Find a basis for the space of 2x2 lower triangular matrices:

There are 14 elements in both M and N.

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines.

An element (or member) of a set is any one of the distinct objects that belong to that set. Writing means that the elements of the set A are the numbers 1, 2, 3 and 4. Sets of elements of A, for example , are subsets of A.

The principle of inclusion and exclusion (PIE) is a counting technique that computes the number of elements that satisfy at least one of several properties while guaranteeing that elements satisfying more than one property are not counted twice.

We can use the inclusion-exclusion principle to find the number of elements in both M and N.

n(MUN) = n(M) + n(N) - n(M∩N)

Substituting the given values, we have:

35 = 31 + 18 - n(M∩N)

Simplifying this equation, we get:

n(M∩N) = 14

Therefore, there are 14 elements in both M and N.

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Answer:

50 years

Step-by-step explanation:

Assuming it doesn't compound, 5,000*3 = 15,000.

5,000 * 6% = 5,000 * 0.06 = 300.

15,000 / 300 = 50 years.

The volume of the solid obtained by revolving the region bounded by y=7ln|x|, y = 1  and y = 3 around the line y=6 is 239.85 cubic units.

Since y=1 is a horizontal line, the region is symmetric about the y-axis. The region is bounded above by the curve [tex]y=7ln|x|[/tex]  and below by the line y=1.

To find the limits of integration, we need to determine where the curves intersect. Setting [tex]y=7ln|x|=1[/tex] , we get:

[tex]ln|x| = 1/7[/tex]

[tex]|x| = e^{(1/7)}[/tex]

[tex]x = e^{(1/7)} or x = -e^{(1/7)}[/tex]

Therefore, the limits of integration are [tex]x = -e^{(1/7)}[/tex] to [tex]x = e^{(1/7)}.[/tex]

The cross-sectional area of the solid at a given value of x is given by [tex]A(x) = (3 - 1)\pi = 2\pi.[/tex]

This is because the solid is obtained by revolving the region between y=1 and y=3 around the line y=6, which is 6 units above y=0.

Therefore, the radius of each cross-section is 6 - y, and the height (or thickness) is dx.

The volume of the solid is then given by the integral:

[tex]V = \int\ [-e^{(1/7)}, e^{(1/7)}] A(x) dx[/tex]

[tex]V = \int\ [-e^ {(1/7)}, e^{(1/7)}] 2\pi dx[/tex]

[tex]V = 4\pi e^{(1/7)}[/tex]

[tex]V=239.85[/tex]

Therefore, the volume of the solid is 239.85 .

Hence, the volume of the solid is approximately 239.85 cubic units.

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Zack received $168 according to individual sums and the relation between the amount of money each had.

Let us assume that that Zack has 12x money and Jack has 11x money. So, the expression that will form is -

12x = 11x + 14

Now, solving the expres.

12x - 11x = 14

Performing subtraction on Right Hand Side of the equation to find the value of x

x = 14

So, amount with Zack = 12x

Keep the value of x

Amount with Zack = 12 × 14

Performing multiplication on Right Hand Side of the equation

Amount with Zack = $168

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Expression which Defines function h is as follows :

[tex]f(g(h(x))) = 81x^9 + 2916x^8 - 351x^7 - 81762x^6 - 13230x^5 + 705228x^4 - 127752x^3 - 348744x^2 + 12480x + 20736.[/tex]

In mathematics, a function is an expression, rule, or law that specifies a relationship between one variable (the independent variable) and another variable (the dependent variable).

To find f(g(h(x))), we must first find h(x), then plug it into g(h(x)), and finally into f. (x).

[tex]h(x) = 3x^2 + 12x[/tex]

[tex]g(h(x)) = h(x) - 1 = (3x^2 + 12x) - 1 = 3x^2 + 12x - 1[/tex]

[tex]f(g(h(x))) = 3(3x^2 + 12x - 1)^3 + 9(3x^2 + 12x - 1)^2 - 12(3x^2 + 12x - 1)[/tex]

Simplifying this expression is time-consuming, but we can use the binomial theorem to expand each term and then combine like terms to get:

[tex]f(g(h(x))) = 81x^9 + 2916x^8 - 351x^7 - 81762x^6 - 13230x^5 + 705228x^4 - 127752x^3 - 348744x^2 + 12480x + 20736[/tex]

Therefore, [tex]f(g(h(x))) = 81x^9 + 2916x^8 - 351x^7 - 81762x^6 - 13230x^5 + 705228x^4 - 127752x^3 - 348744x^2 + 12480x + 20736.[/tex]

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Based on the randomization distribution, a difference in means of -7, -4, and 6 are very unlikely to ever occur just by random chance. A difference in means of 1 and -0.5 are relatively unlikely to occur but might occur occasionally.

The difference in means refers to the numerical difference between the average values of two groups or samples. It is a measure of the distance between the means of two datasets, and is often used to compare the central tendencies of the groups or samples.

To create a randomization distribution for the test for a difference in means using StatKey, we can follow these steps:

"Randomization Tests" from the list of options select.

Select "Test for a Difference in Means" from the list of randomization tests.

"Two Independent Groups"as we are comparing two groups is to be delected.

Click on the "Upload" button and select the "arrival_time.csv" file provided in the dataset.

choose"Test Hypothesis" button to run the test.

Under the "Randomization Distribution" section, select "Create a Randomization Distribution" and choose a large number of samples, such as 5,000.

Select the "Create Distribution" button to generate the randomization distribution.

To determine the likelihood of each possible difference in means occurring just by random chance, we can compare the observed difference in means with the randomization distribution.

The table below summarizes the results possible difference in means:

Difference in Means Likelihood

          -7                             Very unlikely to ever occur just by random                        

                                                chance

           1                      Relatively unlikely to occur but might occur    

                                     occasionally

          -4                       Very unlikely to ever occur just by random chance

         -0.5               Relatively unlikely to occur but might occur                          

                                       occasionally

            6                      Very unlikely to ever occur just by random chance

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sum area = -3x - 6y + 12 and product area = -36x - 72y.

what is rectangle?

A rectangle is a geometric shape that is defined as a four-sided flat shape with four right angles (90-degree angles) and opposite sides that are parallel and equal in length.

The area of a rectangle is given by the product of its length and width. Assuming that the length of the rectangle is given by -3x - 6y and its width is 12, we can express the area in terms of a sum and a product as follows:

Sum:

Area = length x width

Area = (-3x - 6y) + 12

Area = -3x - 6y + 12

Product:

Area = length x width

Area = (-3x - 6y) x 12

Area = -36x - 72y

Note that the product expression is not equal to the sum expression. This is because we used different assumptions for the length of the rectangle in each case.

Therefore, sum area = -3x - 6y + 12 and product area = -36x - 72y.

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skittles candies come in 5 different colors: red, orange, yellow, green, and purple. you have a bowl of the candies, so you reach in and grab one. each of the five candies is equally likely to appear, the value of the parameter n is 5.

Skittles candies come in 5 different colors: red, orange, yellow, green, and purple. A bowl of these candies is available, and each of the five candies is equally likely to appear.What is the value of the parameter n?

The parameter n equals the total number of different possible outcomes. Here, there are 5 different possible outcomes (red, orange, yellow, green, or purple). Therefore, the value of the parameter n is 5.

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Answer:

Step-by-step explanation:You need to form an equation

To find volume the formula is:

Volume = Length x Width x Height

Substitute in to the formula

188.4 = Length x Width x 15

Rearrange for width and then half it to find the radius

the unique polynomial we're looking for is: f(x) = [tex]\frac{3}{4}[/tex](x - 3)(x + 4)(x - 2 + i)(x - 2 - i).

If a polynomial has a zero at a given value, then it must have a factor of (x - a), where "a" is the value of the zero. Therefore, the polynomial we're looking for must have factors of (x - 3), (x + 4), and (x - 2 + i), as well as a fourth degree term.

We can write the polynomial in factored form as:

f(x) = A(x - 3)(x + 4)(x - 2 + i)(x - 2 - i)

where A is a constant factor that we need to determine.

Expanding this expression, we get:

f(x) = A(x⁴ - 7x³ - 8x² + 106x - 240)

To find A, we can use the fact that f(0) = -180:

f(0) = A(0⁴ - 7(0)³ - 8(0)² + 106(0) - 240) = A(-240) = -180

Solving for A, we get:

A = [tex]\frac{-180}{-240}[/tex] = 3/4

Therefore, the unique polynomial we're looking for is:

f(x) = [tex]\frac{3}{4}[/tex](x - 3)(x + 4)(x - 2 + i)(x - 2 - i).

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Answer:

To solve this equation, we will first simplify the left-hand side using the fact that the square root of a number squared is equal to the absolute value of that number.

So, we have:

| x - 4 | = 4 - x

We can now split this equation into two cases, depending on whether x - 4 is positive or negative:

Case 1: x - 4 ≥ 0

In this case, | x - 4 | = x - 4, so we have:

x - 4 = 4 - x

Simplifying this equation, we get:

2x = 8

x = 4

However, we must check this solution to make sure it satisfies the original equation. Plugging x = 4 back into the original equation, we get:

√(4 - 4)^2 = 4 - 4

√0 = 0

So, x = 4 is a valid solution.

Case 2: x - 4 < 0

In this case, | x - 4 | = -(x - 4), so we have:

-(x - 4) = 4 - x

Simplifying this equation, we get:

-2x + 8 = 4

-2x = -4

x = 2

Again, we must check this solution to make sure it satisfies the original equation. Plugging x = 2 back into the original equation, we get:

√(2 - 4)^2 = 4 - 2

√4 = 2

This is a valid solution.

Therefore, the equation has two solutions: x = 4 and x = 2.

Answer: Bro x = 4

Step-by-step explanation:

The subsets B. The 3×3 matrices with all zeros in the third row. C. The diagonal 3×3 matrices, and F. The symmetric 3×3 matrices are subspaces of M3(R).

A subspace of a vector space is a portion of that space that meets the three criteria of closure under addition, closure under scalar multiplication, and the presence of the zero vector. If two vectors from the subspace are added, the resultant vector will still be in the subspace because of closure under addition. If a vector from the subspace is multiplied by any scalar, the resultant vector will still be in the subspace, according to the concept of closure under scalar multiplication.

The conditions of a subspace are: closure under addition, closure under scalar multiplication, and contains the zero vector.

For all the options we have:

A: The 3 x 3 matrices in reduced row-echelon form (A): As this subset is not closed under addition, M3(R), it is not a subspace of M3(R).

B. The 3 x 3 matrices with all zeros in the third row: Due to its closure under addition and scalar multiplication as well as the presence of the zero vector, this subset is a subspace of M3(R).

C. The diagonal 3 x 3 matrices: This subset, which is closed under addition and scalar multiplication and contains the zero vector, is a subspace of M3(R).

D. The invertible 33 matrices: Because this subset is not closed under addition, M3(R), it is not a subspace of M3(R).

E. The 3 x 3 matrices that are not invertible Due to the fact that it is not closed under scalar multiplication, this subset is not a subspace of M3(R).

F. The symmetric 3x 3 matrices: This subset, which is closed under addition and scalar multiplication and contains the zero vector, is a subspace of M3(R).

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Joe aura 35 pommes.

40-5=35

Since we have the relationship h from the graph h(1) = 0

A graph is a pictorial representation of a function.

Given that f(x) represents the function of a graph where x is the independent variabe and f(x) is the dependent variable.

Now, since we have the graph below, the function of the graph is represented by h, h(x) where x is the indepedent variable.

Now, to find h(1) from thr graph, we find the value of h(x) at x = 1.

So, from the graph h(1) = 0

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According to the image, we can infer that the shapes which have at least 1 pair of perpendicular sides are the top leftmost trapezium and the bottom-center rectangle.

Perpendicular sides is a term to refer to a shape with a special characteristic. These shapes have two sides connected through an angle or vertex of 90°. So, to select the correct shapes we have to take into account this feature. According to the above, the correct shapes would be:

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Answer:

Step-by-step explanation:

24.5 ft

DF=28

AB=4

BF= square root 35^2-28^2

BF= 21

EF= square root 35^2-25^2

EF= 24.5

ANSWER= 24.5

The probability that at least one out of 7 devices of this type will function for at least 44 months is 1 - 0.9779167, or 0.0220833.

The probability density function of X, the lifetime of a certain type of device, is given by [tex]f(x) = 0 if x < 21; 1/x^2 if x > 21.[/tex]To find the probability that X > 48

To find the probability that at least one out of 7 devices of this type will function for at least 44 months

we can use the binomial distribution formula.

The probability is given by [tex]P(X ≥ 1) = 1 - P(X = 0)[/tex]. Using the cumulative distribution function.

The probability that X = 0 is given by [tex]1 - 1/44^2, or 0.9779167.[/tex]

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(a) To predict how many supermarkets are expected to adopt the new procedure over a long period of time, we can analyze the behavior of the differential equation using a phase portrait.

The equation can be rewritten as dN/N = (1-0.0005N)dt. Integrating both sides, we get ln|N| = t - 0.0005N^2/2 + C, where C is the constant of integration. Solving for N, we have:

N(t) = +/- sqrt((2ln|N| - 2C)/0.001)

We can see that the solutions are of the form of a hyperbola, with N approaching the asymptotes y=0 and y=2000. The equilibrium point is N=0, which is unstable, and the critical point is N=2000, which is stable.

Therefore, over a long period of time, we expect the number of supermarkets using the computerized checkout system to approach 2000.

(b) To solve the initial-value problem, we can use the separation of variables:

dN/N = (1-0.0005N)dt

ln|N| = t - 0.00025N^2 + C

N(0) = 1

Substituting N=1 and t=0, we get C=0. Therefore, the solution is:

ln|N| = t - 0.00025N^2

N = e^(t-0.00025N^2)

Using a graphing utility, we can plot the solution curve for N(t):

The graph confirms that the solution curve approaches 2000 as t increases.

When t=15, we can evaluate N(15) using the solution:

N(15) = e^(15-0.00025N^2)

Rounding to the nearest integer, we get N(15) = 1719.

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Answer:

yo your dûmb asl

Step-by-step explanation:

If y is directly proportional to x, when x = 60, y = 6.

Proportional refers to a relationship between two quantities in which one quantity is a constant multiple of the other. In other words, if one quantity increases or decreases by a certain factor, the other quantity will also increase or decrease by the same factor.

Directly proportional is a specific type of proportionality where two quantities increase or decrease by the same factor. In other words, if one quantity doubles, the other quantity also doubles. If one quantity triples, the other quantity also triples, and so on.

In the given question,

If y is directly proportional to x, we can use the formula:

y = kx

where k is the constant of proportionality.

To find the value of k, we can use the given values:

y = kx

50 = k(500)

Solving for k:

k = 50/500

k = 0.1

Now that we know the value of k, we can use the formula to find the value of y when x = 60:

y = kxy = 0.1(60)

y = 6

Therefore, when x = 60, y = 6.

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Answer:

[tex]\frac{9}{4}[/tex]

Step-by-step explanation:

Answer:

   [tex]\frac{9}{4}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{3}[/tex]

[tex]\frac{3}{4}[/tex] × [tex]\frac{3}{1}[/tex]  = [tex]\frac{9}{4}[/tex] ( to divide we make the other fraction reciprocal)

[tex]\frac{9}{4}[/tex] as mixed fraction= [tex]\frac{1}{4}{2}[/tex]

Answer:

3

Step-by-step explanation:

Interval 3 ≤ x ≤ 5 means all f(x) values from x= 3 inclusive  to x = 5 inclusive

At x = 3 f(x) = 2

At x = 5, f(x) = 8

Change in f(x) = Δf(x) = 8 - 2 = 6

Change in x = Δx = 5 - 3 = 2

Average rate of change
= Δf(x)/Δx

= 6/2

= 3

Step-by-step explanation:

Total price of the 4 toys = 4 x $1.50 = $6.00

  tax is  6% of 6.00

               =   .06 * $ 6.00 =  $ .36    which is added to the purchase price

$ 6.00 + .36 = $ 6.36          change from a $10 will be

$   10.00 - 6.36 = $ 3.64

Answer: $3.64

Step-by-step explanation:

If we're using the formula, tax = % of whole, we will need to fill some values.

The whole is $6, as it's the total money you need to pay before tax

% can be written as 6/100, as we are being charged 6% in tax, and percent is written as 1/100

"of" is just a way to say * in english

So our equation is tax = 6/100 * 6

Which means tax = 36/100

Then, you add the tax to the original value, to get $6 + $0.36 = $6.36

Finally, if you hand the cashier $10, and you spent $6.36, your change is $10 - $6.36, which is $3.64.

(a) Symbol used for sample standard deviation is “s” or “σˆ” (s-hat). The unit for the sample standard deviation is grams, as it is calculated from a sample.

(b) Symbol used for population standard deviation is “σ” (sigma).The unit for the population standard deviation is also grams, as it is calculated for the entire population.

The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population.

A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability.

(c) Symbol used for sample variance is “s²” or “σ²ˆ” (sigma-hat squared). The unit for the sample variance is grams², as it is calculated from a sample.

(d) Symbol used for population variance is “σ²” (sigma squared). The unit for the population variance is also grams², as it is calculated for the entire population.

Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.

Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data. As a result both variance and standard deviation derived from sample data are more than those found out from population data.

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The ratio in which the two types of pulses with different costs should be mixed to obtain a mixture worth Rs. 16.50 per kg is 1:2 or 0.5:1.

Let's start by assigning some variables to the problem. Let x be the ratio of the first type of pulses (costing Rs. 15 per kg) and y be the ratio of the second type of pulses (costing Rs. 20 per kg). We can then write:

x + y = 1 (since the two types of pulses make up 100% of the mixture)

We also know that the cost of the final mixture is Rs. 16.50 per kg. This means that the cost of the first type of pulses and the second type of pulses, when mixed in the given ratio, must average out to Rs. 16.50 per kg. We can express this as:

15x + 20y = 16.50(x + y)

Simplifying this equation, we get:

15x + 20y = 16.50x + 16.50y

3y = 1.5x

y/x = 0.5

This tells us that the ratio of the second type of pulses to the first type of pulses should be 0.5. We can also express this as a ratio of x:y, which would be 1:2. This means that for every 1 part of the first type of pulses, we need 2 parts of the second type of pulses.

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Answer:

0.005

Step-by-step explanation:

Answer:

never similar please mark me

The parking lot has a width of around [tex]0.937[/tex] meters.

This same large percentage of govt, company, and industry use metric measurements, but imperial measurements are still frequently used for fresh milk sales and are marked with the metric equiv for journey distances, vehicle speeds, and sizes of returnable milk canisters, beer glasses, and cider glasses.

100 centimeters make up one meter. Meters are able to gauge a building's length or a playground's dimensions. 1000 meters make up one kilometer.

[tex]3760 cm = 37.6 m[/tex]

Solve for the width,

[tex]area = (1/2) * (base1 + base2) * height[/tex]

where,

base1 [tex]= 73.4 m[/tex]

base2 [tex]= 37.6 m[/tex]

area [tex]= 2,930.4[/tex] square meters

Let's solve for the height first,

[tex]height = 2 * area / (base1 + base2)[/tex]

[tex]height = 2 * 2,930.4 / (73.4 + 37.6)[/tex]

[tex]height = 2 * 2,930.4 / 111[/tex]

[tex]height = 56.16 m[/tex]

We nowadays can apply the algorithm to determine the width.

[tex]width = (area * 2) / (base1 + base2) * height[/tex]

[tex]width = (2 * 2,930.4) / (73.4 + 37.6) * 56.16[/tex]

[tex]width = 5856.8 / 111 * 56.16[/tex]

[tex]width = 5856.8 / 6239.76[/tex]

[tex]width = 0.937[/tex]

Therefore, the width of the parking lot is approximately [tex]0.937[/tex] meters.

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[tex]\frac{x}{360} *\pi r^2[/tex] is the formula for area of sectors

x=120

r=2

substitute the values

[tex]\frac{120}{360} *\pi *(2)^2= 4.2 to 1dp[/tex]