$8.11 was the percent increase in the median monthly rent prices from 2000 to 2003.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
2000 = $602
2003 = $651
= 651 - 602/602 * 100
= $8.11
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If the common ratio is 1.25, what is the percent change?
Include the percentage symbol with your answer.
With a common ratio of 1.25, the percent change is 25%.
This indicates a relative increase or decrease of 25% from the initial value.
The percent change is a measure of the relative change in a value expressed as a percentage.
To calculate the percent change with a common ratio of 1.25, we can use the formula:
Percent Change = (Common Ratio - 1) [tex]\times[/tex] 100.
Percent Change = (Common Ratio - 1) [tex]\times[/tex] 100.
In this case, the common ratio is 1.25.
Substituting this value into the formula, we have:
Percent Change = (1.25 - 1 )[tex]\times[/tex] 100
[tex]= 0.25 \times 100[/tex]
= 25%.
The percent change, in this case, is 25%.
To understand the meaning of this percent change, consider an initial value of 100.
If we increase this value by 25%, the new value would be 125. Conversely, if we decrease the initial value by 25%, the new value would be 75.
Therefore, a percent change of 25% indicates a relative increase or decrease of 25% from the initial value.
It is important to note that the percent change is a measure of relative change and does not take into account the magnitude of the values.
In this case, a common ratio of 1.25 signifies a 25% increase or decrease, regardless of the specific values involved.
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A triangle with base 7 cm and height 6 cm is dilated by a scale factor of 4. What will be the area of the new triangle?
Answer:
336 square centimeters
Step-by-step explanation:
The area of a triangle is given by the formula:
A = (1/2)bh, where b is the base and h is the height.
The original triangle has a base of 7 cm and a height of 6 cm, so its area is:
A = (1/2)(7 cm)(6 cm) = 21 cm^2
When the triangle is dilated by a scale factor of 4, all of its dimensions are multiplied by 4. So the new base is 4 times the original base (28 cm) and the new height is 4 times the original height (24 cm).
The area of the new triangle is:
A' = (1/2)(28 cm)(24 cm) = 336 cm^2
Therefore, the area of the new triangle is 336 square centimeters.
Hope this helps^^
Drag each tile to the correct location on the table. Each tile can be used more than once but not all tiles will be used. Choose the justification for each step in the solution to the given equation.
The value of x from the given equation is 8/15.
The given equation is 17/3 - 3/4 x= 1/2 x+5
17/3 - 3/4 x= 1/2 x+5 (Given)
17/3 - 3/4 x -17/3= 1/2 x+5 -17/3 (Subtraction property of equality)
-3/4 x = 1/2 x -2/3
-3/4 x -1/2 x = 1/2 x -2/3 -1/2 x (Subtraction property of equality)
-5/4 x=-2/3
-5/4 x × 4/5=-2/3 × 4/5 (Multiplication property of equality)
x= 8/15
Therefore, the value of x from the given equation is 8/15.
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50 Points! Algebra question. Photo attached. Thank you!
Answer:
Step-by-step explanation:
what is the x and y coordinates of the vertex for f(x) = -2x^2 + 12x - 9
Answer:
The vertex of a quadratic function of the form f(x) = ax^2 + bx + c is located at the point (-b/2a, f(-b/2a)).
In this case, the quadratic function is f(x) = -2x^2 + 12x - 9, so we can use the formula above to find the coordinates of the vertex:
x-coordinate of vertex = -b/2a = -12/(2*(-2)) = 3
To find the y-coordinate of the vertex, we can evaluate the function at x = 3:
f(3) = -2(3)^2 + 12(3) - 9 = 9
Therefore, the coordinates of the vertex are (3, 9). The x-coordinate of the vertex is 3, and the y-coordinate of the vertex is 9.
An image of a rectangular prism 4 ft. in length, 2 ft. in width, and 3 ft. in height is shown. Mandy is buying fish for her fish tank shown above. If each fish needs 3 ft. 3 of water, how many fish can Mandy have in her tank? A. 4 fish B. 8 fish C. 12 fish D. 24 fish
Answer:
B. 8 fish
Step-by-step explanation:
Prism Formula = b × h (base × height)
b: 4 ft. ×2 ft.
h: 3 ft.
4 × 2 = 8 ft.
8 × 3 = 24 ft. of water.
Since 3 ft. of water is required for each fish, we will divide.
24 ÷ 3 = 8 fish.
Therefore, Mandy can fit 8 fish in her tank.
Manny bought a brand new car in 2012 for $28,750. If the car depreciates by 12% each year, write an exponential function to model the situation, then find the value of the car in 2018. please round to two decimal places.
note use formula f(t)=a(1+r)^t
Therefore, the value of the car in 2018 was approximately $13,197.36. Rounded to two decimal places, this is $13,197.36.
What is decimal?A decimal is a way of representing a number that is based on powers of ten. It is a number expressed in the base-ten system, which means that each digit in the number represents a power of 10. The decimal point separates the whole number part of the decimal from the fractional part of the decimal.
To model the depreciation of the car over time, we can use the formula:
f(t) = a(1 - r)^t
where:
After t years, f(t) is the car's worth.
a is the initial value of the car, which is $28,750.
r is the annual depreciation rate, which is 12% or 0.12 (expressed as a decimal).
t represents how long it has been since the car been acquired.
Substituting the given values, we get:
f(t) = 28,750(1 - 0.12)^t
To find the value of the car in 2018, we need to substitute t = 6 (since 2018 is 6 years after 2012) and evaluate the function:
f(6) = 28,750(1 - 0.12)^6
Simplifying,
f(6) = 28,750(0.88)^6
Evaluating using a calculator, we get:
f(6) ≈ 13,197.36
Therefore, the value of the car in 2018 was approximately $13,197.36. Rounded to two decimal places, this is $13,197.36.
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The value of the car in 2018 was approximately $14,303.22.
What is exponential functions?
An exponential function is a mathematical function of the form f(x) = [tex]a^{x}[/tex], where a is a positive constant and x is the input variable. The base a is usually a positive real number, but it can also be a complex number.
The initial value of the car is $28,750, and it depreciates by 12% each year. This means that the value of the car after t years can be modeled by the exponential function:
f(t) = [tex]28750(1 - 0.12)^{t}[/tex]
Simplifying the expression inside the parentheses:
f(t) = [tex]28750(0.88)^{t}[/tex]
To find the value of the car in 2018, we need to substitute t = 6, since 2018 is 6 years after 2012:
f(6) = [tex]28750(0.88)^{6}[/tex]
Using a calculator, we get:
f(6) = [tex]28750(0.497^{1})[/tex]
f(6) = 14,303.22
Therefore, the value of the car in 2018 was approximately $14,303.22.
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If i have 3 hours to visit 10 exhibits how lo g would i spend at each exhibit in fraction form
Answer:
18 minutes
Step-by-step explanation:
3 hours = 180 minutes (60*3)
You therefore have 180 minutes to visit 10 exhibits.
180/10=18
Assuming you spent the same amount of time at each exhibit, you would spend 18 minutes at each exhibit.
I hope this helps!
Which is the function represented by the table? A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, negative 1, 0, 1. Column 2 is labeled f (x) with entries negative 8, negative 4, 0, 4. f (X) = 4 x f (x) = x minus 6 f (x) = x + 4 f (x) = negative 4 x
The answer is an option (D) f(x) = One-half (one-half) superscript x.
What is the linear function?
A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
To determine the exponential function represented by the values in the table, we need to look for a function of form f(x) = abˣ that passes through the given points.
Let's plug in the x and f(x) values from the table into the general formula:
When x = -2, f(x) = 16 gives us 16 = ab⁻²
When x = -1, f(x) = 8 gives us 8 = ab⁻¹
When x = 0, f(x) = 4 gives us 4 = ab⁰
When x = 1, f(x) = 2 gives us 2 = ab¹
When x = 2, f(x) = 1 gives us 1 = ab²
We can rewrite the equations as:
16 = a/b²
8 = a/b
4 = a
2 = ab
1 = ab²
We can solve for a and b by using a system of equations:
From the equation 4 = a, we get a = 4.
Substituting a = 4 into the equation 2 = ab, we get b = 2/a = 1/2.
Therefore, the exponential function represented by the values in the table is:
f(x) = 4(1/2)ˣ
Hence, the answer is an option (D) f(x) = One-half (one-half) superscript x.
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We will first find x − x 2 . In column 2 in the table below we will calculate the deviation between each data value and the mean. Then in column 3 we will square each deviation. x x − x x − x 2 50 50 − 40.545 (9.455)2 = 89.397 28 28 − 40.545 (-12.545)2 = 157.377 37 37 − 40.545 (-3.545)2 = 12.567 30 30 − 40.545 (-10.545)2 = 111.197 58 58 − 40.545 (17.455)2 = 304.677 38 38 − 40.545 (-2.545)2 = 6.477 39 39 − 40.545 (-1.545)2 = 2.387 59 59 − 40.545 (18.455)2 = 340.587 47 47 − 40.545 (6.455)2 = 41.667 34 34 − 40.545 (-6.545)2 = 42.837 26 26 − 40.545 (-14.545)2 = 211.557 The sum of the squared deviations in column 3, rounded to three decimal places, is x − x 2 =
For the deviation between each data value and the mean in column 3, there are around 1320.511 squared deviations in all.
How to determine deviation?To find the sum of the squared deviations in column 3, add up all the values in that column.
x x − x (x − x)²
50 50 − 40.545 (9.455)² = 89.397
28 28 − 40.545 (-12.545)² = 157.377
37 37 − 40.545 (-3.545)² = 12.567
30 30 − 40.545 (-10.545)² = 111.197
58 58 − 40.545 (17.455)² = 304.677
38 38 − 40.545 (-2.545)² = 6.477
39 39 − 40.545 (-1.545)² = 2.387
59 59 − 40.545 (18.455)² = 340.587
47 47 − 40.545 (6.455)² = 41.667
34 34 − 40.545 (-6.545)² = 42.837
26 26 − 40.545 (-14.545)² = 211.557
To find the sum of the squared deviations, add up the values in column 3:
x − x² = 89.397 + 157.377 + 12.567 + 111.197 + 304.677 + 6.477 + 2.387 + 340.587 + 41.667 + 42.837 + 211.557 = 1320.511
Rounded to three decimal places:
x − x² ≈ 1320.511
Therefore, the sum of the squared deviations in column 3 is approximately 1320.511.
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A saving account that earns 3.2% interest compounded bi annually has a balance of $6049.15 after 6 years Determine the total amount of interest earned on the account
O1049.15
O1409.15
O4145.24
O5000.0
The total amount of interest earned on the account is $1049.15.
What is simple and compound interest?Simple interest is interest that is just based on the principal. It does not account for any interest accrued in prior periods and is determined as a percentage of the principal. If your principal is $1,000 and your yearly interest rate is 5%, for instance, you would make $50 in simple interest after a year ($1,000 0.05).
Contrarily, compound interest is calculated on the principal amount in addition to any prior quarters' interest. This means that interest is calculated on the new amount after the principal and interest earned during each period have been added.
The compound interest is given by the formula:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
Rearranging for P we have:
[tex]P = A / (1 + r/n)^{(nt)}[/tex]
Substituting the value of r = 3.2%, n = 2 and t = 6 we have:
[tex]P = 6049.15 / (1 + 0.032/2)^{(2*6)}[/tex]
P = 5000
Here, P is the initial balance.
Now, for interest we have:
I = A - P
Substituting the values:
I = $6049.15 - $5000
I = $1049.15
Hence, the total amount of interest earned on the account is $1049.15.
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im having a hard time getting this answer can anyone help me please
The limit of the given expression when we put the values of n and k is: γ = 0
How to find the limits?We want to find the limit of the function as n tends to infinity:
lim n → ∞ [tex]\lim_{n \to \infty} \Sigma \frac{1}{k} - In (n)[/tex] for k = 1
n → ∞ simply means that n is approaching zero. Thus, we can simplify our expression when we put the limit for n to get:
1/k - 1
At k = 1, we have:
(1/1) - 1 = 0
Thus, γ = 0
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Which choice is equivalent to the product below? √3 times √5 times √6
An answer choice that is equivalent to the product below include the following: B. 3√10.
How to determine the equivalent product?In this scenario and exercise, you are required to determine the correct and most accurate answer choice that is equivalent to the product of the given mathematical expression.
In this scenario and exercise, the simplest form of the given expression √3 × √5 × √6 can be determined or calculated by simplifying it as follows;
Expression = √3 × √5 × √6
Expression = √3 × √5 × √(3 ×2)
Expression = √3 × √5 × √3 × √2
Expression = 3 × √(5 × 2)
Expression = 3 × √10
Expression = 3√10.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Solve the inequality. - 2/3 x - 10 < 1/3
Answer:
x > - 31/2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x > −31/2
Please answer the following question.
The area of triangle PQR is approximately 23.07 square units.
How to find areaTo find the area of the triangle PQR, we can use the cross product of two of its sides and then compute half of the magnitude of the cross product vector.
First, let's find the vectors representing the sides PQ and PR:
PQ = Q - P = (2 - 4, 6 - 3, 0 - 3) = (-2, 3, -3)
PR = R - P = (4 - 4, -5 - 3, -3 - 3) = (0, -8, -6)
Now, let's compute the cross product of these two vectors:
PQ × PR = [(-2)(-6) - (3)(-8), (-3)(-8) - (-3)(0), (-2)(-8) - (3)(0)] = [12 + 24, 24, 16] = [36, 24, 16]
Now, we need to find the magnitude of this cross product vector:
|| PQ × PR || = √(36² + 24² + 16²) = √(1296 + 576 + 256) = √2128 ≈ 46.14
Finally, the area of triangle PQR is half the magnitude of the cross product:
Area = 0.5 * || PQ × PR || ≈ 0.5 * 46.14 ≈ 23.07
So, the area of triangle PQR is approximately 23.07 square units.
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The carts need to be as wide as possible. The widest cart that will pass
through the
doorway between the manufacturing floor and the loading dock is 30 inches
wide. The carts also should be as long as possible so they can carry the
largest quantity of finished goods per trip. Arthur tells his mother she can
solve the problem using similarity.
to manufacturing floor
30 in.
to loading dock
B
cart
48 in.
D
36 in.
c) The first similarity that Arthur's mother needs to determine is the
similarity of AABC and AGED. Write a proof to show AABC - AGED.
AABC is similar to AGED with a scale factor of 22.5/48, which means that the width of the cart is proportional to the height, with a ratio of 30:22.5.
Since AABC and Matured are comparative, their relating points are equivalent, and their comparing sides are corresponding.
By definition, point An in AABC is equivalent to point An in Matured, as they are both right points. Likewise, point E in Matured is equivalent to point C in AABC, as they are both vertical points. At long last, point B in AABC is equivalent to point D in Matured, as they are both correlative points to point An and E, separately.
To demonstrate the sides are relative, we can utilize the proportions of comparing sides:
Stomach muscle/AG = BC/ED = AC/Promotion
Subbing the given qualities, we get:
Stomach muscle/48 = BC/36 = AC/x
where x is the length of the truck.
Tackling for x, we get:
x = AC * 36/BC
x = 30 * 36/48
x = 22.5 inches
In this way, AABC is like Matured with a scale variable of 22.5/48, and that implies that the width of the truck is relative to the level, with a proportion of 30:22.5.
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What is 0.2105 rounded to the nearest hundredth
Answer:
Step-by-step explanation: 0.21
Answer:
Step-by-step explanation: 0 is the ones place 2 would be the tenths and 1 the hundreths when rounding you use the fact of if the number following is 5 or more you round up 4 or less it stays the same so the answer is 0.21Given the circle below with secants JKL and NML, find the length of JK. Round to the nearest tenth if necessary.
The length of JK is 42 units, which can be calculated using the theorem that states JK × JL = ML × JN, with the given lengths of KL, LM, and MN.
What is length?Length is a measurement of how long or extended an object or distance is, typically measured in units such as meters, centimeters, feet, or inches.
What is Theorem?A theorem is a statement or proposition that has been proven to be true through deductive reasoning or a mathematical proof, and is often used as a basis for further reasoning and conclusions.
According to the given information:
To find the length of JK, we can use the theorem which states that the product of the lengths of the segments of a secant is equal. In other words, JK × JL = ML × JN. We are given the lengths of KL, LM, and MN, and we know that KL + LM + MN = JL + JN.
We can use this information to solve for JK. First, we need to find JL and JN. We can do this by subtracting KL and MN from LM to get JL = LM - KL and JN = LM - MN. Substituting these values into the equation JK x (LM - KL) = KL × (LM - MN), we can solve for JK.
JK = (KL × (LM - MN)) / (LM - KL) = (14 × (17 - 14)) / (17 - 14) = 14 × 3 = 42.
Therefore, the length of JK is 42.
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The triangle shown has a perimeter of 13 units. The variable x has a
positive value.
Jenny says the length of the missing side of the triangle is 5 units, no
matter what the value x is.
2x+1
?
7-2x
Perimeter: 13 units
Do you agree or disagree? Show your work and explain your thinking.
!! will give brainlist !!
Solve each triangle below. Round answers to the nearest tenth.
Answer:
Set your calculator to degree mode.
4) MU = √(28^2 - 17^2) = √495 = 3√55
= 22.2
sin(U) = 17/28, so U = 37.4°
E = 90° - 37.4° = 52.6°
5) tan(24°) = RT/28
RT = 28tan(24°) = 12.5
cos(24°) = 28/AT
AT•cos(24°) = 28
AT = 28/cos(24°) = 30.6
T = 90° - 24° = 66°
The radius of a circle is 1 foot. What is the length of a 90° arc?
90°
r=1ft
Give the exact answer in simplest form.
According to the given data the length of a [tex]90^{0}[/tex] arc is [tex]\pi /2[/tex] or approximately [tex]1.57[/tex] feet.
What is meant by length of arc?In geometry, the length of an arc is the distance along the curved line that makes up the arc. It is a measure of the "length" of a portion of a circle's circumference, and it is usually expressed in the same units as the circle's radius.
According to the given information:
The length of a [tex]90^{0}[/tex] arc in a circle with radius [tex]1[/tex] foot can be calculated using the formula:
Length of arc = (angle/[tex]360[/tex]) x [tex]2\pi r[/tex]
where angle is the central angle of the arc in degrees, r is the radius of the circle, and [tex]\pi[/tex] is a mathematical constant approximately equal to [tex]3.14159[/tex].
Substituting the given values, we have:
Length of arc = ([tex]90/360[/tex]) x [tex]2\pi(1 ft)[/tex]
Length of arc = [tex](1/4)[/tex] x [tex]2\pi ft[/tex]
Length of arc = [tex]\pi /2 ft[/tex]
Therefore, the length of the [tex]90^{0}[/tex] arc is [tex]\pi /2 feet[/tex] or approximately [tex]1.57 feet[/tex]
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the length of the 90° arc is π/4 feet or approximately 0.785 feet
What is arc of circle?
In geometry, an arc of a circle is a portion of the circle's circumference. It is defined by two endpoints and all points along the circle between those endpoints. The measure of an arc is typically given in degrees or radians and can be used to calculate various properties of the circle, such as its length, area, and sector angles.
The formula for the length of an arc is:
L = (θ/360) × 2πr
where L is the length of the arc, θ is the central angle of the arc in degrees, and r is the radius of the circle.
In this case, θ = 90° and r = 1 ft, so we have:
L = (90/360) × 2π(1) = (1/4) × π = π/4
Therefore, the length of the 90° arc is π/4 feet or approximately 0.785 feet (rounded to 3 decimal places).
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At a large high school, 20% of the students prefer to have a salad for lunch. What is the probability that you must ask four people before you find someone who would prefer a salad for lunch? (The fifth person says yes)
Answer:
There is a 2.56% chance that you would need to ask four people before finding someone who prefers a salad for lunch.
Suppose n ≥ 0 is an integer and all the roots of x³ + αx + 4 − (2 × 2016ⁿ) = 0 are integers. Find all possible values of α.
2016n 2 (mod 217) in this situation because 2016n 1 (mod 31) indicates that 2016n Following the resolution of the question
what is the cube's root?The cube root of a number is a value that, when multiplied by itself three times, returns the original value.
Let r1, r2, and r3 be the three integer roots of x3 + x + 4 (2 2016n) = 0.
According to Vieta's formulae, we have:
r1 + r2 + r3 = 0 r1r2 + r1r3 + r2r3 = r1r2r3 = r1r2r3 = 2 2016n - 4
Because r1, r2, and r3 are integers, their product r1r2r3 is an integer as well. As a result, 2 2016n - 4 must be an integer. That is, 2016n must be an integer plus 2/2n.
Because 2016 is divisible by 25, we may write 2016n as (25)n = 2(5n). As a result, 2/2n can be condensed to 2(1-n).
Thus, 2016n = k + 2(1-n), where k is an integer. That is, 2016n is congruent to 2(1-n) modulo 1.
We see that 2 is a primitive root modulo 31, which indicates that every integer close to 31 may be written as a power of 2 modulo 31. Specifically, 230 1 (mod 31), so 215 1 (mod 31).
We have 2016 0 (mod 2), 9 (mod 31), and 6 (mod 7), since 2016 = 25 32 7. As a result, 2016n = 0 (mod 2), 1 (mod 31), and 1 (mod 7).
We analyse three possible scenarios:
Case 1 consists of 2016n 0 (mod 2) and 2016n 1 (mod 7).
2016n 1 (mod 31) in this situation because 2016n 1 (mod 7) indicates that 2016n 1, 9, 15, or 23 (mod 31) and 2016n is even. As a result, 2016n 1 (mod 31) and 2016n 1 (mod 7).
2016n 1 (mod 217) is the sole possibility.
Case number two: 2016n 1 (mod 31) and 2016n 1 (mod 7).
2016n 1 (mod 217) because 2016n 1 (mod 31) indicates that 2016n 1, 15, or 16 (mod 217), and 2016n 1 (mod 7). As a result, the sole option is 2016n 1 (mod 217).
Cases 3 and 4: 2016n 1 (mod 31) and 2016n 2 (mod 7).
2016n 2 (mod 217) in this situation because 2016n 1 (mod 31) indicates that 2016n.
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The possible values of α are:
-2(504ⁿ - 1) - 2n², where n ≥ 0 is an integer (Case 1)
-2(504ⁿ - 1) - 2
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
Let the three integer roots of the given cubic equation be denoted by p, q and r, so we have:
x³ + αx + 4 - (2 × 2016ⁿ) = (x - p)(x - q)(x - r)
Expanding the right-hand side and equating coefficients with the left-hand side, we get:
p + q + r = 0
pq + qr + rp = α
pqr = 2 × 2016ⁿ - 4 = 4(504ⁿ - 1)
Since p, q, and r are integers, their sum is also an integer, which means that they must have the same parity (i.e., they are either all even or all odd). Moreover, since their product is even, at least one of them must be even. Therefore, we have two cases to consider:
Case 1: p, q, and r are all even
In this case, we can write p = 2m, q = 2n, and r = 2k, where m, n, and k are integers. Substituting these into the equations above, we get:
m + n + k = 0
4mn + 4nk + 4km = α/2
8mnk = 4(504ⁿ - 1)
Since m + n + k = 0, we have k = -(m + n). Substituting this into the second equation, we get:
-4mn - 4nm - 4n² = α/2
-8mn - 8n² = α
Substituting the expression for 8mnk from the third equation, we get:
-2(504ⁿ - 1) - 2n² = α
Therefore, in this case, α is of the form -2(504ⁿ - 1) - 2n², where n ≥ 0 is an integer.
Case 2: p, q, and r are all odd
In this case, we can write p = 2m + 1, q = 2n + 1, and r = 2k + 1, where m, n, and k are integers. Substituting these into the equations above, we get:
m + n + k = -1
4mn + 4nk + 4km = α
8mnk + 2(m + n + k) = 4(504ⁿ - 1)
Since m + n + k = -1, we have k = -(m + n + 1). Substituting this into the second equation, we get:
-4mn - 4nm - 4n² - 4m - 4n - 4 = α/2
-8mn - 8n² - 8m - 8n - 8 = α
Substituting the expression for 8mnk from the third equation, we get:
-2(504ⁿ - 1) - 2n² - 2(m + n + 1) = α
Therefore, in this case, α is of the form -2(504ⁿ - 1) - 2n² - 2(m + n + 1), where m, n, and k are integers such that m + n + k = -1.
In summary, the possible values of α are:
-2(504ⁿ - 1) - 2n², where n ≥ 0 is an integer (Case 1)
-2(504ⁿ - 1) - 2
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5. The cost of tuition at the public university that Mateo plans to attend is $9,600 for the first year. Mateo's parents will pay for one-third of the tuition. Mateo will use $1,500 from his savings to help pay for tuition. What is the minimum amount of money Mateo will need to save every month to reach his goal of paying off the remaining tuition cost at the end of 12 months? < PREVIOUS 1 0² 3 04 5 06
Mateo needs to save at least $408.33 every month to reach his goal of paying off the remaining tuition cost at the end of 12 months.
What is fixed expense and variable expense?Rent or a car payment are examples of monthly costs that are fixed expenses. On the other hand, a variable expense is one that can vary from month to month, like food or entertainment. Variable expenses demand greater flexibility in budgeting because the cost can change, but fixed expenses are often easier to prepare for because the amount is constant.
Given that, cost of tuition fee is $9,600 for the first year.
Now, Mateo's parents will pay for one-third of the tuition thus:
1/3 x $9,600 = $3,200
From the saving the money used is $1500 thus the remining cost is:
$9,600 - $3,200 - $1,500 = $4,900
For 12 months in a year we have:
$4,900 / 12 = $408.33
Hence, Mateo needs to save at least $408.33 every month to reach his goal of paying off the remaining tuition cost at the end of 12 months.
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solve the right triangle with 50° and 15
Answer:
117.2
Step-by-step explanation:
P=a+b+a2+b2=50+15+502+152≈117.20153
What is the length of leg s of the triangle below?
45
90⁰
1012
S
45°
Answer:
s = 10
Step-by-step explanation:
using the cosine ratio with 45° on lower right of right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{s}{10\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
s × [tex]\sqrt{2}[/tex] = 10[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
s = 10
The diagram shows the height of a cone that holds ice cream. The cone has a volume of 4.5 π cubic inches. Which measurement is closest to the radius of the cone in inches?
On solving the query we can say that The slant height, along with the function cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.
what is function?Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
You are informed that the cone in this scenario has a volume of 4.5 cubic inches. Using the aforementioned calculation, you can determine the radius if you know the cone's height.
Alternately, you may use the Pythagorean theorem to calculate for the radius if you know the cone's slant height. The slant height, along with the cone's height and radius, makes a right triangle as it measures from the apex to a certain point on the circular base.
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Please answer my stats question
The t-value is given as follows:
t = 1.82.
How to obtain the t-value?The equation for the t-value is given as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value population mean.s is the standard deviation of the sample.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 86.3, \mu = 83.5, s = 7.2, n = 22[/tex]
Hence the t-value is given as follows:
[tex]t = \frac{86.3 - 83.5}{\frac{7.5}{\sqrt{22}}}[/tex]
t = 1.82.
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Real-life Problems Question 8
After answering the presented question, we may conclude that expressions As a result, Sarah will have E61,600 left over from her loan after purchasing 8 limos.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
a) Sarah can buy 8 limousines because:
600,000 / 67,300 = 8.91
Because she cannot purchase a fraction of a limousine, the maximum number of limos she may purchase is eight.
b) To determine how much of the loan is left over, deduct the total cost of the limos from the loan amount:
8 x 67,300 = 538,400
600,000 - 538,400 = 61,600
As a result, Sarah will have E61,600 left over from her loan after purchasing 8 limos.
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Evaluate and simplify the expression
when X = 3 and y = 5.
2y + 3(x - y) + x2 = [?]
Answer:
13
Step-by-step explanation:
2(5) + 3(3 - 5) + (3)^2
10 + (9 - 15) + 9
19 - 6 = 13