Answers
The quadratic inequality that will represent the parabola will be
y ≤ 2[tex]x^{2}[/tex] - 8x + 3
The given graph is a parabola where the mouth is open upwards. So from here we can clearly say that the coefficient of [tex]x^{2}[/tex] will be positive.
The vertex of the parabola is given as (2 , -5) in the graph.
So let us put value of x in the inequations given to us.
first option is
y ≤ 2[tex]x^{2}[/tex] - 8x + 3
y ≤ 2*[tex]2^{2}[/tex] - 8*2 + 3
y ≤ 8 - 16 + 3
y ≤ -5
Therefore the quadratic inequality that will represent the parabola will be
y ≤ 2[tex]x^{2}[/tex] - 8x + 3
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Related Questions
assume that roger federer announces that he will retire from professional tennis 5 years from now. there will be a total of 20 big competitions (grand slams) that will be played during that time and a recent statistical analysis estimated that federer can win each grand slam with probability 0.1. what is the probability that he wins at least 2 grand slams?
Answers
The probability that Roger Federer wins at least 2 Grand Slam titles is 60.82%
Given data:
To calculate the probability that Roger wins at least 2 Grand Slam titles out of the 20 competitions during the 5-year period, we can use the binomial distribution.
The binomial distribution calculates the probability of obtaining a certain number of successes (in this case, Roger winning a Grand Slam) in a fixed number of independent trials (the 20 competitions), given the probability of success in a single trial (0.1).
We need to calculate the probability of Roger winning 2, 3, 4, ..., up to 20 Grand Slam titles and then sum those probabilities to find the overall probability of winning at least 2 titles.
Using a binomial probability formula, the probability of getting exactly k successes in n trials is given by:
[tex]P(X = k) = C(n, k) * p^k * (1 - p)^{(n - k)}[/tex]
Where:
C(n, k) is the binomial coefficient (n choose k)
p is the probability of success in a single trial (0.1)
n is the number of trials (20)
To find the probability of winning at least 2 Grand Slam titles, we calculate the probabilities for k = 2, 3, 4, ..., 20, and sum them up:
P(X ≥ 2) = P(X = 2) + P(X = 3) + ... + P(X = 20)
P(X ≥ 2) = Σ(P(X = k)) from k = 2 to 20
Calculating each individual probability P(X = k) and summing them up can be tedious. However, use complementary probability to simplify the calculation:
P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)
[tex]P(X = 0) = C(20, 0) * 0.1^0 * (1 - 0.1)^{(20 - 0) }[/tex]
[tex]=(1 - 0.1)^{20}[/tex]
= 0.12157
[tex]P(X = 1) = C(20, 1) * 0.1^1 * (1 - 0.1)^{(20 - 1) }[/tex]
[tex]= 20 * 0.1 * (1 - 0.1)^{19 }[/tex]
= 0.27017
P(X ≥ 2) = 1 - 0.1074 - 0.2684
P(X ≥ 2 ) = 0.60826 (approximately)
Hence, the probability that Roger Federer wins at least 2 Grand Slam titles out of the 20 competitions is approximately 0.60826, or 60.82%.
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NEED HELP WRITING THE EQUATION!!!
Answers
The equation of line with undefined slope and passes through the point
(1/2, 5) will be;
⇒ x = 1/2
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point = (1/2 , 5)
And, The slope = undefined
Now,
Since, We know that;
The equation of line with undefined slope and passes through the point will be;
⇒ x = a
Where, 'a' is the x - intercept.
Here, The point = (1/2 , 5)
The slope = undefined
And, The x - intercept = 1/2
So, The equation of line with undefined slope and passes through the point (1/2, 5) will be;
⇒ x = 1/2
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In the figure alongside, AB⊥BC and a-b =10° then find the value of a and b
Answers
Step-by-step explanation:
a-b=10--(1)
Same side interiors(vertical) have sum 180°
a+b=180--(2)
From both equations
2a=190
a=95
And
a-b=10
b=95-10
b=85
please help me out. it’s more as well but here
Answers
Answer:
[tex]\sf \dfrac{-1}{2}[/tex]
Step-by-step explanation:
Find the slope:
(-9 , -5) ⇒ x₁ = -9 ; y₁ = -5
(-1 , -9) ⇒ x₂ = -1 ; y₂ = -9
[tex]\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{-9-[-5]}{-1-[-9]}\\\\\\=\dfrac{-9+5}{-1+9}\\\\\\=\dfrac{-4}{8}\\\\\\=\dfrac{-1}{2}[/tex]
Answer:
Slope = -1/2
Step-by-step explanation:
Formula we use,
→ (y2 - y1)/(x2 - x1)
Now the value of slope is,
→ (-9 -(-5))/(-1 -(-9))
→ (-9 + 5)/(-1 + 9)
→ -4/8 = -1/2
Hence, the slope is -1/2.
Find the nth term for 13 8 3 -2 -7 and the 100th term
Answers
Answer:
see explanation
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
8 - 13 = 3 - 8 = - 2 - 3 = - 7 - (- 2) = - 5
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 13 and d = - 5 , then
[tex]a_{n}[/tex] = 13 - 5(n - 1) = 13 - 5n + 5 = 18 - 5n
then
a₁₀₀ = 18 - 5(100) = 18 - 500 = - 482
Write down the inequality shown on the number line below.
Answers
Answer:
- 0.5 ≤ x ≤ 3.5
Step-by-step explanation:
since both ends of the interval are closed circles. This indicates that x can equal both - 0.5 and 3.5 and the values between , then
- 0.5 ≤ x ≤ 3.5
The inequality shown on the number line is -0.5 ≤ x ≤ 3.5.
Given is a number line where a value starts from -0.5 and end at 3.5, we need to write down the inequality shown on the number line,
To write down the inequality shown on the number line starting from -0.5 and ending at 3.5, we need to determine the range of values represented by the line segment.
The left endpoint of the line segment is -0.5, which means the value represented by that point is greater than or equal to -0.5.
We can express this as:
x ≥ -0.5
The right endpoint of the line segment is 3.5, which means the value represented by that point is less than or equal to 3.5.
We can express this as:
x ≤ 3.5
Combining these two inequalities, we have:
-0.5 ≤ x ≤ 3.5
This inequality represents all the values on the number line between -0.5 and 3.5, inclusive.
Hence the required inequality is -0.5 ≤ x ≤ 3.5.
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You're shopping for a new shirt and find one that's on sale for $16.25. The sign says it is a 35% discount. What was the original price of the shirt BEFORE the discount?
Answers
The original price of the shirt before the discount will be $25.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
You're looking for another shirt and find one that is discounted to $16.25. According to the sign, it is a 35% markdown.
Then the original price of the shirt before the discount will be given as,
⇒ $16.25 / (1 - 0.35)
⇒ $16.25 / 0.65
⇒ $25
The original price of the shirt before the discount will be $25.
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Given the relation {(3,4),(-2,1),(0,6),
(5,-3)), what is the domain of the
relation?
Answers
Answer:
Domain: {-2, 0, 3, 5}
Step-by-step explanation:
The domain is the list of possible inputs
The scatterplot illustrates the relationship between distance and success rate of field-goal attempts for a sample of football kickers.
Which of the following is an accurate description of the scatterplot?
The kickers have unusually low success rates when the distance is large.
The kickers have unusually high success rates when the distance is small.
As the distance of the attempt increases, the kickers have a lower success rate for their field goals.
As the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.
Answers
The statement that best describes the relationship that is displayed by the scatter plot is: D. As the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.
What is a Scatter Plot?A scatter plot is used to show the relationship between two variables that are different, whereby the trendline formed by each data point determines whether the relationship between the two variables is negative or positive.
If the trendline slopes upwards, it is positive, if it slopes downwards, it is negative.
If it is negative, it means as one variable increases, the other one decreases. On the other hand, if it is positive, it implies that as one variable increases, the other variables decreases.
The scatter plot given shows that the relationship between the distance of the attempt and success rate is negative. This implies that, as the distance of the attempt increases, the success rate decreases.
Therefore, the accurate description is: D. As the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.
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Answer:
D. as the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.
Step-by-step explanation:
Describe the relationship between the point B (5,-3) and the point A (5,3) in terms of reflections.
Answers
Answer:
The point does not lie in the solution sets of the given system of inequalities
Step-by-step explanation:
We need to check whether the point (1,-5) is a solution to the system of inequality
We substitute x=1 and y=-5 into the top inequality:
. This is true
We substitute x=1 and y=-5 into the bottom inequality:
. This is false.
Since the point does not satisfy both inequalities, it is not a solution to the system of inequalities.
your profile pic is pretty btw: and hope my answer helped
A rectangle with dimensions 60 units * 40 units is drawn on a grid paper that has a 1 unit * 1 unit grid. Each vertex of the rectangle is on a node, and each side of the rectangle is on a gridline. Then a diagonal of the rectangle is drawn. How many cells are cut into two(not necessarily equal) parts? PLEASE ANSWER ASAP!!!!!!!
Answers
The number of cells cut into two by the diagonal of the rectangle, found by using Pythagorean theorem, are approximately 51 cells
What is Pythagorean theorem?Pythagorean theorem can be expressed as the square of the hypotenuse side of a right triangle is equal to the sum of the square of the legs of the triangle.
The dimensions of the rectangle = 60 units by 40 units
The dimensions of each grid = 1 unit by 1 unit
The vertices of the rectangle are (0, 0), (60, 0), (60, 40), (0, 40)
The slope of the diagonal is therefore;
m = 40/(60) = 2/3
The equation of the line is; y - 0 = 2/3·(x - 0) = 2/3·x
y = 2/3·x
The number of cells in the diagonal is found using Pythagorean theorem as follows as follows;
Length the diagonal, l = √(60² + 40²) ≈ 72.1
Length of the diagonal of a unit = √(1 + 1) =√2
Number of units in the diagonal, n = 72.1/√(2) ≈ 51 units
The number of cells cut into two ≈ 51 cells
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Select the correct symbol to make 11⎯⎯⎯⎯√ , 1 of 1.
Select Choice
323 a true statement.
Answers
The correct inequality symbol that makes the statement true is:
1000 < (6²)³.
How to choose the inequality symbol?The inequality symbols, and their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.In the context of this problem, the numbers being compared are presented as follows:
1000 and (6²)³.
The power of power property of a number with multiple exponents means that the base is kept while the exponents are multiplied.
The number in which this property is applied in this problem is (6²)³, in which:
The base is of 6.The exponents are of 2 and 3.Hence the equivalent number is given as follows:
(6²)³ = 6^6 = 6 x 6 x 6 x 6 x 6 x 6 = 46,656
Which is a greater number than 1,000, meaning that 1,000 is less than the number, and the inequality is:
1000 < (6²)³.
Missing InformationThe problem is given by the image at the end of the answer.
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Tell whether the sequence is arithmetic. If it is, identify the common difference.
0, 7, 14, 21, ...
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The sequence is arithmetic and has a common difference of [_]
OmB. The sequence is not arithmetic.
Answers
Answer:
A
Step-by-step explanation:
the arithmetic sequence is the one in which the difference between the one and the next term is a constant.
0,7,14,21,28,35,42...
this is an arithmetic sequence with a common difference of [7]
Mikaela purchased a paddleboard originally priced at $899. If all merchandise was on sale for 40% off and the state tax rate is 7.25%, what is the total amount
that Mikaela spent on the paddleboard?
Answers
Total amount that Mikaela spent on the paddleboard is 578.5065.
How to calculate total amount spent on the paddleboard?According to given data,
original price = 899$ and 40% off.
state tax rate is 7.25%.
Solution:-
Applying formula,
⇒ 899 × (7.25% + 1) × (1 - 40%)
⇒ 899 × 1.0725 × 0.6
⇒ 578.5065.
Total amount that Mikaela spent on the paddleboard is 578.5065.
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The length of a rectangle is 5 more than twice the width . If the length is 60 inches ,what is the width?
Answers
Answer:27.5 inches
Step-by-step explanation:
jacob has a jar of nickels and dimes. he has twice as many nickels as dimes. he has 310. how many of each type of coin does he have
Answers
No. of coins in jar of nickels is 207 and of dimes is 103.
Let the no. of coins of dimes = x
No. of coins of nickels = 2x
Total = 310
x + 2x = 310
3x = 310
x = 310/3
= 103.33
≈ 103
No. of coins of dimes = 103
No. of coins of nickels = 310 - 103
= 207
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A rectangular tank with a square base, an open top, and a volume of is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
Answers
The tank with the smallest surface area has dimensions of 6ft.
s = 12ft and h = 6ft.
A(s) = s² + 4 × (V ÷ s)
The rectangular tank has a capacity of 864 feet.
Let the square base's long sides be.
Let h represent the tank's height.
Let A represent the tank's whole area.
A = (Base Area) + (4 × Lateral Area)
Lateral Area = s × h
Lateral Area = s × (V ÷ s²)
Lateral Area = (V ÷ s)
Base Area = s²
Compared to the objective function,
A(s) = s² + 4 × (V ÷ s)
A(s) = s² + 4 × (864 ÷ s)
The area function's derivative,
A'(s) = 2s - (3456 ÷ s²)
The smallest surface area is now.
A'(s) = 0
2s - (3456 ÷ s²) = 0
2 × [tex]s^{3}[/tex] = 3456
[tex]s^{3}[/tex] = 3456
s = [tex]\sqrt[3]{3456}[/tex]
s = 12ft
The volume is,
V = s² × h
864 = 12² × h
h = 6ft
As a result, the tank's height is 6 feet, and the square base's long sides measure 12 feet.
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The question is -
A rectangular tank with a square base, an open top, and a volume of 864 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.
I need help on solving these equations linear. Please helpppp
Answers
The solution of the first set of equations is x = 15 and y = 5 and the second is x = 14.25 and y = 7.75.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation.
a)
As per the given first system of equation,
2x - 4y = 10
x + 5y = 40 → 2x + 10y = 80
Subtract both
10y + 4y = 80 - 10
14y = 70
y = 5
And, x = 40 - 5(5) = 15
b)
As per the given first system of equation,
3x - 5y = 4 and
-2x + 6y = 18 → -x + 3y = 9 → -3x + 9y = 27
Add both
-5y + 9y = 4 + 27
4y = 31
y = 7.75
x = (4 + 5(7.75))/3 = 14.25
Hence "The solution of the first set of equations is x = 15 and y = 5 and the second is x = 14.25 and y = 7.75".
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Question 2 options:
Multiply the radicals.
What is the product in simplest form?
Answers
The product in simplest form is [tex]-250\sqrt[3]{50}[/tex] .
In the question,
It is given that,
[tex]5*\sqrt[3]{5} * (-10\sqrt[3]{50})[/tex]
By radical laws, [tex]\sqrt{a} * \sqrt{b} = \sqrt{ab}[/tex]
So,
The given question becomes:
[tex]-50*\sqrt[3]{50*5} = -50*\sqrt[3]{250} = -250\sqrt[3]{5} }[/tex]
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What are the domain and range of the function f(x) = -
OD: {X E R | X + -2},R: {ye Rly +-8}
E
OD: (x = R X
4),R: {ye Rly -2}
OD: {x € R | x # 2},R: {y = R | y + 8)
x² - 4x-12?
X+2
OD:{X = R | x # -4},R: {y = R | y + 2}
Answers
The domain is { x ∈ R | x ≠ -2 }.
The range is { y ∈ R | x ≠ -8 }.
What are the domain and range of a function?
The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.
A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)
Find domain:
Set the denominator equal to zero and solve for x.
x+2=0
x=-2
This means, domain is set of all real numbers except x=2.
Set builder notation: { x ∈ R | x ≠ -2 }. R= real numbers
Find range:
Replace f(x) by y in the given equation and solve for x.
[tex]y=\frac{x^2-4x-12}{x+2}[/tex]
Write the factors of the numerator
[tex]y=\frac{(x+2)(x-6)}{x+2}[/tex]
common terms x+2 cancel out
y=x-6
x=y+6
substitute x=-2
-2=y+6
y= -8
This means range is the set of all real numbers except y= -8.
Set builder notation: { y ∈ R | y ≠ -8 }. R= real numbers
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You have a gift certificate to a book store worth $95. Each paperback books is $10 and each hardcover books is
$17. You must spend at least $20 in order to use the gift certificate. Write and graph a system of inequalities to
model the number of each kind of books you can buy. Let x = the number of paperback books and y = the number
of hardback books
Answers
Answer: You make a system of inequality to spend at least $20. The word "at least" means you can spend equal to $20 or higher than $20. Or you can write it as,
⇒ what you buy should be ≥ 20
Input the price to the inequality above
⇒ what you buy should be ≥ 20
⇒ paperback price + hardcover price ≥ 20
⇒ 10x + 17y ≥ 20
Because the number of paperback books and the number of hardcover books can't be negative, make new inequality forms
⇒ x ≥ 0
⇒ y ≥ 0
So this is the summary
10x + 17y ≥ 20
x ≥ 0
y ≥ 0
Step-by-step explanation:
Francisco just got his driver's license and wants to rent a car. The platinum car rental company charges $180 plus $92 per hour to rent a car. The plastic car rental company charges $250 plus $75 per hour. For what number of hours would the companies charge the same amount?
Answers
6900 hours, make a list of multiples until lcm is found
A line passes through point (8, 4) and has a slope of - 3/4 Write an equation in Ax + By = C form for this line. Use integers for A, B, and C.
Answers
The equation of the line in the given form Ax + By = C is 3x + 4y = 40
How to determine the equation in the given form?The given parameters from the question are given as
Point = (8, 4)
Slope = -3/4
Start by representing the equation in the slope intercept form
This is calculated as
y = m(x - X) + Y
Where
m, Slope = -3/4
(X, Y), Point = (8, 4)
So, we have
y = -3/4(x - 8) + 4
Multiply through by 4
4y = -3(x - 8) + 16
Evaluate the like terms
4y = -3x + 24 + 16
This gives
3x + 4y = 24 + 16
Evaluate
3x + 4y = 40
Hence, the equation is 3x + 4y = 40
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algebra 2 please help!
Answers
Answer:
The answer is C, I had this same quiz today and I got 100%
In the figure below, o ll m. Find the values of y and x.
Answers
The values of y and x is 117 degrees and 28 degrees.
Given:
o ll m
Let angle beside 63 is a.
63 + <a = 180
<a = 180 - 63
<a = 117 degrees.
y = 117 degrees (since alternate interior angles are equal)
y = 4x + 5(vertically opposite angles are equal)
117 - 5 = 4x
4x = 112
divide by 4 on both sides
x = 112/4
x = 28 degrees.
Therefore the values of y and x is 117 degrees and 28 degrees.
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Simplify the power.
(-3x²y)^4
Answers
Using exponents, the resultant expression after simplification is 81x⁸y⁴.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.For instance, the number 6 is multiplied by itself four times, yielding 6 × 6 × 6 × 6. You can write this as 6⁴. In this case, the exponent is 4 and the base is 6.So, the expression is:
(-3x²y)⁴Now, simplify the power as follows:
(-3x²y)⁴(-3x²y)⁴ = (3x²y)⁴ (Exponent rule)3⁴(x²)⁴y⁴ (Exponent rule)81((x²)⁴y⁴ (3⁴ = 81)81x⁸y⁴Therefore, using exponents, the resultant expression after simplification is 81x⁸y⁴.
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What is the slope of the line that passes through the points (7,-5) and (16,7) in simplest form ?
Answers
Answer:
4/3
Step-by-step explanation:
look for gradientgradient=
[tex] \frac{change \: in \: y}{change \: in \: x?} [/tex]
change in y7--5=12
change in x16-7=9
gradient12÷9=4/3
the gradient is the same as slope
thus the answer is 4/3
complete the statement using angle R + angle A + angle T =
Answers
The complete statement will be;
⇒ angle R + angle A + angle T = 180°
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle RAT is shown in figure.
Now,
We know that;
The sum of all interior angles in a triangle is 180 degree.
Hence, In ΔRAT;
⇒ ∠R + ∠A + ∠T = 180°
Thus, The complete statement will be;
⇒ angle R + angle A + angle T = 180°
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Separate 25 into two parts so that one part is 13 less than the other part.
NEED HELP QUICKLY!!
Answers
Answer:
One number is 19 and the other is 6
Step-by-step explanation:
25 = x + (x- 13)
25 = x + x - 13
38 = 2x
19 = x
x = 19
25 - 19 = 6
a deli bar offers sandwiches with four types of bread, three types of cheese and four types of meat. how many different sandwich combinations are possible?
Answers
Exactly one type of meat required = 5 choices
What is probability?The area of mathematics known as probability deals with numerical 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.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
Exactly one type of meat required = 5 choicesAny number (0–5) of types of meat allowed: 2^5 (ie. binary, eat type of meat is either ‘on’ or ‘off’At least on type of meat required 2^5 - 1 (remove the zero choice)Do similarly for bread and cheese and number of sandwiches combinations =bread combinations X cheese combinations X meat combinationslearn more about probability click here:
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