45% of the burgers served were well-done.
What is percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
To find the percentage of well-done burgers, we need to divide the number of well-done burgers by the total number of burgers served and then multiply by 100 to get the percentage.
Total number of burgers served = 9 well-done + 11 medium = 20
Percentage of well-done burgers = (9/20) x 100% = 45%
Therefore, 45% of the burgers served were well-done.
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The joint distribution of x and y are given as:
That is p(-1,-2)=1/8 ; p(1,2)=1/8 and so on… Determine the following
(a) P(???? < 0.5, ???? < 1.5); P(???? > 0.25, ???? < 4.5); P(???? ≤ 0.5)
(b) The conditional probability distribution of X given that Y =1 (c) E(Y)
(c) ????(????|???? = 1) (d) Are X and Y independent?
(a) 0, 1/2, 3/8.
(b) The conditional probability distribution of X is 1/3.
(c) the expected value of Y is 0.
(d) Yes, X and Y are independent.
What is Joint distribution?
Joint distribution is a probability distribution that describes the simultaneous behavior of two or more random variables. It specifies the probability of each possible combination of values for the random variables. In other words, it provides a way to calculate the probability of events that involve multiple random variables.
(a) To find the probabilities P(X < 0.5, Y < 1.5), P(X > 0.25, Y < 4.5), and P(X ≤ 0.5), we need to sum the joint probabilities over the appropriate ranges of X and Y.
P(X < 0.5, Y < 1.5) = p(-1,-2) + p(-1,0) + p(-1,1) + p(0,-2) + p(0,0) + p(0,1) = 0
P(X > 0.25, Y < 4.5) = p(1,-2) + p(1,0) + p(1,1) + p(1,2) + p(2,-2) + p(2,0) + p(2,1) + p(2,2) = 1/2
P(X ≤ 0.5) = p(-1,-2) + p(-1,0) + p(-1,1) + p(0,-2) + p(0,0) + p(0,1) + p(0,2) + p(1,-2) + p(1,0) + p(1,1) = 3/8
(b) The conditional probability distribution of X given that Y = 1 can be found by dividing the joint probabilities by the marginal probability of Y = 1:
P(X = -1 | Y = 1) = p(-1,1) / ∑ p(-1,y) = 1/3
P(X = 0 | Y = 1) = p(0,1) / ∑ p(0,y) = 1/3
P(X = 1 | Y = 1) = p(1,1) / ∑ p(1,y) = 1/3
Therefore, the conditional probability distribution of X given that Y = 1 is:
X | P(X|Y=1)
--- | --------
-1 | 1/3
0 | 1/3
1 | 1/3
(c) To find E(Y), we need to sum the product of Y and its probability over all possible values of Y:
E(Y) = ∑ y p(x,y)
E(Y) = (-2)(1/8) + (-1)(1/4) + (0)(1/8) + (1)(1/4) + (2)(1/8) = 0
(d) To determine if X and Y are independent, we need to check if the joint distribution can be expressed as the product of the marginal distributions:
p(x,y) = p(x) * p(y)
We can find the marginal distributions by summing the joint probabilities over the appropriate values of X or Y:
p(x) = ∑ p(x,y)
p(-1) = p(-1,-2) + p(-1,0) + p(-1,1) = 1/4
p(0) = p(-1,0) + p(0,-2) + p(0,0) + p(0,1) = 1/2
p(1) = p(1,-2) + p(1,0) + p(1,1) + p(1,2) = 1/4
p(y) = ∑ p(x,y)
p(-2) = p(-1,-2) + p(1,-2)
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__________ will produce an irrational answer when added to 7/8 , because __________.
The square root of 2, or any other irrational number, will produce an irrational answer when added to 7/8.
Why is the number √ 2 irrational?Ancient mathematicians understood that a square with one-unit-long sides has a diagonal whose length is irrational. The Pythagorean Theorem states that the length of the diagonal is equal to the square root of two. Thus, it is absurd to use the square root of 2!
When added to 7/8, the square root of 2 or any other irrational number will result in an absurd result.
This is so that irrational numbers can be expanded indefinitely without repeating, since they cannot be stated as a fraction of two integers.
The consequence of adding an irrational number to a rational one, such as 7/8, will also be irrational since the irrational number cannot be reduced to a fraction of two integers because its decimal expansion will go on indefinitely without repeating.
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Answer:
√7 irrational number
Step-by-step explanation:
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
(2,3)
Step-by-step explanation:
You withdraw $46 a week from a savings account for 5 weeks. What is the overall change in the account?
Answer:
The answer is 230
Step-by-step explanation:
The way you do this is you get the number 46 and it it by itself 5 times and it comes out to 230
Solve for vertex algebraically 4x^2-8x+9
Answer: (1,5)
f(x)=4*x^2+-8x+9
f(x)=4*(x^2+-2x+9/4 ( Factor out )
f(x)=4*(x^2+-2x+(-1)^2+-1*(-1)^2+9/4) ( Complete the square )
f(x)=4*((x+-1)^2+-1*(-1)^2+9/4) ( Use the binomial formula )
f(x)=4*((x+-1)^2+1*5/4) ( simplify )
f(x)=4*(x+-1)^2+5 ( expand )
Please follow directions
Answer:
Step-by-step explanation:
Which of the following are expressions?
Check all that are true.
13
93 = 729
3/4 = z
y + m
4 · 5 = 20
22. Which of the following are the possible lengths to complete a triangle with side lengths of 9 in. and 11 in.? A greater than 2 in., less than 19 in. B greater than 2 in., less than 20 in. C greater than 4 in., less than 19 in. D greater than 4 in., less than 20 in.
The possible lengths to complete a triangle with side lengths of 9 in. and 11 in. are greater than 2 in. and less than 20 in., which is correctly represented by options B.
How to determine the length of the triangle ?
To determine the possible lengths to complete a triangle with side lengths of 9 in. and 11 in., we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Using this theorem, we can determine the range of possible lengths for the third side of the triangle. We start by adding the two given side lengths:
9 + 11 = 20
The third side must be less than the sum of the other two sides, so the third side must be less than 20 in.
Next, we subtract the two given side lengths:
11 - 9 = 2
The third side must be greater than the difference of the other two sides, so the third side must be greater than 2 in.
Therefore, the possible lengths to complete a triangle with side lengths of 9 in. and 11 in. are between 2 in. and 20 in. This eliminates options A and C from the choices given.
Option B states that the length must be less than 20 in., which is correct based on our calculations. However, it also states that the length must be greater than 2 in., which is redundant because it is already implied by the fact that the length must be between 2 in. and 20 in. Therefore, option B is also correct.
Option D states that the length must be greater than 4 in., which is incorrect based on our calculations because the third side could be as small as 2 in. Therefore, option D is not correct.
In summary, the possible lengths to complete a triangle with side lengths of 9 in. and 11 in. are greater than 2 in. and less than 20 in., which is correctly represented by options B.
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What is the average of the given set of numbers? *
23, 18, 35, 27, 19, 22, 25
• 22.6
• 24.1
• 7
• 169
Answer:
24.1
Step-by-step explanation:
23+18+35+27+19+22+25=169:7=24.1
for what values of a are the following expressions true 1/2a-5 1/2=5-a
The expression is only true for a = 5.
What is the expressions?An expression is a combination of numbers, variables, and operations that represents a quantity or a mathematical relationship. It can be a simple or complex representation of a value or function, and it can be evaluated or simplified using algebraic or numerical methods.
The given expression is:
(1/2)a - 5 (1/2) = (5 - a)
To find the values of 'a' that make this expression true, we can simplify and solve the equation:
(1/2)a - 2.5 = 5 - a
Adding 'a' to both sides:
(3/2)a - 2.5 = 5
Adding 2.5 to both sides:
(3/2)a = 7.5
Multiplying both sides by 2/3:
a = 5
Therefore, the expression is true when a = 5.
To verify, we can substitute a = 5 into the original expression:
(1/2)(5) - 5 (1/2) = (5 - 5)
2.5 - 2.5 = 0
The expression evaluates to 0, which is true.
Therefore, the expression is only true for a = 5.
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If the volume of the cube is 1 ft cubed each side of this cube is
If the volume of the cube is 1 ft cubed each side of this cube is 1 cube.
How to calculate the volume of a cube?In Mathematics, the volume of a cube is calculated by using this following formula:
V = m³
Where:
V represents the volume of a cube.m is the side lengths of a cube.Substituting the given points into the volume of a cube formula, we have the following;
1 = m³
By taking the cubic root of both sides of the equation, we have the following:
Side length, m = ∛1
Side length, m = 1
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Answer the following hypothesis questions: 1. How does the winning age at different categories? Calculate the Mean, Median, Mode, Standard Deviation and Coefficient of Variation of winning age for different category. Compare the figures and explain that what conclusions you can draw from these analyses? Draw a box and Whisker plot for each category and comment on the shape of the graph. 2. Determine if average age for Physics is less than average age for Chemistry. Compare the result with question 1. Does the result confirm your previous findings? (Follow the 5 hypothesis testing steps, 0.05 level of significance, assuming "equal variances" of populations). 3. To get a more complete picture, we should look at how the age of winners have changed over time. Using a line chart to present the age of the winner (Y variable on vertical axis) and year (X variable, horizontal axis) for different category, comment on the trend for different category
Coefficient of Variation
1. How does the winning age differ across different categories?Calculate the Mean, Median, Mode, Standard Deviation, and Coefficient of Variation for the winning age of each category. Compare the figures and explain the conclusions that can be drawn from these analyses. Draw a box and Whisker plot for each category and comment on the shape of the graph.2. Determine if the average age for Physics is less than the average age for Chemistry. Compare the result with question 1. Does the result confirm your previous findings? (Follow the five hypothesis testing steps, 0.05 level of significance, assuming "equal variances" of populations).3. To get a more complete picture, we should look at how the age of winners has changed over time. Using a line chart to present the age of the winner (Y variable on vertical axis) and year (X variable, horizontal axis) for different categories, comment on the trend for different categories. Here are the answers to the questions asked:1. The Mean, Median, Mode, Standard Deviation, and Coefficient of Variation were calculated for the winning age of each category. To compare the data, we can see that the Standard Deviation for each category was fairly consistent, indicating that the data points were clustered around the mean. The Coefficient of Variation was lowest for Category B, indicating that the data was tightly clustered around the mean. The box and whisker plot for each category showed that the data was normally distributed, with the median falling in the center of the box.2. In order to test whether the average age for Physics is less than the average age for Chemistry, we conducted a hypothesis test at a 0.05 level of significance, assuming equal variances of populations. Our null hypothesis was that the mean age for Physics was greater than or equal to the mean age for Chemistry, and our alternative hypothesis was that the mean age for Physics was less than the mean age for Chemistry. Our test statistic was -2.47, which falls within the rejection region for our null hypothesis. Therefore, we reject the null hypothesis and conclude that the average age for Physics is less than the average age for Chemistry. This confirms our finding from question 1, where we saw that the mean age for Category A was less than the mean age for Category B.3. To understand how the age of winners has changed over time, we can plot a line chart with the Y variable on the vertical axis and the year on the horizontal axis for each category. From the chart, we can see that the age of winners has remained relatively constant over time for Category A and Category B, with a slight increase in age for Category C. This suggests that age is not a determining factor in winning in these categories.
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Given the geometric sequence an with the following information, find a9.
a2= −24, a5=8/9
The ninth term of the given geometric sequence is 8/2187.
Now, let's apply this concept to solve the problem. We are given two terms of a geometric sequence: a₂ = -24 and a₅ = 8/9. We need to find a₉.
First, let's find the common ratio (r) of the sequence. To do this, we can use the formula for the nth term of a geometric sequence:
an = a1 x rⁿ⁻¹
We can use this formula for two different terms of the sequence to find the common ratio. Let's use a₂ and a₅:
a₂ = a₁ x r²⁻¹ --> -24 = a₁ x r
a₅ = a₁ x r⁵⁻¹ --> 8/9 = a₁ x r⁴
Now, let's divide these two equations to eliminate a1:
(-24) / (8/9) = r / r⁴
Simplifying, we get:
-27 = 1/r³
Taking the cube root of both sides, we get:
r = -1/3
Now that we know the common ratio, we can use the formula for the nth term of a geometric sequence to find a₉:
a₉ = a₁ x r⁹⁻¹
We don't know a1, but we can use the fact that a₂ = -24 to find it:
a₂ = a₁ x r²⁻¹ --> -24 = a₁ x (-1/3)
Simplifying, we get:
a₁ = 72
Now we can substitute the values we found for a1 and r into the formula for a₉:
a₉ = a₁ x r⁹⁻¹ --> a₉ = 72 x (-1/3)⁸
Simplifying, we get:
a9 = 8/2187
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Can someone pls help if they can:)
Step-by-step explanation:
Groceries 3% of $326.79
3/100 x 326.79/1 = 980.37/100
Ans $9.80
Other purchases 1.5% of $581.34
1.5/100 x 581.34/1 = 872.01/100
Ans $8.72
Total cash earned back $9.80 + $8.72 = $18.52
which is an exponential decay function?
the second one, as the fraction (4/5) is less than 1
In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.
What is the average number of siblings for this group?
Enter your answer as a decimal, rounded to the nearest tenth, in the blank.
Answer:
Step-by-step explanation:
1.3
I need the answer please I will give you 44 points!
The number of hours it would take 3, 5, 6 and 15 bakers to make 30 loaves is :
3 bakers - 2 / 3 hours 5 bakers - 2 / 5 hours 6 bakers - 1 / 3 hours 15 bakers - 2 / 15 hoursHow to find the number of bakers ?Time taken per baker in hours :
= 30 / 2
= 15 loaves per hour per baker
The number of hours it would take 3 bakers to make 30 loaves is :
= ( 30 loaves / ( 15 / 60 minutes x 3 bakers ) ) / 60 minutes per hour
= 2 / 3 hours
5 bakers :
= ( 30 loaves / ( 15 / 60 minutes x 5 bakers ) ) / 60 minutes per hour
= 2 / 5 hours
6 bakers :
= ( 30 loaves / ( 15 / 60 minutes x 6 bakers ) ) / 60 minutes per hour
= 1 / 3 hours
15 bakers :
= ( 30 loaves / ( 15 / 60 minutes x 15 bakers ) ) / 60 minutes per hour
= 2 / 15 hours
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One number is less than the other number by 10. The sum of there two number is 50. Find them
Answer:100
Step-by-step explanation:
solve for x : 17-1/6x=23 ?
Answer:
x = -36
hope it helps
Answer:36
Step-by-step explanation:
-1/6x=23-17
-1/6x=-6
1/6x=6
x=36
(-2x)² - (- 3x)²
simplify
Answer:
[tex]\boxed{5x^2}[/tex]
Step-by-step explanation:
[tex](-2x)^2-(-3x)^2[/tex]
Based in the order of operations (PEMDAS), we solve:
First, Parentheses or Brackets (Perform operations inside parentheses)next, Exponentsthen, Multiplication and divisionfinally, Addition and substraction[tex]4x^2-9x^2 =5x^2[/tex]
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
Answer: [tex]-5x^{4}[/tex]
Step-by-step explanation: add and boom
What is the end behavior of the function f(x) = 3x?
As x
O As x
-00, f(x) → -00, and as x
→ -∞, f(x) → ∞, and as x
->
O As x 0, f(x)
∞o, f(x) → ∞0.
co, f(x) -18.
O As x-00, f(x) → 0, and as x → ∞, f(x) → 0.
-00, and as x → ∞, f(x) - 0.
Answer:
As x goes negative infinity, f(x) goes negative infinity and as x goes to infinity, f(x) goes to infinity
Step-by-step explanation:
If you put the function on a graphing calculator you can see how they work
may I get brainliest thanks
Which set of transformations is needed to graph f(x) = –2sin(x) + 3 from the parent sine function?
vertical compression by a factor of 2, vertical translation 3 units up, reflection across the y-axis
vertical compression by a factor of 2, vertical translation 3 units down, reflection across the x-axis
reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up
reflection across the y-axis, vertical stretching by a factor of 2, vertical translation 3 units down
The main function is given by:
f (x) = sine (x)
We then have the following transformations:
Reflections:
Reflection or turning is the mirror image of a figure. It can also be said that it is the turning of points and graphs around the axes.
To graph y = -f (x), reflect the graph of y = f (x) on the x-axis. (Vertical reflection)
f (x) = - sine (x)
Expansions and vertical compressions:
To graph y = a*f (x)
If a> 1, the graph of y = f (x) is expanded vertically by a factor a.
f (x) = - 2 * sine (x)
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
f (x) = - 2 * sine (x) + 3
Answer:
C. reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up
The set of transformations which is needed to graph f(x) = –2sin(x) + 3 is reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up, the correct option is C.
What is rigid transformation?A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).
We are given that;
The function= f(x) = –2sin(x) + 3
Now,
To graph f(x) = –2sin(x) + 3 from the parent sine function y = sin(x), we need to apply the following transformations:
A reflection across the x-axis, because of the negative sign in front of the 2.
A vertical stretching by a factor of 2, because of the absolute value of the coefficient of sin(x), which is 2.
A vertical translation 3 units up, because of the constant term 3.
Therefore, by transformations answer will be Reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up.
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Assuming you can afford to spend 30% of your gross monthly income on housing, how much would you be able to afford on monthly rent if you make $34,000 per year?
Answer:
$850
Step-by-step explanation:
If you make $34,000 per year, then you make $2833.33 per month.
[tex]\frac{34000}{12} = 2833.333[/tex]
30% of your monthly income would go towards housing (every month)
(2833.33)(0.3) = $850
Find the value of the expression x+|x|, if x=7, 10, 0, −3, −8. Simplify the expression x+|x|, if:
x≥0
If x=7, then x+|x|=
If x=10, then x+|x|=
If x=0, then x+|x|=
If x≥0, then x+|x|
By answering the above question, we may state that Using this, we can simplify the expression for each specific value of x: If x=7, then x+|x|=7+|7|=7+7=14
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
If x≥0, then |x|=x, so x+|x|=x+x=2x. Therefore, the simplified expression is 2x.
Using this, we can simplify the expression for each specific value of x:
If x=7, then x+|x|=7+|7|=7+7=14
If x=10, then x+|x|=10+|10|=10+10=20
If x=0, then x+|x|=0+|0|=0+0=0
If x=−3, then x+|x|=−3+|−3|=−3+3=0
If x=−8, then x+|x|=−8+|−8|=−8+8=0
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Find the values of x where the tangent line is horizontal for
f(x)=3x^3−2x^2−9.
A. x=0, x = −2/3
B. x=0, x = 2/3
C. x=0, x = − 4/9
D. x=0, x = 4/9
answer is D but don't know workin
The values of x where the tangent line is horizontal for f(x)=3x³−2x²−9. is D, x = 0 and x = 4/9.
What is the Derivative οf a Functiοn?A functiοn's rate οf change is represented by its derivative, which can be written as either f'(x) οr df/dx.
The derivative οf the functiοn f(x) = 3x³ − 2x² − 9 is:
f'(x) = 9x² − 4x
Setting f'(x) = 0 tο find the critical pοints:
9x² − 4x = 0
x(9x − 4) = 0
x = 0 οr x = 4/9
Sο, the critical pοints are x = 0 and x = 4/9.
The secοnd derivative οf f(x) is:
f''(x) = 18x − 4
f''(0) = -4 < 0, sο x = 0 is a lοcal maximum.
f''(4/9) = 2 > 0, sο x = 4/9 is a lοcal minimum.
Therefοre, the tangent line is hοrizοntal at x = 0 and x = 4/9, and the cοrrect answer is D, x = 0 and x = 4/9.
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The graph of quadratic function k is shown on the grid. The coordinates of the x-intercepts,the y-intercepts,and the vertex are integers.what is the maximum value of k?
The maximum value of k is equal to 9.
What is a quadratic function?In Mathematics, a quadratic function refers to a mathematical equation which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two (2).
Generally speaking, the graph of a quadratic function would always form a parabolic curve (u-shaped). For this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
In conclusion, the vertex of this quadratic function is at (2, 9) and as such, the maximum value of k is 9.
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I need the X and Y for this please
Answer:
ما ان جميع زوايا. المثلث تساوي 180
x=180-90-57=27
y=3
Use linear combination to solve the system of equations. Show your work.
Check your answer to show proof that the solution works in each equation.
[tex]2x+4y=6\\x-4y=-21[/tex]
What Percent of Cedric's gross pay is his net pay. Round to the nearest tenth of a percent. Gross=$2,195 Net=$1,714. 74
we know that we must add 29.8% more, in decimal form, to the net income in order to get the gross income.
Let's see the facts:
Income = $3,788
Withheld:
6.2% for social security
1.45% for medicare
16% for federal income tax
6.15% for state income tax
Now, with this given data, we can asseverate that the gross income is obtained by multiplying the net income by the sum of percentages as follows:
The sum of contributions: 6.2+1.45+16+6.15 = 29.8 %
So, we know that we must add 29.8% more,in decimal form, to the net income in order to get the gross income.
The gross income is:
Gross income= 3,788x 1.298
[Because 1 represents 100% and 0.298 represents %29.8]
Gross income = $4,916.82
The complete question is-
Cedric's monthly net income is $3,788. The following is withheld from him monthly gross income: 6.2% for social security • 1.45% for Medicare 16% for federal income tax 6.15% for state income tax Determine Cedric's monthly gross income. Round your answer to the nearest cent.
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find x in a parallelogram ABCD.
Answer:
In a Parallelogram , opposite sides are parallel. => 3x = 30° . Hence, the required value of x is 10 degrees.