In a given permutation of 52 cards, if the 3 of spades is to follow all of the hearts, that means the 3 of spades must be at least the 14th card in the deck.
Consider some possible orderings of the deck:
• If the 3 of spades is the 14th card, then the deck looks like
[all 13 ♥] … 3 ♠ … [all other 38 cards]
There are 13! ways to arrange the 13 hearts at the beginning and 38! ways to arrange the tail of 38 cards. Hence there are 13! × 38! possible rearrangements of the deck where 3 ♠ is the 14th card.
• If 3 ♠ is the 15th card, then the deck looks like
[13 ♥ and 1 other] … 3 ♠ … [all other 37 cards]
and there would be 14! × 37! ways of arranging the cards in this order.
There are 39 possible positions for 3 ♠. Extrapolating, it follows that the total number of permutations of the deck in which all hearts occur before 3 ♠ is
[tex]\displaystyle \sum_{k=0}^{38} (13+k)! \times (38-k)![/tex]
There are 52! total possible ways of rearranging the deck. Then the probability of rearranging the deck so that all hearts are drawn before 3 ♠ is
[tex]\displaystyle \frac1{52!} \sum_{k=0}^{38} (13+k)! \times (38-k)! = \frac{87,031,512,096,420,449}{221,360,321,731,856,907,600} \approx \boxed{0.000393}[/tex]
9.2 less than 3 times a number is the same as 2114.What is the number?
Answer:
707.7
Step-by-step explanation:
3x-9.2 = 2114
2114+9.2 = 2123.2
3x = 2123.2
x = 707.7
Answer:
10.15
Step-by-step explanation:
3x-9.2 = 21.25
3x = 30.45
x = 10.15
r(2)=120 and r(4)=378 divide the difference in the r(x) values by the difference in the x-value
Answer:
im not sure ask siri
Step-by-step explanation:
she knows everything
Find the measure of the indicated angle.
Answer:
11) x = 21
12) x = 110
13) x = 85
14) x = 137
Step-by-step explanation:
Hope it helped <3
What is theValue of x ?
Answer:
10
Step-by-step explanation:
x is 10
lhaila and her friends organize an overnight swimming pool get together the total amount of Php 24 000 wa allotted for the resort reservation and car rental which would be divided in proportion to the number of attendees laila noted some possible amount of contribution in proportion into the number of attendees
Using the concept of variation, there is an inverse relationship between the number of attendees and the contribution made by each attendee.
Since the amount of chocolate decreases as the number of attendees increase;
We use inverse variation to model the scenario :
y = k/x ; k = constant of proportionalityTaking any pair of points :
3000 = k/8
k = 3000 × 8
k = 24000
Hence, the constant of variation is 24000The variation expression is y = 24000/x This means that the total cost of organising the gettogether is to be shared equally among the attendeesTherefore, the variation statement is "the amount paid per attendee is inversely proportional to the number of people in attendance.
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Two vertical angles have measures (4x-21)° and (x+6)°. Find the measures of the angles
The measure of the two vertical angles is 15°
The two vertical angles have measures (4x-21)° and (x+6)°
Note that:
The measure of two vertical angles are equal
Therefore, equate (4x-21)° and (x+6)° and solve for x
(4x-21)° = (x+6)°
4x - 21 = x + 6
Collect like terms
4x - x = 6 + 21
3x = 27
x = 27/3
x = 9
Substitute x = 9 into 4x - 21
4x - 21 = 4(9) - 21
4x - 21 = 15°
Substitute x = 9 into x + 6
x + 6 = 9 + 6
x + 6 = 15°
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James is going on vacation for 9 days. William is going on vacation for 6 times as long. How long is William going on vacation?
Group of answer choices:
William is going on vacation for 36 days.
William is going on vacation for 45 days.
William is going on vacation for 54 days.
William is going on vacation for 63 days.
Answer:
William is going on vacation for 54 days
Step-by-step explanation:
Answer:
C) William is going on vacation for 54 days
Step-by-step explanation:
We know that James is going on vacation for 9 days. We also know that William goes on vacation for 6 *times* as long. What this means is that we are answering 9 times 6, which is 54
GIVING BRAINLIEST
A submarine is traveling along the surface of the ocean when they spot a pod of dolphins ahead. To avoid the dolphins, the submarine will dive and travel through the ocean. If the submarine wants to be 1.1 nautical miles below the dolphins after traveling 2.5 nautical miles, what dive angle must the submarine make? Write only the number rounded to the nearest angle.
Answer:
26 degrees
Step-by-step explanation:
The attached image shows how I interpret this question, and I assume you're meant to use trigonometry to solve.
From the perspective of the angle, we have a relationship between the opposite side, the hypotenuse, and the angle. Because the 2 sides are the opposite and the hypotenuse, we need the sine function, and because the angle is the unknown, we need the inverse sine function.
(soh cah toa)
[tex]sin(x)=\frac{opposite}{hypotenuse}\\\\sin^{-1}(\frac{opposite}{hypotenuse})=x[/tex]
Now, just plug in the 2 known values and solve for the unknown:
[tex]sin^{-1}(\frac{1.1}{2.5})=x\\\\sin^{-1}(0.44)=x\\\\x=26.1039[/tex]
The angle is 26 degrees, and you can check that by doing it in reverse:
[tex]sin(26.1039)=\frac{1.1}{2.5}\\\\sin(26.1039)=0.44\\\\0.44=0.44[/tex]
can someone help me with this please:)
Answer:
A
Step-by-step explanation:
[tex]2 \sqrt{3} + \sqrt{9} \times \sqrt{ - 1} = 2 \sqrt{3} + 3i[/tex]
please help will mark as brainlist
Answer:
176
Step-by-step explanation:
Answer:
[tex]m[/tex]∠STV = 43°
Step-by-step explanation:
It has the corresponding relation with ∠UTV
El siguiente cuerpo es CUARTA PARTE de un cilindro. ¿Cuál es el volumen? r = 6 cm; h = 9 cm
Answer:
es 54 espero que esto ayude adiós!
Step-by-step explanation:
El volumen de un cilindro con un radio de 6 cm y una altura de 9 cm es 1018 cm³
Un cilindro es una forma tridimensional con dos bases paralelas unidas por una trayectoria curva a una distancia constante.
El volumen de un cilindro es:
Volumen = πr²h
Given that: r = 6 cm; h = 9 cm;
Volumen = πr²h = π(6)²(9) = 1018 cm³
El volumen de un cilindro con un radio de 6 cm y una altura de 9 cm es 1018 cm³
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At which root does the graph of f(x) = (x + 4)(x + 7,5) cross the x-axis?
-7
-4
4
7
Answer:
Answer: -7
Step-by-step explanation:
The roots at which the graph of f(x) =(x + 4[tex])^6[/tex](x + 7[tex])^5[/tex] cross the x axis are -4 and -7.
What is Root of Equation?In mathematics, a root is a solution to an equation that is usually stated as a number or an algebraic formula.
A quadratic equation's roots are the variable values that fulfil the equation. They are also referred to as "solutions" or "zeroes" of the quadratic equation.
We have If(x) = (x + 4[tex])^6[/tex](x + 7[tex])^5[/tex] cross the x-axis then y = f(x) = 0.
Now, if f(x) = 0
then (x + 4[tex])^6[/tex](x + 7[tex])^5[/tex] = 0
Now, calculating in separate the value of x as
x +4 =0 and x+ 7= 0
x = -4 and x = -7
Thus, the roots cross x axis at -4 and -7.
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How to solve quadratic using completing the square.
Answer:
You can solve quadratic equations by completing the square. Completing the square involves creating a perfect square trinomial from the quadratic equation, and then solving that trinomial by taking its square root.
Step-by-step explanation:
Find the perimeter. Simplify your answer.
Answer:
16c-6
Step-by-step explanation:
(7c-6)+(6c-10)+(3c+10)=?
7c-6+6c-10+3c+10=?
Collect like terms.
16c-6-10+10
Add and subtract.
16c-6
Hope this helps :)
Use substitution to solve the system. 5X+3Y=22 Y=2X-11
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day.
We can solve this problem in two steps, Comprehending, and Solving/Checking our answers. I'll be starting off with Comprehending.
Comprehending
We can solve the problem with substitution by finding out what one variable is equal to in terms of the second variable.
This is what we would call System of Equations where we need to find the point where the lines hit.
We can do this either with Graphing, or Algebra. In this case, we need to use substitution, so it has to be Algebraically.
Now that we know how to solve it/what to do, we can start solving.
Solving
We can solve the problem by first replacing y with its correct value in terms of x. Since we know the two equations, we can begin solving.
[tex]y=2x-11\\5x+3y=22[/tex]
We can solve it by inserting our y value into the y value of the second equation.
[tex]5x+3(2x-11)=22\\5x+6x-33=22\\11x=22+33\\11x=55\\x=5[/tex]
Now that we know our x value, we can solve for y by inserting it into an equation.
[tex]y=2(5)-11\\y=10-11\\y=-1[/tex]
Now that we have solved, we have gotten out point of (5,-1)
We can test this by inputting it into an equation. (Any of the latter).
[tex]5(5)+3(-1)=22?\\25-3=22?\\22=22[/tex]
Now that we have checked our answer and it appears correct, we have gotten our answer of (5,-1).
Answer:
(5, - 1 )
Step-by-step explanation:
5x + 3y = 22 → (1)
y = 2x - 11 → (2)
Substitute y = 2x - 11 into (1)
5x + 3(2x - 11) = 22 ← distribute parenthesis and simplify left side
5x + 6x - 33 = 22
11x - 33 = 22 ( add 33 to both sides )
11x = 55 ( divide both sides by 11 )
x = 5
Substitute x = 5 into (2)
y = 2(5) - 11 = 10 - 11 = - 1
solution is (5, - 1 )
What is the total volume of both storage spaces if one side of the large storage space is 4 feet long?
The total volume of both storage is 76 ft³
What is Volume of cube?The number of cubic units that a cube totally occupies is determined by its volume. The cubic unit of measurement for the volume of a cube includes centimetres³, metres³, inches,³ feet³, etc.
A solid three-dimensional shape with six square faces or sides is known as a cube. The total amount of space a cube takes up is its volume. The cube's square form means that all of its sides are square, and as a result, all of its edges will be of equal length. As a result, the cube's length, breadth, and height are all equal.
The formula to compute the volume of cube is a³; where 'a' is the edge of the cube.
Given:
Larger box volume = s³
smaller box volume = 12 ft³
Now, the edge of larger box = 4
So, volume of larger box
= 4 x 4 x 4
= 64 ft³
Hence, the total volume is = 64 +12 = 76 ft³
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When raising a power to a power you________ the exponents.
Answer:
Multiply
Step-by-step explanation:
To raise a power to a power means to raise one exponent to another. Whether the exponents are real, imaginary, monomials or polynomials, to simplify these problems, all we have to do is multiply the exponents together.
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add the following rational number =
3/11 and -5/12
Answer:
-19/132
Step-by-step explanation:
To add fractions, find the lowest common multiple of the two denominators and multiply accordingly to make both denominators the same. In this case, the lowest common multiple of 11 and 12 is 132, so we need to multiply the first number by 12 and the second by 11. So we get [tex]\frac{36}{132} + (-\frac{55}{132} )[/tex] = [tex]\frac{36-55}{132}[/tex]=[tex]\frac{-19}{32}[/tex][tex]-\frac{19}{132}[/tex]
You start driving east for 5 miles, turn left, and drive north for another 12 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
Answer:
13 ≈ 10 miles
Step-by-step explanation:
Have a nice day
You start driving east for 5 miles, turn left, and drive north for another 12 miles. At the end of driving So, the straight-line distance from your starting point is 13 miles.
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
You start driving east for 5 miles, turn left, and drive north for another 12 miles. At the end of driving,
[tex]|AC|^2 = |AB|^2 + |BC|^2 \\\\|AC|^2 = |5|^2 + |12|^2 \\ \\|AC|^2 = 25 + 144 \\\\AC = \sqrt{169} \\\\AC = 13[/tex]
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What is the value of f(x), if x is -8?
Answer:
-8f
Step-by-step explanation:
you will substitute in the numbers and multiply
Because f is a variable you write the -8 and attach the f to it
The value of function for given x value is -1.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)=-(x+8)²-1.
Substitute x=-8 in the given function, we get
f(-8)=-(-8+8)²-1
= -0-1
= -1
Therefore, the value of function for given x value is -1.
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"Your question is incomplete, probably the complete question/missing part is:"
What is the value of f(x)=-(x+8)²-1, if x is -8?
Which is the best example of anticipating a potential accident in a science lab? A student skips the instructions because she has performed the lab before. A student checks for flammable liquids before lighting the Bunsen burner. A student keeps a glass of water on her lab bench in case she gets thirsty. A student works quickly so that she can be on time for her next class
Answer: C
Step-by-step explanation:
i took the test
PERSONALLY I thought it would be 98 Bc like yk..BUT I FEEL LIKE IM WRONGsend help beggin cryin throwin up I hate geometry so much
Answer:
X=98(Being corresponding angle)
You are correct
PLEASE I NEED HELP
The figure shows a quarter circle and an equilateral triangle. What is the area of the shaded part? Give your answer to 3 significant figures. (Take π = 3.14.)
Answer:
14.0
Step-by-step explanation:
First, find the area of the whole circle using the equation pi * r^2.
pi * (7^2) = 49pi
Then, to only get the area of a quarter of the circle, divide this number by 4.
49pi/4 = 38.485
Then, to get only the shaded region, you have to find the area of the triangle and subtract it from the area of the quarter circle. The area of the triangle is found using 1/2 * b * h.
1/2 * (7*7) = 24.5
Then subtract that number from the previous one.
38.485 - 24.5 = 13.985
You need to round this to 3 significant figures, so it would be 14.0.
Hope this helps
х
4.
1
6 11
y
-3
-2
-1
0
slope:
Answer:
slope = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (11, 0) ← 2 ordered pairs from the table
m = [tex]\frac{0-(-3)}{11-(-4)}[/tex] = [tex]\frac{0+3}{11+4}[/tex] = [tex]\frac{3}{15}[/tex] = [tex]\frac{1}{5}[/tex]
Which part of this problem should be simplified first?
(100 – 37 + 15) × 2 ÷ 3
Answer:
the parentheses should be the first.
Step-by-step explanation:
follow the steps using PEMDAS.
P- parentheses
E- exponent
M- multiply
D- divide
A- addition
S- subtraction
Answer:
The answer is 100 - 37. Do not put parenthesis when answering your question.
Step-by-step explanation:
The number of packages of ribbon varies directly to the total amount of ribbon in feet. At a packaging plant 12 packages of ribbon will contain 900 feet of ribbon. If 4 packages of ribbon on ordered, how many feet of ribbon will there be?
Answer:
300 feetStep-by-step explanation:
Direct variation equation:
y = kx, where k is the coefficient of variationWe have y = 900, when x = 12, find the value of k:
900 = 12kk = 900/12k = 75The equation is:
y = 75xNow, find the value of y, when x = 4:
y = 75*4 = 300A cake measures 18 centimeters in diameter. Find how much room there is to spread frosting on the top of the cake.Complete the answer sentence. You may consider writing your answer to the hundredths place and using the calculator to help you solve.
12 lbs of
potatoes
for $15.00
OR
8 lbs of
potatoes
for $9.20
Answer:
12 lbs for $15
Step-by-Step Solution:
12 / $15 = $0.80
8 / $9.20 = $0.87
What is the slope of the equation Y= 5/4 x - 7/4?
a. -7
b. -7/4
c. 5/4
d. 5
Answer:
a
Step-by-step explanation:
Answer: c
Step-by-step explanation:
what is the answer ?????
Answer:
2456≈2500
14725=14700 (to 3sf)
