Answers
• It captures the overall trends and patterns in the data points. It does not necessarily pass through every single data point but approximates the shape and trajectory of the data.
• It has parameters that can be adjusted to optimize how well the model fits the data. Things like coefficients, exponents, intercepts, etc. The good parameter values will depend on the specific data set and model.
• It has an appropriate level of complexity for the data. It does not overfit or underfit the data. An overfit model captures every detail and noise, while an underfit model fails to capture the key dynamics.
• Key features like slope, curvature, periodicity, thresholds, etc. in the data are properly represented in the model.
• It provides insights or useful information, not just a mathematical abstraction of the data. A good model opens the black box and provides interpretable knowledge about the system or phenomenon that generated the data.
• Predictions or extrapolations from the model align well with any additional data points beyond the original data set. The model generalizes purposefully.
• There are objective metrics that can evaluate how good a particular model is for a data set, like R2, mean absolute error, Akaike information criterion, etc. The best model will optimize such metrics.
Related Questions
I need the area choices below
Answers
Answer:
Area of the shape is 244.98cm² is B
Step-by-step explanation:
Area of shape=Area of semi circle+Area of trapezoid
A=1/2 πr² + 1/2(a+b)h
A=1/2×3.142×7² + 1/2(14+18)10.5
A=1/2×3.142×49 + 1/2×32×10.5
A=76.98+168
A=76.98+168
A=244.98cm²
The following residual plot is obtained after a regression equation is determined for a set of data. Does the residual plot indicate that the regression equation is a good model or a bad model of the data? Why or why not?
Answers
The residual plot shows that the regression equation is a good model of the data because it shows a random scatter of points around a horizontal line at zero, with no pattern or trend
What makes a residual plot a good model?A residual plot is a scatter plot of the residuals against the predictor variable(s) or the fitted values. It is used to verify whether the regression equation fits the data well.
In the event that the residual plot shows a random scatter of points around a horizontal line at zero, with no pattern or trend, it shows that the regression equation is a good model of the data.
On the other hand, supposing the residual plot shows a pattern or trend, such as a curve, a U-shape, or a funnel shape, it shows that the regression equation is a bad model of the data.
Therefore, from the graph given, the residual plot shows that the regression equation is a good model of the data.
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how exactly am i supposed to locate? please help
Answers
Answer:
We can use the vector addition property to find the coordinates of the points M, N, and I.
Let
[tex]\bold{ A = (x_1, y_1), B = (x_2, y_2), C = (x_3, y_3), and\: D = (\frac{x_2+x_3}{2}, \frac{y_2+y_3}{2})}[/tex]
To find M, we use the fact that MA + MB = 0. Therefore, we have:
MA = -MB
A - M = -(B - M)
A - M = -B + M
2M = A + B
M =[tex]\frac{A + B}{2}[/tex]
So, the coordinates of point M are
[tex]\bold{(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})}[/tex]
To find N, we use the fact that 3NA + NC = 0. Therefore, we have:
3NA = -NC
3A - N = -(C - N)
3A - N = -C + N
4N = 3A + C
N =[tex]\frac{ 3A + C}{4}[/tex]
So, the coordinates of point N are [tex]\bold{(\frac{3x_1+x_3}{4},\frac{ 3y_1+y_3}{4})}[/tex]
To find I, we use the fact that IM + 2IN = 0. Therefore, we have:
IM = -2IN
M - I = -2(N - I)
M - I = -2N + 2I
3I = M + 2N
I = [tex] \frac{(M + 2N)}{3} [/tex]
Substituting the values of M and N that we found earlier, we get:
I = (A + B + 2(3A + C)/4)/3
Simplifying this expression, we get:
I = [tex]\frac{(7A + 2B + 2C)}{12}[/tex]
So, the coordinates of a point I are[tex]\bold{(\frac{7x_1+2x_2+2x_3}{12}, \frac{7y_1+2y_2+2y_3}{12}).}[/tex]
The distribution of scores on the SAT is approximately normal with a mean of μ- 500 and a standard deviation of a 100. or the population of students who
have taken the SAT
a. What proportion of students have scores less than 380?
b. What proportion of students have scores greater than 639
Answers
a. The proportion of students have scores less than 380 is 11.51%.
b. The proportion of students have scores greater than 639 is 8.23%.
What is the proportion with SAT scores below 380 and above 639?1. Using the z-score formula:
We can calculate that score of 380 corresponds to a z-score of -1.2 since z = (x - μ) / σ.
Using a standard normal distribution table, we find that:
The proportion of students with scores less than 380 is 0.1151.2. Similarly, a score of 639 corresponds to a z-score of 1.39.
Using a standard normal distribution table, we find that:
The proportion of students with scores greater than 639 is approximately 0.0823.Read more about distribution
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Wenona sketched the polynomial P(X) as shown on the axes below.
Which equation could represent P(X)
A.P(X)=(x+1)(x-2)^2
B.P(X)=(x-1)(x+2)^2
C.P(X)=(x+1)(x-2)
D.P(X)=(x-1)(x+2)
Answers
An equation that could represent P(x) include the following: A. P(x) = (x + 1)(x - 2)²
What is a polynomial graph?In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
Also, the graph has a zero of multiplicity 2 at x = 2 and zero of multiplicity 1 at x = -1;
x = 2 ⇒ x - 2 = 0.
(x - 2)²
x = -1 ⇒ x + 1 = 0.
(x + 1)
In this context, an equation that represent the polynomial function is given by:
p(x) = a(x - 2)²(x + 1)
By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, 4), we have;
4 = a(0 - 2)²(0 + 1)
4 = a4
a = 4/4.
a = 1
Therefore, the required polynomial function is given by:
p(x) = (x - 2)²(x + 1)
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Charlie made a start using 1/8 yards of red fabric and 1/3 yards of yellow fabric. How many yards of fabric did he use in all? Write your answer as a fraction in simplest form.
Answers
Answer:
[tex]\frac{11}{24}[/tex] yards
Step-by-step explanation:
[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{3}[/tex] we need a common denominator which is 24
[tex]\frac{1}{8}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{24}[/tex]
[tex]\frac{1}{3}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{8}{24}[/tex]
[tex]\frac{3}{24}[/tex] + [tex]\frac{8}{24}[/tex] = [tex]\frac{11}{24}[/tex] yards
Helping in the name of Jesus.
7.54 Torque on a rusty bolt.
(a) Do you think it is reasonable to apply ANOVA in this case?
(b) Regardless of your answer in part (a), describe hypotheses for ANOVA in this context, and use the table below to carry out the test. Give your conclusion in the context of the data.
(c) The table below are p-values for pairwise t-tests comparing each of the different groups. These p-values have not been corrected for multiple comparisons. Which pair of groups appears most likely to represent a difference?
(d) There are 28 p-values shown in the table in part (c). Determine if any of them are statistically significant after correcting for multiple comparisons. If so, which one(s)? Explain your answer.
Answers
Answer:
Answer is obstacle by giving up yours
5. (10 points) The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 367 ml and a standard deviation of 3 ml. If all cans less than 358 or greater than 373 ml are scrapped, what proportion of cans is scrapped? Solution:
Answers
The proportion of cans that are scrapped is approximately 0.0241.
We know that the fill volume of cans follows a normal distribution with a mean of 367 ml and a standard deviation of 3 ml. Let's define X as the fill volume of a single can. Then we can write:
X ~ N(367, 3)
We want to find the proportion of cans that are scrapped, i.e., the proportion of cans with a fill volume less than 358 ml or greater than 373 ml. Let's call this proportion p:
p = P(X < 358 or X > 373)
To solve this problem, we can use the standard normal distribution and the z-score formula:
z = (X - μ) / σ
where μ is the mean and σ is the standard deviation of the distribution. We can standardize the values 358 and 373 using this formula:
z1 = (358 - 367) / 3 = -3
z2 = (373 - 367) / 3 = 2
Now we can find the probabilities of the two events separately using the standard normal distribution table or a calculator:
P(X < 358) = P(z < -3) ≈ 0.0013
P(X > 373) = P(z > 2) ≈ 0.0228
The probability of either event happening is the sum of the probabilities:
P(X < 358 or X > 373) = P(X < 358) + P(X > 373) ≈ 0.0241
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Victoria bought a box of raisins and gave of the raisins to her younger brother.
About what percent of the raisins did she keep for herself?
F 30%
G 33%
H 66%
J 70%
Answers
The percent of the raisins that Victoria she keep for herself is 70%
How to calculate the percentageBased on the information, a percentage simply has to do with the a value or ratio which can be stated as a fraction of 100.
Since Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother. The percent of the raisins she keep for herself will be:
= (1 - 3/10) × 100
= 70%
Therefore, the percent of the raisins that Victoria she keep for herself is J 70%
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Victoria bought a box of raisins and gave 3/10 of the raisins to her younger brother.
About what percent of the raisins did she keep for herself?
F 30%
G 33%
H 66%
J 70%
A rectangle has sides measuring (2x + 7) units and (5x + 9) units.
Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)
Answers
Answer:
A: (2x + 7)(5x + 9) = 10x^2 + 53x + 63
B: second-degree (quadratic) polynomial
C: The product of two polynomials is a polynomial.
Part A: we simply need to multiply this out using the distributive property:
Area = 2x5x + 2x9 + 75x + 79
= 10x² + 18x + 35x + 63
= 10x² + 53x + 63 (4 points)
Part B:A polynomial of degree 2 is called a quadratic polynomial. So, the classification of this polynomial is "quadratic". (3 points)
Part C:In the case of the set of polynomials, the closure property for multiplication says that multiplying any two polynomials results in another polynomial. This is demonstrated in Part A where we multiplied two polynomials - (2x + 7) and (5x + 9) - and the result was another polynomial - 10x² + 53x + 63. This shows that the set of polynomials is closed under multiplication. (3 points)
Part A:
The area of a rectangle is given by the product of its length and width. Therefore, for a rectangle with sides measuring (2x + 7) units and (5x + 9) units, the area can be represented as:
Area = (2x + 7)(5x + 9)
Now, we simply need to multiply this out using the distributive property:
Area = 2x5x + 2x9 + 75x + 79
= 10x² + 18x + 35x + 63
= 10x² + 53x + 63 (4 points)
Part B:
The degree of a polynomial is the highest power of x in the polynomial. Here, the highest power of x is 2 (in the term 10x²), so the degree of this polynomial is 2.
A polynomial of degree 2 is called a quadratic polynomial. So, the classification of this polynomial is "quadratic". (3 points)
Part C:
The closure property of an operation (like addition, multiplication, etc.) on a set says that applying the operation to any elements in the set always results in an element that is also in the set.
In the case of the set of polynomials, the closure property for multiplication says that multiplying any two polynomials results in another polynomial. This is demonstrated in Part A where we multiplied two polynomials - (2x + 7) and (5x + 9) - and the result was another polynomial - 10x² + 53x + 63. This shows that the set of polynomials is closed under multiplication. (3 points)
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To wrap gift boxes joelle uses 24 yards if ribbon which us 8% of her total amount of ribbon. How many ribbons does she gave jn all
Answers
Joelle gave a total of 300 yards of ribbon in all
How many ribbons does she gave in allLet's assume that the total amount of ribbon Joelle has is "x" yards.
We know that 24 yards of ribbon is 8% of her total amount of ribbon. So we can write an equation:
0.08x = 24
To solve for x, we divide both sides of the equation by 0.08:
x = 24 ÷ 0.08
x = 300
Therefore, Joelle has a total of 300 yards of ribbon.
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Answer:
Step-by-step explanation: the answer is 300 just divide and you’ll get the answer that simple
PLEASE HELP NOW ITS DUE TONIGHT!!!!
A zip line is constructed across a valley, as shown in the diagram. What is the width w of the valley? Round your answer to the nearest tenth.
w ≈__ft
Answers
Answer: 92.5
Step-by-step explanation:
Answer:
w = 92.5
Step-by-step explanation:
You cannot use Law of Sine in this case.
Use Law of Cosine.
They gave you 2 side length and one angle.
plug in your values into the equation and solve for w.
Let just use u, v, & w: Let u be 25 and v be 84.
[tex]w^2 = u^2 + v^2 - 2*u*v*cos(W)[/tex]
[tex]w^2 = 25^2 + 84^2 - 2*25*84*cos(102)[/tex]°
[tex]w^2=625+7056-4200*cos(102)[/tex]
[tex]w^2=7681-4200*(-0.2079116908)[/tex]
[tex]w^2=7681+873.2291014[/tex]
[tex]w^2=8554.229101[/tex]
[tex]w=\sqrt{8554.229101}= 92.48907558[/tex]
You are biking to the library. When you are 75% of the way there, you realize you forgot a book. So you turn around and head back. When you are 1/3 of the way back, you realize you don't need the book, so you turn around again and bike 3.2 miles to the library. How far do you live from the library
Answers
The distance you live from the library, would be 6. 4 miles.
How to find the distance ?Assigning the distance between your house and where you can find books as x miles, we could approximate that initially you cycled 0.75x miles before retracing your route back a third of what had already been travelled; converting to 0.25x mile. Thus, at this stage, you will have covered an accumulated distance of 0.5x - taking into account earlier computations.
Realizing that borrowing such book would be unnecessary, you rode back to the library from whence you started- making it 3.2 miles. As you have advanced some length by travelling a cumulative distance of 0.5x from your private residence on previous trial, only another 0.5x miles stands between you and the target place after spinning around anew.
The equation is:
0. 5 x = 3. 2
x = 3. 2 / 0. 5
x = 6. 4 miles
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Translate this sentence into an equation.
24 more than Craig's height is 68.
Use the variable c to represent Craig's height.
Answers
We can begin by focusing on c on one side of the equation to help us solve it. Craig's height is 44 as a result.
What is Equation?A mathematical equation is a claim that two expressions are equivalent. It is divided into two sections, the left and the right, by the equal sign (=). Equation's left and right sides each have the potential to include variables, constants, and operators.
Finding the value(s) of the variable(s) necessary to make an equation true is the aim of equation solving. Algebraic techniques like simplification, substitution, and elimination can be used to solve equations.
An equation can be used to represent the following sentence:
c + 24 = 68
Craig's height is represented by c in this equation. The equal sign (=) is used to symbolise the phrase "is 68," while the phrase "is 24 more than Craig's height" is symbolised by c + 24. The formula for the problem can be solved to find the value of c, which corresponds to Craig's height.
We can begin by concentrating c on just one side of the equation in order to solve it:
c + 24 - 24 = 68 - 24
c = 44
Therefore, Craig's height is 44.
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Jenna threw a disc 18 yards to Karl, who threw it 11 yards in the same direction to Alice.
Start at 0 on the number line and move _____ to the right to represent Jenna throwing the disc to Karl.
Then move ______ to the right to represent Karl throwing the disc to Alice the result shows that.
Answers
Start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl. Then move 11 yards to the right to represent Karl throwing the disc to Alice the result shows that.
To represent Jenna throwing the disc to Karl, we need to move 18 yards to the right on the number line. This is because Jenna threw the disc directly to Karl, so the distance between them is 18 yards. Therefore, we can start at 0 on the number line and move 18 yards to the right to represent Jenna throwing the disc to Karl.
To represent Karl throwing the disc to Alice, we need to move 11 yards to the right from Karl's position on the number line. This is because Karl threw the disc 11 yards in the same direction as Jenna threw it to him.
So, we can start at Karl's position on the number line (which is 18 yards to the right of 0) and move 11 yards to the right to represent Karl throwing the disc to Alice.
Overall, to represent the entire throwing sequence from Jenna to Karl and then to Alice, we can start at 0 on the number line and move 18 + 11 = 29 yards to the right.
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If 30% of (B-A)= 18% of (A+B), then the ratio A:B will be
Answers
Answer:
1:4
Step-by-step explanation:
30% of (B - A) = 18% of (A + B)
0.3(B - A) = 0.18(A + B) (converting percentages to decimals)
0.3B - 0.3A = 0.18A + 0.18B (distributing on both sides)
0.3B - 0.18B = 0.18A + 0.3A (grouping like terms)
0.12B = 0.48A
Simplifying further gives:
B/A = 0.48/0.12 = 4/1
Therefore, the ratio of A:B is 1:4.
Let's start by simplifying the given equation:
30% of (B-A) = 18% of (A+B)
0.3(B-A) = 0.18(A+B)
0.3B - 0.3A = 0.18A + 0.18B
0.12B = 0.48A
B = 4A
Now we know that B is 4 times A.
To find the ratio A:B, we can express B in terms of A:
B = 4A
A:B = A/4A = 1/4
Therefore, the ratio A:B is 1:4.
Answer the following questions
Answers
Mrs. Thomas made 31⁄2 gallons of tea for the family reunion. She estimates that each of the 17 family members will drink about 3 cups of tea that day. Did she prepare enough?
Answers
Step by step
There are 16 cups in 1 gallon
3.5 gallons tea made x 16 cups per gallon = 56 cups total tea made
17 family members will drink 3 cups each
17 x 3 = 51 cups she needs for the reunion
So yes, she made 56 cups and only needs 51 so she made enough
Plsss help this is hard giving 20 pnts!!!
Answers
Answer:I need part A to answer
Step-by-step explanation:
what’s the value of x and y?
Answers
Answer:
the answer os 53
Step-by-step explanation:
1. Order the following rational numbers from least to greatest: -5/6, -0.2001, 20%, -78
Answers
Answer:
-78, -5/6, -0.2001, 20%
Step-by-step explanation:
The first step is to convert all of the numbers into the same form. In this case, it is easiest to use decimal form.
-5/6 = -0.8333...
-0.2001
20% = 0.2
-78
-78 is the smallest by far
-0.8333... is the next smallest
-0.2 is next
and 0.2 is the largest
Please answer this question, I’ll give brainliest, and no chat gpt
Q7. A 230 kg piano must be lifted onto a stage that is 1.7 m high.
(a) If the piano is lifted straight up by some very strong people, how much force must they apply? [2 marks]
(b) How much work have they done? [2 marks]
(c) If the stage-crew only need to apply a force of 300 N to get the piano onto the stage if they use a 15 m ramp. How much work is done using the ramp? [2 marks]
(d) What is the efficiency of the ramp? [2 marks]
(e) You should notice that the force needed to lift the piano in A is larger than the force needed to lift the piano in C. How is it possible that the piano can be raised with much less force when the incline is used? (In other words, what is the "trade-off" of using an inclined ramp?) [2 marks]
Answers
1. The force they must apply is 2256.3 N
2. The amount of work done = 3835.71 J
3. The work done using the ramp = 4500 J
4. The efficiency of the ramp = 85.24%
5. When the people use inclined ramp, they don't have worry about the gravitational force that is acting on the piano. The trade off with with less force, the ramp is able to cover more distance.
How do we find force applied, work done, and efficiency of ramp?1. To find force applied, used the formula; F = mg
230 x 9.8N
=2256.3N
2. To find the amount of work done, we use the formula;
W = Fd
2256.3 x 1.7 m
= 3835.71J
3. o calculate the work done using the ramp, you use the same formula you used in step 2
300N x 15m
= 4500J
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Can someone explain to me how to find x?
Answers
Answer:
x° = 36°
Step-by-step explanation:
You want to find the angle between a secant and a tangent to a circle, where the intercepted arcs are 126° and 54°.
Exterior angleThe angle at D, labeled x°, is half the difference of the intercepted arcs:
x° = (126° -54°)/2 = 72°/2
x° = 36°
__
Additional comment
The same relationship applies for the angle between two secants.
This is easy to prove by considering triangle ADE. Angle DAE is half of arc CE. The exterior angle to the triangle at E is half of arc AE. That exterior angle is equal to the sum of the remote interior angles at D and A:
AE/2 = x° + CE/2 ⇒ x° = (AE -CE)/2
The weatherman predicted that today's temperature would be 64°F. It was actually 38°F. What was the percent error of the weatherman's
prediction?
A 68.42%
B
40.63%
C 42.55%
D 64.82%
Answers
Answer:
Step-by-step explanation:
B. 40.63
Answer:
Step-by-step explanation:
B. 40.63
7
7
?
?
Find the arc length of the partial circle.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.14, point, 3.14 for
π
πpi and enter your answer as a decimal.
units
Answers
According to given information, the arc length of a partial circle is 14.67 units.
What is partial circle?A partial circle is a portion of a circle, usually defined by an angle that is less than 360 degrees.
According to given information:To find the arc length of a partial circle, we need to know the measure of the central angle, θ, in radians.
Let's say that the central angle of the partial circle is 2π/3 radians, which corresponds to an angle of 120 degrees.
Then, the arc length, denoted by L, can be calculated using the formula:
L = rθ
where r is the radius of the circle.
Plugging in the values we have, we get:
L = 7(2π/3)
L = (14/3)π
Using 3.14 for π, we get:
L ≈ 14.67 units (rounded to two decimal places)
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You have a credit card with a current balance of $1500. The interest rate is 15.99%. If your minimum payment is 15% of your new balance, what is the balance of your card month 24? If your minimum payment is $75, what is the balance of your card month 24?
Answers
a) If the minimum payment is 15% on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,291.99.
b) If the minimum payment is $75 on a credit card with a current balance of $1,500 and an interest rate of 15.99%, the balance of the card at month's end is $1,293.99.
What is the credit card balance?The credit card balance refers to the difference between the beginning balance, payments, and interests.
a) Current balance on a credit card = $1,500
Interest rate = 15.99%
Minimum payment = 15%
= $225 ($1,500 x 15%)
Interest = $16.99 ($1,500 - $225 x 15.99% x 1/12)
Ending Balance = $1,291.99 ($1,500 +$16.99 - $225)
b) Current balance on a credit card = $1,500
Interest rate = 15.99%
Minimum payment = $75
Interest = $18.99 ($1,500 - $75 x 15.99% x 1/12)
Ending Balance = $1,293.99 ($1,500 +$18.99 - $225)
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Look at the simultaneous equations below. (1) 18 = 7x - y (2) 3x + y = 2 a) Rearrange equation (1) to make y the subject. b) Using your answer to part a), solve the simultaneous equations ck to task Watch video
Answer:
Explanation:
Answers
The solution to the simultaneous equations is x = 2 and y = -4. To obtain these values, 18 = 7x - y is rearranged to y = 7x - 18, and then substituted into 3x + y = 2 to obtain the value of x and y.
Rearranging equation (1) to make y the subject
18 = 7x - y
Add y to both sides
18 + y = 7x
Subtract 18 from both sides
y = 7x - 18
Using the answer to part a) to solve the simultaneous equations
Substitute the expression for y from equation (1) into equation (2)
3x + (7x - 18) = 2
Simplify
10x - 18 = 2
Add 18 to both sides
10x = 20
Divide both sides by 10
x = 2
Substitute x = 2 into equation (1) to find y
18 = 7(2) - y
18 = 14 - y
Subtract 14 from both sides
4 = -y
Multiply both sides by -1
-4 = y
Therefore, the solution to the simultaneous equations is x = 2 and y = -4.
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Given f(x)=x−1‾‾‾‾‾√ and g(x)=12x+5, what is the value of (f∘g)(2)?
Enter your answer in the box.
Answers
If f(x)= √(x−1) and g(x)=12x+5, then the value of (f∘g)(2) is 2√7.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
To find the value of (f∘g)(2), we first need to evaluate g(2), and then use the result as the input for f.
So,
g(2) = 12(2) + 5 = 24 + 5 = 29
Now, we use the value g(2) = 29 as the input for f:
f(g(2)) = f(29)
Since f(x) = √(x-1), we have:
f(29) = √(29-1) = √28 = 2√7
Therefore, the value of (f∘g)(2) is 2√7.
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$900 is deposited in an account with 4%
interest rate, compounded continuously.
What is the balance after 10 years?
F = $[?]
Answers
Answer:
[tex]\$1342.64[/tex]
Step-by-step explanation:
We can represent the value [tex]A[/tex] of a quantity [tex]P[/tex] compounded continuously for [tex]t[/tex] years at [tex]r[/tex] rate of interest as:
[tex]A = P\cdot e^{rt}[/tex]
This formula uses the mathematical constant [tex]e[/tex] (approx. 2.72), which is the theoretical limit for continuous compounding.
Plugging the given values into the formula:
[tex]A = \$900 \cdot e^{(0.04 \, \cdot \, 10)}[/tex]
We can now solve for [tex]A[/tex].
↓ simplifying [tex]e[/tex]'s exponent
[tex]A = \$900 \cdot e^{0.4}[/tex]
↓ plugging into a calculator
[tex]A \approx \$1342.64222788[/tex]
↓ rounding to the nearest cent
[tex]\boxed{A \approx \$1342.64}[/tex]
The mean score, overbar(x), on an aptitude test for a random sample of 5 students was 73. Assuming that σ = 15, construct a 95.44% confidence interval for the mean score, μ, of all students taking the test.
Question 14 options:
A)
67.0 to 79.0
B)
59.6 to 86.4
C)
43 to 103
D)
62.9 to 83.1
Answers
The 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.
What is confidence interval?A confidence interval is a range of values that is calculated from a sample of data. It provides a level of certainty, usually expressed as a percentage, that a population parameter lies within this range. It is used to estimate a population parameter, such as a mean, a proportion, or a difference between two means.
The 95.44% confidence interval for the mean score, μ, of all students taking the test can be calculated using the formula:
Confidence Interval = overbar(x) ± (1.96 x (σ/√n))
where overbar(x) is the mean score on the aptitude test, σ is the standard deviation of the population (15 in this case), and n is the sample size (5 in this case).
Plugging in the given values, we get:
Confidence Interval = 73 ± (1.96 x (15/√5))
= 73 ± (1.96 x 3)
= 73 ± 5.88
Therefore, the 95.44% confidence interval for the mean score, μ, of all students taking the test is 59.6 to 86.4.
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