The total probability that a king and pawn are selected without replacement is 1 / 31 .
The area of mathematics known as probability primarily deals with numerical(fractions or decimals) representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Sample space = 32 (16 black and 16 white pieces)
number of kings in the set = 2
Probability that a king is selected first
P(king) = 2 ÷ 32 = 1 / 16
Now the total number of pieces left = 32 - 1 = 31
number of pawns = 8+8 =16
Probability that a pawn is selected = 16 ÷ 31
P(pawn) = 16/31
Now the total probability that a king and pawn are selected without replacement = P(king) × P(pawn) = 1/16 × 16/31 = 1 / 31
Therefore the required probability is 1 / 31 .
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Amare drops a probe into a lake. The elevation of the probe changes
by - 11 feet every second. The probe takes 50 seconds to reach
the bottom of the lake. How deep is the lake? Show your work.
The lake is 12,250 feets deep.
The elevation is changing in the downward direction and at a rate of -11ft/s.
So it means that the downward velocity of the probe is 11ft/s.
The value of downward acceleration is 9.8?m/s² which is equal to acceleration due to gravity.
The total time taken to reach down is 50seconds.
We can use the equation of motion because the acceleration is constant,
Using,
S = ut + 1/2at²
Where,
S is the depth of the pool,
U is initial velocity,
U is zero because the probe is dropped.
S = 1/2at²
S = 1/2××9.8×50×50
S = 12250 feets.
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There are 7 red cards, 6 blue cards, 8 purple cards, and 4 green cards in a hat. In a trial, a card is drawn from the hat and then replaced. In 640 trials a red card is drawn 240 times. How much greater is the experimental probability than the theoretical probability?
Responses
How do I solve this?
Answer:
????
Step-by-step explanation:
17. The area of a square poster is 31 square inches. Find the length of one side of the poster. Explain.
PART A
To the nearest whole inch
PART B
To the nearest tenth of an inch
The length of one side of the poster, when the area of a square poster is 31 square inches is
Part A = 6 inch (To the nearest whole of an inch)
Part B = 5.6 Inch (To the nearest tenth of an inch)
As given in the question,
Area of square poster = 31 sq. inches
Let 'l' be the length of the square poster
Now according to formula
Area of square poster = Length * Length
Substitute the values in the formula we get,
31 = l × l
⇒ l² = 31
⇒ l = √31
⇒ l = 5.568
Length = 5.568
Hence, the length of one side of the poster, when the area of a square poster is 31 square inches is
Part A = 6 inch (To the nearest whole of an inch)
Part B = 5.6 Inch (To the nearest tenth of an inch)
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Please help:The function graphed models the profits, P(c), in thousands of dollars a store earns as a function of the number of clerks, c, working that day.Which statements are true based on the model?Select each correct answer.Maximum profits are earned when there are 4 clerks working.The store earns profits when no clerks are working.Maximum profits are earned when there are 7 clerks working.The store earns about $400,000 in profits on its best days.The store loses money when 8 or more clerks are working.
SOLUTION
The image below will help in answering the following questions
Now, from the graph, the parts above the horizontal line represents profit, while the part below the horizontal line represents loss.
(a) Maximum profits are earned when there are 4 clerks working.
From the graph, we can see that this statement is CORRECT. The maximum profit is at 400 thousand dollars and takes place at 4 on the horizontal axis, this 4 represents 4 clerks working
(b) The store earns profits when no clerks are working.
No clerks are working when we consider 0 on the horizontal plane. From the picture above, tracing 0, it shows us something below the horizontal line which represents loss. So, this statement is INCORRECT. When no clerks work, there is a loss not profit
(c) Maximum profits are earned when there are 7 clerks working.
Tracing 7 from the graph, it doesn't fall on the top part of the curve which indicates maximum profit. Hence, this statement is INCORRECT.
d) The store earns about $400,000 in profits on its best days.
From the image above, we can see that this is correct.
(e) The store loses money when 8 or more clerks are working.
When we traced 8 from the horizontal line, it fell to the part of the graph which indicated loss.
Hence this is CORRECTstatement .
So you will select the 1st, 4th and 5th options
In a recent year an author wrote 162 checks. Use the poisson distribution to find the probability that on a randomly selected day he wrote at least one check
Answer:
44.38%
Step-by-step explanation:
Becuase of 365 days a year, 162 out of 365 is 44.38% meaning that if he would selwcted a fay the probability would be 44.38% chance.
The sticker on Dean's new car states that the car averages 32.6 miles per gallon. If the fuel tank holds 12.3 gallons, then how far can Dean travel on one full tank of gas?
Answer:400.98 miles on one full tank
Step-by-step explanation:
you take 32.6 and multiply it by 12.3
Identify the exponent in the term -3X²
A. 3
B. x
C. minus sign ( - )
D. 2
4x4 + 2x
Pleaseeeeee helpppp
Answer:
2x (2x³ + 1)
Step-by-step explanation:
To get the answer factor 2x^1 / 2x of ( 4x^4 + 2x )
When you factor an expression, you are looking for a number which can perfectly divide into another number.
Remember that the numerical timetable states that (2 x 2 = 4).
And we already know that (2 divided by 4 = 2), as well as, that any rational number divided by itself is equal to 1
Therefore the value 2x is divisible by itself and is also divisible by 4x^4 exactly two times
Note: the reason why (4x^4 ÷ 2x ) becomes (2x³), is that you have to subtract the exponents of each term from each other after you finish dividing. So ( X^4 - X^1 = X^3) -
Always remember that any term in a polynomial expression which doesn't have a visible power attached to it is already at the first power
Can yiu show me how to set it up and the answer please [tex]when \: k {}^{3} - 17k + 32 \: is \: divided \: by \: k + 5[/tex]
When the polynomial is divided by the linear expression we get the quotient k² -5k +8 and the remainder -8.
Polynomials are used in many areas of mathematics. For example, they are used in arithmetic and mathematical methods to approximate other functions. They are also used to describe linear combinations, which are encountered in a variety of situations, from basic physics and biology to economics and science.
From straightforward word problems to intricate scientific conundrums, polynomial equations are utilised to represent a wide range of topics. Algebraic varieties and polynomial rings, two essential concepts in algebra and computational geometry, are constructed in mathematics using harmonics.
The simplest way to do the long division is:
[tex]\begin{array}{r}k^2-5k+8\phantom{)} \\x+5{\overline{\smash{\big)}\,k^3-17k+32\phantom{)}}}\\\underline{-~\phantom{(}(k^3+5k^2)\phantom{-b)}}\\-5k^2-17k+32\phantom{)}\\\underline{-~\phantom{()}(-5k^2-25k+40)}\\ -8\phantom{)}\end{array}[/tex]
Hence the division will give quotient quotient k² -5k +8 and the remainder -8.
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12.7-18.5+15+6.3-1+28.5
Answer:
43
Step-by-step explanation:
Find the value of x.
Answer:
x=12
Step-by-step explanation:
Please Help this is due in 4 minutes!!!!!
Will give Brainiest
Solve the following equation to find the value of x:
9x-4=5x+12
Answer: x=4
Step-by-step explanation:
First find the smallest x which would be 5x and subtract that from the 9x. So now it should be 4x-4=12. Then, move 4 and add that to the twelve which should now be 4x=16. Then, divide it by four and you get x=4.
Answer:
x = 4
Step-by-step explanation:
We start from
9x - 4 = 5x + 12
We move the "5x" to the left side of the "=" sign by changing it's sign from 5x which can be seen as +5x to -5x
9x - 4 - 5x = 12
Now we move the "4" to the right side of the "=" sign by applying the same principle as above, so -4 turns to +4
9x - 5x = 12 + 4
We than solve the subtraction and addition
4x = 16
Then we divide both sides of the equation by 4 and we get
x = 4
24. Carlos bought a cube-shaped aquarium. Write
an expression to represent the volume of the
aquarium.
3s
Volume of the aquarium is 27 [tex]s^{3}[/tex]
What is volume of cube ?The total number of cubic units that a cube totally fills up is referred to as its volume. An object with six square faces that is three dimensional is called a cube. The amount of space an object takes up in total is known as its volume. Space would be taken up by an object having a larger volume.
Volume of cube formula ?Depending on the inputted inputs, many formulas can be used to determine the volume of any cube. You may figure it out by measuring the diagonal of the cube or its sides.
Given that : Carlos bought a cube shaped aquarium with side 3s
As the aquarium have cube shape so the volume will be
Volume of cube is V =[tex]a^{3}[/tex]
a = 3
V = 27 [tex]s^{3}[/tex]
Hence ,Volume of the aquarium is 27 [tex]s^{3}[/tex]
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Express the polynomial in descending order.
4+ y4 - 9y³
y4 - 9y3 +4
Step-by-step explanation:
solo tienes que ordenarlo de mayor a menor de las variables
17. Is the operation of forming Cartesian products commutative? Explain why or why not.
Choose the correct answer below.
OA. The operation of forming Cartesian products is commutative because order does not matter in
the definition of a Cartesian product.
OB. The operation of forming Cartesian products is not commutative because part of the definition of
a Cartesian product is the order of the elements generated by the two sets.
OC.
The operation of forming Cartesian products is commutative because a Cartesian product is
multiplication and multiplication is commutative.
O D. The operation of forming Cartesian products is not commutative because multiplication is not
commutative.
The operation of forming Cartesian products is not commutative because part of the definition of a Cartesian product is the order of the elements generated by the two sets.
==========================================================
Explanation:
Let's go over an example. We'll have these two sets
A = {1,2}
B = {3,4}
The cartesian product is this set of ordered pairs
A x B= {(1,3), (1,4), (2,3), (2,4)}
Each (x,y) pair has x as a value from the first set mentioned (A), and y a value from the second set mentioned (B). It might help to make a 2 by 2 table.
If we swap the order of set A and B then we have
B x A = {(3,1), (4,1), (3,2), (4,2)}
We can see that A x B does not equal B x A in this case. Therefore, the cartesian product operation is not commutative. The order matters.
Side note: Two sets are equal when they are subsets of each other.
susy goes to the grocery store, 3 apples cost 1.50 . find the unit rate in cost per apple
Answer:
1.50/3 Apples=0.5
That means each apple cost 0.5. If it's in rands gonna be R0.5 or 50 Cents per apple.
Select the number line that plots these numbers.5, -2, 1, –4
Find the number line that dotted only the numbers 5,- 2, 1, -4, which is clearly the last option.
Find the intervals of increase for the polynomial. Rounded to the nearest 10th
From the graph we can conclude:
The function is increasing for the following interval:
[tex]x\in\mleft\lbrace(-\infty,0\mright)\cup(2,\infty)\}[/tex]Answer:
(-∞,0), (2,∞)
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The value of the variable 'A' which is a consecutive digit in the card is: 6
What is consecutive digits?
In mathematics, the consecutive digits are those digits whose difference between the two terms are constant. And the pattern of the terms should be continuous. It is used for the calculation based problems.
According to the question, the given data states that the 14 digits of a credit card has sum of the three consecutive digits is 18.
Therefore, at the end the blank box between 8 and 4 can be written as:
8 + m + 4 = 18 ⇒ m = 18 - 12 = 6 ⇒ m =6
Now, the pattern for the last three digits be: 864.
The pattern is repeating and the whole IN number is 64864864864864.
Hence, the value of the variable 'A' which is a consecutive digit in the card is: 6
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AP. The product of two whole numbers is 96 and their sum is less than 30. List all of the possibilities for the
two numbers.
Answer:
12 and 8; 16 and 6; 24 and 4
Step-by-step explanation:
Please help I’ll mark you as brainliest if correct!!
a ) P = { a , n , c , d }
b ) {4 , 7} ⊆ { 4,7,8,12}
c ) {0,1} ⊄ { 1,4,5,6}
are the equations is mathematical symbols
What are sets and subsets ?Subsets are a component of the mathematical concept of sets. A set is anything that is contained in curly brackets, as "a,b,c,d." If set B includes the numbers 2, 4, and 6, it is said to be a subset of set A, and if set A is a collection of even integers, it is said to be the superset of set B.
Calculationa ) P = { a , n , c , d }
b ) {4 , 7} ⊆ { 4,7,8,12}
c ) {0,1} ⊄ { 1,4,5,6}
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The precipitation, in inches, Tampa normally receives each month for the last four months of the year is as follows: 6.3, 2 3/10, 1.6, and 2 1/2. Write and evaluate an expression to determine how much precipitation, in inches, Tampa receives from September through December.
Answer:
12.7 inches======================
Convert the mixed fractions into decimal and find the sum as follows:
6.3 + 2 3/10 + 1.6 + 2 1/2 = 6.3 + 2.3 + 1.6 + 2.5 = 12.7Write the ratio in the simplest form comparing the monetary value of 2 nickels to that os 1 quarter
The ratio of the simplest form of 2 nickels to 1 quarter is 2:5.
What is defined as the ratio?The ratio can be defined as a comparison of two amounts of the same unit to determine that much of one amount is present in the other. Ratios are divided into two types. The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groups. This ratio is represented by the fraction a/b. To simplify a ratio even further, we use the same method we used to simplify a fraction. a:b = a/b.For the given question;
The two monetary values are given as;
2 nickles and 1 quarter.
We know that;
1 nickles = 0.2 quarter.
For 2 nickles multiply both side by 2.
2 nickles = 2×0.2 quarter.
2 nickles = 0.4 quarter.
Find the ratio;
2 nickels to that of 1 quarter
2 nickels/ 1 quarter
Put the value of 2 nickle.
2 nickels/ 1 quarter = 0.4 quarter/1 quarter
2 nickels/ 1 quarter = 2/5
2 nickels: 1 quarter = 2:5
Thus, the ratio of 2 nickels to that of 1 quarter is found as 2:5.
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Thirty-five students attend a math club meeting. The number of girls at the meeting is a multiple of 13, and there are more girls than boys attending the meeting. How many boys are at the meeting?
Answer: 9 boys
Reason:
The multiples of 13 are
13, 26, 39, 52, ...
We only need to focus on the first two since they are smaller than 35
So we focus on 13 and 26
If there are 13 girls, then there are 35-13 = 22 boysIf there are 26 girls, then there are 35-26 = 9 boysThe second option has more girls than boys, so that must mean there are 26 girls and 9 boys.
3) Identify the center and radius
SOLUTION:
Case: Circle equations
Metho:
[tex](x-a)^2+(y-b)^2=r^2[/tex]Given:
[tex]\begin{gathered} (x+11)^2+(y-6)^2=9 \\ (x+11)^2+(y-6)^2=3^2 \end{gathered}[/tex][tex]\begin{gathered} Center(a,b)=(-11,6) \\ radius,r=3 \end{gathered}[/tex]Final answer:
Center (-11, 6)
radius, r= 3
[3−∣∣−56−2(−13)∣∣]÷(−17)
What is the value of the expression?
The answer as a simplified fraction in the box is -1/6
Given the expression
[3-|-5/6 -2(-1/3)|] ÷ (-17)
Using PEDMAS
P is for parenthesis
[3-|-5/6+2/3)|] ÷ (-17)
[3-|2/3 - 5/6)|] ÷ (-17)
[3-|(4-5)/6)|] ÷ (-17)
[3-|-1/6)|] ÷ (-17)
Since the modulus of a negative number is equal to a positive number, the result will give:
[3 - 1/6] ÷ (-17)
[(18-1)/6] ÷ (-17)
17/6 ÷ (-17)
Next is to carry out the division operation
17/6 × (-1/17)
= -1/6
Hence, The answer as a simplified fraction in the box is -1/6
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PLEASE HELP. I HAVE BEEN STUCK ON THIS ASSIGNMENT FOR A WHILE!! I WILL GIVE BRAINLIEST
The answer to the given question is option A that is only the first equation is an identity.
What are trigonometric identities ?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
Sin θ = 1/Csc θ or Csc θ = 1/Sin θ
Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
Tan θ = 1/Cot θ or Cot θ = 1/Tan θ
1) LHS : 8 sec θ sin θ = 8 X 1/ cos θ X sin θ = 8 tan θ
RHS : 8 X sin^2 θ/ cos^2θ X cosθ / sin θ = 8 tan θ
Thus LHS = RHS and it is given above so 1st equation is an identity.
2) LHS: 11 X cot^2 θ/ cosec θ X sec^2 θ = 11 cos^2θ /sin θ
and RHS : 11 cosec^2 θ
since LHS ≠ RHS because the second equation us not an identity.
thus the correct option is A that is Only the first equation is an identity.
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Describe and correct the error a student made when graphing [tex]y+5=-\frac{3}{4}(x-8)[/tex].
Answer/Step-by-step explanation:
3
y + 5 = ( - ) ------- (x - 8)
4
3
y + 5 = ( - ) ------- x + 6
4
3
y + 5 = ( - ) ------- x + 6
-5 4 -5
3
y = ( - ) ------- x + 1
4
m = slope = (-3/4)
b = y-intercept = (0, 1)
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The student's first error was in step 1.
Step 1 should involve plotting a point at (0, 1).
Step 2 should involve plotting a point 3 units down and 4 units right from the point in step 1, at (4, -2).
Step 3, connecting the points with a line was correct.
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I hope this helps!