Suppose {an} is a sequence recursively de ned by a1 = 1 and an 1 = 2an 2n for all integers n, n ? 1. use induction to prove that an = n2n1 for all positive integers n.
Answers
The statement holds for k + 1. To prove that an = n^(2n-1) for all positive integers n using induction, we will follow the steps of mathematical induction:
Step 1: Base Case
Show that the statement holds true for the base case, which is n = 1.
For n = 1, we have a1 = 1^(2*1-1) = 1^1 = 1.
Since a1 = 1, the base case holds.
Step 2: Inductive Hypothesis
Assume that the statement is true for some positive integer k, i.e., ak = k^(2k-1). This is called the inductive hypothesis.
Step 3: Inductive Step
We need to prove that if the statement holds for k, it also holds for k + 1. That is, we need to show that ak+1 = (k + 1)^(2(k + 1)-1).
Using the recursive definition of the sequence, we have:
ak+1 = 2ak - 2(ak/2)
= 2k^(2k-1) - 2((k/2)^(2(k/2)-1))
= 2k^(2k-1) - 2(k/2)^(2(k/2)-1)
= 2k^(2k-1) - 2(k^(k-1))^2
= 2k^(2k-1) - 2k^(2k-2)
= k^(2k-1)(2 - 2/k)
Now, let's simplify further:
ak+1 = k^(2k-1)(2 - 2/k)
= k^(2k-1)(2k/k - 2/k)
= k^(2k-1)(2k - 2)/k
= k^(2k-1)(2(k - 1))/k
= 2k^(2k-1)(k - 1)/k
We notice that (k - 1)/k = 1 - 1/k.
Substituting this back into the equation, we have:
ak+1 = 2k^(2k-1)(k - 1)/k
= 2k^(2k-1)(1 - 1/k)
Next, let's simplify further by expanding the term (1 - 1/k):
ak+1 = 2k^(2k-1)(1 - 1/k)
= 2k^(2k-1) - 2(k^(2k-1))/k
Now, observe that k^(2k-1)/k = k^(2k-1-1) = k^(2(k-1)).
Using this simplification, we get:
ak+1 = 2k^(2k-1) - 2(k^(2k-1))/k
= 2k^(2k-1) - 2k^(2(k-1))
= 2k^(2k-1) - 2k^(2k-2)
= k^(2k-1)(2 - 2/k)
We can see that ak+1 is of the form k^(2k-1)(2 - 2/k). Simplifying further:
ak+1 = k^(2k-1)(2 - 2/k)
= k^(2k-1)((2k - 2)/k)
= k^(2k-1)(k - 1)
Finally, we have arrived at ak+1 = (k + 1)^(2(k + 1)-1). Therefore, the statement holds for k + 1.
By completing the three steps of mathematical induction, we have proven that an = n^(2n-1) for all positive integers n.
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Related Questions
notation: in this course, we will use regular letters as symbols for numbers, vectors, matrices, planes, hyperplanes, etc. you will need to distinguish what a letter represents from the context. recall the dot product of a pair of vectors and : when thinking about and as vectors in -dimensional space, we can also express the dot product as where is the angle formed between the vectors and in -dimensional euclidean space. here, refers to the length, also known as norm, of : what is the length of the vector ?
Answers
The length of a vector 'v' in an n-dimensional Euclidean space is calculated as the square root of the dot product of the vector with itself, or ‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\).
The length of a vector 'v' in an n-dimensional Euclidean space is denoted as ‖v‖ and can be calculated asthe vector's dot product with itself, square root:
‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\)
So, to find the length of the vector 'v', we simply substitute its components in the above equation.
The length of a vector, also known as its magnitude or norm, is a scalar value that represents the magnitude of the vector in a given space. In the context of an n-dimensional Euclidean space, the length of a vector can be calculated as the square root of the dot product of the vector with itself. This calculation is based on the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares formed by the other two sides' lengths.
In mathematical terms, the length of a vector 'v' in an n-dimensional Euclidean space is calculated as follows:
‖v‖ = \(\sqrt{(v.v)}\) = \(\sqrt{(v1^{2}+v2^{2} +.... + vn^{2} )}\)
where 'v' is the vector, and 'v1', 'v2', ..., 'vn' are its components in the n-dimensional space. The dot product of the vector with itself (v · v) is equivalent to the sum of the squares of its components. The square root of this sum is the final length of the vector.
The length of a vector is an important concept in linear algebra and geometry. It is used to measure the distance between two points in a space, to calculate angles between vectors, to normalize vectors, and for various other mathematical and practical applications.
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If f(x) = 4x + 5,, determine f(-2).a. -7/4b. 13c. -3d. 7
Answers
We are given the function: f(x) = 4x + 5
To find f(-2), we substitute the value of x with -2 to get:
f(-2) = 4(-2) + 5
f(-2) = -8 + 5
f(-2) = -3
OPTION C
Find the volume of the solid.
The volume of the solid is
cubic centimeters.
Answers
Answer:
27
Step-by-step explanation:
4.5*3*2 = 27
hi,
You just have to multiply the three measures.
So :
2*3*4.5 = 27 cm³
Easy, is it not ?
Round 453, 605 to the nearest 10,000
Answers
Answer:450,000
Step-by-step explanation:It becomes 450,000 thousand because anything under 5 in the ten thousands place becomes a zero and anything in front of it which is the 4 will stay the same.
a rational number is defined as any number that can be written as a fraction with a non zero denomination
true or false?!
Answers
Answer:
True
Step-by-step explanation:
opposite is irrational number
a coin is flipped, where each flip comes up as either heads or tails. how many possible outcomes contain at least three heads if the coin is flipped 9 times?
Answers
There are 87 possible outcomes that contain at least three heads when a coin is flipped 9 times.
When a coin is flipped nine times, there are 512 possible outcomes, or 29. Using the equation:
P (At least one head) = 1 - 0.5n,
where n is the total number of flips, we can determine the number of outcomes that contain at least three heads.
Therefore, P (At least three heads) = 1 - P (No heads) - P (One head) - P (Two heads)
= 1 - (0.5)⁹ - 9(0.5)⁹ + 36(0.5)⁹
= 0.1718751.
The formula used to calculate the number of possible outcomes that contain at least three heads is C(9,3) + C(9,4) + C(9,5) + C(9,6) + C(9,7) + C(9,8) + C(9,9),
where C(n,r) denotes the variety of options for selecting item(s) r from a set of item(s) n.
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A simple random sample of 36 cans of regular Coke has a mean volume of 12.19 ounces. Assume that the standard deviation of all cans of regular Coke is 0.11 ounces. Use a 0.01 significance level to test the claim that cans of regular Coke have volumes with a mean of 12 ounces, as stated on the label.
a) State the hypotheses.
b) State the test statistic.
c) State the p-value.
d) State your decision.
e) State your conclusion.
Answers
(a) The Null-Hypotheses is H₀ : μ = 12, Alternate-Hypotheses is Hₐ : μ ≠ 12.
(b) The "test-statistic" is 10.36,
(c) The "p-value" is 0.0001,
(d) We make a decision to reject the "Null-Hypothesis",
(e) We conclude that the cans of "regular-Coke" have volumes with mean different from 12 ounces.
Part (a) : The "Null-Hypothesis" is that the mean volume of cans of regular Coke is 12 ounces, as stated on the label. The alternative-hypothesis is that the mean volume is different from 12 ounces.
So, H₀ : μ = 12
Hₐ : μ ≠ 12.
Part (b) : The "test-statistic" for a one-sample t-test is calculated as:
t = (x' - μ)/(s / √n),
where "s" = sample standard-deviation, μ = population mean, x' = sample mean, and n = sample size,
In this case, x' = 12.19, μ = 12, s = 0.11, and n = 36.
So, t = (12.19 - 12)/(0.11/√36) = 10.36,
Part (c) : We know that for "significance-level" of 0.01. The p-value is 0.0001.
Part (d) : Since the p-value is less than the significance-level of 0.01, we reject the null hypothesis.
Part (e) : Based on the results of the hypothesis test, we can conclude that there is sufficient evidence to suggest that cans of regular-Coke have volumes with a mean different from 12 ounces.
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3. You have $2.75. You want to buy trading cards that cost $0.25 each.
How many can you buy?
Answers
Question:
You have $2.75. You want to buy trading cards that cost $0.25 each.
How many can you buy?
Answer:
11 trading cards
Step-by-step explanation:
If you do 2.75 ÷ 0.25 you would get 11 and to check the answer you could simply multiply you would do 0.25 x 11 to get the answer 2.75.
I hope it helps you!
~XxBells is a cute girlxX~
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In a card game, the probability that you will have a hand with five cards in the same suit is about 14%. The dealer wants to know the probability for a player to be dealt this type of hand in one of the first three hands. Should a geometric probability density function or a cumulative distribution function be used? explain.
Answers
The geometric cumulative distribution function should be used.
The geometric cumulative distribution is a discrete likelihood conveyance where the random variable demonstrates the quantity of the Bernoulli trial expected to get the primary achievement. A Bernoulli trial is an experiment that can have just two potential results, ie., achievement or disappointment. All in all, in a mathematical dispersion, a Bernoulli trial is rehashed until a triumph is gotten and afterward halted. Here we are interested in the first success in the three chances, which is completely specified with the distribution function of a geometric distribution, and because the question asked for the probability of having a hand with five cards in the same suit in one of the first three hands. Hence the correct option is the cumulative distribution function.
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Please help! I will give Brainliest!
Who is correct?
Answers
Answer:
Eric is correct; side must be between 4 and 16 inches
Step-by-step explanation:
triangle inequality theorem:
6 + 10 > x; 16 > x
x + 6 > 10; x > 4
4 < x < 16
If a position on the ocean floor is 12 kilometers below the sea level, which value describes the elevation of the ocean floor
Answers
Answer:
- 12
Step-by-step explanation:
The sea level serves as a reference point and may be used to describe objacetsvir positions above or below it. Therefore, the sea level is regarded as a zero point or level. Hence, objects below are describes to be at a negative distance while those above are assigned the positive sign. Hence, for a position which is 12 km below sea level, then the object is said to be at a distance of - 12 km (below sea level takes the negative sign.)
Drag the labels into place in the figure for a market leaving, and then returning to, equilibrium as firms exit after a decrease in demand. original short-run supply* final short-run demand* original short-run demand* long-run supply* final short-run supply* Drag each item above to its appropriate location in the image. Note that every item may not have a match, while some items may have more than one match. Price P2 +--- Q3 Q2 Q2 Market quantity (Q)
Answers
The original short-run supply curve shifts left, causing the market price to decrease to P2 and the quantity to decrease to Q2.
As a result, some firms exit the market, causing the short-run supply to shift back to the right and the market to return to equilibrium at a lower quantity, Q3, and the same price, P2.
When demand decreases, the original short-run supply curve shifts leftward as firms reduce production to meet the lower demand. This causes the market price to decrease to P2 and the quantity to decrease to Q2.
At this lower price, some firms may exit the market if they are unable to cover their costs, causing the short-run supply curve to shift back to the right.
As a result, the market quantity decreases further to Q3, and the market returns to equilibrium at the same price, P2. In the long run, the supply curve may shift further to accommodate the lower demand, resulting in a new equilibrium price and quantity.
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I need help round pleae
Answers
Answer:
Mean=49 pounds
Median=11pounds
Step-by-step explanation:
If all the cats got weighted (5, 11,11,12,10) for each cat you need to add, multiply and divide to get all the answers (P.S. you don't need to round for your answers!)
For solving the Mean you need to add up all the numbers and then divide by how many numbers there are (5+11+11+12+10÷ 5=49)
For solving the Median you need to put the numbers in smallest to biggest order to solve for this (5,10,11,11,12) and then kept crossing them out (left to right) until you get the two middle numbers (11,11) then add them both right and then divide 22 by 2 then you have your answer!
You're going to rock this:)
Kenz
When it comes to money, you are either_____
or a_______
Answers
Answer:
greedy or generous
Use the factor theorem to show that x -c is a factor of P(x) for the given value of c. Factor P(x) completely. P(x) = x3 - x2 - 11x +15, c=3 b) Divide the following: P(x) = 4x2 – 3x - 7; D(x)
Answers
Using the factor theorem, we can show that x - c is a factor of P(x) and then factor P(x) completely. For P(x) = x^3 - x^2 - 11x + 15 and c = 3, we can conclude that x - 3 is a factor of P(x) and factorize P(x) as (x - 3)(x^2 + 2x - 5).
In the second part, to divide P(x) = 4x^2 - 3x - 7 by D(x), we need to provide the divisor polynomial D(x) to continue the calculation.
For the first part, we can use the factor theorem to determine if x - c is a factor of P(x). If P(c) = 0, then x - c is a factor. Evaluating P(3), we find that P(3) = (3)^3 - (3)^2 - 11(3) + 15 = 0. Since P(3) equals zero, we can conclude that x - 3 is a factor of P(x). To factor P(x) completely, we divide P(x) by (x - 3) using long division or synthetic division. The quotient will be the remaining factor, which in this case is (x^2 + 2x - 5).
For the second part, you mention dividing P(x) = 4x^2 - 3x - 7 by D(x). To perform this division, the polynomial D(x) needs to be provided. Without the specific divisor D(x), it is not possible to proceed with the calculation of the division.
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Question 4 of 10
The standard form of the equation of a parabola is y=x²-6x+14.
What is the vertex form of the equation?
OA y=(x-3)2 +15
OB. y = (x+3)(x-3) +5
O C. y=(x-3)2 +23
OD. y=(x-3)² +5
Answers
The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.
To convert the given equation from standard form to vertex form, we need to complete the square.
The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.
Given equation: y = x² - 6x + 14
Move the constant term to the right side:
y - 14 = x² - 6x
Complete the square by adding and subtracting the square of half the coefficient of x:
y - 14 + 9 = x² - 6x + 9 - 9
Group the terms and factor the quadratic:
(y - 5) = (x² - 6x + 9) - 9
Rewrite the quadratic as a perfect square:
(y - 5) = (x - 3)² - 9
Simplify the equation:
y - 5 = (x - 3)² - 9
Move the constant term to the right side:
y = (x - 3)² - 9 + 5
Combine the constants:
y = (x - 3)² - 4
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help write an expression for the area of the shaded part
Answers
Answer:
\([(5x+6)(3x)] - [(4x-3)(2)]\)
Step-by-step explanation:
Find the total area of the shape \((5x+6)(3x)\)
And subtract the non-shaded area \((4x-3)(2)\)
To get this equation:
\([(5x+6)(3x)] - [(4x-3)(2)]\)
Plzzz help plzzzzzzzzzzzzzz
Answers
Given:
The figure of two quadrilaterals.
In \(ABCD,AB=18,BC=20,CD=22,AD=24\)
In \(EFGH,EF=27,FG=30,GH=34, EH=36\)
To find:
Whether the figures are congruent, similar or neither.
Solution:
Ratio of corresponding sides are:
\(\dfrac{AB}{EF}=\dfrac{18}{27}\)
\(\dfrac{AB}{EF}=\dfrac{2}{3}\)
Similarly,
\(\dfrac{BC}{FG}=\dfrac{20}{30}\)
\(\dfrac{BC}{FG}=\dfrac{2}{3}\)
\(\dfrac{CD}{GH}=\dfrac{22}{34}\)
\(\dfrac{CD}{GH}=\dfrac{11}{17}\)
And,
\(\dfrac{AD}{EH}=\dfrac{24}{36}\)
\(\dfrac{AD}{EH}=\dfrac{2}{3}\)
Clearly, \(\dfrac{AB}{EF}=\dfrac{BC}{FG}=\dfrac{AD}{EH}\neq \dfrac{CD}{GH}\).
All corresponding sides are not proportional.
Therefore, the figures are neither similar nor congruent. Hence, third option is correct.
1. If 5tanA=4, Find the value of (5sinA-3cosA)/(4cosA+5sinA)
2. Solve for θ, sinθ/(1+cosθ) + (1+cosθ)/sinθ =4, 0°<θ<90°
3. Prove that tan〖θ-cotθ 〗 = (〖2sin〗^2 θ-1)/sinθcosθ
4. Without using trigonometric tables ,show that
tan 10°tan15°tan75°tan80°=1
5. If x=acosθ-bsinθ and y=asinθ + bcosθ prove that x^2+y^2=a^2+b^2
Answers
Answer:
1. (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) = 1/8
2. θ = 30°
3. tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))
from tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ) and sin²(θ) + cos²(θ) = 1
4. tan10°·tan15°·tan75°·tan80°= 1 from;
sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]
cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]
5. x² + y² = a² + b² where x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ from;
cos²θ + sin²θ = 1
Step-by-step explanation:
1. Here we have 5·tan(A) = 5·sin(A)/cos(A) = 4
∴ 5·sin(A) = 4·cos(A)
Hence to find the value of (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) we have;
Substituting the value for 5·sin(A) = 4·cos(A) into the above equation in both the numerator and denominator we have;
(4·cos(A) - 3·cos(A)/(4·cos(A) + 4·cos(A)) = cos(A)/(8·cos(A)) = 1/8
Therefore, (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) = 1/8
2. For the equation as follows, we have
\(\frac{sin \theta}{1 + cos \theta} + \frac{1 + cos \theta}{sin \theta} = 4\) this gives
\(\frac{2sin (\theta/2) cos (\theta/2) }{2 cos^2 (\theta/2)} + \frac{2 cos^2 (\theta/2)}{2sin (\theta/2) cos (\theta/2) } = 4\)
\(tan\frac{\theta}{2} + \frac{1}{tan\frac{\theta}{2} } = 4\)
\(tan^2\frac{\theta}{2} + 1 = 4\times tan\frac{\theta}{2}\)
\(tan^2\frac{\theta}{2} - 4\cdot tan\frac{\theta}{2} + 1 = 0\)
We place;
\(tan\frac{\theta}{2} = x\)
∴ x² - 4·x + 1 = 0
Factorizing we have
(x - (2 - √3))·(x - (2 + √3))
Therefore, tan(θ/2) = (2 - √3) or (2 + √3)
Solving, we have;
θ/2 = tan⁻¹(2 - √3) or tan⁻¹(2 + √3)
Which gives, θ/2 = 15° or 75°
Hence, θ = 30° or 150°
Since 0° < θ < 90°, therefore, θ = 30°
3. We have tan(θ) - cot(θ) = tan(θ) - 1/tan(θ)
Hence, tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ)
∴ tan(θ) - 1/tan(θ) = (sin²(θ) - cos²(θ))/(cos(θ)×sin(θ))...........(1)
From sin²(θ) + cos²(θ) = 1, we have;
cos²(θ) = 1 - sin²(θ), substituting the value of sin²(θ) in the equation (1) above, we have;
(sin²(θ) - (1 - sin²(θ)))/(cos(θ)×sin(θ)) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))
Therefore;
tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))
4. tan10°·tan15°·tan75°·tan80°= 1
Here we have since;
sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]
cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]
Then;
tan 10°·tan15°·tan75°·tan80° = tan 10°·tan80°·tan15°·tan75°
tan 10°·tan80°·tan15°·tan75° = \(\frac{sin(10^{\circ})}{cos(10^{\circ})} \times \frac{sin(80^{\circ})}{cos(80^{\circ})} \times \frac{sin(15^{\circ})}{cos(15^{\circ})} \times \frac{sin(75^{\circ})}{cos(75^{\circ})}\)
Which gives;
\(\frac{sin(10^{\circ}) \cdot sin(80^{\circ})}{cos(10^{\circ})\cdot cos(80^{\circ})} \times \frac{sin(15^{\circ}) \cdot sin(75^{\circ})}{cos(15^{\circ})\cdot cos(75^{\circ})}\)
\(=\frac{1/2[cos(80 - 10) - cos(80 + 10)]}{1/2[cos(80 - 10) + cos(80 + 10)]} \times \frac{1/2[cos(75 - 15) - cos(75 + 15)]}{1/2[cos(75 - 15) + cos(75 + 15)]}\)
\(=\frac{1/2[cos(70) - cos(90)]}{1/2[cos(70) + cos(90)]} \times \frac{1/2[cos(60) - cos(90)]}{1/2[cos(60) + cos(90)]}\)
\(=\frac{[cos(70)]}{[cos(70) ]} \times \frac{[cos(60)]}{[cos(60) ]} =1\)
5. If x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ
∴ x² + y² = (a·cosθ - b·sinθ)² + (a·sinθ + b·cosθ)²
= a²·cos²θ - 2·a·cosθ·b·sinθ +b²·sin²θ + a²·sin²θ + 2·a·sinθ·b·cosθ + b²·cos²θ
= a²·cos²θ + b²·sin²θ + a²·sin²θ + b²·cos²θ
= a²·cos²θ + b²·cos²θ + b²·sin²θ + a²·sin²θ
= (a² + b²)·cos²θ + (a² + b²)·sin²θ
= (a² + b²)·(cos²θ + sin²θ) since cos²θ + sin²θ = 1, we have
= (a² + b²)×1 = a² + b²
What is the slope of the table of values
Answers
A. “25/1 dollars per day; the cost is $25 for each day.”
(x values) 4-3= 1
(y values) 100-75= 25
25/1 :)
Answer:
I think the answer for this is A.
Step-by-step explanation:
since 25$ is added to get the everyday cost.
Find \( \Delta y \) and \( f(x) \Delta x \) for the given function. 6) \( y=f(x)=x^{2}-x, x=6 \), and \( \Delta x=0.05 \)
Answers
Δy is approximately 30.4525 and f(x)Δx is 1.5 for the given function when x = 6 and Δx = 0.05. To find Δy and f(x)Δx for the given function, we substitute the values of x and Δx into the function and perform the calculations.
Given: y = f(x) = x^2 - x, x = 6, and Δx = 0.05
First, let's find Δy:
Δy = f(x + Δx) - f(x)
= [ (x + Δx)^2 - (x + Δx) ] - [ x^2 - x ]
= [ (6 + 0.05)^2 - (6 + 0.05) ] - [ 6^2 - 6 ]
= [ (6.05)^2 - 6.05 ] - [ 36 - 6 ]
= [ 36.5025 - 6.05 ] - [ 30 ]
= 30.4525
Next, let's find f(x)Δx:
f(x)Δx = (x^2 - x) * Δx
= (6^2 - 6) * 0.05
= (36 - 6) * 0.05
= 30 * 0.05
= 1.5
Therefore, Δy is approximately 30.4525 and f(x)Δx is 1.5 for the given function when x = 6 and Δx = 0.05.
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I’m sad
Tommy is going to get exiled from the dream smp
AGAIN
I FREAKING HATE DREAM FOR THISSSSSS
Tommy literally just got back on 3 weeks ago, burning George’s house was an accident, he shouldn’t be kicked out AGAIN for something so minor. I get it’s acting but I’m kinda salty about this smh
Answers
IF YOU DONT WANT SPOILERS DONT READ THE REST OF THIS ANSWER
dream literally beat tommy to death with a potato..
What is the slope of the line shown in the graph below?
Answers
The points: (2,0) and (0,3)
(3-0)/(0-2) = 3/-2 = -3/2
The solution is -3/2
Answer:
the slope is -1.5
hope this helps
Solve the equation 4(h + 1.5) = -6.
h=
Answers
Answer:
h=3 is the answer
Step-by-step explanation:
The required solution to the given equation 4(h + 1.5) = -6 is
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given in the question as:
4(h + 1.5) = -6
To solve the equation 4(h + 1.5) = -6, we need to isolate the variable "h". We can do this by performing the following steps:
First, we need to get rid of the parentheses around "h + 1.5". We can do this by multiplying everything inside the parentheses by 4:
4(h + 1.5) = 4h + 6
Next, we need to get rid of the coefficient of 4 in front of "h". We can do this by dividing both sides of the equation by 4:
4h + 6 = -6
h + 1.5 = -1.5
Finally, we can subtract 1.5 from both sides of the equation to isolate the variable "h":
h = -1.5 - 1.5
h = -3
Therefore, the value of "h" that satisfies the equation is -3.
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What expression is equivalent to 24a+(-26b)-13a+12b?
Answers
The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.
What is algebraic expression ?
An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.
Examples of algebraic expressions include "3x + 4y", "2a^2 - 5b", and "(x + 3)(x - 2)".
Given expression ,
24a+(-26b)-13a+12b
= 24a - 13a +12 b - 26b
= 11a - 14b
Therefore, The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.
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If the minor arc measures 76 degrees and angle abc measures 75 degrees what is the measure of the arc bec
Answers
To find the measure of arc BEC, we need to use the relationship between the central angle and the measure of the arc. We know that angle ABC is a central angle that intercepts minor arc BC, and we also know the measure of that arc is 76 degrees.
Since angle ABC measures 75 degrees, it is less than the central angle that intercepts minor arc BC. This means that the measure of arc BEC is less than 76 degrees.
To find the measure of arc BEC, we can use the following formula:
Measure of arc BEC = Central angle ABC/360 degrees x Measure of circle
The measure of the circle is not given, but it is not necessary for solving the problem since we are only interested in the proportion of the central angle ABC to the total 360 degrees.
Substituting the values we know:
Measure of arc BEC = 75/360 x Measure of circle
Simplifying:
Measure of arc BEC = 5/24 x Measure of circle
Therefore, we cannot determine the exact measure of arc BEC without knowing the measure of the circle. However, we know that it is less than 76 degrees.
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In the exponential function f(x) = 3^-x 2, what is the end behavior of f(x) as x goes to [infinity]?
Answers
For an exponential function \(f(x) = 3^{-x}2\) as x goes to infinity, f(x) goes to zero.
We have been given an exponential function \(f(x) = 3^{-x}2\)
We need to check the end behavior of f(x) as x goes to infinity.
Consider,
\(\lim_{x \to \infty} f(x)\\\\= \lim_{x \to \infty} 3^{-x}2\\\\=2\times \lim_{x \to \infty} 3^{-x}\\\\=2\times 3^{-\infty}\\\\=2\times 0\\\\=0\)
This means, x \(\rightarrow\) infinity, f(x) goes to 0
As x goes to infinity, f(x) goes to zero.
Therefore, for an exponential function \(f(x) = 3^{-x}2\) as x goes to infinity, f(x) goes to zero.
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Suppose there is a 1.7 f drop in temperature for every thousand feet that an airplane climbs into the sky.If the temperature on the ground is 59.2,what will be the temperature when the plane reaches an altitude of 7,000 ft?
Answers
The temperature when the plane reaches an altitude of 7,000ft is 47.3 degree.
What is temperature?
Temperature, measure of hotness or coldness expressed in terms of any of several arbitrary scales and indicating the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature).
Given,
there is temperature decrease in every thousand feet = 1.7f
temperature decrease in 7000 ft = 7(1.7) = 11.9 f
Therefore, temperature = 59.2- 11.9
=47.3
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in a circle, a sector with central angle is 225 degrees intercepts an arc of length 30pi in. find the diameter of the circle
Answers
The diameter of the circle is approximately 60 inches.
To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.
In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).
To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.
The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.
In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.
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When Gail goes on a hike, she always packs a ratio of 20 protein bars to 15 water bottles in her backpack.
Complete the statement about the ratio of protein bars to water bottles.
CLEARCHECK
For a short hike, Gail should pack
protein bars if she packs 3 water bottles.