The probability that three cards chosen at random from a standard 52-card deck that are not all the same color is 3/4.
Total number of combinations of three cards: There are 52 choose 3 = 22,100 ways to choose three cards from a standard deck of 52 cards.
Number of combinations that are not all the same color: There are two possibilities for the colors of the three cards:
a. Two red cards and one black card: There are 26 choose 2 ways to choose two red cards and 26 choose 1 ways to choose one black card, for a total of (26 choose 2) * (26 choose 1) = 325 * 26 = 8,450 combinations.
b. Two black cards and one red card: There are 26 choose 2 ways to choose two black cards and 26 choose 1 ways to choose one red card, for a total of (26 choose 2) * (26 choose 1) = 325 * 26 = 8,450 combinations.
The total number of combinations that are not all the same color is 8,450 + 8,450 = 16,900.
The probability that three cards chosen at random are not all the same color is:
P(not all the same color) = (number of combinations that are not all the same color) / (total number of combinations of three cards) = 16,900 / 22,100 = 3/4.
Therefore, the probability that three cards chosen at random from a standard 52-card deck are not all the same color is 3/4.
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i promise i will mark as brainliest
Answer: No, you can prove it
Step-by-step explanation:
It is a right angle at both triangles and the sides to points toward the vertex of the triangle have to be the same. So, the bottom side must be the same and the angles are the same. It is congruent.
At Sam's Grocery Store the cost of meat per pound is twice the cost of meat per pound at Lane Grocery Store. Select the equation that shows a cost of meat per pound at Sam's Grocery Store. A.
The correct equation to show the cost of meat per pound at Sam's Grocery Store is x = 2y, where x is the cost of meat per pound at Sam's Grocery Store and y is the cost of meat per pound at Lane Grocery Store.
This equation represents the fact that the cost of meat per pound at Sam's Grocery Store is twice the cost of meat per pound at Lane Grocery Store.
For example, if the cost of meat per pound at Lane Grocery Store is $5, then the cost of meat per pound at Sam's Grocery Store would be 2 * $5 = $10.
So, the equation x = 2y accurately shows the relationship between the cost of meat per pound at Sam's Grocery Store and the cost of meat per pound at Lane Grocery Store.
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a corporate board contains twelve members. the board decides to create a five-person committee to hide corporation debt. suppose four members of the board are accountants. what is the probability that the committee will contain two accountants and three nonaccountants?
The probability that the committee will contain 2 accountants and 3 non-accountants is (6 × 56) / 792 = 6/66 = 3/33.
What do you mean by corporate board?A corporate board refers to a governing body of a corporation, usually consisting of elected or appointed members, who are responsible for overseeing the management of the company and making important decisions related to its strategy, finances, operations, and other aspects. The board serves as a representative of the shareholders and is responsible for overseeing the actions of the CEO and other executives, ensuring that the company is run in a manner that benefits its stakeholders.
The probability that the committee will contain two accountants and three non-accountants can be calculated as follows:
The number of ways to choose 2 accountants out of 4 is 4 choose 2, or 4C2 = 6.
The number of ways to choose 3 non-accountants out of 8 (12-4) is 8C3 = 56.
The total number of ways to choose 5 people from 12 is 12C5 = 792.
Therefore, the probability that the committee will contain 2 accountants and 3 non-accountants is (6 × 56) / 792 = 6/66 = 3/33.
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A puck moves 2.35 m/s in a -22.0° direction. A hockey stick pushes it for 0.215 s, changing its velocity to 6.42 m/s in a 50.0° direction. What is the displacement x
The displacement x of the moving puck is; 0.43 meters
How to find the displacement?The displacement is defined as the change in position of an object. It is also called a vector quantity and has a direction and magnitude
The parameters given here are;
The polar coordinate initial velocity vector; U = 2.35 m/s, -22°
Final velocity vector; V = 6.42 m/s, +50°
This suggests to us that Cartesian x axis is parallel to angle 0° and y axis is parallel to +90°.
Change of velocity component parallel to +90° = magnitude*sinθ,.
Thus, the change of that velocity
Δv = |V|sin(50) - |U|sin(-22)
Δv = 6.42sin(50) - 2.35sin(-22)
Δv = 4.9 - (-0.88)
Δv = +5.8 m/s
The equation for displacement is;
s = ut +1/2at^2
where acceleration time t = Δt = 0.215 s
initial velocity u = |U|sin(-22) = -0.88 m/s
acceleration parallel to u is a = Δv/Δt = +5.8/Δt
a = 5.8/t m/s^2
Thus;
s = -0.88t + ¹/₂* 5.8/t * t²
s = -0.88t +2.9t
s = 2.0t
s = 2.0 * 0.215
s = 0.43 m
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Write an inequality that represents the graph. Write your answer such that y is isolated on one side of the inequality symbol.
Answer:
y ≤ 3/4x-2
The 3/4 is the slope, and -2 is y intercept
Jiah and Michelle made a big pan of brownies during baking class. They decided that it would be fair to share
them equally between the two of them. Each took half of the brownies home. At home their families enjoyed
eating brownies. Jiah shared it with her mom, sister, and brother. If each of them ate one fourth of the brownies,
what part of the whole brownies did Jiah eat?
The part of the whole brownies that Jiah eat will be 1/8.
How to calculate the fractionA fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Fractions help to distribute and judge the numbers easily and make the calculation faster. Instead of using decimal values, the representation of fractions looks simpler.
Jia's mom = 1/4
Jia's sister = 1/4
Jia's brother = 1/4
Jia's share = 1 - (1/4 + 1/4 + 1/4) = 1 - 3/4 = 1/4( of her share)
Jia's share in relation to the whole = 8/8 - 7/8 = 1/8
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What is the inverse of the function f(x)=(14x)3? f−1(x)=x√34
f−1(x)=4x−−√3
f−1(x)=14x−−−√3
f−1(x)=4x√3
Solving multi step equations
Like term- negative coefficients
-9 + x -3x = 5
The required solution of the given equation is x = -7.
What does multi step equations Like term- negative coefficient means?"Multi-step equation" means an equation that requires more than one step to be solved.
"Like terms" refers to terms that have the same variables raised to the same powers. In this equation, there are no like terms, so no simplification of the equation is needed in that regard.
"Negative coefficients" refers to the fact that some of the coefficients in front of the variables in the equation are negative. For example, in this equation, the coefficient of x is -3, and the coefficient of -9 is also negative.
According to question:To solve this equation, you can simplify both sides by combining like terms:
-9 + x -3x = 5
-9 - 3x + x = 5
-9 - 2x = 5
Next, isolate the variable on one side of the equation by adding 9 to both sides:
-9 - 2x + 9 = 5 + 9
-2x = 14
Finally, divide both sides by -2 to find x:
(-2x) / -2 = 14 / -2
x = -7
So the solution is x = -7.
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Solve please algebra
The values of the variables are -4 and -9
How to simply the equationsFrom the information given, we have the equations:
y = 2x - 1
y = x -5
Now, from substitute the value of y in equation 2 to equation 1, we get;
x - 5 = 2x -1
collect the like terms
x -2x = -1 + 5
Add or subtract the like terms
-x = 4
Make 'x' the subject
x = -4
Substitute the value into equation 2
y = -4 - 5
y = -9
Then, the values are-4 and -9
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find the value of y in the proportion (4y+5):3=(y+7):4
Answer:
Step-by-step explanation:
4(4y+5)=3(y+7)
16y+20=3y+21
13y=1
y=1/13
Answer:
y = 1/13
Step-by-step explanation:
(4y + 5) : 3 = (y+7) :4
Product of extremes = (4y + 5) * 4
= 4y *4 + 5*4
= 16y + 20
Product of mean = 3*(y +7)
= 3*y + 3*7
= 3y + 21
Product of extremes = product of mean
16y + 20 = 3y + 21
Subtract 20 from both sides,
16y = 3y + 21 - 20
16y = 3y + 1
Subtract 3y from both sides,
16y - 3y = 1
13y = 1
[tex]\boxed{\bf y =\dfrac{1}{13}}[/tex]
Rey drew the isosceles triangle LMN and the segment LP. How can Rey tell whether the segment drawn is the height of the triangle?
Answer:
Step-by-step explanation:
If LP represented the height of the triangle, then the segment would be the vertical leg of a right triangle. This is due to the fact that the altitude of an isosceles triangle is perpendicular to the base MN.
Thus, by the Pythagorean Theorem, (1.3)^2 + (3.5)^2 = (3.7)^2 if and only if segment LP is the height of the triangle. Calculate for yourself whether this is true.
Two trains leave the station at the same time, one heading east and the other heading west. The eastbound train travels at 75 miles per hour. The westbound train travels at 95 miles per hour. How long will it take for the two trains to be 204 miles apart? Do not do any rounding.
Answer:
Step-by-step explanation:
The two trains are moving apart from each other, so we can add their speeds to find their relative speed:
Relative speed = 75 + 95 = 170 miles per hour
We want to know how long it will take for the trains to be 204 miles apart. We can use the formula:
distance = rate × time
to solve for the time. Let t be the time in hours:
204 = 170t
Solving for t, we get:
t = 204/170
t ≈ 1.2 hours
Therefore, it will take approximately 1.2 hours for the two trains to be 204 miles apart.
question 14 pls help
The graph of f(x) = -0.1 |x| opens. The point (-100, -10) or (100, -10) is on the graph.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
We know that the graph of the function f(x) = a|x| opens upwards if the value of a > 0 and it opens downwards for a< 0.
For the given function the value of a = -0.1 < 0.
So, the graph of f(x) opens downwards.
The coordinates of the graph are determined by substituting the value of y in the given function:
f(x) = -0.1 |x|
-10 = -0.1 |x|
x = -100 or x = 100
So, the two points are (-100, -10) or (100, -10).
Hence, the graph of f(x) = -0.1 |x| opens. The point (-100, -10) or (100, -10) is on the graph.
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At an ocean depth of 8 meters, a buoy bobs up and then down 5 meters from the ocean's depth. Sixteen seconds pass from the time
the buoy is at its highest point to when it is at its lowest point. Assume at x = 0 the buoy is at normal ocean depth.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum
value on the graph closest to the first point.
Answer:
The answer is the equation for the function describing the movement of the buoy:
f(x) = 5 * sin(2 * pi * x / 16) + 8
Step-by-step explanation:
To graph the function, we need to find an equation that describes the buoy's movement. Since the buoy bobs up and down 5 meters from the ocean's depth, we can use the sine function. The amplitude of the function is 5, since the buoy moves 5 meters from the normal ocean depth. The period of the function is 16 seconds, since it takes 16 seconds for the buoy to go from its highest point to its lowest point.
Using this information, we can write the equation for the function as:
f(x) = 5 * sin(2 * pi * x / 16) + 8
where x is the time in seconds.
The first point on the graph would be (0, 8), since at x = 0 the buoy is at normal ocean depth. The second point would be either a maximum or minimum value on the graph closest to x = 0, which can be found by finding the derivative of the function and setting it equal to zero.
The graph of the function would look like a wave that oscillates up and down, with a maximum value of 5 meters above the normal ocean depth and a minimum value of 3 meters below the normal ocean depth.
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complete the square for 3x^2 - 5x - 2
Answer:
[tex]3\left(x-\dfrac{5}{6}\right)^2-\dfrac{49}{12}[/tex]
Step-by-step explanation:
Given quadratic expression:
[tex]3x^2 - 5x - 2[/tex]
To complete the square, factor out the coefficient of the leading term:
[tex]\implies 3\left(x^2-\dfrac{5}{3}x-\dfrac{2}{3}\right)[/tex]
Add and subtract the square of half the coefficient of the term in x inside the parentheses:
[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\left(\dfrac{\frac{-5}{3}}{2}\right)^2-\left(\dfrac{\frac{-5}{3}}{2}\right)^2-\dfrac{2}{3}\right)[/tex]
Simplify:
[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\left(\dfrac{-5}{6}\right)^2-\left(\dfrac{-5}{6}\right)^2-\dfrac{2}{3}\right)[/tex]
[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\dfrac{25}{36}-\dfrac{25}{36}-\dfrac{2}{3}\right)[/tex]
Factor the perfect square trinomial formed by the first three terms inside the parentheses:
[tex]\implies 3\left(\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{36}-\dfrac{2}{3}\right)[/tex]
Distribute:
[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{75}{36}-\dfrac{6}{3}[/tex]
[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{12}-2[/tex]
Simplify:
[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{12}-\dfrac{24}{12}[/tex]
[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{49}{12}[/tex]
Eric invests $3,200 in a fund that pays 8% annually on the principal. The interest earned after 5 years is $1,280…
Is a linear function, exponential function, absolute value function or none of the above function types? Helpppp is a test
The simple interest on a principal amount is the function on time t.
What Is Simple Interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Given here: Principal=$3200, Annual rate of interest =8% and time=5 years
Thus Simple interest is S.I= 3200×8×5 / 100
=$1280
Which is equal to the interest given in the question.
Thus the the interest rate forms a linear function or
Simple Interest is calculated using the following formula: SI = P × R × T /100,
where r and P are constant then S.I can be written as the function of time t
SI(t)= P×r×t/100
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Let's expand our thinking into the Third dimension. Can you think of a few ways to build a sphere? (No formula, just descriptions)
A geometric method is known as "stereographic projection" involves projecting a flat map of a sphere onto a three-dimensional surface with a point at its center.
This is one way to construct a sphere. The construction of geodesic domes, which gained popularity in the 1960s, is one example of an art and construction project that frequently makes use of this approach.
Using a solid material and carving it into the shape you want is another way to make a sphere. This can be accomplished using stone, clay, wood, and other materials. To produce a sphere with perfect symmetry, this method necessitates considerable skill and precision.
A third approach is to construct a sphere from numerous small, flat pieces. Paper or fabric can be used to accomplish this, with each piece being cut into a curved shape and glued together to form the sphere. Origami balls, for example, are a common decorative item made using this method.
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The diameter of a center circle on a soccer field is 20 yards What is the area of the circle? Use 3.14 as an approximation for pi.
Answer:
314 yd²
Step-by-step explanation:
You want the area of a circle that has a diameter of 20 yards.
Area formulaThe usual formula for the area of a circle is ...
A = πr² . . . . . . where r is the radius
The radius of the circle is half the diameter, so is (1/2)(20 yd) = 10 yd.
Using this value in the formula, we find the area to be ...
A = 3.14(10 yd)² = 314 yd²
. Celina reads 16 pages in 8 minutes.
a. How many pages does Regina read per minute?
b. How many minutes does Celina spend reading each page?
Please help.
Answer:
Step-by-step explanation:
A.) To find out how many pages Celina reads per minute, you would have to divide 16 by 8 = 2.
B.) Now that we know she reads two pages every one minute, we are able to calculate how many minutes it takes her to read one. You need to divide 2 by 2 = 1.
A.) = 2
B.) = 1
can someone please help me show my work?
i have the answers!
brainly please help this due in 8 mins!
Answer: Check the numbers that are already there.
Step-by-step explanation:
Example, what times 6 equals 24? then divided 24 by that number. Do this for all the numbers
What happens to the mean of the data set {10, 2, 8, 9, 5, 2, 6} if the number 9 is removed from the data set?
Answer:
If we remove 9 from the data set, the mean reduces by 0.5 from 6 to 5.5
Step-by-step explanation:
Mean of {10, 2, 8, 9, 5, 2, 6}}If 9 is removed from the data set, the total reduces from 42 by 9
Answer
If we remove 9 from the data set, the mean reduces by 0.5 from 6 to 5.5
Liam owns a business earning $43,200 in profits. These profits are appreciating at about 1. 2% each year. What are Liam’s profits after six years?
In light of this, Liam's earnings after six years will be roughly $47,139.92.
Profits from Liam's company have reached $43,200, and they are growing at a 1.2% annual rate.
We can use the compound interest calculation to calculate the number of profits after six years.
The formula is P = P0 *[tex](1 + r/100)^t[/tex], If t is the number of years, which is 6, P0 is the initial sum of $43,200, r is the yearly interest rate of 1.2%, and t is the number of years.
By substituting these values into the formula,
we can calculate the final amount as P = 43,200 * [tex](1 + 1.2/100)^6[/tex] = 43,200 * [tex]1.012^6[/tex] = 43,200 * 1.07711 = $47,139.92.
In light of this, Liam's profits after six years will be roughly $47,139.92.
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9 percent of what is 15
Answer:
60%
Step-by-step explanation:
2b x b
is this answer only 2b ^ 2 or is there any other answer without using exponentiation
The answer to the expression 2b x b is simply 2b^2. Exponentiation is a mathematical operation that raises a number to a power, and in this case, b is raised to the power of 2.
Alternatively, if exponentiation is not allowed, the answer to the expression is simply 2b * b, which can be simplified to 2b^2 as well.
So, the answer to the expression 2b x b is 2b^2, regardless of whether or not exponentiation is used.
The expression 2b x b represents the product of two scalars, 2 and b, multiplied by a scalar b.
The expression could represent a variety of quantities in mathematics and science, including the area of a rectangle, the volume of a cube, or the kinetic energy of an object, among others.
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Last question giving the rest of my points!!!!!!! please explain how you got it
Answer:
Below
Step-by-step explanation:
From mile 3 to mile 18 is 15 miles
He needed 2 hrs - .75 hr = 1.25 hr to run 15 miles
15 miles / 1.25 hr = 12 miles per hour ( VERY fast !)
Decimal of one hundred twenty ten thousandths
Answer:
120.010
Step-by-step explanation:
18. Suppose A (red, blue, yellow), B = (Red, yellow, green), and C= (green, red, purple). Which set is equivalent to (AUB)NC? (a) (purple) (b) (red) (c) {red, green) (d) {yellow, purple)
Based on the information from the sets, it can be inferred that the correct answer is: red, green (option C).
How to identify the correct answer?To identify the correct answer we must take into account the elements that are in each set. Once we identify this information, we must analyze the elements in common between the sets. In accordance with the above, we must take into account this:
∪= Union of sets, refers to all the elements of the operands. ∩ = Intersection of sets, refers to the common elements between the operands.Based on the above, the correct answer is red and green because these are the elements that have the sets A, B, and C.
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6. How many three-digit palindrome's can be created using the digits 1, 2, 3, and 4, if the digits can repeat?
A. 16
B. 24
C. 12
D. 4
E. 6
The three-digit palindromes that can be created using the digits are 16 numbers.
What are palindromes?A word, number, phrase, or other group of characters that reads the same backwards as it does forwards is called a palindrome. Examples include the words "madam" or "racecar," the date and time 12/21/33 12:21, and the phrase "A man, a plan, a canal — Panama."
The three-digit palindromes are of the form: ABA.
Here, A can be selected in 4 ways.
Digits can be repeated hence, B can be selected in 4 ways.
The last A is the same number as the first A, hence the selection is 1 way.
The number of three digits palindrome that we can form is:
(4)(4)(1) = 16 ways
Hence, the three-digit palindromes that can be created using the digits are 16 numbers.
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The local grocery store is having a sale on sports drinks. For a particular brand of sports drink, a 6 -pack of 20 -ounce bottles costs $4.96 . What is the unit price (per ounce) for the sports drink? Round your answer to the nearest cent.
$0.04 is the unit price (per ounce) for the sports drink.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that local grocery store is having a sale on sports drinks.
For a particular brand of sports drink, a 6 -pack of 20 -ounce bottles costs $4.96
We need to find the the unit price (per ounce) for the sports drink.
6×20
120 ounce bottles in total which cost $4.96.
Now 4.96/120 is the cost of each bottle
$0.04 is the unit price of the sport drink.
Hence, $0.04 is the unit price (per ounce) for the sports drink.
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Four years ago Inka became an employee of TrakRight Tourism, where her starting annual salary was $55 600. After her first year she received a 2% pay rise. The next year she received a 3% pay rise. Last year she received an x% pay rise. If her annual salary is now $61 042, determine the value of x, correct to 1 decimal place.
The fourth year increase in salary is 4.5 percent.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Inka's starting annual salary was $55,600.
After her first year she received a 2% pay rise.
Now, 2% of 55,600
= 2/100 ×55,600
= 1112
So, salary of 2nd year is 55,600+1112=$56712
The next year she received a 3% pay rise.
Now, 3% of 56712
= 3/100 ×56712
= 1701.36
So, salary of 3rd year is 56712+1701.36=$58413.36
Last year she received an x% pay rise.
Now, x% of 58413.36+58413.36=61,042
x/100 ×58413.36=61,042-58413.36
584.1336x=2628.64
x=2628.64/584.1336
x=4.5%
Therefore, the fourth year increase in salary is 4.5%.
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