Answer:
Practical domain: 0 ≤ x ≤ 3.907Practical Range: 0 ≤ y ≤ 84 where y is an integer, so we have the set {0,1,2,...,83,84}The 3.907 is approximate.
====================================
Explanation:
x = number of hours that elapse
y = f(x) = number of tokens
If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907
At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.
The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907
------------
Plug in x = 0 to find y = 84. This is the largest value in the range.
The smallest value is y = 0.
The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84
Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.
The x value can be fractional because 3.907 hours for instance is valid.
------------
Extra info:
The function is decreasing. It goes downhill when moving to the right.The points (0,84) and (1,78) and (2,66) and (3,42) are on this exponential curve.A point like (2,66) means x = 2 and y = 66. It indicates: "after 2 hours, they will have 66 tokens remaining".Which equation is correct?
triangle ACB, angle C is a right angle, angle B measures g degrees, angle A measures h degrees, segment AC measures x, segment CB measures y, and segment AB measures z
sin h° = z ÷ x
sin h° = x ÷ z
cos h° = z ÷ x
cos h° = x ÷ z
The correct equation is sin h° = z ÷ x, which states that the sine of angle A is equal to the ratio of the length of side AB to the length of side AC.
The correct equation relating the angles and segments in triangle ACB depends on the specific trigonometric function and the angle we are considering.
In triangle ACB, angle C is a right angle, which means it measures 90 degrees. The other two angles, angle A and angle B, are complementary angles, meaning their sum is also 90 degrees. Therefore, angle A measures h degrees and angle B measures g degrees, where h + g = 90.
Now let's consider the segments in the triangle. Segment AC measures x, segment CB measures y, and segment AB measures z.
When it comes to trigonometric functions, sine (sin) and cosine (cos) are commonly used. These functions relate the angles and sides of a right triangle.
The correct equation involving the angles and segments can be determined based on the trigonometric function that relates the desired angle to the desired segment.
If we want to relate angle A (measuring h degrees) to the segment AB (measuring z), we can use the sine function. Therefore, the correct equation is:
sin h° = z ÷ x
This equation relates the sine of angle A to the ratio of the lengths of the side opposite angle A (segment AB) and the hypotenuse (segment AC).
In summary, the correct equation is sin h° = z ÷ x, which states that the sine of angle A is equal to the ratio of the length of side AB to the length of side AC.
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Which system of equations is represented by the graph?
PLEASE HELP WILL GIVE THE BRAINLIEST
The system of equations that is represented by the graph include:
D. y = x - 4
[tex]y=\frac{x-4}{x+2}[/tex]
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of the red line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 + 5)/(4 + 1)
Slope (m) = 5/5
Slope (m) = 1
At point (4, 0) and a slope of 1, a linear equation for C can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 0 = 1(x - 4)
y = x - 4
Since the rational function has a y-intercept of (0, -2), it would have a vertical asymptote and the denominator would be undefined at x = 2;
[tex]y=\frac{x-4}{x+2}[/tex]
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Help with these precalc problem
The equation of the lines expressed in point-slope form and the average rate of change of the functions indicates that we get;
(a) y - 6 = (5/3)·(x + 2), (b) y + 7 = 2·(x - 2), (c) y = -4, (d) y = -1(a) 5, (b) 50, (c) h + 7The point-slope form of the equation of a line can be represented in the following form; y - y₁ = m(x - x₁), where; m is the slope of the line and (x₁, y₁) is a point on the line.
1. (a) The slope of the line parallel to the line; 5·x - 3·y = 10, can be obtained by writing the equation of the line in slope-intercept form as follows;
5·x - 3·y = 10, therefore; y = 5·x/3 - 10/3
The slope of the parallel line is therefore; 5/3
The point-slope form of the equation of the line is therefore;
y - 6 = (5/3)·(x - (-2)) = (5/3)·(x + 2)
y - 6 = (5/3)·(x + 2)
3·y - 18 = 5·x + 10
3·y - 5·x = 10 + 18 = 18
(b) The equation of the line, 2·x + 4·y - 12 = 0, indicates;
The slope of the line is; -2/4 = -1/2
The slope of the perpendicular line = -1/(-1/2) = 2
The equation of the perpendicular line passing through the point (2, -7) in point-slope form is therefore;
y - (-7) = 2·(x - 2)
y + 7 = 2·(x - 2)
(c) The line passing through point (-2, -4), and parallel to y = -3 is the line y = -4
(d) The line passing through point (4, -1), and perpendicular to x = 0 is the line y = -1
2. (a) f(-1) = 2 × (-1)² + (-1) - 1 = 0
f(3) = 2 × (3)² + (3) - 1 = 20
The average is; (f(3) - f(-1))/(3 - (-1)) = 20/4 = 5
(b) f(1) = 150, f(3) = 50
Average = (f(3) - f(1))/(3 - 1)
Average = (150 - 50)/(3 - 1) = 50
(c) f(4) = 4² - 4
f(4 + h) = (4 + h)² - (4 + h) = (h + 3)·(h + 4)
Average = (f(4 + h) - f(4))/(4 + h - 4) = ((h + 3)·(h + 4) - (4² - 4))/(h)
((h + 3)·(h + 4) - (4² - 4))/(h) = (h² + 7·h + 12 - 12)/h = h + 7
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Please help me understand this
The quadratic function with the solutions given in the problem is defined as follows:
x² + 3x + 3 = 0.
How to solve a quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
The solutions are given as follows:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Comparing the standard solution to the solution given in this problem, the parameters a and b are given as follows:
2a = 2 -> a = 1.-b = -3 -> b = 3.The coefficient c is then obtained as follows:
b² - 4ac = -3.
9 - 4c = -3
4c = 12
c = 3.
Hence the function is:
x² + 3x + 3 = 0.
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A portion of a game board design is shown. Determine the value of x to the nearest tenth.
A)5
B)9
C)13.6
D)20.6
The measure of line segment x in the game board is approximately 13.6.
What is the value of x?The secant-tangent power theorem states that "if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.
It is expressed as:
( tangent segment )² = External part of the secant segment × Secant segment.
From the given figure:
Let;
Tangent segment = 12
Secant segment = 7 + x
External part of the secant segment = 7
Plug these values into the above formula and solve for x.
( tangent segment )² = External part of the secant segment × Secant segment.
12² = 7( 7 + x)
144 = 49 + 7x
7x = 144 - 49
7x = 95
x = 95/7
x = 13.6
Therefore, the value of x is approximately 13.6.
Option C) 13.6 is the correct answer.
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Monthly deposits of $480 were made at the end of each month for eight years. If interest is 4.5% compounded semi-annually, what amount can be withdrawn immediately after the last deposit?
The amount that can be withdrawn immediately after the last deposit is approximately $8,876.80.
To solve this problemWe can use the formula for the future value of an ordinary annuity. The formula is given by:
[tex]FV = P * [(1 + r/n)^(^n^t^) - 1] / (r/n)[/tex]
Where
Future value is represented by FVmonthly deposit amount by Pannual interest rate by rnumber of compounding periods by n years by tGiven:
P = $480 (monthly deposit)r = 4.5% = 0.045 (annual interest rate)n = 2 (compounded semi-annually)t = 8 yearsPlugging in the values, we have:
[tex]FV = 480 * [(1 + 0.045/2)^(^2*^8^) - 1] / (0.045/2)[/tex]
Calculating the expression inside the brackets
[tex](1 + 0.045/2)^(^2^*^8^) = 1.0225^1^6[/tex]≈ 1.4197
Substituting this value back into the formula:
FV = 480 * (1.4197 - 1) / (0.045/2)
FV = 480 * 0.4197 / 0.0225
FV ≈ $8,876.80
So, the amount that can be withdrawn immediately after the last deposit is approximately $8,876.80.
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Solve (t-3)^2=6
The arrow is at a height of 48 ft after approx. ___ s and after ___ s.
The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.
To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:
s = v0t - 16t^2
Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.
Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:
48 = 96t - 16t^2
Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.
Rearranging the equation:
16t^2 - 96t + 48 = 0
Dividing the equation by 16 to simplify:
t^2 - 6*t + 3 = 0
We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.
Using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
t = (6 ± √((-6)^2 - 413)) / (2*1)
t = (6 ± √(36 - 12)) / 2
t = (6 ± √24) / 2
Simplifying the square root:
t = (6 ± 2√6) / 2
t = 3 ± √6
Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.
In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.
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Note the complete question is
The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?
Solve (t-3)^2=6
The arrow is at a height of 48 ft after approx. ___ s and after ___ s.
A business student is interested in estimating the 99% confidence interval for the proportion of students who bring laptops to campus. He wants a precise estimate and is willing to draw a large sample that will keep the sample proportion within five percentage points of the population proportion. What is the minimum sample size required by this student, given that no prior estimate of the population proportion is available? (You may find it useful to reference the z table. Round up final answer to nearest whole number.)
To determine the minimum sample size required to estimate the proportion of students who bring laptops to campus with a 99% confidence level and a margin of error within five percentage points, we can use the formula:
[tex]n = \frac{(Z^2 \times p \times (1 - p))}{ E^2}[/tex]
Where:
n is the required sample size,
Z is the Z-score corresponding to the desired confidence level,
p is the estimated population proportion (since no prior estimate is available, we use 0.5 as a conservative estimate),
E is the margin of error.
For a 99% confidence level, the Z-score is approximately 2.58 (obtained from the z table).
Plugging in the values:
[tex]n = \frac{(2.58^2 \times 0.5 \times (1 - 0.5))} { (0.05^2)}[/tex]
Simplifying the equation:
n = 663.924
Rounding up to the nearest whole number, the minimum sample size required is approximately 664 students.
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The roster method of the set X ∪ (Y ∩ Z) = {p, q, r, s, 21, 22, 23, 25}
How to find sets using roster method?The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.
A typical example of the roster method is to write the set of numbers from 1 to 5 as {1, 2, 3, 4, 5}.
Therefore,
X = {p, q, r, 21, 22, 23}
Y = {q, s, t, 21, 23, 25}
Z = {q, s, 22, 23, 25}
Therefore, let's find X ∪ (Y ∩ Z) as follows:
(Y ∩ Z) = {q, s, 23, 25}
X = {p, q, r, 21, 22, 23}
Therefore,
X ∪ (Y ∩ Z) = {p, q, r, s, 21, 22, 23, 25}
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a. From Tammy's results, compute the experimental probability of landing on red or yellow.
b. Assuming that the spinner is fair, compute the theoretical probability of landing on red or yellow.
c. Assuming that the spinner is fair, choose the statement below that is true.
a. As the number of spins increases, we expect the experimental and theoretical probabilities to
become closer, though they might not be equal.
b. As the number of spins increases, we expect the experimental and theoretical probabilities to
become farther apart.
c. The experimental and theoretical probabilities must always be equal.
a) The experimental probability of landing on red or yellow is:
P(red or yellow) = 33/40
b) The theoretical probability can be computed as follows:
P(red or yellow) = 8/10
c) As the number of spins increases: Option A: we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
How to solve Experimental and Theoretical Probability?Theoretical probability represents the likelihood of an event occurring. The theoretical probability of getting heads is 1/2, because we know that the probability of heads and tails on a coin is equal. Experimental probability describes how often an event actually occurred in an experiment.
a) The experimental probability of landing on red or yellow is:
P(red or yellow) = (20/40) + (13/40) = 33/40
b) The theoretical probability can be computed as follows:
P(red or yellow) = (4/10) + (4/10) = 8/10
c) As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
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In this triangle what is the value of x
Answer:
Step-by-step explanation:
error
Answer:
x ≈ 75.2
Step-by-step explanation:
using the tangent ratio in the right triangle
tan62° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{40}[/tex] ( multiply both sides by 40 )
40 × tan62° = x , then
x ≈ 75.2 ( to the nearest tenth )
6 ft
4 ft
1ft
Find the area of
this irregular shape.
a = [?] ft²
4 ft
1ft
12 ft
4 ft
4 ft
The area of the irregular shape is 34 square feet.
What is the area of this irregular shape?To find the area of the irregular shape, we need to break it down into smaller components and calculate their individual areas.
We will assume the irregular shape is composed of three rectangles.
Rectangle 1: Length = 6 ft, Width = 4 ft.
Area = Length × Width
Area = 6 ft × 4 ft
Area = 24 square feet.
Rectangle 2: Length = 4 ft, Width = 1 ft.
Area = Length × Width
Area = 4 ft × 1 ft
Area = 4 square feet.
Rectangle 3: Length = 1 ft, Width = 6 ft.
Area = Length × Width
Area = 1 ft × 6 ft
Area = 6 square feet.
Total Area = Area of Rectangle 1 + Area of Rectangle 2 + Area of Rectangle 3
Total Area = 24 square feet + 4 square feet + 6 square feet
Total Area = 34 square feet.
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The number of subsets in the given set is as follows:
128.
How to obtain the number of subsets in a set?Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:
[tex]2^n[/tex]
The set in this problem is composed by integers between 2 and 8, hence it has these following elements:
{2, 3, 4, 5, 6, 7, 8}.
The set has four elements, meaning that n = 7, hence the number of subsets is given as follows:
[tex]2^7 = 128[/tex]
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P=x-2 ÷ x+1 for what value of x is P undefined
Answer:
x = - 1
Step-by-step explanation:
P = [tex]\frac{x-2}{x+1}[/tex]
the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.
x + 1 = 0 ( subtract 1 from both sides )
x = - 1
P is undefined when x = - 1
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
(A) AA similarity
Step-by-step explanation:
In ΔABC,
∠A + ∠B + ∠C = 180
∠A + 27 + 90 = 180
∠A = 180 - 90 - 27
∠A = 63
Comparing ΔABC and ΔMNP,
∠A = ∠M = 63
∠C = ∠P = 90
Therfore, by AA property, the two triangles are similar