The dimensions and the mentioned element for matrix 1 are 3x1 and a₂₁=-3 matrix 2, 3x3 and a₂₃=-3, matrix 3, 2x3 and a₂₁=-3. matrix 4, 3x3 and a₃₂=-3, matrix 5, 3x2 and a₃₁=-3, matrix 6, 1x3 and a₁₄=-3.
A collection of integers organised in rows and columns to form a rectangular array. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics. Matrices have also found usage in computer graphics, where they have been utilised to represent picture rotations and other transformations.
Now,
For Matrix 1. Dimension are 3x1 and a₂₁=-3.
For Matrix 2. Dimension are 3x3 and a₂₃=-3.
For Matrix 3. Dimension are 2x3 and a₂₁=-3.
For Matrix 4. Dimension are 3x3 and a₃₂=-3.
For Matrix 5. Dimension are 3x2 and a₃₁=-3.
For Matrix 6. Dimension are 1x3 and a₁₄=-3.
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Which expression is equivalent to √148
A. 12
B. 12√4
C. 14
D, 2√37
Answer:
D
Step-by-step explanation:
You put square roots of 148 in the calculator than it will give you the answer
Answer:
D) 2√37
Step-by-step explanation:
√148 = √4x37 = 2√37
Solve for x !!!!!!!!!!!
Answer:
C
Step-by-step explanation:
Please help I don’t know this
Step-by-step explanation:
you need to put the specific x value into the place of x and calculate.
that's it.
all you need to remember is that a negative exponent means 1/...
and x⁰ = 1
g(-3) = (1/6)^-3 = 6³ = 216
g(-2) = (1/6)^-2 = 6² = 36
g(-1) = (1/6)^-1 = 6¹ = 6
g(0) = (1/6)⁰ = 1
g(1) = (1/6)¹ = 1/6
that was really all for this.
Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 3 x minus 5 = negative 2 x + 10? Select two options.
x = 5
–15 = –5x
5x = 15
–15 = 5x
x = -5
Answer: Its B and C
Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 3 x minus 5 = negative 2 x + 10? Select two options.
x = 5
–15 = –5x
5x = 15
–15 = 5x
x = -5
HELP ASAP
A picture is 7 inches wide and 9 inches long. A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long. What scale factor was used to enlarge the picture?
9/7
7/9
31.5/7
7/31.5
The Scale factor was used to enlarge the picture is 7/ 31.5.
What is Scale factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
Given:
A picture is 7 inches wide and 9 inches long.
A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.
So, scale factor is
= Original dimension / Enlarged dimension
= 9/ 40.5
= 90/ 405
= 10/45
= 2/9
Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.
= 7/ 3.15
= 70/31.5
= 2/9
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Use the graph that shows the solution f(x) = g(x)
F(x) = x^2 + 4x +2
G(x) (1/2)^2 + 1
What is the solution to f(x) = G(x)
A -1
B 0
C 2
D 3
The solution of both the functions, f(x) = g(x) = 2, is option(c).
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealised relationship between two changing quantities.
Given two functions,
f(x) = x² + 4x + 2
g(x) = \((1/2)^{x} + 1\)
observe the graphs below
We are asked to find the solution of f(x) = g(x)
The solution that satisfies both functions is the intersecting point of both graphs.
From the graph, it is observed as (0,2)
Hence when x =0, the solution of both the functions f(x) = g(x) = 2, which is option(c).
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A student says that the solution of 375 = x – 28 is 347. Explain the student’s error and find the correct answer
Answer:
x = 403
Step-by-step explanation:
We can start off by rewriting the equation as
x - 28 = 375
Next, we can further restate it as
375 + 28 = x
So, all we need to do to find the value of x is add 375 + 28, which is 403
Student Error
The student made the error of rewriting the equation incorrectly.
He/She/They subtracted 28 from 375 instead of adding.
Thus, they got 347
A watermelon is shot out of an air cannon and travels 22 yards. How many feet does the watermelon travel?Which conversion factor could you use to answer the question?A. 1 yard/3 feetB. 1 foot/3 yardsC. 3 yards/1 footD. 3 foot/1 yard
the factor is the division between feet and yards
so
\(\frac{3\text{feet}}{1\text{yard}}\)so, the option is C
What is the solution to this system of linear equations x − 3y − 2x 3y 16?
solution of the linear equation is x = (2a - 16)/ 3 and y = - (a+16)/ 9
What is linear equation?An algebraic expression that shows a relationship between two variables that have only first order term. One of the main criteria for linear equation is that we get a straight line when plot this equation in a coordinate system.
.
What is the solution of the system of linear equation?we are given, two linear equations x - a -3y = 0
and a - 2x -3y - 16 =0
from the first equation, x = a + 3y
we put the value of x in the second equation, a - 2(a +3y) - 3y -16= 0
a - 2a - 6y - 3y -16 = 0
- a - 9y -16 =0
- (a + 16) = 9y
y = - (a+16) / 9
now we put the value of y in the equation, x = a + 3y
get, x = a+ 3 [ - (a+16)] / 9
x = a + [ - (a+16)] / 3
x = (3a - a -16) / 3
x = (2a - 16)/ 3
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Martin earned the following scores on his last five tests.
98, 78, 84, 75, 91
What is the mean of his scores?
85.2
106.5
71
84
Answer:
The mean of Martin's scores is 85.2
Step-by-step explanation:
In order to find the mean of a set of numbers, you will have to add up all of the numbers and divide the result by the total numbers in the set.
98 + 78 + 84 + 75 + 91 = 426
Since there are 5 numbers in total, we will do 426 divided by 5.
426 ÷ 5 = 85.2
So, the mean of Martin's scores is 85.2
Question 1 (1 point)
Find the area of the circle.
A) 37.82
B) 43.86
C) 17.72
D) 28.26
Answer:
ok
Step-by-step explanation:
Determine whether the side lengths of roof beams form a right triangle by placing them in the right columns.
see picture
The triangles with right angles triangle measurement is
5, √50, 5 0.75, 1.25, 118, 80, 82 What is Pythagoras theorem?According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
Given:
First, 5, √50, 5
So, applying Pythagoras theorem
H² = 5² + 5²
H² =25+25
H= √50
So, 5, √50, 5 are sides of Right angle triangle.
second, 6.5, 3.2, 7.8
So, applying Pythagoras theorem
H² = 6.5² + 3.2²
H² = 42.25 + 10.24
H= √52.49
and, 7.8² = 60.84
So, 6.5, 3.2, 7.8 are not the sides of Right angle triangle.
Third, √2, √3, 4
H= √2² + √3²
H= 2+3
H=5
So, √2, √3, 4 are not the sides of Right angle triangle.
Fourth, 12, 13, 20
H= 12² + 13²
H= 144+ 169
H= 313 < 20² = 400
So, 12, 13, 20 are not the sides of Right angle triangle.
Fifth, 0.75, 1.25, 1
H= 0.75² + 1²
H= 0.5625 + 1
H= 1.5625 = 1.25²
So, 0.75, 1.25, 1 are sides of Right angle triangle.
sixth, 18, 80, 82
H= 18² + 80²
H= 324 + 6400
H= 6724 = 82²
So, 18, 80, 82 are sides of Right angle triangle.
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The sum of three times a number and −4 is less than 17?
Answer:
3(n + 4) ≤ 10 is the equation and the solution is n ≤ -2/3 Decimal Form: -0.666667
hope this helps you
Step-by-step explanation:
Which graph is used to model piece rate pay?
A. Piecewise
B. Piece rate
C. Scatterplot
D. Quadratic equation
Answer:
C
Step-by-step explanation:
The equation of graph is solved and graph that is used to model piece rate pay is the "piece rate" graph
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
The graph that is used to model piece rate pay is the "piece rate" graph. The piece rate graph shows how much money is earned for each unit of work completed. It is a linear graph with a slope that represents the rate of pay per unit of work completed.
The other graphs mentioned are used for different purposes:
A piecewise graph is used to represent a function that is defined by multiple equations on different intervals.
Hence , the graph is solved
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If two distinct members of the set $\{ 2, 4, 12, 14, 21, 28, 98 \}$ are randomly selected and multiplied, what is the probability that the product is a multiple of 196
The probability that the product of any two distinct members of the set is a multiple of 196 is 0.2857.
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.
If two distinct members of the set { 2, 4, 12, 14, 21, 28, 98 } are randomly selected and multiplied, then the total number of possible outcomes is:
7C2 = 21
Counting all the possible pairs of numbers whose product is a multiple of 196, there are 6 possible ways.
(98 x 4) , (98 x 12) , (98 x 14) , (98 x 28) , (28 x 14) , (28 x 21)
Solve for the probability.
p = 6 / 21 = 0.2857
Therefore, the probability is 0.2857.
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What is the square root of 25
Answer: 5
Step-by-step explanation:
5*5 is equal to 25
Answer:
5
Step-by-step explanation: The square root of 25 is 5 because 5x5=25 or \(5^{2}\)=25
What are the domain and range of the function? f(x)=x−3−−−−√3 Domain: [3, [infinity]) Range: (−[infinity], [infinity]) Domain: [3, [infinity]) Range: [0, [infinity]) Domain: (−[infinity], [infinity]) Range: (−[infinity], [infinity]) Domain: [0, [infinity]) Range: [3, [infinity])
Option (â): ˆ’[infinity], [infinity])` is the correct answer.
The given function is `f(x) = x - 3 - sqrt(3)`. To find the domain and range of this function, we can follow the steps mentioned below:
Domain of a function:
The domain of a function is the set of all possible values of x for which the function is defined or the input values of a function. A function is not defined if:
1. The denominator is zero.
2. We have a negative square root.
3. The logarithm of a negative number.
In the given function, we do not have any denominator or logarithm. We only have a square root, which is subtracted from `x-3`. Therefore, the function is defined for all real values of `x` greater than or equal to `3`. Hence, the domain of the function `f(x)` is `[3, [infinity])`.
Range of a function:
The range of a function is the set of all possible values of `y` that we get after putting different values of `x` in a function. In this case, we can see that the value of the square root is subtracted from `x-3`. Therefore, the minimum value of the function `f(x)` will be when the square root is maximum. The maximum value of the square root is `0`, which occurs when `x=3`. Hence, the minimum value of the function `f(x)` is `3-sqrt(3)`.
Similarly, the maximum value of the function will occur when the square root is `0` (i.e., when `x` approaches infinity). Hence, the maximum value of the function `f(x)` is `+infinity`.
Therefore, the range of the function `f(x)` is `(−[infinity], [infinity])`.
Hence, the correct option is `(−[infinity], [infinity])`. Therefore, option `(−[infinity], [infinity])` is the correct answer.
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7) Original price: ?
Discount: 25%
Sale price:
$28
Answer:
Step-by-step explanation:
let be x the price before the discount
original price= 28/(1-0.25)=28/0.75=37.33
original price=37.33
Answer:
37.3
Step-by-step explanation:
The original price = x which represents 100% of the price. So we subtract 100%-25, which is 100-25=75 or 75%(0.75)
So, $28 is 75% off the original price.
28 divided by .75 = 37.3
Then, 37.3 would be the original price.
esitmate the value of y when x=2.5
1. (5 pts) The (per hour) production function for bottles of coca-cola is q=1000K L
, where K is the number of machines and L is the number of machine supervisors. a. (2 pts) What is the RTS of the isoquant for production level q? [Use the following convention: K is expressed as a function of L b. (1 pt) Imagine the cost of operating capital is $40 per machine per hour, and labor wages are $20/ hour. What is the ratio of labor to capital cost? c. (2 pts) How much K and L should the company use to produce q units per hour at minimal cost (i.e. what is the expansion path of the firm)? What is the corresponding total cost function?
The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.
The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.
Given the production function q = 1000KL, we can differentiate it with respect to L:
d(q)/d(L) = 1000K
Therefore, the RTS of the isoquant for production level q is 1000K.
The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.
Labor cost = $20/hour
Capital cost = $40/machine/hour
Ratio of labor to capital cost = Labor cost / Capital cost
= $20/hour / $40/machine/hour
= 0.5
The ratio of labor to capital cost is 0.5.
To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.
Let C(K, L) be the total cost function.
The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:
C(K, L) = 40K + 20L
To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.
The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.
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regina writes an expression y+9 x 3/4 what expression is equivalent?
Answer:
y + 27/4
Step-by-step explanation:
Took the test
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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NEED HELP ASAP!!!! GIVING BRAINLIEST+ 30 POINTS TO WHOEVER CAN ANSWER THESE TWO QUESTIONS THE BEST!!!
A toy manufacturer needs a piece of plastic in the shape of a right triangle with one leg 4 cm longer than the other and the hypotenuse 8 cm longer than the shorterleg. What is the perimeter of the triangle?The perimeter is ___(Simplify your answer.)
It is given that the longer leg is 4 cm longer than the shorter leg.
It is also given that the hypotenuse is 8 cm longer than the shorter leg.
ExplanationLet the shorter leg be x.
The longer leg be y.
Then the relation formed is
\(y=x+4\)It is also given that the hypotenuse is 8 cm longer than the shorter leg.
Let the hypotenuse is z.
\(z=8+x\)Then the perimeter of the right triangle is the sum of all the sides.
\(x+y+z\)But to find the value of x , use the Pythagoras theorem.
\(z^2=y^2+x^2\)Substitute the values.
\(\begin{gathered} (8+x)^2=(4+x)^2+x^2 \\ 64+x^2+16x=16+x^2+8x+x^2 \\ 64+16x=16+8x+x^2 \\ 64-16+16x-8x-x^2=0 \\ -x^2+8x+48=0 \end{gathered}\)Solve the quadratic equation to find the value of x.
\(\begin{gathered} (x-12)(x+4)=0 \\ x=12,-4 \end{gathered}\)As x cannot be negative , then the value of x is 12.
The length of shorter leg is 12.
The length of longer leg is 12+4=16.
The hypotenuse is 12+8=20.
Now , the perimeter of right triangle is
\(\begin{gathered} P=12+16+20 \\ P=48cm \end{gathered}\)AnswerThe perimeter of the triangle is 48 cm.
What is the solution to the system of linear equations?
Answer:
(0,2)
Step-by-step explanation:
The equations must be derived from the graph:
First, find the slope of f(x):
\(m=\frac{y_2-y_1}{x_2-x_1}\) let \((x_1,y_1)=(-3,3)\) and \((x_2,y_2)=(3,1)\)
\(m=\frac{(1)-(3)}{(3)-(-3)}\\m=\frac{-2}{6}\\m=-\frac{1}{3}\)
Then use \(y-y_1=m(x-x_1)\)
\(y-3=-\frac{1}{3}[x-(-3)]\\y-3=-\frac{1}{3}x-1\\y=-\frac{1}{3}x+2\\f(x)=-\frac{1}{3}x+2\)
For g(x), let:
\((x_1,y_1)=(-3,0)\\(x_2,y_2)=(0,2)\)
\(m=\frac{(2)-(0)}{(0)-(-3)}\\m=\frac{2}{3}\)
\(y-0=\frac{2}{3}[x-(-3)]\\y=\frac{2}{3}x+2\\g(x)=\frac{2}{3}x+2\)
Now, to solve for x, allow the two expressions written in terms of x equal each other.
\(-\frac{1}{3}x+2=\frac{2}{3}x+2\\(-\frac{1}{3}x+2)+\frac{1}{3}x=(\frac{2}{3}x+2)+\frac{1}{3}x\\2=x+2\\(2)-2=(x+2)-2\\x=0\)
To solve for y, substitute 0 for x in f(x):
\(y=-\frac{1}{3}x+2\\y=-\frac{1}{3}(0)+2\\y=0+2\\y=2\)
So, the solution to this system of equations would be the ordered pair (0,2). This solution is seen on the graph as the intersection of the two lines.
Wayne Gretzky holds the NHL record for the most points scored In a career. He scored 2857 points in 1487 games. a. Calculate his average points per game b. At this rate,how many more points might he have scored if he had played 79 more games?
Answer:
Step-by-step explanation:
a) The formula for determining average is expressed as
Average point per game = number of points scored/total number of games played
Average point per game = 2857/1487 = 1.92
b) if he had played 79 more games, since his average point per game is 1.92, then the number of points that he might have scored would be
1.92 × 79 = 95 points
The total number of points would have been
2857 + 95 = 2952 points
Answer:
a. 1.92
b. 152
Step-by-step explanation:
Wayne Gretzky had 2857 points in 1487 games.
a. His average points per game can be determined by dividing the total number of points by number of games. So that:
average points per game = \(\frac{2857}{1487}\)
= 1.92132
Therefore, he scored an average of 1.92 (2 d.p) points per game.
b. The number of points he would have scored having played 79 more games can be determined by multiplying the points for 79 more games by his average points.
His points for 79 more games = 79 × 1.92132
= 151.78428
He would have scored 152 (3 s.f) more points if he had played 79 more games.
Someone help please
The measure of the angles that is supplementary to the given angles is as follows:
4. 52°
5. 20°
6. 130°
How to find supplementary angles?Supplementary angles are those angles that sum up to 180 degrees. In
other words, supplementary angles refer to the pair of angles that always
sum up to 180°. Therefore, let's find the measure of the angles that are
supplementary angles to the following angles.
Therefore,
4.
180 - 128 = 52 degrees
5.
180 - 160 = 20 degrees
6.
180 - 50 = 130 degrees
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In the figure there are 5 equal rectangles and each of its sides is marked with a number as indicated in the drawing. Rectangles are placed without rotating or flipping in positions I, II, III, IV, and V in such a way that the sides that stick together in two rectangles have the same number. Which of the rectangles should go in position I?
The rectangle which should go in position I is rectangle A.
We are given that;
The rectangles A,B,C and D with numbers
Now,
To take the same the number of side
If we take A on 1 place
F will be on second place
And B will be on 4th place
Therefore, by algebra the answer will be rectangle A.
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Please discuss whether or not the following problems are data mining tasks. Explain why. [30 points]
3(a). Retrieve students' records from a relational table with grade = "A". [5 points]
3(b). From the table of students' information, check if attributes last name and address have any correlations. [5 points]
3(c). Find all the documents from the text database containing keywords "data mining". [5 points]
3(d). Divide the text database into several groups, each group containing near-duplicate or similar documents. [5 points]
3(e). Based on historical stock data, as well as other attributes (e.g., gold price, gas price, etc.) for the past few days, predict the trend of a stock tomorrow. [5 points]
3(f). Please provide your own example of the data mining.
All the following problems are data mining tasks.
(a) Retrieving students' records from a relational table with a grade = "A" involves extracting specific data from a database, which is a fundamental task in data mining.
(b) Checking correlations between attributes like last name and address in a table of students' information involves analyzing the relationship between different variables, which is a data mining task.
(c) Finding documents containing specific keywords ("data mining") from a text database involves searching for patterns in unstructured data, which is a typical data mining task.
(d) Dividing a text database into groups of near-duplicate or similar documents requires identifying similarities or patterns within the data, which is a common task in data mining, such as clustering or classification.
(e) Predicting the trend of a stock based on historical stock data and other attributes involves analyzing patterns and relationships within the data, making it a predictive data mining task.
(f) Example: Analyzing customer purchase history to identify patterns and associations between products and customer preferences, enabling personalized product recommendations and targeted marketing campaigns.
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Which equation gives the value of the circumference, , of a circle with a diameter of 56 feet? =π·562 =28·π. =56·π =56π
Answer:
C=2πr=2·π·56≈351.85838
Step-by-step explanation: