27 similar cubes have a total volume of 3375 cm3. what is the edge of 1 cube?

Simplified would be 4xy + 3x^2 + 6x

Answer:

4xy+3x²+6x

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

she can paint 2/5 of the fence

The smallest perimeter is P = 2L + 2W = 2(2) + 2(2) = 8 in, and the dimensions of the rectangle are 2 in by 4 in.

To find the smallest perimeter for a rectangle with an area of 4 in² using derivatives, we can set up an optimization problem. Let's denote the length of the rectangle as L and the width as W.

The formula for the area of a rectangle is given by A = L × W. Since we know the area is 4 in², we can write the equation as 4 = L × W.

To find the smallest perimeter, we need to minimize the perimeter function P = 2L + 2W while satisfying the area constraint.

We can rewrite the area equation as W = 4/L and substitute it into the perimeter equation to get P = 2L + 2(4/L).

Now, we find the derivative of the perimeter function with respect to L: \($dP/dL = 2 - \frac{8}{L^2}$\).

To find the minimum perimeter, we set the derivative equal to zero and solve for L:

\(2 - \frac{8}{L^2} = 0\\\\ 2 = \frac{8}{L^2}\\\\ L^2 = \frac{8}{2}\\\\ L^2 = 4\\\\ $L = \pm 2$\)

Since we're dealing with lengths, we take L = 2 (we discard the negative solution). Substituting this value back into the area equation, we find W = 4/L = 4/2 = 2

Therefore, the smallest perimeter is P = 2L + 2W = 2(2) + 2(2) = 8 in, and the dimensions of the rectangle are 2 in by 4 in.

Now, consider finding the largest perimeter. Since we're not given any constraints on the dimensions, the largest perimeter is unbounded and not defined for a fixed area of 4 in². As one side of the rectangle approaches infinity, the perimeter also approaches infinity. Therefore, there is no upper limit to the perimeter.

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The two linear equations are:

1)  y = -x + 5

2) y = (-1/2)*x - 1

Remember that two linear equations are parallel if and only if have the same slope and different y-intercept.

So to find a linear equation:

y = m*x + b

Parallel to:

x + y = 4

y = -x + 4

The slope needs to be m = -1 and the y-intercept b ≠ 4

So our line will be:

y = -x + b

To find the value of b, we use the fact that this line passes through (2, 3), replacing the values of the point in the line we get:

3 = -2 + b

3 + 2 = b

5 = b

The linear equation is y = -x + 5

For the second case, we want to find a line perpendicular to:

2x - y = 5

y = 2x - 5

Two lines are perpendicular if the product of the slopes is -1, then:

m*2 = -1

m = -1/2

So the perpendicular line is something like:

y = (-1/2)*x + b

To find the value of b we use the fact that this line needs to pass through (6, -4)

Replacing these values we get

-4 = (-1/2)*6 + b

-4 = -3 + b

-4 + 3  =b

-1 = b

The line is:

y = (-1/2)*x - 1

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At the grand opening, al's furniture store, there is offering spin wheel for discount. The probability that a customer gets a 10% or 20% discount is equals to the 0.75.

At the grand opening, al's furniture store, it offered a spin the wheel for a discount to its customers. The wheel is divided into 12 equal slices.

The percentage of discount awarded by 6 slices = 10%

The percentage of discount awarded by 3 slices = 20%

The percentage of discount awarded by 2 slices = 40%

The percentage of discount awarded by 1 slices

= 100%

We have to determine the probability that a customer gets a 10% or 20% discount. As we see all slices are independent to each other so events related to these also independent.

We have total 12 slices. Since, 6 slices awarded for 10% discount i.e. chances of getting 10% discount is equal = 6/12

Similarly, 3 slices awarded for 20% discount i.e. chances of getting 20% discount is 3/12.

Hence chances of getting 10% or 20% discount is

= P( X = 20%) + P( X= 10%)

= 6/12 + 3/12

= 1/2 + 1/4

= 0.50 + 0.25

= 0.75

Hence, required value is 0.75.

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The equation of the line in point-slope form is:

y - 8 = 3(x + 6) or y - 2 = 3(x + 8).

The equation, y - b = m(x - a), represents the equation of a line in point-slope form, where:

Given two points, (-8, 2) and (-6, 8), find the slope (m) of the line that passes through the two points:

Slope (m) = change in y / change in x = (8 - 2)/(-6 -(-8))

Slope (m) = 6/2

Slope (m) = 3

Substitute m = 3 and (-6, 8) into y - b = m(x - a):

y - 8 = 3(x - (-6))

y - 8 = 3(x + 6)

Or substitute m = 3 and (-8, 2) into y - b = m(x - a):

y - 2 = 3(x - (-8))

y - 2 = 3(x + 8)

Therefore, the equation of the line in point-slope form is:

y - 8 = 3(x + 6) or y - 2 = 3(x + 8).

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Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

As the level of significance increases, the probability of making a type II error decreases.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

If the level of significance of a hypothesis test is raised from 0.05 to 0.1, the probability of a type II error will decrease.

Type II error occurs when we fail to reject a null hypothesis that is actually false. It is the probability of accepting a false null hypothesis. By increasing the level of significance, we are making it easier to reject the null hypothesis, which in turn decreases the probability of accepting a false null hypothesis.

Hence, as the level of significance increases, the probability of making a type II error decreases.

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Answer:

1019/250 x

Step-by-step explanation:

4x1+

0x1

10

+

7x1

100

+

6x1

1000

a) The order of execution for the expression is: parentheses, multiplication, addition, division.

b) The order of execution for the conditional statement is: exponentiation, multiplication, comparison.

a) For the expression −X∗(Y+2)/Z:

The parentheses (Y+2) are evaluated first.

Then, the negation -X is applied.

Next, the multiplication -X*(Y+2) is performed.

Finally, the division (-X*(Y+2))/Z is executed.

b) For the conditional statement If Sum ∧ 2<= Sum* ∗ 6 then:

The exponentiation Sum ∧ 2 is computed first.

Then, the multiplication Sum* ∗ 6 is performed.

Finally, the comparison 2<= Sum* ∗ 6 is evaluated to determine the truth value of the condition.

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Answer:

A

Step-by-step explanation:

First, we should put this equation in slope-intercept form by isolating y.

Thus, we have:

\(2x-\frac{4}{3}y=4\\ -\frac{4}{3}y=4-2x\\ y=\frac{3}{2}x-3\)

The slope-intercept equation shows that the y-intercept is -3 and the slope is 3/2.

Only answer A meets these requirements.

Answer:

$1.42

Step-by-step explanation:

Since, The first customer paid $12 for 14 postcards and 5 large envelopes.

That is, 14 x + 5 y = 12        ------ (1)

And, The second customer paid $24.80 for 10 postcards and 15 large envelopes.

That is, 10 x + 15 y = 24.80  -------(2)

3 × equation (1),

We get, 42 x + 15 y = 36 ---------(3)

Equation (3) - Equation (2)

32 x = 11.20

⇒ x = 11.20/32

⇒ x = 0.35

By putting the value of x in equation (1),

We get, 14 × 0.35 + 5 y = 12

⇒ 4.9 + 5 y = 12

⇒ 5 y = 7.1

⇒ y = 1.42

Thus, the cost of one postcard = $ 0.35

And, the cost of each large envelope = $ 1.42

Step-by-step explanation:

(3X-20)+(3X+5)=111(( SINCE 111 IS TOTAL ANGLE

6X-15=111

6X=126

X=21

EFG=3×21-20

=63-20=43

The combined perimeter of

2b (14y - 12)

2c (18y + 4)

2d (14y - 16), is

Add the like terms

The combined perimeter is (46y - 24)

The combined area of

1b (10y^2 - 27y +5)

1c (20y^2 + 11y - 3)

1d (12y^2 -24y), is

Add the like terms

The combined area is (42y^2 - 40y + 2)

Answer:

5.95

Step-by-step explanation:

Answer:

third expression

Step-by-step explanation:

the surface area (SA) is the area of the 6 faces.

Note that opposite faces are congruent.

the surface area is the the area of each face multiplied by 2 , since they are congruent.

SA = 2(front area ) + 2(side area ) + 2(area of base)

   = 2(5 × 7 ) + 2(4 × 7 ) + 2(4 × 5 ) ← third option

  = 2(35) + 2(28) + 2(20)

 = 70 + 56 + 40

= 166 cm²

We assume that G is a connected planar graph with no vertex of degree <= 5. We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices. Let d be the maximum degree of G.

Qa. Contrapositive of an implication is a new implication formed by negating both the hypothesis and the conclusion.

The contrapositive of the implication "If G is a connected planar graph, then G has at least one vertex of degree <= 5" is "If G has no vertex of degree <= 5, then G is not a connected planar graph."

Qb. Proof: We assume that G is a connected planar graph with no vertex of degree <= 5.

We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices.

Let d be the maximum degree of G. Since G has no vertex of degree <= 5, then d >= 6.

Thus, the sum of degrees of all vertices in G is greater than or equal to 6v/2, which is equal to 3v.

Hence, 2e >= 3v.

Substituting this inequality in e <= 3v - 6, we get 2e >= 3e - 6, which implies that e >= 6.

Since e >= 6, it follows that G is not planar.

Qc. Proof: We use proof by induction on the number of vertices of G. For a graph with one vertex, the statement is trivially true.

For a graph with n > 1 vertices, assume that every planar graph with at most n - 1 vertices can be colored with 6 (or less) colors.

Let G be a planar graph with n vertices.

By part (a), there exists a vertex v of G with degree <= 5.

We remove v and all its edges from G to get a new graph G' with n - 1 vertices.

By the induction hypothesis, we can color G' with 6 (or less) colors.

We add back v and its edges to G.

Since v has degree <= 5, at most 5 colors are used on its adjacent vertices.

We use a new color for v.

Thus, G can be colored with 6 (or less) colors.

Therefore, by induction, the statement is true for all planar graphs.

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Answer:

Step-by-step explanation:

step 1 : finding the area of a floor using trapezius area formula

A= \(\frac{(10+14)*6}{2} = \frac{24*6}{2} =72 m^{2} \\\)

step 2 : the problem said 1 litre of paint convers an area of 2.5 m^2, so let's calculate how many liters of paint are needed to paint the floor

\(\frac{72 m^2}{2.5 m^2} = 28.8 litre\\\)

so we need 28.8 litre to paint the floor

step 3 : Each tin is 5 litre of paint so let's calculate how many tins do we need

n=\(\frac{28.8}{5} = 5.76 \\\)

we can't by 5.76 tins so it's 6 tins

step 4 : Each tin costs 21.99 and now we calculate how much 6 tins cost for us

cost = 6 × 21.99 = 131.94

step 5 : Gary has a budget of 150 and the total cost is 131.94. So, Gary has enough money to buy all the paint he needs.

The sample means are distributed along the x-axis for a sampling distribution of a sample mean.

A sample mean is an average of a set of data, that can be used to calculate the central tendency, standard deviation and the variance of a data set.

Now,

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The probability that the actual tracking weight is greater than the prescribed weight, P(X > 3), is 1/2.

The given pdf of a stereo cartridge is `f(x) = Sk[1 - (x - 3)²]`.

The value of k can be found by integrating the pdf from negative infinity to infinity and equating it to 1, i.e.,`∫f(x)dx = ∫Sk[1 - (x - 3)²]dx = 1`.

Now, integrating the expression we get:`∫Sk[1 - (x - 3)²]dx = k ∫[1 - (x - 3)²]dx`.Substituting `u = x - 3`, we have `du/dx = 1` and `dx = du`.

Putting the value of x in terms of u, we get:`k ∫[1 - u²]du`.Integrating this expression, we get:`k [u - (u³/3)]`The limits of integration are from negative infinity to infinity. Substituting these limits we get:`k { [infinity - (infinity³/3)] - [-infinity - (-infinity³/3)] } = 1`.

Now, `[infinity - (infinity³/3)]` and `[-infinity - (-infinity³/3)]` are not defined. So, the integral is not convergent. This implies that `k = 0`.b. We are given `f(x) = Sk[1 - (x - 3)²]`, and `f(x) = -11 if 2 ≤ x ≤ 4` otherwise. We are to find the probability that the actual tracking weight is greater than the prescribed weight, i.e., `P(X > 3)`.We have,`P(X > 3) = ∫3 to infinity f(x)dx`.We know that `f(x) = 0` if `k = 0`.

Hence, the pdf in the range `[2,4]` can be defined by any value of k. We can choose `k = -1/2`. Therefore, `f(x) = -1/2[1 - (x - 3)²]` in the range `[2,4]`.Putting this in the above expression, we get:`P(X > 3) = ∫3 to infinity -1/2[1 - (x - 3)²]dx`.Now, substituting `u = x - 3`, we have `du/dx = 1` and `dx = du`. Putting the value of x in terms of u, we get:`P(X > 3) = -1/2 ∫0 to infinity[1 - u²]du`.

Integrating this expression, we get:`P(X > 3) = -1/2 [u - (u³/3)]`.The limits of integration are from 0 to infinity. Substituting these limits, we get:`P(X > 3) = 1/2`.Hence, the main answer is `k = 0` and `P(X > 3) = 1/2`.Summary:a) The value of k is 0.b)

Hence, The probability that the actual tracking weight is greater than the prescribed weight, P(X > 3), is 1/2.

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Common ratio is 1/5

5 * 1/5 = 1

1 * 1/5 = 1/5

1/5 * 1/5 = 1/25

Missing terms: 1 and 1/5

The smallest diameter of the wrapper that will fit the candy bar ABC is 2√2 cm.

The candy company wants to create a cylindrical container that will fit the candy bar ABC. To find the smallest diameter of the wrapper, we need to consider the cross-sectional view of the candy bar.

The diameter of the wrapper should be equal to the diagonal of the rectangle formed by the candy bar's cross-section. In this case, the diagonal is represented by the symbol "=" and has a length of 4 cm.

To find the smallest diameter of the wrapper, we can use the Pythagorean theorem. According to the theorem, the square of the diagonal (4 cm) is equal to the sum of the squares of the width and height of the rectangle.

Let's assume the width of the rectangle is "x" cm. Using the Pythagorean theorem, we can write the equation:

4^2 = x^2 + x^2

Simplifying the equation, we have:

16 = 2x^2

Dividing both sides of the equation by 2, we get:

8 = x^2

Taking the square root of both sides of the equation, we find:

x = √8

Simplifying further, we have:

x = 2√2

Therefore, the width of the rectangle (and the diameter of the wrapper) is 2√2 cm.

So, the smallest diameter of the wrapper that will fit the candy bar ABC is 2√2 cm.

COMPLETE QUESTION:

This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If = 4 cm, what is the smallest diameter of wrapper that will fit the candy bar?

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Answer:

a)£30

b)£50

c)£65

Step-by-step explanation:

a) £36=120%

10%=£3

100%=£30

b) £60=120%

10%=£5

100%=£50

c)£78=120%

10%=£6.5

100%=£65

hope this helps, please can i get brainliest.

Answer: a) £30

b) £50

c) £65

Step-by-step explanation:  To find the price before the tip, we need to divide the total amount by 1.20. This is because 20% is equal to 0.20, and 1 + 0.20 = 1.20.

For option (a), £36 / 1.20 = £30.

For option (b), £60 / 1.20 = £50.

For option (c), £78 / 1.20 = £65.

Therefore, the price before the tip was £30 when Scarlett paid £36, £50 when she paid £60, and £65 when she paid £78.

Answer:

(Some textbooks describe a proportional relationship by saying that " y varies proportionally with x " or that " y is directly proportional to x .") This means that as x increases, y increases and as x decreases, y decreases-and that the ratio between them always stays the same.

Step-by-step explanation:

google

and I know that the second one is the answer I dont know the others

Answer:Area of part 1:

A1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

Area of part 2:

A2=length*width=(8+2)*1=10 ft2

Area of part 3:

A3=length*width=8*2=16 ft2

Total shaded area : A1+A2+A3=41 ft2

Total area of the reactangle : A=16*8=128 ft2

Total area of the nonshaded region : 128-41=87 ft2

Step-by-step explanation: Plz make brainliest

Answer:

Total shaded area : A1+A2+A3=41 ft2

Total area of the reactangle : A=16*8=128 ft2

Total area of the nonshaded region : 128-41=87 ft2

Answer:

x=3

Step-by-step explanation:

f(x)=2x+6

f(x)=12

Hence:

2x+6=12

2x+6-6=12-6

2x=6

x=6/2

x=3

Answer

70.000 в  10 раз больше 7.000

Step-by-step explanation: