(2 points) conditional probability. a fair coin is tossed twice. (a) (1 point) what is the probability of two heads if we know that the first toss is a head? (b) (1 point) what is the probability of two heads if we know that at least one toss is a head?

Work Shown:

y+47 = 90

y = 90-47

y = 43

Given :-

To find:-

Answer:-

Firstly as we know that the measure of a straight line is 180° . The given line is made up of 3 angles , which are 47° , y° and one right angle i.e. 90°.

So the sum of all these angles will be 180° as these are the angles of a straight line.

So that,

[tex]\implies 47^o + y^o + 90^o = 180^o\\[/tex]

[tex]\implies 137^o + y^o = 180^o \\[/tex]

[tex]\implies y^o = 180^o-137^o\\[/tex]

[tex]\implies \underline{\underline{ y = 43}} \\[/tex]

Hence the value of y is 43 .

and we are done!

Answer: 0.4

Step-by-step explanation:

1/25 = 0.04 which is also 4% (.04 * 100)

The value of x is 20 degrees.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two two angles are two pairs of supplementary angles. Meaning that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

a ║ b, m∠3 = 5x + 10, and m∠5 = 3x + 10.

Thus interior angles are supplementary;

m∠3+ m∠5 = 180°

5x+ 10 + 3x + 10 = 180°

8x + 20 = 180

8x = 160

x= 160/8

x= 20°

Hence, the value of x is 20 degrees.

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Answer:

It has no solution.

Step-by-step explanation:

5(x - 2) = 8 + 5x

5x - 10 = 8 + 5x

5x = 18 + 5x

0 = 18

The variable cancels out, so there is no solution to substitute it for.

Answer:

2

Explanation:

you need to find the common denominators. Looking at the problem, there are 3 different denominators. 8, 16, and 4. To tell the difference, here they are bolder and italicized to see the difference.

1 3/8+13/16-3/16+2/8-1/4

We can combine the common denominators, leaving us with this:

1 5/8+10/16-1/4

Then you need to make the denominators the same, and since 4 times 2 is 8, you can multiply the numerator and denominator by 2 so the denominator is 8. Then since you can divide 16 by 2 and it equals 8, and the numerator is even, you can divide the numerator and denomorator by 2 so the denominator is also 8. This ends up looking like this:

1 5/8+5/8-2/8

Then you need to combine the common denominators again, leaving you with this:

1 8/8

You can simplify that to simply “2”

(From the start you can also take the 1 and make the original operation into 11/8+13/16 etc., but for this equation it was possible to leave it out until the end and only write it as a placeholder and reminder until the very end. Then at the end I added back in.)

If a woman's uncle has Lesch-Nyhan syndrome and her father carries the mutation, the probability of her first son being affected is 50%.

Lesch-Nyhan syndrome is an X-linked recessive genetic disorder, which means it is caused by a mutation on the X chromosome and is passed down through families primarily from affected fathers to their daughters. The probability that a son of a woman with an affected uncle (mother's brother) will be affected depends on the genetic status of the woman's father and the mother's X chromosome that she inherited from her mother.

If the woman's father does not carry the mutation, she will not carry the mutation herself and cannot pass it on to her children. In this case, the probability of her first son being affected is 0%.

If the woman's father carries the mutation, she has a 50% chance of inheriting the mutated X chromosome from her father and a 50% chance of inheriting a normal X chromosome from her mother. In this case, if the woman is a carrier of the mutation, her first son has a 50% chance of inheriting the mutation from her and being affected.

It's important to note that this is a simplified answer and that more complex genetic testing and counseling may be necessary to determine the specific risk in a particular family.

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A polynomial in standard form that represents the area of paper that can be painted is equals to the x² - 48x + 540.

We have, a painter wants to painting on a paper. He starts with a blank piece of rice paper with dimensions 30 inch by 18 inch .

The total length of paper, l = 30 inch

Total width of paper , w = 18 inch

Area of paper = l× w = 18× 30

= 540 inch²

Now, painter wants to leave a uniform border.

The width of border = x inches

length of border = x inches

and paint the remaining paper. So, the length of paper which is painted = l - x

= (30 - x) inches

Width of paper which is painted = w - x = ( 18 - x) inches

Now, the painted area of paper, A = painted length × painted width

= (30 - x)( 18- x)

= 540 - 18 x - 30x + x²

= x² - 48 x + 540

which is a standard polynomial form of painted area.

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Answer:

Please send a clearer image so I can answer question 1 and 3

Step-by-step explanation:

2: "One of the parallel lines can be translated so that it lands on the other line. After that, you would notice that the angles of the two lines have exactly the same measurement. Therefore, the interior and exterior angles of two parallel lines cut by transversal are equal."

5: The angles congruent to <8 are <6, <4, and <2

6: The value of m<6 = 70°

7: The equation to find <8 = 180 - <1

   The measure m<8 = 85°

8: The value of x must be equal to 34

There are 180 grams of cocoa in the resulting mixture.

When the 200 grams of dark chocolate and the 200 grams of milk chocolate are mixed together, the amount of cocoa in the mixture is found by adding the amount of cocoa in each type of chocolate.

First, the amount of cocoa in the dark chocolate is calculated by multiplying the total weight of the dark chocolate by its cocoa percentage:

200 grams(0.60) = 120 grams

Next, the amount of cocoa in the milk chocolate is calculated in the same manner:

200 grams(0.30) = 60 grams

Finally, the total amount of cocoa in the mixture is found by adding the amount of cocoa in each type of chocolate:

120 grams + 60 grams = 180 grams

Therefore, the total amount of cocoa in the resulting mixture is 180 grams.

The problem seems incomplete, it must have been...

"Luke melts 200 grams of dark chocolate that contains 60% cocoa and mixes it with 200 grams of milk chocolate that contains 30% cocoa. How many grams of cocoa are in the resulting mixture?"

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Answer:

75 degrees

Step-by-step explanation:

on the long line that goes out to 132 is a supplementary line so that means the angle next to 132 will make the line equal 180

180 - 132 = 48

so now we know the inside angles are 48 and 57

A triangle has 180 degrees in it so

x + 48 + 57 = 180

x + 105 = 180

x = 75

Answer:

200 seconds

Step-by-step explanation:

1 km = 1000m

3 km = 3000m

How long would it take to travel 3 km at a speed of 15 m/s?

The equation to solve this is:

Time = Distance / Rate

D = 3km or 3000m

R = 15 m/s

3000 divided by 15 = 200 seconds

So, it would take 200 seconds to travel 3 km at a speed of 15 m/s

Answer:

Below

Step-by-step explanation:

You need to have consistent units

  3 km = 3000 m

Distance / rate = time

 3000 m / 15 m/s = 200 seconds

The whole band gets 1/2 of the fee.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

The writer gets 4/12 of the fee, the singer gets 1/12 of the fee and the guitarist gets 1/12 of the fee, so the total fraction of the fee that the band members get is 4/12 + 1/12 + 1/12 = 6/12.

So, the whole band gets 6/12 or 1/2 of the fee. This means that half of the fee paid by the company goes to the band members, while the other half goes to other costs or expenses.

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The expression that represents the amount of money after t years when $10,000 is compounded quarterly at 12% interest is C. $10,000 (1 + 0.12)^4t.

The compound interest formula or equation for finding the final amount after some years of the principal compounded at an interest rate is given as follows:

Formula for the Final Amount:

A = P(1 + r/n)^{nt}

Where:

A = The Final amount

P = The initial principal

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Thus, the correct expression for finding the final amount after t years under the compound interest system is given by Option C.

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The value of x and y are 25 and 25√3 respectively.

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Given a right angled triangle and an angle 30°.

Length of hypotenuse = 50 units

Sine of an angle in a right angled triangle is the ratio of opposite side to hypotenuse.

sin (30°) = x / 50

x = sin (30°) × 50

x = (1/2) × 50

x = 25 units

Cosine of an angle in a right angled triangle is the ratio of adjacent side to hypotenuse.

cos (30°) = y / 50

y = cos (30°) × 50

y = (√3 / 2) × 50

y = 25√3 units

Hence the value of x is 25 units and the value of y is 25√3 units.

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The value of the given ratio for triangle ACE and BCD include the following:

1.)25/16

2.)10/7

3.) 1

4.) 14/19

5.) 4/5

6.) 4/1

7.) 16/5

8.) 29/45

In order to calculate the ratio, the value of the missing parts of the triangle should be calculated such as line BD, and CE, by the use of Pythagorean formula.

The Pythagorean formula = c² = a² + b²

For first triangle:

BC = a = 20

CD = b = 14

BD = c = ?

C² = 20²+14²

c² = 400+196

c² = 596

C = √596

C = 24 = BC

The ratio of the given sides of the triangle include the following:

1.) = AC = 20+5 = 25; CE = 25/16

2.) BC:CD = 20/14 = 10/7

3.) BD:AE = 24/24 = 1

4.) CD:CE = 14/19

5.) BC:AC = 20/25 = 4/5

6.) BC:AB = 20/5 = 4/1

7.) CD:DE = 16/5

8.) perimeter of BCD = 20+14+24 = 58; perimeter of ACE =25+24+21 = 70

The ratio of perimeter of BCD:ACE = 58/70 = 29/45

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The blanks are filled as follows

coordinate   key feature    does the coordinate        justification

                                                   make sense  

(-7.565, 0)   it is a key feature          yes                      This is a zero

(0, 37)          it is a key feature          yes                      it is the y - intercept

(6, 46)          it is a key feature          yes                      it is the vertex

The constraint is that the range will always be

{y | y ∈ R ≤ 46}

The vertex of a quadratic function is the highest or lowest point of the parabolic graph of the function, which is also the turning point of the graph.

The vertex of a quadratic function in the form of y = ax^2 + bx + c is given by the coordinates

(x, y) = (-b/(2a), -(b^2 - 4ac)/(4a)).

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In a linear equation, 9 cups of milk are needed to make 108 cookies .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

1 cup of milk makes 12 cookies.

If you wanted to make twice as many cookies (24), then you would need 2 cups.

If you wanted to make three times as many cookies (36), then you would need 3 cups.

1 cup / 12 cookies = X cups / 108 cookies

    1/12 = X/108

        X =  9

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The number of sides in the regular polygon would be -

n{sides} = 360/K.

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

The segments of a polygonal circuit are called its edges or sides.

Given is that exterior angle of a regular polygon measures {K°}.

In a regular polygon, the size of each exterior angle =

m∠E = 360° ÷ n{Sides}

m∠E = 360°/n{Sides}

n{sides} = 360°/m∠E

n{sides} = 360/K

Therefore, the number of sides in the regular polygon would be -

n{sides} = 360/K.

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The degrees in radian measures of the angle is 240 degrees or 4.188 radians.

The central angle of a circle is the angle formed by two of its radii. the two places on either side of the circle where the radii meet.

The angle measure between two consecutive numbers on a clock is 360/12 = 30 degrees.

At 2 the clock hand is at 2, the angle is:

30(2) = 60 degrees.

At 10, the angle is:

30(10) = 300 degrees

The angle between 2 and 10 is:

300 - 60 = 240 degrees.

Hence, the degrees in radian measures of the angle is 240 degrees or 4.188 radians.

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Answer:

156.8

Step-by-step explanation:

1.6 * 98

Answer: At 12:00 p.m., the minute hand points straight up at (0,10).

At 12:05 p.m., the minute hand has rotated 30 degrees clockwise. The tip of the minute hand would be approximately:

x = 10 * cos(30) = 8.66

y = 10 * sin(30) = 5

So, the coordinates would be approximately (8.66, 5).

At 12:45 p.m., the minute hand has rotated 180 degrees. The tip of the minute hand would be approximately:

x = 10 * cos(180) = -10

y = 10 * sin(180) = 0

So, the coordinates would be approximately (-10, 0).

At 12:55 p.m., the minute hand has rotated 330 degrees clockwise. The tip of the minute hand would be approximately:

x = 10 * cos(330) = -5.77

y = 10 * sin(330) = -8.66

So, the coordinates would be approximately (-5.77, -8.66).

Step-by-step explanation:

The measure of 2D is five-halves the measure of ZY, the measure of each angle of the deck.

D and R are opposite sides & G and Y are also opposite sides.

So, we have:

∠D = ∠R = 5/2 ∠Y

and

∠G = ∠Y

The sum of angles is given as:

∠D + ∠G + ∠Y + ∠R = 360

Substitute values for ∠D, ∠G, ∠R

5/2 ∠Y + 5/2 ∠Y + ∠Y + ∠Y = 360

Multiply both sides by 2/14,

∠Y = 51.43

So:

∠G , ∠Y = 51.43

∠D = 5/2 ∠Y

∠D = 128.57

Therefore, measure of angle m∠D = 128.57°, m∠G = 51.43°, m∠R = 128.57°, m∠Y = 51.43°.

A parallelogram is a two-dimensional flat shape with four angles. The internal angles on either side are equal. The transversal's angles on the same side are supplementary, which means they sum to 180 degrees. As a result, a parallelogram's internal angles add up to 360 degrees.

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Answer:

Step-by-step explanation:

A reasonable number of pages Carlos can write in 5 hours is between 20 and 25 pages.

Therefore the answer is C.

First, we need to find the average number of pages Carlos can write in one hour by dividing the number of pages he can write in 3/4 hour by 3/4:

(3 to 4 pages) / (3/4 hour) = 4 to 5.33 pages per hour

So, we can see that Carlos can write between 4 to 5.33 pages in an hour.

Next, we'll multiply that number by 5 to find the number of pages he can write in 5 hours:

(4 to 5.33 pages/hour ) * 5 hours = 20 to 26.65 pages

Since we can say that, he reads between 20 and 26 pages.

Therefore, the reasonable number of pages Carlos can write in 5 hours is between 20 and 25, which corresponds to option C.

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The ratio of the area of the two similar figures is 9 : 16.

Based on the question above, by comparing side shape 1 with side shape 2.

6 : (6+2)

6 : 8

3 : 4

For the ratio of area between the two figures, you can square each one.

3 : 4 = 3² : 4² = 9 : 16

Similar polygons have the same angles and proportional sides. "Proportional" means that the lengths occur in equal proportions (e.g., if the base of triangle 1 is twice the length of the shortest side of triangle 1, then the base of triangle 2 is the length of triangle 2). twice the length of the shortest side).

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With the values sin x= 3/5 and sin y= 2/3 , where x and y are both in first quadrant, then after calculation sin(x + y) = (3 * √(7/9)) / 5 + 1/2.

To evaluate sin(x + y), we can use the identity sin(a + b) = sin a cos b + cos a sin b.

Given that sin x = 3/5 and sin y = 2/3, we have:

sin(x + y) = sin x cos y + cos x sin y

          = (3/5) * √(1 - (2/3)^2) + (√(1 - (3/5)^2)) * (2/3)

          = (3/5) * √(7/9) + (4/5) * (2/3)

          = (3 * √(7/9)) / 5 + (8/15)

          = (3 * √(7/9)) / 5 + (8/15)

          = (3 * √(7/9)) / 5 + (16/30)

          = (3 * √(7/9)) / 5 + (1/2)

          = (3 * √(7/9)) / 5 + 1/2

So, sin(x + y) = (3 * √(7/9)) / 5 + 1/2.

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Total 4 dummy variables would be needed to include this categorical variable in a regression model.

A regression analysis serves as the foundation for many types of forecasting and determining the effects on target variables. When you hear about studies in the news about fuel efficiency, pollution causes, or the effects of screen time on learning, a regression model is frequently used to back up their claims.

A dummy variable (also known as an indicator variable or simply dummy) in regression analysis is one that takes the values 0 or 1 to indicate the absence or presence of some classification impact that may be predicted to shift the result.

Total 4 dummy variables would be needed to include this categorical variable in a regression model.

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Answer:

command+shift+3

Step-by-step explanation:

hope this helped :)