show that the image of a set of linearly dependent vectors under a linear operator is still linearly dependent. is the same thing true for linearly independent sets?

Answer:

ans=8.80inch

Step-by-step explanation:

given,

radius(r)=1.6 inch

height(h=2.5 inch

laternal area of cone = AL=√πrh2+r2

√3.14*2.5^2+1.6^2

8.80 inch

The approximate lateral area of the cone is,

⇒ LSA = 10.5 inches

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

To find the approximate lateral area of the cone, we need to know the height of the cone.

Since we are not given the height, we can use the Pythagorean theorem to find it:

Slant height² = h² + r²

2.5² = h² + 1.6²

6.25 = h² + 2.56

h² = 6.25 - 2.56

h² = 3.69

h = √3.69

h = 1.92 in

We know that;

The lateral surface area of a cone is calculated using the formula,

LSA =πr√(r² + h²) square units.

Substitute all the values, we get;

LSA =πr√(r² + h²) square units.

LSA = 3.14 × 1.4√(1.6² + 1.9²) square units.

LSA = 5 √2.6 + 3.6

LSA = 5 √4.2

LSA = 5 × 2.1

LSA = 10.5 inches

Thus, The approximate lateral area of the cone is,

⇒ LSA = 10.5 inches

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Answer:

231.01

Step-by-step explanation:

The area of the largest rectangle that can be inscribed in an ellipse is given by the formula: Area = 4ab, where 'a' represents the semi-major axis of the ellipse and 'b' represents the semi-minor axis.


The area of the largest rectangle that can be inscribed in an ellipse depends on the shape of the ellipse. The largest rectangle will have its sides tangent to the ellipse at four points. The dimensions of this rectangle can be found using the properties of ellipses.

To find the area of the largest rectangle inscribed in an ellipse, we need to consider the semi-major axis (a) and the semi-minor axis (b) of the ellipse. The semi-major axis represents half the length of the longest diameter of the ellipse, while the semi-minor axis represents half the length of the shortest diameter.

The area of the largest rectangle can be calculated using the formula: Area = 4ab.

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Answer: Squared because it equals to the 5 squared

Step-by-step explanation: Its because 5 to the second power is the same as 5 squared Hope this helped :)

Answer:

five squared

Step-by-step explanation:

Answer:

The answer is zero.

Step-by-step explanation:

When you put the coordinates in the point-slope formula, it will be 7 - (-1) over  -2 - (-2), which is 8/0. When the denominator is zero in the fraction, the answer is zero.

For the polygon the individual value of the interior angles.

a) 15 sides is 145°

b) 20 sides is 108°

c) 3 sides is 60°

d) 4 sides is 90°

e) 100 sides is 18°

A regular polygon is one where all sides are the same length and all interior angles are the same. The number of sides of a regular polygon can affect the value of its interior angles.

a) 15 sides: The sum of the interior angles of a regular polygon with 15 sides is equal to 2180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 2180 / 15 = 145 degrees per angle.

b) 20 sides: The sum of the interior angles of a regular polygon with 20 sides is equal to 2160 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 2160 / 20 = 108 degrees per angle.

c) 3 sides: The sum of the interior angles of a regular polygon with 3 sides is equal to 180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 180 / 3 = 60 degrees per angle.

d) 4 sides: The sum of the interior angles of a regular polygon with 4 sides is equal to 360 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 360 / 4 = 90 degrees per angle.

e) 100 sides: The sum of the interior angles of a regular polygon with 100 sides is equal to 1800 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 1800 / 100 = 18 degrees per angle.

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Answer:

750 would be ur answer

Step-by-step explanation:

happy new year!

Answer:750 desks

Step-by-step explanation: I would start by setting up an equation. 5d=250 (d means days). Then, to isolate the d, I would divide both sides of the equation by 5. I would get d=50. So there are 50 desks made daily. To find out the number of desks made in 15 days, I would just multiply both sides of the equation d=50 by 15 and I would get 15d=750. That means, there are 750 desks produced in 15 days. I hope this helps you out a bit!

Using the z-distribution, the 95% confidence interval to describe the total percentage of students who do not like ice cream is:

(8.34%, 17.66%).

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

In this problem, we have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

For this problem, the estimate and the sample size are given, respectively, by:

\(\pi = 0.13, n = 200\)

Hence the bounds of the interval are:

As a percentage, the interval is:

(8.34%, 17.66%).

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Answer:

Step-by-step explanation:

1. convert 2/7

2/7 = 6/21

2. convert 1/3

1/3 = 7/21

3. add 6/21 and 7/21

6/21 + 7/21 = 13/21

4. subtract 13/21 from 21/21

21/21 - 13/21 = 8/21

5. reduce

8/21 is already in the lowest form

The distance of 7km in miles is 4.349597 miles.

It's important to note that kilometers are the primary unit of distance measurement in most countries, while miles are used primarily in the United States and a few other countries. To convert 7km to miles, we need to know the conversion factor between the two units.

By knowing how to convert between these two units is a useful skill when traveling internationally or when working with different units of measurement. Here, One kilometer is equal to 0.621371 miles.

Therefore, to convert 7km to miles, we simply multiply 7 by the conversion factor:

7km x 0.621371 miles/km = 4.349597 miles

So, 7km is equal to approximately 4.35 miles.

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Answer:

Step-by-step explanation:

200 Items were sold

For A total of $130

The Items sold were 0.50

and 0.75.

130 Cans of soda were sold

86 Bags Of popcorn were sold.

Combination tells the number of ways an object can be arranged. The number of all of the possible combinations Gabby can have is 9.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

\(^nC_r = \dfrac{n!}{r!(n-r)!}\)

where,

n is the number of choices available,

r is the choices to be made.

We know that the number of options of the flower with Gabby is 3( daisies, carnations, or sunflowers) and the color choices she has is (clear, red, or blue), therefore, she \(^3C_1\) choices for the flower, also, she has \(^3C_1\) choices for color.

\(\text{Total number of choices with Gabby} = \text{Choices of flower} \times \text{Choices of color}\)

                                                         \(= ^3C_1 \times ^3C_1 \\\\= 9\)

Hence, the number of all of the possible combinations Gabby can have is 9.

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The volume of the balloon is 32π/3 ft³, and the rate at which the surface area is increasing is 16π square feet per minute.

The volume V of a balloon is given as V = (4/3)πr³, where r is the radius of the balloon.

Differentiating both sides of the equation concerning time t, we get

dV/dt = 4πr²(dr/dt).

Here, dV/dt represents the rate at which the volume is changing, which is 4 ft³/min as given in the problem.

the volume is 32π/3 ft³, we can substitute these values into the equation

4 = 4πr²(dr/dt)

To simplifying, we have

r²(dr/dt) = 1/π

The surface area A of a balloon, we can use the formula

A = 4πr².

Differentiating both sides of the equation concerning time t, we get dA/dt = 8πr(dr/dt).

We need to find dA/dt when V = 32π/3 ft³.

From the volume formula, we know that V = (4/3)πr³. Setting V = 32π/3, we can solve for r

(4/3)πr³ = 32π/3

r³ = 8

r = 2

Now, substitute r = 2 into the equation for dA/dt

dA/dt = 8π(2)(dr/dt)

Substituting the value of dr/dt from earlier

dA/dt = 8π(2)(1/π)

dA/dt = 16π

Therefore, when the volume of the balloon is 32π/3 ft³, the rate at which the surface area is increasing is 16π square feet per minute.

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For the given function f(x) the graph has a domain of (-5 , 0). For the function g(x) represented by the table the domain is given by the values (-3, 3).

The set of all potential inputs or independent variables for which a function is defined is known as the domain of the function in mathematics. In other words, it is the collection of all possible x-values for the function. On the other hand, the collection of all potential dependent variables or outputs that a function may produce for the specified inputs is known as the range of the function. It is the collection of all y-values that the function is capable of producing.

Given that the function f(x) is the graph while the function g(x) is represented by the table.

For the given function f(x) the graph has a domain of (-5 , 0). The range of the function is (4, infinity). The vertex of the function is given by the coordinates (2, 4). The axis of symmetry of the parabola is x = -2.

For the function g(x) represented by the table the domain is given by the values (-3, 3). The range of the function is given as (25, 1). The x-intercept is at the point 2. The y-intercept is at the point 4.

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Marlene will have to pay a Total of $131.89 if there is a 9% government tax on bills.

Marlene had a meal at KFC which cost her $110, and there was an additional 10% service charge. We have to determine the total cost of her meal, including the 9% government tax on bills. To find out the total cost of the meal, we'll use the following steps:

Step 1: Calculate the service charge service Charge = 10% of $110Service Charge = (10/100) × $110Service Charge = $11

Step 2: Calculate the subtotal Subtotal = Cost of meal + Service charge Subtotal = $110 + $11Subtotal = $121

Step 3: Calculate the government tax Government Tax = 9% of Subtotal Government Tax = (9/100) × $121Government Tax = $10.89

Step 4: Calculate the total cost Total Cost = Subtotal + Government Tax Total Cost = $121 + $10.89Total Cost = $131.89

Therefore, Marlene will have to pay a total of $131.89 if there is a 9% government tax on bills.

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Given that the correlation between two variables is r=0.23. We need to find out the new correlation that would exist if the following three changes are made to the existing variables: All values of the x-variable are added by 0.14. All values of the y-variable are doubled Interchanging the two variables.  the correct option is B. 0.37.

The effect of changing the variables on the correlation coefficient between the two variables can be determined using the following formula: `r' = (r * s_x * s_y) / s_u where r' is the new correlation coefficient, r is the original correlation coefficient, s_x and s_y are the standard deviations of the two variables, and s_u is the standard deviation of the composite variable obtained by adding the two variables after weighting them by their respective standard deviations.

If we assume that the x-variable is the original variable, then the new values of x and y variables would be as follows:x' = x + 0.14 (since all values of the x-variable are added by 0.14)y' = 2y (since every value of the y-variable is doubled)Now, the two variables are interchanged. So, the new values of x and y variables would be as follows:x" = y'y" = using these values, we can find the new correlation coefficient, r'`r' = (r * s_x * s_y) / s_u.

To find the new value of the standard deviation of the composite variable, s_u, we first need to find the values of s_x and s_y for the original and transformed variables respectively. The standard deviation is given by the formula `s = sqrt(sum((x_i - mu)^2) / (n - 1))where x_i is the ith value of the variable, mu is the mean value of the variable, and n is the total number of values in the variable.

For the original variables, we have:r = 0.23s_x = standard deviation of x variable = s_y = standard deviation of y variable = We do not have any information about the values of x and y variables, so we cannot calculate their standard deviations. For the transformed variables, we have:x' = x + 0.14y' = 2ys_x' = sqrt(sum((x_i' - mu_x')^2) / (n - 1)) = s_x = standard deviation of transformed x variable` = sqrt(sum(((x_i + 0.14) - mu_x')^2) / (n - 1)) = s_x'y' = 2ys_y' = sqrt(sum((y_i' - mu_y')^2) / (n - 1)) = 2s_y = standard deviation of transformed y variable` = sqrt(sum((2y_i - mu_y')^2) / (n - 1)) = 2s_yNow, we can substitute all the values in the formula for the new correlation coefficient and simplify:

r' = (r * s_x * s_y) / s_ur' = (0.23 * s_x' * s_y') / sqrt(s_x'^2 + s_y'^2)r' = (0.23 * s_x * 2s_y) / sqrt((s_x^2 + 2 * 0.14 * s_x + 0.14^2) + (4 * s_y^2))r' = (0.46 * s_x * s_y) / sqrt(s_x^2 + 0.0396 + 4 * s_y^2)Now, we can substitute the value of s_x = s_y = in the above formula:r' = (0.46 * * ) / sqrt( + 0.0396 + 4 * )r' = (0.46 * ) / sqrt( + 0.1584 + )r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = r' = Therefore, the new correlation coefficient, r', would be approximately equal to.

Hence, the correct option is B. 0.37.

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The question is incomplete. Here is the complete question.

A organizational psychologist measures levels of job satisfaction in a sample of 30 participants. To measure the variance of job satisfaction, it is calculated that the SS = 120 for this sample.

What are the degrees of freedom for the variance?

Compute the variance and standard deviation.

Answer: Degrees of freedom = 29

Variance = 4.138

Standard Deviation = 2.034

Step-by-step explanation: Degrees of freedom is a number of values in calculation of statistics that are free to vary, i.e., in how many ways a system can move independently. To determine it:

df = n - 1

which n is the quantity of the sample or population

For this sample: df = 30 - 1 = 29

The degrees of freedom is 29.

SS is the sum of the squared deviation, i.e., ∑(x - mean)².

Variance is calculated as:

variance = ∑(x - mean)² / n - 1 = SS / n - 1

variance = \(\frac{120}{29}\)

variance = 4.138

Standard deviation is the spread from the mean and is the square root of variance:

standard deviation = \(\sqrt{variance}\)

standard deviation = \(\sqrt{4.138}\)

standard deviation = 2.034

Rounding to the nearest whole degree, the measure of Angle J is approximately 34 degrees.

The correct answer is B°.

To find the measure of Angle J, we can use the Law of Cosines:

\(a^2 = b^2 + c^2 - 2bc \times cos(A)\)

In this case, the side opposite Angle J is KL (length 11), and the other two sides are JK (length 13) and LJ (length 19).

Plugging in the values:

\(11^2 = 13^2 + 19^2 - 2 \times 13 \times 19 \times cos(A)\)

Simplifying:

\(121 = 169 + 361 - 494 \times cos(A)\)

Combine like terms:

\(-409 = -494 \times cos(A)\)

Dividing both sides by -494:

\(cos(A) =\frac{-409 }{-494}\)

\(cos(A) \approx 0.82802547771\)

To find the measure of Angle J, we can use the inverse cosine function:

\(A \approx cos^{(-1)}(0.82802547771)\)

\(A \approx 34.043\)

Rounding to the nearest whole degree, the measure of Angle J is approximately 34 degrees.

Therefore, the correct answer is B.

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Answer:

A) x = -3

the line is undefined

The equation of the graphed line written in slope-intercept form is x = -3

The graphed line in slope-intercept form, y = mx + b

To Convert it into the standard form of the equation, ax + by = c.

Consider that the points be (0, 3) and (5,0).

A Slope exists how many units it brought to go vertically or horizontally.

Which Slope doesn't exist.

The y-intercept in slope-intercept form, y = mx + b  

where, m = undefined

x = -3

Therefore, the correct answer is option (A), x = -3 because the line is undefined.

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The molarity of the solution is 300 M. The student needs 1.33 L of the concentrated acid. The molarity of the solution is 1 M. The molarity of the diluted solution will be 0.1 M.

To find the molarity of the solution, we divide the number of moles of solute (HNO3) by the volume of the solution. Given that 150.0 grams of HNO3 are dissolved in 0.500 L of solution, we first convert the mass of HNO3 to moles using its molar mass. Then we divide the moles by the volume to find the molarity. The molarity is calculated as 300 M.

The concentration of the available acid (12.0 M) is given along with the desired concentration (4.00 M) and volume (9.00 L). To find the volume of the concentrated acid needed, we can use the equation: (concentration of concentrated acid) × (volume of concentrated acid) = (desired concentration) × (desired volume). Rearranging the equation, we find that the volume of the concentrated acid needed is 1.33 L.

Similar to the first question, we can calculate the molarity by dividing the number of moles of solute (NaCl) by the volume of the solution. Given that 40.0 grams of NaCl are dissolved in 2.00 L of solution, we convert the mass of NaCl to moles and divide by the volume. The molarity is determined to be 1 M.

To calculate the molarity of the diluted solution, we need to consider the dilution formula, which states that the initial molarity times the initial volume equals the final molarity times the final volume. Given that 50.0 mL of water is added to 250.0 mL of a 0.500 M K2SO4 solution, we can substitute the values into the dilution formula and solve for the final molarity. The molarity of the diluted solution is calculated to be 0.1 M.

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Answer:

15 hours

Step-by-step explanation:

150 divided by 10 equals 15

Answer:

It will take him 15 hours

Step-by-step explanation:

Because if you divide 150 by 10 you get fifteen.

So its basically like divide 150 by the 10$ and then it will take 15 hours.

Answer:

√5

Step-by-step explanation:

The volume of the solid is 603.19 cubic feet

The formula for the volume of a hemisphere is (2/3)πr³.

Since the radius of the hemisphere is not given,

Assume it to be the same as the radius of the cone, which is 6 feet.

So, the volume of the hemisphere is,

⇒ (2/3)π(6³) = 144π cubic feet

The formula for the volume of a cone is (1/3)πr²h,

where r is the radius and h is the height.

Put in the values we have, we get,

⇒ (1/3)π(6²)(12) = 144π/3

                        = 48π cubic feet

Find the total volume of the composite solid by adding the volumes of the hemisphere and the cone,

⇒ Total volume = Volume of hemisphere + Volume of cone

⇒ Total volume = 144π + 48π

⇒ Total volume = 192π cubic feet

Finally, rounding to the nearest hundredth,

The volume of the composite solid is 603.19 cubic feet.

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Answer:

b

Step-by-step explanation:

The coordinate matrix of x relative to the orthonormal basis b is then: [x]b = [19, -9, 10]

To get the coordinate matrix of x relative to the orthonormal basis b in Rn, we need to express x as a linear combination of the basis vectors in b. We can do this by using the formula: x = [x · b1]b1 + [x · b2]b2 + [x · b3]b3
where · denotes the dot product and b1, b2, and b3 are the orthonormal basis vectors in b.
First, we need to normalize the basis vectors:
|b1| = √(3^2 + 4^2) = 5
b1 = (3/5, 4/5, 0)
|b2| = √(4^2 + 3^2) = 5
b2 = (-4/5, 3/5, 0)
|b3| = 1
b3 = (0, 0, 1)
Next, we compute the dot products:
x · b1 = (5, 20, 10) · (3/5, 4/5, 0) = 19
x · b2 = (5, 20, 10) · (-4/5, 3/5, 0) = -9
x · b3 = (5, 20, 10) · (0, 0, 1) = 10
Using these values, we can express x as a linear combination of the basis vectors:
x = 19b1 - 9b2 + 10b3
The coordinate matrix of x relative to the orthonormal basis b is then:
[x]b = [19, -9, 10]
Note that this matrix is a column vector since x is a column vector.

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Answer:

A (-3,9)

Step-by-step explanation:

ok easy they they us

R(2,1) and R'(-4,8)

subtract 6 from y and add 7 to y

ok lets solve for S'

S(3,2) now subtract 6 and add 7

(3,2)+(-6,7)

(-3,9)

Answer:

y>4

Step-by-step explanation:

8y+9>41

subtract 9

8y>32

divide by 8

y>4

Answer:

y>4

Step-by-step explanation:

8y+9>41

subtract 9 from both sides

8y>32

divide 8 on both sides

y>4

The mistake is that since a=9, the 2a in the denominator should be 2x9 and not 2