a fraction.} \\ \text{Let us now convert Ronda's part to a decimal;} \end{gathered}[/tex]

To convert 2/5 to a decimal;

[tex]undefined[/tex]

X) *11.4.14 Find the volume of the cylinder in terms of it and to the nearest tenth. 2 in 1 in The volume in terms of it is V= in3

Answers

We can calculate the volume of the cylinder as the product of the area of the base and the height of the cylinder.

[tex]V=A_b\cdot h[/tex]

The area of the base is equal to:

[tex]A_b=\pi r^2=\pi\cdot2^2=4\pi[/tex]

Then, the volume becomes:

[tex]V=A_b\cdot h=4\pi\cdot1=4\pi\approx12.6\text{ in}^3[/tex]

Answer:

The volume in function of π is V = 4π in^3.

The volume rounded to the nearest tenth is 12.6 in^3.

Four more than three times a number, is less than 30. Which of the following is not a solution?61278

Answers

Solution

- To solve the question, we simply need to interpret the question line by line.

- Let the number be x.

- "Four more than three times a number" can be written as:

[tex]\begin{gathered} \text{ Three times a number is: }3x \\ \text{ For more than three times a number becomes: }4+3x \end{gathered}[/tex]

- "Four more than three times a number is less than 30" can be written as:

[tex]4+3x<30[/tex]

- Now, we can proceed to solve the inequality and find the appropriate range of x. This is done below:

[tex]\begin{gathered} 4+3x<30 \\ \text{ Subtract 4 from both sides} \\ 3x<30-4 \\ 3x<26 \\ \text{ Divide both sides by 3} \\ \frac{3x}{3}<\frac{26}{3} \\ \\ \therefore x<8\frac{2}{3} \end{gathered}[/tex]

- This means that all correct solutions to the inequality lie below 8.666...

- This further implies that any number greater than this is not part of the solutions of the inequality.

- 12 is greater than 8.666

Final Answer

The answer is 12

there are 14 square and 18 rectangles. what is the simplest ratio of squares to rectangles?

Answers

The simplest ratio of squares to rectangles can be obtained as follows:

There are 14 squares and 18 rectangles. The ratio of squares to rectangles is:

[tex]\frac{14}{18}=\frac{7}{9}[/tex]

Then, the simplest ratio is 7/9 because 7 is a prime number and the ratio cannot be simplified any more. To obtain 7/9 we divided the numerator by 2 and the denominator also by 2.

There are 39 chocolates In a box call identically sheet dear 16 off filled with nuts 13 with caramel and 10 are solid chocolate you randomly select one piece eat it and then select a second piece find the probability of selecting to solid in a row

Answers

The probability of selecting two solid chocolates in a row is 0.0607 .

In the question ,

it is given that

there are total 39 chocolates in the box .

number of chocolates filled with nuts = 16

number of chocolates filled with caramel = 13

number of chocolates filled with solid = 10

Probability of selecting first chocolate as a solid is  10/39.

Now , there are 38 chocolates , with 9 solid chocolates ,

hence the probability of selecting second chocolate as a nut is = 9/38

So, the probability of selecting two solid chocolates in a row = 10/39×9/38

= 90/1482

= 0.0607

Therefore , the probability of selecting two solid chocolates in a row is 0.0607 .

The given question is incomplete , the complete question is

There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.

Learn more about Probability here

https://brainly.com/question/14003918

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theres 2 fill in the blank boxes and 3 drop down menus, below i will list the options in the drop down menus.box 1 - apply quotient identities, apply Pythagorean identities, apply double-number identities, apply even-odd identities.box 2 - apply cofunction identities, use the definition of subtraction, apply even-odd identities, Write as one expresssion combine like terms.box 3 - apply cofunction identities, apply double-number identities, apply Pythagorean identities, apply even-odd identities.

Answers

Solution

Box 1 : Apply Quotient Identities

[tex]cotx-tanx=\frac{cosx}{sinx}-\frac{sinx}{cosx}[/tex]

The answer for the first box is

[tex]\begin{equation*} \frac{cosx}{sinx}-\frac{sinx}{cosx} \end{equation*}[/tex]

Box 2: Write as one expression

[tex]\begin{gathered} cotx-tanx=\frac{cosx}{s\imaginaryI nx}-\frac{s\imaginaryI nx}{cosx} \\ cotx-tanx=\frac{cosx(cosx)-sinx(sinx)}{sinxcosx} \\ cotx-tanx=\frac{cos^2x-sin^2x}{sinxcosx} \end{gathered}[/tex]

The answer for the second box is

[tex]\frac{cos^{2}x-s\imaginaryI n^{2}x}{s\imaginaryI nxcosx}[/tex]

Before the box 3, please note the identity

Note: Trigonometry I dentities

[tex]\begin{gathered} cos^2x-s\mathrm{i}n^2x=cos2x \\ 2sinxcosx=sin2x \end{gathered}[/tex]

Box 3: Apply Double - Number Identities

[tex]\begin{gathered} cotx-tanx=\frac{cos^{2}x-s\imaginaryI n^{2}x}{s\imaginaryI nxcosx} \\ Applying\text{ the above trigonometry identities} \\ cotx-tanx=\frac{cos2x}{sinxcosx} \\ cotx-tanx=\frac{cos2x}{sinxcosx}\times\frac{2}{2} \\ cotx-tanx=\frac{2cos2x}{2sinxcosx} \\ cotx-tanx=\frac{2cos2x}{sin2x} \end{gathered}[/tex]

in the graph below line k,y = -x makes a 45 degree angle with the X and Y axes complete the following

Answers

The point with a coordinate of (2,5) will be translated into y=-x line.

The transformation for y=-x would be:

1. x'= -y

2. y'= -x

For x=2 and y=5 would be:

x'= -y

x'= -5

y'= -x

y'= -2

The translated coordinate would be: (-5, -2)

how do we do this one there two parts to i t

Answers

Given:

[tex]8\sqrt{y}=x-5y[/tex]

Find: differentiation

Explanation: on differentitaion with respect to x

[tex]\begin{gathered} 8\sqrt{y}=x-5y \\ \frac{8}{2}y^{\frac{-1}{2}}\frac{dy}{dx}=1-5\frac{dy}{dx} \\ 4y^{\frac{-1}{2}}\frac{dy}{dx}+5\frac{dy}{dx}=1 \\ (4y^{\frac{-1}{2}}+5)\frac{dy}{dx}=1 \\ \frac{dy}{dx}=\frac{1}{4y^{\frac{-1}{2}}+5} \end{gathered}[/tex]

[tex]\begin{gathered} \frac{-4}{2}y^{\frac{-3}{2}}\frac{dy}{dx}\frac{d^2y}{dx^2}+5\frac{d^2y}{dx^2} \\ 0=(-2y^{\frac{-3}{2}}\frac{dy}{dx}+5)\frac{d^2y}{dx^2} \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]

put the value of

[tex]\frac{dy}{dx}[/tex]

we get,

[tex]\begin{gathered} (-2\frac{y^{\frac{-3}{2}}}{4y^{\frac{-1}{2}}+5}+5)\frac{d^2y}{dx^2}=0 \\ \frac{d^2y}{dx^2}=0 \end{gathered}[/tex]

Factor the expression. 12y + 14

Answers

Answer:

2(6y+7)

Explanation:

To factor the expression:

[tex]12y+14[/tex]

First, find the greatest whole number that divides 12 and 14.

The number = 2, therefore:

[tex]\begin{gathered} 12y+14=2\mleft(\frac{12y}{2}+\frac{14}{2}​\mright) \\ =2(6y+7) \end{gathered}[/tex]

Other Questions
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