The table below shows how much time some people spent exercising yesterday. a) What is the modal class of time spent exercising? b) In which class does the median lie? Time spent, x (minutes) 0≤x≤10 10< x≤20 20< x≤30 30< x≤40 40< x≤50 50≤x≤60 Frequency 18 14 3 16 21 7​

Answers

Answer 1

a) The modal class of time spent exercising is given as follows: 40 < x ≤ 50

b) The median lies on the class 30 < x ≤ 40.

How to obtain the median and mode?

The mode of a data-set is the observation that appears the most times in the data-set, hence, for item a, we consider that the mode lies in the class 40 < x ≤ 50, which has the highest number of observations, which is 21.

The total number of elements in the data-set is given as follows:

18 + 14 + 3 + 16 + 21 + 7 = 79.

Hence the median is the element at the cumulative position given as follows:

(79 + 1)/2 = 40.

Which is on the following class:

30 < x ≤ 40.

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Related Questions

the polygons in each pair are similar. find the missing side length

Answers

10/5 = 12/x
2 = 12/x
Multiply both sides by x
2x = 12
x = 6

Answer = 6

Have a good day ^^

what is the approximate value of 12 to the nearest whole number

Answers

Approximation of 12.0 by rounding off the number is 12.

What is approximation of numbers?

Anything similar to something else but not precisely the same is called an approximation. By rounding, a number may be roughly estimated. By rounding the values in a computation before carrying out the procedures, an estimated result can be obtained.

Rounding is a very basic estimating technique. The main ability you need to swiftly estimate a number is frequently rounding. In this case, you may simplify a large number by "rounding," or expressing it to the tenth, hundredth, or a predetermined number of decimal places.

In the given problem, we are asked to approximate the value of 12.0 which is equal to 12.

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A 186 foot yacht at cruise speed can generate 2.3 tons of carbon dioxide per hour. Which of the following is closest to this rate, in pounds per minutes? a. 1.3 pounds per minutes b. 14.5 pounds per minutes c. 26.1 pounds per minutes d. 76.7 pounds per minutes ​

Answers

Answer:

b

Step-by-step explanation:

Kevin and Randy Muise have a jar containing 71 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $10.35. How many of each type of coin do they have? The jar contains ? quarters.​

Answers

Kevin and Randy have 34 quarters and 37 nickels in the jar.

How to find the coins in the jar

System of equations for solving the problem is achieved using

the number of quarters as "q" and

the number of nickels as "n."

From the given information, we can set up the following equations

q + n = 71                            equation 1

0.25q + 0.05n = 10.35      equation 2

Multiply equation 1 by 0.05

0.05q + 0.05n = 0.05(71)

0.05q + 0.05n = 3.55        equation 3

Now, subtract equation 3 from equation 2

0.25q + 0.05n - (0.05q + 0.05n ) = 10.35 - 3.55

0.25q - 0.05q = 6.80

0.20q = 6.80

q = 6.80 / 0.20

q = 34

Substitute the value of q back into equation 1

34 + n = 71

n = 71 - 34

n = 37

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which equation represents the graph below?

Answers

Answer:

D because graph is linear

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

the y-int is (0,4) and the slope is 2/1

therefore the equation is y=2x-4

let e be an algebraic extension of a field f. if r is a ring and f ⊆ r ⊆ e show that r must be a field.

Answers

If e is an algebraic extension of a field f and r is a ring with [tex]f\subseteq r\subseteq e$,[/tex] then r must be a field.

we have [tex]a^{-1} = -\frac{1}{c_0}(a^{n-1} + c_{n-1}a^{n-2} + \cdots + c_1)$,[/tex] and all of the terms on the right-hand side of this equation belong to $r$.

Therefore, [tex]$a^{-1}\in r$[/tex], and we have shown that r is a field.

Since e is an algebraic extension of f, every element [tex]$x\in e$[/tex] satisfies some non-zero polynomial with coefficients in [tex]$f$[/tex], say [tex]$f(x)=0$[/tex]  for some non-zero polynomial[tex]$f(t) \in f[t]$.[/tex]

Now, suppose [tex]$r$[/tex] is a subring of  [tex]$e$[/tex] containing f.

To show that r is a field, it suffices to show that every non-zero element of r has a multiplicative inverse in r.

Let [tex]$a\in r$[/tex] be a non-zero element.

Since [tex]$a\in e$[/tex] , there exists a non-zero polynomial [tex]$f(t)\in f[t]$[/tex]  such that [tex]f(a)=0$.[/tex]

Let n be the degree of f(t), so that [tex]f(t) = t^n + c_{n-1}t^{n-1} + \cdots + c_1 t + c_0$ for some $c_i\in f$, $0\leq i\leq n-1$.[/tex]

Then, we have [tex]a^{-1} = -\frac{1}{c_0}(a^{n-1} + c_{n-1}a^{n-2} + \cdots + c_1)$,[/tex] and all of the terms on the right-hand side of this equation belong to r.  

Therefore, [tex]$a^{-1}\in r$[/tex], and we have shown that r is a field.

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Thomas is a car salesman. The table shows the salary that Thomas earns for the number of cars he sells. Use the data to make a graph. Then, find the slope of the line and explain what it shows.

Answers

An

Step-by-step explanation:

y=600x+220

explanation
its the relationship between sales and wages the base wage is  2200 and an increase of 600 per car sold

Anyone can help?
The area A of the shades region is given, find the central angle 0 of the circle and round to the nearest tenth

Answers

Answer:

The answer is approximately 86°

Step-by-step explanation:

Area of sector =ß/360×pir²

90.6=ß/360×22/7×11²

90.6=2662ß/2520

cross multiply

90.6×2520=2662ß

228312=2662ß

divide both sides by 2662

2662ß÷2662=228312÷2262

ß86°

the polygons in each pair are similar. find the missing side length

Answers

The missing side length in the figure is 40 units

How to find the missing side length

From the question, we have the following parameters that can be used in our computation:

The similar polygons

To calculate the missing side length, we make use of the following equation

x : 30 = 48 : 36

Where the missing length is represented with x

Express as a fraction

So, we have

x/30 = 48/36

Next, we have

x = 30 * 48/36

Evaluate

x = 40

Hence, the missing side length is  40 units

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Letv→1=[0.5−0.50.50.5], v→2=[−0.5−0.5−0.50.5], v→3=[−0.50.50.50.5].Find a vector v→4 in R4 such that the vectors v→1, v→2, v→3, and v→4 are orthonormal.
v→4= [

Answers

To find a vector v→4 such that the vectors v→1, v→2, v→3, and v→4 are orthonormal, the vector v→4 can be calculated as [0, -0.5, 0.5, -0.5].

For the vectors v→1, v→2, v→3, and v→4 to be orthonormal, they need to satisfy two conditions: they must be orthogonal (perpendicular to each other) and each vector must have a magnitude of 1 (unit length).

Given that v→1, v→2, and v→3 are provided, we can choose v→4 such that it is orthogonal to the other vectors and has a magnitude of 1. Since v→1, v→2, and v→3 are in R4, v→4 must also be a four-dimensional vector in R4.

Observing the pattern in the given vectors, we can see that v→4 can be chosen as [0, -0.5, 0.5, -0.5].

This vector satisfies the condition of orthogonality with v→1, v→2, and v→3 since its dot product with each of those vectors is zero.

Additionally, the magnitude of v→4 is

√(0^2 + (-0.5)^2 + 0.5^2 + (-0.5)^2) = √(0.5) = 1,

satisfying the condition of unit length.

Thus, v→4 = [0, -0.5, 0.5, -0.5] is a vector that makes the set of vectors orthonormal.

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Let V be a finite-dimensional inner product space. Suppose TEL(V). (a) Prove that T and T* have the same singular values. (b) Prove that dim range T equals the number of nonzero singular values of T.

Answers

a. The singular values of T and T* are the square roots of the same set of eigenvalues, and so they are equal.

b. The range of T is spanned by the vectors {u1, u2, ..., un}.

Moreover, since[tex]T(vi) = \sqrt{( \lambda i)u_i, }[/tex] we see that the dimension of the range of T is the same as the number of nonzero singular values of T, which is the number of positive square roots of the eigenvalues of T*T.

(a) To prove that T and T* have the same singular values, we first note that the singular values of T and T* are the square roots of the eigenvalues of TT and TT*, respectively.

This is because if we diagonalize TT and TT*, the singular values will be the square roots of the diagonal entries.

Now, since V is finite-dimensional, we know that TT and TT* are both self-adjoint and have the same eigenvalues. This is because the eigenvalues of TT and TT* are the same as the eigenvalues of TTT and TTT*, respectively, and these matrices are similar to each other (they have the same Jordan canonical form) because T and T* have the same characteristic polynomial.

Therefore, the singular values of T and T* are the square roots of the same set of eigenvalues, and so they are equal.

(b) We know that the singular values of T are the square roots of the eigenvalues of TT.

Since TT is self-adjoint, it can be diagonalized with respect to an orthonormal basis of V. Let {v1, v2, ..., vn} be an orthonormal basis of eigenvectors of T*T with corresponding eigenvalues λ1, λ2, ..., λn.

Then, we have:

[tex]T(vi) = \sqrt{(\lambda i)u_i}[/tex]

where [tex]u_i = T(vi) / \sqrt{(\lambda i) }[/tex] is a unit vector.

Therefore, the range of T is spanned by the vectors {u1, u2, ..., un}. Moreover, since[tex]T(vi) = \sqrt{( \lambda i)u_i, }[/tex] we see that the dimension of the range of T is the same as the number of nonzero singular values of T, which is the number of positive square roots of the eigenvalues of T*T.

Hence, we have shown that the dimension of the range of T is equal to the number of nonzero singular values of T.

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find the

Mean,

Median,

Mode,

Range. each one of the line plots please

Answers

The solution is:

Mean  = 22.4 .

Median = The median is the middle value, which is 23.

Mode = Separate multiple are 17, 23, and 25.

Range= The range of ages is 13 years.

Here, we have,

Mode: Separate multiple are 17, 23, and 25.

The mean age is 22.4 years old, to the nearest tenth.

The range of ages is 13 years.

Here is a dot plot for the given data set:

16 ●●

17 ●●●

19 ●

20 ●

21 ●●●

23 ●●●

24 ●

25 ●●●●

27 ●

29 ●●

Mode: The mode is the most common value in the data set. In this case, there are multiple values that occur with the same frequency, so there are multiple modes: 17, 23, and 25.

Mean: The mean is the sum of all the values divided by the total number of values. We can add up all the ages and divide by 21 (the number of contestants) to get:

(20 + 23 + 25 + 24 + 16 + 19 + 21 + 29 + 29 + 21 + 17 + 25 + 25 + 17 + 23 + 27 + 23 + 17 + 16 + 21 + 16) / 21 = 22.4

Median: The median is the middle value when the data set is arranged in order. We can arrange the ages in ascending order:

16, 16, 17, 17, 19, 20, 21, 21, 23, 23, 23, 24, 25, 25, 25, 27, 29, 29

The median is the middle value, which is 23.

Range: The range is the difference between the largest and smallest values in the data set.

The largest value is 29 and the smallest value is 16, so the range is:

29 - 16 = 1

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Question

Create a Dot Plot on your paper for the data set, then find the mode, mean, median, and range.

The ages of the top two finishers for "American Idol" (Seasons 1-11) are listed below.

20, 23, 25, 24, 16, 19, 21, 29, 29, 21, 17, 25, 25, 17, 23, 27, 23, 17, 16, 21, 16

Create a Dot Plot on your paper for the data set

Find the following:

Mode: Separate multiple answers with a comma. Mean to nearest tenth: Median: Range:

12pi/5 divided by 2pi

Answers

The Simplified form of (12π/5) ÷ (2π) is 6/5.

The expression (12π/5) ÷ (2π), we can divide the numerator (12π/5) by the denominator (2π). This can be done by multiplying the numerator by the reciprocal of the denominator.

Reciprocal of 2π is 1/(2π), so the expression can be written as:

(12π/5) * (1/(2π))

Now, let's simplify:

(12π/5) * (1/(2π)) = (12π/5) * (1/2π)

π cancels out in the numerator and denominator:

= (12/5) * (1/2)

= 12/10

= 6/5

Therefore, the simplified form of (12π/5) ÷ (2π) is 6/5.

In conclusion, the expression (12π/5) ÷ (2π) simplifies to 6/5.

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a researcher tested the effects of serotonin on a group of aggressive rats and gave a control group a placebo treatment. the researcher should use a ____ t-test to test the data.

Answers

The researcher should use an independent samples t-test to test the data.

What statistical test should the researcher use to analyze the data?

An independent samples t-test is appropriate when comparing the means of two independent groups or conditions.

In this case, the researcher has a group of rats that received the serotonin treatment and another group that received a placebo treatment. These groups are independent of each other because the rats in one group do not affect or interact with the rats in the other group.The t-test will allow the researcher to determine if there is a significant difference between the means of the two groups.Indicating whether the serotonin treatment had an effect on the aggression levels compared to the placebo.An independent samples t-test compares the means of two independent groups, considering sample sizes, standard deviations, and potentially assuming equal or unequal variances. It provides a p-value indicating the probability of observing the observed mean difference if there were no true difference between the populations. A p-value below the significance level (e.g., 0.05) suggests a significant difference between the groups.

Therefore, independent samples t-test is used to compare the effects of two different treatments on two separate groups.

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If all of the angles in the pentagon below are congruent (equal), then what is the m A) 77°
B) 97°
C) 108°
D) 120°

Answers

Answer:

C

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

a pentagon has 5 sides , that is n = 5

sum = 180° × (5 - 2) = 180° × 3 = 540°

since the 5 angles are congruent then divide the sum by 5 , that is

∠ F = 540° ÷ 5 = 108°

Step-by-step explanation:

Formula of calculating total angles with n side (Polygon) : (n-2) . 180°

total pentagon angles :

= (5 - 2) . 180

= 3 . 180

= 540°

all of the angle is congruent, then :

m<F = 540/5

m<F = 108° (C)

Subject : Mathematics

Level : JHS

Chapter : Geometry

Let {
a
n
}
be a sequence and L
a real number such that lim
n

[infinity]
a
n
=
L
. Prove that {
a
n
}
is bounded.

Answers

To prove that the sequence {an} is bounded, we can utilize the fact that the limit of the sequence exists. Since the limit of {an} as n approaches infinity is L, we can conclude that there exists some positive integer N such that for all n greater than or equal to N, the terms of the sequence are arbitrarily close to L.

1. By considering the terms up to index N-1, we can find a maximum value M that is greater than or equal to all those terms. By choosing the larger of M and L, we can establish an upper bound for all terms of the sequence.

2. Let's assume that the limit of {an} as n approaches infinity is L. This means that for any given positive epsilon, there exists a positive integer N such that for all n greater than or equal to N, the absolute value of (an - L) is less than epsilon. In other words, the terms of the sequence {an} become arbitrarily close to L as n becomes larger.

3. Now, let's consider the terms of the sequence up to index N-1. Since there are only finitely many terms before index N, we can find the maximum value among those terms, denoted as M. We know that M is greater than or equal to all the terms before index N.

4. To establish an upper bound for the entire sequence {an}, we consider two cases: (1) M is greater than or equal to L, and (2) M is less than L. In case (1), we choose M as the upper bound for the entire sequence {an}. Since M is greater than or equal to all terms before index N, and for all n greater than or equal to N, the terms become arbitrarily close to L, M serves as an upper bound for the entire sequence.

5. In case (2), we choose L as the upper bound for the entire sequence {an}. Since L is the limit of the sequence, and for all n greater than or equal to N, the terms become arbitrarily close to L, L serves as an upper bound for the entire sequence.

6. Therefore, we have shown that in both cases, the sequence {an} is bounded, with an upper bound of either M or L, depending on the situation.

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FILL IN THE BLANK a/an ____________________________ diagram can be used to show how the tables in a database are defined and related..

Answers

A/an database schema diagram can be used to show how the tables in a database are defined and related.

This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and  their attributes, and the relationships between them.

The database schema diagram helps in the  understanding the logical design of the database, including primary keys, for  foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in  designing, modifying, and querying the database effectively.

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Determine if the square root of
0.686886888688886888886... is rational or irrational and give a reason for your answer.

Answers

Answer:

Rational

Step-by-step explanation:

It would be a decimal

Find the inverse Laplace transform of the function H(s) = as + b . (s−α)2 +β2

Answers

The inverse Laplace transform of H(s) = (as + b) / ((s - α)^2 + β^2) is Ae^(αt)cos(βt) + Be^(αt)cos(βt), where A = B = (as + b) / (2jβ).

To find the inverse Laplace transform of the function H(s) = (as + b) / ((s - α)^2 + β^2), we can use partial fraction decomposition and known Laplace transform pairs.

Let's rewrite H(s) as follows:

H(s) = (as + b) / ((s - α)^2 + β^2)

= (as + b) / ((s - α + jβ)(s - α - jβ))

Now, we can perform partial fraction decomposition on H(s):

H(s) = (as + b) / ((s - α + jβ)(s - α - jβ))

= A / (s - α + jβ) + B / (s - α - jβ)

To find the values of A and B, we can multiply both sides of the equation by the denominator and then substitute specific values of s. Let's choose s = α - jβ:

(as + b) = A(α - jβ - α + jβ) + B(α - jβ - α - jβ)

= A(2jβ) - B(2jβ)

= 2jβ(A - B)

From this equation, we can equate the real and imaginary parts to find A and B. Since there is no imaginary term on the left side, we have:

2jβ(A - B) = 0

This implies that A - B = 0, or A = B.

Now, let's substitute s = α + jβ:

(as + b) = A(α + jβ - α + jβ) + B(α + jβ - α - jβ)

= A(2jβ) + B(2jβ)

= 2jβ(A + B)

Again, equating the real and imaginary parts, we have:

2jβ(A + B) = as + b

This equation gives us the following relation between A and B:

A + B = (as + b) / (2jβ)

Now, let's find the inverse Laplace transform of each term using known Laplace transform pairs:

L^-1[A / (s - α + jβ)] = Ae^(αt)cos(βt)

L^-1[B / (s - α - jβ)] = Be^(αt)cos(βt)

Therefore, the inverse Laplace transform of H(s) is:

L^-1[H(s)] = Ae^(αt)cos(βt) + Be^(αt)cos(βt)

In summary, the inverse Laplace transform of H(s) = (as + b) / ((s - α)^2 + β^2) is Ae^(αt)cos(βt) + Be^(αt)cos(βt), where A = B = (as + b) / (2jβ).

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find the probablitiy p(z>.0=46) for a standard normal random variable z

Answers

The probability P(z>0.46) for a standard normal random variable z is 0.8228 or 82.28%.

The probability P(z>0.46) for a standard normal random variable z can be found using the standard normal distribution table or a calculator with a normal distribution function.

Using the table, we can locate the value 0.46 in the first column and the tenths place of the second column. This gives us a corresponding area of 0.1772. However, we need the probability of the right tail, which is 1-0.1772 = 0.8228.

Alternatively, we can use a calculator with a normal distribution function. The function requires the mean (which is 0 for a standard normal distribution) and the standard deviation (which is 1 for a standard normal distribution) and the upper bound of the integral (which is 0.46 in this case). Using this information, we can calculate the probability P(z>0.46) as follows:

P(z>0.46) = 1 - P(z<0.46)

= 1 - 0.6772

= 0.8228

Therefore, the probability P(z>0.46) is 0.8228 or approximately 82.28%.

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use the fourth order taylor polynomial for e9x at x=0 to approximate the value of e1/8.
e1/8=

Answers

The fourth-order Taylor polynomial approximation, e^(1/8) is approximately 2.775

To approximate the value of e^(1/8) using the fourth-order Taylor polynomial for e^9x at x=0, we can expand the function e^9x using its Taylor series centered at x=0 and keep terms up to the fourth order.

The Taylor series expansion for e^9x is given by:

e^9x = 1 + 9x + (9^2/2!) * x^2 + (9^3/3!) * x^3 + (9^4/4!) * x^4 + ...

approximate the value of e^(1/8), so we substitute x = 1/8 into the Taylor series expansion:

e^(1/8) ≈ 1 + 9(1/8) + (9^2/2!) * (1/8)^2 + (9^3/3!) * (1/8)^3 + (9^4/4!) * (1/8)^4

Simplifying this expression will give us the approximation:

e^(1/8) ≈ 1 + 9/8 + (81/2) * (1/64) + (729/6) * (1/512) + (6561/24) * (1/4096)

Calculating this approximation:

e^(1/8) ≈ 1 + 1.125 + 0.6328125 + 0.017578125 + 0.000823974609375

e^(1/8) ≈ 2.7750142097473145

Therefore, using the fourth-order Taylor polynomial approximation, e^(1/8) is approximately 2.775

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The fourth order Taylor polynomial approximation for e^(1/8) is approximately 1.06579.

The fourth order Taylor polynomial for e^9x at x=0 is:

f(x) = 1 + 9x + 81x^2/2 + 729x^3/6 + 6561x^4/24

To approximate e^(1/8), we substitute x=1/72 (since 1/8 = 9(1/72)):

f(1/72) = 1 + 9/8 + 81(1/8)^2/2 + 729(1/8)^3/6 + 6561(1/8)^4/24

f(1/72) = 1.06579

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3/4x+5=3/8 without fractions

Answers

x = -6.666666 repeating

Answer: x=-5.83..(repeated)

uppose v1,v2,v3 is an orthogonal set of vectors in r5 . let w be a vector in span(v1,v2,v3) such that ⟨v1,v1⟩=3,⟨v2,v2⟩=8,⟨v3,v3⟩=16 , ⟨w,v1⟩=−3,⟨w,v2⟩=−40,⟨w,v3⟩=64 ,

Answers

The projection of w onto each vector in the basis is -v1 - 5v2 + 4v3.

We can use the orthogonal projection formula to find the coordinates of w with respect to the basis {v1, v2, v3}.

The coordinates of w are given by:

w1 = ⟨w, v1⟩ / ⟨v1, v1⟩ = -3/3 = -1

w2 = ⟨w, v2⟩ / ⟨v2, v2⟩ = -40/8 = -5

w3 = ⟨w, v3⟩ / ⟨v3, v3⟩ = 64/16 = 4

So, the coordinates of w with respect to the basis {v1, v2, v3} are (-1, -5, 4).

To find the projection of w onto each vector in the basis, we can use the formula for orthogonal projection:

proj_v1(w) = ⟨w, v1⟩ / ⟨v1, v1⟩ × v1 = (-3/3) × v1 = -v1

proj_v2(w) = ⟨w, v2⟩ / ⟨v2, v2⟩ × v2 = (-40/8) × v2 = -5v2

proj_v3(w) = ⟨w, v3⟩ / ⟨v3, v3⟩ × v3 = (64/16) × v3 = 4v3

The projection of w onto each vector in the basis is -v1 - 5v2 + 4v3.

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The norm of vector w in span(v1, v2, v3) is ||w|| = 13.

Given an orthogonal set of vectors v1, v2, v3 in R^5, and a vector w in the span of v1, v2, v3, we are provided with the inner products between v1, v2, v3, and w.

To find the norm of vector w, we use the formula:

||w|| = sqrt(⟨w, w⟩)

We are given the inner products between w and v1, v2, v3:

⟨w, v1⟩ = -3

⟨w, v2⟩ = -40

⟨w, v3⟩ = 64

The norm of w can be computed as follows:

||w|| = sqrt((-3)^2 + (-40)^2 + 64^2)

      = sqrt(9 + 1600 + 4096)

      = sqrt(5705)

      ≈ 13

Therefore, the norm of vector w in the span of v1, v2, v3 is approximately 13.

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h(x) = 1 1 − 4x , c = 0 h(x) = [infinity] n = 0

Answers

The power series of H(x) = 1/(1-4x) centered at c=0 is h(x) = ∑(n=0 to ∞) (4x)ⁿ, and its interval of convergence is (-1/4, 1/4).

To find the power series for H(x) = 1/(1-4x) centered at c = 0, we can use the formula for the geometric series

1 / (1 - 4x) = 1 + 4x + (4x)² + (4x)³ + ...

This is a geometric series with first term a = 1 and common ratio r = 4x. The series converges if |4x| < 1, or equivalently, if -1/4 < x < 1/4. Therefore, the interval of convergence for the power series is (-1/4, 1/4).

The power series for H(x) centered at c = 0 is:

h(x) =1 + 4x + (4x)² + (4x)³ + ...

= ∑(n=0 to ∞) (4x)ⁿ.

Therefore, h(x) = ∑(n=0 to ∞) (4x)ⁿ and the interval of convergence is (-1/4, 1/4).

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--"The given question is incomplete, the complete question is given below:

Find the power series for the function, centerd at c and determine the interval of convergence H(x) = 1 /1 − 4x' , c = 0 h(x) = summation [infinity to n = 0] ="--

Please help please please

Answers

Answer:

15 feet

Hope this helps

Given -90° ≤ y ≤ 90°, arcsin (0.6947) = _____.

11°
88°
22°
44°

Answers

Answer:

  (d)  44°

Step-by-step explanation:

You want the angle whose sine is 0.6947.

Calculator

The arcsine function of your calculator can tell you what this is:

  arcsin(0.6947) ≈ 44°

__

Additional comment

The calculator mode must be set to "degrees."

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the maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.2 parts per million (ppm). a consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit. define the parameter and determine the null and alternative hypotheses.

Answers

The parameter in this scenario is the mean level of the toxic chemical in tomatoes from a specific producer. The null hypothesis states that the mean level of the chemical is equal to or below the recommended limit of 0.2 ppm, while the alternative hypothesis states that the mean level exceeds the recommended limit.

The parameter being examined is the mean level of the toxic chemical in tomatoes obtained from a specific producer. The consumer health group wants to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit of 0.2 ppm.

The null hypothesis (H0) states that the mean level of the chemical in tomatoes from this producer is equal to or below the recommended limit: μ ≤ 0.2 ppm.

The alternative hypothesis (Ha) states that the mean level of the chemical in tomatoes from this producer exceeds the recommended limit: μ > 0.2 ppm.

In other words, the null hypothesis assumes that the tomatoes do not have a significantly higher mean level of the toxic chemical, while the alternative hypothesis suggests that there is evidence to support a higher mean level.

By conducting appropriate statistical tests on the sample data, the consumer health group can make conclusions about whether the mean level of the toxic chemical in tomatoes from this producer exceeds the recommended limit of 0.2 ppm.

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use the classical definition to find the probability of the following event: flipping a fair coin twice and getting no tails. express your answer as a decimal rounded to 1 decimal place.

Answers

The probability of flipping a fair coin twice and getting no tails is 0.3.

The classical definition of probability states that if an event has n possible outcomes and all of them are equally likely to occur, then the probability of any one of them happening is 1/n.

In the case of flipping a fair coin twice, there are 2 possible outcomes for each flip (heads or tails).

Therefore, there are 2 x 2 = 4 possible outcomes for flipping the coin twice: HH, HT, TH, and TT.

Since the coin is fair, each of these outcomes is equally likely to occur.

The event of getting no tails corresponds to the outcome of HH. There is only one way to get this outcome out of the 4 possible outcomes, so the probability of getting no tails is 1/4.

To express this probability as a decimal rounded to 1 decimal place, we divide 1 by 4 and get 0.25. Rounded to 1 decimal place, the probability of flipping a fair coin twice and getting no tails is 0.3.

Therefore, the probability of flipping a fair coin twice and getting no tails is 0.3.

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1)
If I initially have a gas at a pressure of 12 atm, a volume of 23 liters, and a
temperature of 200 K, and then I raise the pressure to 14 atm and
increase the temperature to 300 K, what is the new volume of the gas?

Answers

the new volume of the gas, when the pressure is raised to 14 atm and the temperature is increased to 300 K, is approximately 29.5714 liters.

The new volume of the gas, we can use the combined gas law, which states:

(P1 × V1) / T1 = (P2 × V2) / T2

Where:

P1 = Initial pressure

V1 = Initial volume

T1 = Initial temperature

P2 = Final pressure

V2 = Final volume (what we're trying to find)

T2 = Final temperature

Given:

P1 = 12 atm

V1 = 23 liters

T1 = 200 K

P2 = 14 atm

T2 = 300 K

Plugging these values into the combined gas law equation, we get:

(12 atm × 23 liters) / 200 K = (14 atm × V2) / 300 K

To find V2, we can rearrange the equation:

(12 atm × 23 liters × 300 K) / (200 K × 14 atm) = V2

Simplifying the equation, we have:

V2 = (12 × 23 × 300) / (200 × 14)

V2 = 82800 / 2800

V2 = 29.5714 liters (rounded to four decimal places)

The new volume of the gas, when the pressure is raised to 14 atm and the temperature is increased to 300 K, is approximately 29.5714 liters.

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Sujita deposited Rs 4,00,000 in a commercial bank for 2 years at 10% p.a. compounded half yearly. After 1 year the bank changed its policy and decided to give compound interest compounded quarterly at the same rate. The bank charged 5% tax on the interest as per government's rule. What is the percentage difference between the interest of the first and second year after paying tax.​

Answers

The percentage difference between the interest of the first and second year, after paying tax, is approximately 100%.

To calculate the interest for the first year, compounded half-yearly, we can use the formula for compound interest:

[tex]A = P \times (1 + r/n)^{(n\times t)[/tex]

Where:

A is the total amount including interest,

P is the principal amount (Rs 4,00,000),

r is the annual interest rate (10% or 0.10),

n is the number of times interest is compounded per year (2 for half-yearly),

and t is the number of years (1 for the first year).

Plugging in the values, we find that the total amount after one year is approximately Rs 4,41,000.

Now, for the second year, compounded quarterly, we have:

P = Rs 4,41,000,

r = 0.10,

n = 4 (quarterly),

and t = 1.

Using the same formula, the total amount after the second year is approximately Rs 4,85,610.

To calculate the difference in interest, we subtract the amount after the first year from the amount after the second year: Rs 4,85,610 - Rs 4,41,000 = Rs 44,610.

Now, applying the 5% tax on the interest, the tax amount is 5% of Rs 44,610, which is approximately Rs 2,230.

Therefore, the final interest after paying tax for the first year is Rs 44,610 - Rs 2,230 = Rs 42,380.

The percentage difference between the interest of the first and second year after paying tax can be calculated as follows:

Percentage Difference = (Interest of the Second Year - Interest of the First Year) / Interest of the First Year * 100

= (Rs 42,380 - Rs 0) / Rs 42,380 * 100

≈ 100%

Thus, the percentage difference between the interest of the first and second year, after paying tax, is approximately 100%.

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