If chord is 3 inches from the center and chord is 5 inches from the center of the same circle, then chord CD is the longer chord.

Final answer:

Using Bayes' Theorem, the probability that a person is infected when testing positive and not infected when testing negative can be calculated given the provided probabilities.

Explanation:

(a) Using Bayes' Theorem:

Let A be the event that the person is infected and B be the event that the person tests positive.

From the problem, P(A) = 1/200 (probability of being infected) and P(B|A) = 0.7 (probability of testing positive given infection).

To find P(A|B) (probability of being infected given positive test), we can use Bayes' Theorem: P(A|B) = (P(B|A) × P(A)) / P(B).

P(B) can be calculated using the law of total probability: P(B) = P(B|A) * P(A) + P(B|¬A) × P(¬A), where P(¬A) = 1 - P(A) (probability of not being infected).

From the problem, P(B|¬A) = 0.05 (probability of testing positive given not infected).

Substituting the values, P(B) = (0.7 × 1/200) + (0.05 × 199/200).

Finally, we can calculate P(A|B) = (0.7 × 1/200) / ((0.7 × 1/200) + (0.05 × 199/200)).

(b) Using Bayes' Theorem:

Let A be the event that the person is infected and B be the event that the person tests negative.

Similar to part (a), we can calculate P(B) using the law of total probability: P(B) = P(B|A) × P(A) + P(B|¬A) × P(¬A).

From the problem, P(B|¬A) is the probability of testing negative given not infected, which can be calculated as 1 - P(B|A).

To find P(¬A|B) (probability of not being infected given negative test), we can use Bayes' Theorem: P(¬A|B) = (P(B|¬A) ×P(¬A)) / P(B).

Substituting the values, P(¬A|B) = (P(B|¬A) × (1 - P(A))) / P(B).

Answer:0.76

0.58

Conclusion you are More likely to win by playing regular defense

Step-by-step explanation:

Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

Taking the strategy of "regular" defense,

P(winning) = 42

P(losing) = 8

Total regular defense games = 50

Taking the strategy of "prevent" defense,

P(winning) = 35

P(losing) = 15

Total regular prevent games = 50

Total games = 100

Probability of winning when playing regular defense = 42 / 50 = 0.84

Probability of winning when playing prevent defense = 35 / 50 = 0.7

Hence, Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.

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Answer:

Where's the list?

The three consecutive even integers such that the sum of the least integer and the middle integer is 22 more than the greatest integer are 24, 26, and 28.

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Let the first consecutive number be x and the second consecutive number be (x+2).

And the third consecutive number be (x+4).

The sum of the least integer and the middle integer is 22 more than the greatest integer is given by;

x + x  + 2 = 22 + x + 4

2x + 2 = 26 + x

2x - x = 26 - 2

x = 24

The first consecutive number is = x = 24.

And the second consecutive number is = x + 2 = 24 + 2 = 26

And the third consecutive number is = x + 4 = 24 + 4 = 28

Hence, the three consecutive even integers such that the sum of the least integer and the middle integer is 22 more than the greatest integer are 24, 26, and 28.

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Question 9:

cos x = 10/36

Take the inverse on both sides.

arccos(cos x) = arccos(10/36)

x = 73.8723797868

x = 73.87

Question 10:

tan 89 = x

57.2899616308 = x

57.29

Answer: D. 4167 Hertz

Step-by-step explanation:

We know that the formula to calculate frequency by using time period is given by :-

[tex]\nu= \dfrac{1}{T}[/tex], where T is the time period.

We are given that the time period of a musical note :

[tex]T=0.00024\text{ seconds}[/tex]

Then , the frequency of the musical note is given by :-

[tex]\nu= \dfrac{1}{0.00024}=4166.66666667\approx4167\text{ Hertz}[/tex]

Hence, the frequency of the musical note = 4167 Hertz

Answer:

She's being paid six hours per hour

Step-by-step explanation:

She's being paid six hours per hour

72/6 = 6

Answer:

The rule is [tex]\implies f(n)=4n+1[/tex]

Step-by-step explanation:

The ordered for Larry's inputs and the corresponding outputs displayed by the calculator are:

(1, 5), (2, 9), (3, 13), (4, 17)

We use the y-values of the ordered pairs to obtain the rule.

The y-values are:

[tex]5,9,13,17[/tex]

The y-values form a sequence. The first term of this sequence is:

[tex]a=5[/tex]

The common difference of this sequence is

[tex]d=9-4=5[/tex]

The rule is given by:

[tex]f(n)=a+d(n-1)[/tex]

We substitute the values to obtain:

[tex]f(n)=5+4(n-1)[/tex]

[tex]\implies f(n)=5+4n-4[/tex]

The rule is [tex]\implies f(n)=4n+1[/tex]

Answer:

480

Step-by-step explanation:

This is a problem you can solve by using proportions.  If 32 out of 100 prefer sci-fi, then the ratio representing that looks like this:

[tex]\frac{sci-fi}{total}:\frac{32}{100}[/tex]

Since you have the sci-fi "stuff" on top and the "total number of customers" on the bottom, the next ratio you set up with your unknown needs to follow the same set up.  You are asked how many customers (x) out of 1500 (total number of customers) would prefer sci-fi?  That ratio would look like this in the proportion:

[tex]\frac{sci-fi}{total}:\frac{32}{100}[/tex]×[tex]\frac{x}{1500}[/tex]

Cross multiply to get 100x = 48,000

Solve for x by dividing both sides by 100:

x = 480

ANSWER

(-2,4)

EXPLANATION

The given equations are:

4x + 5y = 12

7x + 5y = 6

Subtract the first equation from the second equation.

7x-4x+5y-5y=6-12

3x=-6

Divide both sides by 3 to obtain:

x=-2

Put x=-2 into the first equation to get:

4(-2)+5y=12

-8+5y=12

5y=12+8

5y=20

y=20/5

y=4

Checking

4(-2)+5(4)=12

-8+20=12

12=12

Also

7(-2)+5(4)=6

-14+20=6

6=6

Answer:

The solution is (-2,4)

Step-by-step explanation:

* Lets revise how to solve the system of equations algebraically

- If the system of equation is ax+by=c and dx+ey=f, then we can use

 the elimination method to solve

- The steps of the elimination method

# Change the coefficient of one variable in one of the two equation

  to have the same coefficient with opposite sign of this variable in the

  second equation (a = -d)

# Add the two equations to eliminate this variable (by+ey=c+f)

# Solve to find the second variable (y=(c+f)/(b+e))

# Substitute the the value of the second variable in any equation to

  find the first variable

* Now lets solve the problem

∵ 4x+5y=12 ⇒ (1)

∵ 7x+5y=6 ⇒ (2)

- The variable y has the same coefficient in the two equations, then

 eliminate it by multiply one of the equation by -1 to make

 opposite sign

- Multiply equation (2) by -1

∴-7x-5y=-6 ⇒ (3)

- Add (1) and (3)

∴ -3x=6 ⇒ divide both sides by -3

∴ x=-2

- Substitute the value of x in (1) or (2)

∴ 4(-2)+5y=12

∴ -8+5y=12 ⇒ add 8 to both sides

∴ 5y=20 ⇒ divide each side by 5

∴ y = 4

- The solution of the system is the point which has the values of x and y

∴ The solution is (-2,4)

Answer:

[tex]4,066\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of the bedspread that is red is equal to the area of rectangle minus the area of the circle

step 1

Find the area of rectangle

The area is equal to

[tex]A=72*60=4,320\ in^{2}[/tex]

step 2

Find the area of the circle

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=18/2=9\ in[/tex] ----> the radius is half the diameter

assume

[tex]\pi=3.14[/tex]

substitute

[tex]A=(3.14)(9)^{2}[/tex]

[tex]A=254.34\ in^{2}[/tex]

step 3

Find the area of the bedspread that is red

Find the difference of the areas

[tex]4,320\ in^{2}-254.34\ in^{2}=4,066\ in^{2}[/tex]

Answer:

A)

62/3 = 20.67 hours

B)

60.00 hours

C)

2074.29 miles

Step-by-step explanation:

If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.

A)

In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;

(24/360) = (x/310)

solving for x;

x = (24/360) * 310 = 62/3 = 20.67 hours

B)

In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;

(24/2π radians) = (x/5π radians)

Solving for x;

x = (24/2π radians)*5π radians = 60 hours

C)

If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;

circumference = 2*π*R = π*D

                         = 7920π miles

Therefore, the speed of the earth is approximately;

(7920π miles)/(24 hours) = 330π miles/hr

The distance covered by a point in 2 hours will thus be;

330π * 2 = 660π miles = 2074.29 miles

Answer:

Do Addition

Step-by-step explanation:

x=76+78

x= 154

Answer:

x = 77°

Step-by-step explanation:

The measure of x is half the sum of the measures of the arcs intercepted by the angle and it's vertical angle, that is

x = 0.5 × (78 + 76)° = 0.5 ×154° = 77°

Answer: [tex]300x^{2}[/tex]

Step-by-step explanation: Please see the image below!

The surface area of the composite figure given to us is 300m². Hence option 2 is the right option.

The space enclosed in the given boundary of a 2-D cross-section of a figure is its surface area.

We are asked to find the surface area of the composite figure.

The figure consists of a cube and a pyramid.

The surface area of one face of the cube = a², where a is the length of a side (since its a square)

∴ The surface area of one face = 6² = 36m²

We have 5 faces of the cube, so the total area of the cube is

Area of the cube = 5 * 36m² = 180m².

The surface area of one face of the pyramid = (1/2)*base*height, as it is a triangle.

∴ The surface area of one face = (1/2)*6*10 = 30m²

We have 4 faces of the pyramid, so the total area of the pyramid is

Area of the pyramid = 4*30m² = 120m².

∴ The total surface area of the figure = Area of cube + Area of the pyramid = 180m² + 120² = 300m².

∴ The surface area of the composite figure given to us is 300m². Hence option 2 is the right option.

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2sin^2xcos^2x

Using trig functions we know:

sin^2(x) = 1- cos(2x)/2

cos^2(x) = 1 + cos(2x) /2

Now we have:

2sin^2xcos^2x  =  2 * 1- cos(2x)/2 * 1 + cos(2x) /2

Simplify to: (1- cos(2x) * 1+cos(2x))/2

Difference of squares is (a-b) (a+b) = a^2 -b^2

(1- cos(2x) * 1+cos(2x))/2 = 1^2 -cos^2(x)/2 *1^2 +cos^2(x) /2

Multiply to get 1-cos(4x) /4

The answer is D.

Answer:

Step-by-step explanation:

Their point of intersection, assuming there is one, will be somewhere on the line y = x.  This line, y = x, is the line of symmetry between a function and its inverse.  So if the two do in fact intersect, it will be at some point on that line

Answer:

Step-by-step explanation:

The goal to solving any equation is to have x = {something}.  That means we need to get the x out from underneath that radical.  It's a square root, so we can "undo" it by squaring.  Square both sides because this is an equation.  Squaring both sides gives you

[tex]x^2=-3x+40[/tex]

Get everything on one side of the equals sign and set the quadratic equal to 0:

[tex]x^2+3x-40=0[/tex]

Throw this into the quadratic formula to get that the solutions are x = 5 and -8.  We need to see if only one works, both work, or neither work in the original equation.

Does [tex]5=\sqrt{-3(5)+40}[/tex]?

[tex]5=\sqrt{-15+40}[/tex] and

[tex]5=\sqrt{25}[/tex]

and 5 = 5.  So 5 works.  Let's try -8 now:

[tex]-8=\sqrt{-3(-8)+40}[/tex] and

[tex]-8=\sqrt{24+40}[/tex] so

[tex]-8=\sqrt{64}[/tex]

-8 = 8?  No it doesn't.  So only 5 works. Your choice is the third one down.

we know that f(1)=2 so f^-1(2)=1

so B is correct!

Answer:  The correct option is

(B) [tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Step-by-step explanation:  We are given to select the correct expression that is the inverse of the following function :

[tex]f(x)=\dfrac{x+1}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Let y denotes f(x). Then,

[tex]y=f(x)~~~~~~\Rightarrow x=f^{-1}(y).[/tex]

Substituting this value in equation (i), we get

[tex]f(x)=\dfrac{x+1}{x}\\\\\\\Rightarrow y=\dfrac{f^{-1}(y)+1}{f^{-1}(y)}\\\\\\\Rightarrow yf^{-1}(y)=f^{-1}(y)+1\\\\\Rightarrow yf^{-1}(y)-f^{-1}(y)=1\\\\\Rightarrow (y-1)f^{-1}(y)=1\\\\\Rightarrow f^{-1}(y)=\dfrac{1}{y-1}\\\\\Rightarrow f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Thus, the required inverse of the given function is

[tex]f^{-1}(x)=\dfrac{1}{x-1}.[/tex]

Option (B) is CORRECT.

Answer:

c. (2, 1) and (−1, −2)

Step-by-step explanation:

Assuming you intended y=x²-3 and x-y=1, you can graph the parabola and the straight line (rewrite x-y=1 as y = x-1).

You can then see the intersections at x=-1, y=-2 and x=2, y=1.

Answer:

22 min 13 sec

Step-by-step explanation:

Calculate the following:

      1 clearance                                      1

---------------------------------------- = ---------------------------------  =  22 min 13 sec

1 clearance      1 clearance       1/(50 min)+ 1/(40 min)

------------------ + ------------------

   50 min            40 min

Note:  The LCD here is 200 min.

Also note:  1 / [ 1 / 40 min ] has units "min."

Answer:

It would be:

50 * 40 / (50 + 40) = 2,000 / 90 = 22.222222 minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

alright,  lets get started.

Side 5 is opposite.

Side 12 is adjacent.

Side 13 is hypotenuse.

Using SOH CAH TOA,

sin Θ = [tex]\frac{opposite}{hypotenuse}[/tex]

sin Θ = [tex]\frac{5}{13}[/tex]

cos Θ=[tex]\frac{adjacent}{hypotenuse}[/tex]

cos Θ=[tex]\frac{12}{13}[/tex]

tan Θ=[tex]\frac{opposite}{adjacent}[/tex]

tan Θ=[tex]\frac{5}{12}[/tex]   :   Answer

Hope it will help :)

Answer:

5 units

Step-by-step explanation:

Let's take point X and X' (it will be the same regardless of the point).

The distance is 3 units to the right then 4 units up.

A direct line will be diagonal and can be found using the pythagorean theorem (refer to visual).

(D: a > 0) 3² + 4² = a² --> 9 + 16 = a² --> a² = 25 --> a = 5

So the distance is 5 units.

When a figure is translated, or moved without rotation or change in size, the distances between corresponding points on the original and new figure remain the same. Therefore, the distance between any two corresponding points on Triangle XYZ and Triangle X'Y'Z' is the same as it was prior to the translation.

In this case, the triangle XYZ is being translated, which means that it is being shifted in the plane. The student has moved the triangle 4 units up and 3 units left. This operation does not alter the size, shape or orientation of the triangle, just its position. Therefore, the distance between any two points on the triangle remains the same before and after the translation. To clarify, if the distance between point X and Y initially is 'd', after the triangle has been translated to yield triangle X'Y'Z', the distance between X' and Y' remains 'd'. This is an important characteristics of translation, a core concept in geometry.

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Answer:

6.5 Gallons

Step-by-step explanation:

288 miles / 12 gallons = 24 mpg

156 miles / 24 mpg = 6.5 gallons

Answer:

C 3

Step-by-step explanation:

5x^2 + 6x + 7 = 2(x + 2)

Distribute the 2

5x^2 + 6x + 7 = 2x + 4

Subtract 2x from each side

5x^2+6x-2x +7 = 2x-2x+4

5x^2 + 4x + 7 = 4

Subtract 4 from each side

5x^2 +4x+7-4 = 4-4

5x^2 +4x+3 = 0

This is in the form ax^2 + bx +c  where c is 3

Answer:

Step-by-step explanation:

[tex]ax^2+bx+c=0\\\\5x^2+6x+7=2(x+2)\qquad\text{use the distributive property}\\\\5x^2+6x+7=2x+4\qquad\text{subtract}\ 2x\ \text{and 4 from both sides}\\\\5x^2+4x+\boxed{3}=0[/tex]

Answer:

The distance across the river from Omkar to the big rock is 131343149 meters

Step-by-step explanation:

* Lets study the information in the problem

- Let Omkar position is point A

- Let Melissa position is point B

- Let big rock position is C on the other side of the river

* Now we have triangle ABC

- The distance between Omkar and Melissa is 100100100 meters

  along the river

- The angle between Omkar and the big rock is angle BAC

∴ m∠BAC = 33°

- The angle between Melissa and the big rock is angle ABC

∴ m∠ABC = 98°

- The big rock is at angle C

* Now we can find the distance between Omkar and the big rock

 by finding the length of side AC in the triangle

- By using the sine rule

∵ sin A/BC = sin B/AC = sin C/AB

∵ AB = 100100100 meters

∵ m∠ABC = 98°

- Lets find m∠C

∵ In any triangle the sum of the measures of the interior angles is 180°

∴ m∠A + m∠B + m∠C = 180°

∵ m∠A = 33° , m∠B = 98°

∴ 33° + 98° + m∠C = 180° ⇒ add

∴ 131° + m∠C = 180° ⇒ subtract 131 from both sides

∴ m∠C = 49°

- Now lets use the sine rule

∵ sin ABC/AC = sin C/AB

∴ sin 98/AC = sin 49/100100100 ⇒ by using cross multiplication

∴ AC = (sin 98 × 100100100) ÷ sin 49 = 131343148.8

∴ AC ≅ 131343149 meters

* The distance across the river from Omkar to the big rock is

 131343149 meters

Answer:

The distance across the river from Omkar to the big rock is 72 meters.

Step-by-step explanation:

Using the given information draw as triangle as shown below.

According to angle sum property, the sum of interior angles of a triangle is 180°.

In triangle ABC,

[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]

[tex]98^{\circ}+33^{\circ}+\angle C=180^{\circ}[/tex]

[tex]131^{\circ}+\angle C=180^{\circ}[/tex]

[tex]\angle C=180^{\circ}-131^{\circ}=49^{\circ}[/tex]

The measure of angle C is 49°.

Sine formula:

[tex]\frac{a}{\sin a}=\frac{b}{\sin b}=\frac{c}{\sin c}[/tex]

Using sine formula in triangle ABC, we get

[tex]\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]

[tex]\frac{AC}{\sin 33^{\circ}}=\frac{100}{\sin 49^{\circ}}[/tex]

[tex]AC=\frac{100}{\sin 49^{\circ}}\times \sin 33^{\circ}[/tex]

[tex]AC=\frac{100}{0.7547}\cdot0.544639[/tex]

[tex]AC=72.166[/tex]

[tex]AC\approx 72[/tex]

Therefore the distance across the river from Omkar to the big rock is 72 meters.

Answer:

  b = 18

Step-by-step explanation:

From an external point, the products of distances to the near circle intercept and the far circle intercept are the same. For a tangent, such as AC, point A is both the near and far intercept point, so that product is the square of the length of AC.

  (AC)² = (CG)(CV)

  b² = 12·27 = 324 . . . . substitute known values

  b = √324 . . . . . . . . . . take the square root

  b = 18

Answer:

18 is it ;)

Step-by-step explanation:

because it is

value will be 46, because absolute value is always positive

0.79370053 is the answer

Answer:

0.125

Step-by-step explanation:

Cube 0.5 to find the value of which 0.5 is the cube root

Working with proper fractions, then

([tex]\frac{1}{2}[/tex])³

= [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{8}[/tex]

and [tex]\frac{1}{8}[/tex] = 0.125

Answer:

Step-by-step explanation:

the answer is $22.95

In order to break even store need to charge $22.25 per pair of shorts.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given,

Fixed cost = $450

Cost of each pair = $11

Number of pairs = 40

So,

The total cost of manufacturing

450 + 11(40) = $890

Now,

Let's say the store charges x per short

Total income = 40x

Now,

At break-even point

The total cost of manufacturing = Total income

890 = 40x

x = $22.25

Hence, In order to break even store need to charge $22.25 per pair of shorts.

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Answer:

The mean absolute deviation is 5.952 ⇒ 3rd answer

Step-by-step explanation:

* Lets talk about the mean absolute deviation

- Mean absolute deviation (MAD) of a data set is the average distance

 between each data value and the mean

1- To find the mean absolute deviation of the data, start by finding

   the mean of the data set.

2- Find the sum of the data values, and divide the sum by the

   number of data values.

3- Find the absolute value of the difference between each data value

   and the mean ⇒ |data value – mean|

4- Find the sum of the absolute values of the differences.

5- Divide the sum of the absolute values of the differences by the

   number of data values

* Now lets solve the problem

- The set of data is 31.8 , 22.6 , 13.8 , 16.4 , 28.1

# Find the mean

∵ The mean = sum/ number

∴ The mean = (31.8 + 22.6 + 13.8 + 16.4 + 28.1)/5 = 112.7/5 = 22.54

# Find |data value – mean|

∵ I31.8 - 22.54I = 9.26

∵ I22.6 - 22.54I = 0.06

∵ I13.8 - 22.54I = 8.74

∵ I16.4 - 22.54I = 6.14

∵ I28.1 - 22.54I = 5.56

# Find the sum of the absolute values

∴ The sum = 9.26 + 0.06 + 8.74 + 6.14 + 5.56 = 29.76

# Find the mean absolute deviation

∵ The mean absolute deviation = sum of absolute values/number

∴ The mean absolute deviation = 29.76/5 = 5.952

* The mean absolute deviation is 5.952

Answer:

18.75

Step-by-step explanation: