Which statements about this situation are true?

Probability of choosing the biased coin if you won a prize is 0.30

Let "B" be the event of selecting biased coin and "H" be the event of getting head.

P(B) = 0.5

P(getting head when coin was biased) = 100% - 78%

= 22% = 0.22

Using conditional Probability that biased coin was selected given that you have won the prize that is getting head

we have to calculate ,

P(B | H ) = P(B∩H)/P(H)

here , P(B∩H) = P(biased coin selected and getting head) = 0.5 × 0.22

and P(H) = P(getting head)

P(getting head when coin was biased) + P(getting head when coin was unbiased) = 0.5 × 0.22 + 0.5 × 0.5

putting all together ,

P(B | H ) = P(B∩H)/P(H) = 0.5 × 0.22 / 0.5 × 0.22 + 0.5 × 0.5

cancelling 0.5 from numerator and denominator

= 0.22 / 0.5+ 0.22

= 0.22 / 0.72 = 22/72

=0.30

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The first quadrant that lies between the circle x² + y² =4 is 1.09587

The graph of x² +y² = 4 is a circle of radius 2, centered at (0, 0). In polar coordinates, this equation becomes simply r = 0.

The second equation requires a bit more work. To convert it to a polar equation, we

substitute, r cos θ for x and r sin θ for y:

r²cos ²θ + r²sin ²θ

   = 2r cos Ф

⇒r² = 2r cos θ

⇒r = 2 cos θ

This is the polar equation for a circle of radius 1, centered at the point (x, y) = (1, 0). (This can be seen directly from the original equation by completing the square, which results in the equation (x − 1)²+ y² = 1.)

To describe the region between the circles in polar coordinates, we can let θ range from 0 to π/2. Our values for r should range from the smaller circle to the larger one

Recalling again that x = r cos θ and dA = rdrdθ, our integral becomes

∫ ∫ₐ  x DA  = 8/3 - π/2

We can get a rough check of this answer as follows. The area of the region D is easily computed to be π/2. The average value of the function x in the region is somewhat less than 1, since D is thicker on the left. Doing these sorts of visual estimates can be very tricky, but let’s say the average value of x in D is about 0.70. Thus

∫∫ₐ x dA ∼=π/2· 0.70 ∼= 1.09956

Since 8/3 − π/ 2∼= 1.09587, this estimate agrees quite well with our answer.

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The angle of half past eight between the hour and minute hands of a clock is 255°.

Given that,

We have to find look for the smaller angles half past eight between the hour and minute hands of a clock.

We know that,

The clock is in circle.

A clock has 12 different parts. Between any two divisions, there is a 30° angle. Each division is then divided into 5 equal pieces, each of which is divided by an angle of 60° and equals 1 minute.

We know the total angle of the circle is 360°.

So, 12 hours is 360°.

Then 1 hours is

1 hour= 360/12=30°

So, 1 hour is 30°

60mins=1 hour

60 mins = 30°

1 min =30/60

1 min=1/2

So,

8 hour and 30 min

(8× 1 hour)+( 30×1 min)

(8×30)+(30×1/2)

240+15

255°

Therefore, The angle of half past eight between the hour and minute hands of a clock is 255°.

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Answer:

C

Step-by-step explanation:

(-2x -9y^2) (-4x - 3)

= 8x^2+6x + 36y^2x+27y^2

False, one can tell if a data set is close to symmetric or not by watching a histogram.

             The histogram exhibit a symmetrical distribution of given data. The data is symmetrical if we are able to draw a vertical line at some point in the histogram such that its shape on both sides of the left and the right of the vertical line exactly reflected images to each other. The mean, the median, and the mode are can be taken as examples to prove the symmetricity using histogram for these data.  

         In an altogether symmetrical distribution, the mean and the median are alike. Such as the mode has one mode (unimodal), and the mode is the alike as the mean and median.

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Step-by-step explanation:

Please refer to photo for drawing

Answer: c = 30

Step-by-step explanation:

[tex]12=\frac{c-6}{2}\\ \\12(2)=c-6\\\\24=c-6\\\\c=24+6=30[/tex]

n/16 lies between 4/16 and 8/16

So, n can be 5,6,7

Answer:

5, 6 , 7

Step-by-step explanation:

Change 1/4 and 1/2 to the values they would be if their denominator was 16

1/4 will become 4/16

1/2 will become 8/16

the values between these are 5/16, 6/16, 7/16

n can be 5, 6 or 7

O Carys gets to Norwich station at 0750. To know how long will she have to wait for a train directly to Colchester.

Lets assume the values to be

a = 0848

b = 1 hour 2 minutes

c = 5 minutes

And let us look into it in detail as below

a = The first train arrive in London is 0848

b = Norwich to Colchester gets the trains in 1 hour 2 minutes

c = Carys gets to Norwich at 0750

So she need to wait for 5 minutes in a a train to get directly to Colchester.

Hence the answer is 5 minutes.

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Answer:

Step-by-step explanation:

EQUATION: F = km / d²100 = k(8) / (5)²100 = k 8 / 25100 ÷ 8 / 25 = k 8 / 25 ÷ 8 / 25625 / 2 = kF = (625 / 2)(2) / (15)²F = 625 / 225F = 25 / 9

Inequality: 23x + $8 ≤ $110

Inequality:

$110 = Amount of money they have

$8 = Parking Cost

$23 = Cost of tickets per person

23x + $8 ≤ $110

23x=$110-8

23x=$102

In mathematics, a courting among expressions or values that aren't the same as every other is referred to as 'inequality. This term is used to examine the significance, wide variety, and intensity of two values or expressions. Equations and inequalities are both mathematical sentences fashioned by using referring to two expressions for every difference. In an equation, the two expressions are deemed equal's shown with the aid of the symbol =.

whereas in inequality, the two expressions aren't necessarily the same that's indicated by means of the symbols: >, <, ≤ or ≥. Inequality is critical to poverty due to the fact the relative role of people or families in society is taken into consideration as a crucial aspect of their welfare.

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The solution of the mathematical statement is 102.5

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

"What is -5/2 times -41"

This means that

-5/2 times -41

Express as numbers

So, we have

-5/2 * -41

Divide 5 by 2

So, we have

-2.5 * -41

Evaluate the product

102.5

Hence, the result is 102.5

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The answer of resulting box volume = 576[tex]x[/tex] - 100[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]

What are example and volume?

The volume of an object serves as a gauge for its capacity. For instance, if the brim of a cup can hold 100 ml of water, that cup is said to have a 100 ml capacity.. Another way to quantify volume is how much room a three-dimensional object occupies.

Volume = length x breath x height

length = 32-2[tex]x[/tex]
Breath = 18-2[tex]x[/tex]

Height = [tex]x[/tex]

Volume = (32-2[tex]x[/tex]) x (18-2[tex]x[/tex]) x ([tex]x[/tex])

= 576 - 64[tex]x[/tex] - 36[tex]x[/tex] - 4[tex]x^{2}[/tex] x ([tex]x[/tex])

= 576[tex]x[/tex] - 100[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]
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Answer:

P(x) = $31x - $840

Step-by-step explanation:

Let x be the number of bicycles.  The total cost for purchasing and repairing the bikes is $47x, plus a one-time purchase of $840 for a workshop and tools.  Total cost, C is therefore:

  C(x) = $47x + $840

We learn Aidan sells the bikes for $75 each.  Total revenue, R, is:

  R(x) = $75x

Profit, P, would be the difference of revenue, R, and costs, C:

  P(x) = R(x) - C(x) or $75x -($47x + $840)

    P(x) = $75x -$47x - $840

    P(x) = $31x - $840

P(x) represents the total profit for x bicycles.

See the attached graph.  Note the key features of the graph are the breakeven (27 bikes) and the initial investment (-$840).  We can find the breakeven point by looking for the value of x when the profits are $0.  A more accurate determination can be found by solving the equation we developed for the case in which P(x) = $0:

P(x) = $31x - $840

0 = $31x - $840    for P(x) = 0 (breakeven)

$31x = $840

x = 27.1 units.  We need to round to 27 units since 0.1 of a bicycle makes no sense in this context.

The volume of a cone having the same radius and same height as that of the cylinder is equal to 100 cm³.

Given that:

The volume of a cylinder is 300 cm³.

We assume that,

The radius of the cylinder = radius of the cone = r cm.

Height of cylinder = height of cone = h cm.

We have to find the volume of a cone having the same radius and same height as that of the cylinder.

The formula for the volume of a cylinder is = π x radius² x height

The formula for the volume of a cylinder is = πr²h cm³ = 300 cm³ ..... (1)

We know that,

The formula for the volume of cone = (1/3) x π x (radius)² x h

Volume of cone = (1/3) x π x (radius)² x h

Volume of cone = (1/3) x (πr²h)

Putting the value of πr²h from equation (1).

Volume of cone = (1/3) * 300

Hence, the volume of the cone is equal to 100 cm³.

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The values of the variables x in the  equations are;

An equation is a mathematical statement that connects two mathematical expression with an equals sign.

x + 9 = 13

Subtracting 9 from both sides of the equation, we get;

x = 13 - 9 = 4

3•x = 12

Dividing both sides of the equation by 3, we get;

x = 12 ÷ 3

x + 5 - 9 = 0

Subtracting (5 - 9) from both sides of the equation, we get;

x = 9 - 5 = 4

2•x + 5 = 17

Subtracting 5 from both sides of the equation, we get;

2•x  = 17 - 5 = 12

2•x = 12

Dividing both sides of the equation by 2, we get;

x = 12 ÷ 2 = 6

5•x - 3 = 17

Adding 3 to both sides of the equation, we get;

5•x = 17 + 3 = 20

5•x = 20

Dividing both sides of the equation by 5, we get;

x = 20 ÷ 5 = 4

x - 3 = 1

Adding 3 to both sides of the equation, we get;

x = 1 + 3

7•x = 35

Dividing both sides of the equation by 7, we get;

x = 35 ÷ 7 = 5

[tex]\frac{4\cdot x}{4} = 4 [/tex]

Multiplying both sides of the equation by 4 and dividing the result by 4, we get;

x = 4 × 4 ÷ 4 = 4

3•(x + 4) = 15

Dividing both sides of the equation by 3, we get;

x + 4 = 15 ÷ 3 = 5

x + 4 = 5

Subtracting 4 from both sides of the equation, we get;

x = 5 - 4 = 1

8 + x - 5 = 7

Adding 5 and subtracting 8 from both sides of the equation, we get;

x = 7 + 5 - 8 = 4

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Answer:

Series calculator is a free online tool that gives the summation value of the given function for the given limits.

please make my answer as brainelist

The zeros of the cubic function f(x) = 2x³ - 6x² - 16x - 20 are given as follows:

x = 5, x = -1 + i, x = -1 - i.

The equation is defined by the rule presented as follows:

f(x) = 2x³ - 6x² - 16x - 20.

One solution for the equation is given as follows:

x = 5.

Because f(5) = 0.

Then (x - 5) is a linear factor of the function f(x), which can be written as follows:

2x³ - 6x² - 16x - 20 = (ax² + bx + c)(x - 5).

This is because the product of a linear function and a quadratic function results in a cubic function.

Now we expand the right side to begin finding the coefficients of the quadratic function that we are going to solve to find the remaining zeros:

2x³ - 6x² - 16x - 20 =  = ax³ + (b - 5a)x² + (c - 5b)x - 5c.

Then these coefficients are obtained comparing the left and the right side of the equality as follows:

Hence the equation is:

2x² + 4x + 4.

Using a quadratic equation calculator, the remaining zeros are given as follows:

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Answer:

D

Step-by-step explanation:

Since Δ QTS is isosceles then the base angles are congruent , that is

∠ TQS = ∠ QST = y

∠ QST and ∠ RST are a linear pair and sum to 180° , that is

∠ QST + ∠ RST = 180

y + ∠ RST = 180 ( subtract y from both sides )

∠ RST = 180 - y

the sum of the 3 angles in Δ TRS = 180° , that is

∠ RTS + ∠ TRS + ∠ RST = 180

∠ RTS + x + 180 - y = 180 ( subtract 180 from both sides )

∠ RTS + x - y = 0 ( subtract x - y from both sides )

∠ RTS = y - x

Answer:

  a.  9.56 × 10^3

Step-by-step explanation:

You want the sum (3.45 × 10^3)+ (6.11 ×10^3).

Distributive property

The distributive property works when adding numbers in scientific notation:

  (3.45 × 10^3)+ (6.11 × 10^3) = (3.45 +6.11) × 10^3 = 9.56 × 10^3

Answer:

14

Step-by-step explanation:

Check the file

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5(2)^2 - 6}[/tex]

[tex]\mathsf{= 5(2 \times 2) - 6}[/tex]

[tex]\mathsf{= 5(4) - 6}[/tex]

[tex]\mathsf{= 20 - 6}[/tex]

[tex]\mathsf{= 14}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{14}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Yes, he is correct

Step-by-step explanation:

100% : x

62%   : 19

Cross multiply

19*100% = 62%x

19 = 0.62x

19/0.62 = x

x = 30.645

Rounds up to 31

Answer:

-6

Step-by-step explanation:

-7 x -1 = 7

7 - 13 = -6

Answer:

Yes, the relation is proportional

Step-by-step explanation:

For a proportional relation, the ratio of X/Y (and thus Y/X) should be constant. You can verify, for examply dividing each Y by the corresponding X:

9 / -3 = -3

6 / -2 = -3

-3 / 1 = -3

-6 / 2 = -3

-9 / 3 = -3

As you can see, the ratio is the same, so the relation is proportional.

The student council sold $273$ t-shirts were sold at $\$10$ per shirt.

Let $x$ be the number of shirts sold at $\$10$

Let $y$ be the number of shirts sold at $\$12$

$x+y=661$

$10x+12y=3780$

$x=y+101$

$10y+12y=3780$

$22y=3780$

$y=172$

$x=172+101$

$x=273$

Hence $273$ t-shirts were sold at $\$10$ per shirt.

If they sold $661$ t-shirts in total, and they made a mistake when recording the amount of t-shirts sold at each price, then they actually sold more t-shirts at $\$10$ than they thought. This means that they thought they sold fewer t-shirts at $\$10$ than they actually did.

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Answer:

(-3,5)

Step-by-step explanation:

we just plug the solutions in the equation to see if it’s true

y<x+12

12<-4+12

12<8

Not true 12 is not less than 8

9<-7+12

9<5
not true 5 is not greater than 9

8<-5+12

8<7

Not true 8 is not less than 7

5<-3+12

5<9
true 5 is less than 9

Hopes this helps please mark brainliest

Answer:

Area under the curve f (x) = 38 on interval [88, 132]: 38 132 -3344 (Decimal: 1672)

Step-by-step explanation: