Solve. Show all of your work.
1. A construction worker was preparing wood for a project.
He had 1/4 of a meter of wood that he needed to cut
into equal size pieces. If he cut the wood into 6 pieces,
how long will each piece be?

Answer:

360 in

Step-by-step explanation:

To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:

\(\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}\)

So, the dressmaker has 360 in of ribbon.

The result obtained when a decision alternative is chosen and a chance event occurs is known as consequence. The answer is: b.

When a decision alternative is chosen and a chance event occurs, the result is referred to as a consequence. A consequence represents the outcome or outcome state that arises from the combination of a decision and a chance event.

It is the result or effect that occurs based on the chosen alternative and the unpredictable element introduced by the chance event.

Consequences are an essential concept in decision theory and decision analysis, as they help evaluate the potential outcomes and impacts of different choices and events. By considering the consequences associated with each decision alternative, decision-makers can assess the desirability or utility of different outcomes and make informed choices.

Hence, the correct option is: b. consequence.

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       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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Answer:

24.

Step-by-step explanation:

I think. I'm not sure sorry! I hope I helped a little though.

Answer: 8 cups

Step-by-step explanation: 16 cups in a gallon, Half of 16 is 8. (16 divided by 2 = 8)

Answer:

is d because one of the characteristics of the functions is that there cannot be x that have multiple images in the range (y)

Question: If the subspace of all solutions of

Ax = 0

has a basis consisting of vectors and if A is a ​matrix, what is the rank of​ A.

Note: The rank of A can only be determined if the dimension of the matrix A is given, and the number of vectors is known. Here in this question, neither the dimension, nor the number of vectors is given.

Assume: The number of vectors is 3, and the dimension is 5 × 8.

Answer:

The rank of the matrix A is 5.

Step-by-step explanation:

In the standard basis of the linear transformation:

f : R^8 → R^5, x↦Ax

the matrix A is a representation.

and the dimension of kernel of A, written as dim(kerA) is 3.

By the rank-nullity theorem, rank of matrix A is equal to the subtraction of the dimension of the kernel of A from the dimension of R^8.

That is:

rank(A) = dim(R^8) - dim(kerA)

= 8 - 3

= 5

Answer: The blank spot is 3

Step-by-step explanation:

I used this, this is the link you copy and paste it to your search bar.

Answer:

3/35

Step-by-step explanation:

i think?

Answer: 7w - 28

7*w - 7*4

7w - 28

Brainliest pwease if the answer is correct! <3

Answer:

the slope is m=29/10

Step-by-step explanation:

Y2-Y1 over X2-X1

The slope of the line that passes through the points (6, 7) and (16, 22) is 3/2.

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. Thats why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.

So, the slope of the line that passes through the points (6, 7) and (16, 22);

slope =  22-7/ 16 - 6

slope = 15/10

slope =3/2

Therefore, the slope of the line that passes through the points (6, 7) and (16, 22) is3/2.

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Trigonometric expression sin²θ + cos²θ + tan²θ simplifies to 1 / cos²θ.To simplify the trigonometric expression sin²θ + cos²θ + tan²θ, we can use the Pythagorean identities.

These identities relate the trigonometric functions of an angle to each other. The Pythagorean identity for sine and cosine is sin²θ + cos²θ = 1. This means that the sum of the squares of the sine and cosine of an angle is always equal to 1.
So, sin²θ + cos²θ simplifies to 1.
Now, let's simplify tan²θ. The tangent of an angle is equal to the sine of the angle divided by the cosine of the angle. Using this relationship, we can rewrite

tan²θ as (sinθ / cosθ)².
To simplify (sinθ / cosθ)², we can square both the numerator and the denominator. This gives us sin²θ / cos²θ.

Now, we can substitute this simplified expression into our original expression:
sin²θ + cos²θ + tan²θ = 1 + sin²θ / cos²θ
To combine these two terms, we need a common denominator. The common denominator is cos²θ. Multiplying the numerator and denominator of sin²θ by cos²θ gives us:
1 + sin²θ / cos²θ = cos²θ / cos²θ + sin²θ / cos²θ
Combining the fractions, we get:
cos²θ + sin²θ / cos²θ
Using the fact that cos²θ + sin²θ = 1, this expression simplifies to:
1 / cos²θ

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Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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Answer:

a is the answer because I just did that question and got 100 percent.

Answer:

Michael is 320 yards from the top when Justine starts. So, one point on the line representing Michael’s function is (0, 320).

He gains 80 yards in an hour. That is, after 1 hour he should be 320 − 80 = 240 yards from the top. So, another point on the line representing Michael’s function is (1, 240).

Two points that can be used to graph Michael’s function for the yards left to hike in terms of the hours he’s spent hiking are (0, 320) and (1, 240).

Step-by-step explanation:

This is the answer I copied down from the test. Yes it is correct but its word for word, change up some words to make it seem like you didn't just get the answer from a cite

The coordinates (1, 240) and (2, 160) represent points on Michaels graph is attached.

The general equation of a straight line is -

Other possible equations of lines are -

We have Michael and his friend Justine enjoy hiking.

We can write the equation for Michael as -

y = 320 - 80x

For [x] = 1, we can write -

y = 320 - 80

y = 320 - 80

y = 240

(1, 240)

For [x] = 2, we can write -

y = 320 - 80 x 2

y = 320 - 160

y = 160

(2, 160)

Refer to the graph attached for Michael's function.

Therefore, the coordinates (1, 240) and (2, 160) represent points on Michaels graph is attached.

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Answer:

52.5

Step-by-step explanation:

180-75=105

105/2=52.5

Answer:

b) 105°

Step-by-step explanation:

After set s1.addAll(s2), s1 is [1, 2, 5, 2, 3, 6].

After performing the operation s1.addAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become[1, 2, 5, 2, 3, 6].

To determine the value of s1, the following steps has to be taken:

1. Start with sets s1 [1, 2, 5] and s2 [2, 3, 6].

2. Apply the addAll operation with set s2: [2, 3, 6]

3. Add each element from set s2 to set s1, while avoiding duplicates (since sets cannot have duplicate elements).

4. Therefore, suppose if set s1 is [1, 2, 5] and set s2 is [2, 3, 6] then, after s1.addAll(s2), the set s1 becomes [1, 2, 5, 2, 3, 6].

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To find the exact length of the curve given by x = et − 9t, y = 12et/2, 0 ≤ t ≤ 3, we can use the arc length formula:
L = ∫(a to b) √[dx/dt]^2 + [dy/dt]^2 dt
Substituting the given values, we get:
L = ∫(0 to 3) √[e^t - 9]^2 + [6e^(t/2)]^2 dt
Simplifying the expression under the square root, we get:
L = ∫(0 to 3) √(e^(2t) - 18e^t + 81 + 36e^t) dt
L = ∫(0 to 3) √(e^(2t) + 18e^t + 81) dt
L = ∫(0 to 3) (e^t + 9) dt
L = [e^t + 9t] from 0 to 3
L = [e^3 + 9(3)] - [e^0 + 9(0)]
L = e^3 + 27 - 10.99
L ≈ 25.5
Therefore, the exact length of the curve is approximately 25.5 units.

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The relation 2 represents a function.

In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.

To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.

The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.

If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.

We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.

Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.

Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.

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The joint PDF of X and Y is fx.x (x, y) = λ * exp(-λx) / x for 0 < y < x, and 0 elsewhere.

The joint probability density function (PDF) of X and Y can be obtained by multiplying the individual PDFs of X and Y, as they are independent random variables.

Given:

X ~ Exponential(λ), with mean 1 (λ = 1)

Y ~ Uniform(0, X), for 0 < y < x

To find the joint PDF, we first need to express the PDFs of X and Y.

PDF of X:

fX(x) = λ * exp(-λx) for x > 0 (Exponential distribution with parameter λ)

PDF of Y:

fY(y|x) = 1 / x for 0 < y < x (Uniform distribution on interval [0, x])

Now, we can find the joint PDF by multiplying these individual PDFs:

fx.x (x, y) = fX(x) * fY(y|x)

Substituting the PDFs:

fx.x (x, y) = (λ * exp(-λx)) * (1 / x)

fx.x (x, y) = λ * exp(-λx) / x for 0 < y < x

Therefore, the fully specified joint PDF of X and Y is:

fx.x (x, y) = λ * exp(-λx) / x for 0 < y < x, and 0 elsewhere.

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Line y=6x−2 and line 6y=−x are perpendicular.

Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.

In the equation of line y=mx+c, m represents the slope of the line.

The given lines are

a: y=6x−2           (1)

b: 6y= -x            (2)

and c: y+6x=1     (3)

To determine lines are parallel or perpendicular,

Find the slope of the lines, use the standard equation of line is y=mx+c,

Compare the given equations with standard equation of line,

Slope of line (1) m₁= 6

Slope of line (2) m₂ = -1/6

Slope of line (3) m₃ = -6

By multiplying slope of line (1) and (2), gives -1

Implies that line (1) and (2) are perpendicular to each other.

Therefore, Line y=6x−2 and line 6y=−x are perpendicular.

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The average rate change of over the interval [-1,1] is 2.

What is an interval?

In mathematics, an interval is expressed in numerical terms. All the numbers between two specific numbers are referred to as an interval. All actual numbers between those two are included in this range.

Given points on the graph is

x   -2     -1     0     1        

y   -4     -3     -1     3

The average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,

Average rate of change = [f(b) - f(a)]/(b - a)

Here a = -1, b = 1, f(a) = -3, and f(b) = 3

The average rate is (3 - (-3))/ (1 - (-1)) = 2

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The volume of a square based pyramid is 927.7 cubic centimeter.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a square base pyramid with the side length of the base is 16.6 and the height of the pyramid is 10.1 m.

We know that, the volume of square based pyramid =a²h/3.

Here, volume = 16.6²×10.1/3

= 275.56×10.1/3

= 927.7 cubic centimeter

Therefore, the volume of a pyramid is 927.7 cubic centimeter.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the volume of a pyramid with a square base, where the side length of the base is 16.6 and the height of the pyramid is 10.1 m. Round your answer to the nearest tenth of a cubic meter.

Answer:

Step-by-step explanation:

Yes, it is a linear equation

Answer:

Yes, it is Linear

Step-by-step explanation:

This is the answer because A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable y is 1 and the degree of variable x is 1.

Hope this helps!

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer: x = -5

Step-by-step explanation:

4−2(x+7)=3(x+5)4-2(x+7)=3(x+5)Simplify 4−2(x+7)4-2(x+7).Tap for more steps...−2x−10=3(x+5)-2x-10=3(x+5)Simplify 3(x+5)3(x+5).Tap for more steps...−2x−10=3x+15-2x-10=3x+15Move all terms containing xx to the left side of the equation.Tap for more steps...−5x−10=15-5x-10=15Move all terms not containing xx to the right side of the equation.Tap for more steps...−5x=25-5x=25Divide each term in −5x=25-5x=25 by −5-5 and simplify.Tap for more steps...x = −5

Answer:

500 miles

Step-by-step explanation:

81-11 is 70. 70 divided by .14 is 500 so that's 500 miles she can bike.

Answer:

500 miles

Step-by-step explanation:

To find out how many miles Candice can hike at max, use the equation 11 + 0.14x = 81.

11 + 0.14x = 81

Subtract 11 from both sides. This undoes the +11.

0.14x = 81 - 11

Subtract 11 from 81 to get 70.

0.14x = 70

Divide both sides by 0.14. This undoes the multiplication by 0.14.

x = 70/0.14

I recommend converting 0.14 into a fraction. That would be 7/50.

x = 70/(7/50)

Find the reciprocal of 7/50 (50/7). Switch the sign from division to multiplication.

x = (70 * 50)/7

Multiply 70 by 50 to get 3500.

x = 3500/7

Divide 3500 by 7 to get 500.

x = 500

At max, Candice can hike 500 miles.

a) The time required to assemble the 8th unit is 0.876 hours.

b) The total time required to assemble the last 5 units is 1.752 hours

(a) the time required to assemble the 8th unit.

To solve this, we can first find the time required to assemble 7 units and then subtract it from the time required to assemble 8 units.

Time required to assemble the first unit = 3 hours

Given, the time required to assemble the 6th unit = 1 hour and 23 minutes = 1 + 23/60 hours = 1.383 hours

Average time required to assemble 1 unhours production= [(time required to assemble the first unit) + (time required to assemble the sixth unit)]/5= [(3) + (1.383)]/5= 0.876 hours

Time required to assemble 7 units= 7 × 0.876= 6.132 hours

Now, time required to assemble the 8th unit= Time required to assemble 8 units - Time required to assemble 7 units= 8 × 0.876 - 6.132= 7.008 - 6.132= 0.876 hours

(b) the total time required to assemble the last 5 units.

We have already calculated the time required to assemble the first 6 units.

Time required to assemble the first 6 units= 6 × 0.876= 5.256 hours

Now, the total time required to assemble the last 5 units= Time required to assemble 8 units - Time required to assemble the first 6 units= 8 × 0.876 - 5.256= 7.008 - 5.256= 1.752 hours

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The orthogonal complement w⊥ of w has a basis given by {v1, v2} = {(1, 0, 0), (0, 1, 2)}.

To find the orthogonal complement w⊥ of w, we need to find the set of all vectors that are orthogonal (perpendicular) to w.

Given w = (x, y, z) = (12t, -12t, 6t), we can find a vector v = (a, b, c) that is orthogonal to w by taking their dot product equal to zero:

w · v = 0

Substituting the values of w and v:

(12t, -12t, 6t) · (a, b, c) = 0

(12t)(a) + (-12t)(b) + (6t)(c) = 0

12at - 12bt + 6ct = 0

Now, we can solve this equation to find the values of a, b, and c that satisfy the orthogonal condition for all values of t.

12at - 12bt + 6ct = 0

Factor out t:

t(12a - 12b + 6c) = 0

For this equation to hold true for all values of t, the expression inside the parentheses must equal zero:

12a - 12b + 6c = 0

Divide by 6:

2a - 2b + c = 0

This equation represents a plane in three-dimensional space. To find a basis for w⊥, we can express this equation in the form of a linear combination of vectors. Let's solve for c:

c = 2b - 2a

Now, we can express the basis vectors for w⊥ in terms of a and b:

v = (a, b, 2b - 2a)

We can choose any values for a and b to get different vectors in the orthogonal complement w⊥. For example, we can set a = 1 and b = 0:

v1 = (1, 0, 0)

Or we can set a = 0 and b = 1:

v2 = (0, 1, 2)

These two vectors, v1 and v2, form a basis for w⊥.

Therefore, the orthogonal complement w⊥ of w has a basis given by {v1, v2} = {(1, 0, 0), (0, 1, 2)}.

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Answer:

Step-by-step explanation:

its 6 2 + 5 = 9-2 = 6