Consider another ubiquitous probability-course urn containing well-mixed black and white balls. There are 19 balls in total, 7 white and 12 black. 2 are chosen, one at a time and at random. Let X, be 1 if the ith ball selected is black, and 0 otherwise For parts (a) and (b), assume that the balls are selected without replacement (a) Calculate the conditional probability mass function X, given that X2 = 1 PXlXe (011) 7/18 PX1X2 (111)= 11/18 (b) Calculate the conditional probability mass function X, given that X2 = 0 2x1x2 (010) = PXix, (110) = For parts (c) and (d), assume that the balls are selected with replacement (c) Calculate the conditional probability mass function X, given that X2 = 1 Pax, (011) = 2x1x2 (111) = (d) Calculate the conditional probability mass function X1 given that X20 Park, (010) = 7x1x2 (110) =

The distance between the cars changes by 60.42mph.

Distance is a measurement of how far apart two objects or locations are. Distance in physics or common language can refer to a physical length or an assumption based on other factors. |AB| is a symbol that can be used to represent the distance between two points. "Distance from A to B" and "Distance from B to A" are frequently used interchangeably. A distance function or metric is a technique to describe what it means for elements of some space to be "close to" or "far away" from each other in mathematics. It is a generalization of the idea of physical distance. Through dimensions like time, space, and isolation, an object may be psychologically distanced from itself.

Calculations:

\(d=\sqrt{80^{2}+50^{2} } \\\)

d=94.34

1st car -- 40mph/hr

2nd car-- 50 mph/hr

The positions of cars at 4pm

Distance travelled by 1st car = 80m

Distance travelled by 2nd car = 50m

\(d^{2}=a^{2} +b^{2}\)

2d.dd/dt=2a(da/dt) +2b(db/dt) =d(dd/dt) =a(da/dt)+b(db/dt)=94.34(dd/dt)=50*50+80*40

dd/dt=(2500+3200)(94.34)  =60.419

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The answer that you are looking for is b) 5(a – 2)(a – 4). In order to factor the formula, we must first locate two numbers whose sum is equal to -30 and whose product is equal to 40. Both constraints are met by the values -4 and -10, and as a result, we are able to factor the statement as 5(a – 2)(a – 4).(option b)

The following procedures can be used by us while factoring polynomials:

Find two numbers that, when added together, give you the coefficient of the middle term, and then multiply those two values by themselves to get the constant term.

Create the expression as the product of two binomials, with each binomial having one of the two numbers discovered in step 1. Write the equation as a product of two binomials.

Eliminate any factors that are frequent.

In this particular instance, the coefficient of the intermediate term is -30, while the value of the constant term is 40. When added together, the numbers -4 and -10 equal -30, and when multiplied together, they equal 40. Therefore, the expression can be factored as 5(a minus 2)(a minus 4).

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The average speed for the first part of the trip is 60 miles.

Given:

1st leg DATA:

distance = 120 miles ;

rate = x mph ;

time = d/r = 120/x hrs

2nd leg DATA:

distance = 220 miles ;

rate = x-5 mph ;

time = 220/(x-5) hrs

hence the equation we frame is:

Equation:

120/x + 220/(x-5) = 6

120(x-5) + 220x = 6x(x-5)

120x - 600 + 220x = 6x² - 30x

-6x² + 340x + 30x - 600 =0

-6x² + 370x - 600 = 0

-3x² - 185x + 300 = 0

(3x-5)(x-60)

3x = 5 or x-60=0

x = 5/3 or x = 60

hence x-5 = 60-5

= 55 miles per hour.

Hence we get the answer as 60 miles.

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Answer:

22(c)

Step-by-step explanation:

Our current proportion is

15 miles

-------------

1 hour

We need feet per second.

Lets convert!

15 miles= 79200 feet(used googl to find this)

1 hour=3600 seconds(also used googl to find this)

( i know its not spelled that way brainly wont let me write the whole word out)

Now, our proportion is:

79200 feet

-----------------

3600 seconds

HOWEVER, this can be simplified!!!!

79200/3600=22

Final answer: 22, or C.

We can conclude that the number of possible schedules for next semester could she make is 7920.

In more mathematical terms, the factorial of a number (n!) is equal to

n(n-1). For example, if you want to calculate the factorial for four, you would write: 4! = 4 x 3 x 2 x 1 = 24.

Given that,

The student needs 11 more classes to graduate.

And, possible schedules for next semester could she make if she plans to take 4 classes

Based on the given expression, the calculation is as follows:

The combination formula is given to be:

\(n_{C} _{r} =\frac{n!}{r!(n-r)!}\)

= \(11_{C} _{4}\) ! * 4 !

= \(\frac{11 !}{4!(11-4)!}\)  * 4 !

= \(\frac{11!}{4!7!}\) * 4 !

= \(\frac{11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1*7*6*5*4*3*2*1}\) * 4 !

We can cancel the coefficients,

= \(\frac{11*10*9*8}{4*3*2*1}\) * 4 !

= \(\frac{7920}{24}\) * 4 !

= 330* 4 !

= 330 * 4*3*2*1

= 7920

Therefore,

We can conclude that the number of possible schedules for next semester could she make is 7920.

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Therefore , the solution of the given problem of volume comes out to be the response is 900 cubic units.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. These symbols for cubic dimensions are liter and in3. However, understanding an object's volume is necessary to calculate its measurements. It is standard practice to convert the weight of an object into mass units like grams and kilograms.

Here,

The formula V = Bh, when B is the area of the bottom and h is the height of the prism, determines the volume of a right triangle prism.

The prism has an area of because its foundation is a right triangle with 8 and 15-foot-long legs.

=> B = (1/2)bh = (1/2)(8)(15) = 60

The prism's height is specified as 15 inches.

As a result, the prism's capacity is:

=>  900 cubic units are equal to V = Bh = 60(15).

Therefore, the response is 900 cubic units.

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Answer:

900 cubic units

Step-by-step explanation:

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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If the composite functions f(g(x)) and g(f(x)) both equal to x, then the function g is the Inverse function of f.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. 

Let us take the Example.

Suppose f(x)= x/4 and g(x)=4x.

Let x=1

then f(g(x))= f(g(1))=f(4)=1

and g(f(x))=g(f(1))=g(1/4)=1

Here, f(g(x))=g(f(x))=1

Therefore , we can say that f(g(x)) and g(f(x)) are inverse of each other.

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Answer:

The length of the shorter leg of the triangle can be calculated using the Pythagorean Theorem. The formula is a^2 + b^2 = c^2, where a is the length of the shorter leg, b is the length of the longer leg and c is the length of the hypotenuse. In this case, a^2 + 52^2 = c^2. The hypotenuse can be calculated by using the sine formula. c = (52/sinA). Substituting this value into the Pythagorean Theorem equation, a^2 + 52^2 = (52/sinA)^2. Solving for a, a = sqrt(52^2 - (52/sinA)^2).

Answer:

\(\frac{x+8}{8} =5\)

(x+8)/8 = 5 (make sure you use the parentheses)

Step-by-step explanation:

The unknown number is 'x'.

\(\frac{x+8}{8} =5\)

(x+8)/8 = 5 (parentheses matter if you write it this way!)

(Add 8, then divide by 8, and the answer is 5.)

If you solve for x, the answer is 32.

You can double check that this works:

(32+8)/8 = 5

(40)/8 = 5

5=5

Answer:

the answer to your question is 9.73

Answer:

A

Step-by-step explanation:

Because according to my calculations there are supposed to be 5 digits and for the answers for the question A is the only letter with an answer with 5 digits.

My answer was 9.7325(even though the answers is different they still have the same number of digits) and for A it is 9.7324 which is another 5 digits.

Here is why I got 5 digits.

4.0125

5.7200

_______

When we add these we have to add 0er's to 5.72 because it doesn't have enough digits to add so you add zero's to it.

So 5 +0=5  2 +0=2  1 +2=3  0 +7=7  and for our last number 4 + 5=9 and so our answer is ?

9.7325

and the 9 = 1 digit 7=2 digit 3= 3 digits 2= 4 digits and last 5 = 5 digits.

Hope this helps have a great day:)

Based on the ratio, Anders uses 72.73g of sugar, 145.46g of butter, and 581.84g of flour to make his scones.

Anders makes scones using the ratio 1:2:8 for sugar, butter, and flour respectively. This means that for every 1 gram of sugar, he uses 2 grams of butter and 8 grams of flour.

To find out how much of each ingredient he uses, we can use the following steps:

1. Add the ratios together: 1 + 2 + 8 = 11

2. Divide the total amount of ingredients by the sum of the ratios: 100 + 300 + 400 = 800 / 11 = 72.73

3. Multiply each ratio by the result from step 2 to find the amount of each ingredient:

Sugar: 1 x 72.73 = 72.73g

Butter: 2 x 72.73 = 145.46g

Flour: 8 x 72.73 = 581.84g

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The statement cross-tabulation with two variables is known as twice-tabulation is false because there is no such term as "twice-tabulation" in the context of statistical analysis.

Cross-tabulation, also known as contingency table analysis, involves the analysis of categorical variables by creating a table that shows the frequency or distribution of one variable based on the levels of another variable.

It allows for the examination of the relationship between two variables, highlighting any associations or patterns that may exist. Each cell in the cross-tabulation table represents the count or proportion of observations that fall into specific combinations of categories from the two variables.

The term "twice-tabulation" does not exist in statistical literature and is not commonly used to refer to cross-tabulation with two variables. The correct term to describe this statistical technique is simply cross-tabulation or contingency table analysis.

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Answer:

0.607142857, = About 60 percent

Step-by-step explanation:

When the question says that much out of that, you divide by. For example, 99 out of 102, you do 99 divided by 102. Then just round to the nearest hundredth. So answer of that would be 97 percent.

Answer:

1.717

Step-by-step explanation:

Given :

We have to find value of m\(.\)

➠ 9(m + 5) - 3(m - 2) = 8m + 31

➠ 9m + 45 - 3m + 6 = 8m + 31

➠ 9m - 3m + 45 + 6 = 8m + 31

➠ 6m + 51 = 8m + 31

➠ 51 - 31 = 8m - 6m

➠ 20 = 2m

➠ m = 20/2

➠ m = 10

Je suis désolé, mais en tant que modèle basé sur du texte, je ne suis pas en mesure de créer des représentations graphiques ou de dessiner des figures. Cependant, je peux vous expliquer comment construire les points que vous avez mentionnés.

Pour construire les points dans cet exercice, nous avons besoin d'un quadrilatère ABCD. Voici les étapes pour construire les points demandés :

1) En bleu, le point D tel que ABCD soit un parallélogramme :

2) En vert, le point E tel que AEBC soit un parallélogramme :

3) En rouge, le point F tel que ABFC soit un parallélogramme :

Assurez-vous de suivre les étapes avec précision en utilisant une règle et un compas pour obtenir des résultats précis.\(\)

The coordinate of E will be (1, -3) if the coordinates of E if E divides CH three -fourths of the way from C to H

Midpoint of a line is a point that divides a line into two equal parts.

If the line is divided in the ratio a:b, then the midpoint formula will be expressed as:

\(M(X,Y) =(\frac{ax_1+bx_2}{a+b}, \frac{ay_1+by_2}{a+b})\\\)

Given the coordinate points, C(2, 1) and H(-2, 15) divided in the ratio of 3:4

\(X = \frac{3(2)+1(-2)}{3+1}\\X= \frac{6-2}{4}\\X=\frac{4}{4}\\X = 1\)

Get the coordinates Y:

\(Y = \frac{3(1)+1(-15)}{3+1}\\Y= \frac{3-15}{7}\\Y=\frac{-12}{4}\\Y= -3\)

This shows that the coordinate of E will be (1, -3)

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Hi! I'm happy to help!

To solve this, we first have to understand the terms and the way they arrange the equation.

First, we have the difference of ____and_____=. (the "is" after 4 refers to equals)

We will write this as:

_______-_______= ,because difference means subtraction.

For our first blank, we have 3 times a number. Because we do not know this number, we will use a variable.(n) 3 times a number is 3 multiplied by a number. We can just write 3n, because it represent multiplication.

3n-______=

Now, we see the part of the equation after the "and". We just see 4, so we can insert that here:

3n-4=

Now, we see what is shown after the "is".

We just have -19, so we can insert that here:

3n-4=-19

Now, let's solve (not sure if I need to):

To solve for n, we have to isolate it on one side of the equation. To do this, let's cancel out the -4 on the left side of the equation by adding 4 to both sides:

3n=-15

From here, we need to get rid of the 3 next to the n by dividing both sides by 3:

n=-5

So, we write it as 3n-4=-19, and n=-5.

I hope this was helpful, keep learning! :D

28 and 45 centimeters, because they are the two shortest sides.

Option D is the correct answer.

We have,

In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

In this case,

The side lengths given are 28 centimeters, 45 centimeters, and 53 centimeters.

To determine the lengths of the legs, we need to identify the two shorter sides.

In this triangle,

28 centimeters and 45 centimeters are the two shorter sides, and 53 centimeters are the hypotenuse.

We can verify that 28 and 45 centimeters are the lengths of the legs by using the Pythagorean theorem:

28² + 45² = 784 + 2025 = 2809

53² = 2809

The equation is satisfied, indicating that 28 and 45 centimeters are indeed the lengths of the legs in this right triangle.

Thus,

28 and 45 centimeters, because they are the two shortest sides.

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Step-by-step explanation:

Using Trignometry,

tan77° = Opposite/Adjacent = FG/GE.

Therefore FG = GEtan77°

= (2.6)tan77° = 11.3 feet.

Answer:

Rate r = 2500 cm^3 per minute.

the volume of water that flows from the tap each minute is 2,500 cm^3

Step-by-step explanation:

Given;

Dimension of fish tank = 40 cm by 25 cm by 24 cm

Volume of tank V = l×b×h = 40×25×24 cm^3

V = 24000 cm^3

From the question;

The fish tank is 5/8 full in 6 minutes

The volume of water in the tank in 6 minutes is;

V(6) = 5/8 × V = 5/8 × 24000

V(6) = 15000 cm^3

The rate of flow of water from tap per minute is;

Rate r = V(6) ÷ time

r = V(6) ÷ 6 minutes

r = 15000 ÷ 6

r = 2500 cm^3 per minute.

the volume of water that flows from the tap each minute is 2,500 cm^3

Answer:

5 people will get 3 tickets and one person will get 2.

Step-by-step explanation:

5x3= 15 , 2 tickets left.

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

For a graph, put the bottom(x) with the teachers and the side(y) with the number of students. Maybe that kind of helps?  You can choose how you want to space out the numbers on the side

Step-by-step explanation:

a pie chart is a circle with differently sized pizza slices designating how many or how much in every category in relation to the whole (the full circle).

a full circle = 360°.

the listed teachers together have obviously 200 students.

that means 200 is the whole, and correlates to 360° (everything takes the whole circle).

20 students for Michelle means then 20 of 200 :

20/200 = 1/10 = 360/10 = 36°

38 students for Rose Grace.

38/200 = 19/100 = 19×360/100 = 0.19 × 360 = 68.4°

28 students for Melanie.

28/200 = 7/50 = 7×360/50 = 7×36/5 = 50.4°

36 students for Joy.

36/200 = 9/50 = 9×360/50 = 9×36/5 = 64.8°

42 students for Josephine.

42/200 = 21/100 = 21×360/100 = 21×36/10 = 75.6°

36 students for Daisy.

36/200 = 9/50 = 9×360/50 = 9×36/5 = 64.8°

you need to draw a circle with the sectors having the listed degrees. of course, you round to the nearest full degree.

if done right, these sectors fill the whole circle.

The explanation of quadratic equation using the quadratic formula is

The resulting expression gives the solutions to the quadratic equation. If the discriminant is positive, you will have two distinct real solutions; if the discriminant is zero, you will have one real solution; and if the discriminant is negative, you will have two complex solutions.

Here, we have,

Explaining a quadratic equation using the quadratic formula:

Step 1: Write the quadratic equation in the standard form: ax² + bx + c = 0. Make sure that the equation is equal to zero.

Step 2: Identify the values of a, b, and c in the quadratic equation.

Step 3: Substitute the values of a, b, and c into the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Step 4: Simplify the expression inside the square root: b² - 4ac. This is called the discriminant.

Step 5: Calculate the discriminant to determine the nature of the roots:

If the discriminant is positive (b² - 4ac > 0), there are two distinct real roots.

If the discriminant is zero (b² - 4ac = 0), there is one real root (the roots are repeated).

If the discriminant is negative (b² - 4ac < 0), there are two complex roots.

Step 6: Calculate the square root of the discriminant (√(b² - 4ac)).

Step 7: Substitute the values of b, ±√(b² - 4ac), and 2a into the quadratic formula, and simplify the expression.

Step 8: The resulting expression gives the solutions to the quadratic equation. If the discriminant is positive, you will have two distinct real solutions; if the discriminant is zero, you will have one real solution; and if the discriminant is negative, you will have two complex solutions.

Let's consider an example to illustrate the steps:

Example: Solve the quadratic equation 2x² - 5x + 3 = 0.

Step 1: The equation is already in standard form.

Step 2: a = 2, b = -5, c = 3.

Step 3: Substitute the values into the quadratic formula: x = (-(-5) ± √((-5)² - 4(2)(3))) / (2(2)).

Step 4: Simplify the discriminant: (-5)² - 4(2)(3) = 25 - 24 = 1.

Step 5: Since the discriminant is positive, we will have two distinct real roots.

Step 6: Calculate the square root of the discriminant: √1 = 1.

Step 7: Substitute the values into the quadratic formula: x = (5 ± 1) / 4.

Step 8: Simplify the expression:

For the plus sign: x = (5 + 1) / 4 = 6 / 4 = 3 / 2.

For the minus sign: x = (5 - 1) / 4 = 4 / 4 = 1.

The solutions to the quadratic equation 2x^2 - 5x + 3 = 0 are x = 3/2 and x = 1.

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Solving quadratic equations can be done using three main methods: factoring, completing the square, and the quadratic formula. The quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), provides the solutions to any quadratic equation. The discriminant, b^2 - 4ac, determines the nature of the solutions.

There are three main methods to solve quadratic equations:

The quadratic formula is derived by completing the square on the general form of a quadratic equation. It provides the solutions to any quadratic equation in the form ax^2 + bx + c = 0. The formula is:

x = (-b ± √(b^2 - 4ac)) / (2a)

The discriminant, b^2 - 4ac, determines the nature of the solutions:

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Once you have computed the expected value, you can mark your guess on the graph by finding the point where the curve is balanced. This is the point where the area to the left of the point is equal to the area to the right of the point.

A probability density function is a function that describes the likelihood of a random variable taking on a certain value. The area under the curve of a probability density function must be equal to 1. The normalizing constant, denoted by k, is a constant that is multiplied by the probability density function to ensure that the area under the curve is equal to 1. In other words, k is the value that makes the integration of the probability density function equal to 1.

To find the value of k, you would need to integrate the probability density function over its entire range and set the result equal to 1. Once you have found k, you can sketch the density function by plotting the function on the y-axis and the possible values of x on the x-axis.

The expected value of a random variable is a measure of the center of its distribution. It represents the average value that the variable would take if it were repeated many times. To compute the expected value of a continuous random variable, you would need to integrate the product of the random variable and its probability density function over its entire range.

Once you have computed the expected value, you can mark your guess on the graph by finding the point where the curve is balanced. This is the point where the area to the left of the point is equal to the area to the right of the point.

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The width of a rectangular piece is 28 and the length is 58.

let us consider

w=width

w+30=length

After cutting:

w-12 =width

w + 30-12=length, or w + 18

Now to calculate the length and width consider the area of a rectangle:

Area of a rectangle=w*l

substitute the values in the above formula:

(w-12)(w+18)(6) = 2400

(w-12 )(w+18) = 400

w²+6w-216 = 400

w²+6w-616 = 0

(w + 28)(w - 22) = 0

The roots of the equation are {-22, 28}.

to find the length just substitute in the length formula:

length=28+30

length=58.

The width is 28 and the length is 58.

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