The sample space for drawing 3 marbles from a bag of 8 marbles is 56. This is determined using the combinations formula in statistics and probability, which takes into account the number of items and the number of draws.
Explanation:The question you're asking relates to the concept of combinations in probability and statistics. When Pablo picks three marbles from a bag of eight marbles without replacement, he changes the number of possibilities with each draw. The sample space of his experiment consists of all possible outcomes he could get when drawing the three marbles.
The number of outcomes is determined by calculating the combination of 8 items taken 3 at a time. The formula for combinations is:
C(n, r) = n! / r!(n - r)!
Substituting the given values:
C(8, 3) = 8! / 3!(8 - 3)!
C(8, 3) = 8! / 3!5! = (8 x 7 x 6) / (3 x 2 x 1) = 56
So, the sample space for this experiment contains 56 possible outcomes.
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The question is about calculating combinations in combinatorics, a topic in mathematics. For a bag containing 8 marbles and picking 3 at a time, there are 56 possible outcomes or ways in which the marbles can be drawn from the bag.
Explanation:The number of outcomes in the sample space can be found by multiplying the number of choices for each marble. In this case, Pablo is picking three marbles from a bag of eight marbles. The number of outcomes is determined by the combination formula: nCr = n! / (r! * (n - r)!). So, for Pablo picking three marbles from eight marbles, the number of outcomes in the sample space is:
nCr = 8! / (3! * (8 - 3)!)
nCr = 8! / (3! * 5!)
nCr = 8 * 7 * 6 / (3 * 2 * 1) = 56.
Therefore, there are 56 outcomes in the sample space.
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For either linear regression or multiple regression, the standard error of estimate can be computed as ____.
a. the square root of msresidual
b. the square root of msregression
c. msresidual/(n – 2)
d. msregression/(n – 2)
The correct computation for the standard error of estimate in regression analysis is the square root of the residual mean square (MSresidual), which is option a. This metric represents the average distance that data points fall from the regression line.
The standard error of estimate in regression analysis, whether it's linear regression or multiple regression, provides us with a measure of the accuracy of predictions made with the regression equation. It represents the average distance that the observed values fall from the regression line.
The correct formula for computing the standard error of the estimate is the square root of the residual mean square (MSresidual), which can be denoted as the square root of MSE or RMS/RMSE. Therefore, the correct answer to the question is a. the square root of msresidual.
This is because the MSE or MSresidual is the average of the squares of the residuals (or deviations of points from the regression line), while the standard error of the estimate is its square root, providing a measure of these residuals in the original units of the dependent variable.
Q # 13, write a rule for the linear function in the graph
What number should be added on both sides of the equation to complete the square x2 -6x =5
Answer:
We should add 9 on the both sides of the given equation.
Step-by-step explanation:
Since, for making a perfect square on the left side of a quadratic equation,
We add the square of the half of the coefficient of x on both sides,
The given equation,
[tex]x^2-6x = 5[/tex]
Here, the coefficient of x is 6,
Half of 6 = 3
Square of 3 = 9,
Thus, we should add 9 on the both sides of the given equation.
Verification :
[tex]x^2 - 6x + 9 = 5 + 9[/tex]
[tex](x-3)^2 = 14[/tex]
plz help and explain thanks
Use synthetic division and the Remainder Theorem to find P(a)
P(x)=x^4+10x^3+8x^2+4x+10 ; a=2
2
–114
56
146
What is 9.8 divided by 7
hayden delivers pizza for papa john's. His average tip is $1.50 for each pizza that he delivers. How many pizzas must he deliver to earn at least $20 in tips?
let us assume that the number of pizzas he must deliver = x
The tip obtained for one pizza = $1.50
Total tips that he must earn = 20
So, we frame the equation as shown below:
1.50*x = 20
1.50x = 20
x = 20/1.5 = 13.333
So he must deliver 13.333 pizzas
Since he cannot deliver fractional pizzas, the number of pizzas he must deliver = 14 pizzas
simple interest $4000 at 7% for 8 mo.
x 13 16 18 21 23 25 26 31
p(x) .07 .21 .17 .25 .05 .04 .13 .08
the mean of the discrete random value variable x is the 20.59. What is the variance of X?
Round your answer to the nearest hundredth
a 27.89
b27.89
c33.15
d23.18
The variance of a discrete random variable calculation involves working out (x-µ)^2 * p(x) for each x value and summing them up. Using given data and mean as 20.59, variance ≈ 27.89 (options a and b).
Explanation:To calculate the variance of a discrete random variable, we use the formula: Variance = Σ[(x-µ)^2 * p(x)] where 'x' is each value of the variable, 'µ' is the mean and 'p(x)' is the probability of 'x'
Given that the mean µ is 20.59 we perform the calculation, (x-µ)^2 * p(x) for each value of 'x' and sum them all up:
(13-20.59)^2 * .07 = 14.08(16-20.59)^2 * .21 = 4.38Continuing this process for all given values of 'x' and summing them up, we find that the variance ≈ 27.89.So, the correct answer is 27.89, which corresponds to option a and b.
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PLZ HELP ASAP TANGENTS OF CIRCLES PROBLEMS
Milt built a prism using a 3 unit cubes. He adds two more layers of 3 unit cubes each.how many unit cubes are used for the prism?
Milt used a total of 9 unit cubes to build his prism. This was calculated by multiplying the quantity of unit cubes in each layer (3 cubes) by the total number of layers (3).
Explanation:This is a Mathematics question about the concept of volume in prisms, specifically a cube. Milt starts by building a prism using 3 unit cubes and then adds 2 more layers of 3 unit cubes each. This means he has 3 layers of 3 cubes each.
We can calculate the total number of unit cubes used by multiplying the number of cubes in each layer by the number of layers. Here's the step-by-step calculation:
Start with quantity in a single layer: 3 unit cubes.
Multiply by the total number of layers to get the total quantity: 3 layers * 3 cubes/layer = 9 unit cubes.
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In 2012, the population of a city was 6.81 million. the exponential growth rate was 1.61% per year. a) find the exponential growth function. b) estimate the population of the city in 2018. c) when will the population of the city be 10 million? d) find the doubling time.
A pound of chocolate costs 7 dollars. Tiffany buys p pounds. Write the equation to represent the total cost c that Tiffany pays.
Final answer:
The equation to represent the total cost c that Tiffany pays for p pounds of chocolate, when a pound costs 7 dollars, is c = 7 × p. This is a simple linear equation with 7 as the price per pound.
Explanation:
The question asks to write an equation to represent the total cost c that Tiffany pays for p pounds of chocolate, with the knowledge that a pound of chocolate costs 7 dollars.
To find the total cost c, we simply need to multiply the cost per pound of chocolate by the number of pounds Tiffany buys. If each pound costs $7, then the equation showing the total cost for p pounds would be:
c = 7 × p
Where:
c represents the total cost
p represents the number of pounds of chocolate
This is a straightforward linear equation with the coefficient 7 representing the price per pound of chocolate.
PLZZZ HELP NOOOOWWW!!!
What is the probability that celia is first in line and felicity is last in line?
The probability of Celia being first and Felicity last in a line is found by multiplying the probabilities of each independent event. For a line of n people, it would be [tex](1/n) \(*\) (1/(n-1))[/tex]. For 10 people, this probability would be 1/90.
The scenario implies that there's a line of people, and we are interested in the probability of Celia being the first and Felicity being the last in this line. This is a combinatorial probability problem. To calculate the probability, we must first acknowledge that each person in the line is equally likely to be in any position. If we assume there are n people in total, the probability that Celia is first is 1/n, and once Celia is in place, assuming Felicity is not first, the probability that Felicity is last is 1/(n-1). Since these two events are independent (Celia being first does not affect the probability of Felicity being last), we multiply these probabilities together to find the combined probability.
Using the formula for independent events:
P(Celia first and Felicity last) = P(Celia first) * P(Felicity last given that Celia is first)P(Celia first and Felicity last) = (1/n) * (1/(n-1))If there are 10 people in the line, for example, the probability would be (1/10) * (1/9) = 1/90.
Annie is planning a business meeting for her company. her budget is 1,325 for renting the meeting room at the local hotel and providing lunch. she expects 26 people to attend the meeting the room cost $270 which inequality show how to find the amount × Annie can spend for lunch on each person
Answer:
26x + 270 ≤ 1,325
Step-by-step explanation:
Suppose x be the amount ( in dollars ) of lunch of each person,
So, the cost of lunch for 26 people = 26x,
Also, the cost of meeting room = $ 270,
Thus, the total cost = total cost of lunch + meeting room cost
= 26x + 270,
According to the question,
The budget of meeting is $ 1,325,
That is, the total cost can not exceed to $ 1325,
[tex]\implies 26+270 \leq 1325[/tex]
Which is the required inequality that will used to find the cost of each lunch.
What are the zeros of the function f(x) =(x^2 - 3x - 10)(x + 4)
!!Please help!!!
Two balls are drawn in succession out of a box containing 6 red and 6 white balls. find the probability that the second ball was red, given that the first ball was:
Final answer:
The probability that the second ball is red, given the color of the first ball, is 11/22.
Explanation:
To find the probability that the second ball was red, given that the first ball was either red or blue, we need to consider two cases:
If the first ball drawn was red: In this case, there are 5 red balls and 11 balls remaining. So, the probability of drawing a red ball as the second ball is 5/11.If the first ball drawn was blue: In this case, there are 6 red balls and 11 balls remaining. So, the probability of drawing a red ball as the second ball is 6/11.Since the first ball can be either red or blue with equal probability, we need to consider both cases. Thus, the total probability is (1/2) * (5/11) + (1/2) * (6/11) = 11/22.
Which of the following represents the zeros of f(x) = 6x3 − 35x2 + 26x − 5?
the answer choices are
A. -5, one third, one half
B. 5, negative one third, one half
C. 5, one third, negative one half
D. 5, one third, one half
if you laid 9 bolts end-to-end that each measure seven eighths of an inch, how long would that row of bolts be?
A card is selected at random from a standard 52-card deck. (a) what is the probability that it is an ace? 4/52 (b) what is the probability that it is a heart? .25 (c) what is the probability that it is an ace or a heart
I need help on this please
What is the area of the given circle in terms of pi? Diameter 6.6. Please Help
A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is h = -16t2 + 272t + 1344. When will the ball strike the ground?
Answer:
Time taken to reach the ball to the ground is 21 seconds.
Step-by-step explanation:
Given : A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is [tex]h = -16t^2 + 272t + 1344[/tex].
To find : When will the ball strike the ground?
Solution :
The equation for the ball's height 'h' at time 't' is given by,
[tex]h(t)= -16t^2 + 272t + 1344[/tex]
When the ball strike the ground the height of the ball became zero.
Substitute h=0 in the given equation,
[tex]-16t^2 + 272t + 1344=0[/tex]
Taking 16 common,
[tex]16(-t^2 + 17t + 84)=0[/tex]
or [tex]t^2-17t-84=0[/tex]
Solve by middle term split,
[tex]t^2-21+4t-84=0[/tex]
[tex]t(t-21)+4(t-21)=0[/tex]
[tex](t-21)(t+4)=0[/tex]
[tex]t=21,-4=0[/tex]
Reject t=-4 as time can never be negative.
Therefore, Time taken to reach the ball to the ground is 21 seconds.
Bristol is analyzing positive daily customer feedback on different restaurants to find the perfect place to invest. She would like to choose a restaurant with a high median of positive mark counts and a small interquartile range. She constructed box plots shown in the diagram below. Which restaurant has a median positive mark count above 75 and the smallest interquartile range? Burrito bros, pasta pals, make your own pie, pap smurfys
Answer:
A. Burrito Bros
Find the magnitude and direction (in degrees) of the vector. v = ‹ - sqrt(7)/9, - sqrt(2)/3 ›
PLEEZ HELP ME I AM STUCK AND I REALLY NEED THE ANSWER ASAP!!
A wooden block in the shape of a rectangular prism is cut into two congruent pieces. Which statement best compares the surface areas of the pieces to the surface area of the original block?
A. The surface area of each piece is equal to 1/2 surface area of the original block.
B. The surface area of each piece is equal to the sum of half the surface area of the original block plus half the area of the face created by the cut.
C. The surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut.
D. The surface area of each piece is equal to the surface area of the original block minus the area of the face created by the cut.
The option c is correct
What is rectangular prism ?A rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.
According to the question,
The surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut.
Hence, option c is correct for given condition.
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What is the area of this composite figure? 12ft2 80 ft2 88 ft2 100 ft2
If f(x) = x^2 and g(x) = 1/2x + 3, find g(f(-1)).
A.) -1
B.) 1/25
C.) 1/5
D.) 1
At the end of the past month the cash account of a company had an ending balance of 6750. During the last month the account was debited for a total of 11350 and credited for a total of 10500. What was the balance in the cash account at the of the last month