Suppose a paper describes a study that investigated the usefulness of using MRI (magnetic resonance imaging) to diagnose breast cancer. MRI exams from 650 women were reviewed. Of the 650 women, 19 had breast cancer, and the MRI exam detected breast cancer in 18 of these women. Of the 631 women who did not have breast cancer, the MRI correctly identified that no cancer was present for 541 of them. The accompanying table summarizes this information.


Suppose that an MRI exam is used to decide between the two hypotheses.

--> H0: A woman does not have breast cancer.

--> Ha: A woman has breast cancer.

(Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.)


(a) One possible error would be deciding that a woman who has breast cancer is cancer-free. Is this a Type I error or a Type II error?

a. Type I

b. Type II

Use the information in the table to approximate the probability of this type of error. (Hint: See Example 10.8. Enter your probability as a fraction.) ____?_____


(b) There is a second type of error that is possible in this context. Describe this error.

a. In this scenario, a Type I error is concluding that a woman has cancer when she really does not have cancer.

b. In this scenario, a Type II error is concluding that a woman has cancer when she really does not have cancer.

Use the information in the table to approximate the probability of this type of error. (Enter your probability as a fraction.) _____?______

The diagonal of the rectangular box will be 9.7 inches.

Given that:

Length, L = 3 inches

Width, W = 2 inches

Height, H = 9 inches

The diagonal of the rectangular prism is given as,

d² = L² + W² + H²

The diagonal of the rectangular box will be calculated as,

d² = 3² + 2² + 9²

d² = 9 + 4 + 81

d² = 94

d = √94

d = 9.7 inches

The diagonal of the rectangular box will be 9.7 inches.

More about the rectangular prism link is given below.

https://brainly.com/question/12649592

#SPJ1

Just the 1 (corresponding to the tallest bar between 45.0 and 52.5 on the horizontal axis)

Answer: 4 pounds is equal to 16 four-ounce (1/4 pound) increments.

To find the number of 3/4 pound bags Ann needs to buy, we can convert 16 four-ounce increments to three-fourth pound increments:

16 four-ounce increments = 16 x 4 = 64 ounces

64 ounces = 64/16 = 40 three-fourth pound increments

Therefore, Ann will need to buy 40 bags of walnuts, each weighing 3/4 of a pound.

Step-by-step explanation:

Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note a variable is a alphabet can be assigned to any value, while a constant is a fixed number or value.

Answers:

variable = t

constant = -7

Step-by-step explanation:

So we know that a variable is a letter while a constant is a number

in here -7 is the constant (the number) and t is the variable (the letter)

Therefore, the variable is t and the constant is -7.

Answer:

  y - x

Step-by-step explanation:

You want the simplified form of |y -x| if y > x.

The absolute value function is defined as ...

  |a| = a . . . . for a ≥ 0

  |a| = -a . . . . for a < 0

We have the expression |y -x|. Using the above function rule, it is ...

  |y -x| = y -x . . . . for y -x ≥ 0   ⇒   y ≥ x

  |y -x| = -(y -x) = x -y . . . . for y -x < 0   ⇒   y < x

The problem statement tells us we're interested in the case y > x, so the first version applies:

  |y -x| = y -x . . . . if y > x

let's convert those $1.60 to pennies, that's 160 pennies, now, let's divide those 160 by (5 + 3) and distribute between the girls accordingly

\(\stackrel{Girl1}{5}~~ : ~~\stackrel{Girl2}{3} ~~ \implies ~~ \stackrel{Girl1}{5\cdot \frac{160}{5+3}}~~ : ~~\stackrel{Girl2}{3\cdot \frac{160}{5+3}} ~~ \implies ~~ \stackrel{Girl1}{5\cdot 20}~~ : ~~\stackrel{Girl2}{3\cdot 20} \\\\\\ \stackrel{Girl1}{100}~~ : ~~\stackrel{Girl2}{60}\qquad \textit{one girl got \underline{40 more cents } than the other girl}\)

The correct answer is option A: "If x doesn't equal 3, then 2x + 5 doesn't equal 11."

More precisely, if f is a function that maps elements from a set A to elements in a set B, then the inverse function of f, denoted as f^(-1), is a function that maps elements in set B back to elements in set A.

The given statement is: "If x equals 3, then 2b + 5 equals 11."

Therefore, the correct answer is option A: "If x doesn't equal 3, then 2x + 5 doesn't equal 11."

The inverse function f^(-1) is defined such that f(f^(-1)(x)) = x for all x in B, and f^(-1)(f(x)) = x for all x in A. In other words, applying the inverse function to the output of the original function returns the input value.

The existence of an inverse function depends on the properties of the original function. For example, a function must be one-to-one (or injective) to have an inverse function, which means that each input maps to a unique output. If a function is not one-to-one, then its inverse function may not exist or may have limited domain and range.

To know more about inverse visit:

https://brainly.com/question/30194642

#SPJ1

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

a) The statement " The intersection of two events A and B can be larger than the union of the same two events A and B" is False.

b) The statement " The probability of a single event A must be smaller than or equal to the union of two events A and B" is False.

c) The statement " The condition probability of A given B must be smaller than the intersection of the same two events A and B"  is False.

(a) False. The intersection of two events A and B represents the set of outcomes that are common to both A and B, while the union of the same two events A and B represents the set of outcomes that belong to either A or B or both. Hence, it cannot be larger than the union of A and B.

(b) False. The probability of an event A must be between 0 and 1 (inclusive), while the union of two events A and B represents the set of outcomes that belong to either A or B or both. The probability of the union of A and B is the sum of the probabilities of A and B, which can be larger than the probability of A.

(c) False. The conditional probability of A given B, denoted as P(A|B), represents the probability of event A occurring given that event B has already occurred.  Since the intersection of A and B must be less than or equal to 1, the conditional probability of A given B must also be less than or equal to 1.

To learn more about intersection click on,

https://brainly.com/question/14019104

#SPJ4

Answer:

Step-by-step explanation:

10 * 10 and you find the square, add (6 * 4) : 2 (triangle) and you have the total area

10 * 10 = 100

(6 * 4) : 2 = 12

100 + 12 = 112in²

Answer:

28%

Step-by-step explanation:

hope this helps, have a good day

Answer:

Too many answers could be correct

Step-by-step explanation:

This one is hard because it will depend on what numbers you pick for each measurement.

-----------------------------------------------------------------------------

if a = 1, b = 2, c = 3, d = 4, and e = 5

find the volume for all the shapes

The post

V = lwh = (1)(1)(2) = 2

The bottom of the mailbox

V = lwh = (3)(4)(5) = 60

The top of the mailbox

V = πr²h = (3)(5)π = 15π = 48.2

Then add them all together:

2 + 60 + 48.2 = 110.2 is the total Volume

Answer:

In what figure?

I cannot determine the answer without proper information.

Answer:

she would probably drive 520 miles in she is driving 65 mph for a whole 8 hours

Step-by-step explanation:

Answer:

520

Step-by-step explanation:

This is a very simple explanation.

Mrs. Garcia drives eight hours...at 65mphs throughout the trip.

How many miles has she drove?

All you need to do is multiply 8x65 and you will get 520.

Mrs. Garcia drove a total of 520 miles.

Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

A sample is only a small portion of the population.

Let's imagine you were interested in determining the average income for all Americans in your population.

Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.

Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.

And the gardener decides to conduct an experiment using 28 individual plants.

Plan A will be a biased sampling and the experiment would not yield

desired results.

Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

learn more about samples here :

https://brainly.com/question/8222250

#SPJ1

Answer:

f(x) \(\leq\) 3x + 4

g(x)  ≥ -1/2x - 5

Step-by-step explanation:

Point D is below f(x)  and above g(x)

Helping in the name of Jesus.

Answer:

100 km/hr

Step-by-step explanation:

11:00 a.m. less 7:30 a.m. works out to 3:30 hours (3 hours 30 minutes).

Then the speed of the bus was

 350 km

--------------- = 100 km/hr, or about 62.5 mph

  3.5 hrs

Answer:

100 km/hr

Step-by-step explanation:

Givens

T = 11:00 - 7:30

T = 3  hours 30 minutes

T = 3 1/2 hours

t = 3.5 hours

d = 350 km

Formula

d = v * t

Solution

350 km = v * 3.5           Divide by 3.5

350 km / 3.5 hours = v

350 / 3.5 = v

v = 100 km/hour

Answer:

principal of first loan = $7,000

principal of second loan = $5,000

Step-by-step explanation:

Let x = principal of first loan

Let y = principal of second loan

Given:

Create two equations with the given information:

Equation 1:  x + y = 12000

Equation 2:  0.08x + 0.09y = 1010

Rewrite Equation 1:

⇒ x = 12000 - y

Substitute into Equation 2 and solve for y:

⇒ 0.08(12000 - y) + 0.09y = 1010

⇒ 960 - 0.08y + 0.09y = 1010

⇒ 0.01y = 50

⇒ y = 5000

Substitute found value of y into Equation 1 and solve for x:

⇒ x + 5000 = 12000

⇒ x = 7000

Answer:

78

Step-by-step explanation:

(5+8)×12/2=78

(5+8)×12/2=78

Answer:

q = -1/8

Step-by-step explanation:

You're trying to solve for q
32q+4=0

Subtract 4 both sides
32q=-4

Now Divide -4 by 32 (This means you have to simplify)
-4/32 = -1/8 due to the common factor of 4.

q = -1/8

Answer:

4(8q+1)

Step-by-step explanation:

32q+4

4*8q+4*1

4(8q+1)

The conjecture for the average weight of the water over the time period required to fill the cylindrical tank of radius 15 ft and height 10 ft is 937.5 lb. This can be checked by integrating the weight density of water (62.4 lb/ft3) multiplied by the rate of flow (3 ft3/min) with respect to time. The answer is 937.5 lb, which confirms the conjecture.

To calculate the average weight of the water over the time period required to fill the cylindrical tank of radius 15 ft and height 10 ft, a conjecture can be made that the average weight is 937.5 lb. This can then be checked by integrating the weight density of water (62.4 lb/ft3) multiplied by the rate of flow (3 ft3/min) with respect to time. The equation for the integration can be expressed as: ∫(62.4 lb/ft3 x 3 ft3/min) dt, where t is the time. Therefore, the answer is 937.5 lb, which confirms the conjecture. This means that for every minute, the tank is being filled with 186.5 lb of water. Since the tank is being filled at a constant rate, the average weight of the water over the time period required to fill it is 937.5 lb.

Learn more about radius here

https://brainly.com/question/15047456

#SPJ4

Answer:  a) 0.7

               b)  70%

Step-by-step explanation:

a) There are 10 marbles.The red marbles are 7

                so that  7/10

                 then change to decimal 7/10=0.7

b) if we get percentage *100

        so,    7÷10*100%

                 70%                            

Answer:

9

Step-by-step explanation:

5x-3= 2x+24

5x=2x+27

3x=27

X=9

Answer: A.  9

Step-by-step explanation:

The diagonal is bisected by the other diagonal.  So the 2 parts of the diagonal are equal

5x - 3 =  2x + 24                 >Bring like terms to 1 side

3x = 27                                >Divide both sides by 3

x = 9

The solution of the differentiated equation is dy/dx = -6x⁵

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

x = ⁶√t

y = 8 - t

To start with:

We need to make the variable t the subject of the formula in the equation x = ⁶√t

Make t the subject

So, we have

t = x⁶

Substitute t = x⁶ in the equation y = 8 - t

y = 8 - x⁶

The rule of first principle of differentiation is represented as

If y = axⁿ, then dy/dx = naxⁿ⁻¹

Using the above as a guide, we have

y = 8 - x⁶

dy/dx = 0 * 8x⁰⁻¹ - 6 * x⁶⁻¹

Evaluate the difference

So, we have

dy/dx = 0 * 8x⁻¹ - 6 * x⁵

Evaluate the products

So, we have

dy/dx = 0 - 6x⁵

Evaluate the sum

So, we have

dy/dx = -6x⁵

Hence, the equation result is dy/dx = -6x⁵

Read more about differentiation at

brainly.com/question/25081524

#SPJ1

Answer:

please send the picture of the number line.

Answer:me not know

Step-by-step explanation:

Hehuehuejejejje

If bought a variety of fruits to bring to a party, the probability that Johnny chooses an apple or a pear after making a random selection from the bag is 0.066 or 6.6%.

The probability that Johnny chooses an apple or a pearl is the chance that either an apple or a pearl is chosen from the 50 pieces of fruits, which is determined by the multiplication of the two probabilities.

Probability refers to the likelihood of achieving an expected outcome or result amid the possibility of many outcomes.

Fruits      Units

Bananas   24

Apples      15

Pear           11

Total        50

The Probability of choosing a banana = 0.48 (24 ÷ 50)

The chance of choosing an apple = 0.3 (15 ÷ 50)

The likelihood of choosing a pear = 0.22(11 ÷ 50)

The probability of choosing an apple or a pear = 0.066 (0.3 x 0.22)

Learn more about probability at https://brainly.com/question/13604758.

#SPJ1

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

Learn more about the area here:

https://brainly.com/question/27683633.

#SPJ1

It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

To know more about mixed number, visit:
https://brainly.com/question/414559
#SPJ1