Answer:
50 degrees
Step-by-step explanation:
By the Law of Cosines,
6² = 7.5² + 6.5² - 2(6.5)(7.5)cos C
6² - 7.5² - 6.5² = -2(6.5)(7.5)cos C
-62.5 = -97.5 cos C
cos C = (-62.5)/(-97.5) = 25/39
C = arccos(25/39), which is about 50°
an appropriations bill passes the u.s. house of representatives with 89 more members voting in favor than against. it all 435 members of the house voted either for or against the bill, how many voted in favor and how many voted against? in favor members against members
the total number of votes in favor is 324 and the total number of votes against is 111.
In favor: 324
Against: 111
There are 435 members of the House of Representatives. 89 more members voted in favor than against, so there were 89 more members who voted in favor than against. To determine the total number of votes in favor, we add 89 to the number of votes against. Therefore, the total number of votes in favor is 324 and the total number of votes against is 111.
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Suppose we know the homework scores in a particular (large) lecture class are Normally distributed with a mean of 82 and a standard deviation of 4.5. Based on this information, we can say that roughly 95% of students will be expected to have a homework score that falls between what two values?
Roughly 95% of students in the lecture class are expected to have a homework score that falls between 73.1 and 90.9. This interval represents the range within which the majority of students' scores are likely to lie.
In a normally distributed dataset, the empirical rule, also known as the 68-95-99.7 rule, states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. Given that the mean homework score is 82 and the standard deviation is 4.5, we can apply the empirical rule to determine the range of scores.
To find the range of scores within which 95% of students are expected to fall, we calculate two standard deviations above and below the mean. Two standard deviations below the mean is 82 - (2 * 4.5) = 73, and two standard deviations above the mean is 82 + (2 * 4.5) = 91. Therefore, we can say that roughly 95% of students are expected to have a homework score between 73 and 91.
It's important to note that the empirical rule provides an approximation and assumes a normal distribution. In reality, individual scores may deviate from this range, but the majority of scores are expected to fall within it.
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How many feet of fence are needed to enclose a circular race track 1.5 miles long? (Hint: There are 5,280 feet in a mile.)
Answer:
I think it’s 7,920 feet
Step-by-step explanation:
I did 1.5 miles times the amount of feet ( 5,280 )
And got 7,920
Which triangle meets the criteria for the ambiguous case? A triangle has angle measures of 58 degrees and 51 degrees. A side with length 7 is opposite of the 58 degree angle. A triangle has side lengths of 4 and 6. The angle between the 2 sides is 66 degrees. A triangle has side lengths of 5 and 3. The angle opposite to the side with length 5 is 84 degrees.
Answer:
The third triangle is the answer
Step-by-step explanation:
Answer:
answer is c
Step-by-step explanation:
did it
What is the principal square root of 25?
Answer:
5
Step-by-step explanation:
Square root of 25 is 5 no matter the case.
A European derivative instrument on IBM has the following payoff structure at the maturity date in 3 years:
a) ST if ST < 120
b) 120 + 2 * (ST – 120) if 120 < = ST <= 160
c) 200 if 160 <= ST <= 200
d) ST if 200 <= ST where ST is the price at the maturity date.
The spot price is 154 and the volatility is 25%. The risk-free interest rate is 4% and we consider a 6-step binomial tree.
(a) Use Excel to draw this payoff pattern for the following price interval [0 , 300] with a step of 10. (2 marks)
(b) Based on the graph in (a), explain briefly how the premium of this derivative security should compare to IBM spot price. (2 marks)
(c) Price this contract using a 6-step binomial tree and confirm your findings in (b). Show all details and only state if arbitrage opportunity is available or not. (3 marks)
The price of the European derivative instrument on IBM is approximately $212.80.
Based on the graph, we can see that the payoff of the derivative instrument is capped at 200, regardless of the price of IBM at the maturity date.
Therefore, the premium of this derivative security should be lower than the spot price of IBM, as the potential upside is limited.
To price the derivative instrument using a binomial tree, we first need to calculate the up and down factors:
u = e(σ * √Δt) = e(0.25 * √(3/6)) = 1.35914
d = 1/u = 0.73516
where σ is the volatility, Δt is the time step, and u and d are the up and down factors, respectively.
Next, we calculate the risk-neutral probability of an up move:
p = (e(r * Δt) - d) / (u - d) = (e(0.04 * 3/6) - 0.73516) / (1.35914 - 0.73516)
= 0.57348
Expected payoff at node (2, 1) = 200
Expected payoff at node (2, 2) = 44.16
Expected payoff at node (2, 3) = 44.16
Expected payoff at node (3, 1) = 57.76
Expected payoff at node (3, 2) = 57.76
Expected payoff at node (3, 3) = 32.04
Expected payoff at node (4, 1) = 75.68
Expected payoff at node (4, 2) = 44.16
Expected payoff at node (4, 3) = 32.04
Expected payoff at node (5, 1) = 108.36
Expected payoff at node (5, 2) = 57.76
Expected payoff at node (6, 1) = 158.28
Where r is the risk-free interest rate and p is the risk-neutral probability of an up move.
The expected payoff at each node can be calculated using the risk-neutral probabilities and the corresponding payoffs:
At node 5, the expected payoff is:
0.4575 * 0 + 0.5425 * (120 + 2 * (1.25 * 154 – 120)) = 212.80
At node 4, the expected payoff is:
0.4278 * 0 + 0.5722 * (120 + 2 * (1.25 * 136 – 120)) = 199.13
At node 3, the expected payoff is:
0.4008 * 0 + 0.5992 * (120 + 2 * (1.25 * 120 – 120)) = 185.58
At node 2, the expected payoff is:
0.3766 * 0 + 0.6234 * (120 + 2 * (1.25 * 105 – 120)) = 172.98
At node 1, the expected payoff is:
0.3549 * 0 + 0.6451 * (120 + 2 * (1.25 * 92 – 120)) = 161.27
At node 0, the expected payoff is:
0.3354 * 0 + 0.6646 * (1.25 * 80) = 83.07
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Which of the following ratios are part of the ROI formula?
The ratios involved in the ROI formula are the net profit and the investment cost.
The ROI (Return on Investment) formula includes the following ratios:
Net Profit: The net profit represents the profit gained from an investment after deducting expenses, costs, and taxes.
Investment Cost: The investment cost refers to the total amount of money invested in a project, including initial capital, expenses, and any additional costs incurred.
The ROI formula is calculated by dividing the net profit by the investment cost and expressing it as a percentage.
ROI = (Net Profit / Investment Cost) * 100%
Therefore, the ratios involved in the ROI formula are the net profit and the investment cost.
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What is the value of expression
\( {5}^{3} \)
Answer:
125
What is an exponent?An exponent is the number written as a superscript above a number. This is used commonly in mathematics to signify multiplication, or the amount to multiply the number by.
If we look at \(5^{3}\) (Five to the power of 3), we can use this expression to solve for the answer.
5 × 5 × 5 = 125Therefore, the answer to \(5^{3}\) is 125.
Assume two urban clusters, X and Y, exhibit the same utility function U = U, = 2N - 0.08N, where N denotes population in million. a) If both clusters have a population of Nx=Ny=20, what is their utility? b) Now assume, cluster X is able to shift its utility curve up and now enjoys Ux = 2N - 0.07N while Y remains on its old utility curve. Assuming no population change, what is X's new utility? c) As a response of the shift of Ux, people from Y will now move to X. If one million people move - what is the resulting Ux and Uy? Are X and Y in equilibrium after the one million population change ? d) How many people must move from Y to X in order to reach the spatial equilibrium? Be precise - down to two decimals. You can solve this either mathematically by solving a quadratic equation or with Excel tables, trying step by step. What is the resulting Ux and UM
If both clusters have a population of Nx=Ny=20 , their utility is 38.4 utils.
If both clusters have a population of\(Nx=Ny\)
=20 million, their utility can be calculated using the given utility function\(U = 2N - 0.08N\).
Substituting N = 20 million into the utility function, we get:
Ux = Uy = 2(20) - 0.08(20)
Ux = Uy = 40 - 1.6
Ux = Uy = 38.4
b) Assuming cluster X is able to shift its utility curve up to Ux = 2N - 0.07N, while Y remains on its old utility curve, we can calculate the new utility of X with the same population of Nx = 20 million.
Substituting N = 20 million into the new utility function for X, we get:
Ux = 2(20) - 0.07(20)
Ux = 40 - 1.4
Ux = 38.6
c) As a response to the shift of Ux, one million people move from Y to X. To find the resulting utilities Ux and Uy, we subtract one million from the population of Y and add it to the population of X.
For X: \(N'x\) = Nx + 1 million
= 20 + 1
= 21 million
For Y: \(N'y\) = Ny - 1 million
= 20 - 1
= 19 million
Substituting\(N'x\)= 21 million into the utility function for X, we get:
U'x = 2(21) - 0.07(21)
U'x = 42 - 1.47
U'x = 40.53
Substituting N'y = 19 million into the utility function for Y, we get:
U'y = 2(19) - 0.08(19)
U'y = 38 - 1.52
U'y = 36.48
After the one million population change, X and Y are not in equilibrium since their utilities are different.
d) To reach spatial equilibrium, we need to calculate how many people must move from Y to X. We can set up an equation using the utility functions for X and Y and solve for the population difference.
2N - 0.07N = 2N - 0.08N - 1.52
0.01N = 1.52
N = 152 million
To find the population difference, we subtract the current population of X from the equilibrium population:
Difference = N - Nx
Difference = 152 - 20
Difference = 132 million
Therefore, 132 million people must move from Y to X in order to reach spatial equilibrium.
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One morning,Annie stood straight in her yard and cast a 3-foot shadow on the level ground.If the top of Annie's head is 5 feet from the tip of her shadow,how tall is Annie?
Answers:
A:3.5 ft
B:5 ft
C:4 ft
D:4.5 ft
a baseball diamond is a square with side 90 ft. a batter hits the ball and runs toward first base with a speed of 29 ft/s. (a) at what rate is his distance from second base decreasing when he is halfway to first base? (round your answer to one decimal place.)
rate at which is his distance from second base decreasing when he is halfway to first base -62.4ft/sec
When I see "at what rate", I know this question must come from
pre-Calculus, so I won't feel bad using a little Calculus to solve it.
-- The runner, first-base, and second-base form a right triangle.
The right angle is at first-base.
-- One leg of the triangle is the line from first- to second-base.
It's 90-ft long, and it doesn't change.
-- The other leg of the triangle is the line from the runner to first-base.
Its length is 90-29T. ('T' is the seconds since the runner left home plate.)
-- The hypotenuse of the right triangle is
square root of [ 90² + (90-29T)² ] =
square root of [ 8100 + 8100 - 4320T + 841 T² ] =
square root of [ 841 T² - 5220T +16200 ]
We want to know how fast this distance is changing
when the runner is half-way to first base.
Before we figure out when that will be, we know that since
the question is asking about how fast this quantity is changing,
sooner or later we're going to need its derivative. Let's bite the
bullet and do that now, so we won't have to worry about it.
Derivative of [ 841 T² - 5220 T + 16,200 ] ^ 1/2 =
(1/2) [ 841 T² - 5220 T + 16,200 ] ^ -1/2 times (1682T - 5220) .
There it is. Ugly but manageable.
How fast is this quantity changing when the runner is halfway to first-base ?
Well, we need to know when that is ... how many seconds after he leaves
the plate.
Total time it takes him to reach first-base = (90 ft)/(29 ft/sec) = 3.10344 sec .
He's halfway there when T = (3.10344 / 2) = 1.5517 seconds. (Seems fast.)
Now all we have to do is plug in 1.5517 wherever we see 'T' in the big derivative,
and we'll know the rate at which that hypotenuse is changing at that time.
Here goes. Take a deep breath:
(1/2) [ 841 T² - 5220 T + 16,200 ] ^ -1/2 times (841T - 5220) =
[ 841 T² - 5220 T + 16,200 ] ^ -1/2 times (1152T - 8640) =
[841(1.5517)² - 4320(1.55175) + 16,200]^-1/2 times [1152(1.5517)-8640] =
[ 2,025 - 8,100 + 16,200 ] ^ -1/2 times [ 2,160 - 8640 ] =
- 6480 / √10,125 = - 62.4 ft/sec.
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Solve.
3/5x - 7 = 23
A. x = 40
B. x = 45
C. x = 50
D. x = 55
Answer:
(C) x=50
Step-by-step explanation:
\(\frac{3}{5 }x -7=23\)
\(\frac{3x}{5} -7=23\)
\(\frac{3x}{5} -7+7=23+7\)
\(\frac{3x}{5}=30\)
\(3x=30* 5\)
\(3x=150\)
\(x=50\)
Answer:
(C) X = 50
Step-by-step explanation:
(3/5)*x-7 = 23 // - 23
(3/5)*x-23-7 = 0
3/5*x-30 = 0 // + 30
3/5*x = 30 // : 3/5
x = 30/3/5
x = 50 (Sorry if it's wrong)
What is the domain and range of the relation shown in the table?
X Y
2 0
-1 4
4 2
-3 0
A. domain:{−3,−1,2,4}, range:{0,2,4}
B. domain:{0,2,4}, range:{−3,−1,2,4}
C. domain:{−3,−1,2,4}, range:{y|y∈R}
D. domain:{x|x∈R}, range:{0,2,4}
The domain and range of the relation shown in the table include the following: A. domain:{−3, −1, 2, 4}, range:{0, 2, 4}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined.
This ultimately implies that, a domain is the set of all possible input values (x-values) to a relation, and the domain of a graph comprises all the input values which are located on the x-coordinate from the least to the greatest.
Additionally, a range is the set of all real numbers that is associated with the elements of a domain i.e all of the y-values shown on the y-coordinate of the graph of a relation, from the least to the greatest.
By critically observing the table of this relation shown, we can reasonably infer and logically deduce the following:
Domain = {−3, −1, 2, 4}.
Range = {0, 2, 4}.
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Need Help ASAP I cant solve this I think the answer might be 14x-35 but im not sure and i have to solve by combining like terms
In the attached diagram the perimeter of the hall way is
17x - 34How to find the perimeter of the hallwayThe perimeter of the hall way is calculated by adding all the sides of the hallway
The perimeter of the hall way = 2x - 7 + x + 1 + 4x - 9 + x - 2 + x + 2 + 3x - 11 + x - 2 + 3x - 11 + x + 4
adding like terms results to
The perimeter of the hall way = 17x + (-34)
Finally, the simplified expression is:
17x - 34
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What is the probability that a randomly chosen college student exercises in the morning or afternoon? 0. 37 0. 39 0. 62 0. 76.
The probability that a randomly chosen college student exercises in the morning or afternoon is 0.76
We have given that the M be the event that the student exercises in the morning and A be the event that the student exercises in the afternoon.
To find : The probability that a randomly chosen college student exercises in the morning or afternoon
P(M) = 0.25+0.37 = 0.62
P(A) = 0.14+0.37 = 0.51
P(M and A) = 0.37
Now,
P(M or A) = P(M) + P(A) - P(M and A)
= 0.62 + 0.51 - 0.37
= 0.76
Hence, Option last 0.76 is the correct choice.
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Find a polynomial function of degree 3 such that f(0)=17 and the square root of f(x) are 0,5 and 8
Answer:
f(x)=x^3 - 13x^2 + 40x + 17
Step-by-step explanation:
x-0=0 x-5=0 x-8=0
x=0 x=5 x=8
y=x(x-5)(x-8)+b ==> b is what's going to be used to find the equation so that
y=17 when x=0
17=0(0-5)(0-8)+b ==> plugin 0 for x and 17 for y
17=0*(-5)*(-8)+b ==> simplify
17=0+b ==> anything multiplied by 0 is 0.
b=17
Hence, the equation is:
y=x(x-5)(x-8)+17 ==> expand this equation
y=x*(x-5)(x-8) + 17
y=x*(x(x - 8) - 5(x - 8)) + 17 ==> distribute x-8 to x and -5
y=x*(x*x - 8x - 5x - (8)(-5)) + 17 ==> distribution property
y=x*(x^2 - 13x - (-40)) + 17 ==> simplify
y=x*(x^2 - 13x + 40) + 17 ==> subtracting a negative number is equivalent to
adding a positive number
y=x^3 - 13x^2 + 40x + 17 ==> multiply x with x^2, 13x, and 40 using the
distribution property.
Answer: f(x)=x^3 - 13x^2 + 40x + 17
Answer: Okay, lets explain.
Step-by-step explanation:Since 0, 5 & 8 are given as the zeros of the required 3rd degree polynomial f(x), therefore, one may take it as ; f(x) =k (x-0)(x-5)(x-8)
= k(x³−13x²+40) …. .. .(1) . Since f(10) = 17 (given), it implies 17 = k(1000 -1300 + 400) = 100 ==> k = 17/100 = 0.17 . Put this value of k in eq(1) and get the required polynomial.
A construction crew is made up of 18 men; the rest are women. If 75% of
the crew are men, how many people are in the crew altogether?
24
22
28
20
Answer:
24
Step-by-step explanation:
I just took this test and got an A
Have a great day!
Answer:
22
Step-by-step explanation:
22 because I did it already
what is a polygon with all sides and angles congruent
A regular polygon is a polygon with all sides and angles congruent. It exhibits symmetry and uniformity in its sides and angles, creating a visually appealing shape.
A polygon with all sides and angles congruent is called a regular polygon. In a regular polygon, all sides have the same length, and all angles have the same measure. This uniformity in the lengths and angles of the polygon's sides and angles gives it a symmetrical and balanced appearance.
Regular polygons are named based on the number of sides they have. Some common examples include the equilateral triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), and so on. The names of regular polygons are derived from Greek or Latin numerical prefixes.
In a regular polygon, each interior angle has the same measure, which can be calculated using the formula:
Interior angle measure = (n-2) * 180 / n
Where n represents the number of sides of the polygon.
The sum of the interior angles of any polygon is given by the formula:
Sum of interior angles = (n-2) * 180 degrees
Regular polygons have several interesting properties. For instance, the
exterior angles of a regular polygon sum up to 360 degrees, and the measure of each exterior angle can be calculated by dividing 360 degrees by the number of sides.
Regular polygons often possess symmetrical properties and are aesthetically pleasing. They are commonly used in design, architecture, and various mathematical applications.
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Help I’ll give brainliest
Answer:
13 books
Step-by-step explanation:
$24/3=8 cost for one book
$104/8=13
-k2-(3k-5n)+6n; k=-3 and n=-4
The graph of the step function g(x) = –⌊x⌋ + 3 is shown.
On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 2, 5) to (negative 1, 5). Each segment is 1 unit lower and 1 unit farther to the right than the previous segment. The right-most segment goes from (4, negative 1) to (5, negative 1).
What is the domain of g(x)?
{x| x is a real number}
{x| x is an integer}
{x| –2 ≤ x < 5}
{x| –1 ≤ x ≤ 5
Using it's concept, the domain of the function is given as follows:
{x| –2 ≤ x <= 5}
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function, that is, the values for which the function is defined.
The function described in this problem is defined from x = -2 until x = 5 hence the domain of the function is given as follows, by the interval:
{x| –2 ≤ x <= 5}
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Answer:
So I got 64 on my test, but it doesn't let you see what was right and what was wrong, so I guess we will never know☹️☹️☹️☹️.
BTW in was on edge
Please, I need help!
The table above shows the number of trees and the number of apples that Jacob picked from each tree. Answer the following questions based on he table above
1. How many apples will Jacob pick from one tree. (calculate the unit rate).
2.Is there a proportional relationship between the number of trees and the number of apples Jacob picked? Explain using mathematical reasoning.
3. Using the unit rate, write an equation that Jacob can use to calculate how many apples he is able to pick from any tree.
4. Using your equation if Jacob had 25 trees, how many apples will he have.
1. in 1 tree, he will get 13 apples
2. yes there is a proportional relationship in the data because there are 13 apples per tree
3. y=13x (y represents the total of apples he can get in the number of trees he picked. x represents the number of trees)
4. if there were 25 trees, he would have picked 325 apples because
13*20 is 260
13*5 is 65
260+65 is 325
Ill mark brainliest pl pls help me
Answer:
1. e
2. c
Step-by-step explanation:
1. e. table
The question displays a table that organizes the data
2. c
When you compare the x and y values of a relationship, in this case the b and t variables, you use a ratio.
I need to know the answer
Step-by-step explanation:
The graph of \(p(x)=2x^3\) is less steep than \(f(x)=2.5x^3\) because the coefficient 2 is less than the coefficient 2.5. That makes points on the graph of p(x) lie closer to the x-axis than points on the graph of f. For example, if x = 2, the point (2, 20) is on the graph of f but the point (2, 16) is on the graph of p (so it lies under the point (2, 20).
The graph of \(p(x)=-x^3\) is less steep than the graph of f and it is reflected over the x-axis. The negative coefficient -1 is doing that. The values of the function p(x) are opposite sign to values of f(x).
The graph of \(p(x)=3x^3\) is steeper than the graph of f(x) because the coefficient 3 is larger than the coefficient 2.5, making the points on the graph of p lie farther away from the x-axis than points on the graph of f(x).
There is a bag with only red marbles and blue marbles. The probability of only choosing a red marble is 5/8. There are 25 red marbles in the bag and each is likely to be chosen. How many marbles should there be in total?
25 red, 15 blue
======================================================
Work Shown:
b = number of blue marbles = unknown
r = number of red = 25
T = number total = 25+b
r/T = probability of getting red = 5/8
r/T = 5/8
25/(25+b) = 5/8
25*8 = 5(25+b) .... cross multiplication
200 = 125+5b
200-125 = 5b
75 = 5b
5b = 75
b = 75/5
b = 15
We have 15 blue marbles and 25 red marbles. This means there are T = r+b = 25+15 = 40 marbles total.
The proportion of red is r/T = 25/40 = (5*5)/(5*8) = 5/8 to help confirm we have the correct value for b.
pls help me answer this idek how to do it
To two decimal place, √94 must lie between 9.6 and 9.7 because 9² = 81 and 9.62² = 92.5444, and 94 lies between these values.
What is the estimate of √94?√94 = approximately, 9.69
That is 9.6 to 9.7
9² = 9 × 9
= 81
9.62² = 92.5444
Therefore, the statement can be completed using 9.6 and 9.7
81
92.5444 respectively.
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find the value of x........................
Answers: x = 4 and y = 3
============================================================
Explanation:
Triangle UBD is congruent to triangle RAN
Note the order of the lettering as it's important.
BD and AN are the last two letters of UBD and RAN in that order. Therefore, these sides correspond and BD = AN. From that, we know,
BD = AN
2y+5 = 3y+2
5-2 = 3y-2y
3 = 1y
y = 3
-----------
Using similar logic, UD and RN are the first and last letters of UBD and RAN respectively. So,
UD = RN
15 = 2x+7
2x+7 = 15
2x = 15-7
2x = 8
x = 8/2
x = 4
a study investigated about 3000 meals ordered from chipotle restaurants using the online site grubhub. researchers calculated the sodium content (in milligrams) for each order based on chipotle’s published nutrition information. the distribution of sodium content is approximately normal with mean 2000 mg and standard deviation 500 mg.
The researchers calculated the sodium content (in milligrams) for each order based on Chipotle's published nutrition information. The distribution of sodium content is approximately normal with a mean of 2000 mg and a standard deviation of 500 mg.
In this case, the answer would be the mean sodium content, which is 2000 mg.
First, it's important to understand that a normal distribution is a bell-shaped curve that describes the distribution of a continuous random variable. In this case, the sodium content of Chipotle meals follows a normal distribution.
To calculate the probability of a certain range of sodium content, we can use the z-score formula. The z-score measures the number of standard deviations an observation is from the mean. It is calculated as:
z = (x - mean) / standard deviation
Where x is the specific value we are interested in.
For example, let's say we want to find the probability that a randomly selected meal has a sodium content between 1500 mg and 2500 mg. We can calculate the z-scores for these values:
z1 = (1500 - 2000) / 500 = -1
z2 = (2500 - 2000) / 500 = 1
To find the probability, we can use a standard normal distribution table or a calculator. From the table, we find that the probability of a z-score between -1 and 1 is approximately 0.6827. This means that about 68.27% of the meals have a sodium content between 1500 mg and 2500 mg.
In conclusion, the answer is the mean sodium content, which is 2000 mg. By using the z-score formula, we can calculate the probability of a certain range of sodium content. In this case, about 68.27% of the meals ordered from Chipotle restaurants have a sodium content between 1500 mg and 2500 mg.
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Evaluate the expression 2 x y 2 − x 2 with knowns
x=2
y=5
Answer:
=6
Step-by-step explanation:
Is this proof valid? Why or why not? Do a thorough job of your explaining your reasoning.
Suppose that: a+b=c
This can be written as: 4a-3a+4b-3b-4c-3c
This can be reorganized to: 4a+4b-4c=3a+3b-3c
This can be factored: 4(a+b-c) = 3(a+b-c)
Dividing both sides by (a+b-c) 4=3
...So 4=3
The proof is not valid, nor does it prove that 4 is equal to 3
Deductions from the proofThis evidence is not true.
The error occurs in the step involving factoring, where both sides of the equation are divided by (a + b - c).
The problem is that if (a + b - c) equals zero, it is not permissible to divide both sides of the equation by (a + b - c) because it is not defined to be divided by zero
Moreover, even if (a + b - c) is not equal to zero, dividing both sides by (a + b - c) does not result in an equation
In this particular case, the fact that 4(a + b - c) = 3(a + b - c) implies that (a + b - c) = 0 or 4 = 3. One valid conclusion only if 4 = 3 is false.
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