Critical Thinking Consider a family with three children . Assume the prob- ability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5 and that the events "boy" and "girl" are independent . ( a ) List the equally likely events for the gender of the three children , from oldest to youngest (b) What is the probability that all three children are male ? Notice that the complement of the event " all three children are male " is "at least one of the children is female ." Use this information to compute the probability that at least one child is female .

Answer:

explain m ore

Step-by-step explanation:

a. Acceleration of the system (a) = 6.125 m/s^2

b. The tension in the rope (T) = 110.25

What is the definition of acceleration ?

Acceleration  defines that the rate at which velocity changes with time, in terms of both speed and direction.

For 30 kg mass

m . g - T = m . a

30 x 9.8  - T = 30. a   ⇒  (1)

For 10 kg mass

T - m base 2 g Sin θ = m base 2 a

T - 10 x 9.8 Sin 30° = 10 x a         ⇒  (2)

a. Adding equation (1) and (2)

    294 - 49 = 30 a + 10 a

    245 = 40 a

     a = 245/40

     a = 6.125 m/s^2

  Therefore, acceleration = 6.125 m/s^2

b. Sub a value in equation (1) we get,

    T = 110.25

   Therefore , tension in the role = 110.25

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Keith live 480 miles far way from the mountains.

The distance between two locations is represented by the length of the line linking them. If the two points are on the same horizontal or vertical line, subtracting the various coordinates will show how far apart they are.

Consider the provided information.

Keith drove to the mountains last weekend. The trip took 12 hours because of the high traffic on the way there.

Let the distance is D and average rate or speed is x miles.

Distance = speed × time

Substitute the respective values.

D = x  * 12

D= 12x

When Keith drove home, there was no traffic and the trip only took  

hours. The average rate was  8 miles per hour faster on the trip home,

The average rate or speed during return is x+20 miles.

Substitute the respective values in the above formula.

D = (x+20) ×8

D= 8x+160

Equate both the equations.

8x+160 = 12x

4x= 160

x=160/4

=40

Substitute the value of x in D= 12x

D=12(40)

D= 480

Hence, Keith live 480 miles far way from the mountains.

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The expected payoff from the raffle is given as follows:

$3.

The payoff is modeled by a discrete distribution, hence the expected payoff is the expected value of the said discrete distribution.

There are 500 tickets in the raffle, hence the probabilities are given as follows:

The expected value of a discrete distribution is calculated as the sum of all outcomes multiplied by it's respective probability, hence:

E(X) = 560 x 1/500 + 490 x 1/500 + 270 x 1/500 + 180 x 1/500 + 0 x 496/500 = $3.

(all the outcomes and their probabilities are taken from the distribution built in this problem).

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The measure of [tex]\angle 1[/tex] is [tex]60^{\circ}[/tex] because it is related to one of the angles of the triangle by the alternate interior angles theorem.

The measure of [tex]\angle 2[/tex] is [tex]120^{\circ}[/tex] because it is adjacent to one of the angles in the triangle.

Answer: C) $83.25

Step-by-step explanation: First you multiply 124 by whatever amount equivocates to 10,323 then multiply 1 by that same amount and you get the answer, 124 x 83.25 = 10,323, and 1 x 83.25 = 83.25

The number of days it will take the bacteria to multiply to 10,000,000 colonies will be 39,493.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

There were 700 provinces of microbes on day 1 of refined. With a development pace of 2.3. Then the equation is given as,

[tex]\rm A = 700 \times (2.3)^{t - 1}[/tex]

Then the number of days it will take the bacteria to multiply to 10,000,000 colonies will be given as,

[tex]\rm 10,000,000 = 700 \times (2.3)^{t - 1}\\[/tex]

Take log on both sides, then we have

(t - 1) × log 2.3 = 14,285.71

t - 1 = 39,492.99

t ≈ 39,493 days

The number of days it will take the bacteria to multiply to 10,000,000 colonies will be 39,493.

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Answer:

(-8, -10)

Step-by-step explanation:

(-4 + x)/2 = -6

-4 + x = -12

x = -8

(4 + y)/2 = -3

4 + y = -6

y = -10

Answer: (-8, -10)

The linear regression equation in this problem is given as follows:

y = 4.774x + 39.474.

Then the estimates are given as follows:

a) x = 3 hours: 53.8.

b) x = 4.5 hours: 61.

c) x = 13 hours: 101.5.

d) x = 1.5 hours: 46.6

The linear regression equation is obtained inserting the points of the table into a linear regression calculator.

From the table in this problem, the points are given as follows:

(0,39), (1,45), (2,52), (4, 49), (5, 61), (5,72).

Inserting these points into a calculator, the equation is given as follows:

y = 4.774x + 39.474.

Then the estimates are obtained with the numeric values, as follows:

a) x = 3 hours: y = 4.774(3) + 39.474 = 53.8.

b) x = 4.5 hours: y = 4.774(4.5) + 39.474 = 61.

c) x = 13 hours: y = 4.774(13) + 39.474 = 101.5.

d) x = 1.5 hours: y = 4.774(1.5) + 39.474 = 46.6.

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Answer:

Line t:  y = 1/9x + 8

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

The formula for finding the slope the line perpendicular to line s is:

[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the line we don't know (in this case, line t) and m1 is the slope of the line we're given (in this case, line s).

Currently line s is in point-slope form or

[tex](y-y_{1})=m(x-x_{1})[/tex].  Since m is the slope, we know that the slope of line s is -9.

By plugging in -9 for m1 in our equation, we have:

[tex]m_{2}=-\frac{1}{-9}\\ m_{2}=-\frac{1}{9}[/tex]

Since we know -1/9 is the slope of line t, we can plug this in for m and (9,9) for x and y in the slope-intercept equation to find b:

[tex]9=1/9(9)+b\\9=1+b\\8=b[/tex]

Thus, the equation of line t in slope intercept form is y = 1/9x + 8

Answer:

2. C

3. BCEF

4. C

Step-by-step explanation:

2. In a function, the x value cannot have two y values (for example: if the points are (1,2) and (1,3) then that is not a function).

In this question, none of the x values repeat with multiple y values, so it is a function. the answer is C.

It is not D, because not all straight lines are functions. If the straight line is vertical, then there is only one x value and it has infinitely many values for y. So, not all straight lines are necessarily functions.

3. Range is the y values. The points are (3,4), (-2,3), (7,1), (2, 1/2)

Here, the y values are 4, 3, 1, and 1/2

Choices B,C,E,F are the answers.

4. If the domain is x[tex]\geq[/tex]0, then 0 is the lowest we can plug into x.

y=2(0)+6

y=6

So, the answer is C. y[tex]\geq[/tex]6

You were on the right track :)

Answer: You would have eaten 31/32 of the pizza.

Step-by-step explanation:

1/2 + 1/2^2+1/2^3+1/2^4+1/2^5 =

1/2(1-(1/2)^5)/1-1/2 =

1-1/32=

31/32

good question.

Answer:

[tex]2\sqrt{281}[/tex] inches

Step-by-step explanation:

Using the 3D Pythagorean theorem, the diagonal has length [tex]\sqrt{32^2+6^2+8^2}=2\sqrt{281}[/tex] inches.

The markup from cost to sale price is $135.

What is the cost price?

Cost price, for instance, equals selling price plus profit ( when selling price and profit are given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given ).

Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)

Given the selling price of the item = $650

The cost = $450

Therefore,

10% × $650 = $585

$585-$450=$135

Hence,  the markup from cost to sale price is $135.

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Complete question:

The selling price of an item is ​$650 It is marked down by 10%, but this sale price is still marked up from the cost of ​$450.Find the markup from cost to sale price.

The number of hours will be 10 hours if Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Eliza has = 14 + 7x

x is the number of weeks

For Sahana:

y - 8.40 = (16.80-8.40)/(2-1)[x - 1]

y = 8.4x - 8.4 + 8.4

y = 8.4x

14 + 7x = 8.4x

x = 10 hours

Thus, the number of hours will be 10 hours if Eliza and Sahana have agreed to go to the movies the weekend after they have earned the same amount of money.

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Based on the information given the constant of variation is 11.67.

What is the rate of change?

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time

by using this formula

Constant of variation = Amount earned/Time

Where:

Amount earned=$175

Time=15 hours

Let's plug in the formula

Constant of variation=$175/15

Constant of variation=11.66

Constant of variation=11.67 (Approximately)

Hence, the constant of variation is 11.67.

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Using the Pythagorean Theorem for the right angled triangles and observing the given figure, The value of x can't be solved because the hypotenuse must be the longest side of the right angled triangle which is violated in this question.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees.

The required formula is:

[tex]h^{2}=p^{2}+b^{2}[/tex]

In the triangle, Hypotenuse is not the biggest side. So, We can't solve for the value of x.

[tex]10^{2} = 15^{2}+x^{2}[/tex]

[tex]x=\sqrt{10^{2}-15^{2}}[/tex]

which yields a negative number inside square root which is not possible to solve.

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D is the midpoint of AC, and E is the midpoint of BC, hence the value of x for the given problem will be 9 units.

If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same shape but may not be the exact same size. According to the fundamental principles of triangles, two triangles are said to be congruent if their size and shape are the same, but two triangles are said to be similar if their shape is the same but their sizes differ. The proportions of similar triangles are the same.

Here,

Since these are similar triangle,

BE=EC

BC=BE+EC

BC=2BE

6/(3x-15)=1/2

12=3x-15

3x=27

x=9

The value of x for the given problem where D is the Midpoint of AC and E is the midpoint of BC will be 9 units.

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Answer:1235160000 beats

Step-by-step explanation:

There are 525600 minutes in a year

47*525600= 24703200

24703200*50= 1235160000

The answer to Question based on Conversion of Units is 1008gm

What is Conversion OF Units?

It is a method to convert units from one version from another.

Solution:

Here in this Question we must know the conversion that 1 ounce is nearly equal to 28gms

Hence if Doreen Schmidt needs to prepare 36 ounces of 11% solution he needs to have exact measurement of chemicals

Hence we can say must have that 36 ounces of chemicals to make that

Hence by unit conversion 36 multiplied by 28 which comes out to be 1008gm of chemical he needs to have

to make 11% solution

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1 meter and 59 centimeters.

The longest side in a right triangle is called the hypotenuse. In other terms, the hypotenuse is the side that faces the right angle.

theorem of Pythagoras

[tex]a^{2} +b^{2} = c^{2}[/tex]

A is a right triangle's side.

B is the right triangle's side.

c = hypotenuse

Think of a right triangle where the height and distance are the legs and the hypotenuse is the rope.

We are aware that:

cos(45°) =x/10

cos(30°) =y/10,

where x represents the distance between the ship and the dock at low tides and y represents the distance during high tides.

We are searching for the y-x distance difference (since it will be farther away during high tides).

Using the previous equations:

x=cos(45°) and y=cos(30°)

Hence:

y - x = 10(cos(30°) - cos(45°))

Hence, the exact value of the distance is 10(cos30° - cos45°)

Using a calculator, this is approximately 1.59 meters.

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Answer:

60

Step-by-step explanation:

Step-by-step explanation:

y = 3.52x

This equation states that the total amount paid, y, is equal to 3.52 multiplied by the number of pounds of potatoes, x.

The equations will be 20x and 500w.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, when offered a job in sales where you can choose to either make a salary $500 (constant) every week or commission of $20 per sale. This will be:

Let the sales be x

The equation will be:

= 20 × x

= 20x.

The second equation will be:

= 500 × w

where w = number of weeks.

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The second place player must earn 0.0467 points per game in each of the next three games to take the lead in this category.

What is PPG Statistics?

First, calculate the PPG earned by the current leader of the season.

The total points earned by the current leader amount to 2112 and he had participated in a total of 77 games.

The following formula can be used to determine the PPG earned by the current leader per game,

PPG = Total Points / Total Games

[tex]\implies PPG=\frac{2112}{77}\\ \implies PPG = 27.42[/tex]  -----(1)

Now, calculate the PPG of the player who is ranked in the second place for the season.

The total number of points earned by the second place player is 2020 and he played a total of 74 games.

The second place player earned the following points per game,

PPG = Total Points / Total Games

[tex]\implies PPG=\frac{2020}{74}\\ \implies PPG = 27.29[/tex]  ---(2)

The difference in score with the leading team can be found by subtracting (2) from (1),

[tex]\implies 27.42-27.29=0.13[/tex]

So, to be the leading player, the second place player must obtain a lead of 0.14 points per game in the next three games if the current player plays no more games.

In such a situation, the total PPG of the player should be 27.43 and the number of games to be played is 3.

So, the number of points required to take lead can be calculated as,

PPG = Total Points / Total Games

[tex]\implies 27.43=P/3[/tex]

So, the Total Points required, [tex]P=27.43 \times 3 =82.29[/tex]

And, the PPG required by the second place player to score in each of the next three games is calculated as,

[tex]\frac{0.14}{3}=0.0467[/tex]

Therefore, the second place player must earn 0.0467 points per game in each of the next three games to take the lead in this category.

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Therefore, the equation that best fits these facts as the answer to this problem is y=661-0.1x.

The term "scatter plot" refers to a particular sort of graph in which the x- and y-axes are used to represent the values of two variables, with the dots that arise indicating any association between the data.

Given the correlation between the data at this moment and the graph provided in the question, y=661-0.1x is an equation that best captures the scatterplot's line of best fit.

y=661-0.1x is the equation whose solution best fits this data.

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