find the length of UX

Answer:

C. Distributive property

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

did you ever fine out the answer to this lol

Step-by-step explanation:

Oil is spilled onto a kitchen floor. The area covered by the oil at time t is given by the function A, where A(t) is measured in square centimeters and t

is measured in seconds. The rate at which the area covered by the oil is changing at time t = 10 is  A'(10).

Given that:

To determine the rate at which the area covered by the oil is changing with time, we need to differentiate  A(t) with respect to time t.

∴

By differentiation:

\(\mathbf{\dfrac{dA}{dt} =A'(t)}\)

∴

\(\mathbf{\dfrac{dA}{dt} \Big| _{t=10}=A'(t)\Big|_{t=10}}\)

\(\mathbf{\dfrac{dA}{dt} =A'(10)}\)

Therefore, we can conclude that the rate at which the area covered by the oil is changing at time t=10 is  A'(10).

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Answer:

Answer for the given question is 54.

Step-by-step explanation:

Given the data:

3+2+1+1+4+2+4+4+1+5+5+5-5+4+1+8+5+4

22+15-5+4+1+8+9

59-5

54

Therefore,

Summation of given equation is 54

Based on the given information, with a deposit of $18,000 and an ending balance of $18,756 after 6 years, the annual interest rate is approximately 4.1%.

To find the annual interest rate, we can use the simple interest formula: I = P * r * t, where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate, and t is the time period in years.

In this case, Mary deposited $18,000 into the savings account and after 6 years, the ending balance was $18,756. We can calculate the interest earned as the difference between the ending balance and the principal:

I = $18,756 - $18,000 = $756

Substituting the values into the formula:

$756 = $18,000 * r * 6

Simplifying the equation, we find:

r ≈ 0.041 or 4.1%

Therefore, the annual interest rate on Mary's savings account is approximately 4.1%.

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No, there is only one outlier at 58 minutes.

An observation that differs abnormally from other values in a population-based random sample is referred to as an outlier. In a way, this definition defers to the analyst's (or a consensus process') judgment as to what constitutes aberrant behavior. It is vital to define typical observations before distinguishing aberrant ones.

A data point is considered an outlier if it is more than 1.5 times the IQR below the first quartile or more than 1.5 times the IQR above the third quartile, according to the general criterion for utilizing it to compute outliers. The first and third quartile percentiles must be known in order to compute the IQR.

The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list.

9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58

One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5×IQR rule for outliers, is there evidence to support the student's claim?

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A: 2.508 is the critical value you would use to obtain a 98% confidence interval for the mean m of the population if s is unknown.

The critical value to obtain a 98% confidence interval for the mean of a normally distributed population with an unknown standard deviation, based on a sample size of 23, can be found using a t-distribution with 22 degrees of freedom (since we lose 1 degree of freedom for estimating the sample mean).

Using a t-distribution table, we can find the critical value that corresponds to the 1% level of significance in a two-tailed test with 22 degrees of freedom, which is the area beyond which we want to find the critical value. This critical value is given by:

t(0.01/2, 22) ≈ 2.508

Therefore, the answer is (a) 2.508.

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The 95% confidence interval for the difference between the proportion of the population who would survive at least 15 years can be used to estimate the range within which the true difference lies.

It provides a measure of uncertainty around the point estimate. The confidence interval can be interpreted as follows: we are 95% confident that the true difference in proportions of the population who would survive at least 15 years falls within the calculated interval. To construct the confidence interval, we first need to obtain sample data from the population. Let's assume we have collected data from two independent samples. From Sample 1, we find that out of n1 individuals, x1 survive at least 15 years. Similarly, from Sample 2, we have n2 individuals, with x2 surviving at least 15 years. To calculate the confidence interval, we use the formula: CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)) Where p1 = x1 / n1 and p2 = x2 / n2 are the sample proportions, and Z is the critical value corresponding to the desired confidence level (in this case, 95%). The critical value is determined based on the standard normal distribution. Once we have the confidence interval, let's say [lower limit, upper limit], we can interpret it as follows: We are 95% confident that the true difference in proportions between the two populations who would survive at least 15 years lies between the lower limit and the upper limit. In other words, there is a high likelihood that the actual difference falls within this range. The confidence interval allows us to make inferences about the population based on our sample data. It provides a range of plausible values for the difference in proportions, taking into account the variability of the sample. The wider the confidence interval, the greater the uncertainty in our estimate. Conversely, a narrower interval indicates a more precise estimation.

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Answer:

he would have to ride for 3 miles each of the six days left to meet his goal

Step-by-step explanation:

The probability P(GH) is 0%.

Since we know that,

Probability denotes the likelihood of something happening. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one.

Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. Probability is defined as the degree to which something is likely to occur.

This is the fundamental probability theory, which is also utilized in probability distribution, in which you will learn about the possible results of a random experiment.

To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.

Now to find the probability of GH,

We can see that there is no any poit G and H are showing in the given number line,

Therefore,

Favorable outcomes = 0

Since we know that,

Probability = number of favorable outcomes/total number of outcomes

Thus,

⇒ P(GH) = 0/total number of outcomes

Hence,

⇒ P(GH) = 0%

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Using Cramer's rule the solutions to the system of equations are:

X1 = 21 / (-J2 - 9)

X2 = -12 / (-J2 - 9)

Using Cramer's rule, we can solve the system of equations:

J2X1 - X2 - 3 = 0

X1 + 3X2 - 7 = 0

3X1 + 2X2 - 1 = 0

4X1 + 5X2 = 14

The values of X1 and X2, we'll calculate the determinants.

Let D be the determinant of the coefficient matrix:

D = |J2 -1 0| = J2(-1) - 3(3) = -J2 - 9

D1 is the determinant obtained by replacing the first column of the coefficient matrix with the constants:

D1 = |0 -1 0| = 0(-1) - (-7)(3) = 21

D2 is the determinant obtained by replacing the second column of the coefficient matrix with the constants:

D2 = |J2 0 0| = J2(0) - 3(4) = -12

Now, we can calculate the values of X1 and X2 using the determinants:

X1 = D1 / D = 21 / (-J2 - 9)

X2 = D2 / D = -12 / (-J2 - 9)

Therefore, the solutions to the system of equations are:

X1 = 21 / (-J2 - 9)

X2 = -12 / (-J2 - 9)

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Answer:

b.

Step-by-step explanation:

α=36∘   β=90 ∘   α+β+γ = 180∘  γ = 180∘  −α−β = 180∘  −36∘  −90∘ = 54∘

a=43

a b  =  sinα sinβ  b=a⋅   sinα  sinβ b=43⋅   sin36  ∘  

sin90∘ =73.16

 a  c   =  sinα  sinγ  c=a⋅  sinα  sinγ  c=43⋅   sin36 ∘ sin54 ∘  =59.18

a=43

b=73.16

c=59.18

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

To establish that S is a subspace of ℝ^3, we must confirm that S is closed under vector summation and scalar multiplication.

A pertinent theorem from linear algebra that can be applied here is the "Subspace Criterion" theorem. This principle states that a non-empty subset S of a vector space V is a subspace if and only if it fulfills the following conditions:

For any vectors a, b ∈ S, their addition a + b ∈ S.

For any vector a ∈ S and any scalar k, the product ka ∈ S.

Now, let's define a vector m = v - e.

Observe that for any y in S, we have:

m • y = (v - e) • y = (v • y) - (e • y) = 0.

This implies that y is orthogonal to the vector m.

Geometrically, S represents a plane in ℝ^3 that is orthogonal (perpendicular) to the vector m.

As the plane is closed under vector summation and scalar multiplication, S is indeed a subspace of ℝ^3.

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Suppose v = (2, 4, 5) and e = (6, 7, 3) are a pair of vectors in ℝ^3. Let S be the collection of all y in ℝ^3 such that the inner product of v and y equals the inner product of e and y (i.e., v • y = e • y).

What principle can be utilized to demonstrate that S is a subspace of ℝ^3? Describe S in geometric terms.

Answer:

C.97

Step-by-step explanation:

The maximum area would be a square with 4 identical sides.

36/4 = 9

Each side would be 9 feet long.

Area = 9 x 9 = 81 square feet

Answer: 81 square feet

Rebecca and Mohammed sold 16 shirts and 6 hats.

To solve this problem, we can write an equation on the information provided. Let x be the number of shirts sold and y be the number of hats sold. Such that:

x + y = 22 {the total number of pieces sold}

12x + 9y = 350 - 125 {the total profit, including the savings they started with}

We can solve for one variable in terms of the other using the first equation:

x = 22 - y

Then we can substitute this expression into the second equation:

12(22 - y) + 9y = 350 - 125

Simplifying this equation:

264 - 12y + 9y = 350 - 125

y = 6

Therefore, Rebecca and Mohammed sold 6 hats and 16 shirts

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Answer: -4

Work: So, to get -4, we need to simplify the equation. If you see any equation with +(- that's subtraction. So, with the rule, this equation is basically 8-12, and that's -4.

Answer:

-4

Step-by-step explanation:

8+(-12)

= 8-12

12-8=4

the answer is -4

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Algebra

Factor

Factor the polynomial.

(

x

+

3

)

(

x

+

5

)

Tap to view FREE steps...

()|[]√≥

789≤

456/^×>∩∪

123-+÷<π∞

,0.%=

Factor

x

2

+

8

x

+

15

+

0

Regroup terms.

x

2

+

0

+

8

x

+

15

Add

x

2

and

0

.

x

2

+

8

x

+

15

Factor

x

2

+

8

x

+

15

using the AC method.

Tap for fewer steps...

Consider the form

x

2

+

b

x

+

c

. Find a pair of integers whose product is

c

and whose sum is

b

. In this case, whose product is

15

and whose sum is

8

.

3

,

5

Write the factored form using these integers.

(

x

+

3

)

(

x

+

5

)

Answer:

(x+3)(x+5)

Step-by-step explanation:

Answer:

treatment iijiijiuej325ufffufuvufuuuuuuuuuuuuuu

Answer:

16m

Step-by-step explanation:

Using the formula A=h_b*b/2

56=h_7*7/2

h_7*7=112

divide both sides by 7

h_7=16

Ans of your question . in which class do u read?

A population is the set of all individuals of interest in a particular study.

The concept of population and sample are used to solve this problem. The population is the collection of the units under study and the sample is a part of the population that is studied to draw the required conclusions. Statistical inference consists of hypothesis testing and estimation of unknown population parameters.

Population: A population is defined as every unit that is covered under research. The population is a larger group for which any study is conducted.

Sample: A sample is a part of the population that represents the whole population. The unknown population parameters are estimated using the sample results.

‎Statistic: A statistic is the characteristic of a sample, such as mean, standard deviations, etc.

‎

‎Parameter: A parameter is the same as a statistic but it represents the characteristics of the population. A parameter is an unknown value that is to be estimated from the sample statistic.

‎

‎Variable: A variable is an attribute that can describe the characteristics, number, or quantity that can be measured or counted. A variable is also considered a data item. Age, gender, number of students in a class, country of birth, capital expenditure, class grades, and different types of vehicles are examples of variables. It is called a variable because the value of the variable may vary from time from one entity to another.

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Answer:

Profit % = 111.1 %

Step-by-step explanation:

Cost of glove = £4

Sales price of glove and skirt = £48

100% profits on the cost of the glove

20% profit on the total cost

Profit on the total cost = 20% = 0.20

Total cost + 0.20 total cost = Sale value

1.20 * total cost = 48

Total cost = 48 / 1.20

Total cost = 40

Cost of the skirt = Total cost - cost of the gloves

Cost of the skirt = 40 - 4

= 36

Price of the skirt = total value - price of the gloves

Total value = £48

100% of £4 = 100/100 * £4

= £4

Profits + cost of glove = $8

Amount remaining = £48 - £8

= £40

Profit percentage on the skirt = price of the skirt / cost of the skirt

= 40 / 36 * 100

= 1.1111 * 100

Profit % = 111.1 %

I)

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 3 +1}{2}~~~ ,~~~ \cfrac{ 9 +5}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 14 }{2} \right)\implies (2~~,~~7)\)

II)

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the line AB

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 4 }{ 2 } \implies 2 \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ 2 \implies \cfrac{2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{2} }}\)

so we're really looking for the equation of a line whose slope is -1/2 and it passes through (2 , 7)

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{2}) \\\\\\ y-7=- \cfrac{1}{2}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{2}x+8 \end{array}}\)

Answer: 6 inches.

Step-by-step explanation:

Answer:

I think the answer is twenve

The complete product is:

Every fraction has a numerator and a denominator separated by a horizontal bar known as the fractional bar.

As, the length of the painted area is 3 1/5 and width of the painted area is 2/3.

So, multiplication of length and width is as follows:

3 1/5 x 2/3

= 3 x 2/3 + 1/5 x 2/3

= 6/3 + 2 / 15

= 30 + 2 / 15

= 32/ 15

= 2 2/15

Thus, the required fraction is 2 2/15.

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