Here, y can be expressed as a linear combination of a1, a2, and a3 is y = (-1/8) a1 + (9/4) a2 - (5/2) a3.
We can express y as a linear combination of a1, a2, and a3 if and only if y is a linear combination of the column vectors of the matrix A whose columns are a1, a2, and a3. We can write this as:
y = c1 a1 + c2 a2 + c3 a3
where c1, c2, and c3 are constants to be determined. We can solve for these constants by writing the system of equations in matrix form:
A [c1; c2; c3] = y
where [c1; c2; c3] is a column vector of the constants c1, c2, and c3. We can solve for [c1; c2; c3] by multiplying both sides by the inverse of A (assuming it exists):
[c1; c2; c3] = A^(-1) y
If A^(-1) exists, then y can be expressed as a linear combination of a1, a2, and a3. Otherwise, y cannot be expressed as a linear combination of a1, a2, and a3.
For y = [1 2 4 0], we have:
A = [-1 3 0 1; 3 1 2 0; 1 1 1 1]
We can compute the inverse of A using row reduction:
[A | I] = [-1 3 0 1 | 1 0 0;
3 1 2 0 | 0 1 0;
1 1 1 1 | 0 0 1]
[R2 - 3R1, R3 - R1] = [-1 3 0 1 | 1 0 0;
0 -8 2 -3 | -3 1 0;
0 -2 1 0 | -1 0 1]
[R2 / (-8), R3 + 2R2] = [1/8 -3/8 0 3/8 | 3/8 -1/8 0;
0 1 0 -1/4 | 3/4 -1/4 0;
0 0 1 -1/2 | 1/2 -1/2 1]
Therefore, A^(-1) = [1/8 -3/8 0 3/8;
0 1 0 -1/4;
0 0 1 -1/2;
0 0 0 0]
We can now compute [c1; c2; c3]:
[c1; c2; c3] = A^(-1) y = [1/8 -3/8 0 3/8;
0 1 0 -1/4;
0 0 1 -1/2;
0 0 0 0] [1; 2; 4; 0] = [-1/8; 9/4; -5/2; 0]
Therefore, y as a linear combination of a1, a2, and a3:
y = (-1/8) a1 + (9/4) a2 - (5/2) a3
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_____The given question is incomplete, the complete question is given below:
Exercise 1.3.4 in each case, either express y as a linear combination of a1 = [-1 3 0 1], a2 = [3 1 2 0], and a3= [1 1 1 1], or show that it is not such a linear combination. here: y = [1 2 4 0]
Solve the polynomial equation by factoring and then using the zero-product principle.
2
8x-4=2x-x
Rewrite the equation in factored form.
(Blank)= 0
What is the solution pair?
the factored form of the equation is 2(13x - 2) = 0, and the solution to the equation is x = 2/13.
Why it is and what is Zero-Product formula?
First, we can simplify the equation by combining like terms:
28x - 4 = 2x - x
Simplifying further:
26x - 4 = 0
Now, we can factor out 2 from the left side of the equation:
2(13x - 2) = 0
Using the zero-product principle, we can set each factor equal to zero:
2 = 0 or 13x - 2 = 0
The first equation is impossible since 2 is not equal to zero. Solving the second equation, we get:
13x - 2 = 0
Adding 2 to both sides:
13x = 2
Dividing both sides by 13:
x = 2/13
Therefore, the factored form of the equation is 2(13x - 2) = 0, and the solution to the equation is x = 2/13.
The zero-product property or formula states that if the product of two factors is zero, then at least one of the factors must be zero. In other words, if a and b are real numbers such that ab = 0, then either a = 0, b = 0, or both a and b are zero. This property is often used to solve polynomial equations by factoring the expression and then setting each factor equal to zero.
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Consider the following equation: X3 + 4x2 + 4x + 16 = 0. Solve for x. Your answer should be stored in a variable result , which will be a list containing three sympy expressions. Starter code (click to view) Answer* 1 import sympy
Considering the following equation x³ + 4x² + 4x + 16 = 0 we have the value of x as [-4, -2*I, 2*] in sympy expressions.
Symbolic math is supported by the Python library SymPy (http://www.sympy.org). In symbolic mathematics, mathematical expressions are represented by symbols. This is an illustration of a symbolic arithmetic expression: x2+y2=z. The three variables x, y, and z are present in the formula above.
Considering the following equation x³ + 4x² + 4x + 16 = 0.
CODE:
import sympy #importing SymPy
x = sympy.Symbol('x') #declaring the variable 'x' as the only variable for the expression
result = sympy.solve(x**3 + 4*x**2 + 4*x + 16,x) #using the function solve() to solve the expression.
print(result) #displaying the list 'result'
OUTPUT:
[-4, -2*I, 2*]
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The dot plot below shows the number of hours of sleep preferred by 25 patients chosen randomly in a particular medical office.
Calculate the mean, median, and mode of the data. Based on the results, which list shows a comparison of the measures of central tendency, from least to greatest?
A) Median, mode, mean
B) Median, mean, mode
C) Mode, median, mean
D) Mean, median, mode
The list that shows a comparison of the measures of central tendency from the least to the greatest is mean, median and mode. (option D)
What is the correct order?The dataset represented with the dot plot is 2, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8,8, 8, 8, ,8, 8, 8, 8, 8, 8
Mean is the average of the dataset.
Mean = sum of numbers / total number in the dataset
[(2 x 1) + (5 x 4) + (6 x 4) + (7 x 6) + (8 x 10)] / 25 = 6.72
Median is the number at the center of the dataset.
The median = 1/2(n + 1)
1/2 x (26) = 13th number = 7
Mode is the number that occurs most frequently. The number that occurs the most in the dataset is 8.
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Find the surface area of the triangular pyramid. The side lengths of the base are equal.
The surface area of the triangular pyramid is the sum of the lateral surface area and the base area.
Lateral Surface Area: The lateral surface area of a triangular pyramid is equal to the product of the slant height and the perimeter of the base.
Slant height = √ ( (length of side)2 + (height)2 )
Perimeter of the base = 3 x length of side
Therefore, the lateral surface area = √ ( (length of side)2 + (height)2 ) x 3 x length of side
Base Area: The base area of the triangular pyramid is equal to one-half of the product of the three side lengths.
Therefore, the base area = 1/2 x (length of side) x (length of side) x (length of side)
Surface Area: The total surface area of the triangular pyramid = lateral surface area + base area
Therefore, the surface area = √ ( (length of side)2 + (height)2 ) x 3 x length of side + 1/2 x (length of side) x (length of side) x (length of side)
Which equation defines y as a linear function of x?
Select all that apply.
□ A. y = 3x² +7
□ B. x - 4y = 5
□ C. 5x² + y = 3
OD. 2(x+3y) = 6
O E. y = 5x - 3x + 4
Among the given equations, the equation E. y = 5x - 3x + 4 is the only equation that is in the form y = mx + b.
What is linear equation ?
A linear function is defined as a function that has a constant rate of change, meaning that as x increases by a certain amount, y also increases by a certain amount. Therefore, the equation that defines y as a linear function of x is of the form y = mx + b, where m is the slope and b is the y-intercept.
Among the given equations, the equation E. y = 5x - 3x + 4 is the only equation that is in the form y = mx + b. By combining like terms, we can simplify it to y = 2x + 4. This equation has a constant rate of change of 2, which means that for every 1 unit increase in x, y will increase by 2 units.
The other equations are not linear functions because they either have an x² term, which causes a non-constant rate of change, or they have multiple variables, which means that changes in x will not produce a consistent change in y.
Therefore, the answer is E. y = 5x - 3x + 4.
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use the methods taught in this class to find the slope and y-intercept of the regression line. round your answers to 3 decimal places.
The slope and Y-intercepts of the regression lines can be found using the formulae: m = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²) and b = (Σy - mΣx) / n
To find the slope and y-intercept of a regression line, you can use the formula y = mx + b, where m is the slope and b is the y-intercept. Regression Line is a method in which the dependent variable serves as the explanatory variable, and the former is utilized to infer information about the latter and create a forecast for it.
To calculate the slope of a regression line, you can use the formula m = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²), where n is the number of data points, x and y are the variables, and Σ represents summation.
To calculate the y-intercept of a regression line, you can use the formula b = (Σy - mΣx) / n.
Once you have calculated these values, you can substitute them into the equation y = mx + b to get your regression line.
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Correct question is:
Use the methods taught in this class to find the slope and y-intercept of the regression line. Round your answers to 3 decimal places.
0 / 1
It is November 1 of Year 1. Sales for Dee Company for November and December of Year 1 and January of Year 2 are forecasted to be as follows:
November, 400,000; December 600,000; January, 200,000
60% of sales are credit sales; the remaining sales are cash sales. Of these credit sales, 5% are collected during the month of sale, 25% in the following month, and 65% in the second following month; 5% are never collected. Total sales for September and October of Year 1 were 100,000 and 150,000, respectively.
What is the forecasted amount of total cash collections in November of Year 1?
Answer:
Step-by-step explanation:
To find the forecasted amount of total cash collections in November of Year 1, we first need to determine the credit sales for September, October, November, and December of Year 1, and January of Year 2.
Credit sales for September and October of Year 1 have already been given as 100,000 and 150,000, respectively.
For November, credit sales are 60% of 400,000 = 240,000.
For December, credit sales are 60% of 600,000 = 360,000.
For January of Year 2, credit sales are 60% of 200,000 = 120,000.
Now, we need to calculate the amount of credit sales that will be collected in November of Year 1.
5% of credit sales for November will be collected in November itself, which is 5% of 240,000 = 12,000.
25% of credit sales for November will be collected in December, which is 25% of 240,000 = 60,000.
65% of credit sales for November will be collected in January of Year 2, which is 65% of 240,000 = 156,000.
The remaining 5% of credit sales for November, which is 5% of 240,000 = 12,000, will never be collected.
Therefore, the total cash collections in November of Year 1 will be the sum of cash sales for November, and the amount of credit sales collected in November:
Cash sales for November = 40% of 400,000 = 160,000
Credit sales collected in November = 12,000
Total cash collections in November of Year 1 = 160,000 + 12,000 = 172,000.
Hence, the forecasted amount of total cash collections in November of Year 1 is $172,000.
Help i need this question solved
Answer: D. Square
Step-by-step explanation:
The shape created by the cross section of the cut through a square pyramid is a square.
To see why, imagine the pyramid sitting on a table with its square base flat against the surface. The cut goes through the vertex, which is the point at the top of the pyramid. Since the cut is perpendicular to the base, it divides the pyramid into two smaller pyramids with congruent, but not identical, bases. Each of these smaller pyramids has a triangular base that is an isosceles right triangle. The two triangles share a common hypotenuse, which is the line of the cut.
The cross section of the cut is the shape formed where the two triangles meet along the hypotenuse. Since both triangles are congruent and the hypotenuse is the same for both, the cross section is a square. The sides of the square are equal to the base of the original pyramid, which is one of the legs of the isosceles right triangles formed by the cut. Therefore, the answer is D, a square.
(Evaluating Reports MC)
The dot plot below shows the number of hours of sleep preferred by 25 patients chosen randomly in a particular medical office.
Calculate the mean, median, and mode of the data. Based on the results, which list shows a comparison of the measures of central tendency, from least to greatest?
A) Median, mode, mean
B) Median, mean, mode
C) Mode, median, mean
D) Mean, median, mode
Answer:
D
Step-by-step explanation:
Mean- 6.78
Median- 7
Mode- 8
What is the perimeter of the football field without the end zones?
Answer:
30623 yards
Step-by-step explanation:
Answer:
In the NFL, the perimeter of a football field, excluding the end zones, is 30623 yards. The field is how many feet wide... A football field in the United States is 120 yards long (including the end zones).
Step-by-step explanation:
Brainliest pls
please answer question i cannot do it
The value of the height of the trapezium is 10.3 cm.
What is the area of a trapezium?The area of a trapezium is given by the formula:
Area = (1/2) x (sum of parallel sides) x (distance between the parallel sides)
The parallel sides of the trapezium are given as 18 cm and 13 cm
The area of the trapezium is given as 160 cm²
The height of the trapezium = h
The value of the height of the trapezium is calculated as follows;
160 = ¹/₂ (18 + 13) h
2 x 160 = (31)h
320 = 31h
h = 320 / 31
h = 10.3 cm
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Estimate a 15% tip on a dinner bill of $58.12 by first rounding the bill amount to the nearest ten dollars.
Answer: an estimated 15% tip on a dinner bill of $58.12 would be $8.72.
Step-by-step explanation:
First, we can calculate 10% of $58.12 by moving the decimal point one place to the left, which gives us $5.81.
Then, we can calculate half of 10%, which is 5%, by dividing $5.81 by 2, giving us $2.91.
Finally, we add 10% and 5% to get the estimated tip amount:
$5.81 + $2.91 = $8.72
Therefore, an estimated 15% tip on a dinner bill of $58.12 would be $8.72.
6.) The sum of two numbers is 45.
The larger number y is 6 less than twice the smaller number
a.
Write a system of linear equations.
What is the smaller number?
Answer:
x= 13 =smaller number
Step-by-step explanation:
let x=smaller number
y=2x-6=larger number
x+y=45
x+2x-6=45 (equation)
3x=39
x=13
Answer:
[tex]x = 13[/tex] ..... smaller number
and
[tex]y = 32[/tex] ....... larger number
Step-by-step explanation:
Greetings!!!
Let the two numbers be X and Y
[tex]x + y = 45........ \:equation \: 1[/tex]
The larger number is y and is 6 less than twice the smaller number. which means:-
[tex](y - 6) = 2x........... \: equation \: 2[/tex]
so, now solve for y. from equation 2
[tex]y - 6 = 2x \\ y = 2x + 6[/tex]
Substitute equation 1 into equation 2
[tex]x + y = 45 \\ x + (2x + 6) = 45 \\ 3x + 6 = 45 \\ 3x = 45 - 6 \\ 3x = 39....divide \: both \: sides \: by \: 3 \\ x = 13[/tex]
To solve for y substitute x into the first equation
[tex](13) = + y = 45 \\ y = 45 - 13 \\ y = 32[/tex]
Finally, to be more sure make a cross check
[tex]y - 6 = 2x \\ 32 - 6 = 2(13) \\ 26 = 26[/tex]
If you have any questions tag it on comments
Hope it helps!!!
2. Urn A contains 4 black, 3 red, and 3 white balls, whereas urn B contains 3 white, I red, and 3 black balls. A ball is drawn at random from urn A and placed in urn B. A ball is then drawn from urn B. It happens to be red. What is the probability that the ball transferred was red?
The probability that the ball transferred was red, given that a red ball was drawn from urn B, is 21/55, or about 0.382.
What is probability ?
Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to happen.
To calculate probability, we usually take the number of favorable outcomes and divide it by the total number of possible outcomes. For example, if we flip a coin, the probability of getting heads is 1/2 because there is only one favorable outcome (heads) out of two possible outcomes (heads or tails).
According to the question:
Let's use Bayes' theorem to find the probability that the ball transferred was red:
Let R be the event that a red ball is drawn from urn B, and T be the event that the transferred ball was red.
Then we want to find P(T = red | R = red).
By Bayes' theorem, we have:
P(T = red | R = red) = P(R = red | T = red) * P(T = red) / P(R = red)
We can calculate each of these probabilities as follows:
P(R = red | T = red): The probability of drawing a red ball from urn B, given that a red ball was transferred from urn A to urn B, is 1/4, since urn B originally contained 1 red ball out of 7 total balls (3 black, 3 white, and 1 red) and we added one more red ball to it.
P(T = red): The probability that a red ball was transferred from urn A to urn B is 3/10, since urn A originally contained 3 red balls out of 10 total balls and we transferred one ball at random.
P(R = red): The overall probability of drawing a red ball from urn B is:
P(R = red) = P(R = red | T = black) * P(T = black) + P(R = red | T = red) * P(T = red)
where T = black means that a black ball was transferred from urn A to urn B. We can calculate each of these conditional probabilities as follows:
P(R = red | T = black): The probability of drawing a red ball from urn B, given that a black ball was transferred from urn A to urn B, is 1/7, since urn B originally contained 1 red ball out of 7 total balls (3 black, 3 white, and 1 red) and we did not add any more red balls to it.
P(T = black): The probability that a black ball was transferred from urn A to urn B is 4/10, since urn A originally contained 4 black balls out of 10 total balls and we transferred one ball at random.
Therefore, we have:
P(R = red) = 1/7 * 4/10 + 1/4 * 3/10 = 1/35 + 3/40 = 11/140
Putting it all together:
P(T = red | R = red) = (1/4) * (3/10) / (11/140) = 21/55
So the probability that the ball transferred was red, given that a red ball was drawn from urn B, is 21/55, or about 0.382.
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Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER RIGHT HELP EASY THANK UU
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment.
Answer:
going from left to right:
AA
BD
CB
DC
I need help with this
Answer:
(x -14)² +(y -7)² = 1²
Step-by-step explanation:
You want the equation of the circle that represents the border of a logo centered 14 m right and 7 m up from the lower left corner of a soccer field. The logo is 2 m in diameter.
Equation of a circleThe equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
Since the origin of the coordinate system is the lower left corner of the field, the center is located at (h, k) = (14, 7). The diameter of 2 m means the radius is 1 m. Using these values in the equation, it becomes ...
(x -14)² +(y -7)² = 1²
what is the cost of sales
The expense incurred by a cοmpany tο prοduce the gοοds οr services sοld within a specific time periοd is knοwn as the cοst οf sales.
What dοes cοst cοmprise οf ?It cοmprises all cοsts that are directly related tο the prοductiοn prοcess, such as thοse fοr labοr, utilities, raw materials, and manufacturing equipment depreciatiοn.
Grοss prοfit, which is the amοunt οf mοney a firm makes frοm its cοre οperatiοns befοre deducting extra cοsts like marketing, administrative, and financing charges, is calculated by subtracting the cοst οf sales frοm revenue. Tο apprοpriately price their prοducts and assess the prοfitability οf their οperatiοns, firms must have a thοrοugh understanding οf their cοst οf sales.
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Complete question:
What is the definition of cοst οf sales?
Cells ire approximately round with a diameters ranging from 1 to >100 micrometers. The graph below shows the cross section of half a cell with a diameter of 2μm. The curvature of the cell surface determines if and how vesicles can form. Find the curvature of the cell surface y at the red point x=0.25 from the equation for a circle: y= (2−x)x
The curvature of the cell surface that has a shape of circle y at the red point x=0.25 is 1.75.
What is diameter?Diameter is a line segment that passes through the center of a circle or sphere and has its endpoints on the circumference of the circle or sphere. The diameter of a circle is twice the length of its radius, so if the radius is given, the diameter can be calculated by multiplying the radius by two.
The equation is given as y = (2 - x)2, where x is the distance from the centre of the circle and y is the curvature of the circle at that distance. To calculate the curvature of the cell surface at any given point, the distance from the centre needs to be known. In this example, the distance from the centre is 0.25, and the curvature of the cell surface at this point is 1.75.
A low curvature, such as 1.75, will allow for more vesicles to form on the surface of the cell. A low curvature will allow for more vesicles to form, and a high curvature will prevent the formation of vesicles.
The equation for a circle with a diameter of 2μm is given as y = (2 - x)2. Substituting x = 0.25 into the equation yields y = (2 - 0.25)2 = 1.75.
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The circle-shaped cell surface's (or circumference's) curvature at the red spot x=0.25 is 0.66.
What is diameter?A circle or sphere's diameter is defined as a line segment with its endpoints on the circumference and that travels through the middle of the object. If the radius is known, the diameter can be determined by multiplying the radius by two since the diameter of a circle is twice the length of its radius.
It is possible to compute the cell surface's curvature at x = 0.25 as follows:
Let's look at the circle's calculation.
y = √(2 - x)x
Now, when x = 0.25,
y = √(2 - 0.25)×0.25
y = √1.75×0.25
y = 0.66
As a result, the cell surface's slope at x = 0.25 is 0.66.
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I need help I really don’t get this
The result of multiplying [tex]5,230[/tex] by [tex]25[/tex] is a quotient of [tex]209.2[/tex] rupees.
What in arithmetic is a quotient?In this example, the number being divided (15) is known as the reward, and the number being divided by (3 in this instance) is known as the divisor. The consequence of divide is the quotient.
What is the ratio between two numbers?When we divided one number by another, the result is a quotient. As an instance, when we divide 6 with 3, we obtain the answer 2, which corresponds to the division.This quotient may be either an integer or a decimal. For describing the presence or intensity of a quality in someone or something, the quotient is utilized.
25)5230(209.2
-50
--------------
230
-225
-----------------
50
-50
------------
0
-----------
So the quotient is [tex]209.2[/tex]
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Uri paid a landscaping company to mow his lawn. The company charged $74 for the service plus
5% tax. After tax, Uri also included a 10% tip with his payment. How much did he pay in all?
Uri paid a total of $85.47 for the landscaping service including tax and tip.
What is tax?Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.
Given that company charged $74 for the service plus 5% tax.
The tax is 5%, that is:
Tax = 5% of $74 = 0.05 x $74 = $3.70
Cost after tax = $74 + $3.70 = $77.70
Now, tip is 10%:
Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77
Total cost = $77.70 + $7.77 = $85.47
Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.
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The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of the given set.
n(A ∩ B ∩ C^c) = 15 there are 15 elements in the intersection of sets A and B but not in set C.
What is a circle?
A circle is a two-dimensional geometric figure that consists of all the points in a plane that are equidistant from a given point called the center. The distance from the center to any point on the circle is called the radius, which is denoted by the letter "r".
To find the cardinality of n(A∩B∩C^c), we need to know the number of elements that are in the intersection of A and B but not in C.
One way to approach this is to use the principle of inclusion and exclusion. This states that:
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)
We can rearrange this formula to solve for n(A ∩ B ∩ C^c):
n(A ∩ B ∩ C^c) = n(A ∩ B) - n(A ∩ B ∩ C) - n(B ∩ C) + n(A ∩ C) + n(B) + n(C) - n(A)
Plugging in the values we have been given, we get:
n(A ∩ B ∩ C^c) = 4 - 3 - 9 + 7 + 11 + 15 - 10
Simplifying this expression, we get:
n(A ∩ B ∩ C^c) = 15
Therefore, there are 15 elements in the intersection of sets A and B but not in set C.
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What is 15426.82 rounded to the nearest hundredth
Answer:
Step-by-step explanation:
15426.80
Answer: 15426.82
Step-by-step explanation:
15426.82 is also 15426.82000
Since 2 is the hundredth number (behind the decimal point) and the next number is 0, it will be rounded down.
Therefore 15426.82 to the nearest hundredth is 15426.82
Chau had 4/5 of a spool of yarn. He used 3/5 of his yarn for a project. What fraction of the spool was used for the project?
Answer: 3/5
Step-by-step explanation:
Chau had 4/5 of a spool of yarn, and he used 3/5 of it for a project.
The fraction of the spool used for the project is:
3/5
So, 3/5 of the spool was used for the project.
A type of wood has a density of 250 kg/m3. How many kilograms is 75,000 cm3 of the wood? Give your answer as a decimal.
Hoang has worked as a nurse at Springfield General Hospital for 5 years longer than her friend Bill. Two years ago, she had been at the hospital for twice as long. How long has each been at the hospital?
5 years longer then Bill, 2x5=10.
10+2=12.
12-5=7
Hoang has be there for 12 years. Bill has for 7 years.
Help I don’t just this
The conditional relative frequency that a student rides the bus, given that the student is in middle school is 0.16 / 0.96 ≈ 0.17.
Describe conditional relative frequency ?Conditional relative frequency is a statistical measure that describes the proportion or percentage of a specific group or category within a subset of data. It is calculated by dividing the frequency of the specific category in the subset by the frequency of the total subset.
To find the conditional relative frequency that a student rides the bus, given that the student is in middle school, we need to divide the frequency of middle school students who ride the bus by the total number of middle school students.
From the table, we see that the frequency of middle school students who ride the bus is 0.16. The total number of middle school students is the sum of the frequencies in the first row, which is 0.20 + 0.16 + 0.12 + 0.48 = 0.96.
So, the conditional relative frequency that a student rides the bus, given that the student is in middle school is:
0.16 / 0.96 ≈ 0.17
Rounded to the nearest hundredth, the answer is 0.17. Therefore, about 17% of middle school students ride the bus.
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A water cooler springs a leak and empties in 2 minutes. The graph below shows the rate at which water leaks from the cooler as a function of time.
The amount of water that was in the cooler before it started leaking was 6 gallons.
Describe Integration?Integration is a mathematical process that involves finding the integral of a function. It is the reverse operation of differentiation, which involves finding the derivative of a function. The integral of a function is a measure of the area under the curve of the function, between two given limits of integration.
The graph shows the rate at which water leaks from the cooler as a function of time, which means that the y-axis represents the rate of leakage in gallons per minute (gal/min), and the x-axis represents the time in minutes.
Since we know that the cooler emptied in 2 minutes, we can integrate the leakage rate over the time interval [0, 2] to find the total amount of water that leaked out:
Total amount of water leaked = ∫[0,2] leakage rate(t) dt
The leakage rate is given by the graph, which consists of a straight line connecting two points: (0,6) and (2,0). We can express this line as a linear equation in slope-intercept form:
leakage rate(t) = mt + b
where m is the slope of the line and b is the y-intercept. To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (0,6) and (x2, y2) = (2,0). Plugging in the values, we get:
m = (0 - 6) / (2 - 0) = -3
So the equation of the line is:
leakage rate(t) = -3t + 6
Now we can integrate this equation over the time interval [0, 2] to get the total amount of water leaked:
Total amount of water leaked = ∫[0,2] (-3t + 6) dt
= [-3t²/2 + 6t] from 0 to 2
= (-3(2)²/2 + 6(2)) - (-3(0)²/2 + 6(0))
= (6 - 0) - (0 - 0)
= 6 gallons
Therefore, the amount of water that was in the cooler before it started leaking was 6 gallons.
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The complete question is :
Help what’s the answer
Answer:
Difference=£2.4
Step-by-step explanation:
Here in shop A
130 cm=£1.82
1 cm=£1.82/130
1 cm=0.014
Now
400 cm=0.014*400
=£5.6
Again, In shop B
235cm=£1.88
1 cm=£1.88/235
1 cm=£0.008
Now
400cm=0.008*400
=£3.2
Now,
Difference=£5.6-£3.2
=£2.4
which is correct answer?
a (a value)
b
c
d
Indeed, the intermediate value theorem demonstrates that the equation [tex]x + sin(x) = -1[/tex] must have at least one solution on the interval [-/2, /4]. Thus option B is correct.
What is the intermediate valve theorem?The intermediate value theorem states that if a continuous function exhibits values with opposite signs at two places, there must be at least one location in the interval where it equals zero (or crosses the x-axis).
Note that x + sin(x) is a continuous function to see why. When x + sin(x) is evaluated at the interval's left endpoint, x = -/2, the result is [tex]-/2 + sin(-/2) = -/2 - 1[/tex] , which is less than -1.
The intermediate value theorem states that because x + sin(x) is continuous and can have values both less than and greater than -1 at either end of the range, it must also have a value of -1 somewhere in between.
Therefore, When x + sin(x) is evaluated at the interval's right endpoint, x = /4, the result is [tex]x + sin(x) = x + 2/2,[/tex] Which is greater than -1.
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Can I please get help it's an EMERGENCY!
The number of hours it will take the same dog to run 26 1/10 miles is 7.2 hours
How long will it take the dog to run 26 1/10 miles?7 1/4 miles in 2 hours
26 1/10 miles in x hours
Equate miles ratio hours
7 ¼ miles : 2 hours = 26 ⅒ miles : x hours
7.25 / 2 = 26.10 / x
cross product
7.25 × x = 26.10 × 2
7.25x = 52.20
divide both sides by 7.25
x = 52.20 / 7.25
x = 7.2 hours
Ultimately, it will take 7.2 hours for the dog to run 26⅒ miles.
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