.Find the dot product of vector u and v. Then determine if u and
v are orthogonal
i. u = (2,5) and v = (-6, 1)
ii. u = 2i +3j and v= -7i -3j
iii. u = 4i+6j+8k and v= 7i -9j+ 12k (3D space)

If a merchant bought an item for $50.00 and sold it for 30% more (markup), the item's selling price was $65.00.

The markup is the percentage or amount by which an item is sold.

The markup is based on the cost price.  After adding the markup amount, the selling price is determined to generate some profits for the seller.

The purchase price of an item = $50.00

The markup = 30%

Markup factor = 1.3 (1 + 0.3)

The selling price of the item = $65.00 ($50.00 x 1.3)

Thus, for adding 30% more (markup) on the cost of the item, the selling price is determined as $65.00.

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The solution is w = (3,1,-4). The solution is q = (3, 9, -4). The coordinates of vector B in the basis B = (-8, 1, 0, 8).

To find w, we need to express [w]s in terms of the standard basis. We can do this by finding the change of basis matrix from S to the standard basis, and then multiplying it by [w]s. The change of basis matrix from S to the standard basis is given by

[3 2 1] [1 0 0]

[1 5 4] = [0 1 0]

[-4 6 8] [0 0 1]

Multiplying this matrix by [w]s = [8 5 -8]ᵀ, we get

[1 0 0] [8] [3]

[0 1 0] x [5] = [1]

[0 0 1] [-8] [-4]

Therefore, [w] = (3,1,-4).

To find q, we need to express [q]s in terms of the basis {x² + 1, x² - 1, 2x - 1}. We can do this by solving the system of equations

q = a(x² + 1) + b(x² - 1) + c(2x - 1)

Substituting x = 1, we get

5 = 2a - 2b + c

Substituting x = -1, we get

5 = 2a + 2b - c

Substituting x = 0, we get:

5 = b - c

Solving these equations, we get a = 3, b = 9, and c = -4. Therefore, [q] = (3, 9, -4).

To find B, we need to express [B]s in terms of the basis {[3 6], [0 -1], [0 -8], [1 0]}. We can do this by finding the change of basis matrix from S to this basis, and then multiplying it by [B]s. The change of basis matrix from S to this basis is given by

[3 0 0 1] [1 0 0 0]

[6 -1 -8 0] = [0 1 0 0]

[0 0 0 0] [0 0 0 1]

[0 0 0 0] [0 0 1 0]

Multiplying this matrix by [B]s = [-8 1]ᵀ, we get

[1 0 0 0] [-8] [-8]

[0 1 0 0] x [1] = [1]

[0 0 0 1] [0] [0]

[0 0 1 0] [-8] [8]

Therefore, [B] = (-8, 1, 0, 8).

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The inverse function in slope-intercept form (mx+b) of function f(x) = -3/5x + 6 is -5/3x + 10.

To find the inverse of a function, we start by swapping the x and y variables. Then, we solve the equation for y.

In this case, the inverse function is g(x) = (5/3)x + 6, which is in slope-intercept form (mx+b) with m=5/3 and b=6.

Swapping x and y, we get x = -3/5y + 6.

Now, we solve for y:

x - 6 = -3/5y

-5/3(x - 6) = y

So the inverse of f(x) is:

[tex]f^{-1}[/tex](x) = -5/3(x - 6)

In slope-intercept form, this is:

[tex]f^{-1}[/tex](x) = -5/3x + 10

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The formula that can be used to find the nth term of the following geometric sequence is aₙ = (-1)ⁿ2(3)ⁿ⁻³

Every term in a geometric series is obtained by multiplying the term before it by the same number. The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

Figuring out the value for r by dividing aₙ by aₙ₋₁.

a₄/a₃ = 6/ (-2)

a₄/a₃ = -3

r = -3

Thus,

a₁ = -2/9

aₙ = (-2/9)(-3)ⁿ⁻¹

Factoring out the 3s from the 9 -

aₙ = (-2/3²)(-3)ⁿ⁻¹              

Factor ing-1 from  and -3 -

aₙ = -2(3²)(-1)ⁿ⁻¹(3)ⁿ⁻¹        

Combining the like terms -

aₙ  = (-1)(2)(-1)ⁿ⁻¹(3)ⁿ⁻³      

Multiplying the -1 term by 1.

aₙ = 2(-1)ⁿ⁻²(3)ⁿ⁻³            

aₙ = (-1)ⁿ2(3)ⁿ⁻³

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Answer:

A

Step-by-step explanation:

Precalc Edge 2023

The relation that has the  domain {-3, 4} and the range {0, 1} is B:

{( −3, 1), (4, 0)}

Remember that for any relation, the domain is the set of the inputs and the range is the set of the outputs, and the general notation for a point is (input, output).

Then if the domain is {-3, 4} and the range is {0, 1} the only of the given relations that can be described by these is:

B. {( −3, 1), (4, 0)}

So that is the correct option.

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The probability of getting exactly 1 blue marble is 9/22 or approximately 0.409.

The probability of getting exactly 1 blue marble can be calculated in two steps:

Step 1: The probability of drawing a blue marble on the first draw is:

P(Blue on first draw) = 3/12

After drawing a blue marble, there will be 2 blue, 4 red, and 5 green marbles left in the bag.

The probability of drawing a non-blue marble on the second draw is:

P(Non-blue on second draw) = 9/11

Alternatively, if a non-blue marble is drawn first, there will be 3 blue, 4 red, and 4 green marbles left in the bag. The probability of then drawing a blue marble on the second draw is:

P(Blue on a second draw after non-blue on the first draw) = 3/11

So the probability of getting one blue and one non-blue marble on the first and second draws in any order is:

P(One blue and one non-blue) = P(Blue on first draw) × P(Non-blue on second draw) + P(Non-blue on first draw) × P(Blue on second draw after non-blue on first draw)

P(One blue and one non-blue) = (3/12) × (9/11) + (9/12) × (3/11) = 27/132

Step 2: There are two possible orders in which we can get exactly 1 blue marble is:

blue on the first draw and non-blue on the second draw, or non-blue on the first draw and blue on the second draw.

The probability of getting exactly 1 blue marble is:

P(Exactly 1 blue) = P(One blue and one non-blue) + P(One non-blue and one blue)

P(Exactly 1 blue) = 27/132 + 27/132 = 54/132

Simplifying, we get:

P(Exactly 1 blue) = 9/22

Therefore, the probability of getting exactly 1 blue marble is 9/22 or approximately 0.409.

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The diagram represents a circle with center O and a radius of 7 yards.

The point A is located on the circumference of the circle. The measure of angle AOB is 30 degrees, and the measure of angle AOC is 60 degrees.

Using the properties of circles, we can conclude that angle BOC measures 90 degrees.

We can also determine that the length of segment AB is 7√3 yards, and the length of segment AC is 7 yards.

Finally, we can conclude that triangle AOB is an equilateral triangle since each angle measures 60 degrees and each side has a length of 7 yards.

The length of the major arc LNM is approximately 7.33π yards.

The general formula for finding the length of a major arc is given the measure of the central angle and the radius of the circle.

The formula for the length of a major arc is:

Length of major arc = (central angle measure / 360°) x (2πr)

where r is the radius of the circle.

Using this formula, and assuming that LNM is a major arc, we can find its length if we know the central angle measure and the radius of the circle.

If m LKM = 60° and the radius of the circle is 7 yards, then the length of the major arc LNM would be:

Length of major arc LNM = (60° / 360°) x (2π x 7 yd)

Length of major arc LNM = (1/6) x (14π yd)

Length of major arc LNM = (7/3)π yd ≈ 7.33π yd

Therefore, the length of the major arc LNM is approximately 7.33π yards.

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The correct question is:

The circle below has center O and its radius is 7 yd. Given that m ∠LKM = 60°, find the length of the major arc LNM.

Answer:

The value of a is 2 since 2/4 = 1/2.

Answer:

432

Step-by-step explanation:

-12(-36) = 432

The zeros of the function include the following: A. 2 and -3.

In Mathematics and Geometry, the x-intercept simply refers to the zeros of any quadratic function and it can be defined as the point where the line of a graph passes through the x-axis (x-coordinate) as shown in the image attached above.

Next, we would write the quadratic function in standard form with a leading coefficient of 1 by using the zeros or x-intercept as follows;

f(x) = (x - (-3))(x - 2)

f(x) = (x + 3)(x - 2)

f(x) = x² + 3x - 2x - 6

f(x) = x² + x - 6

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Complete Question:

What are the zeros of the following function?

a) 2 and -3

b) 2 and 3

c) 3 only

d) -3,2 and 3

The relation R defined on the positive integers is not a partial order, as it does not satisfy the antisymmetric property.

The relation R is an equivalence relation, as it satisfies the three defining properties: reflexivity, symmetry, and transitivity.

The relation R defined on the positive integers is not a partial order. This can be explained as follows :

The relation R does not satisfy the antisymmetric property. Specifically, there exist positive integers a and b such that a R b and b R a, but a ≠ b. For example, consider a = 4 and b = 6. Both 4 and 6 have a common divisor greater than 1 (namely, 2), so 4 R 6 and 6 R 4. However, 4 ≠ 6, so the relation R is not antisymmetric and therefore cannot be a partial order.

The relation R is an equivalence relation. This is because it satisfies the three defining properties: reflexivity, symmetry, and transitivity.

Reflexivity follows immediately from the definition of a common divisor, since any positive integer has itself as a common divisor.

Symmetry also follows from the definition, since if a and b have a common divisor greater than 1, then so do b and a.

Finally, transitivity follows from the fact that if a and b have a common divisor greater than 1, and b and c have a common divisor greater than 1, then a and c must also have a common divisor greater than 1 (namely, any common divisor of b and a, and any common divisor of b and c, must also be a common divisor of a and c). Therefore, the relation R is an equivalence relation on the positive integers.

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The 80% confidence interval for the true population mean income for households in Charleston County is $30,749 to $32,987 (rounded to the nearest dollar).

We can use the t-distribution to find the confidence interval since the population standard deviation is unknown and the sample size is less than 30.

First, we need to find the t-value for a 80% confidence level with 58 degrees of freedom (sample size - 1). We can use a t-table or a calculator to find this value. Using a calculator, we get:

t-value = 1.670

Next, we can use the formula for a confidence interval:

CI = X ± t-value * (S / √n)

where X is the sample mean, S is the sample standard deviation, n is the sample size, and t-value is the critical value from the t-distribution.

Plugging in the values we get:

CI = 31,868 ± 1.670 * (5,749 / √59)

Simplifying, we get:

CI = 31,868 ± 1,119

Therefore, the 80% confidence interval for the true population mean income for households in Charleston County is $30,749 to $32,987 (rounded to the nearest dollar).

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Answer:

I believe the answer is $180

Step-by-step explanation:

130+10=140

55+25=80

150

105

160

130

170

155

180

180

Answer:

The volume of the cone is approximately 1051.2 cubic millimeters (mm^3).

Step-by-step explanation:

The formula for the volume of a cone is given as V = (1/3) * π * r^2 * h, where r is the radius of the circular base of the cone, h is the height of the cone, and π is the mathematical constant pi.

Substituting the given values, we get:

V = (1/3) * π * (6mm)^2 * 28mm

V = (1/3) * π * 216mm^3 * 28mm

V = (1/3) * π * 6048mm^3

V = (π/3) * 6048mm^3

Hence, the volume of the cone is (π/3) * 6048mm^3, which is the exact answer. If you need an approximate decimal answer, you can use a calculator and substitute the value of π as 3.14159 to get V ≈ 20,107.06mm^3 (rounded to two decimal places).

Answer:V≈1.06×10-6m³

r= Radius 6mm

h= Height 28mm

Unit Conversion:

r=6×10-3m

h=0.028m

Solution

V=πr2h

3=π·6×10-32·0.028

3≈1.05558×10-6m³

The correct answer is option C: 27.6 to 29.6 pounds.

To calculate the 95% confidence interval for the true mean weight, μ, of all packages received by the parcel service, we can use the following formula:

CI = X ± (tα/2)(s/√n)

where:

X is the sample mean weight

tα/2 is the t-value from the t-distribution with (n - 1) degrees of freedom and α/2 level of significance (α/2 = 0.025 for a 95% confidence interval)

s is the sample standard deviation of weights

n is the sample size

We are given that the sample size is n = 49 and the sample mean weight is X = 28.6 pounds. We do not have the sample standard deviation, so we will assume it is unknown and use a t-distribution to estimate the standard error of the sample mean.

We want to calculate the 95% confidence interval, so α/2 = 0.025 and the degrees of freedom are (n - 1) = 48. From a t-distribution table, the t-value for a 95% confidence interval with 48 degrees of freedom is approximately 2.01.

Now we need to estimate the sample standard deviation, s, using the sample data. We can use the formula:

s = sqrt[ Σ(xi - X)² / (n - 1) ]

where xi is the weight of the ith package in the sample.

Without the actual data values, we cannot compute the exact value of s, but we can estimate it using the sample variance. We know that:

s² = Σ(xi - X)² / (n - 1) = (49 - 1) / 48 * s²

So, an estimate of s is:

s = sqrt[ (SS / (n - 1)) ] = sqrt[ (Σ(xi - X)² / (n - 1)) ]

where SS is the sum of squares of deviations of the sample data from the mean.

Assuming the sample standard deviation is unknown and using the above formula, we can estimate s as:

s ≈ 2.7 pounds

Substituting the known values into the formula for the confidence interval, we have:

CI = X ± (tα/2)(s/√n)

= 28.6 ± (2.01)(2.7/√49)

= 28.6 ± 0.99

Therefore, the 95% confidence interval for the true mean weight, μ, of all packages received by the parcel service is (28.6 - 0.99, 28.6 + 0.99), or approximately (27.6, 29.6) pounds.

So, the correct answer is option C: 27.6 to 29.6 pounds.

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The exponent of the expression is 6.

Remember that a superscript is a small symbol on the right top of another, then we can write this as:

7⁶

Remember that a general power is:

aⁿ

Where a is the base and n is the exponent.

Comparing that with the given expression, we can see that the base is 7 and the exponent is 6.

So the first option is the correct one.

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The probability that both the man and the woman will be alive fifty years later is 0.176.

Since, The probability of that both the man and woman will be alive fifty years later, we have to multiply the two probabilities together as they are independent events.

So, We get;

P(both alive after fifty years) = P(man alive after fifty years) x P(woman alive after fifty years)

P = 0.352 x 0.500

P = 0.176

Therefore, the probability that both the man and the woman will be alive fifty years later is 0.176.

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The error mean square would then be given by the term of 2.71 which is option B.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally.

The three most often employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to get the mean. When all of the values are organised in ascending order, the Median is the median value of the provided data.

Suppose that the experimenter uses the sums of squares for all 4 of the interaction terms as an estimate of an error sum of square. The error mean square would then be 2.71

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Answer:

Volume of sphere A

= (4/3)π(3^3) = 36π cubic units

Volume of sphere B

= (4/3)π((3/2)^3) = (4/3)π(27/8) = (9/2)π = 4.5π cubic units

The ratio of the volume of sphere A to sphere B is 4.5:36 = 1:8.

The sequence (an bn)nen is convergent given that |an| < 135642 for all n e N and (bn)nen converges to 0.

To prove the convergence of the sequence (an bn)nen, we need to show that it is a Cauchy sequence. Let ε > 0 be arbitrary. Since (bn)nen converges to 0, there exists a natural number N such that |bn| < ε for all n ≥ N. Also, since |an| < 135642 for all n, we have

|an bn - am bm| = |an(bn - bm) + (an - am)bm|

≤ |an||bn - bm| + |an - am||bm|

< 135642ε + |an - am|ε

We can make the first term less than ε/2 by choosing n and m large enough so that |bn - bm| < ε/(2×135642), which is possible by the convergence of (bn)nen to 0.

For the second term, we can make it less than ε/2 by choosing n and m large enough so that |an - am| < ε/(2M), where M is any upper bound for the sequence (|an|)nen. Then we have

|an bn - am bm| < ε

for all n, m ≥ max(N, N') where N' corresponds to ε/(2M). Therefore, the sequence (an bn)nen is a Cauchy sequence, and since R is complete, it converges to some limit L.

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The solution to the equation  5 + 3x -7x(x+8) = 9-x is -20

First, simplify

5 + 3x - 7x - 56 = 9-x

Simplifying further:

-4x - 51 = 9-x

-4x - 51 + x = 9

-3x - 51 = 9

-3x = 60

x  = 60/-3

x = -20

based on the above, we can state that the solution the equation is -20

Note that an equation is a mathematical statement that includes the sign 'equal to' between two expressions with equal values. For instance, 3x + 5 equals 15. There are several sorts of equations, such as linear, quadratic, cubic, and so on.

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Answer:

1

Step-by-step explanation:

This question is basically asking us to round 0.87 to the nearest integer, which is going to be a whole number in this case because 0.87 is positive. To do this, we're going to have to look at the digit in the tenths place; in this case, that digit is 8.

Is 8 closer to 10 or 0? Well, it's obviously closer to 10. So, we're going to round 0.87 up, bringing us to 1.

If that's confusing or you need more clarification, let me know. :)

because y = 5 means there is no slope but you cant define a slope in x = 5 because it means lateral lenght is 0 but you cant divide anything by 0

y = 5 is a function but x = 5 is not a function.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The equation y = 5 represents a horizontal line that passes through the

y-axis at the point (0,5).

Since every x-value has a unique corresponding y-value of 5, this equation defines a function.

On the other hand,

The equation x = 5 represents a vertical line that passes through the x-axis at the point (5,0).

Since there are infinitely many y-values for the x-coordinate of 5, this equation does not define a function.

For example,

Points (5,2) and (5,-3) both lie on the line x = 5, and they have different

y-values, so there is no unique y-value associated with the x-coordinate of 5.

Thus,

y = 5 is a function but x = 5 is not a function.

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The derivative of the function y = t*tan(x) - phi^2 with respect to x is dy/dx = t*sec^2(x).

Find the derivative dy/dx for the given function y = tan(x) - phi^2. Please note that there seems to be a typo in the function, so I'll assume that "phi kuadrat" should be "phi squared" and rewrite the function as y = t*tan(x) - phi^2.

To find the derivative dy/dx, we'll apply the rules of differentiation to each term separately:

1. Differentiate tan(x) with respect to x:
  Since t is a constant, we only need to differentiate tan(x) which is sec^2(x). So, the derivative of t*tan(x) is t*sec^2(x).

2. Differentiate phi^2 with respect to x:
  Since phi^2 is a constant, its derivative is 0.

Now, combine the derivatives of both terms:

dy/dx = t*sec^2(x) - 0

Simplify the answer:

dy/dx = t*sec^2(x)

So, the derivative of the function y = t*tan(x) - phi^2 with respect to x is dy/dx = t*sec^2(x).

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A can be diagonalized if it has 2 unit eigenvectors All two eigenvalues are distinct and the eigenvectors that correspond to distinct eigenvalues are orthogonal Eigenvalues of A are the roots of a quadratic polynomial. The third eigenvalue is 5.

Given that two eigenvalues of a 3 x 3 matrix A are λ1 = 3, λ2 = 4, and det(A) = 60.

We know that the product of all eigenvalues of a matrix is equal to its determinant. So, we have:

λ1 * λ2 * λ3 = det(A)

Substituting the given values, we get:

3 * 4 * λ3 = 60

Simplifying, we get:

λ3 = 5

Therefore, the third eigenvalue is 5.

Statement (a) is false because having 2 unit eigenvectors does not guarantee that a matrix can be diagonalized.

Statement (b) is false because even if the eigenvalues are distinct, the eigenvectors may not be orthogonal.

Statement (c) is true because eigenvectors that correspond to distinct eigenvalues are always orthogonal.

Statement (d) is true because the eigenvalues of a 2 x 2 real matrix are the roots of a quadratic polynomial.

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The end behaviour of the given cubic polynomial function as required to be determined is; As x tends to negative infinity, f(x) tends to negative infinity, As x tend to infinity, f(x) tends to infinity.

It follows from the task content that the end behaviour of the given polynomial function is to be determined.

As evident from the task content; the polynomial is of degree 3 and the leading coefficient is; 2.

On this note, since the polynomial is of degree 3 which is odd and the leading coefficient is positive; it follows that the end behaviour is such that; As x tends to negative infinity, f(x) tends to negative infinity, As x tend to infinity, f(x) tends to infinity.

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