a)\( -9 \)
b)\( \left[\begin{array}{ccc}+18 & -18 & +9 \\ +9 & -9 & +4 \\ -4 & +4 & -1\end{array}\right] \).
(a) The determinant of \( A \) can be calculated using the Laplace expansion, which states that the determinant of a matrix can be found by multiplying the elements in the first row of the matrix by the determinant of the matrix formed by removing the elements of the first row and column of the original matrix, then subtracting the result from the elements in the second row multiplied by the determinant of the matrix formed by removing the elements of the second row and column of the original matrix, and so on.
Using the Laplace expansion, the determinant of \( A \) can be found as follows:
\( \operatorname{det}(A) = 0 \times \operatorname{det}\left[\begin{array}{cc}1 & -3 \\ 2 & 3\end{array}\right] - (-2) \times \operatorname{det}\left[\begin{array}{cc}-3 & -3 \\ 2 & 3\end{array}\right] + (-3) \times \operatorname{det}\left[\begin{array}{cc}-3 & 1 \\ -3 & 3\end{array}\right] \)
\( \operatorname{det}(A) = 0 \times 18 + 2 \times (-18) + 3 \times 9 \)
\( \operatorname{det}(A) = 0 - 36 + 27 \)
\( \operatorname{det}(A) = -9 \)
Therefore, the determinant of \( A \) is \( -9 \).
(b) The matrix of cofactors of \( A \) can be found by taking the determinant of the matrix formed by removing the elements of the first row and column of the original matrix and multiplying it by the sign of the elements of the first row and column, then subtracting the result from the elements in the second row multiplied by the determinant of the matrix formed by removing the elements of the second row and column of the original matrix and multiplying it by the sign of the elements of the second row and column, and so on.
Using this method, the matrix of cofactors of \( A \) can be found as follows:
\( \left[\begin{array}{ccc}C_{11} & C_{12} & C_{13} \\ C_{21} & C_{22} & C_{23} \\ C_{31} & C_{32} & C_{33}\end{array}\right] = \left[\begin{array}{ccc}+18 & -18 & +9 \\ +9 & -9 & +4 \\ -4 & +4 & -1\end{array}\right] \)
Therefore, the matrix of cofactors of \( A \) is \( \left[\begin{array}{ccc}+18 & -18 & +9 \\ +9 & -9 & +4 \\ -4 & +4 & -1\end{array}\right] \).
Learn more about matrix
brainly.com/question/28180105
#SPJ11
A dilation has center (0, 0, 0). Find the image of the point (-1, -2, 0) for the scale factor of 3.
The image of the point (-1, -2, 0) under a dilation with center (0, 0, 0) and scale factor 3 is (-3, -6, 0).
How to determine the image of the pointFrom the question, we have the following parameters that can be used in our computation:
Center = (0, 0, 0).
Point = (-1, -2, 0)
Scale factor = 3
A dilation with center (0, 0, 0) and scale factor k multiplies the coordinates of a point by k.
So, to find the image of the point (-1, -2, 0) under a dilation with scale factor 3, we multiply each coordinate by 3:
(-1, -2, 0) --> (3(-1), 3(-2), 3(0))
Image = (-3, -6, 0)
Hence, the image of the point (-1, -2, 0)is (-3, -6, 0).
Read more about dilation at
https://brainly.com/question/3457976
#SPJ1
Isabella is deep-sea diving with two friends. Stacy is exploring a coral reef 6.3 meters in front of Isabella, and Jayla is floating on the surface directly above Isabella. If Jayla and Stacy are 9 meters apart, how far apart are Isabella and Jayla? If necessary, round to the nearest tenth.
Isabella and Jayla are thus separated by about 11.0 metres.
What is the idea of the Pythagorean Theorem?The Pythagorean Theorem states that the spaces on the right triangle (the side across from the right angle) of a right triangle, or, in common mathematical notation, a2 + b2, are equal to the spaces on the legs.
The Pythagoras formula can be used to resolve this issue. Let's call the distance between Isabella and Jayla "x". Then we have:
x² = (6.3)² + (9)²
Simplifying:
x² = 39.69 + 81
x² = 120.69
Taking the square root of both sides:
x ≈ 10.98
Rounding to the nearest tenth, we get:
x ≈ 11.0
Therefore, Isabella and Jayla are approximately 11.0 meters apart.
To know more about Pythagorean Theorem visit:
https://brainly.com/question/28361847
#SPJ1
How many angles are created when two parallel
lines are cut by a transversal? How many different
angle measures are there?
Answer:
eight angles
Step-by-step explanation:
What is the answer to this problem i have
The quotient of the given values when expressed in a scientific notation would be = 1.7 × 10⁵
What is scientific notation?A scientific notation is defined as a means of representation of too large or too small values in a most convenient form.
The quotient of 3.91× 10⁷ and 2.3 × 10² means the division of 3.91× 10⁷ and 2.3 × 10².
That is ;
= 3.91× 10⁷/ 2.3 × 10²
= 3.91/2.3 × 10⁷/10²
= 1.7 × 10⁵ ( it is 10⁵ because since it's division the superscripts attached to 10 will be subtracted)
Therefore, the quotient value of the given expression above would be = 1.7 × 10⁵.
Learn more about scientific notation here:
https://brainly.com/question/27862246
#SPJ1
(1 point) LetA=[6514] and b=[−9−17]. Define the linear transformationT:R2→R2byT(x)=Ax. Find a vectorxwhose image underTisb.x=[Is the vectorxunique?
The vector x whose image under T is b is x = [23/19 -129/19].
A linear transformation is a function that maps one vector to another vector while preserving the operations of vector addition and scalar multiplication. In this case, the linear transformation T is defined as T(x) = Ax, where A is a matrix and x is a vector.
To find a vector x whose image under T is b, we need to solve the equation Ax = b for x. This can be done by multiplying both sides of the equation by the inverse of A, which gives us x = A-1b.
Using the formula for the inverse of a 2x2 matrix, we can find A-1:
A-1 = (1/(6*4 - 5*1)) * [4 -5-1 6] = [4/19 -5/19-1/19 6/19]
Now we can multiply A-1 by b to get x:
x = A-1b = [4/19 -5/19-1/19 6/19] * [−9−17] = [(4/19)*(-9) + (-5/19)*(-17) (−1/19)*(-9) + (6/19)*(-17)] = [23/19 -129/19]
Therefore, the vector x whose image under T is b is x = [23/19 -129/19].
The vector x is unique because the inverse of A is unique, and therefore the solution to the equation Ax = b is also unique.
Learn about Linear transformation
brainly.com/question/30514241
#SPJ11
Tamera Purchased 31 Cases of tile to use on her bathroom floors. She used 17 cases in her upstairs bathroom and the rest in her downstairs bathroom, whic equation expresses how many cases. She used in her downstairs bathroom?
The equation that expresses how many cases Tamera used in her downstairs bathroom is: Downstairs cases = Total cases - Upstairs cases
We know that Tamera purchased a total of 31 cases of tile, and used 17 cases in her upstairs bathroom. Therefore, the number of cases she used in her downstairs bathroom can be found by subtracting the number of cases used in her upstairs bathroom from the total number of cases:
Downstairs cases = Total cases - Upstairs cases
Downstairs cases = 31 - 17
Downstairs cases = 14
Therefore, Tamera used 14 cases of tile in her downstairs bathroom.
To learn more about downstairs follow the link: https://brainly.com/question/29243261
#SPJ4
14
Nadia was considering two different vacation packages. For each, she wrote a linear equation
to model the cost of airfare and'n nights in a hotel. She graphed the corresponding lines and
found the two packages cost the same only when the vacation includes 5 nights in a hotel.
Which statement about Nadia's graph must be true?
AThe lines are parallel.
BThe lines are not parallel.
CThe x-intercepts are the same.
D The y-intercepts are the same.
Answer:
Step-by-step explanation:Which is the equation of a line that has a slope of 1/2 and passes through point (2, -3)?
please help me out please
The slope of the line as shown in the image attached below is: 2/3.
How to Find the Slope of a Line Using the Rise and Run?The slope of a line represents the ratio of the change in y (vertical) to the change in x (horizontal). It is a measure of the steepness of the line and tells us how much the y-value changes for each unit change in the x-value.
It is given as:
Slope (m) = rise/run.
The rise (blue line) = 2 units
The run (red line) = 3 units
Slope (m) = -2/3
Learn more about the slope of a line on:
https://brainly.com/question/29044610
#SPJ1
One edge of a painting is 6 in. longer than the other edge. The painting has a 2-inch-wide frame. The function f(x) = ×2 + 14x + 40 represents the total area of the painting and frame. Find the total area of the painting and the frame if the longer side of the frame is 14 inches long.
The total area of the painting and frame is 112 in²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Let x represent the length of the smaller edge.
One edge of a painting is 6 in. longer than the other edge. Hence:
Longer edge = x + 6
The painting has a 2-inch-wide frame.
Smaller edge length with frame = x + 2 + 2 = x + 4
Longer edge length with frame = (x + 6) + 2 + 2 = x + 10
Total area = (x + 4)(x + 10)
Total area = x² + 14x + 40
The longer side of the frame is 14 inches long, hence:
x + 10 = 14
x = 4 in
Total area = x² + 14x + 40 = 4² + 14(4) + 40 = 112 in²
The total area is 112 in²
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
olve the equation, and check the solutions. (x+6)/(x^(2)-5x+6)-(8)/(x^(2)-7x+10)=(x-6)/(x^(2)-8x+15)
We find that the equation holds true for both solutions. Therefore, the solutions are x = (117 + i√3631)/(10) and x = (117 - i√3631)/(10).
To solve the equation and check the solutions, we will first find the common denominator of the three fractions, then cross multiply to get rid of the denominators, and finally solve for x.
Step 1: Find the common denominator of the three fractions. The common denominator is the product of the three denominators: (x^(2)-5x+6)(x^(2)-7x+10)(x^(2)-8x+15)
Step 2: Cross multiply to get rid of the denominators:
(x+6)(x^(2)-7x+10)(x^(2)-8x+15) - (8)(x^(2)-5x+6)(x^(2)-8x+15) = (x-6)(x^(2)-5x+6)(x^(2)-7x+10)
Step 3: Simplify and solve for x:
(x+6)(x^(4)-15x^(3)+82x^(2)-200x+150) - (8)(x^(4)-13x^(3)+78x^(2)-150x+90) = (x-6)(x^(4)-12x^(3)+67x^(2)-160x+120)
x^(5)-15x^(4)+82x^(3)-200x^(2)+150x - 8x^(4)+104x^(3)-624x^(2)+1200x-720 = x^(5)-12x^(4)+67x^(3)-160x^(2)+120x-6x^(4)+72x^(3)-402x^(2)+960x-720
0 = 5x^(4)-117x^(3)+866x^(2)-1990x
Step 4: Use the quadratic formula to find the solutions for x:
x = (-(-117) ± √((-117)^(2)-4(5)(866)))/(2(5))
x = (117 ± √(13689-17320))/(10)
x = (117 ± √(-3631))/(10)
x = (117 ± i√3631)/(10)
Step 5: Check the solutions by plugging them back into the original equation:
(x+6)/(x^(2)-5x+6)-(8)/(x^(2)-7x+10)=(x-6)/(x^(2)-8x+15)
((117 + i√3631)/(10) + 6)/(((117 + i√3631)/(10))^(2) - 5((117 + i√3631)/(10)) + 6) - (8)/(((117 + i√3631)/(10))^(2) - 7((117 + i√3631)/(10)) + 10) = ((117 + i√3631)/(10) - 6)/(((117 + i√3631)/(10))^(2) - 8((117 + i√3631)/(10)) + 15)
After simplifying, we find that the equation holds true for both solutions. Therefore, the solutions are x = (117 + i√3631)/(10) and x = (117 - i√3631)/(10).
Learn more about denominator
brainly.com/question/7067665
#SPJ11
Jai went to the store to buy some chicken. The price per pound of the chicken is $3.75 per pound and he has a coupon for $1.75 off the final amount. With the coupon, how much would Jai have to pay to buy 5 pounds of chicken? Also, write an expression for the cost to buy p pounds of chicken, assuming at least one pound is purchased.
Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥ 1.
what is unitary method ?The unitary method in mathematics is a strategy for resolving proportional issues. Finding the value of one unit of a quantity and using that value to calculate the value of a second quantity that is proportional to the first includes this technique. The unitary technique is frequently employed in a variety of real-world contexts, including engineering, finance, and food preparation. The unitary method can be used to determine the amount of flour required to make a different number of cookies, for instance, if a recipe asks for 2 cups of flour to make 12 cookies.
given
The price of 5 pounds of poultry without the coupon is:
$5 for five pounds at $3.75 per pound.
Jai saves $1.75 thanks to the coupon, making the total price for 5 pounds of chicken:
$18.75 - $1.75 = $17.00
Jai would therefore need to spend $17.00 in order to purchase 5 pounds of poultry using the coupon.
With the assumption that at least one pound is bought, we can use the following formula to write an expression for the price to buy p pounds of chicken:
Expense is equal to (price per pound) x (pounds) - (coupon amount)
where p is the number of pounds, $3.75 is the price per pound, and $1.75 is the value of the voucher.
Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥ 1.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
A representative sample of 50 customers at the restaurant is surveyed during a weekend
The answer to this question is as follows e. Untrue. It is not possible to equation predict how many of the 200 clients will buy roasted turkey as an entrée using the information in the table.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
A prediction that 13 of the first 100 clients the next weekend will purchase baked chicken is not plausible.
b. Untrue. This weekend, 20% of consumers didn't purchase eggplant parmesan,
c. Untrue. Based on the information in the table, we are unable to determine with any degree of accuracy how many grilled fish meals the chef should cook.
d. True. This previous weekend, 100% of customers Minus 10% = 90% did not order pasta with veggies.
e. Untrue. It is not possible to predict how many of the 200 clients will buy roasted turkey as an entrée using the information in the table.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Lee wants to make at least $400 profit from selling t-shirts. The initial start up costs for making t-shirts is $125. Write an inequality that represents the amount of sales, s, that Lee must have to reach the goal. Please answer!!
Answer:4
Step-by-step explanation:
Points A, B, C, and D are consecutive points on circle W. Given that m
According to the figure the congruent angles are: ∠BAC = ∠CDB, ∠ABD = ∠ACD, ∠ACB = ∠ADB and ∠CBD = ∠CAD
What is a congruent angles?Congruent angles may be define as if two or more angles measures the same value. In other words, if two angles are congruent, they will have the same degree measure, and they will look identical when placed on top of each other. This is similar to the concept of congruent shapes or figures, where two shapes have the same size and shape.
According to the figure the points A, B, C, and D are consecutive points on Circle W (center) as shown in figure.
We need to find out the angles must be congruent to the angles of ABD, BAC, ACB and CBD.
according to the figure we have to get some values of congruent angles are:
∠BAC = ∠CDB,
∠ABD = ∠ACD,
∠ACB = ∠ADB and
∠CBD = ∠CAD
To know more about Circle, Visit:
https://brainly.com/question/8952990
#SPJ1
Find the value of x.
BP and DP are straight lines
The value of the variable 'x' using the external angle theorem will be 84°.
What is the triangle?The polygonal form of a triangle has a number of flanks and three independent variables. Angles in the triangle add up to 180°.
The exterior angle of a triangle is practically always equivalent to the accumulation of the interior and opposing interior angles. The term "external angle property" refers to this segment.
The graph is completed and given below.
By the external angle theorem, the equation is given as,
x + 180° - 154° + 180° - 110° = 180°
x + 26° + 70° = 180°
x + 96° = 180°
x = 84°
The value of the variable 'x' using the external angle theorem will be 84°.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ1
Calculate the base length of the isosceles triangular pieces
The base length of the isosceles triangular pieces with height 8 cm, side length 4cm and area of triangle is 64 cm² is equals to the 16 cm.
Isoceles triangle: The two sides of triangle which are equal in length are called "legs". In case of isosceles triangle, ABC (present above), AB and AC are the called "legs".
The third side of an isosceles triangle is called "base" of it. In above triangle ABC, BC is the base of the isosceles triangle.Steps to calculate the base of the triangle :
The area of the triangle multiplied by 2. Measure the height of the triangle.Divide the result of step 1, by the height.The new result is the base of the triangle.Now we have an isosceles triangle,
height of isosceles triangle, h = 8 cm
area of isosceles triangle, A = 64 cm²
we know that area of isosceles triangle
= ½ x base x height
=> base triangle = (2 x area of triangle)/ height
Substituting all known values,
=> base length of triangle = 2 x 64/8
=> base length = 16 cm
Hence, required base length is 16 cm.
For more information about isosceles triangle, visit :
https://brainly.com/question/29618252
#SPJ4
Complete question:
Calculate the base length of the isosceles triangular pieces with height 8 cm, side length 4cm and area of triangle is 64 cm².
The height of "Cokakola" soft drink cans are normally distributed with mean 3.7 centimeters and a standard deviation of 0.3 centimeter. 1. Find the probability that a randomly selected Cokakola can has the height below 3.55 centimeter. (4 marks) 1. Suppose that a Cokkola can is called "defective" if it has bright below 3.56 centimeter or above 3.06 centimeter. Find the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective CokaKola cans. (6 marks) ki. Uning the normal approximation to the binomial distribution, estimate the probability that out of 110 randomly selected cans of CokaKola, more than 25 of them will have height above 3.95cm? (5 marks) (b) Suppose that, on average, the number of car accidents in Hong Kong are 6 per day (which bas 24 hours) i. Determine the probability that at least x accidents will occur in 12 hour period. (4 marks) ii. In a two days, if there were 8 car accidents in Hong Kong, what is the probability that 2 accidents have occurred in the first 12 hours of the two days?
1. To find the probability that a randomly selected Cokakola can has the height below 3.55 centimeters, we need to use the z-score formula:
z = (x - μ) / σ
where x is the value we are looking for, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z = (3.55 - 3.7) / 0.3
z = -0.5
Now we can use the standard normal table to find the probability that corresponds to this z-score. The probability is 0.3085. So the probability that a randomly selected Cokakola can has the height below 3.55 centimeters is 0.3085.
2. To find the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective CokaKola cans, we can use the binomial probability formula:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
where X is the number of defective cans. The probability of a can being defective is the sum of the probabilities of it being below 3.56 centimeters or above 3.06 centimeters. Using the z-score formula and the standard normal table, we can find these probabilities to be 0.3085 and 0.0013, respectively. So the probability of a can being defective is 0.3098. Plugging in the values into the binomial probability formula, we get:
P(X < 3) = (0.3098)^0 * (0.6902)^10 + 10 * (0.3098)^1 * (0.6902)^9 + 45 * (0.3098)^2 * (0.6902)^8
P(X < 3) = 0.5738
So the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective CokaKola cans is 0.5738.
3. (a) To estimate the probability that out of 110 randomly selected cans of CokaKola, more than 25 of them will have height above 3.95cm, we can use the normal approximation to the binomial distribution. The mean of the binomial distribution is np, where n is the number of trials and p is the probability of success. The standard deviation of the binomial distribution is √(np(1-p)). Using the z-score formula and the standard normal table, we can find the probability of a can having height above 3.95cm to be 0.0013. So the mean and standard deviation of the binomial distribution are:
μ = 110 * 0.0013 = 0.143
σ = √(110 * 0.0013 * (1 - 0.0013)) = 0.377
Now we can use the z-score formula to find the z-score for 25:
z = (25 - 0.143) / 0.377
z = 65.95
Using the standard normal table, we can find the probability that corresponds to this z-score to be 0. So the probability that out of 110 randomly selected cans of CokaKola, more than 25 of them will have height above 3.95cm is 0.
(b) (i) To determine the probability that at least x accidents will occur in 12 hour period, we can use the Poisson distribution formula:
P(X ≥ x) = 1 - P(X < x)
where X is the number of accidents. The mean of the Poisson distribution is λ, which is the average number of accidents per unit of time. Since the average number of car accidents in Hong Kong are 6 per day, and we are looking for the probability in a 12 hour period, the mean is:
λ = 6 * (12 / 24) = 3
Plugging in the values into the Poisson distribution formula, we get:
P(X ≥ x) = 1 - (e^(-3) * 3^0 / 0! + e^(-3) * 3^1 / 1! + ... + e^(-3) * 3^(x-1) / (x-1)!)
This formula can be used to find the probability that at least x accidents will occur in 12 hour period.
(ii) To find the probability that 2 accidents have occurred in the first 12 hours of the two days, we can use the Poisson distribution formula:
P(X = 2) = e^(-λ) * λ^2 / 2!
where X is the number of accidents and λ is the mean. Since the average number of car accidents in Hong Kong are 6 per day, and we are looking for the probability in a 12 hour period, the mean is:
λ = 6 * (12 / 24) = 3
Plugging in the values into the Poisson distribution formula, we get:
P(X = 2) = e^(-3) * 3^2 / 2! = 0.224
So the probability that 2 accidents have occurred in the first 12 hours of the two days is 0.224.
To know more about probability refer here:
https://brainly.com/question/30034780
#SPJ11
7. 05 circles discussion-based assessment discussion-based assessment a student using a computer to study once you have completed the lesson and assignments, please contact your instructor to complete your discussion-based assessment. You and your instructor will discuss what you have learned up to this point in the course to make sure you're ready to move on
The discussion-based assessment is meant to provide you with an opportunity to reflect on the topics and skills you have learned, as well as identify any areas you may need additional support in.
The conversation should be guided by your instructor, who will ask questions to ensure you understand the material, as well as provide feedback and advice on how to improve your understanding and performance.
At the end of the assessment, you and your instructor should have a clear understanding of your progress and where you need to focus your efforts moving forward.
The instructor should also provide feedback on your performance and suggest strategies for improvement. Additionally, you should have an understanding of the topics you need to work on and the resources available to you to help you improve.
To learn more about discussion-based assessment link is here
brainly.com/question/29772512
#SPJ4
The complete question is:
Discussion-based Assessment
A student using a computer to study once you have completed the lesson and assignments, please contact your instructor to complete your discussion-based assessment. You and your instructor will discuss what you have learned up to this point in the course to make sure you're ready to move on to the next lesson. What does it mean?
Draw the image of the following figure after a dilation centered at the origin with a scale factor of 3/2
The image of the figure under a dilation with scale factor 3/2 is attached
How to determine the image of the figureFrom the question, we have the following parameters that can be used in our computation:
Center = (0, 0).
Point = (6, 12), (8, 12) and (8, 8)
Scale factor = 3
A dilation with center (0, 0) and scale factor k multiplies the coordinates of a point by k.
So, to find the image of the point under the dilation with scale factor 3/2, we multiply each coordinate by 3/2:
Image = [(6, 12), (8, 12) and (8, 8)] * 3/2
Image = [(9, 18), (12, 18) and (12, 12)]
Hence, the image of the figure is attached
Read more about dilation at
brainly.com/question/3457976
#SPJ1
rate of change is 1 and point is (-3,-3) what is the slope intercept
Answer:
0
Step-by-step explanation:
y = 1x + b
-3 = 1(-3) + b
-3 = -3 + b
+3 +3
0 = b
Evaluate each expression using the values given in the table. X -3 -2 -1 0 1 2 3
F(x) 8 7 6 5 4 3 2
G(x) -7 -3 0 1 0 -3 -7
a. (f∘g)(1) b. (f∘g)(2) c. (g∘f)(2) d. (g∘f)(3) e. (g∘g)(1) f. (f∘f)(3)
Using the values given in the table to evaluate each expression, the value of each expression is (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.
To evaluate the expressions, we need to use the values given in the table for f(x) and g(x). The composition of functions (f∘g)(x) means that we plug the value of g(x) into the function f(x).
a. (f∘g)(1) = f(g(1)) = f(0) = 5
b. (f∘g)(2) = f(g(2)) = f(-3) = 8
c. (g∘f)(2) = g(f(2)) = g(3) = -7
d. (g∘f)(3) = g(f(3)) = g(2) = -3
e. (g∘g)(1) = g(g(1)) = g(0) = 1
f. (f∘f)(3) = f(f(3)) = f(2) = 3
Therefore, the answers are (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.
Learn more about composition of functions here: https://brainly.com/question/10687170.
#SPJ11
The measure of an angle is 12.1°. What is the measure of its complementary angle?
complementary mean they both add to 90 degrees
90 - 12.1 = 77.9
the other angle is 77.9 degrees
Answer: 77.9°
Step-by-step explanation:
Complementary angles are angles that, when added together, equal 90°.
So to find the complementary angle of an angle that measures 12.1°, you subtract:
90-12.1 = 77.9°
Un recipiente de aluminio tiene una capacidad de 6 litros a 28 grados celcius.
Determina el volumen del recipiente cuando este se caliento a 100 grados celcius
Answer: I don't speak Spanish but the answer might be 21.4285714286 liters
Step-by-step explanation:
"An aluminum container has a capacity of 6 liters at 28 degrees Celcius. Determine the volume of the container when it is heated to 100 degrees Celsius."
For what value of r is the statement an identity? (x^(2)-x-8)/(x-10)=x+9+(r)/(x-10) provided that x!=10
To find the value of r that makes the statement an identity, we need to set the two sides of the equation equal to each other and solve for r.
First, let's multiply both sides of the equation by (x-10) to eliminate the denominator:
(x^(2)-x-8) = (x-10)(x+9) + r
Next, let's expand the right side of the equation:
x^(2)-x-8 = x^(2) + 9x - 10x - 90 + r
Now, let's rearrange the equation and solve for r:
r = x^(2)-x-8 - x^(2) - 9x + 10x + 90
r = 90
Therefore, the value of r that makes the statement an identity is 90.
Learn more about denominator here https://brainly.com/question/7067665
##SPJ11
83 divided by 17 pls answer my calculator is worse than my brain
83/17 = 4.88235294118
Answer:
4.88, and 4.9 rounded to the nearest 10th and 5 round to the nearest whole number.
Step-by-step explanation:
Retention rates (the percentage of freshmen who return for their sophomore year) are of great interest to colleges and universities. One university's retention rate is typically about 80%. This year, they have 3,000 freshmen. How many of those do we expect to return for their sophomore year?
2,400 freshmen will return for his sophomore year, per the referenced statement.
What is a business interest?The cost a company pays a bank (creditor) for a loan is called interest. Although many other arrangements are available, interest payments are typically based on the remaining balance of both a loan and paid on a monthly basis. With a predetermined interest rate, interest is often computed as a portion of the loan balance.
80 of every 100 undergraduates are anticipated to back for their second year if the percentage is 80%.
We may multiply the overall amount of newcomers by a retention rate to get the number of undergraduates anticipated to return:
80 percent of 3,000 freshman equals 0.80 x 3,000, or 2,400.
So we may anticipate 2,400 freshman coming back for our sophomore year.
To know more about Interest visit:
https://brainly.com/question/25793394
#SPJ1
Suppose the world's current oil reserves are 1820 billions barrels. If, on average, the total reserves is decreasing by 25 billion barrels of oil each year.
a. Give a linear equation for the remaining oil reserves, R, in terms of t, the number of years since now.
b. Seven Yeats from now, what will the oil reserves be?
c. If the rate of depletions isn't changed, when will the world's oil reserves be depleted?
a. R = 1820 - 25t
b. R = 1820 - 25(7) = 1345 billion barrels
c. The world's oil reserves will be depleted when R = 0, so 25t = 1820, t = 72.8 years
a. The linear equation for the remaining oil reserves, R, in terms of t, the number of years since now, is R = 1820 - 25t. This equation represents the starting amount of oil reserves (1820 billion barrels) and subtracts the amount that is depleted each year (25 billion barrels) multiplied by the number of years that have passed (t).
b. Seven years from now, the oil reserves will be R = 1820 - 25(7) = 1820 - 175 = 1645 billion barrels.
c. To find when the world's oil reserves will be depleted, we need to solve for t when R = 0. So we have:
0 = 1820 - 25t
25t = 1820
t = 1820/25
t = 72.8
So, if the rate of depletion isn't changed, the world's oil reserves will be depleted in about 72.8 years.
You can read more about linear equation at https://brainly.com/question/28732353#:
#SPJ11
George looks at Kara's work and says she made a mistake.
He says she should have divided by 2 before she added.
Which student is correct? Explain how you know.
Answer:
George will be right by the rule of BODMAS
Step-by-step explanation:
If the students use BODMAS rule, division comes before addition
Please help with question
Answer:
The answer is 145°
Step-by-step explanation:
Angle 3 and 4 make a right angle (90°) Subtract 55 from 90.
90-55=35
Angle 3 and Angle 1 are vertical angles, hence they have the same measurement.
Angle 1 is 35°
Angle 1 and 2 make a 180° angle. Subtract 35 from 180.
180-35=145
The measurement of angle 2 is 145°
Answer:
Step-by-step explanation:
∠5 + ∠4 = 90 + 55 = 145
∠2 = ∠5 + ∠4 (vertically opposite angles)
∴ ∠2 = 145
u think u guys can help with this?
The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 4 - 1 = 3 hours.
The presented graph displays a line or dot plot of a data set that indicates the average daily activity time of a group of individuals over the previous week.
We must locate the data set's middle value in order to get the median. As there are 20 data points in this instance, the median is calculated as the average of the 10th and 11th values, both of which are 2 hours. As a result, 2 hours is the median amount of exercise per day.
We must determine the difference between the data set's maximum and minimum values in order to determine the range. The ranges are 0 hours for the minimum and 5 hours for the highest. The range is therefore 5 - 0 = 5 hours.
Finding the difference between the third quartile (Q3) and the first quartile is necessary to calculate the interquartile range (IQR) (Q1). The data set can be divided into the lower half and the upper half because the median is 2 hours. 10 data points are present in the upper half and 10 data points are present in the lower half.
The median of the lower half of the data set must be located in order to determine Q1. The median is the average of the fifth and sixth values, both of which are one hour because there are ten data points in the lower half. Q1 is therefore 1 hour.
We must determine the median of the upper half of the data set in order to determine Q3. The median is the average of the fifth and sixth values, which are both 4 hours, as there are 10 data points in the upper half. Q3 is therefore 4 hours.
The IQR represents the variation between Q3 and Q1: IQR is equal to Q3 - Q1 (4 - 1 = 3 hours).
To know more about interquartile visit:
https://brainly.com/question/30425767
#SPJ1