Answer:
Para el punto a. tenemos 312 elementos en el espacio muestral
Para el punto b. la probabilidad pedida es [tex]\frac{1}{26}[/tex]
Step-by-step explanation:
Comencemos explicando el principio de multiplicación. Supongamos que se tiene un experimento por etapas, es decir, una primera etapa que se puede llevar a cabo de '' [tex]x_{1}[/tex] '' maneras distintas, una segunda etapa que se puede llevar a cabo de '' [tex]x_{2}[/tex] '' maneras distintas y así sucesivamente hasta una etapa final que se puede llevar a cabo de '' [tex]x_{n}[/tex] '' maneras distintas. La cantidad total de formas de desarrollar todo el experimento se puede calcular como el producto de las distintas maneras en que se puede ejecutar cada etapa :
Formas de desarrollar todo el experimento = [tex]x_{1}x_{2}[/tex] ... [tex]x_{n}[/tex]
Para el punto a. del ejercicio vamos a utilizar este principio para calcular la cantidad de elementos del espacio muestral. La primera etapa del experimento sería el lanzamiento del dado y una segunda etapa el sacar una carta de una baraja de poker (52 cartas distintas). Entonces, para un dado tenemos 6 posibles opciones y cuando sacamos una carta podemos obtener 52 resultados distintos. Por lo tanto ⇒
[tex](6)(52)=312[/tex]
Tenemos un total de 312 elementos en el espacio muestral (todos distintos) y con la misma probabilidad de ocurrencia ya que suponemos que en el dado tenemos la misma probabilidad de obtener un uno, un dos, etc; así como en la baraja tenemos la misma probabilidad de sacar cada una de las cartas.
Para el punto b. utilizaremos el hecho de que estamos frente a un espacio muestral equiprobable y calcularemos la probabilidad del evento ''sale un número par en el dado y un AS en la baraja'' contando los casos favorables a este evento y dividiendo por la cantidad de elementos totales del espacio muestral. Podremos hacerlo de esta manera ya que el espacio muestral es equiprobable. Definimos para ello
[tex]A:[/tex] ''Sale un número par en el dado y un AS en la baraja''
[tex]P(A)=\frac{CasosFavorablesAlEventoA}{CasosTotales}[/tex]
Los casos totales son 312 (calculados en el inciso a.)
Los casos favorables al evento A se pueden escribir utilizando el principio de multiplicación como
[tex](3)(4)=12[/tex]
El 3 es por los tres números pares que podemos obtener del dado (estos números son el dos, cuatro y el seis).
El 4 se debe a la cantidad de ases en una baraja de Póker de 52 cartas (estos son el as de corazones, el as de picas, el as de trébol y el as de diamantes).
Reemplazando en la expresión de [tex]P(A)[/tex] obtenemos :
[tex]P(A)=\frac{12}{312}=\frac{1}{26}[/tex]
Otra forma de haber calculado esta probabilidad es utilizando el hecho de que tirar el dado y sacar una carta de la baraja son dos eventos independientes. Por ende, la probabilidad se puede calcular como el producto de la probabilidad parcial de cada evento. Esto es :
B : ''Sale un número par en el dado''
C : ''Saco un as en la baraja''
[tex]P(B)=\frac{3}{6}=\frac{1}{2}[/tex]
Tres casos favorables a que salga un número par de seis posibles.
[tex]P(C)=\frac{4}{52}[/tex]
Cuatro casos favorables a obtener un as de la baraja de 52 casos posibles.
Ahora escribimos
P ( B ∩ C ) = P(B).P(C)
Por ser B y C dos eventos independientes. Entonces
[tex]P(B)P(C)=(\frac{1}{2})(\frac{4}{52})=\frac{1}{26}[/tex]
Obteniéndose la misma probabilidad ya calculada.
Working together, two pumps can drain a certain pool in 3 hours. If it takes the older pump 9 hours to drain the pool by itself, how
long will it take the newer pump to drain the pool on its own?
Do not do any rounding.
Type the correct answer in the box.
C
square units.
m
AADC is formed by reflecting AABC across line segment AC, as shown in the figure.
If the length of AC is 4 units, the area of AADC is
The area of ΔADC is equal to 6 unit².
What is the triangular area formula?The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h.
A abc = A adc because the areas of the initial and reflected triangles are equal.
Using the formula area=1/2 base height, determine the area of triangle ABC.
ABC in a triangle:
base = 4 units + AC
height = 3 units + BE
AΔ= abc = 1/2×4×3 =6 unnit²
Hence,
ΔADC = 6 unit²
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Plz help me with this worksheet, I will give brainliest
Answer:
Step-by-step explanation:
You don't seriously want someone to answer all those problems, do you?
I will tell you that you need to use the Pythagorean theorem, the side relationship in a 30-60-90 and a 45-45-90 triangle. Get off your rear and go for it!!!
HOW TO DO THIS QUESTION PLEASE
9514 1404 393
Answer:
£6/h
Step-by-step explanation:
Molly is paid £280 for 35 hours' work, so
£280/(35 h) = £8/h
In the next 5 hours, her pay jumps to £350, so she earns at a rate of ...
(£350 -280)/(5 h) = £70/(5 h) = £14/h
The difference in her pay rates is £14/h -£8/h = £6 per hour.
Plz, help me with this question!
Answer:
I think D is right, because usually congruent angles have the same angle measure, and there's no answer choice for 1 and 3.
The data below shows the survey result of 75 randomly selected students.
The school has 1,138 students total. Based on the results of the poll, how many of the school's students should be expected to travel by car? Round your answer to the nearest whole number.
Show your work using the sketch board OR you may insert an image of your work on the following slide.
Chart relating to the question is attached below.
Answer:
349 students
Step-by-step explanation:
Based on the chart given, we can obtain the experimental probability or proportion for the travel plan of 75 students :
Proportion who would be traveling by car :
Number traveling By car / number of samples
p(car) = 23 / 75 = 0.30666
If total number of students = 1138
Using the proportion obtained from the sample, the number of students who would be traveling by car from the population would be :
= 0.30666 * 1138
= 348.98 students
= 349 students
what number comes next in 18,30,48,72,96
Step-by-step explanation:
the answer is 108 because your counting by 12
Answer:
Hello There!!
Step-by-step explanation:
I believe the answer is 108.
hope this helps,have a great day!!
~Pinky~
7m-8=3(2m+4)+m please help
Answer:
m=20
Step-by-step explanation:
Solve the equation:
7m - 8 = 3 ( 2 m + 4)
Multiply 3 and (2m+4)
7m - 8 = 6m + 12
Add 8 to each side
7m = 6m + 20
Subtract 6m from both sides
m = 20
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
What is an intractable problem?
Answer: A problem is said to be intractable if there is no efficient algorithm to solve it.
Intractable problems are common. We need to discuss how we approach it when we actually encounter it.
Step-by-step explanation:
How many colours do you need to colour a graph such that no adjacent vertices are of the same colour showed in the image below?
Conclusion : Provided the graph with a large number of vertices, we see that we are again faced with resorting to a systematic tracing of all paths, comparison of the neighbour's colours, backtracking, etc resulting in exponential time complexity once again.
It’s supposed to say true or false but can someone help giving brainliest
Answer:
True
Step-by-step explanation:
e^{i\pi} + 1 = 0
Simplifying and therefore meaning that the answer is true.
But in all seriousness 6*3 = 18
6*4a = 24a
So yes it is true :)
Forming Equations with a given variable
1. The ages of three cats are and. Their total age is
21. Determine.
The value of {a} in the given modelled statement equation is 5.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is that the ages of three cats are (a) , (a + 4) and (2a - 3). Their total age is 21.
We can model the given equation is -
(a) + (a + 4) + (2a - 3) = 21
a + a + 4 + 2a - 3 = 21
4a + 1 = 21
4a = 20
a = 5
Therefore, the value of {a} in the given modelled statement equation is 5.
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{
Complete question is given below -
The ages of three cats are a, a+4 and 2a-3. Their total age is 21. Determine a.
}
elsa received a $80 dollar gift card for a coffee store. she used it in buying some coffee that cost $7.52 per pound. after buying the coffee, she had $34.88 left on her card. how many pounds of coffee did she buy?
Elsa purchased 6 pounds of coffee.
What is product pricing?The process of figuring out a product's quantitative worth based on both internal and external elements is called product pricing. Product price directly affects your company's entire success, including cash flow, profit margins, and client demand.
Here is an easy example of value-based pricing. When you bring a young child to a petting zoo, she expresses a desire to feed the goats. The goat food dispenser is topped off with a quarter. From a financial standpoint, there is the price of the goat food, which is around two cents.
Calculate the total cost of all the items you bought. To calculate the cost price, divide the total cost by the quantity of units purchased. To determine the ultimate price, use the selling price formula: Cost price plus profit margin equals selling price.
Since she started with $80 and ended with with $34,88, we can find the total amount she spent by subtracting these amounts:
$80 - $34.88 = $45.12
This means that she spent $45.12 on coffee. If each pound cost $7.52, we can divide $45.12 by $752 to see how many pounds she bought (ignoring tax):
45.12 / 7.52 = 6 pounds of coffee purchased
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Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool
The number of units that tile will he need to surround his pool is 19.82units.
this question is of quadratic equation ,
The number of units of tile simply refers to the perimeter.
So, we need to find all the sides of the rectangle.
Now, we have,
AB = 4.24 units
BD = 7.07 units.
So, we can find AD using pythagoras theorem.
So,
(AD)² + 4.24² = 7.07²
(AD)² + 17.978 = 49.985
(AD)² = 49.985 - 17.978
AD = √32.007
AD = 5.66 units
AD = BC = 5.66 units
Likewise, AB = DC = 4.24 units
Thus,
perimeter = 2(5.66) + 2(4.24) = 19.8 units.
The number of units that tile will he need to surround his pool is 19.82units.
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Jada earns $7 dollars per hour mowing her neighbors’ lawns. Name the two quantities in Jada’s situation that are in a functional relationship. Which did you choose to be the independent variable? What is the variable
The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works (independent variable) and the amount of money she earns (dependent variable).
The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works and the amount of money she earns. The number of hours worked is the independent variable because it is the variable that affects the amount of money earned. The amount of money earned is the dependent variable because this is the variable that is dependent on the number of hours worked.If she works 8 hours, she would earn $56.Jada earns $7 per hour, so if she works 3 hours, she would earn
$21 (3 x 7 = 21).
If she works 5 hours, she would earn
$35 (5 x 7 = 35).
If she works 8 hours, she would earn
$56 (8 x 7 = 56).
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when you multiply or divide a negative and a negative integer the product will be ? positive or negative?
Answer: The product of a positive integer and a negative integer is negative. RULE 2: The product of two positive integers is positive. RULE 3: The product of two negative integers is positive.
When you multiply a negative number by a positive number then the product is always negative
HOPE THIS HELPS
SUKHMANJOT
Ok can someone help me with this?
Answer:
1. 14
2. 2.83
3. 6.71
4. 8.77
5. 9.22
6. 5.20
7. 2.45
8. 19
9. I would love to help you with this but I don't know what it means by "circled problems"
Step-by-step explanation:
Answer:
Circle questions 2, 3, 4, 5, 6, 7
Simplified square root:
1. 14
2. 2.8
3. 6.7
4. 8.8
5. 9.2
6. 5.2
7. 2.4
8. 19
Step-by-step explanation:
I'm sure you can do the line plot. It's pretty mandatory.
Question #9:
If a number can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then it is said to be rational and if not then it is irrational.
If you don't understand how to draw a line graph then check the two photos as a guide. Hope it helped :)
If p(x) is a polynomial function with p ( 3/4 ) = 0 , which statement is true?
A.The function has a factor of (4x + 3).
B. The function has a factor of (4x – 3).
C. The function has a factor of (3x + 4).
D. The function has a factor of (3x – 4).
If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
If p(x) is a polynomial function with p ( 3/4 ) = 0
Then we need to find which of the given statements are true.
A. The function has a factor of (4x + 3).
If x=3/4 then 4(3/4)+3 which is not equal to zero
B. The function has a factor of (4x – 3).
If x=3/4 then 4(3/4)-3 which is equal to zero
C. The function has a factor of (3x + 4).
If x=3/4 then 3(3/4)+4 which is not equal to zero
D. The function has a factor of (3x – 4).
If x=3/4 then 3(3/4)-4 which is not equal to zero
Hence, If p(x) is a polynomial function with p ( 3/4 ) = 0 , then the function has a factor of (4x – 3).
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The equation x^3-5x=59 has a solution between 4 and 5. Use a trial and improvement method to find this solution. Give your answer to one decimal place. You must show all your working. On the same line as your final answer, you must write to "1 decimal place".
Answer:
The answer is "4.3".
Step-by-step explanation:
Given:
[tex]\to x^3 - 5x - 59 = 0[/tex]
When [tex]x = 4.1:[/tex]
[tex]\to f(4.1) = (4.1)^3 - 5(4.1) - 59 = -10.579[/tex]
When [tex]x= 4.2:[/tex]
[tex]f(4.2) = 4.2^3 - 5(4.2) - 59 = -5.912[/tex]
When [tex]x = 4.3:[/tex]
[tex]\to f(4.3) = -0.993[/tex] (closer to 0)
[tex]\to f(4.4) = 4.184[/tex]
It changes the sign so, the root lies in 4.3 and 4.4.When [tex]x = 4.35:[/tex]
[tex]\to f(4.35) = 1.563[/tex]
When the root is closer to 4.3 than 4.4 So, 1.563 is closer to zero than 4.184.
When [tex]x = 4.32:[/tex]
[tex]\to f(4.32) = 0.0216[/tex] close to zero.
So the answer is 4.3 to 1 decimal place.
Mrs Anderson has 185 pieces of wood he sold 25 peacas of wood to his neighbor and distract the rest of the world into piles around his house each pile of wood contained 40 pieces of wood which equation can be used to find peat the number of piles of wood Mr. Anderson made?
Answer: Let x be the number of piles of wood that Mr. Anderson made.
We know that he sold 25 pieces of wood to his neighbor, and the rest of the pieces of wood were divided into piles around his house, with each pile containing 40 pieces of wood.
Therefore, we can set up the equation:
185 pieces - 25 pieces = x * 40 pieces
Simplifying the equation:
160 = x * 40
To find the value of x, we need to divide 160 by 40
160/40 = x
x = 4
Therefore, Mr. Anderson made 4 piles of wood after he sold 25 pieces of wood to his neighbor.
It's worth noting that this equation was used to find the number of piles of wood Mr. Anderson made after selling 25 pieces to his neighbor, and assuming that he didn't use the rest of the wood for anything else except for making the piles.
Step-by-step explanation:
Mr. cole is shopping around to find a new gym. Fitness Extreme charges a flat fee of $30 plus $6 per session. Lift for Life charges a flat fee of $50 plus $2 per session. After how many sessions will the two gyms have the same cost?
Answer:
87$
Step-by-step explanation:
the volume of a cube is 64in squared (2). what’s the length of each side of the cube please help asap
Answer:
4in squared
Step-by-step explanation:
We know that cubes have equal parts all around, and it is basic knowledge for the most part to know 4x4x4 = 64. Therefore, each length must be 4, length, width,and height are all 4.
Read the passage. Bee Stings: The Aftermath You don't have to have a life-threatening allergy to have a negative response to bee stings. Many people experience uncomfortable itching and swelling when stung. But are such reactions merely an annoyance, or might they serve a purpose? Several years ago, researchers who study the immune system wanted to find out. To do this, they injected a group of mice with bee venom. Some of the mice had allergic reactions (such as swelling) to the venom, and others did not. Three weeks later, the researchers injected the same mice with venom for a second time—this time with a dose so large it could be deadly. They found that the mice who had previously had allergic reactions to the venom were much more likely to survive the potentially lethal dose. What is the main idea of the passage?
Researchers found that allergic reactions to bee venom can be as mild as swelling or as severe as death.
Researchers found that mild allergic reactions may help prevent severe reactions to the same allergin in the future.
Researchers found that bee venom courses allergic reaction in some mice but not others.
Answer:
Researchers found that mild allergic reactions may help prevent severe reactions to the same allergin n the future.
Step-by-step explanation:
I currently have this on IXL & I got it correct.
Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. 3 red marbles and 2 blue marbles What is the best prediction for the number of times that Ellen will draw a blue marble? Choose 1 answer:
The probability best prediction for the number of times that Ellen will draw a blue marble is 200.
Number of blue marbles: 222
Number of red marbles: 333
Total number of marbles: 555
Probability of drawing a blue marble:
222/555
= 0.4
Number of times drawing a blue marble:
300300300 x 0.4
= 120,120,120
Rounded to nearest whole number:
120,120
Ellen has a bag with 333 red marbles and 222 blue marbles in it. She is going to randomly draw a marble from the bag 300300300 times, putting the marble back in the bag after each draw. The best prediction for the number of times that Ellen will draw a blue marble is 200. This prediction is based on the fact that there are more red marbles than blue marbles in the bag. To calculate this, we first need to determine the probability of drawing a blue marble; there are 222 blue marbles out of 555 total marbles, so the probability is
222/555
= 0.4.
Multiplying this by the total number of draws (300300300) gives us 120,120,120. Rounding this to the nearest whole number gives us our prediction of 200 times.
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Three Baby penguins and their father were sitting on an iceberg 0.75 meters above the surface of the water. The father dove down 5.7 meters from the iceberg into the water to catch dinner for his kids. What is the father penguin's position relative to the surface of the water? Solve this problem and explain how you solved this problem and came to your answer.
A, B & C form the vertices of a triangle.
∠ CAB = 90°, ∠ ABC = 73° and AB = 9.4
Answer:
cos37= 9.4/BC,cos37=0.8
BC= 9.4/0.8
bc = 11.75
Answer:
BC ≈ 32.2
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos73° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{9.4}{BC}[/tex] ( multiply both sides by BC )
BC × cos73° = 9.4 ( divide both sides by cos73° )
BC = [tex]\frac{9.4}{cos73}[/tex] ≈ 32.2 ( to 3 sf )
According to the linear regression model, the men’s world record mile run time in 1940 would have been how many seconds?
The men’s world record mile run time in 1940 would have been 10.454 seconds
Here, the equation of the linear function that best fits the data (the line of best fit) is Finishing time = 10.878 - 0.0106(Year after 1900)
Let k be the finishing time in seconds and t be the number of years after 1900
So, the equation of regression line becomes,
k = 10.878 - (0.0106) t
To find the the men’s world record mile run time in 1940 first we find the the number of years (t)
t = 1940 - 1900
t = 40 years
So, the finishig time (k) would be,
k = 10.878 - (0.0106) × 40
k = 10.454 seconds
Therefore, the finishing time was 10.454 seconds
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help help help help help help help
The required point-slope form of the equation of the line is y - 20= -5(x + 1).
Given that, To determine an equation in point-slope form for the line that passes through the point with the given slope. point: (-2,-20) and m=-5.
What is the slope of the line?The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.To learn more about point-slope refer to:
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If the figure is translated 4 units left what are the coordinates
Answer: (-4,0)
Step-by-step explanation:
Answer: A
Step-by-step explanation:
- Left and right translations affect the x-coordinate
- subtract 4 from the x-coordinate
Which statement correctly identifies an asymptote of f (x) = StartFraction 16 x squared minus 35 Over x squared minus 5 EndFraction using limits?
Because Limit of f (x) as x approaches plus-or-minus infinity = 7, the function has a vertical asymptote at x = 7.
Because Limit of f (x) as x approaches plus-or-minus infinity = 7, the function has a horizontal asymptote at y = 7.
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a vertical asymptote at x = 16.
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.
Answer:
D
Step-by-step explanation:
Edge
The limit of x approaching infinite of a function gives it's horizontal assymptote. We use this to solve the question, getting the following answer:
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.
Horizontal asymptote:
An horizontal asymptote is the value of y given by:
[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]
In this question:
[tex]f(x) = \frac{16x^2 - 35}{x^2 - 5}[/tex]
The horizontal asymptote is:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{16x^2 - 35}{x^2 - 5}[/tex]
Considering it is a limit of x going to infinite, we just consider the terms with the highest exponents both in the numerator and in the denominator, so:
[tex]y = \lim_{x \rightarrow \infty} \frac{16x^2 - 35}{x^2 - 5} = \lim_{x \rightarrow \infty} \frac{16x^2}{x^2} = \lim_{x \rightarrow \infty} 16 = 16[/tex]
Thus, the correct answer is:
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.
From the graph of the function, given at the end of this answer, you can check that as x goes to infinity, y(green line) approches 16(blue line).
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What is the mole of H2?
One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.
What is mole?A mole is a unit of measurement in chemistry that expresses the amount of a substance. It is defined as the number of entities (such as atoms, ions, or molecules) in a sample of the substance. The number of entities in one mole of a substance is known as Avogadro's number.
What is Avogadro's number?Avogadro's number is a fundamental constant of physics and chemistry, defined as the number of atoms, ions or molecules in one mole of substance. It is approximately 6.022 x 10^23 and is used in many calculations in chemistry and physics, such as the number of atoms in a sample of an element, the number of ions in a salt, or the number of molecules in a gas sample. The constant is named after Amedeo Avogadro, an Italian scientist who first proposed the concept in 1811.
One mole of a substance is equal to Avogadro's number, which is approximately 6.022 x 10^23.
The mole of H2 (hydrogen gas) is the number of H2 molecules in a sample of hydrogen gas. One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.
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