what similarity is it when triangles are similar if they have two congruent angles

The value of arc CD in the intersecting chords is determined as 57⁰.

The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

arc BCD = arc CD +  arc CB

arc BCD = 2 x 84⁰

arc BCD = 168⁰

168 = CD + CB

arc BAD = BA + AD

angle DCB = 180 - 84 ( opposite angles of a cyclic quadrilateral are supplementary)

angle DCB = 96⁰

arc BAD = 2 x 96 = 192⁰

192 = BA + AD

192 = 127 + AD

AD = 65⁰

The value of arc CD is calculated as follows;

Arc ADC = AD + CD

arc ADC = 2 x 61 = 122

122 = AD + CD

122 = 65 + CD

CD = 57⁰

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Probability of selecting an athlete that stretches = 7/16

Percentage of athlete that do not stretch and got injured = 51.33%

a)

From table,

Athletes that stretch = Athletes that got injured while stretching + Athletes that do not got injured while stretching

Athletes that stretch = 55 + 295

Athletes that stretch = 350

Total number of athletes = stretch + does not stretch

total number of athletes = 350 + 450 = 800

Probability of an event to occur = Number of favourable outcomes / Total number of outcomes.

Probability of selecting an athlete that stretches = 350/ 800

Probability of selecting an athlete that stretches = 7/16

b)

Given

Athlete that do not stretch = 450

Athlete that got injured that do not stretch = 231

Now,

Percentage of athlete that do not stretch and got injured = 231/450 × 100

Percentage of athlete that do not stretch and got injured = 51.33%

Hence from the data given in table the required values can be found out.

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n³a⁹= (9/64)r³ this equation shows that 125ncubica(a³) = 9 cubic r, as desired by cone and sphere

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

Since we have n ice spheres of radius a

the total volume of the ice spheres is given by V_ice = n × (4/3)πa³.

The volume of a cone is given by the formula V_cone = (1/3)πr²h

where r is the radius of the base and h is the height of the cone.

The slant height of the cone is also given as r.

Using the Pythagorean theorem, we can find the height of the cone, h, in terms of r:

h =√(r² - a²)

Substituting this value of h into the formula for the volume of the cone, we get:

V_cone = (1/3)πr² √(r² - a²)

V_ice = V_cone

n(4/3)πa³= (1/3)πr²√(r² - a²)

Simplifying this equation, we can cancel out the common factors of (1/3)π:

4na³= r²√(r² - a²)

Now, let's cube both sides of the equation to eliminate the square root:

(4na³)³ = (r²√(r² - a²))³

64n³a⁹ = r⁶ (r² - a²)

n³a⁹= (9/64)r³

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Answer: The values of the six trigonometric functions for the angle formed by the positive x-axis and the line segment from (0,0) to (4,-3) are:

sinθ = -3/5

cosθ = 4/5

tanθ = -3/4

cscθ = -5/3

secθ = 5/4

cotθ = -4/3

Step-by-step explanation: To find the values of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) of an angle formed by the positive x-axis and a line segment, we need to determine the lengths of the sides of the right triangle formed.

In this case, the line segment goes from (0,0) to (4,-3). The horizontal length (adjacent side) is 4 units, and the vertical length (opposite side) is -3 units (since it goes downward).

Now, we can calculate the trigonometric functions:

Sine (sinθ) = opposite/hypotenuse = -3/5

Cosine (cosθ) = adjacent/hypotenuse = 4/5

Tangent (tanθ) = opposite/adjacent = -3/4

Cosecant (cscθ) = 1/sinθ = -5/3

Secant (secθ) = 1/cosθ = 5/4

Cotangent (cotθ) = 1/tanθ = -4/3

Therefore, the values of the six trigonometric functions for the angle formed by the positive x-axis and the line segment from (0,0) to (4,-3) are:

sinθ = -3/5

cosθ = 4/5

tanθ = -3/4

cscθ = -5/3

secθ = 5/4

cotθ = -4/3

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The measures of the angles are ∠PQR = 96° and ∠PSR = 84°

Given is a cyclic quadrilateral, with angles ∠PQR = (7x - 2)° and ∠PSR = (5x+14)°.

We need to find the measure of the angles PQR and PSR,

So,

We know that the cyclic quadrilaterals have their opposite angles supplementary,

So,

∠PQR + ∠PSR = 180°

7x - 2 + 5x + 14 = 180°

12x + 12 = 180°

12x = 168°

x = 14°

Put the value of x in the angles, we get,

∠PQR = (7x - 2)°

∠PQR = 7 × 14 - 2

∠PQR = 96°

And,

∠PSR = 5 × 14 - 2

∠PSR = 84°

Hence the measures of the angles are ∠PQR = 96° and ∠PSR = 84°

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Answer:

Minimum value = -6

Step-by-step explanation:

The minimum value is the y-coordinate of the minimum on the parabola.

Currently 3/4x^2 + 6x + 6 is in standard form, whose general equation is:

ax^2 + bx + c

Step 1:  We can first find the x-coordinate of the maximum using the following formula:

-b / 2a

From the function, we see that 6 is b and 3/4 is a.  Now, we plug these values into the formula and simplify:

-6 / (2 * 3/4)

-6 / (6/4)

-6 / (3/2)

-6 * 2/3

-12/3

-4

Step 2:  Now we can plug in -4 for x in the function to find the minimum value:

y = 3/4(-4)^2 + 6(-4) + 6

y = 3/4(16) -24 + 6

y = 48/4 - 24 + 6

y = 12 - 24 + 6

y = -12 + 6

y = -6

Thus, the minimum value of the function y = 3/4x^2 + 6x + 6 is -6

Answer:

A. Add Equation A and Equation B.

Step-by-step explanation:

When you add Equation A and Equation B, you'd get (when combining like terms)

(7y + 3y) + (-4x + 4x) = (5 + 25), which becomes 10y = 30

This show us that adding the equations allows us to cancel (eliminate) the x variable.  Then we'd solve for y and later we'd solve for x by plugging in the value for y into either equation A or equation B.

The solution of the equation 2|2x - 1| - 8 = 18 is x = 7 or x = -6.

The solution of the equation 2|2x - 1| - 8 = 18 can be obtained as follows:

Step 1: Add 8 to both sides of the equation2|2x - 1| = 26

Step 2: Divide both sides of the equation by 2|2x - 1| / 2 = 26 / 2|2x - 1| = 13

Step 3: The absolute value of a number is always positive, so we can divide the equation into two separate equations.|2x - 1| = 13 or -|2x - 1| = 13

Step 4: Solve for x in each equation.

Solution for the first equation:|2x - 1| = 132x - 1 = 13 or 2x - 1 = -13 2x = 14 or 2x = -12 x = 7 or x = -6

Solution for the second equation:-|2x - 1| = 13|2x - 1| = -13

There is no solution to this equation because the absolute value of a number cannot be negative.

Therefore, the solution of the equation 2|2x - 1| - 8 = 18 is x = 7 or x = -6.

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The value of x using the theorem of intersecting secants is 10

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

intersecting secants

Using the intersecting secants equation, we have

8 * (8 + x) = 6 * (6 + 18)

Evaluate the like terms

So, we have

8 * (8 + x) = 6 * 24

Divide both sides by 8

8 + x = 6 * 3

So, we have

8 + x = 18

Subtract 8 from both sides

x = 10

Hence, the value of x is 10

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The volumes of the shapes are:

V = 90π in³, V = 1875.78π ft³, V = 240 cm³, V =500π cm³, V = 30 cm³.

Here, we have,

1.) Volume of cylinder

V= π×r²×h

Where

π=3.14

r=3

h=10in

V=3.14×3²×10

V = 90π in³

2.) Volume of cylinder

V=  π×r²×h

Where

π=3.14

r=17.5/2 ft

h=24.5 ft

V = 1875.78π ft³

3.) Volume of prism

V = l×w×h

so, we get,

l = 6cm, w = 8cm, h = 5cm

V = 240 cm³

4.)Volume of cylinder

V= π×r²×h

Where

π=3.14

r=20/2 cm

h=5 cm

V =500π cm³

5.) Volume of rectangular box

V = l×w×h

so, we get,

l = 2cm, w = 5cm, h = 3cm

V = 30 cm³

Hence, The solutions are: the volumes of the shapes are:

V = 90π in³, V = 1875.78π ft³, V = 240 cm³, V =500π cm³, V = 30 cm³.

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The value of cos (A+B) in simplest form is -136/305.

The standard formula for the cosine of the sum of two angles is:

cos(A+B) = cos A cos B - sin A sin B

We are given that cos A = 11/61 and sin B = 3/5. We can use this information to find the values of sin A and cos B by using the Pythagorean identity:

sin^2 A +[tex]cos^2[/tex]A = 1  =>  sin A = [tex]\sqrt(1 - cos^2[/tex] A)

cos^2 B + [tex]sin^2[/tex] B = 1 => cos B = [tex]\sqrt(1 - sin^2 B)[/tex]

Substituting the given values, we get:

sin A =[tex]\sqrt(1 - (11/61)^2) ~~ 60/61[/tex]

cos B = [tex]\sqrt(1 - (3/5)^2) = 4/5[/tex]

Now we can use these values to find the cosine of the sum of the angles:

cos(A+B) = cos A cos B - sin A sin B

= (11/61)(4/5) - (60/61)(3/5)

= (44/305) - (36/61)

= (44 - 180)/305

= -136/305

Note that since A and B are positive acute angles, A+B is also an acute angle, which means that its cosine is negative.

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Answer:

1048 student tickets were sold and 1452 adult tickets were sold

Step-by-step explanation:

We can use a system of equations to find the quantity of both the adult and student tickets.  We can allow A to represent the quantity of adult tickets and S to represent the quantity of student tickets.

First equation:  (For the context of my explanation, revenue is defined as the product of price of an item and the quantity) We know that the sum of the revenues earned from the adult tickets equals the total revenue as

(price of adult tickets * quantity of adult tickets) + (price of student tickets * quantity of student tickets) = total revenue

Since we know that the adult tickets cost $3, the student tickets cost $2, and the total revenue earned was $6452, our first equation is:

3A + 2S = 6452

Second Equation:  We further know that the sum of the quantities of adult and student tickets equals the total amount of tickets sold as

quantity of adult tickets + quantity of student tickets = total amount of tickets sold

Since we know that there were 2500 fans in the gym, our second equation is:

A + S = 2500

Method to solve:  We can isolate A in the second equation by subtracting S from both sides.  This will allow us to substitute it in the first equation to first solve for S , the quantity of student tickets sold:

Step 1:  Isolating S in second equation:

(A + S = 2500) - S

A = -S + 2500

Step 2:  Plugging in (substituting) A = -S + 2500 for A in 3A + 2S = 6452:

3(-S + 2500) + 2S = 6452

-3S + 7500 + 2S = 6452

-S + 7500 = 6452

-S = -1048

S = 1048

Now that we know the quantity of student tickets sold was 1048, we can plug in 1048 for S in any of the two equations in our system to solve for A, the quantity of adult tickets sold.  Let's use the first equation:

Step 3:  Plugging in 1048 for S in 3A + 2S = 6452

3A + 2(1048) = 6452

3A + 2096 = 6452

3A = 4356

A = 1452

Thus, the quantity of adult tickets sold was 1452.

Optional Step 4:  We can check that we've found the correct answers by plugging in 1048 for S and 1452 for A in both equations in our system and checking that we get 6452 for the first equation and 2500 for the second equation:

Plugging in 1048 for S and 1452 for A in 3A + 2S = 6452 (i.e., the first equation in our system):

3(1452) + 2(1048) = 6452

4356 + 2096 = 6452

6452

Plugging in 1048 for S and 1452 for a in A + S = 2500 (i.e., the second equation in our system):

1048 + 1452 = 2500

2500 = 2500

The exponential function that could be represented by the graph is given as follows:

[tex]y = 10^x[/tex]

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The graph crosses the y-axis at y = 1, hence the parameter a is given as follows:

a = 1.

When x is increased by one, y is multiplied by 10, as we have that when x = 1, y = 5 and when x = 2, y = 50, hence the parameter b is given as follows:

b = 10.

Hence the function is given as follows:

[tex]y = 10^x[/tex]

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Let's call the amount Susan invested in the fund that paid a 12% profit "x" and the amount she invested in the stock that suffered a 4% loss "y".

We know that Susan's overall net profit was $2,160, so the total amount of profit she earned from both investments was $2,160.

The profit from the investment in the fund that paid a 12% profit was 0.12x (since the profit rate was 12%). The loss from the investment in the stock that suffered a 4% loss was -0.04y (since the profit rate was negative 4%).

We can set up two equations based on this information:

The total amount invested was $22,000:

x + y = 22,000

The total profit was $2,160:

0.12x - 0.04y = 2,160

We can use the first equation to solve for one of the variables in terms of the other:

x = 22,000 - y

Now we can substitute this expression for "x" into the second equation:

0.12(22,000 - y) - 0.04y = 2,160

Simplifying:

2,640 - 0.12y - 0.04y = 2,160

Combining like terms:

2,640 - 0.16y = 2,160Subtracting 2,640 from both sides:

-0.16y = -480

Dividing both sides by -0.16:

y = 3,000

So Susan invested $3,000 in the stock that suffered a 4% loss.

To find the amount she invested in the fund that paid a 12% profit, we can substitute this value for "y" in one of the equations we set up earlier:

x + y = 22,000

x + 3,000 = 22,000

x = 19,000

So Susan invested $19,000 in the fund that paid a 12% profit.

Therefore, the amount invested at 12% was $19,000 and the amount invested in stock was $3,000.

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The amount invested in the in account that had an 12% profit is $19,000

The amount invested in the in account that had a 4% loss is $3,000.

[tex]\sf a + b = 22,000[/tex] equation 1

[tex]\sf 0.12a - 0.04b = 2160[/tex] equation 2

Where:

Multiply equation 1 by 0.12

[tex]\sf 0.12a + 0.12b = 2640[/tex] equation 3

Subtract equation 2 from equation 3

[tex]\sf 0.16b = 480[/tex]

Divide both sides of the equation by 0.16

[tex]\sf b = 3000[/tex]

Subtract 3,000 from 22,000

[tex]\sf a = 22,000 - 3,000 = 19,000[/tex]

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The equation for the water level, L, after d days can be written as:

L = 340 - 0.5d

To find in how many days the water level will be 260m, we can substitute L = 260 into the equation and solve for d:

260 = 340 - 0.5d

0.5d = 340 - 260

0.5d = 80

d = 80 / 0.5

d = 160

Therefore, the water level will be 260m after 160 days.

The angle m∠BAC is 54 degrees.

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore, let's find the angle BAC.

Hence,

10x + 4 = 1 / 2 (12x + 15 + 9x - 12)

10x + 4 = 1 / 2 (21x + 3)

10x + 4 = 10.5x + 1.5

10x - 10.5x = 1.5 - 4

-0.5x = -2.5

divide both sides by -0.5

x = -2.5 / -0.5

x = 5

Therefore,

m∠BAC = 10(5) + 4

m∠BAC = 50 + 4

m∠BAC = 54 degrees

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The solution to the system of equations is x = 4 and y = 8. The lines represented by the equations y = 2x and 6x - 2y = 8 Intersect at the point (4, 8).

To analyze the given equations:

Equation 1: y = 2x

Equation 2: 6x - 2y = 8

We can begin by examining Equation 1, which is in slope-intercept form (y = mx + b). In this equation, the coefficient of x is 2, representing the slope of the line. Therefore, the line described by Equation 1 has a slope of 2.

Now, let's move on to Equation 2. It can be rewritten by rearranging the terms:

6x - 2y = 8

-2y = -6x + 8

Dividing by -2 on both sides:

y = 3x - 4

By comparing Equation 2 with the slope-intercept form (y = mx + b), we can see that its slope is 3.

Comparing the slopes of the two equations, we observe that they are not equal. Since the slopes are different, the lines represented by the equations y = 2x and y = 3x - 4 are not parallel.

To determine if they intersect, we can equate the right-hand sides of the two equations:

2x = 3x - 4

By rearranging terms, we get:

x = 4

Substituting x = 4 back into Equation 1:

y = 2(4)

y = 8

Therefore, the solution to the system of equations is x = 4 and y = 8. The lines represented by the equations y = 2x and 6x - 2y = 8 intersect at the point (4, 8).

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En un número decimal, la parte que está antes del punto decimal se conoce como la parte entera del número, mientras que la parte que está después del punto decimal se conoce como la parte decimal.

La parte entera representa la cantidad completa de unidades o números enteros que se encuentran en el número. Por ejemplo, en el número decimal 12.345, la parte entera es 12, lo que significa que hay 12 unidades completas.

La parte decimal representa una fracción o porción del número que es menor que uno. En el ejemplo anterior, la parte decimal es .345, lo que significa que es una fracción de una unidad. La parte decimal se puede expresar en forma de fracción o como un número decimal.

La relación entre la parte entera y la parte decimal es que, juntas, representan el número decimal completo. Por ejemplo, el número decimal 12.345 se compone de la parte entera 12 y la parte decimal .345. La parte entera siempre se coloca a la izquierda del punto decimal, mientras que la parte decimal se coloca a la derecha del punto decimal.

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From the given system of linear equations there are no solutions.

The given system of equations are 5x+y=3 and 10x+2y=-6.

Here, 5x+y=3 -----(i) and 10x+2y=-6 ⇒ 5x+y=-3 --------(ii)

Subtract equation (i) from equation (ii), we get

5x+y-(5x+y)=-3-3

5x+y-5x-y=-6

0≠ -6

There are no solutions

Hence, from the given system of linear equations there are no solutions.

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The probability that the newspaper Mario buys has reviewed both performances, given that he buys the first newspaper, is 0.72 or 72%.

a) Let's assume the probability of the first newspaper reviewing his performance is 2/7 and the probability of the second newspaper reviewing his performance is 5/7. The probability of both papers reviewing his performance is (2/7) * (5/7) = 10/49.

b)Since Clarissa buys both newspapers, there are two scenarios: either the first newspaper reviews her performance and the second one doesn't, or the second newspaper reviews her performance and the first one doesn't. The probability of only one paper reviewing her performance is 2 * (3/7) * (4/7) = 24/49.

c) If Mario buys one newspaper at random, there is a 2/7 chance that he buys the first newspaper and a 5/7 chance that he buys the second newspaper. Since each newspaper has reviewed one performance, the probability that the newspaper he buys has reviewed both performances is (2/7) * (5/7) = 10/49.

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A. Matrix AB is [tex]\left[\begin{array}{cc}24&37\\6&25\end{array}\right][/tex]

B. Matrix BA is [tex]\left[\begin{array}{cc}10&-12\\-1&39\end{array}\right][/tex]

C. No, in general, AB does not always equal BA.

A. To find AB we say [tex]\left[\begin{array}{cc}-3&5\\1&3\end{array}\right][/tex] × [tex]\left[\begin{array}{cc}-3&1\\3&8\end{array}\right][/tex]

which becomes [tex]\left[\begin{array}{cc}-3*-3 + 5*3& -3*3 + 5*8\\1*3 +3*3&1*1 + 8*3\end{array}\right][/tex] ⇒   [tex]\left[\begin{array}{cc}24&37\\6&25\end{array}\right][/tex]

B. To find Matrix BA  [tex]\left[\begin{array}{cc}-3&1\\3&8\end{array}\right][/tex] ×  [tex]\left[\begin{array}{cc}-3&5\\1&3\end{array}\right][/tex]

Which becomes [tex]\left[\begin{array}{cc}-3*3 + 1*1 &-3*5 + 1*3\\3*-3 + 8*1&3*5 + 8*3\end{array}\right][/tex] ⇒  [tex]\left[\begin{array}{cc}10&-12\\-1&39\end{array}\right][/tex]

C. For matrices A and B such that AB and BA both exist, AB will equal BA if and only if the matrices commute. A matrix commutes with another matrix if the order in which they are multiplied does not matter.

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If jill has graded 45% of her assessments and she has 27 assessments graded then total assessments are 60

The total number of assessments Jill needs to grade as "x".

According to the information provided, Jill has already graded 45% of her assessments, which is equivalent to 0.45 when expressed as a decimal.

So, we can set up the proportion:

(graded assessments) / (total assessments) = (graded percentage) / 100

Substituting the known values:

27 / x = 45 / 100

To solve for x, we can cross-multiply and solve the resulting equation:

100 × 27 = 45×x

2700 = 45x

Divide both sides of the equation by 45:

2700 / 45 = x

60 = x

Therefore, Jill needs to grade a total of 60 assessments.

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The trigonometric ratio include the following:

In order to determine each of the trigonometric ratios, we would apply each of the trigonometric ratios because the given side lengths represent the adjacent side, opposite side and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp, sin(θ) = Opp/Hyp, tan(θ) = Opp/Adj

Where:

sin(θ) = Opp/Hyp

sin B = b/c

sin(θ) = Opp/Hyp

sin A = a/c

tan(θ) = Opp/Adj

tan A = a/b

cos(θ) = Adj/Hyp

cos B = a/c

cos(θ) = Adj/Hyp

cos A = b/c

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Complete Question:

Use the right triangle to determine the each of the trigonometric ratio.

Step-by-step explanation:

1/2×13×12= 78

12×14= 132

13×14= 182

total surface area

= (78×2)+(132×2)+182

= 602 ft^2

Answer: The equation x^n + y^n = (x + y)^n represents Fermat's Last Theorem for the case when the exponents are equal. According to Fermat's Last Theorem, there are no positive integer solutions (x, y, z) for the equation x^n + y^n = z^n, where n is a positive integer greater than 2.

However, in this case, we are looking for solutions where x ≠ y, so the equation x^n + y^n = (x + y)^n may have infinitely many positive integer solutions for certain values of n.

To find the values of n for which the equation has infinitely many positive integer solutions (x, y) with x ≠ y, we need to consider the equation x^n + y^n = (x + y)^n and see if there are any such values.

Let's analyze the equation for different values of n:

When n = 2:

When n = 3:

Therefore, when n = 3, the equation has infinitely many positive integer solutions (x, y) with x ≠ y.

When n > 3:

In summary, the equation x^n + y^n = (x + y)^n has infinitely many positive integer solutions (x, y) with x ≠ y when n = 3. For all other values of n greater than 1, there are no such solutions.

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

We have,

To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.

Now,

Prevalence of coronavirus in California: 3 out of 1000

False positive rate of the antigen test: 0.05 (5 out of 100)

Let's calculate the probability of a positive test result.

The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):

True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)

The probability of a positive test result can be calculated using Bayes' theorem:

P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)

P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)

P(Positive test) = 0.0024 + 0.04985

P(Positive test) = 0.05225

Therefore,

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

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Answer:

11.8 cm²

Step-by-step explanation:

Cosine rule: a ² = b ² + c ²  - 2bc COS A

COS A = (b ²  +  c ²   -  a ²) / (2bc)

Area of triangle = ½ ab sin C

name the angle that joins the '3' side to either of the '8' sides. label that angle as A.

now, Cos A = (8² + 3² - 8²) / [(2)(3)(8)]

= 3/16.

A = inverse Cos (3/16)

= 79.193°.

Area of triangle = 1/2 ab Sin C (we'll just use letter A instead of C)

= 1/2 (3)(8) sin (3/16)

= 11.8 cm².

another way you can find it is by this simpler method:

think of one side of 8, the side of 3 and the height that you do not know by using Pythagoras' Theorem for right-angled triangle. (a² + b² = c²). go halfway up the '3' side, then cut across straight to where the '8' sides meet. we now have right-angled triangle. let's call the height you don't know h.

we have 1.5² + h² = 8²

h² = 8² - 1.5²

h² = 61.75

h = √61.75

so area = 1/2 X 1.5 X √61.75

= 11.8 cm²

After 9 months, both Plant A and Plant B will be 172 cm tall.

To find the number of months it will take for Plant A and Plant B to be the same height, we need to set up an equation. Let's use the variable "t" to represent the number of months.

The height of Plant A after t months can be represented as: 64 + 12t

The height of Plant B after t months can be represented as: 28 + 16t

To find the number of months when both plants will be the same height, we set the two expressions equal to each other:

64 + 12t = 28 + 16t

Simplifying the equation:

12t - 16t = 28 - 64

-4t = -36

Dividing both sides of the equation by -4:

t = -36 / -4

t = 9

Therefore, after 9 months, Plant A and Plant B will be the same height. To find the height they will reach at that time, we substitute t = 9 into either equation. Let's use the equation for Plant A:

Height of Plant A after 9 months = 64 + 12 * 9

= 64 + 108

= 172 cm

Therefore, after 9 months, both Plant A and Plant B will be 172 cm tall.

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