find an equation of the sphere with center and radius . what is the intersection of this sphere with the -plane?

The number of different uniforms that the girl's choir can choose is given as follows:

560 uniforms.

The number of uniforms for the girl's choir  is obtained using the Fundamental Counting Theorem, with the multiplication of the number of outcomes for each trial.

The options are given as follows:

As the options for the blouse, skirt and sweater are independent, the number of uniforms is obtained as follows:

10 x 8 x 7 = 80 x 7 = 560 uniforms.

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The equation for the length of the legs is:

0.5*(x + 2)*x = 24

Remember that the area of a right triangle is equal to the product between the lengths of the legs over 2.

Then, if here the area is 24ft.

And the legs measure x and (x + 2), then the area equation will be:

x*(x + 2)/2 = 24

We can rewrite the 1/2 as 0.5, so we will get.

0.5*(x + 2)*x = 24

That is the equation on the first option.

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The system of equation x = 4y - 1 and 2x - 8y = 7 has no solutions

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Given the equations:

x = 4y - 1  

multiply the equation by 2:

2x = 8y - 2

2x - 8y = -2     (1)

Also:

2x - 8y = 7     (2)

Subtracting equation 2 from 1 to solve by elimination method:

0 = -9

The equation has no solutions

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The cost of a taco and burrito respectively $1.70 and $0.40.

Let x be the cost of a taco and y be the cost of a burrito.

From the first given information, Thelma ordered 2 tacos and 1 burrito and paid $3.79. So we can write an equation:

2x + y = 3.79

From the second given information, Louise ordered 2 burritos and 1 taco and paid $4.58. So we can write another equation:

2y + x = 4.58

To find x and y, we need to solve the system of linear equations. One way to do this is by using the elimination method. We can subtract the first equation from the second to eliminate x:

2y = 0.79

y = 0.395

Now that we have y, we can substitute it back into the first equation to find x:

2x + 0.395 = 3.79

2x = 3.395

x = 1.698

So the cost of a taco is $1.70 and the cost of a burrito is $0.40.

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Answer:

6 feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the cost of a 33-minute taxi ride, we first need to determine the cost per minute of the taxi ride. We can do this by dividing the cost of a 14-mile taxi ride ($11.20) by the time it took (16 minutes):

$11.20 ÷ 16 minutes = $0.70 per minute

Now that we know the cost per minute, we can find the cost of a 33-minute taxi ride by multiplying the cost per minute by 33:

$0.70 x 33 minutes = $23.10

So a 33-minute taxi ride at this vacation spot would cost $23.10.

The system of equations for this problem can be represented as:

y = 0.50x - 15 (for Team A's popcorn sales)

y = 0.75x - 25 (for Team B's cotton candy sales)

where x represents the number of items sold and y represents the profit earned. To graph the system of equations, we can plot the two lines on the same coordinate plane and find the point where they intersect, which represents the point at which both teams earn the same amount of profit.

At the point of intersection, both teams earn the same amount of profit. To find the profit earned, we can substitute the x-value of the point of intersection into one of the equations and solve for y. The profit earned would be the y-value at the point of intersection.

can't graph sorry

The function C = 2x + 12y, has minimum value 60 at points (18,2) and (30,0).

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given objective function -

C = 2x + 12y

Subjected to the constraints -

2x + 12y ≥ 60

x + y ≥ 20

x ≥ 0, y ≥ 0

First consider the inequality 2x + 12y ≥ 60.

The equation of the above inequality is as follows -

2x + 12y = 60

Find two points that satisfies the above equation.

Take x = 6, then -

2(6) + 12y = 60

12 + 12y = 60

12y = 60 - 12

12y = 48

y = 4

The first point is (6,4).

Take x = 0, then -

2(0) + 12y = 60

0 + 12y = 60

12y = 60

y = 5

The second point is (0,5).

Substitute (x,y) = (0,0) and see the direction of the region for 2x + 12y ≥ 60.

2(0) + 12(0) ≥ 60

0 ≥ 60

This is not true.

Therefore, the region is non-origin side.

Now consider the inequality x + y ≥ 20.

The equation of the above inequality is as follows -

x + y = 20

Find two points that satisfies the above equation.

Take x = 0, then -

0 + y = 20

y = 20

The first point is (0,20).

Take y = 0, then -

x + 0 = 20

x = 20

The second point is (20,0).

Substitute (x,y) = (0,0) and see the direction of the region for x + y ≥ 20.

0 + 0 ≥ 20

0 ≥ 20

This is not true.

Therefore, the region is non-origin side.

Plot the graph.

From the graph see that the corner points are (0,20), (18,2) and (30,0).

Now plug these points in the objective function and see for which point the objective function has the minimum value.

C = 2x + 12y

C = 2(0) + 12(20)

C = 0 + 240

C = 240

C = 2(18) + 12(2)

C = 36 + 24

C = 60

C = 2(30) + 12(0)

C = 60 + 0

C = 60

Therefore, the minimum value 60 is at points (18,2) and (30,0).

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The rock that Angela found is likely a sedimentary rock, formed from the accumulation and solidification of sediment, such as shells and pebbles, in a marine environment.

The type of rock that Angela found is likely a sedimentary rock. Sedimentary rocks are formed from the accumulation and solidification of sediment, such as sand, silt, and clay. The shells and pebbles embedded in the rock suggest that it was formed from the buildup of material in a marine environment, such as the ocean or a lake. The shells and pebbles were once separate materials, but over time, they were compacted and cemented together to form the rock.

Sedimentary rocks are typically layered, which is a characteristic formed from the accumulation of sediment over time. The shells and pebbles in the rock sample could be evidence of different layers of sediment that were compacted and cemented together.

It is also possible that the rock is a conglomerate, which is a type of sedimentary rock composed of rounded pebbles and cobbles held together by a finer-grained matrix. Conglomerates form in environments where high-energy water, such as rivers or streams, carry large rocks and sediment and deposit them in areas of low energy, such as a delta or a floodplain.

Therefore, In conclusion, the rock that Angela found is likely a sedimentary rock, formed from the accumulation and solidification of sediment, such as shells and pebbles, in a marine environment.

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The rock that Angela found is likely a sedimentary rock, formed from the accumulation and solidification of sediment, such as shells and pebbles, in a marine environment.

The type of rock that Angela found is likely a sedimentary rock. Sedimentary rocks are formed from the accumulation and solidification of sediment, such as sand, silt, and clay. The shells and pebbles embedded in the rock suggest that it was formed from the buildup of material in a marine environment, such as the ocean or a lake. The shells and pebbles were once separate materials, but over time, they were compacted and cemented together to form the rock.

Sedimentary rocks are typically layered, which is a characteristic formed from the accumulation of sediment over time. The shells and pebbles in the rock sample could be evidence of different layers of sediment that were compacted and cemented together.

It is also possible that the rock is a conglomerate, which is a type of sedimentary rock composed of rounded pebbles and cobbles held together by a finer-grained matrix. Conglomerates form in environments where high-energy water, such as rivers or streams, carry large rocks and sediment and deposit them in areas of low energy, such as a delta or a floodplain.

Therefore, In conclusion, the rock that Angela found is likely a sedimentary rock, formed from the accumulation and solidification of sediment, such as shells and pebbles, in a marine environment.

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The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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) The probability that a randomly selected

medical student who took the test had a total

score that was less than 484 = .

) The probability that a randomly selected study

participant's response was between 504 and 516

= .

) The probability that a randomly selected study

participant's response was more than 528 =

.

) Option D is

Only the event in (c) is unusual as its probability is

less than .

The and parts of the question are not

complete.

B) Find the probability that a randomly selected

study participant's response was between 504

and 516

C) Find the probability that a randomly selected

study participant's response was more than 528.

D) Identify any unusual event amongst the three

events in A, B and C. Explain the reasoning.

a) None.

b) Events A and B.

C) Event A

D) Event C

Solution

This is a normal distribution problem with

Mean = μ =

Standard deviation = o = .

A) Probability that a randomly selected medical

student who took the test had a total score that

was less than 484 = P(x < 484)

We first normalize or standardize 484

The standardized score for any value is the value

minus the mean then divided by the standard

deviation.

z = (x-μ)/o = (484 - 500)/10.4 = - 1.54

To determine the required probability

P(x < 484) = P(z < -1.54)

We'll use data from the normal distribution table

for these probabilities

P(x < 484) = P(z < -1.54) = 0.06178

B) Probability that a randomly selected study

participant's response was between 504 and 516

= P(504 ≤ x ≤ 516)

We normalize or standardize 504 and 516

For 504

z = (x -μ)/σ = (504 500)/10.4 = 0.38

For 516

z = (x - μ)/σ = (516-500)/10.4 = 1.54

To determine the required probability

P(504 ≤ x ≤ 516) = P(0.38 ≤ Z ≤ 1.54)

We'll use data from the normal distribution table

for these probabilities

P(504 ≤ x ≤ 516) = P(0.38 ≤ Z ≤1.54)

= P(z ≤ 1.54) - P(z ≤ 0.38)

= 0.93822 - 0.64803

= 0.29019

C) Probability that a randomly selected study

participant's response was more than 528 = P(x >

528)

We first normalize or standardize 528

z = (x - μ)/σ = (528 - 500)/10.4 = 2.69

To determine the required probability

P(x > 528) = P(z > 2.69)

We'll use data from the normal distribution table

for these probabilities

PP(x > 528) = P(z > 2.69) = 1 - P(z ≤ 2.69)

= 1-0.99643

= 0.00357

) Only the in () is as its probability

is less than ..

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The complete question is as follows -

In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.4.

A) Find the probability that a randomly selected medical student who took the test had a total score that was less than 484. The probability that a randomly selected medical student who took the test had a total score that was less than 484 is:_______.

B) Find the probability that a randomly selected study participant's response was between 4 and 6 The probability that a randomly selected study participant's response was between 4 and 6 is:_______.

C) Find the probability that a randomly selected study participant's response was more than 8. The probability that a randomly selected study participant's response was more than 8 is:________.

The probability that a randomly selected medical student who took the test had a total score that was less than 480 is 0.49, which means that approximately 49% of medical students had a score lower than 480.

To calculate the probability that a randomly selected medical student who took the test had a total score that was less than 480, we need to start by looking at the data given. In this case, the data tells us that the mean score was 500 and the standard deviation was 50. This means that the scores are normally distributed, which means that the probability of finding a score lower than 480 can be calculated using the normal distribution formula. We can use this formula to calculate the area under the curve (or probability) below the score of 480. The result of this calculation is 0.49, which means that approximately 49% of medical students had a score lower than 480.

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At t = 10ms, the current can be found by substituting t=10 into the given equation for the current: [tex]I(t) = 5e^(-t/6). This gives I(10) = 5e^(-10/6) = 0.25 A.[/tex]

[tex]I(t) = 5e^(-t/6)[/tex]

[tex]At t = 1ms: I(1) = 5e^(-1/6) = 3.26 AAt t = 6ms: I(6) = 5e^(-6/6) = 0.77 AAt t = 10ms: I(10) = 5e^(-10/6) = 0.25 A[/tex]

At t = 1ms, the current can be found by substituting t=1 into the given equation for the current: [tex]I(t) = 5e^(-t/6).[/tex] This gives [tex]I(1) = 5e^(-1/6) = 3.26 A.[/tex]

At t = 6ms, the current can be found by substituting t=6 into the given equation for the current: [tex]I(t) = 5e^(-t/6)[/tex]. This gives [tex]I(6) = 5e^(-6/6) = 0.77 A.[/tex]

At t = 10ms, the current can be found by substituting t=10 into the given equation for the current: [tex]I(t) = 5e^(-t/6)[/tex]. This gives [tex]I(10) = 5e^(-10/6) = 0.25 A.[/tex]

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The probability that a student studied for 4 hours is 0.3.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1.

Given A group of students was surveyed in a middle school class,

the table for records,

Number of Hours          Total Number of Students

0                                                      1

1                                                       3

2                                                      2

3                                                      10

4                                                       9

5                                                       7

6                                                        3

To determine the probability;

The number of students that has 4 hours is 9

The total number of students = 30

P(4 hours) = 9/30

P(4 hours) = 0.3

Hence probability is 0.30.

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Answer:

Option 1 : x² + 4x + 4

Option 2 : x² + 20x + 100

Option 3 : x² + 6x + 9

Step-by-step explanation:

Looks like you got two of them right, one wrong and one missing. The first option is also a perfect square.

Here is how it evaluates:

If a trinomial expression can be a perfect square then it can be of the form (x + a)^2 = x² + 2ax + a² . Therefore the last term must be a perfect square of a number and the second term is twice the first term x and a = 2ax

So examining the choices we get

The length of the other leg is 14.14 cm rounded to two decimal places.

Given data :

Given, The hypotenuse of a right triangle measures 15 cm, and one of its legs measures 5 cm.

We know,

Hypotenuse² = Base² + Adjacent².

Therefore,

15² = 5² + Adjacent².

Adjacent = √(225 - 25).

Adjacent = √200.

Adjacent = 14.14.

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Answer:

Y=5x+2

first find the rise over run (slope) (m value in the y=mx+b equation) you do this by using your table. notice how much the y side rises by (5) and how much the x side runs by (1) the slope is 5/1 (5) the y-intercept is 2, we know this from the table.

The value of x in the triangle is given by x = 33.7°

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of hypotenuse = AC = 18 cm

The measure of the opposite side = AB = 10 cm

From the trigonometric relations ,

sin θ = opposite / hypotenuse

Substituting the values in the equation , we get

sin x = 10 / 18

On simplifying the equation , we get

sin x = 0.555556

Taking inverse on both sides of the equation , we get

x = sin⁻¹ ( 0.555556 )

On further simplification , we get

x = 33.7°

Hence , the value of x is 33.7°

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The expression improper fractions to mixed numbers will be 1 ¹/₄, 2 ¹/₃, and 1 ²/₃.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expressions are given below.

(5 x 1/4), (3 x 7/9), and (2 x 5/6)

Then simplify each expression, then we have

⇒ 5 x 1/4

⇒ 1/4 + 1/4 + 1/4 + 1/4 + 1/4

⇒ 5 / 4

⇒ 1 ¹/₄

⇒ 3 x 7/9

⇒ 7/9 + 7/9 + 7/9

⇒ 7/3

⇒ 2 ¹/₃

⇒ 2 x 5/6

⇒ 5/6 + 5/6

⇒ 5/3

⇒ 1 ²/₃

The expression improper fractions to mixed numbers will be 1 ¹/₄, 2 ¹/₃, and 1 ²/₃.

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The answer inequality of the given line will be -4<n<5.

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0).

These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

The endpoints of the given line are -4 and +5.

So the value of inequality should lie between these two lines only.

The inequality can be written as n< 5 and n>-4

or -4<n<5

Hence the answer inequality of the given line will be -4<n<5.

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The matrix v is the left singular vector, and the matrix σ is a diagonal matrix containing the singular values of the matrix a, but inverted. The matrix uT is the transpose

The singular value decomposition of a is:

a = uσvT

where

u = (1/√2, 0, -1/√2)

σ = (5, 0, 0)

vT = (3/5, 4/5, 0)

The pseudoinverse of a is:

a = vσuT

where

v = (3/5, 4/5, 0)

σ = (1/5, 0, 0)

uT = (√2/5, 0, -√2/5).

The singular value decomposition and pseudoinverse of the 1-by-3 matrix a = 3 4 0 are u = (1/√2, 0, -1/√2), σ = (5, 0, 0), vT = (3/5, 4/5, 0) and v = (3/5, 4/5, 0), σ = (1/5, 0, 0), uT = (√2/5, 0, -√2/5), respectively.

The singular value decomposition of the 1-by-3 matrix a = 3 4 0 is u = (1/√2, 0, -1/√2), σ = (5, 0, 0), vT = (3/5, 4/5, 0). This means that the matrix can be written as a product of three matrices, u, σ and vT. The matrix u is a unitary matrix, and the matrix σ is a diagonal matrix containing the singular values of the matrix a. The matrix vT is the transpose of the matrix v, which is the right singular vector. The pseudoinverse of a is v = (3/5, 4/5, 0), σ = (1/5, 0, 0), uT = (√2/5, 0, -√2/5). This means that the matrix a can be written as a product of three matrices, v, σ and uT, which is the inverse of the matrix u. The matrix v is the left singular vector, and the matrix σ is a diagonal matrix containing the singular values of the matrix a, but inverted. The matrix uT is the transpose

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The letter represented by the star symbol is 1.

We can start by using the rules of arithmetic. Since each symbol represents a different digit, we can represent the symbols with the numbers 0 to 9. Then we can write the equation as an algebraic expression and solve for the star symbol.

Let's assign the value of the letter represented by the star symbol to x.

A + B = 10x + x = 11x

We know that the maximum value for the result of the addition (C) is 18 (9 + 9) and that the maximum value for 11x is 990 (90 * 11), so x cannot be greater than 9.

Let's try the lowest value for x, which is 0.

A + B = 10 * 0 + 0 = 0

Since 0 cannot be a digit in A or B, x cannot be 0.

Let's try the next value for x, which is 1.

A + B = 10 * 1 + 1 = 11

Since 11 is a valid result of the addition, x = 1 is a solution.

Therefore, the letter represented by the star symbol is 1.

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The complete question is:

In the following addition problem, different letters represent different digits, and equal letters represent equal digits. Find the value of the letter represented by the star symbol. A + B = C

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The value for the Equation x- 6 = 53 is 59.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x- 6 = 53

Now, make as the subject of formula and solve for x

So, add 6 on both side

x- 6+ 6= 53 + 6

x = 59

Hence, the value of x is 59.

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Answer: $ 495. 41

Step-by-step explanation:

First, multiply $32 by 3 days and get $96.

Then multiply .69 and 289 and get $ 199.41

Lastly, add those to get and get your answer.

(32 x 3) + .69 x 289 = 495. 41

Answer:

A. Positive Correlation

Step-by-step explanation:

The dots seem to be going upward throughout the graph, therefore making it a [positive correlation]

If the population variable x is normally distributed , then (b) Both intervals are equally likely to contain μ with probability ≈ 0.95.

The two intervals are :

(i) the z-interval [tex]\bar{x}[/tex] ± 1.960σ/√n   and    (ii) the t-interval [tex]\bar{x}[/tex]± t₀.₀₂₅,ₙ₋₁S/√n  ;

the critical value of z interval is = 1.96  ;

by using the normal table , we get , p = 0.95  ;

So , the z interval is with p = 95% ;

the t interval is t₀.₀₂₅,ₙ₋₁ = critical value ,

On comparing with [tex]t_{\frac{\alpha}{2} }[/tex],ₙ₋₁ = t₀.₀₂₅,ₙ₋₁ ,

we get , α/2 = 0.025 ⇒ So , α = 0.05   .

this interval is also 95% confidence interval .

Therefore , both the intervals are equally likely to contain μ with probability ≈ 0.95.

The given question is incomplete , the complete question is

Which is more likely to contain µ, the z-interval [tex]\bar{x}[/tex] ± 1.960σ/√n or the t-interval [tex]\bar{x}[/tex]± t₀.₀₂₅,ₙ₋₁S/√n? Assume that the population variable x is normally distributed.

Choose the correct answer below.

(a) The interval [tex]\bar{x}[/tex]±t₀.₀₂₅,ₙ₋₁S/√n has a higher probability of containing µ.

(b) Both intervals are equally likely to contain μ with probability ≈ 0.95.

(c) The interval  [tex]\bar{x}[/tex]± 1.96σ/√n has a higher probability of containing μ.

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Answer:

Step-by-step explanation:

To determine if they can use 26 of one type and 14 of the other, we need to calculate the cost for each scenario and compare it to their budget of $400.

If they use 26 round tables, it would cost 26 * $10 = $260.

And if they use 14 square tables, it would cost 14 * $10 = $140.

The total cost would be $260 + $140 = $400, which is equal to their budget.

Now, we need to make sure that they can seat all the guests with the tables they plan to rent.

If they use 26 round tables, they can seat 26 * 6 = 156 guests.

And if they use 14 square tables, they can seat 14 * 8 = 112 guests.

The total number of guests they can seat would be 156 + 112 = 268.

since they expect at least 260 guests to attend and they can seat 268 guests, the table rental plan of 26 round tables and 14 square tables is feasible both financially and in terms of seating capacity.

The identity matrix of C is invertible, when its determinant is zero.

A matrix is a collection of numbers arranged in rows and columns. In linear algebra, we often work with square matrices, which are matrices with the same number of rows and columns.

Here we have given that for which numbers c is this matrix not invertible.

Here we have to consider that an important property of a square matrix is its invertibility, which determines whether or not the matrix can be "reversed" to get back to the identity matrix.

Therefore, the number "c" for which the matrix is not invertible is when the determinant of the matrix is zero. In other words, the matrix is singular and has no inverse. This can occur when the rows of the matrix are linearly dependent, meaning that one row can be written as a linear combination of the other rows. When this happens, the matrix collapses to a lower-dimensional space, and its determinant becomes zero.

In conclusion, a matrix is not invertible when its determinant is zero, and this is because the matrix has linearly dependent rows and collapses to a lower-dimensional space.

Complete Question:

For which three numbers c is this matrix not invertible, and why not?

[tex]A = \begin{bmatrix}2 &c &8 \\ c& c &7 \\ c&c & c\end{bmatrix}[/tex]

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The work required to pump all of the olive oil to the rim of the tank is equal to the weight of the olive oil multiplied by height of the tank.

Work = 41 lb/ft3 x (height of the tank)

For example, if the height of the tank is 6 ft,

Work = 41 lb/ft3 x 6 ft = 246 lb-ft

The work required to pump all of the olive oil to the rim of the tank is equal to the weight of the olive oil multiplied by the height of the tank.

The work required to pump all of the olive oil to the rim of the tank is equal to the weight of the olive oil (which is typically measured in pounds per cubic foot) multiplied by the height of the tank in feet. Thus, the work required can be expressed as: Work = (Weight of olive oil) x (Height of tank in feet). For example, if the olive oil has a weight of 41 pounds per cubic foot and the height of the tank is 6 feet, the work required to pump the olive oil to the rim of the tank would be 246 lb-ft (41 lb/ft3 x 6 ft).

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