Answer:
1750ml
Step-by-step explanation:
2L=2000ml
2000-250
1750ml
Question content area top
Part 1
Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes be equal to 6 if she rolls the two number cubes 252 times?
A sample space is a collection or a set of possible outcomes of a random experiment and using it we know that Tamara should assume that the sum of the two dice is 5 x 20.
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment.
The sample space is represented using the symbol, “S”.
The subset of possible outcomes of an experiment is called events.
A sample space may contain a number of outcomes that depends on the experiment.
So, Let X = a number of times the sum of the two numbers on two cubes is 5.
Two numbered cubes are rolled n = 180 times.
The event of getting a sum of 5 in independent of the other results.
The random variable X follows a Binomial distribution with parameters n = 180 and n = 1/9.
Then,
E(X) = np
Calculate how many times Tamara expects the two dice to sum to 5 as follows:
= E(X) = np
= 180 * 1/9
= 20
Therefore, a sample space is a collection or a set of possible outcomes of a random experiment, and using it we know that Tamara should assume that the sum of the two dice is 5 x 20.
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Complete question:
Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes to be equal to 5 if she rolls the two number cubes 180 times?
is this a supplement or congruent
Answer:
The angles are supplementary.
List down three (3) equations that can be seen in the graph for each type of function and identify their
domain and range. Please helpp
constant funtion
Function,Domain,Range=
linear function
function,domain,range=
quadratic function
function,domain,range=
Equatiοns such as f(x) = x² - 4x + 3, f(x) = -2x² + 4x - 1, and f(x) = 0.5x² + 2x - 1 are examples.
what is functiοns ?A mathematical entity knοwn as a functiοn cοnverts an input frοm οne set (knοwn as the dοmain) tο a singular οutput frοm anοther set (called the range). A functiοn, then, is a rule that designates precisely οne οutput fοr each input in the dοmain. The nοtatiοn f(x), where f is the functiοn's name and x is the input value, is frequently used tο denοte a functiοn. Fοr instance, the functiοn f(x) = 2x + 1 takes any input x, dοubles it, adds 1, and returns the οutcοme.
Cοntinuοus Functiοn
Functiοn: If c is a cοnstant, f(x) = c
All real numbers dοmain
Range: {c}
Examples οf equatiοns are f(x) = 2, f(x) = -5, and f(x) = 0.
Linear Prοcess:
m is the slοpe and b is the y-intercept in the equatiοn f(x) = mx + b.
All real numbers dοmain
the entire real number range
Examples οf equatiοns include: f(x) = 2x + 1, f(x) = -3x + 5, and f(x) = 0.5x - 2.
Functiοn: where a, b, and c are cοnstants and a 0; f(x) = ax² + bx + c
All real numbers dοmain
Range: If a > 0 οr if a 0, then y | y h, where h is the vertex's y-cοοrdinate
Equatiοns such as f(x) = x² - 4x + 3, f(x) = -2x²+ 4x - 1, and f(x) = 0.5x² + 2x - 1 are examples.
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gabriel bought 16 pens 12 of the pens are blue what is
the percentage of the blue pens
Answer: 75%
Step-by-step explanation: 12 of 16 is expressed as 12/16. 12/16 is equal to .75 and a percent requires you to move the decimal place 2 to the right.
khloe walks from school 20 miles due west, 8 miles due north, and 3 miles due east how far is khloe from school?
The approximate distance between Khloe and school is given by 18.78 miles.
Representing Khloe's movements on a coordinate plane.
Let us assume that Khloe's starting point (her school) is at the origin (0,0).
She walks 20 miles due west,
which means she moves 20 units to the left on the x-axis. Her new position is (-20,0).
She then walks 8 miles due north,
which means she moves 8 units up on the y-axis.
Her new position is (-20,8).
Finally, she walks 3 miles due east,
which means she moves 3 units to the right on the x-axis.
Her new position is (-17,8).
Distance between Khloe's final position and her starting point (the school),
Use the Pythagorean theorem,
Distance = √((change in x)^2 + (change in y)^2)
⇒Distance = √((-17-0)^2 + (8-0)^2)
⇒Distance = √(289 + 64)
⇒Distance = √353
⇒Distance ≈ 18.78 miles
Therefore, Khloe is approximately 18.78 miles away from her school.
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a cube and a sphere both have volume 512 cubic units. which solid has a greater surface area? explain your reasoning.
If the cube and sphere both have volume as 512 cubic units, then the solid that has a greater surface area is Cube.
we first find the side length of the cube and the radius of the sphere.
The volume of the cube is 512 cubic units,
We have,
⇒ side³ = 512,
⇒ side = 8
So, the side length of the cube is 8 units.
Volume of sphere is also 512 cubic units,
We have,
⇒ (4/3)πr³ = 512,
On Simplifying,
We get,
⇒ r = 4.96 units.
So, radius of sphere is = 4.96 units.
Next we can find the surface area of each solid.
The surface-area of cube is = 6×(side)²,
⇒ 6(side²) = 6(8²) = 384 square units,
The surface area of the sphere is = 4πr²,
⇒ 4π(r²) = 4π(4.96²) ≈ 309 square units.
Therefore, the Cube has a greater surface area than the sphere.
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FELICIA CREATED A FLOOR PLAN FOR A PLAY HOUSE AS SHOWN BELOW WHAT WILL BE THE PERIMETER AND AREA OF FELICIA PLAY HOUSE
The perimeter of Felicia's playhouse is 60ft, and its area is 144ft².
In order to determine the perimeter and area of Felicia's playhouse, we must first analyze the provided diagram:
There are two rectangles and a triangle, therefore we must calculate the area of each shape, and then add the areas together to get the total area.
Area of Rectangle A = lw = 8ft x 10ft = 80ft²
Area of Rectangle B = lw = 4ft x 10ft = 40ft²
Area of Triangle C = (1/2)bh = (1/2)(8ft)(6ft) = 24ft²
Total Area = Area of Rectangle A + Area of Rectangle B + Area of Triangle C = 80ft² + 40ft² + 24ft² = 144ft²
To determine the perimeter, we must add up the lengths of all four sides of the rectangle and the three sides of the triangle.
P = 2l + 2w + a + b + c
P = 2(10ft) + 2(8ft) + 6ft + 10ft + 8ft
P = 20ft + 16ft + 6ft + 10ft + 8ft
P = 60ft
Therefore, the perimeter of Felicia's playhouse is 60ft, and its area is 144ft².
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Question
Felicia created a floor plan for a playhouse, as shown below. 2 ft 23 ft 7 ft 8 ft 844 What will be the perimeter and area of Felicia's playhouse?
Write a system of inequalities for each graph
a)System of inequalities of the graph is
y-x-2≤0
y-x+3≥0
b)System of inequalities of the graph is
y-x≥0
y+x≥0
c)System of inequalities of the graph is
y-1≤0
y-x-1≤0
define inequalityIn mathematics, an inequality is a statement that two quantities or expressions are not equal. Specifically, an inequality describes a relationship between two values, indicating whether one value is greater than, less than, or equal to another value.
Part a)First line coordinates
X y
-2 0
0 2
slope=2-0/0+2=1
Equation of line is y=x+2
Second line coordinates
X y
3 0
0 -3
slope=-3-0/0-3=1
Equation of line is y=x-3
System of inequalities of the graph is
y-x-2≤0
y-x+3≥0
Part b)First line coordinates
X y
0 0
-1 -1
slope=-1-0/-1-0=1
Equation of line is y=x
Second line coordinates
X y
0 0
1 -1
slope=-1-0/1-0=-1
Equation of line is y=-x
System of inequalities of the graph is
y-x>0
y+x≥0
Part c)First line coordinates
y=1
Second line coordinates
X y
0 1
-1 0
slope=0-1/-1-0=1
Equation of line is y=x+1
System of inequalities of the graph is
y-1≤0
y-x-1≤0
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What is the measure of JML
Answer:
94
Step-by-step explanation:
∠JKL and ∠JML are supplementary( they add to 180°).
Set their values equal to 180 to find the value of x.
15x - 19 + 13x + 3 = 180
Combine like terms
28x - 16 = 180
Add 16 to both sides to isolate the x
28x = 196
Divide both sides by 28
x = 7
Substitute the value of x into the expression for ∠JML
13(7) + 3 = ∠JML
91 + 3 = ∠JML
94° = ∠JML
To check our answer we can substitute the value of x into the expression for ∠JKL and if they add up to 180 we are correct
15(7) - 19 =∠JKL
105 -19 =∠JKL
86 =∠JKL
94° + 86° = 180°
Therefore we are correct
Find f'(x), where f(x)= (2√x+1){(2-x)/(x^2+3x)}
The derivative of f(x) of (2√x+1){(2-x)/(x^2+3x)}, is f'(x) = (-x^3+5x+6)/[x(x+3)^2√x].
To find the derivative of the function f(x) = (2√x+1){(2-x)/(x^2+3x)}, we can use the product rule and the quotient rule.
First, let's find the derivative of (2-x)/(x^2+3x):
f1(x) = (2-x)/(x^2+3x)
f1'(x) = [(-1)(x^2+3x)-(2-x)(2x+3)]/(x^2+3x)^2
= (-x^2-3x-4x+6)/(x^2+3x)^2
= (-x^2-x+6)/(x^2+3x)^2
Next, let's find the derivative of 2√x+1:
f2(x) = 2√x+1
f2'(x) = 2(1/2√x) = 1/√x
Using the product rule, we get:
f'(x) = f1(x)f2'(x) + f2(x)f1'(x)
= [(2-x)/(x^2+3x)](1/√x) + (2√x+1)(-x^2-x+6)/(x^2+3x)^2
= (2-x)/(x^2√x+3x√x) - (x^2+4x-6)/(x^2+3x)^2√x
= (2-x)/(x(x+3)√x) - (x^2+4x-6)/(x^2+3x)^2√x
Simplifying the expression, we get:
f'(x) = [(2-x)(x^2+3x) - (x^2+4x-6)x]/[x(x+3)^2√x]
= (-x^3+5x+6)/[x(x+3)^2√x]
Therefore, the derivative of f(x) is:
f'(x) = (-x^3+5x+6)/[x(x+3)^2√x]
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PLS HELP AND GIVE THE CORRECT ANSWER WITH EXPLANATION WILL GIVE BRAINIEST!!!
Answer:
Even
Step-by-step explanation:
Its even because a parabola as the equation of x^2, that is an even graph!
:)
Answer:
even
(sorry if it's wrong but I'm pretty sure it's even.)
Geometry 1. Which of the following may not be true? Select all that apply. A. If a point and a plane intersect, the intersection is a line. B. If two lines intersect, both lines are in one plane. C. If two lines intersect but do not coincide, the intersection is a point. D. If two planes intersect but do not coincide, the intersection is a line. E. If two points lie in a plane, then the line that contains the points is in that plane. F. There is exactly one line through any two points.
Answer:
There are two statements that may not be true:
B. If two lines intersect, both lines are in one plane.
F. There is exactly one line through any two points.
Statement B is not true because if two lines intersect at an angle, they are not in the same plane. This is known as skew lines.
Statement F is not true in non-Euclidean geometries, such as spherical or hyperbolic geometry. In these geometries, there can be multiple lines that pass through two points. However, in Euclidean geometry (which is what is typically taught in high school), there is exactly one line that passes through any two points.
Step-by-step explanation:
Answer: B. If two lines intersect, both lines are in one plane.
F. There is exactly one line through any two points
Step-by-step explanation:
The rest are true because I remember learning those in Geometry but B and F aren’t true because they just don’t make sense and aren’t true in general.
There are 18 flower seeds in each packet. Mr. Doyle buys 14 packets of seeds. How many flower seeds are in the 14 packets? 18 A (A) 612 seeds B) 252 seeds C222 seeds D 60 seeds
There are 252 flower seeds in the 14 packets that Mr. Doyle bought, which is option B.
What is Multiplication?
Multiplication is a mathematical operation that involves combining or adding a number to itself a certain number of times, resulting in a product that represents the total value of those added numbers. It is often represented using the "×" symbol or the asterisk symbol "*".
To find out how many flower seeds are in the 14 packets that Mr. Doyle bought, we can multiply the number of seeds in one packet by the number of packets he bought:
Number of seeds = 18 seeds/packet x 14 packets
Number of seeds = 252 seeds
Therefore, there are 252 flower seeds in the 14 packets that Mr. Doyle bought, which is option B.
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company xyz know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 16 years and a standard deviation of 1.4 years. find the probability that a randomly selected quartz time piece will have a replacement time less than 11.9 years?
The probability that a randomly selected quartz timepiece will have a replacement time less than 11.9 years is 0.0007 or 0.07%.
The given information is that a company XYZ knows that the replacement times for the quartz timepieces it produces are normally distributed with a mean of 16 years and a standard deviation of 1.4 years. We need to calculate the probability that a randomly selected quartz timepiece will have a replacement time of less than 11.9 years. Let us solve this problem using the standard normal distribution.
The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the given distribution into the standard normal distribution using the formula:
z = (x - μ)/σ
Where x is the replacement time, μ is the mean and σ is the standard deviation.
Putting the given values, we get:
z = (11.9 - 16)/1.4
z = -3.21
We need to find the probability that the replacement time is less than 11.9 years. This can be calculated as the area under the standard normal distribution curve to the left of z = -3.21.
Using the standard normal distribution table, we find that the area to the left of
z = -3.21 is 0.0007.
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SOMEONE PLEASE HELP ME WITH THIS ASAP <3
Answer:
Mohsin could be first, Yousuf could be second and luke could be third it doesn't matter really wich way roun it could be that yousuf is first or luke thirst.
Step-by-step explanation:
Which of the following options have the same value as
30
%
30%30, percent of
81
8181?
Choose 3 answers:
Choose 3 answers:
Answer: 30, 30%, 8181
Step-by-step explanation:
Step 1: I looked at the question and saw that it was asking which of the given options had the same value as 30%30 and 81 8181.
Step 2: I looked at the list of options and saw that 30, 30%, and 8181 all had the same value as the given numbers.
Step 3: I chose those three options as my answer.
HELPPPPPP MEEEEE PLEASEEEEEEEEE
Answer:6x-2y=8
Step-by-step explanation:
[tex]\left \{ {{3x-y=4} \atop {Ax-By=8}} \right. \\\frac{3x}{Ax} =\frac{y}{By} =\frac{4}{8}=\frac{1}{2}\\\frac{3}{A} =\frac{1}{2}\\A=6\\\frac{1}{B} =\frac{1}{2}\\B=2\\so, 6x-2y=8[/tex]
Answer:
6x - 2y = 8
Step-by-step explanation:
If:
3x - y = 4
⇒ 4* 2 = 8
then:
3*2 = 6
-1 * 2 = -2
The answer is:
6x - 2y = 8
please answer , I really need an answer
1/2 perecnt as decimal
Answer:
0.5
Step-by-step explanation:
trust me
Determine the values of x where the function f(x) is not continuous. Label each discontinuity as removable, jump or infinite. f(x)={1/2x+5. x<=2 { x+3. x>2 Enter your answers as integers in increasing order. If there are no discontinuities, enter NA in both response areas and select continuous in both drop-down menus. If there is only one discontinuity, enter NA in the second response area and select continuous in the second drop-down menu.
The values of x where the function f(x) is not continuous are x = 2, and the discontinuity at x = 2 is a jump discontinuity.
The function f(x) is defined as:
f(x) = {1/2x+5, x<=2
{x+3, x>2
To find the values of x where f(x) is not continuous, we need to check for three types of discontinuities: removable, jump, and infinite.
Removable discontinuity: This occurs when a function has a hole at a certain point, but can be made continuous by defining or redefining the value of the function at that point. In order for a discontinuity to be removable, the limit of the function as x approaches that point must exist.
To check for removable discontinuity, we need to check if the limit of the function as x approaches a certain point exists, but the function value is different from the limit. In this case, we only need to check the function at x = 2.
lim x->2- f(x) = lim x->2- 1/2x+5 = 6
lim x->2+ f(x) = lim x->2+ x+3 = 5
Since the limits from both sides are not equal, there is a removable discontinuity at x = 2. We can redefine the value of f(x) at x = 2 as 6 to remove the discontinuity.
Jump discontinuity: This occurs when the function has two distinct finite limits from both sides of a point, but the limits are not equal.
To check for jump discontinuity, we need to check if the limit of the function as x approaches a certain point exists from both sides, but they are not equal. In this case, we only need to check the function at x = 2.
lim x->2- f(x) = lim x->2- 1/2x+5 = 6
lim x->2+ f(x) = lim x->2+ x+3 = 5
Since the limits from both sides are not equal, there is a jump discontinuity at x = 2.
Infinite discontinuity: This occurs when the function approaches infinity or negative infinity as x approaches a certain point.
To check for infinite discontinuity, we need to check if the limit of the function as x approaches a certain point approaches infinity or negative infinity. In this case, there is no such point where f(x) approaches infinity or negative infinity.
Therefore, the values of x where the function f(x) is not continuous are x = 2, and the discontinuity at x = 2 is a jump discontinuity.
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Romain knows the following information about the 323232 classes he took in high school: He studied for but did not pass 333 classes. He passed 272727 classes in total. He studied for 262626 classes in total. Can you help Romain organize the results into a two-way frequency table? Studied for the class Did not study for the class Passed the class Did not pass the class
Classes studied for, Classes he did not study for Total
Classes Passed, 23 4 27
Classes Failed, 3 2 5
Total, 26, 6 32
Please find attached the two way frequency table formatted on Excel spreadsheet
the details provided are;
32 classes were taken by Romain in total during his high school years.
Three of the classes he attempted but failed to pass
27 out of the total classes Romain took and passed
26 classes were studied for by Romain.
Therefore;
26 - 3 = 23 is the number of classes Romain took, passed, and studied for.
32 - 27 = 5 is the total number of classes Romain failed.
Total classes Romain passed without paying attention: 27 - (26 - 3) = 4.
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find the equation of the parabola below:
The equation of the parabola that passes through (-4, 0) and (-2, 0) and has a touch point at (-3, -1) is: y = 4x² + 24x + 32.
What is an equation?
Since the parabola is symmetric with respect to the vertical line passing through the vertex (which is in the second quadrant), its axis of symmetry is the line x = -3.
Let's first find the vertex of the parabola. The x-coordinate of the vertex is simply the average of the x-coordinates of the two given points on the x-axis:
x = (-4 + (-2))/2 = -3
To find the y-coordinate of the vertex, we can use the fact that the vertex lies on the axis of symmetry. Therefore, it must also be the midpoint of the distance between the touch point (-3, -1) and the y-axis.
The distance between (-3, -1) and the y-axis is 3 units. Therefore, the y-coordinate of the vertex is:
y = -1 - 3 = -4
So the vertex of the parabola is V(-3, -4).
Since the parabola is open in the second quadrant and its vertex is in the second quadrant, its equation has the form:
y = a(x + 3)²- 4
where a is a positive constant that determines the "steepness" of the parabola.
To find the value of a, we can use one of the given points on the x-axis. Let's use (-2, 0):
0 = a(-2 + 3)² - 4
4 = a
Therefore, the equation of the parabola is:
y = 4(x + 3)² - 4
or
y = 4x² + 24x + 32
So the equation of the parabola that passes through (-4, 0) and (-2, 0) and has a touch point at (-3, -1) is:
y = 4x² + 24x + 32.
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Complete question is: The equation of the given parabola is: y = 4x^2 + 24x + 32.
Find the missing length.
Answer:
The missing length is 45
Step-by-step explanation:
CD || AB
[tex]\mathrm{\cfrac{EC}{AC} =\cfrac{ED}{BD} }[/tex]
[tex]\mathrm{\cfrac{20}{8} =\cfrac{?}{18} }[/tex]
[tex]\mathrm{\cfrac{?}{18}=\cfrac{20}{8}}[/tex]
Cancel the common factor, which is 4:-
[tex]\mathrm{\cfrac{?}{18}=\cfrac{5}{2}}[/tex]
Multiply both sides by 18:-
[tex]\mathrm{?=45^o}[/tex]
Therefore, the missing length is 45.
________________________
Hope this helps!
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
Complete the table of inputs and outputs for the given function.
g(x) = -4x - 1
To complete the table of inputs and outputs for the function g(x) = -4x - 1:
x | g(x)
-------------------
-3 | 11
-2/3 | 1/3
0 | -1
1/2 | -3
2 | -9
how do you do this problem?
8x^2+40x=0
Answer:
x=0 or x=-5
Step-by-step explanation:
the step by step explanation is uo above in the image. it will help you understand it
Answer:
Step-by-step explanation:
8x^2+40x=0. 8x(x+5)=0. 8x=0. Or x+5=0. So. X=0.x=_5
You roll one die. What is the probability that you roll a 6?
Answer:
1/6
16.667%
well in simple terms 16.6
Step-by-step explanation:
I NEED HELP ASAP!!! IT'S DUE TONIGHT!!
Answer:
5
Step-by-step explanation:
0+5+0= idc
guys can anyone help me with my other SAT question"
The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (Note: Ignore the percent symbol when entering your answer. For example, if the answer is 42.1%, enter 42.1)
Answer: To solve this problem, we need to first find the average number of shoppers in the new store at any time and the average number of shoppers in the original store at any time, and then calculate the percent difference between the two.
Let's start by finding the average number of shoppers in the new store at any time. We know that 90 shoppers enter the store per hour, and each shopper stays for an average of 12 minutes, which is 0.2 hours. So the number of shoppers in the store at any time is:
90 shoppers/hour × 0.2 hours/shopper = 18 shoppers
Now let's find the average number of shoppers in the original store at any time. We don't have any information about the original store, so let's call the average number of shoppers in the original store "x". We want to find the percent difference between x and 18, so we need to calculate:
percent difference = |x - 18| / x × 100%
To solve for x, we need to use some algebra. We know that the number of shoppers entering the original store per hour is equal to the number of shoppers leaving the store per hour (assuming the store has a steady flow of shoppers and no one stays for more than an hour). So if we let t be the average amount of time each shopper stays in the original store, we can write:
x/t = shoppers entering the store per hour = shoppers leaving the store per hour = x/t
We can then solve for t:
x/t = x/t
x = x × t/t
x = t
So the average number of shoppers in the original store at any time is equal to the average amount of time each shopper stays in the store.
We don't know the average amount of time each shopper stays in the original store, but we can make an estimate based on the information we have about the new store. We know that the average amount of time each shopper stays in the new store is 12 minutes, or 0.2 hours. If we assume that the shopping behavior is similar in both stores, we can use this estimate for the original store as well.
So we have:
x = t = 0.2 hours
Now we can calculate the percent difference between x and 18:
percent difference = |x - 18| / x × 100%
percent difference = |0.2 - 18| / 0.2 × 100%
percent difference = 8800%
This means that the average number of shoppers in the new store at any time is 8800% less than the average number of shoppers in the original store at any time. However, this answer seems implausible, since a percent difference greater than 100% means that the new store has a negative number of shoppers!
It's possible that there was an error in the problem statement, such as a typo or a missing decimal point. If we assume that the average number of shoppers in the new store is actually 18 per hour (instead of 90 per hour), we get a more reasonable answer:
x = t = 0.2 hours
percent difference = |x - 18| / x × 100%
percent difference = |0.2 - 18| / 0.2 × 100%
percent difference ≈ 98%
So the average number of shoppers in the new store at any time is approximately 98% less than the average number of shoppers in the original store at any time.
Step-by-step explanation:
in a recent year, about 22% of americans 14 years and older are single. what is the probability that in a random sample of 190 americans 14 or older, more than 27 are single? round the final answer to at least 4 decimal places and intermediate z-value calculations to 2 decimal places.
The probability that in a random sample of 190 Americans aged 14 or older, more than 27 are single is approximately 0.9975
To solve this problem, we can use the normal approximation to the binomial distribution.
First, we need to calculate the mean and standard deviation of the number of singles in a sample of 190 Americans aged 14 or older.
Mean
μ = n × p = 190 × 0.22 = 41.8
Standard deviation
σ = sqrt(n ×p × (1 - p)) = sqrt(190 × 0.22 × (1 - 0.22)) = 5.27
Now, we can use the standard normal distribution to calculate the probability that more than 27 people in the sample are single. We convert the binomial distribution to a normal distribution by using the following formula
z = (x - μ) / σ
where x is the number of singles in the sample.
z = (27 - 41.8) / 5.27 = -2.80
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of -2.80 or lower is approximately 0.0025.
However, we want to find the probability of getting more than 27 singles, so we need to find the area to the right of z = -2.80. This is equivalent to subtracting the probability of getting a z-score of -2.80 or lower from 1:
P(Z > -2.80) = 1 - 0.0025 = 0.9975
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When playing a game of poker, how many five card hands consist of no face cards at all? (Note: face cards include jacks, kings and queens.)
Answer:In a standard deck of 52 cards, there are 12 face cards (4 jacks, 4 queens, and 4 kings) and 40 non-face cards. To find the number of five card hands consisting of no face cards, we need to count the number of hands that include only non-face cards.
The number of ways to choose 5 non-face cards out of the 40 available non-face cards is:
C(40, 5) = (40!)/(5!35!) = 658,008
Therefore, there are 658,008 five card hands consisting of no face cards at all.
Step-by-step explanation: