We know that there is no universal acceptance meaning of a percentile. When someone told you that you are in the 80th percentile, the meaning of that is you have achieved the lowest score that is greater than 80 percent of the score. It is calculated by using the formula R = P/100 x (N + 1)
Final answer:
The 80th percentile represents the score below which 80% of the scores fall.
Explanation:
The 80th percentile represents the score below which 80% of the scores fall. It is calculated by finding the value at which 80% of the data is below and 20% is above. For example, if you scored in the 80th percentile on a 60-point assignment, it means that 80% of students scored equal to or below 49 points and 20% scored above.
A and B are vertical angles. If A = 4x - 10 and B = 6x - 30, find mA.
Which triangle has 0 reflections of symmetry
Answer:
The answer would be option A the scalene triangle
Answer:
The first triangle, or, A !!
Step-by-step explanation:
7/6 - 4/3n = -3/2n + 2(n + 3/2)
Suppose you are taking the bus home, and can take either the 51 or the 82. you know that the 82 will arrive in exactly 10 minutes, but because the 51 is unreliable, you suspect that the amount of time until it arrives is uniformly distributed between 0 and 30 minutes. you take the first bus that arrives. let t be the number of minutes you wait until you board a bus. find e[t].
Final answer:
The expected waiting time for a bus, E[t], is 8.33 minutes, which is calculated considering the possibility of either bus 51, which has a uniform arrival time between 0 to 30 minutes, or bus 82, which arrives in exactly 10 minutes.
Explanation:
The problem you are dealing with involves finding the expected waiting time, E[t], for either bus 51 or bus 82 to arrive. The expected value of a uniformly distributed random variable on an interval [a, b] is given by the formula (a + b)/2. However, we need to account for the fact that if bus 82 arrives in exactly 10 minutes, then if the 51 bus hasn't arrived by then, you will take the 82 bus.
To compute E[t], if the 51 bus arrives within the first 10 minutes, the expected waiting time is the average of 0 and 10 minutes, which is 5 minutes. If the 51 bus does not arrive within 10 minutes, you will take the 82 bus at exactly 10 minutes. Therefore, the expectation must only account for the time if the 51 bus arrives before the 82. This gives us:
The probability that the 51 bus arrives in the first 10 minutes is 10/30 = 1/3.
The expected waiting time if 51 arrives in the first 10 minutes is 5 minutes.
If the 51 bus does not arrive within 10 minutes, you'll wait exactly 10 minutes for the 82 bus.
So, E[t] = (1/3) * 5 minutes + (2/3) * 10 minutes = (5 + 20)/3 = 25/3 minutes.
Therefore, the expected waiting time E[t] is 8.33 minutes (rounded to two decimal places).
Consider the linear function that is represented by the equation y=-10x+6 and the linear function that is represented by the equation y-36=8(x-4). Which statement is correct regarding their slopes and y-intercepts?
a. The function that is represented by the equation y=-10x+6 has a steeper slope and a greater y-intercept.
b. The function that is represented by the equation y=-10x+6 has a steeper slope, and the function that is represented by the equation y-36=8(x-4) has a greater y-intercept.
c. The function that is represented by the equation y-36=8(x-4) has a steeper slope, and the function that is represented by the equation y=-10x+6 has a greater y-intercept.
d. The function that is represented by the equation y-36=8(x-4) has a steeper slope and a greater y-intercept.
This is about understanding slopes.
Option A is correct.
We are given two linear functions which are;y = -10x + 6 - - - (eq 1)
y - 36 = 8(x - 4) - - - (eq 2)
Formula for straight line equation is;y = mx + c
Where m is slope and c is the y intercept.
Let's expand eq 2 to be in the form of y = mx + c
Thus;
>>y - 36 = 8(x - 4)
>> y - 36 = 8x - 32
>> y = 8x - 32 + 36
>> y = 8x + 4 - - - (eq 3)
Thus, slope of eq 1 is -10 and y-intercept is 6.
Similarly, slope of eq 3 is 8 and y-intercept is 4.
This means y = -10x + 6 has a greater y-intercept than y - 36 = 8(x - 4).
Also, the slope in y - 36 = 8(x - 4) which is 8 will slope to the right while the slope of y = -10x + 6 which is -10 will slope to the left. This means that line represented by y = -10x + 6 has a steeper slope.
This is because the higher the slope, the steeper the line.
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After rewriting both equations in slope-intercept form, we find that the function y = -10x + 6 has a steeper slope and the function y - 36 = 8(x - 4) has a greater y-intercept, making option (b) the correct answer.
The question involves comparing the slopes and y-intercepts of two linear functions, represented by the equations y = -10x + 6 and y - 36 = 8(x - 4). To compare them, we need to write both equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
The first equation, y = -10x + 6, is already in slope-intercept form, with a slope of -10 and a y-intercept of 6. For the second equation, y - 36 = 8(x - 4), we first distribute the 8 to get y - 36 = 8x - 32 and then add 36 to both sides to get the slope-intercept form, y = 8x + 4, which has a slope of 8 and a y-intercept of 4.
Comparing the slopes, -10 for the first equation and 8 for the second, we see that the first equation has a steeper slope because -10 has a greater magnitude than 8. Comparing the y-intercepts, 6 for the first equation and 4 for the second, the first equation has a greater y-intercept. Therefore, the correct statement regarding their slopes and y-intercepts is (b) The function that is represented by the equation y = -10x + 6 has a steeper slope and the function that is represented by the equation y - 36 = 8(x - 4) has a greater y-intercept.
Consider the exponential function f(x) = 3 and its graph. Which statements are true for this function and graph? Check all that apply. The initial value of the function is . The growth value of the function is . The function shows exponential decay. The function is a stretch of the function f(x) = . The function is a shrink of the function f(x) = 3x. One point on the graph is (3, 0).
The function shows exponential growth a stretch of the function f(x) = (1/3)^x .
What are exponential functions?When the expression of a function is such that it involves the input to be present as the exponent (power) of some constant, then such a function is called an exponential function. Their usual form is specified below. They are written in several equivalent forms.
Given that the exponential function f(x) = 3
The initial value of the function is 2.
The base of the function is 3.
When the intial value is where x=0
where x=0, the value of f(0)=3
The growth is 1/3 but it is decay, that might be correct, or not because it is decay.
It is a stretch of the function f(x)=(1/3) power of x
when x=3, then f(3)=1/9
The function shows exponential growth a stretch of the function f(x) = [tex](1/3)^x[/tex].
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Using sum or difference formulas, find the exact value of sin(165∘)
Express your answer in the form
sin(165∘)=√a(√b−1)/4 for some numbers a and b
We have a = 2 and b = 3.
To find the exact value of sin(165°) using sum or difference formulas, we notice that 165° can be expressed as the sum of two angles whose sine and cosine values we know exactly, for example, 120° and 45°. The sum formula for sine is sin(A + B) = sin(A)cos(B) + cos(A)sin(B).
Therefore, sin(165°) = sin(120° + 45°) = sin(120°)cos(45°) + cos(120°)sin(45°).
From here, we use the known values:
sin(120°) = sin(180° - 60°) = sin(60°) = √3/2
cos(45°) = √2/2
cos(120°) = cos(180° - 60°) = -cos(60°) = -1/2
sin(45°) = √2/2
Plugging these values into our formula gives:
sin(165°) = ( √3/2)(√2/2) + (-1/2)(√2/2) = (√6 - √2)/4
This fraction can be rewritten to match the given form by factoring out √2 in the numerator:
sin(165°) = √2(√3 - 1)/4
Hence, in the form sin(165°) = √a(√b - 1)/4, we have a = 2 and b = 3.
This graph shows a portion of an even function. Use the graph to complete the table of values.
1, 1, 3, 3 - I just did it on e2020 and got it correct
which function is an even function?
describe how you would Use the distributive property to simplify 39 * 5
Find the volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane.
The volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane is 6 cubic unit.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
It is given that
The solid between the planes z = 3x + 2y + 1 and z = x + y, and above the
triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane.
r(u) = (1, 2)
r(v) = (-2, -1)
|r(u)xr(v)| = 3
The volume of the solid:
∬S(3x + 2y + 1 − x − y)ds = ∫₀¹ ∫(u, 0)(2x + y +1)3 dv du
After solving:
= 3(4/3 - 5 /6 + 3/2)
= 6
Thus, the volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane is 6 cubic unit.
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Final answer:
The volume of the solid region between the planes z = 3x + 2y + 1 and z = x + y, above the triangular region in the xy-plane, can be found using a double integral over the triangular area defined by vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0).
Explanation:
To find the volume of the solid region between the planes z = 3x + 2y + 1 and z = x + y, and above the triangular region in the xy-plane, we can use a double integral over the triangular region. The volume is given by the difference between the two planes integrated over the area of the triangle formed by the vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0).
First, define the vertices of the triangle in the xy-plane: A(1, 0), B(2, 2), and C(0, 1).
Second, find the equations of the lines forming the sides of the triangle, which helps in defining the limits of the integral.
Lastly, set up the double integral:
∫∫ (3x + 2y + 1) - (x + y) dA,
after solving, we get volume = 6
where dA is the differential area element in the xy-plane, and the limits of integration are determined by the triangular region.
The integration can be simplified by determining a suitable ordering for dx and dy, often choosing to integrate in x first and then y, or vice versa, based on the geometry of the triangle. The exact bounds for x and y need to be worked out from the equations of the lines defining the triangle's edges.
The result of this integral will give the volume of the solid region bounded by the two planes and above the triangle.
Write the fact family for the numbers 32,8,and 4
How to solve -5 3/14 to the thousandths place?? Please help
**I really need help on this! Please answer!*
The table shows the scoring system for quarterbacks in Jeremy's fantasy football league. In one game, Jeremy's quarterback had 2 touchdowns passes, 16 complete passes, 7 incomplete passes, and 2 interceptions. How many total points did Jeremy's quarterback score?
**QUARTERBACK SCORING**
Touchdown pass - 6
Complete pass - 0.5
Incomplete pass - -0.5
Interception - -1.5
The total number of points = 13.5 points
What is the total amount of points gained?
We are given the scoring method as:
Touchdown pass: 6
Complete pass : 0.5
Incomplete pass : -0.5
Interception : -1.5
Now, we are told that Jeremy's quarterback had the following:
2 touchdowns passes,
16 complete passes,
7 incomplete passes,
2 interceptions.
Thus:
Total points = (2 * 6) + (0.5 * 16) + (-0.5 * 7) + (-1.5 * 2)
Total points = 13.5 points
the product of two consecutive even positive integers is 10 more than seven times the larger . find the integers?
Wilbur's widgets, a widget company, produces 100 widgets. its average fixed cost is $5 and its total variable cost is $300. what is the total cost of producing 100 widgets?
a. $300
b. $305
c. $500
d. $800
The total cost of producing 100 widgets will be $800. Then the correct option is D.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Wilbur's widgets, a widget company, produce 100 widgets. its average fixed cost is $5 and its total variable cost is $300.
Then the equation is given as,
y = 5x + 300
Where 'x' is the number of widgets and 'y' is the total cost.
Then the total cost of producing 100 widgets will be given as,
y = 5 × 100 + 300
y = 500 + 300
y = $800
The total cost of producing 100 widgets will be $800. Then the correct option is D.
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Brenda can deliver 644 newspapers in 7 hours. How many newspapers can Brenda deliver in 9 hours?
Evaluate the series 50 + 10 + 2 + . . .
A child types the letters q, w, e, r, t, y, randomly producing 1000 letters in all. what is the expected number of times that the sequence qqqq appears, counting overlaps
The expected number of times the sequence 'qqqq' appears in 1000 random typings of 6 different letters is approximately 0.769 times.
Explanation:
This problem falls under the category of discrete probability in mathematics. The child randomly types one of 6 different letters.
Therefore, the probability of typing any one specific letter, such as 'q', is 1/6. The sequence 'qqqq' is a sequence of 4 specific letters. Thus, the probability of typing this sequence at any given point is (1/6)^4 or 1/1296. To find the expected number of times the sequence 'qqqq' will appear in 1000 typed letters, we multiply the probability of the event by the number of attempts. However, because 'qqqq' is a sequence of 4 letters, our attempts are based on 4-letter sequences and not individual letters. So, instead of 1000 letters, we have 1000 - 4 + 1 = 997 possible 4-letter sequences in 1000 letters.The expected number of times the sequence 'qqqq' will appear is then 997 * (1/1296) which is approximately 0.769. In simple words, we would expect the sequence 'qqqq' to occur around 0.769 times or less than once in 1000 random typings of the 6 different letters.Learn more about Expected Value here:https://brainly.com/question/35639289
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It is important to re-evaluate financial goals periodically. In which of the following situations would it be necessary to change an existing financial goal?
a. You fell sharply behind your expected schedule with regard to saving.
b. You recovered from an unexpected expense and are rattled that you did not see it coming.
c. You married, and your spouse has a similar financial goal.
d. You came across unexpected income.
Please select the best answer from the choices provided
A
B
C
D
Is y=7x+2 x+7y=8 parallel, perpendicular, or neither?
what is the basic ratio for 30:42
The basic ratio of 30:42 is 5:7. This was found by simplifying the ratio to its lowest terms, which is done by dividing both sides of the ratio by the largest number that can evenly divide both numbers, the greatest common factor (GCF).
Explanation:The basic ratio of 30:42 is found by simplifying the ratio to its lowest terms. To do this, find the greatest common factor (GCF) of the two terms, which is the largest number that can evenly divide both numbers. In this case, the GCF of 30 and 42 is 6. Therefore, by dividing both sides of the ratio by 6, we get the simplified ratio: 5:7. So, the basic ratio for 30:42 is 5:7.
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This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y, z) = 8x + 8y + 4z; 4x2 + 4y2 + 4z2 = 36
The extreme max value is "[tex]f(x,y,z) = 36[/tex]" and min value is "[tex]f(x,y,z) = -36[/tex]".
According to the question,
[tex]f(x, y, z) = 8x + 8y + 4z[/tex]let,
[tex]g(x,y,z) = 4x^2 + 4y^2 + 4z^2 - 36[/tex]By using Lagrange multipliers,
→ [tex]\bigtriangledown f= \lambda \bigtriangledown g[/tex]...(equation 1)
[tex]\bigtriangledown f = <8,8,4>[/tex][tex]\bigtriangledown g = <8x, 8y,8z>[/tex]∴ [tex]<8,8,4>=<8\lambda x, 8 \lambda y, 8 \lambda z >[/tex]
then,
[tex]8 \lambda x = 8[/tex]...(equation 2)[tex]8 \lambda y =8[/tex]...(equation 3)[tex]8 \lambda z = 4[/tex]...(equation 4)→ [tex](x = \frac{1}{\lambda}, y=\frac{1}{\lambda}, z =\frac{1}{2 \lambda} )[/tex]
As we know,
→ [tex]4x^2 +4y^2+4z^2=36[/tex]
By substituting the values, we get
→ [tex]4(\frac{1}{\lambda} )^2+ 4(\frac{1}{\lambda} )^2+4(\frac{1}{2\lambda} )^2 =36[/tex]
→ [tex]\frac{4}{\lambda^2} +\frac{4}{\lambda^2} +\frac{1}{\lambda^2} =36[/tex]
→ [tex]\frac{9}{\lambda^2}=36[/tex]
[tex]\frac{1}{\lambda}= \pm \frac{6}{3}[/tex]
[tex]\frac{1}{\lambda} = \pm 2[/tex]
∴ x = 2, y = 2, z = 1
then,
→ [tex]f(x,y,z) = 36[/tex] (Extreme max value)
and,
∴ x = -2, y = -2, z = -1
then,
→ [tex]f(x,y,z) = -36[/tex] (min value)
Thus the above answer is correct.
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Someone please help me!
Chris plans to mulch the Border surrounding a rectangular Garden in his backyard if the length of L of the garden (exculding its border) is 3 more than twice its width w and the width of the border is 1/4w which function repersents tje area A to be mulched in terms of w?
Kayla is knitting red sweaters to sell in her online store. The pattern requires 3 ounces of white yarn to trim each sweater. Kayla has 57 ounces of white yarn. How many sweaters can she trim with the yarn she has on hand?
Answer:
She can trim 19 sweaters.
Step-by-step explanation:
Kayla has a particular pattern in which she needs 3 ounces of white yarn.
That is in order to make a sweater of that particular pattern she requires white wool = 3 ounces
Kayla has total white wool = 57 ounces
one sweater requires = 3 ounces
number of sweater =[tex]\frac{total wool}{wool required for one sweater}[/tex]
=[tex]\frac{57}{3} = 19[/tex]
She can trim 19 sweaters with the Yarn she has on hand
Answer:
She can trim 19 sweaters.
Step-by-step explanation:
i have 3 1/8 pounds of macaroni and want to make 10 equal serving of macaroni salad. how many pounds of macaroni do i have for each serving
what is 3w(p +18) equal?
a diamond's density is 3.2 g/cm3
determine the volume of a diamond that has a mass of 1 g
The perimeter of a rectangle is 400 yards. What are the dimensions of the rectangle if the length is 80 yards more than the width?
The width is 60 yards and the length, being 80 yards more, is 140 yards.
To find the dimensions of the rectangle when the perimeter is 400 yards and the length is 80 yards more than the width, we can set up two equations based on the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Let the width be w. Then the length is w + 80 yards.
Using the perimeter formula:
400 = 2(w + 80) + 2w
400 = 2w + 160 + 2w
400 = 4w + 160
Subtract 160 from both sides:
240 = 4w
Divide by 4:
w = 60 yards
Now, calculate the length:
l = w + 80 = 60 + 80
l = 140 yards
The width is 60 yards, and the length is 140 yards.