Answer:
first answer is correct
y = -1/2 x^2 + x + 1
Step-by-step explanation:
based on the graph, you can find two points
(2,1) and (0,1)
I input (2, 1) to each equation to check
y = -1/2 x^2 + x + 1 is correct
a gambling game pays 4 to 1 and has one chance in five of winning. suppose someone plays the game 50 times, betting $2 each time, and keeps track of the number of wins. what should be the tickets in the box model?
The tickets in the box model should be:
- 1 ticket with a value of $6 (representing a win)
- 4 tickets with a value of -$2 (representing a loss).
In this gambling game, you have a 4 to 1 payout and a 1 in 5 chance of winning.
To create a box model for this scenario, follow these steps:
Identify the possible outcomes:
In this game, there are two possible outcomes:
winning (with a 1 in 5 chance) and losing (with a 4 in 5 chance).
Determine the payout for each outcome:
If a player wins, they receive a 4 to 1 payout on their $2 bet, so they win $8.
However, they also lose the original $2 bet, so the net gain is $6.
If a player loses, they lose their $2 bet.
Assign tickets to the box model based on the probability of each outcome:
Since there is a 1 in 5 chance of winning, there should be 1 ticket representing a win (net gain of $6) and 4 tickets representing a loss (net loss of $2).
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For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.
(a) 1,0,1,1,0,0,1,1,1,0,0,0,1,.
(b) 1,2,2,3,4,4,5,6,6,7,8,8,.
(c) 1,0,2,0,4,0,8,0,16,0,.
(d) 3, 6, 12, 24, 48, 96, 192,.
(e) 15, 8, 1, -6, -13, -20, -27,.
(f) 3, 5, 8, 12, 17, 23, 30, 38, 47,
The next three terms of the sequence.
(a) The sequence alternates between a run of "1"s and a run of "0"s.
Specifically, the nth term is 1 if the number of "1"s in the first n-1 terms is
odd, and 0 if the number of "1"s in the first n-1 terms is even.
(b) The nth term is[tex]\lfloor (n+1)/2\rfloor[/tex] if n is odd, and n/2 if n is even.
(c) The nth term is[tex]2^{(n-1)/2}[/tex] times the parity (i.e., 0 or 1) of n.
(d) The nth term is [tex]3\cdot 2^{n-1}[/tex].
(e) The nth term is 15-7(n-1).
(f) The nth term is the sum of the first n positive integers minus 3, i.e.,
[tex]1+2+3+\cdots+n-3.[/tex]
To determine the next three terms of each sequence, we simply apply the rule or formula given above. For example, for sequence (a), the next three terms are 0, 1, 1, since the next term is 0 (since there are an even number of 1's so far), followed by two 1's (since there are now an odd number of 1's).
For sequence (b), the next three terms are 9, 10, 10, since the next term is 9 (since the next term in the pattern is odd), followed by two 10's (since the next two terms in the pattern are even). And so on for the other sequences.
(a) The sequence alternates between a run of "1"s and a run of "0"s.
Specifically, the nth term is 1 if the number of "1"s in the first n-1 terms is
odd, and 0 if the number of "1"s in the first n-1 terms is even.
(b) The nth term is[tex]\lfloor (n+1)/2\rfloor[/tex] if n is odd, and n/2 if n is even.
(c) The nth term is[tex]2^{(n-1)/2}[/tex] times the parity (i.e., 0 or 1) of n.
(d) The nth term is [tex]3\cdot 2^{n-1}[/tex].
(e) The nth term is 15-7(n-1).
(f) The nth term is the sum of the first n positive integers minus 3, i.e.,
[tex]1+2+3+\cdots+n-3.[/tex]
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This is precalc trig please help
The answer to the trigonometry question in the picture attached is:
= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)
Here is the step by step approach to solving the trigonometrySimplify 1-csc θ as follows:
1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)
= 1 - csc^2 θ / (1 + csc θ)
= 1 - 1/sin^2 θ / (1 + 1/sin θ)
= 1 - sin^2 θ / (sin θ + 1)
= (sin θ - sin^2 θ) / (sin θ + 1)
Simplify 1+csc θ as follows:
1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)
= 1 - csc^2 θ / (1 - csc θ)
= 1 - 1/sin^2 θ / (1 - 1/sin θ)
= 1 - sin^2 θ / (sin θ - 1)
= (sin θ + sin^2 θ) / (sin θ - 1)
Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:
cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)
Simplify the expression by canceling out the sin^2 θ terms:
cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)
= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)
Simplify further by factoring out common terms in the numerator and denominator:
cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)
= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]
Finally, simplify the expression by factoring out a sin θ term from the denominator:
cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]
= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]
= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)
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!!PLEASE HELPPPP MEEE!!
Answer:
Step-by-step explanation:
5989.87
Rewrite the expression with rational exponents.
[tex]7^{(1/3)}[/tex] is the equivalent expression to ∛7 with rational exponents.
What are rational exponents?
Rational exponents are exponents that are expressed as fractions. Specifically, a rational exponent of the form m/n is equivalent to taking the nth root of a number and then raising it to the power of m.
When we talk about rational exponents, we are referring to exponents that are written as fractions. Specifically, a rational exponent of the form m/n is equivalent to taking the nth root of a number and then raising it to the power of m.
So, in the case of ∛7, we can rewrite the cube root symbol (∛) as a rational exponent with a denominator of 3. That is, ∛7 can be expressed as [tex]7^{(1/3)}[/tex] , where the 1/3 exponent means "take the cube root of 7".
Therefore, [tex]7^{(1/3)}[/tex] is the equivalent expression to ∛7 with rational exponents.
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5. Select Yes or No to indicate whether each ordered pair is a point of intersection
between the line x - y = 6 and the circle y² - 26 = -x².
Ordered Pair
(1,-5)
(1,5)
(5,-1)
To determine if each ordered pair is a point of intersection between the line x - y = 6 and the circle y² - 26 = -x², we need to substitute the values of x and y in both equations and see if they are true for both.
Select Yes or No to indicate whether each ordered pair is a point of intersectionFor the ordered pair (1, -5):
x - y = 6 becomes 1 - (-5) = 6, which is true.
y² - 26 = -x² becomes (-5)² - 26 = -(1)², which is false.
Therefore, (1, -5) is not a point of intersection.
For the ordered pair (1, 5):
x - y = 6 becomes 1 - 5 = -4, which is false.
y² - 26 = -x² becomes (5)² - 26 = -(1)², which is true.
Therefore, (1, 5) is a point of intersection.
For the ordered pair (5, -1):
x - y = 6 becomes 5 - (-1) = 6, which is true.
y² - 26 = -x² becomes (-1)² - 26 = -(5)², which is false.
Therefore, (5, -1) is not a point of intersection.
So the answer is:
(1,-5) - No
(1,5) - Yes
(5,-1) - No
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Maxine graphs the function m(x) which has a vertex of (-3,4) and passes through the point (-1,-8). Ricardo graphs p(x) = (x+3)² +4
Maxine thinks that both functions have the same axis of symmetry equation. Do you agree or disagree?
Both functions have the same axis of symmetry equation, which is x = -3.
Given that, Maxine graphs a function m(x) which has a vertex of (-3,4) and passes through the point (-1,-8).
Ricardo graphs p(x) = (x+3)² + 4
We need to check if both the function axis of symmetry equation.
So,
Both functions have a vertex of (-3,4), which means that the axis of symmetry must be a vertical line passing through x = -3.
Axis of symmetry = The axis of symmetry is an imaginary straight line that divides the shape into two identical parts or that makes the shape symmetrical.
For the function p(x) = (x+3)² +4, the axis of symmetry is indeed x = -3.
For the function m(x), since it has a vertex of (-3,4), the equation of the axis of symmetry is x = -3.
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To celebrate the first day of school, Grace brought in a tray of caramel brownies and walnut brownies. She brought 80 brownies in all. 56 of the brownies were caramel. What percentage of the brownies were caramel?
Answer: 70% of the brownies are caramel.
Step-by-step explanation: First take 56/80 because 56 of the brownies were caramel out of the 80. Which divided that give you 0.7. Multiply then by 100 which will give you 70. So the answer is there are 70% caramel brownies.
c. what is the probability that the duration of a rainfall event at this location is between 2 and 3 hours? d. what is the probability that a rainfall duration exceeds the mean value by more than 2 standard deviations?
The probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.
a. The exponential distribution with a mean of 2.725 hours can be expressed as λ = 1/2.725. Using this parameter, we can calculate the probabilities as follows:
P(X ≥ 2) = [tex]e^{(-λ2) }= e^{(-1/2.7252)[/tex] ≈ 0.4800
P(X ≤ 3) = 1 - [tex]e^{(-λ3)} = 1 - e^{(-1/2.7253)[/tex] ≈ 0.6674
P(2 ≤ X ≤ 3) = [tex]e^{(-λ2)} - e^{(-λ3)} = e^{(-1/2.7252)} - e^{(-1/2.7253)}[/tex] ≈ 0.1474
b. The standard deviation of an exponential distribution is equal to the mean, so 2 standard deviations above the mean would be 2*2.725 = 5.45 hours. The probability that a rainfall event exceeds this duration can be calculated as follows:
P(X > 5.45) =[tex]e^{(-λ5.45)} = e^{(-1/2.7255.45)}[/tex] ≈ 0.0498
Therefore, the probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.
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Complete Question:
Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.
a. What is the probability that the duration of a particular rainfall event is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)
b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? (.0498)
1/2 x^4=8
Solve the equation
Answer:
x=2
Step-by-step explanation:
x^4=16
x=[tex]\sqrt[4]{16}[/tex]
x=[tex]2[/tex]
cuantos números
primos son a la vez la suma y la diferencia
Answer: there is only one number
Answer:
Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.
Espero haber ayudado :D
please help me with all the blank ones hurry i am running outta time
Answer:see below
Step-by-step explanation:
10.600
11.80000
12.17
13.48
14.4000
21. 1km=100m;0.5km=500m;0.1km=100m
22.50m=5000cm; 5m=500cm; 0.5m=50cm
a password consists of four alphanumeric characters (case insensitive). a valid password must contain at least one digit and at least one letter. how many different passwords are there
There are 1,280,240 different passwords that meet the criteria of containing at least one letter and at least one digit, and consisting of four alphanumeric characters (case insensitive).
How to calculate the total number of different passwords?To calculate the total number of different passwords, we can break the problem down into several steps:
Step 1: Calculate the number of possible characters for each position in the password. Since the password consists of four alphanumeric characters, there are 26 letters (A-Z) and 10 digits (0-9) for each position.
Therefore, there are 36 possible characters for each position.
Step 2: Calculate the total number of possible passwords without any restrictions.
Since there are 36 possible characters for each position and the password has four positions, the total number of possible passwords without any restrictions is:
36 x 36 x 36 x 36 = 1,679,616
Step 3: Calculate the number of passwords that do not contain at least one digit or at least one letter.
To do this, we can calculate the number of passwords that do not contain any digits and subtract it from the total number of possible passwords, and then do the same for passwords that do not contain any letters.
The number of passwords that do not contain any digits is:
26 x 26 x 26 x 26 = 456,976
The number of passwords that do not contain any letters is:
10 x 10 x 10 x 10 = 10,000
However, we have to be careful not to double-count the passwords that do not contain both letters and digits.
The number of passwords that do not contain both letters and digits is:
26 x 26 x 10 x 10 = 67,600
So the total number of passwords that do not contain at least one digit or at least one letter is:
456,976 + 10,000 - 67,600 = 399,376
Step 4: Subtract the number of invalid passwords from the total number of possible passwords:
1,679,616 - 399,376 = 1,280,240
Therefore, there are 1,280,240 different passwords that meet the criteria of containing at least one letter and at least one digit, and consisting of four alphanumeric characters (case insensitive).
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Trigonometric funcions
Which equation are true
Answer:
C and D
Step-by-step explanation:
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{4}{5}[/tex] ⇒ C
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{5}[/tex] ⇒ D
write it as a fraction
Answer:
[tex] \frac{11}{13} \times \frac{1}{4} \times \frac{1}{3} = \frac{11}{156} [/tex]
So the volume of this rectangular prism is 11/156 of a cubic foot.
PLEASE HELP ME I BEEGGGG
Answer:miami is 43431.16 rounded to 43431 because you can't have .16 of a person.
washington dc is 4249.22 which is round to 4249 because you can't have .22 of a person.
and new york city is 27348.99 which is rounded to 27349 because you can't have .99 of a person.
Step-by-step explanation:
im smart and im really good at math
The answers are in the picture. I need help ASAP!
The perimeter and the area of the regular polygon are 20 inches and 27.53 square inches.
How to calculate the area and the perimeter of a regular polygon
The figure representing a regular polygon with five sides of same length, whose perimeter and area is well described by following formulas:
Perimeter
p = n · l
Area
A = (n · l · a) / 2
Where:
A - Area of the polygon, in square inches. n - Number of sides.l - Side length, in inches. a - Apothema, in inches. p - Perimeter, in inches.Where the apothema is:
a = 0.5 · l / tan (180° / n)
If we know that l = 4 in and n = 5, then the perimeter and the area of the polygon are:
Perimeter
p = 5 · (4 in)
p = 20 in
Area
a = 0.5 · (4 in) / tan (180° / 5)
a = 0.5 · (4 in) / tan 36°
a = 2.753 in
A = [5 · (4 in) · (2.753 in)] / 2
A = 27.53 in²
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Problem
The table compares the heights (in centimeters) and the weights (in kilograms) of Karim's friends.
Can the weight of Karim's friends be represented as a function of their height?
Height (centimeters) Weight (kilograms)
163
163163
65
6565
167
167167
70
7070
154
154154
60
6060
172
172172
70
7070
167
167167
68
6868
159
159159
58
5858
160
160160
64
6464
166
166166
69
6969
Choose 1 answer:
Choose 1 answer:
(Choice A) Yes
A
Yes
(Choice B) No
B
No
Weight cannot be represented as a function of height.
Can the weight be represented as a function of their height?No, the weight of Karim's friends cannot be represented as a function of their height.
To represent weight as a function of height, there should be a consistent relationship between the height and weight values.
However, from the given data, we can see that for the same height, there are different weight values, and for the same weight, there are different height values.
This indicates that there is no one-to-one relationship between height and weight, and hence weight cannot be represented as a function of height.
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Of the 8 parent functions discussed. Select ALL of the parent functions
that have 180 degree rotational symmetry around the point (0,0)
We have identified three parent functions that exhibit 180-degree rotational symmetry around the point (0,0): the constant function f(x) = 0, the odd power functions f(x) = x²ⁿ⁺¹ for any integer n, and the tangent function f(x) = tan(x) on the interval (-π/2, π/2).
A function f(x) exhibits 180-degree rotational symmetry around the point (0,0) if and only if f(-x) = -f(x) for all x. To see why, consider rotating the graph of f(x) by 180 degrees around the origin.
Using this criterion, we can identify the parent functions that have 180-degree rotational symmetry around the point (0,0). These functions are:
The constant function f(x) = 0. This function is symmetric about the origin, and any rotation around the origin preserves this symmetry.
The odd power functions f(x) = x²ⁿ⁺¹ for any integer n. These functions are also symmetric about the origin, and any rotation around the origin preserves this symmetry. To see why, note that f(-x) = (-x)²ⁿ⁺¹ = -x²ⁿ⁺¹ = -f(x) for all x.
The tangent function f(x) = tan(x) on the interval (-π/2, π/2). This function has vertical asymptotes at x = π/2 and x = -π/2, but these do not affect its rotational symmetry around the origin.
To see why, note that f(-x) = tan(-x) = -tan(x) = -f(x) for all x in the interval (-π/2, π/2).
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All help is appreciated thank you.
Using the fact that the triangles are similar we can see that the value of x is 36
How to find the value of x?We can see that the triangles are similar due to the same interior angles, then ther is a scale factor k between them.
So we can write:
20*k = 48
k = 48/20 = 2.4
Then:
x = 15*2.4
x = 36
That is the value of x.
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3. On Monday, James scored 9,755 points while playing a video game. On Tuesday, he scored 13,783 points while playing the same game. How many more points did he score on Tuesday than on Monday?
Answer:
4028
Step-by-step explanation:
Answer:
4028
Step-by-step explanation:
You need to subtract 9,755 from 13,783 on a calculator and you get your answer.hope it helps
Isabella was asked to solve the following trigonometric equation for 0 < x < 2π.
sin(x) = cos(2x) = 0
-
Isabella worked the problem the following way:
Line 1: sin(x) (1 - 2 sin²(x)) =
-
Line 2: sin(x) - 1+2 sin²(x) = 0
Line 3: 2 sin² (x) + sin(x) = 1
Line 4: sin(x) (2 sin(x) + 1) = 1
Line 5: sin(x) = 1,
Line 6: sin(x) = 1,
Line 7: x = 0, π
2 sin(x) + 1 = 1
sin(x) = 0
A. Isabella made a mistake in her work. In what line did the mistake occur? Justify your answer. (6
points)
B. What are the correct answers? Leave answers as exact values. WORK DOES NOT NEED TO BE
SHOWN. (6 points)
1. The equation she was supposed to solve was sin(x) = cos(2x), but she mistakenly added an extra "= 0" term.
2. The correct answers are x = π/6 and x = 5π/6.
How do we find the correct answers for the trigonometric equation?
To find the correct answers, we will solve the correct trigonometric equation sin(x) = cos(2x).
Since cos(2x) = 1 - 2sin²(x), the equation becomes:
sin(x) = 1 - 2sin²(x)
Now we can rewrite this equation as a quadratic equation in sin(x):
2sin²(x) + sin(x) - 1 = 0
This equation can be solved using the quadratic formula:
sin(x) = [-b ± sqrt(b² - 4ac)] / 2a
where a = 2, b = 1, and c = -1:
sin(x) = [-1 ± sqrt(1² - 42(-1))] / (2*2)
sin(x) = [-1 ± sqrt(9)] / 4
sin(x) = (-1 ± 3) / 4
There are two possible solutions for sin(x):
sin(x) = 1/2
sin(x) = -1
For sin(x) = 1/2, we have:
x = π/6, 5π/6
For sin(x) = -1, there is no solution in the interval 0 < x < 2π because the sine function does not reach -1 within this range.
So the correct answers are x = π/6 and x = 5π/6.
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IF YOU ANSWER CORRECTLY I WILL GIVE YOU BRAINLIEST***
Find the area of the shaded sector. Round to the nearest tenth.
167°
17. 8 yd
Area = [ ? ]yd? Enter
The area of the shaded sector is approximately 463.8 square yards.
To find the area of the shaded sector, we need to use the formula for the area of a sector, which is given by
Area of sector = (central angle / 360°) x πr²
where r is the radius of the sector, and the central angle is the angle between the two radii that form the sector.
In this case, we are given that the central angle of the shaded sector is 167°, and the radius is 17.8 yards. So, we can substitute these values into the formula as follows
Area of sector = (167° / 360°) x π(17.8)²
Simplifying this expression, we get:
Area of sector = 0.464 x 998.92
Multiplying these two numbers, we get
Area of sector = 463.8 square yards
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The given question is incomplete, the complete question is:
Find the area of the shaded sector. Round to the nearest tenth.
Anyone have the answers
Answer:
The answer is 7 pens
Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine, as in Example 4.
The expression in terms of the first power of sine is 1 + 3[tex]sin^{4}[/tex]x - 3[tex]sin^{2}[/tex]x - [tex]sin^{6}[/tex]x. The solution has been obtained by using the trigonometric identities.
What are trigonometric identities?
All possible values of the variables in the equation must satisfy the equality condition known as a trigonometric identity. A triangle's side length and angle can be used to express a variety of unusual trigonometric identities.
We are given expression as [tex]cos^{6}[/tex] (x).
This can be written as a cosine function as [tex](cos^{2} x)^{3}[/tex].
We know that [tex]sin^{2}[/tex]x + [tex]cos^{2}[/tex]x = 1.
So, we get
⇒ (1 - [tex]sin^{2}[/tex]x[tex])^{3}[/tex]
⇒ 1 + 3[tex]sin^{4}[/tex]x - 3[tex]sin^{2}[/tex]x - [tex]sin^{6}[/tex]x
Hence, the required expression has been obtained.
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The diameter of a semicircle is 4 feet. What is the semicircle's perimeter?
what is the expected ratio of two heads : heads/tails : tails/heads : two tails when two coins are repeatedly flipped? (this question is asking about probability, which is a prediction, rather than your actual observed results.)
When two coins are repeatedly flipped, the probability of getting two heads is 1/4, the probability of getting a head and a tail is 1/2, and the probability of getting two tails is also 1/4.
Therefore, the expected ratio of two heads : heads/tails : tails/heads : two tails is 1:2:2:1, respectively. This means that out of every six flips, we would expect to see one outcome of two heads, two outcomes of heads/tails and tails/heads each, and one outcome of two tails.
However, it is important to note that this is only a prediction and the actual results may differ due to chance.
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Evan takes 100 milligrams of medicine. The amount of medicine in his bloodstream decreases by 0.4 milligram each minute for a number of minutes, m, after that. He writes the expression 100 - 0.4m to find the amount of medicine in his bloodstream after m minutes. Which statement about his expression is true?
The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.
The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.
The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.
Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
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what is the confidence interval estimate of the population mean examination score if a sample of applications provided a sample mean (to the nearest whole number
This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.
The confidence interval estimate of the population means examination score can be calculated using the sample mean and the margin of error. The margin of error depends on the level of confidence and the sample size.
For example, if a sample of 100 applications provided a sample mean score of 80, and a 95% confidence level is used, the confidence interval estimate of the population mean examination score would be:
Margin of error = (critical value) x (standard error)
The critical value for a 95% confidence level with 99 degrees of freedom is 1.984. The standard error can be calculated using the formula:
Standard error = (standard deviation) / sqrt(sample size)
If the standard deviation of the examination scores is known, it can be used in the formula. If not, the sample standard deviation can be used as an estimate.
Assuming a sample standard deviation of 10, the standard error would be:
[tex]Standard\ error = \frac{10} { \sqrt{(100)}} = 1[/tex]
Therefore, the margin of error would be:
Margin of error = 1.984 x 1 = 1.984
The confidence interval estimate of the population means examination score would be:
80 ± 1.984, or between 78.016 and 81.984.
This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.
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The 95% confidence interval for the population mean examination score would be between 72.23 and 77.77, to the
nearest whole number.
To determine the confidence interval estimate of the population mean examination score based on a sample mean
provided to the nearest whole number, we need to know the sample size and the level of confidence.
Assuming a normal distribution and a level of confidence of 95%, we can use the following formula to calculate the
confidence interval estimate:
Confidence interval = sample mean +/- (critical value) x (standard error)
The critical value can be found using a t-distribution table or a calculator, based on the sample size and degrees of
freedom (n-1). For a sample size of 30 or more, we can use the z-score instead of the t-score.
The standard error is the standard deviation of the sample divided by the square root of the sample size.
For example, if a sample of 50 applications provided a sample mean of 75, and the standard deviation was 10, the
standard error would be 10/sqrt(50) = 1.41.
Assuming a level of confidence of 95%, the critical value for a sample size of 50 and degrees of freedom of 49 would be 1.96.
Therefore, the confidence interval estimate would be:
75 +/- 1.96 x 1.41 = 75 +/- 2.77
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9. Patricia has 5 cups of rice cereal. She
uses 3 cups of rice cereal to make
granola bars, then borrows 0.5 cup of
rice cereal from her friend. Her recipe
for cereal clusters calls for 3 cups of
rice cereal. Does Patricia have enough?
How much will she have left over, or
how much more will she need?
A Yes, she has 1/2cup left.
B No, she needs 1/2cup more.
C Yes, she 1/4 has cup left.
D No, she needs 1/4cup more.
Therefore, the correct answer is (B) No, she needs 1/2 cup more.
To determine if Patricia has enough rice cereal for her recipe, we need to calculate the total amount of rice cereal she has after all her actions and compare it to the 3 cups required for the cereal clusters.
Initially, Patricia had 5 cups of rice cereal. She used 3 cups to make granola bars, leaving her with 2 cups. She then borrowed 0.5 cup from her friend, which brings her total to 2.5 cups.
Finally, she needs 3 cups of rice cereal for the cereal clusters recipe. Since she only has 2.5 cups, she does not have enough rice cereal and needs to get more. Therefore, the correct answer is B) No, she needs 1/2 cup more.
She then borrows 0.5 cup, so she now has 2 + 0.5 = 2.5 cups.
needs 3 - 2.5 = 0.5 cups more.
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