120 is the number divisible by 6, 8, and 10.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The common multiples to 6, 8, and 10.
6 x 20 = 120
8 x 15 = 120
10 x 12 = 120
So,
120 is divisible by 6, 8, and 10.
Thus,
120 is the number.
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if given two numbers of the following forms, which ones do not result in the correct mathematical result in the same form? assume there is no overflow (i.e., the result can fit in the available wires).
The two numbers of the form a+bi and c+di where a,b,c, and d are real numbers, and i is the imaginary unit, always resulting in the correct mathematical result in the same form.
This is because complex numbers are a mathematical construct and the operations defined on them, such as addition, subtraction, multiplication, and division, follow the rules of arithmetic. These operations preserve the form of the numbers, so that the result of any two complex numbers, when operated upon, will always be in the form of a complex number.
For example, when adding two complex numbers (a + bi) and (c + di), the real parts add up to form a new real part, and the imaginary parts add up to form a new imaginary part, resulting in a new complex number in the form (a + c) + (b + d)i.
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Suppose a basketball player makes 55.3% of shots and that the probability of making each shot is independent. If the basketball player attempts 6 shots, what is the probability of making at least one shot?
There is a probability of 98.1% or around 0.98 of making at least one shot.
We can solve this problem using the binomial distribution. Let X be the number of shots the basketball player makes out of 6 attempts. Then X follows a binomial distribution with parameters n = 6 (number of trials) and p = 0.553 (probability of success).
The probability of making at least one shot can be calculated as the complement of the probability of missing all six shots. That is:
P(X ≥ 1) = 1 - P(X = 0)
Using the binomial probability formula, we can calculate P(X = 0) as:
P(X = 0) = (6 choose 0) * (0.553)^0 * (1 - 0.553)^(6-0) = 0.019
where (6 choose 0) = 1 is the number of ways to choose 0 shots out of 6.
Therefore,
P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.019 = 0.981
So the probability of making at least one shot is approximately 0.981 or 98.1%.
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what is the value of the expression shown below when x=7? 3x^2 - 2x+3
The expression value of 3x^2 - 2x+3 is 6x^2 - 13x + 6
What is expression value?Value of an Expression The value of the expression is the result of the calculation described by this expression when the variables and constants in it are assigned values. Letters can be used to represent numbers in an algebraic expression.
Apply the distributive property:
→ 3x (2 - 3) - 2 (2x - 3)
Apply the distributive property:
→ 3x (2x) + 3x ⋅ -3 - 2 (2x - 3)
Apply the distributive property:
→ 3x (2x) + 3x ⋅ -3 - 2 (2x) - 2 ⋅ -3
Simplify each term:
→ 6x^2 - 9x - 4x + 6x
Subtract 4x from -9x
→ 6x^ - 13x + 6
Therefore, the expression value of 3x^2 - 2x+3 is 6x^2 - 13x + 6
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The value of the expression given is 136.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression is,
3x² - 2x + 3
We have to find the value of the expression when x = 7.
Substitute x = 7.
(3 × 7²) - (2 × 7) + 3 = (3 × 49) - 14 + 3
= 147 - 14 + 3
= 136
Hence the value of the expression is 136.
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Help me pls asap …..
Based on the information, it can be inferred that the volume of a cube with a side length of 30 cm is 27,000cm³ and the area would be 90cm².
How to calculate the volume and area of the cube?To calculate the volume and area of the cube we must perform the following mathematical procedures:
Volume:
We must multiply side * base * depth = volume.
30cm * 30cm * 30cm = 27,000cm³Area:
We must multiply the base by the side
30cm * 30cm = 90cm²According to the above, the area and volume of this cube would be 90cm² and 27,000cm³ respectively.
Note: This question is incomplete. Here is the complete information:
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evaluate the following: f open parentheses x close parentheses equals 3 x squared minus 2 x plus 1 comma space e v a l u a t e space f open parentheses negative 1 close parentheses
The value of the function f(x) = 3x^2 - 2x + 1 at x = -1, will be 6
In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Algebraic expressions are expressions that are made up of variables and constants. Any value can be assigned to a variable. The value of an expression changes depending on the values assigned to the variables it includes. There are an unlimited number of points on a number line.
To evaluate the function f(x) = 3x^2 - 2x + 1 at x = -1,
we simply substitute -1 for x in the expression:
f(-1) = 3(-1)^2 - 2(-1) + 1
= 3(1) + 2 + 1
= 6
Therefore, f(-1) = 6.
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Use the remainder theorem and synthetic division to find the value of
f(3) if f(3) = x^3 - 6x^2 + 13x - 11
SHOW THE STEPS OF THE SYNTHETIC DIVISION!
The quotient is x² - 3 - 4 and remainder is 1.
So, The value of f (3) is, 1
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
The value of f(3) is told by the remainder theorem to be the remainder from division of f(x) by (x -3). That division is shown in the attachment. The remainder is 1, hence we have;
⇒ f(3) = 1
The number at upper left in the synthetic division table is the value of x for which we are evaluating f(x).
When the polynomial is written in Horner Form:
⇒ f(x) = ((x -6)x +13)x -11
Here, the coefficient of x at each point in the evaluation is the same as the number on the bottom row of the synthetic division. The result of the evaluation is the same as the remainder from the division.
Now, Add the obtained result to the next coefficient of the dividend and write down the sum as;
3 | 1 - 6 13 - 11
3 - 9 3x4 = 12
-----------------------
1 - 3 4 (- 11) + 12 = 1
Thus, We have complete table and have obtained the resulting coefficient are,
1 , - 3, 4, 1
Thus, The quotient is x² - 3 - 4 and remainder is 1.
So, The value of f (3) is, 1
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What is the area of the trapezoid?
8 cm-8 cm-8 cm
10 cm
The area of the trapezoid is given as follows:
160 cm².
How to obtain the area of a trapezoid?The area of a trapezoid is obtained adding the bases, multiplying by the height, and dividing by 2.
For the trapezoid in this problem, the parameters are given as follows:
Bases 8 and 24 cm.Height of 10 cm.Hence the area is given as follows:
A = 0.5 x (8 + 24) x 10
A = 160 cm².
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In Problems 37 through 42, determine by inspection at least one solution of the given differential equation. That is, use your knowledge of derivatives to make an intelligent guess. Then test your hypothesis. 37. y" = 0 38. y' = y 39. xy' + y = 3x2 40. (y')2 + y2 = 1 41. y' + y = ex 42. y" + y = 0
Previous question
37. A possible solution is y(x) = ax + b, where a and b are constants. Taking two derivatives gives y''(x) = 0, which satisfies the differential equation.
38. A possible solution is y(x) = Ce^x, where C is a constant. Taking the derivative of y(x) gives y'(x) = Ce^x, which satisfies the differential equation.
39. A possible solution is y(x) = 3 + 2x^2, which can be checked by taking the derivative and plugging it into the differential equation: xy'(x) + y(x) = x(4x) + (3 + 2x^2) = 3x^2 + 2x^2 + 3 = 5x^2 + 3, which is equal to 3x^2 when x=0.
40. A possible solution is y(x) = sin(x), which can be checked by taking the derivative and plugging it into the differential equation: (y'(x))^2 + (y(x))^2 = cos^2(x) + sin^2(x) = 1.
41. A possible solution is y(x) = ex - 1, which can be checked by taking the derivative and plugging it into the differential equation: y'(x) + y(x) = e^x + e^x - 1 = 2e^x - 1.
42. A possible solution is y(x) = Asin(x) + Bcos(x), where A and B are constants. Taking the second derivative gives y''(x) = -Asin(x) - Bcos(x), which satisfies the differential equation.
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Determine which of the vectors is (are) parallel to z_ Use a graphing utility to confirm your results. (Select all that apply.) z has initial point (5, 4, 1) and terminal point (-2, -4, 4). a. 7i + 6j + 2k
b. -7i- 6j -2k c. 14i +16j+ 6k d. -14i -16j + 6k
e. i + 4j - 2k f. i - 4j + 2k g. None of these vectors are parallel to z.
The vectors that are parallel to z that has has initial point (5, 4, 1) and terminal point (-2, -4, 4) are -7i - 6j - 2k and -14i - 16j + 6k. So, the correct options are B and D.
To determine which vectors are parallel to z, we need to compare their direction to the direction of z. Two vectors are parallel if they have the same direction or are opposite in direction.
The direction of z can be found by subtracting the initial point from the terminal point:
z = (-2 - 5)i + (-4 - 4)j + (4 - 1)k
z = -7i - 8j + 3k
Now let's compare the direction of each given vector to the direction of z:
a. 7i + 6j + 2k: This vector is not parallel to z because it has a different direction.
b. -7i- 6j -2k: This vector is parallel to z because it has the opposite direction.
c. 14i +16j+ 6k: This vector is not parallel to z because it has a different direction.
d. -14i -16j + 6k: This vector is parallel to z because it has the opposite direction.
e. i + 4j - 2k: This vector is not parallel to z because it has a different direction.
f. i - 4j + 2k: This vector is not parallel to z because it has a different direction.
Therefore, the vectors that are parallel to z are b. -7i - 6j - 2k and d. -14i - 16j + 6k.
To confirm these results using a graphing utility, we can plot z and each of the given vectors on a 3D coordinate system and visually check their directions.
Here is an example using Wolfram Alpha:
vectorplot3d {<-7, -8, 3>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<7, 6, 2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<-7, -6, -2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<14, 16, 6>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<-14, -16, 6>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<1, 4, -2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
vectorplot3d {<1, -4, 2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}
This will generate a 3D plot with all the vectors plotted. We can see that only the vectors with opposite directions to z, namely -7i - 6j - 2k and -14i - 16j + 6k, are parallel to z.
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convert the binary fractional number 0.000112 to a decimal representation. you can use fractions or floating point values, but your answer must be precise. you can use expressions if that's useful.
The decimal representation of the given binary fractional number 0.000112 is 0.109375.
Binary numbers are composed of only 0s and 1s, while decimal numbers are composed of 0-9. Additionally, binary numbers follow a different place value system, where each digit represents a power of 2 rather than a power of 10.
Now, let's focus on the given problem - converting a binary fractional number 0.000112 to a decimal representation. We can use the following formula to convert any binary fraction to decimal:
(decimal equivalent) = (binary digit 1/2¹) + (binary digit 2/2²) + (binary digit 3/2³) + ...
Using this formula, we can start by breaking down the given binary fraction 0.000112 into its individual binary digits:
0.000112 = 0/2¹ + 0/2² + 0/2³ + 1/2⁴ + 1/2⁵ + 1/2⁶
Now, we can simply evaluate each term in the equation and add them up to get the decimal equivalent:
0/2¹ = 0
0/2² = 0
0/2³ = 0
1/2⁴ = 0.0625
1/2⁵ = 0.03125
1/2⁶ = 0.015625
(decimal equivalent) = 0 + 0 + 0 + 0.0625 + 0.03125 + 0.015625 = 0.109375
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What values of x
and y
satisfy the system {y=−2x+3
{y=5x−4?
Enter your answer as an ordered pair, like this: (42, 53)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution to the system of equation y = -2x + 3 and y = 5x - 4 is (1,1).
What is the solution to the system of equation?Given the system of equation in the question;
y = -2x + 3
y = 5x - 4
To solve the system of equation, plug equation one to into equation two and solve for x.
y = 5x - 4
Plug in y = -2x + 3
-2x + 3 = 5x - 4
Solve for x
-2x - 5x = - 4 - 3
-7x = -7
x = -7 / -7
x = 1
Now, plug x = 1 into equation one and solve for x.
y = -2x + 3
Plug in x = 1
y = -2( 1 ) + 3
y = -2 + 3
y = 1
Therefore, the value of x is 1 and y is also 1.
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Please solve quickly! Within 30 minutes would be great!
Please solve for the variable indicated.
A=1/2bh(h+b), solve for h
If you could break it down step by step that would be super helpful! I’m very confused. Thank you!
The equation solved for the variable h is h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]
How to determine the subject of formulaTo solve for a variable in a given equation is to make it the subject of formula.
The variable is made to stand alone on one end of the equality sign.
We have the equation given as;
A=1/2bh(h+b)
First, cross multiply
2A = bh(h+b)
2A = bh² + b²
collect like terms
2A - b² = bh²
Now divide by the coefficient of h²
h² = 2A - b²/b
Find the square root of both sides
h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]
Hence, the equation is h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]
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What is the length of XZ? Step by step.
The measure of XZ is equivalent to 24. Option C is correct
Solving similar trianglesThe given triangles in question are similar in nature. For every similar triangles, the ratio of the similar sides of the triangle is equal to a constant as shown:
k+3/36 = k+5/44
Cross multiply and expand
36(k + 5) = 44(k + 3)
36k + 180 = 44k + 132
36k - 44k = 132-180|
-8k = -48
k = 6
For the measure of XZ
k/XZ = k+5/44
6/XZ = 11/44
6/XZ = 1/4
XZ = 24
Hence the measure of XZ from the given diagram is equivalent to 24
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A tree is struck by lightning and snaps off 34 feet above the ground. The top part of the tree comes to rest creating a 17-degree angle with the ground. How tall was the tree before it broke to the nearest tenth of a foot?
We conclude that the angle at the top measures 65.8°.
What is right angle triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangled triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.
here, we have,
What angle does the top part?
The whole tree measures 117 ft, and it is broken 34 ft above the ground, forming this way a right triangle.
Then one cathetus of the right triangle measures 34ft, and the hypotenuse measures 117ft - 34ft = 83ft
The angle at the top is θ, the adjacent cathetus to it is the one that measures 34 ft, then to get the angle we can use the relation:
cos(θ) = (adjacent cathetus)/(hypotenuse)
Replacing what we know, we get:
cos(θ) = (34 ft)/(83ft) = 34/83
Solving for θ, we get:
θ = Acos( 34/83) = 65.8°
So we conclude that the angle at the top measures 65.8°.
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Help please I’m dying and it is dew tomorrow and I have no clue what it could be
The effect on the graph for the given function if the slope of the function is changed to -10 include the following: D. the line is less steep.
The effect on the graph for the given function if the y-intercept of the function is changed to a smaller positive number is: C. the line shifts down.
What is a slope?In Mathematics, a slope is sometimes referred to as rate of change and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.
Generally speaking, a slope simply refers to a measure of the steepness of a straight line. This ultimately implies that, the higher the slope of a line, the more steep it is and vice-versa.
Based on the information provided about this function y = 8 - 2x, we can logically deduce that the line would be shifted downward when its y-intercept is changed to a smaller positive number.
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¿ Como despejar B en esta variable
The simplified form of the expression (4 - a²b³)/5 = (9 - 3b³)/7 is
b³(15 - 7a²) = 17.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, An equation (4 - a²b³)/5 = (9 - 3b³)/7, in variables 'a' and 'b'.
7(4 - a²b³) = 5(9 - 3b³).
28 - 7a²b³ = 45 - 15b³.
15b³ - 7a²b³ = 45 - 28.
b³(15 - 7a²) = 17.
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(x − 3)(x² - 7x - 2)
Answer:
[tex]\huge\boxed{\sf x\³ - 10x\² + 19x + 6}[/tex]
Step-by-step explanation:
Given expression:= (x - 3)(x² - 7x - 2)
Distribute= x(x² - 7x - 2) - 3(x² - 7x - 2)
= x³ - 7x² - 2x - 3x² + 21x + 6
Combine like terms= x³ - 7x² - 3x² - 2x + 21x + 6
= x³ - 10x² + 19x + 6[tex]\rule[225]{225}{2}[/tex]
A box contains 24 tiles. Each tile has certain properties:
Each tile is made of wood or plastic.
Each tile is red, yellow, or blue.
Each tile is a triangle, square, pentagon, or circle.
There is exactly one tile for each combination of properties. For example, there is one red circle that is made of wood.
Steve chooses one tile, and Ellen chooses a different tile.
What is the probability that both tiles are red?
Answer: 12
Step-by-step explanation:
8 ft. 3 ft. is what in geometry
In geometry, 8 ft. 3 ft. specifies the dimension of an object. That is the length and the width.
What does 8 ft. 3 ft means means in geometry?
8 ft. 3 ft. is a dimension, specifically a length and a width. It could refer to the size of a rectangular object, such as a room or a piece of furniture.
In geometry, such a dimension is often used to calculate the area of the rectangle.
The area of a rectangle can be found by multiplying its length by its width.
So, in this case, the area of the rectangle with dimensions 8 ft. * 3 ft. would be 8 ft * 3 ft = 24 ft².
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help please
i give brainliest
mack is selling beaded necklaces and beaded wristbands at the craft market. a. a necklace requires 40 minutes to make. b. a wristband requires 25 minutes to make. c. mack has 360 minutes to make the necklaces and wristbands. additionally, a. mack wants to make no more than 12 items. b. when mack sells the necklaces and wristbands at the craft market, he will make $3.00 profit per necklace and $2.00 profit per wristband. let x = the number of necklaces mack maker.
Let y = the number of wristbands mack makes.
Mack should make 4 necklaces and 8 wristbands to maximize his profit while staying within his time and quantity constraints.
His profit would be:
Profit = 3(4) + 2(8) = $20.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
From the information given, we know:
a) Necklace requires 40 minutes to make.
Let x be the number of necklaces made, then the total time spent on necklaces is 40x.
b) Wristband requires 25 minutes to make.
Let y be the number of wristbands made, then the total time spent on wristbands is 25y.
c) Mack has a total of 360 minutes to make necklaces and wristbands. Therefore, the equation for time is:
40x + 25y = 360
d) Mack wants to make no more than 12 items, so we have the inequality:
x + y ≤ 12
e) Mack makes a profit of $3.00 per necklace and $2.00 per wristband. Therefore, the equation for profit is:
Profit = 3x + 2y
Now we have the following system of equations:
40x + 25y = 360
x + y ≤ 12
Profit = 3x + 2y
From equation (2), we have y = 12 - x.
Substitute y = 12 - x into equations (1) and (3):
40x + 25(12 - x) = 360
Profit = 3x + 2(12 - x)
Simplify and solve for x:
40x + 300 - 25x = 360
15x = 60
x = 4
Substitute x = 4 into equation (2) to find y:
y = 12 - x = 12 - 4 = 8
Therefore, His profit would be, Profit = 3(4) + 2(8) = $20.
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surface area
42 in.
11 in.
21 in
Answer:
3150
Step-by-step explanation:
...2(42x11+21x11+42x21)
BTW: This isn´t college-level math this is like 2nd-grade math.
It takes 6 hours to travel 372 miles. How long
will it take to travel 279 miles?
The time to travel 279 miles is 4.5 hours
How to determine the time takenWe can use the formula:
time = distance ÷ speed
To find the time it will take to travel 279 miles, given that it takes 6 hours to travel 372 miles.
The speed is constant, so we can find it by dividing the distance by the time for the first trip:
speed = distance ÷ time = 372 miles ÷ 6 hours = 62 miles/hour
Now we can use the speed to find the time it will take to travel 279 miles:
time = distance ÷ speed = 279 miles ÷ 62 miles/hour ≈ 4.5 hours
Hence, it will take approximately 4.5 hours to travel 279 miles at this speed.
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use fractions from the number lines in problem 1 complete the sentence. use words, pictures, or numbers to explain how you made that comparison
Based on the data, we can infer that the following numbers fill in the blanks: 100 is greater than 10.
How to fill in the blanks?To fill in the blanks we must carefully read the information in the fragment. Once we understand this information we can select the two numbers that meet the rule mentioned in the statement.
According to the above, a correct statement would be:
100 is greater than 10.Additionally, we could put other values that comply with this rule, for example:
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Find x in the right triangle
The solution is, the value of x=4.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
We can modify the Pythagorean Theorem to fit our needs and solve x. We know our c and our a so to find x or b
we use c^2-a^2=b^2.
from the given figure , we get,
Lets input our known.
5^2-3^2=x^2.
Lets start solving by squaring.
25-9=x^2
Subtract
16=x^2
Take the square root
4=x
Hence, The solution is, the value of x=4.
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Charlotte and Pablo are each making purple paint by mixing blue
paint and red paint. Charlotte uses 1 cup of red paint for every
2 cups of blue paint. Pablo uses 2 cups of red paint for every
3 cups of blue paint. Whose paint is a bluer shade of purple?
Answer:
Charlotte's mix has a bluer shade of purple
Step-by-step explanation:
Since we are asked whose paint is a bluer shade it would be easier to express the ratios of the paint mix as blue:red
Charlotte: 1 cup red for every 2 cups blue ==> 2 cups blue for every 1 cup red
This can be expressed as the ratio
[tex]\dfrac{ 2 \;blue}{1\;red} = \dfrac{2}{1} = 2[/tex]
[tex]-------------------[/tex]
Pablo : 2 cups red for every 3 cups blue ==> 3 cups blue for every 2 cups red
The ratio of blue to red
= [tex]\dfrac{3 \;blue}{2\;red} = \dfrac{3}{2} = 1\dfrac{1}{2} \;\; (or\; 1.5)[/tex]
Since
[tex]2 > 1\dfrac{1}{2} \;\;\;(or\; 2 > 1.5)[/tex]
Charlotte's mix has a bluer shade of purple
Albinism in humans is autosomal and fully recessive to normal color. A couple, who are both normal, have a daughter who is albino and a son who is normal. The couple wants to have 3 more children. What is the probability that they will have 3 normal girls?
The probability that the couple will have 3 normal girls is approximately 0.422
Since both parents are normal, they both have to be heterozygous carriers for the recessive allele that causes albinism. We can represent the normal allele with the letter N and the albino allele with the letter n. Then, we can write the genotypes of the parents as Nn x Nn.
The daughter is albino, so her genotype must be nn. The son is normal, so his genotype must be Nn.
We want to find the probability that the couple will have 3 normal girls. We can use the multiplication rule of probability to find this probability:
P(3 normal girls) = P(normal girl) x P(normal girl) x P(normal girl)
The probability of having a normal girl is 3/4 since there are three possible genotypes that result in a normal phenotype (NN, Nn, Nn) out of a total of four possible genotypes. The probability of having a normal boy is also 3/4, for the same reason.
Therefore, the probability of having 3 normal children (in this case, girls) is:
P(3 normal girls) = (3/4) x (3/4) x (3/4) = 27/64 ≈ 0.422
So, the probability that the couple will have 3 normal girls is approximately 0.422, or about 42.2%.
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which statement describes the relationship between X and Y in these two equations y = 2x Y = X + 2
The relationship between X and Y in the equations y = 2x and y = x + 2 is that they represent two different linear equations.
How to describe the relationship in the equationsFrom the question, we have the following parameters that can be used in our computation:
y = 2x
y = x + 2
Using the above as a guide, we have the following:
The equations are linear equationsThe linear equations are not equivalentHence, the relationship is different linear equations
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Find the sum and express it in simplest form.
(-3n³-3n²) + (8n³ + 6n² - 4)
Answer:
= 5n³ + 3n² - 4
Step-by-step explanation:
(-3n³-3n²) + (8n³ + 6n² - 4)
= -3n³-3n²+8n³+6n²-4
= -3n³+8n³-3n²+6n²-4
= 5n³+3n²-4.
A game is played in which a card is randomly drawn from a well-shuffled standard deck of 52 cards. The card is recorded and then returned to the deck. Another card is drawn and the process is repeated 10 times. Let K =the number of kings observed in the 10 trials. Note that there are four kings in a standard deck of 52 cards.
A. Calculate and interpret the mean of K. b. Calculate and interpret the standard deviation of K.
B. Calculate and interpret the standard deviation of K
C. What is the probability of getting more than 4 kings?
D. Compute P(K≤ 3).
E. As described, this setting is binomial. Describe a setting using a well-shuffled standard deck of 52 cards that would not be binomial. Briefly explain your reasoning.
As a result of answering the question, we may state that equation In ten attempts, there is a 0.0407 percent chance of getting more than four kings, which is a very little chance.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals symbol (=). A theoretical statement that proves the equality of two formulas is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14.
A. With n=10 and p=4/52, the binomial distribution of the number of kings seen in the 10 trials, K, is followed (since there are 4 kings in a standard deck of 52 cards). K's average is:
mean(K) is equal to[tex]n * p (10 * 4/52 = 0.7692).[/tex]
Meaning: On average, we anticipate seeing 0.77 kings per 10 trials.
B. This is the variance of K:
The formula for var(K) is [tex]n * p * (1 - p) = 10 * 4/52 * (1 - 4/52) = 0.7255.[/tex]
K's standard deviation:
[tex]\sqrt(var(K)) = \sqrt(0.7255) = 0.8524[/tex] where sd(K) =
D. The binomial distribution can be used to calculate the likelihood of receiving more than four kings:
P(K > 4) = 1 - P(K 4) = 1 - 0.0407 for binom.cdf(4, 10, 4/52).
Interpretation: In ten attempts, there is a 0.0407 percent chance of getting more than four kings, which is a very little chance.
D. The binomial distribution can be used to get P(K 3):
Binom.cdf(3, 10, 4/52) = P(K 3) = 0.8789
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