match each expression to its equivalent expression

Answer:

1.61

Step-by-step explanation:

72/18 = 4cents per inch

4*41 = 161

1.61$

Answer:

13.8 oz

14.15 oz

14.2 oz

Step-by-step explanation:

trust me

Answer:

B, C, D

Step-by-step explanation:

The correct answer is option D

Therefore, the correct answer is option D: The set of all elements that are in C but not in B, or are in A.

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the derivative of the function, then evaluate it at x=1 and finally multiply it by δx.

δy = -0.04 and f'(x)δx = -0.04.

An example of a differentiable function is f, and its derivative is f ′. If f has a derivative, it is denoted by the symbol f ′ and is known as f's second derivative. Similar to the second derivative, the third derivative of f is the derivative of the second derivative, if it exists. By carrying on with this method, the nth derivative can be defined, if it exists, as the derivative of the (n1)th derivative.

To find δy and f'(x)δx for the function y=f(x)=x−x^3 with x=1 and δx=0.02, we'll first find the derivative of the function, then evaluate it at x=1, and finally multiply it by δx.

1. The derivative of f(x)=x−x³ is f'(x)=1-3x²
2. Evaluating f'(x) at x=1, we get f'(1)=1-3(1)²=1-3=-2.
3. Now, we'll multiply f'(x) by δx: f'(1)δx = (-2)(0.02)=-0.04.

So, δy = -0.04 and f'(x)δx = -0.04.

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Answer:

Part 1; The volume of the box Thomas wants to make is 224 = 2·w² + 12·w

Part 2; The zeros for the equation of the function, are w = -14, or w = 8

Part 3

The width of the box is 8 inch

The length of the box, is 14 inches

The height of the box, is given as 2 inches

Part 4

Please find attached the graph of the function

Step-by-step explanation:

Part 1

The volume of the box Thomas wants to make, V = 224 in.³

The dimensions he cuts out from the length and width = 2 in² each

The length of the box = 6 inches + The width of the box

Let l represent the length of the box and let w represent the width of the box, we have;

l = 6 + w

The height of the box, h = The length of the cut out square = 2 inches

The volume of the box, V = Length, l × Width, w × Height, h

∴ V = l × w × h

l = 6 + w, h = 2

∴ V = (6 + w) × w × 2

V = 2·w² + 12·w,

The equation of the volume of the box, V = 2·w² + 12·w, where, V = 224

∴ 224 = 2·w² + 12·w

Part 2

The zeros of the equation for the volume of the box, V = 2·w² + 12·w, where, V = 224 are found as follows;

V = 224 = 2·w² + 12·w

∴ 2·w² + 12·w - 224 = 0

Dividing by 2 gives;

(2·w² + 12·w - 224)/2 = w² + 6·w - 112 = 0

∴ (w + 14) × (w - 8) = 0

The zeros for the equation of the function, are w = -14, or w = 8

Part 3

We reject the value, w = -14, therefore, the width of the box, w = 8 inch

The length of the box, l = 6 + w

∴ l = 6 + 8 = 14

The length of the box, l = 8 inches

The height of the box, h, is given as h = 2 inches

Part 4

The graph of the function created with MS Excel is attached

Answer:

77.4

Step-by-step explanation:

Answer:

1.2

Step-by-step explanation:

Delta math :)

Answer:

Step-by-step explanation: The length of q to the nearest 10th of a centimeter is 0.2 cm.

Describe Law of Sines?

The Law of Sines is a trigonometric formula used to find the missing sides or angles of a non-right triangle (a triangle that does not have a 90-degree angle). It states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all three sides and angles:

a/sin(A) = b/sin(B) = c/sin(C)

where:

a, b, c are the lengths of the sides of the triangle, and

A, B, C are the measures of the angles opposite to those sides.

This formula is useful when we have some information about the sides or angles of a triangle, but not enough to solve it completely. By using the Law of Sines, we can set up and solve equations to find the missing values.

Using the Law of Sines, we have:

q / sin(2°) = p / sin(149°)

Solving for q:

q = p * sin(2°) / sin(149°)

= 6.3 * sin(2°) / sin(149°)

≈ 0.23 cm

Therefore, the length of q to the nearest 10th of a centimeter is 0.2 cm.

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The calculated average cost of each candy is $0.02

From the question, we have the following parameters that can be used in our computation:

using the above as a guide, we have the following:

Average cost = Unit rate * Each candy's weight

Substitute the known values in the above equation, so, we have the following representation

Average cost = 4/0.2 * 0.001

Evaluate

Average cost = 0.02

Hence, the average cost of each candy is $0.02

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Answer:

B

Step-by-step explanation:

This is literlly the same question I had 2 minutes ago

Answer:

762 + 4n > 1300

Step-by-step explanation:

Answer:

y = -27.6

Step-by-step explanation:

To solve for y, you need to isolate the variable on one side of the equation. \(5(y+25)=-13\) ⇒ \(y + 25 = -2.6\) ⇒ \(y = -27.6\).

Answer:

-27.6

Step-by-step explanation:

\(5(y + 25) = -13\)

First, distribute the problem.

\(5y + 125 = -13\)

Secondly, subtract 125 from -13 and 125.

\(125 - 125 = 0\)

\(-13 - 125 = -138\)

Now, we are left with 5y = -138.

Lastly, we divide -138 by 5.

\(-138 / 5 = -27.6\)

Therefore, y is -27.6.

Here's an attachment to make this explanation clearer.

Answer:

108  gadgets

Step-by-step explanation:

We can use a ratio to solve

24 gadgets           x gadget

------------------- = ---------------

2.5 hours           11.25 hours

Using cross products

24 * 11.25 = 2.5 *x

270 = 2.5x

Divide by 2.5

270/2.5 = 2.5x/2.5

108 = x

Answer:

The gradient of the parallel line is -2.

Step-by-step explanation:

Parallel lines have the same gradient.

We find the gradient of the given line by solving the equation for y.

2x + y = 4

Subtract 2x from both sides.

y = -2x + 4

The equation is now written in the y = mx + b, where m is the gradient.

The gradient of the given line is -2.

The gradient of the parallel line is -2.

Sum of angles,

∠6 +∠2 +∠5 = 180°

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

Given,

y || x

To prove,

∠5 +∠2 +∠6 = 180°

∠1, ∠2, ∠3 are on straight line,

∠1 +∠2 +∠3 = 180°

∠1 = ∠5    (alternate angles on transversal AC)

∠3 = ∠6    (alternate angles on transversal AB)

∠5 +∠2 +∠6 = 180°

Hence, ∠5 +∠2 +∠6 = 180° is proved.

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Answer:

x > - 5

Step-by-step explanation:

\(4 - x < 9 \\ - x < 9 - 4 \\ - x < 5 \\ \red{ \boxed{ \bold{ x > - 5}}}\)

The inequality 4 - x < 9 is x > -5.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

4 - x < 9

Adding x on both sides.

4 < 9 + x

Subtracting 9 on both sides.

4 - 9 < x

-5 < x

x > -5

Thus,

x is greater than -5.

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21 + (36 + 0 + 19) Equals 76.

A final result is obtained by adding two or more integers together. Commutative, associative, distributive, and additive identity are the four major characteristics of b. b means that even if the order changes, the addition result will remain the same.

Equation to be used: 21 + (36 + 0 + 19)

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I understand that the you are looking for is :

Several properties are used to evaluate this expression. Identify the property used in each step.

21 + (36 + 0 + 19)

21 + (36 + 19):

21 + (19 + 36):

(21 + 19) + 36:

40 + 36

76

Answer:

X^2+x-30

What two numbers multiply to -30 and add to 1,

6, -5

so the factored equation is

(x-5) (x+6)

Answer:

1. 250x12= 3000. So she earned $3000 in that 12 weeks, if you include the 500 then it would be 3500 dollars if not then it would be 3000 dollars.

2. Divide 75 and 12 and you get 6.25 if you want to estimate. Then the answer would be, all of the fields will be harvested in just 6 days.

3. Divide 54 and 3 and you get 18. 18 weeks if they frame the sanem number each week.

4. If you divide 8,000 and 450 you get 17.7777777778. If you want to estimate then the it would be 18. So it would take about 18 days to fill up the 8,000 gallons of water.

5. This graph is y=20x

6. Don't really know, if the 0 is 360 then 10 and 300 are pretty easy because 10=30. so 0, 10, 20 is 360, 300,240 likes the graph and I would think you can solve this

Answer:

1. $11

2. $10.75

3. new median: 12

new mean: $11.75

Step-by-step explanation:

the best is to pick 1-2 specific points to compare.

as we can see, the vertex of g(x) is at x = -2. and the vertex of f(x) is at x = 4.

so, g(-2) = f(4) = f(-2 + k)

and therefore, k = 6

A sphere thrown upward at a 45-degree angle to the horizontal in a classroom elastically bounces off the ceiling while still rising

At time t = 0, a sphere is launched with an initial velocity at a 45-degree angle to the horizontal in a classroom. The sphere follows a parabolic trajectory as it rises due to the upward component of its initial velocity and experiences the downward pull of gravity. While the sphere is still ascending, it reaches the ceiling and collides with it.

During the elastic collision, the sphere's motion is reversed. It rebounds off the ceiling, changing its direction but maintaining its kinetic energy. As a result, the sphere starts descending with the same speed it had before the collision but in the opposite direction. The angle of descent will also be 45 degrees to the horizontal, mirroring the angle of the initial launch.

Throughout the entire process, neglecting air resistance, the total mechanical energy of the sphere is conserved since the collision with the ceiling is elastic.

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Answer:

A = 49/pi

Step-by-step explanation:

C = 2 * pi *r

14 = 2 * pi *r

Divide each side by 2 pi

14/2pi = r

7/pi = r

The area is given by

A = pi r^2

A = pi ( 7/ pi)^2

A  = pi * 49 / pi^2

A = 49/pi

Answer:

\(area = {15.61m}^{2} \)

explanation is attached to the picture

Hope this helps you

Let \($\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$\) be the nonzero rows of \($R$\) starting from the 1st row to the \(k\)th row.

Step 1: We want to show that

R(R)= span \($\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$\)

For any vector \(v $$\in \mathcal{R}(R)$$\), We may write

v= \($$c_{1} \boldsymbol{r}_{1}+c_{2} \boldsymbol{r}_{2}+\cdots+c_{k} \boldsymbol{r}_{k}+c_{k+1} \mathbf{0}+\cdots+c_{m} \mathbf{0}$$\)

Then v= \($$c_{1} r_{1}+c_{2} r_{2}+\cdots+c_{k} r_{k}$$\)

So \(v\) belongs to span{ \($\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$\)}

Thus R(R)\(\leq\) Span \($\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$\)

But trivially,

span \($\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$\)≤ span{\($\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$\), 0, . . . , 0} = R(R),

span \($\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$\)=R(R)

Step 2: We want to show that  \($\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$\)are linearly independent. Suppose otherwise,

then we can write

\($$c_{1} \boldsymbol{r}_{i_{1}}+\cdots+c_{\ell} \boldsymbol{r}_{i_{\ell}}=\mathbf{0}$$\)

From Steps 1 and 2, we have proven that the nonzero rows of R form a basis for the row space.

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Answer:

x = 3

Step-by-step explanation:

3x + 1 = 10

subtract 1 from both sides of the equation

3x + 1 - 1 = 10 - 1

3x = 10 - 1

3x = 9

divide both sides of the equation by 3

3x/3 = 9/3

x = 9/3

x = 3

Answer:

X=3

Step-by-step explanation:

3x+1=10 -> switch 1 3x = 10 - 1

3x = 9

9/3 = 3

Answer:

slope = - \(\frac{2}{9}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 6) and (x₂, y₂ ) = (- 7, 8)

m = \(\frac{8-6}{-7-2}\) = \(\frac{2}{-9}\) = - \(\frac{2}{9}\)

The Perpetuity formula is used to calculate the Present Value (PV) of an infinite series of cash flows at a 6% rate of return. PV = $2,000 / 6% = $33,333.33, so, option C is the correct answer.

The question requires that we calculate the Present Value (PV) of the infinite series of cash flows at a 6% rate of return. The formula to use in solving this problem is the Perpetuity formula. P = C / r

Where, P = Present Value (PV)

C = Cash flow (which in this case is $2,000) each period

r = discount rate, which is 6% in this case.

Substituting the figures, we have; PV = $2,000 / 6% = $33,333.33

The present value of the infinite series of cash flows is $33,333.33

. Therefore, option C is the correct answer.

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Answer: the answer to this is true

Answer: Subtract 3 from each side of the equation(A)

Step-by-step explanation:

3n2−15n=3

1:Subtract 3n2 from both sides.

-15n=3-3n2

2:Divide both sides by -15.

-15n/-15=3-3n2/-15

3:Dividing by −15 undoes the multiplication by −15.

n=3-3n2/-15

4:Divide 3−3n 2 ​ by −15

n=n2-1/5

​

​  

​  

​  

​  

An equation is formed of two equal expressions. The first step in solving the given equation is to Subtract 3 from each side of the equation.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the equation 3n²-15n=3 can be done as,

3n²-15n=3

3n²-15n-3=3-3

3n²-15n-3=0

(3n²-15n-3)/3=0/3

n²-5n-1=0

Therefore, the first step in solving the given equation is to Subtract 3 from each side of the equation.

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The function is \(e^{(x^3)}\) whose Maclaurin expansion is 1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

The Maclaurin series of a given function is represented as a sum of terms with increasing powers of x and decreasing factorials. The Maclaurin series you provided is:

1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

This series can be rewritten as:

∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

This expansion resembles the Maclaurin series for \(e^x\), which is:

\(e^x\) = ∑ \(x^n\)/n! for n=0 to infinity.

However, in the given series, the powers of x are in multiples of 3. To adjust the standard exponential function to match the provided series, you can use the substitution \(x^3\) = u:

\(e^u\) = ∑ \(u^n\)/n! for n=0 to infinity.

Now, substitute \(x^3\) back for u:

\(e^{(x^3)}\) = ∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

Therefore, the function whose Maclaurin expansion matches the given series is f(x) = \(e^{(x^3)}\).

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The original expression \($\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$\) was rationalized by multiplying both numerator and denominator by \($\sqrt[3]{4} \sqrt[3]{2}$\), and then dividing numerator and denominator by \($\sqrt[3]{4}$\).

\($\frac{2}{\sqrt[3]{4} \sqrt[3]{32}} = \frac{\sqrt[3]{8}}{4}$\)

Minimum possible value of \($ab = 32$\)

\(= \frac{\sqrt[3]{4} \sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{4} \sqrt[3]{2}}$= \frac{\sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{2}}$= \frac{\sqrt[3]{8}}{4}$\)

We start with the given expression, \($\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$\), which is in the form \($\frac{p}{qr}$\). To rationalize the denominator, we need to multiply both numerator and denominator by qr (which is \($\sqrt[3]{4} \sqrt[3]{2}$\) in this case). This gives us\($\frac{\sqrt[3]{4} \sqrt[3]{8}}{\sqrt[3]{4} \sqrt[3]{4} \sqrt[3]{2}}$\). We can simplify this expression further by dividing both numerator and denominator by \($\sqrt[3]{4}$\), giving us \($\frac{\sqrt[3]{8}}{\sqrt[3]{2} \sqrt[3]{4}}$\). Finally, we can simplify the denominator further by multiplying both numerator and denominator by \($\sqrt[3]{2}$\), giving us the final result of \($\frac{\sqrt[3]{8}}{4}$\). The minimum possible value of ab is 32.

The original expression \($\frac{2}{\sqrt[3]{4} \sqrt[3]{32}}$\) was rationalized by multiplying both numerator and denominator by \($\sqrt[3]{4} \sqrt[3]{2}$\), and then dividing numerator and denominator by \($\sqrt[3]{4}$\). The final result was\($\frac{\sqrt[3]{8}}{4}$\), and the minimum possible value of ab was 32.

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