The probability of getting a full house is approximately 0.0014
To calculate the probability of getting a full house, we need to first count the total number of possible 5-card hands that can be dealt from a deck of 52 cards.
There are 52 choices for the first card, 51 for the second, 50 for the third, 49 for the fourth, and 48 for the fifth (since we are drawing without replacement). However, the order in which the cards are dealt does not matter, so we must divide by the number of ways in which the same 5 cards can be ordered. Therefore, the total number of possible 5-card hands is
C(52,5) = 52! / (5! × 47!) = 2,598,960
Now we need to count the number of full house hands we can get. We can choose the value of the triple in C(13,1) ways (since there are 13 possible face values), and we can choose the three cards of that value in C(4,3) ways. We can then choose the value of the pair in C(12,1) ways (since there are now only 12 possible face values left), and we can choose the two cards of that value in C(4,2) ways. Therefore, the number of full house hands is
C(13,1) × C(4,3) × C(12,1) × C(4,2) = 13 × 4 × 12 × 6 = 3,744
Finally, the probability of getting a full house is
P(full house) = number of full house hands / total number of hands
= 3,744 / 2,598,960
= 0.0014
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can you help me with this
The correct options for the average speed of both runners are:
B: Candace ran 4 meters per second
F: Candice ran at a faster rate
How to find the average speed between two coordinates?The formula for slope between two coordinates is:
Slope = (y2 - y1)/(x2 - x1)
For Antonio, we take two coordinates from the table to find the average speed.
The coordinates are: (8, 29) and (12, 41)
Thus:
Average speed = (41 - 29)/(12 - 4)
= 12/8 = 1.5 m/s
For candice, we take two coordinates which are:
(10, 42) and (15, 62)
Thus:
Average Speed = (62 - 42)/(15 - 10)
= 20/5
= 4 m/s
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Ally needs 90 meters of tape for a project. Tape comes in different size rolls. If she bought 50 meters, 22.86 meters, and an 18.288-meter roll, how much tape will she have in all? ___________ meters
Ally will have 91.148 meters of tape in all if Ally needs 90 meters of tape for a project.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.
Ally needs a total of 90 meters of tape for her project. She bought three rolls of tape, one with 50 meters, another with 22.86 meters, and the last one with 18.288 meters. To find the total amount of tape she has, she needs to add the length of all three rolls together.
Adding the length of the first two rolls, we get:
50 meters + 22.86 meters = 72.86 meters
Then adding the length of the third roll to the sum above, we get:
72.86 meters + 18.288 meters = 91.148 meters
Therefore, Ally will have 91.148 meters of tape in all.
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if team a is the underdog in playing team b and has probability 1/4 of winning every game it plays against team b. what is the probability that it wins the best-of-three series over team b? (prefer to put answer as the simplest form of fraction, like 1/2 rather than 2/4)
The probability that team A wins the best-of-three series over team B is 3/16.
If team A is the underdog and has a probability of 1/4 of winning every game it plays against team B,
The probability that it wins the best-of-three series over team B :
Let us first begin by determining the probability of team A winning two games in a row. Since each game is independent, we can use multiplication to calculate the probability of winning two games in a row:
P(Team A wins 2 in a row) = P(Team A wins Game 1) x P(Team A wins Game 2)
Using the probability given in the problem, we can substitute:
P(Team A wins 2 in a row) = (1/4) x (1/4) = 1/16
Now we must determine the probability of team A winning two games in the series. There are three ways that Team A could win the series:
Winning the first two games;
Winning the second two games;
Winning the first and third games.
Assuming that each of these scenarios is equally probable, the probability of team A winning the series is the sum of the probabilities of these scenarios:
P(Team A wins series) :
= P(Team A wins first two games) + P(Team A wins second two games) + P(Team A wins first and third games)P(Team A wins series)
= (1/16) + (1/16) + (1/16)P(Team A wins series)
= 3/16
Therefore, the probability that team A wins the best-of-three series over team B is 3/16.
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Find the missing dimension of the triangle.
Area = 32 m²
16 m
h
pls help I'll mark brainlisest
Answer:
4 m
Step-by-step explanation:
The formula to find the area of the triangle is:
[tex]\sf Area = \frac{1}{2} *base*height[/tex]
Given that,
Area = 32m²
Base = 16m
Height =?
Let us use the given formula to find the height of the triangle.
[tex]\sf Area = \frac{1}{2} *base*height\\\\\sf 32m^2 = \frac{1}{2} *16*h\\\\32= \frac{16h}{2} \\\\32=8h\\\\\frac{32}{8} =\frac{8h}{8} \\\\4m = height[/tex]
will mark u brainliest!!!
Answer:
It really just deleted my answer..
Solve.
4p^2 - 50 = 350
O {-100, 100}
O {-400, 100}
O {-10, 10}O {-10, 100}
Step-by-step explanation:
You're welcome.
Which of the choices shown is a correctly identified ordered pair? Responses A A = (2, 1)A = (2, 1) B none of these none of these C B = ( 1, 2)B = ( 1, 2) D C = (-1, -2)C = (-1, -2) E D = (-1, -2)
The ordered pairs in the quadrants are option A and option D:
A. A= (2, 1)
D. C = (-1, -2)
Define quadrants?The quadrant is the area that is bounded by the point where the X and Y axes connect. The cartesian plane's two axes, the X and Y axes, intersect at a 90° angle, forming four zones surrounding the intersection that are known as quadrants.
The points are given as:
A = (2, 1)
B = (1, 2)
C = (-1, -2)
D = (-1, -2)
Now, point A is in 1st quadrant so both the points will be positive.
So, A = (2, 1) is an ordered pair.
Now, B is in 2nd quadrant, so x coordinate will be negative and y coordinate will be positive.
B = (1,2) is hence not an ordered pair.
Now, C is in 3rd quadrant, so both the points will be negative.
C = (-1, -2) is an ordered pair.
Similarly, D is in 4th quadrant and x coordinate will be positive and y coordinate will be negative.
D = (-1, -2) is not an ordered pair.
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HELP PLSSS!!!
Write and solve an equation to find the value of x . Show work in the box below.
The value of x is ??
Step-by-step explanation:
(x+90°)=7x (vert opp angles)
x-7x=-90°
-6x/-6=-90°/-6
x=15
what element is defined by the following information? p = 17 n° = 20 e- = 17
The element defined by the given information p = 17 n° = 20 e- = 17 is Chlorine (Cl).
An atom consists of protons, neutrons, and electrons. The atomic number of an element corresponds to the number of protons present in the nucleus of an atom. Hence, the atomic number (p) of the given element is 17. A neutral atom contains an equal number of protons and electrons.
Therefore, the number of electrons (e-) of the given element is 17 as well. The number of neutrons (n°) can be calculated as the difference between the atomic mass number (A) and the atomic number (p).
In the case of the given element, the atomic number is 17, and the atomic mass number is 37 (as chlorine has two stable isotopes of mass numbers 35 and 37). Hence, n° = 37 - 17 = 20. Therefore, the element defined by the given information p = 17 n° = 20 e- = 17 is Chlorine (Cl).
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(9r³-73r² +64r +37)÷(r-7)
Dividing using box method
Show work
It should be noted that the quotient of the division is 9r^2 + 2r - 5 and the remainder is -5
How to solve the divisionIn this case, to solve this polynomial division, we can use either long division or synthetic division. Here, we'll use long division:
9r^2 + 2r - 5
___________________________
r - 7 | 9r^3 - 73r^2 + 64r + 37
- 9r^3 + 63r^2
--------------------
- 10r^2 + 64r
+ 10r^2 - 70r
----------------
-6r + 37
-6r + 42
--------
-5
Therefore, the quotient is 9r² + 2r - 5 and the remainder is -5. Therefore: (9r³-73r² +64r +37)÷(r-7) = 9r^2 + 2r - 5 + (-5)/(r-7).
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help me pleaseeeeeeeeee!!!!!!!!
Answer:
4³, 8², and 2⁶ are all equivalent to 64¹
Answer:
A, C, F
Step-by-step explanation:
A. 4 x 4 x 416 x 4= 64
C. 8 x 8 = 64
F. 2x2=4x2= 8x2=16x2=32 x 2= 64
There are red tiles and blue tiles in a box. The ratio of red tiles to blue tiles is 3 to 5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box?
To solve this problem, we can set up a system of equations to represent the given information. Let R be the number of red tiles and B be the number of blue tiles. We are trying to find the value of R, the number of red tiles.
The first piece of information we are given is that the ratio of red to blue tiles is 3:5. This can be written as:
[tex]\dfrac{\text{R}}{\text{B}} =\dfrac{3}{5}[/tex]
The second piece of information we are given is that there are 12 more blue tiles than red tiles in the box.
This can be written as:
[tex]\text{B = R}+12[/tex]
We can solve this system of equations by substituting the second equation into the first equation and solving for R.
Substituting [tex]\text{B = R}+12[/tex] into the first equation, we get:
[tex]\dfrac{\text{R}}{\text{R}}+12 =\dfrac{3}{5}[/tex]
We can then simplify this equation to get:
[tex]\text{R} = 15[/tex]
Thus, there are 15 red tiles in the box.
Find the 25th term for the arithmetic sequence when the domain is x=1,2,3,4,5 (Use the formula from the previous question.)
5,7,9,11,13...
find the 25th Term
By answering the presented question, we may conclude that Therefore, the 25th term of the arithmetic sequence is 53.
What is Sequences?In mathematics, a sequence is an ordered list of items. Elements can be numbers, functions, or other mathematical objects. A series is commonly expressed by putting the phrases in parentheses and separating them with commas. A natural number series, for example, can be denoted as: (1, 2, 3, 4, 5, ...) Similarly, the even number series is labelled as follows: (2, 4, 6, 8, 10, ...) A series can be finite or infinite depending on whether it has a finite or infinite number of words.
To find the 25th term,
an = a1 + (n - 1)d
In this case, a1 = 5 and d = 2. Plugging these values into the formula, we get:
a25 = 5 + (25 - 1)2
a25 = 5 + 48
a25 = 53
Therefore, the 25th term of the arithmetic sequence is 53.
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Find the equation of the exponential function that goes through the points (0,4) and (4,0.25).
The answer of the given question based on the exponential function is the exponential function that goes through the points (0,4) and (4,0.25) is: f(x) = 4(0.5)ˣ.
What is Equation?An equation is a statement that two expressions are equal. It contains an equal sign (=) which separates the two expressions, and it can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.
The general form of exponential function is:
f(x) = a(b)ˣ
where a is the initial value, b is the base, and x is the independent variable.
We can use the two given points to form a system of equations and solve for the values of a and b.
Using the point (0,4):
f(0) = a(b)⁰ = a = 4
Using the point (4,0.25):
f(4) = a(b)⁴ = 0.25
Now we can substitute a = 4 into the second equation and solve for b:
4(b)⁴ = 0.25
(b)⁴ = 0.25/4 = 1/16
b = (1/16)⁽¹/⁴⁾ = 0.5
Therefore, the exponential function that goes through the points (0,4) and (4,0.25) is: f(x) = 4(0.5)ˣ
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An airplane is flying over the ocean at 2,500 feet in the air. A diver is swimming below and is 25 feet below the ocean surface. How far apart are the plane and the diver?
Answer:
2,525 FEET
Step-by-step explanation:
This data set represents the number of cups of coffee sold in a café between 8 a.m. and 10 a.m. every day for 14 days.
Answer:
The answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6
Step-by-step explanation:
Numbers in order:
4,5,6,6,7,8,9,9,10,10,12,12,14,15
List into two equal parts:
4,5,6,6,7,8,9 and 9,10,10,12,12,14,15
Find middle numbers:
4,5,6,6,7,8,9 and 9,10,10,12,12,14,15
Lower quartile: 6
Upper quartile: 12
Thus the answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6
a child enters a carousel that takes one minute to revolve once around. the child enters at the point ( 1 , 0 ) . assume the carousel revolves counter clockwise. what are the coordinates of the child after 75 seconds?
The coordinates of the child after 75 seconds on a carousel that revolves once every minute counter-clockwise, assuming the child entered at point (1,0), are (-0.766, -0.643).
Since the carousel revolves once around in one minute, its angular velocity is 2π/60 radians per second or π/30 radians per second.
Let's find the angle that the child has covered in 75 seconds.
angle = (angular velocity) x (time) = (π/30) x 75 = 2.5π
After 2.5π radians, the child has completed 2.5 full revolutions and is back at the starting point. Therefore, the coordinates of the child at point (1, 0) are (-0.766, -0.643).
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bias binding is to be sewn around the edge of a rectangular tablecloth measuring 73 in. by 46 in. if the bias binding comes in packages containing 13 ft of binding, how many packages of bias binding are needed for the tablecloth?
the required number of packages of bias binding for the tablecloth is 2.
As the rectangular tablecloth measures 73 in. by 46 in., the perimeter of the tablecloth can be calculated by the following formula:
Perimeter of the tablecloth = 2(Length + Width)= 2(73 + 46)= 2(119)= 238 inches
Therefore, the length of the bias binding required to sew around the tablecloth will be equal to the perimeter of the tablecloth. The length of the bias binding available in a single package is 13 feet, which is equal to 156 inches.Therefore, the number of packages required can be calculated as:
Number of packages of bias binding required= Length of bias binding required / Length of bias binding in a package= 238 / 156= 1.52
Therefore, 1.52 packages of bias binding will be needed for the tablecloth. However, we cannot purchase a fractional part of a package. Therefore, we need to round up the decimal to the nearest whole number. Hence, 2 packages of bias binding are required for the tablecloth.
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what percentage of compounds formed from the extract of this plant fall within 2 standard deviations of the mean? answer:
The percentage of compounds formed from this plant extract fell within two standard deviations of the mean, equal to 95.45%.
We tested an extract of a plant native to Taiwan as a possible treatment for leukemia. The amounts of collagen were found to be normally distributed with a mean = 62
standard deviation = 6.9 g/ml.
This is true for any normal distribution, regardless of the actual values of the mean and standard deviation.
The standard normal distribution is a normal distribution with mean zero and standard deviation 1. The standard normal distribution is centered around zero and the degree to which measurements deviate from the mean is represented by the standard deviation.
For a standard normal distribution, 68% of observations are within one standard deviation of the mean95% are within 2 standard deviations of the mean and 99.9% are within 3 standard deviations of the mean.Therefore, the required percentage is approx. 95.45% are within 2 standard deviations of the mean 62.
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Complete question:
The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 62 and standard deviation of 6.9 grams per mililiter.What percentage of compounds formed from the extract of this plant fall within 2 standard deviations of the mean?
Divide 15x5-3x³-9x² by -3x².
choices:
12x³ - 6x - 12
-5x³ - 6x + 3
−5x3 + X + 3
-5x³ + x-3
Answer:
(C) −5x^3 + x + 3.
Step-by-step explanation:
To divide 15x^5 - 3x^3 - 9x^2 by -3x^2, we can follow these steps:
Divide the coefficient of the first term by the coefficient of the divisor: (-15x^5) / (-3x^2) = 5x^3.
Multiply the divisor by the quotient obtained in step 1: -3x^2 * 5x^3 = -15x^5.
Subtract the product obtained in step 2 from the dividend: 15x^5 - (-15x^5) = 30x^5.
Repeat steps 1 to 3 for the next term: (-3x^3) / (-3x^2) = x, -3x^2 * x = -3x^3, -3x^3 - (-3x^3) = 0.
Repeat steps 1 to 3 for the last term: (-9x^2) / (-3x^2) = 3, -3x^2 * 3 = -9x^2, -9x^2 - (-9x^2) = 0.
Therefore, the result of the division is:
5x^3 + 0x + 3
Simplifying the expression, we get:
5x^3 + 3
Therefore, the correct answer is (C) −5x^3 + x + 3.
Answer:
C:−5x3 + X + 3
Step-by-step explanation:
I took the test and got it right
A cylinder has a base radius of 10m and a height of 18m. What is its volume in
cubic m, to the nearest tenths place?
Answer: 5654.9
Step-by-step explanation:
V=pi*r^2*h
r=10
h=18
V=pi*10^2*18
V=pi*100*18
V=pi*1800
V=5654.866776
tenths place:
V=5654.9
A kite is flying 86 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 56 degrees . Find the length of the string. Round your answer to the nearest tenth.
Sean has 14 friends n are in grade 7 and 9 are in grade 8 what is the equation
Answer:
n+9 = 14
Step-by-step explanation:
Let's Sean friends in grade 7 be n.
Then In grade 8, 9 persons are there.
Equation: n+9 = 14.
n = 14-9 = 5.
can yall pls help me!!!!
Answer: (-3u + -3) -5
Step-by-step explanation:
Use distributive property
HELP ME PLEASE BECAUSE THE QUATER IS ALMOST OVER
The terms and properties of operations that complete the statement and reasons for the equivalent expressions are;
3. Same
4.The properties of operations to write the equivalent expressions are; (-4), (-4) Distributive property
(-4), (-4), Associative property
(-4), (-3) Distributive property
5. When x = 2, and y = -5 -28·x + 12·y is -116 = -116
What are equivalent expressions?Equivalent expressions are expressions that have the same value for the values of the input variable.
3. The completed statement is presented as follows;
Equivalent expressions evaluate to the same value when a given set of values of x and y are substituted into both expressions.
4. The expressions in the question can be expanded to collect like terms as follows;
Expression; -28·x + 12·y
The common factor of 28 and 12 is 4, therefore, we get;
-28·x + 12·y = (4 × (-7))·x + (4 × 3)·y
To make the coefficient of the leading term positive, we get;
-28·x + 12·y = (-4 * 7)·x + (-4 * (-3))·y; Distributive property
Factoring the algebraic expression on the right, where the common factor is -4, we get;
(-4 * 7)·x + (-4 * (-3))·y = -4 × (7·x) + -4 × (-3·y); Associative property
= -4 × ((7·x) + (-3·y));
Therefore; -28·x + 12·y = -4 × (7·x + -3·y); Distributive property
5. Evaluation of the left and right side of the expression, where; x = 2, and y = 5, we get;
-28 × 2 + 12 × -5 = -116
(-4) × ((7 × 2) + (-3 × -5)) = -4 × 29 = -116
The completed equations are therefore;
-28·x + 12·y = -4 × (7·x + -3·y)
-28 × 2 + 12 × (-5) = -4 × (7 × 2 + -3 × (-5))
-116 = -116
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please help. i dont understand math
The value of x in the parallelogram is 10.
How to find the angle of a parallelogram?A parallelogram is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
The sum of angles in a parallelogram is 360 degrees. The parallelogram JKPQ has the following angles.
Therefore,
m∠J = 2x + 10
m∠P = 3x - 20
Hence, the opposite angles of a parallelogram are congruent.
Therefore,
m∠J = m∠P
2x + 10 = 3x - 20
2x - 3x = -20 - 10
-3x = -30
divide both sides by -3
x = -30 / -3
x = 10
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Express the function graphed on the axes below as a piecewise function.
Answer:
y = 2/3x +6 for x< -3.
y = 2/3x +1 for x> 3.
Step-by-step explanation:
Explanations are given in attachment!
help me please and thank you
What value of b completes f(x)=2x^2+bx+74 If the vertex is (-6,2)
Answer:
The value of b will be completed when b = 24
Step-by-step explanation:
f(x) can also be determined as y.
(-6, 2)
y = 2x²+bx+74
Plug it in.
2 = 2(-6) ² + b (-6) + 74
2 = 2(36) - 6b + 74
2 = 72 - 6b + 74
2 + 6b = 72 + 74
6b = 70 + 74
6b = 144
b = 24
PLEASE HELP QUICK PLEASE
The value of x in the similar triangle is 9 units.
How to find mid segment of a triangle?The midsegment of a triangle is a line connecting the midpoints between two sides of a triangle. Therefore, the midsegment theorem states that a line segment connecting the midpoints of any two sides of a triangle is parallel to the third side of a triangle and is half of it.
Hence,
9 / 72 = 3x - 20 / 56
cross multiply
9 × 56 = 72(3x - 20)
504 = 216x - 1440
504 + 1440 = 216x
1944 = 216x
divide both sides by 216
x = 1944 / 216
x = 9
Therefore,
x = 9
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write a comparison question that can be answered using the date on the bar graph (its for my little sister pls)
Answer:
Step-by-step explanation:
In mathematics and statistics, a bar graph is commonly employed. Bar graphs, generally referred to as bar charts, are graphic illustrations of grouped data. A bar graph is a graph that displays all of the data in the form of rectangular bars with heights proportionate to the values they represent. The graph’s bars can be depicted vertically or horizontally. The bars provide a visual representation of quantities in various categories.
Graphical Representation is a way of analyzing numerical data. It exhibits the relation between data, ideas, information, and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:
Line Graphs – A line graph or linear graph is used to display continuous data and it is useful for predicting future events over time.
Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.
Histograms – The graph that uses bars to represent the frequency of numerical data that are organized into intervals. Since all the intervals are equal and continuous, all the bars have the same width.
Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.
Frequency Table – The table shows the number of pieces of data that falls within the given interval.
Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered 100% and the categories occupied are represented with that specific percentage like 15%, 56%, etc.
Stem and Leaf Plot – In the stem and leaf plot, the data are organized from the least value to the greatest value. The digits of the least place values from the leaves and the next place value digit from the stems.
Box and Whisker Plot – The plot diagram summarises the data by dividing it into four parts. The box and whisker show the range (spread) and the middle ( median) of the data.