The approach of using a Cartesian coordinate system to study geometry differs from other approaches in that it allows for the use of algebraic equations to describe geometric figures and relationships. This approach is more analytical in nature and can be used to prove theorems and solve problems that may not be easily solvable using other approaches. It also allows for the extension of geometry beyond two dimensions, which is not always possible with other approaches.
In my opinion, the approach of using a Cartesian coordinate system is more beneficial because it allows for a more rigorous and precise understanding of geometry. It also allows for the use of algebraic equations to solve geometric problems, which can be more efficient and easier to understand than other methods. Additionally, this approach is easier to extend beyond two dimensions, which is becoming increasingly important in fields such as computer graphics and engineering.
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Please help me with these two, i’ll give 15 points!!
Explain the difference between finding the vertex of a function written in vertex form and finding the vertex of a function written in standard form.
The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
Convert the standard equation into a vertex form, then we have
x² + (b/a)x + (c/a) = 0
x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0
(x + b/2a)² - b²/4a² + c/a = 0
Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be
(x - h)² + k = 0
The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.
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What is the volume of this sphere? Use 3.14 and round your answer to the nearest hundredth. 1777561 cubic inches ST
we have that
the radius is
r=12.1 in
the volume of a sphere is
\(V=\frac{4}{3}\cdot\pi\cdot r^3\)substitute the given values
\(\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot12.1^3 \\ \\ V=7,416.94\text{ in3} \end{gathered}\)Part 2
In this problem we have the diameter of the sphere
D=13.6 mm
so
r=D/2=13.6/2=6.8 in
substitute in the formula
\(\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot6.8^3 \\ V=1,316.42\text{ in3} \end{gathered}\)The graph shows a proportional relationship between the number crates and the number of apples per crate.
What is the constant of proportionality in terms of the number of apples to the number of crates?
A. 30
B. 35
C. 40
D. 50
Answer:
its 40
Step-by-step explanation:
Answer:
b40
Step-by-step explanation:
it is 40 because on the graph it shows that you don't start at the first crate but the 2nd you do and you have to figure out if the crate was one how many apples would their be
please choose me as Brainliest
A teacher wants to test whether his students will perform better on their exam if the room where they take the exam is cooled to a freezing temperature. On the day of an exam, he randomly assigned his class into two groups. One group took the exam under regular conditions and one group took the exam in a freezing cold room. After the exam, the teacher calculated the average score in each group. Assume that all conditions for inference have been met. Which of these is the most appropriate test and alternative hypothesis?.
Considering the situation described in the text, we have that:
A two-sample t-test is used.The null hypothesis is \(H_0: \mu_F - \mu_R = 0\). The alternative hypothesis is \(H_1: \mu_F - \mu_R > 0\).In this problem, we consider that:
\(\mu_R\) is the mean score of students who took the exam in regular conditions.\(\mu_F\) is the mean score of students who took the exam in freezing cold conditions. What are the hypothesis tested?At the null hypothesis, we test if both groups have the same mean score, that is, the subtraction of the means is of 0, hence:
\(H_0: \mu_F - \mu_R = 0\)
At the alternative hypothesis, we test if students that did the test in freezing cold conditions performed better, that is, the subtraction is positive, hence:
\(H_1: \mu_F - \mu_R > 0\).
We have the comparison(subtraction) of two samples, and we have the standard deviation for each sample, not for the population, hence a two-sample t-test is used.
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paid after the grace period, on average, more than 4 times in 2018, what are the null and alternative hypotheses? Select the correct answer below: H0: μ=4; Ha: μ>4 H0: μ>4; Ha: μ=4 H0: μ=4; Ha: μ<4 H0: μ=4; Ha: μ≠4
Answer:
H₀: μ = 4 vs. H ₐ: μ > 4
Step-by-step explanation:
A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.
It is a hypothesis of no difference.
It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.
Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.
The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.
It is also known as the research hypothesis and is denoted by H ₐ.
In this case we need to test whether the amount is paid after the grace period, on average, more than 4 times in 2018.
The hypothesis can be defined as follows:
H₀: μ = 4 vs. H ₐ: μ > 4
Please help asap! :)
Answer:
g(x)= -2 x+1
Step-by-step explanation:
g(x)= -2 x+1
there isnt much for my to explain, sorry.
Please ASAP
Add: 1234 + 202
1234 + 202 = 1,436
Hope this helps!!
Answer:
1436 is your answer
Step-by-step explanation:
Consider a Feistel cipher with r rounds and n=128 (half the block length); ℓ=256(the key bit size). Then M={0,1} 24
(the plaintext space), C={0,1} 276
(the ciphertext space), and K={0,1} 2%
(the key space). A key scheduling algorithm determines subkeys k 1
,k 2
from a key K∈K={0,1} 206
. Each subkey k i
determines a function f i
:{0,1} 12×
→{0,1} 12×
. Eneryptio. takes r rounds: - Plaintext is m=(m 0
,m 1
) with m 0
,m 1
∈{0,1} 12κ
, - Round 1: (m 0
,m 1
)→(m 1
,m 2
) with m 2
=m 0
⊕f 1
(m 1
). - Round 2: (m 1
,m 2
)→(m 2
,m 3
) with m 3
=m 1
⊕f 2
(m 2
). - Round r: (m r−1
,m r
)→(m r
,m r+1
) with m r+1
=m r−1
⊕f r
(m r
). - The ciphertext is c=(m r
,m r+1
). For the Feistel cipher described above: Exercise 2 (Security of Feistel ciphers 1. Consider the above Feistel cipher with r=2 rounds. Is this Feistel cipher secure against an exhaustive key search attack, in the known-plaintext attack model? What does the complexity of such an attack depend on? Explain. 2. Consider the above Feistel cipher with r=2 rounds. Imagine a key scheduling algorithm that works as follows. Given K∈K={0,1} 2π
, set k 1
to be the leftmost 128 bits of K, and k 2
to be the rightmost 128 bits of K, then define f i
(x)=x∈
/
k i
. Show that this block cipher is totally insecure - that is, given a single plaintext-ciphertext pair (m,c), the secret key K can be easily recovered. Hint: linearity is the problem here.
Answer:
Step-by-step explanation:654\(\sqrt[n]{x} \sqrt[n]{x}\)+++++++
2 3 4 5 6 7 8
4
Answer:
-5 -4 -3 -2 -1 0 1
Step-by-step explanation:
I am confused by your question but I believe this is the anwser.
find the coordinates of the verticesof each figure after the given transformation
Given,
The coordinates of the given figure are J(1, 3), U(0, 5), R(1, 5), C(3, 2)
Here, the reflection about only y axis,
The coordinates of the x-axis remain the same,
This finds the distance from the point to y = 2 by subtracting the point's y-coordinate from 2, then moves the point that far to the other side of y = 2 by adding 2.
The reflected coordinates are,
\(\begin{gathered} J(1,\text{ 3)}\rightarrow J^{\prime}(1,\text{ 2+(2-3))}\rightarrow J^{\prime}(1,1)_{} \\ U(0,\text{ 5)}\rightarrow U^{\prime}(0,\text{ 2+(2-5))}\rightarrow U^{\prime}(0,-1) \\ R(1,\text{ 5)}\rightarrow R^{\prime}(1,\text{ 2+(2-5)}\rightarrow R^{\prime}(1,-1) \\ C(3,\text{ 2)}\rightarrow C^{\prime}(3,\text{ 2+(2-2))}\rightarrow C^{\prime}(3,2) \end{gathered}\)
Compare the solution of each equation to 0. Write the equation in the correct box.
The following are the solution to each equation;
5(d + 2) = 3(d - 6) Solution is less than 0-6m = 2(3m - 1) Solution is greater than 0⅔(3y + 6) = 0 Solution is less than 0-4 = ½p - 7 Solution is greater than 015 - (4z + 3) = 12 Solution is less than 00.4(3.2x + 2) = 2x + 1.8 Solution is less than 0What are the solution to the equations?5(d + 2) = 3(d - 6)
open parenthesis
5d + 10 = 3d - 18
5d - 3d = -18 - 10
2d = -28
divide both sides by 2
d = -28/2
d = -14
Solution is less than 0
-6m = 2(3m - 1)
-6m = 6m - 2
combine like terms
-6m - 6m = -2
-12m = -2
divide both sides by -12
m = -2/-12
m = 1/6
Solution is greater than 0
⅔(3y + 6) = 0
option parenthesis
6/3y + 12/3 = 0
2y + 4 = 0
2y = -4
y = -4/2
y = -2
Solution is less than 0
-4 = ½p - 7
-4 + 7 = ½p
3 = ½p
divide both sides by ½
p = 3 ÷ ½
multiply by the reciprocal of ½
p = 3 × 2/1
p = 6
Solution is greater than 0
15 - (4z + 3) = 12
15 - 4z - 3 = 12
12 - 4z = 12
-4z = 12 - 12
-4z = 0
Solution is less than 0
0.4(3.2x + 2) = 2x + 1.8
1.28x + 0.8 = 2x + 1.8
1.2x - 2x = 1.8 - 0.8
- 0.8x = 1
x = 1/-0.8
x = -1.25
Solution is less than 0
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consider a symmetric matrix a. if the vector v is in the image of a and w is in the kernel of a, is v necessarily orthogonal to w?
Yes, the vector v is necessarily orthogonal to w if v is in the image of the symmetric matrix A and w is in the kernel of A.
Yes, the vector v is necessarily orthogonal to w if v is in the image of the symmetric matrix A and w is in the kernel of A. This is due to the fact that for any symmetric matrix A, the image (column space) and kernel (null space) are orthogonal subspaces. Since v is in the image of A and w is in the kernel of A, their dot product must be zero, indicating orthogonality.
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The probability that Mike has to work overtime and it rains is 0.028. Mike hears the weather forecast, and there is a 50% chance of rain. Find the probability that he will have to work overtime, given that it rains.
So, the probability that Mike will have to work overtime, given that it rains, is 0.056 or 5.6%.
To find the probability that Mike has to work overtime given that it rains, we will use conditional probability. We are given the joint probability of Mike working overtime and it raining (0.028) and the probability of rain (0.5).
Let A be the event of Mike working overtime, and B be the event of rain. We want to find the probability of A given B, or P(A|B). We can use the formula for conditional probability: P(A|B) = P(A and B) / P(B).
Plugging in the values we have:
P(A|B) = P(A and B) / P(B) = 0.028 / 0.5
Now, divide 0.028 by 0.5:
P(A|B) = 0.056
So, the probability that Mike will have to work overtime, given that it rains, is 0.056 or 5.6%.
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Solve these two questions for 50 pts.
Answer:
RS = 26x = 6Step-by-step explanation:
Question 1V and W are midpoints of RU and ST ⇒ VW is a midsegment
VW = 1/2(RS + UT) ⇒ RS = 2*VW - UT
Substitute values:
2x + 15 = 2(2x + 5) - (6x - 37)2x + 15 = 4x + 10 - 6x + 372x + 15 = -2x + 472x + 2x = 37 - 154x = 22x = 5.5RS = 2x + 15 = 2(5.5) + 15 = 11 + 15 = 26
Question 2
Trapezoid given with congruent sides, JM = KLAngle J and K are congruent, both are (7x + 2)Angles M and L are congruent, both are (2x - 14)J and M are supplementary, so sum to 180°
7x + 2 + 25x - 14 = 18032x = 192x = 192/32x = 6Answer:
RS = 26
x = 6
Step-by-step explanation:
Write an equation of the line that passes through (−6, 0) and (0, −24)
Answer:
y=4x+24
Step-by-step explanation:
1: find slope
\(\frac{0+24}{-6-0}\)
\(\frac{24}{-6}\)
4
2:plug into point-slope form
y-0=4(x+6)
y=4x+24
Answer:
y = -4x - 24
Step-by-step explanation:
slope = -4
this topic is parametric curves for ln equations.
Please explain how to graph using ln restrictions for these parametric equations and please dont use graphing calculator or desmos.
please explain only if you truly know as i spent too much time figuring out.
Also i am showing what graph i got using a calculator but i dont understand how. i am not supposes to use calculator on test.
x(t) = Ln(t)
y(t) = (Ln(t))^2
Given parametric equations are x(t) = Ln(t) and y(t) = (Ln(t))^2. We have to graph the given parametric equations using ln restrictions without a calculator or desmos.
Here, we are going to find the value of t, which helps us to graph the given parametric equation using ln restrictions.Step-by-step explanation to find the value of t are:We have,
x(t) = Ln(t) ⇒ t = e^x(t) ....(1)y(t) = (Ln(t))^2⇒ t = e^(y(t)/2) ...
.(2)From (1) and (2),
we get e^x(t) = e^(y(t)/2)e^(2x(t)) = y(t) ...
(*)We know that the domain of ln x is (0, ∞). Let's determine the range of x(t) and y(t):From equation (1), if t → 0, then x(t) → - ∞From equation (1), if t → ∞, then x(t) → ∞From equation (2), if t → 0, then y(t) → 0From equation (2), if t → ∞, then y(t) → ∞Now,
we can graph the given parametric equations using the following steps: Assign values to t such as
t = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, .7, 0.8, 0.9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
Step 2: Calculate x(t) and y(t) corresponding to t values.Step 3: Plot the points obtained in step 2.Step 4: Join all the points obtained in step 3 using a smooth curve.The graph of the given parametric equation is shown below.
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Theorem: If n is an odd integer, and m is an odd integer then n+m is even. If I want to prove this by contradiction, which of the following is my set of premises a. n is odd, mis odd, n+m is odd b. n is odd, mis odd c. n is even or m is even d. n+m is odd
To prove the theorem "If n is an odd integer and m is an odd integer, then n + m is even" by contradiction, the set of premises would be: n is an odd integer and m is an odd integer.
To prove a statement by contradiction, we assume the opposite of the statement and show that it leads to a contradiction or inconsistency. In this case, we assume that the sum n + m is odd.
If we choose option (d) "n + m is odd" as our set of premises, we are assuming the opposite of what we want to prove. This approach would not lead to a contradiction and therefore would not be suitable for a proof by contradiction.
Instead, we need to start with the premises that n is an odd integer and m is an odd integer. From these premises, we can proceed to show that their sum n + m is indeed even. By assuming the opposite and arriving at a contradiction, we establish the truth of the original statement.
Therefore, the correct set of premises for a proof by contradiction in this case is option (b) "n is odd, m is odd." This allows us to arrive at a contradiction when assuming the sum n + m is odd, leading to the conclusion that n + m must be even.
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Which equation does the graph represent (see picture)
A. y = -2x
B. y= -1/2x
C. y = 2x
D. y = 1/2 x
round 2.33459 to the hundreths place
Answer:
2.33
Step-by-step explanation:
Answer:
go to your hundredths place. since 4 is not greater than 5 then it would round down. so the final answer would be 2.33
The doctor tells the patient to cut back on coffee. the patient usually has four 8-oz cups of coffee per day. if the doctor told him to cut back by 25%, how many ounces of coffee can the patient have each day? (enter numeric value only. if rounding is necessary, round to the whole number.)
The ounces of coffee the patient have each day is 24 oz.
What is reduction of percentage?A difference among starting and final numbers is the percentage drop. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decline.
Some characteristics of percentage change are-
Any amount that is measured over time can be changed as a percentage.The percentage difference between a value and its starting point is known as a percentage decline.A percentage decline indicates a reduction in value from the starting quantity.Calculation for the coffee that the patient consume each day,
Determination for the coffee he consumes daily.
4 cups x 8 oz = 32 oz
Now, multiply the outcome by the decimal equivalent of the percentage (i.e., 25% = 25/100).
32 x (25/100) = 8
Finally, remove the percentage from the weekly coffee consumption.
32-8 = 24 oz per day
Therefore, the consumption of the coffee by the patient reduced to 24 oz per day from 32 oz per day.
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a. Explain the concept of loss aversion. How is loss aversion
typically modelled in a Prospect Theory value function? Provide an
algebraic example.
b. Explain the concept of a reference point. How is
Loss aversion can be explained as the fact that people tend to feel the negative consequences of loss more strongly than the positive effects of an equal gain. This means that people will often take risks in order to avoid a loss rather than in order to make a gain.
Loss aversion is typically modelled in a Prospect Theory value function. This function takes into account both the probability and magnitude of a gain or loss. The value function has two different curves, one for gains and one for losses. These curves are both steeper in the loss domain than they are in the gain domain. This means that losses are generally seen as more important than gains of the same magnitude. Let's take an algebraic example to illustrate this: Suppose that a person has to choose between two options: A 50% chance of winning $100 A sure win of $50In this case, a rational decision maker would choose option A, .
However, if the person has loss aversion, they might choose option B because the thought of losing $100 is too painful to bear. This is reflected in the value function, where the curve for losses is steeper than the curve for gains. b. A reference point can be defined as the starting point from which a person evaluates their gains and losses. This reference point can be subjective and will vary from person to person. However, once a reference point has been established, people will tend to evaluate gains and losses relative to this point. This means that they will view gains above this point as positive and losses below this point as negative. A reference point can be anything from a person's initial investment to their current wealth status. The reference point is important because it determines how people view the outcomes of their decisions.
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Write an equation in slope intercept form for the line that passes through (5, -4) and is perpendicular to the line described by 2x-10y=0
Benjamin bought bags of chips for $0.95 each and two sodas for $1.14 each. He spent $5.13 altogether. Let c equal the number of chip bags Henry bought. Which equation would you use to find c?
Answer:
he brought 3 bags of chips
Step-by-step explanation:
1.14×2=2.28
5.14-2.28= 2.85
2.85÷0.95=3
Write the next term in the sequence. Then write a rule for the nth term. 9, 36, 81, 144, . . .
The next term in the sequence is 225.
The rule for the nth term of the sequence is:
\(n^4, for n > = 1\)
This means that the nth term of the sequence is obtained by raising n to
the fourth power, for any positive integer value of n.
Using this rule, we can see that the first five terms of the sequence are
obtained by computing \(1^4 = 1, 2^4 = 16, 3^4 = 81, 4^4 = 256\), and
\(5^4 = 625\), respectively.
The fourth term of the sequence, which is 144, corresponds to n = 3, since\(3^4 = 81.\)
The next term in the sequence is then obtained by computing\(4^4 = 256\),
and the term after that is obtained by computing \(5^4 = 625\).
Therefore, the sequence continues as follows:
9, 36, 81, 144, 225, 256, 625, ...
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Billy Bob has 23 coins that total $1.70. He found some nickels and dimes in the couch.
How many nickels and dimes did he find?
Answer:
12 nickels
11 dimes
Step-by-step explanation:
Let n = no. of nickels
d = no. of dimes
5n = value of nickels in cents
10d = value of dimes in cents
170 = total value in cents
(1) n + d = 23 (2) 5n + 10d = 170
d = 23 - n 5n + 10(23 - n) = 170
5n + 230 - 10n = 170
- 5n = - 60
n = 12 nickels
d = 23 - 12 = 11 dimes
Check: 12(5) + 11(10) = 60 + 110 = 170 cents or $1.70
Giving away a lot of points please don't put something random, no explanation is needed only the answer.
Thank you
The theoretical probability is: 12.5%. After 100 trials, the experimental probability is of: 20%. After 400 trials, the experimental probability is of: 11%. After more trials, the experimental probability is closer to the theoretical probability.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:
1/8 = 0.125 = 12.5%.
(eight sides, each of them is equally as likely).
The experimental probabilities are obtained considering the trials, hence:
100 trials: 20/100 = 0.2 = 20%. -> results given in the text.400 trials: 44/400 = 0.11 = 11%.The more trials, the closer the experimental probability should be to the theoretical probability.
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a triangle has the following measures: 2x degrees, 3x degrees, and 22 degrees. find the actual measures of 2x degrees and 3x degrees
Answer:
Step-by-step explanation:
The sum of the angles in a triangle is always 180 degrees. Therefore,
2x + 3x + 22 = 180
Simplifying the equation,
5x = 158
Dividing by 5 on both sides,
x = 31.6
To find the actual measures of 2x and 3x, we substitute the value of x:
2x = 2(31.6) = 63.2 degrees
3x = 3(31.6) = 94.8 degrees
Therefore, the actual measures of 2x and 3x are 63.2 degrees and 94.8 degrees, respectively.
Classify the following polynomials by the highest power of each of its terms. Combine any like terms first. -x^2+x-x^2+1,x^2+x+2x^3-x,4x+x+x-2,3x^2+4-3x^2-1
Polynomials are algebraic expressions consisting of terms that include real numbers, variables, and positive integer exponents. Each term in a polynomial has a variable raised to a non-negative integer power, and the coefficient of each term is a real number. Polynomials are classified by the degree of their highest power. If two or more terms in a polynomial have the same variable raised to the same power, they can be combined into a single term.
1. -x² + x - x² + 1
Combine like terms: -x² + x - x² + 1 = -2x² + x + 1
This polynomial has degree 2 because the highest power of the variable is 2.
2. x² + x + 2x³ - x
Rearrange terms: 2x³ + x² + x - x = 2x³ + x²
This polynomial has degree 3 because the highest power of the variable is 3.
3. 4x + x + x - 2
Combine like terms: 4x + x + x - 2 = 6x - 2
This polynomial has degree 1 because the highest power of the variable is 1.
4. 3x² + 4 - 3x² - 1
Combine like terms: 3x² - 3x² + 4 - 1 = 3
This polynomial has degree 0 because there is no variable term.
Therefore, the four given polynomials have degrees 2, 3, 1, and 0, respectively.
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Solve the equation.
g/4 =3.2
g=?
the value of g is 12.8.
To solve the equation g / 4 = 3.2 and find the value of g, we can multiply both sides of the equation by 4 to isolate g.
By multiplying both sides of the equation by 4, we have:
( g / 4 ) * 4 = 3.2 * 4
This simplifies to :
g = 12.8
Therefore, the value of g is 12.8. In the original equation, dividing g by 4 yields a quotient of 3.2, confirming that g = 12.8 is the solution that satisfies the equation g / 4 = 3.2.
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