Part B (30 points!!)
The table holding Juanita's pennies gets bumped, and the stack becomes slanted.
How is the volume of the stack affected? Explain your reasoning.

Answer:

Option D. 2x⁷ - 12x⁶ + 10x⁵

Step-by-step explanation:

From the question given:

Length (L) = 2x²

Width (w) = x³

Height (h) = x² - 6x + 5

Volume (V) =?

Volume (V) = length (L) x width (w) x height (h)

V = L x w x h

V = 2x² × x³ × x² - 6x + 5

V = (2x²) (x³) (x² - 6x + 5)

V = (2x⁵) (x² - 6x + 5)

Clear bracket

V = 2x⁷ - 12x⁶ + 10x⁵

Therefore, the volume of the cube is 2x⁷ - 12x⁶ + 10x⁵

Step-by-step explanation:

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The percent yield is calculated as the ratio of the actual yield to the theoretical yield, multiplied by 100.

Percent yield is a measure of how efficient a chemical reaction or process is in producing the desired product.

The formula for percent yield is:

Percent Yield = (Actual Yield / Theoretical Yield) * 100

The actual yield is the amount of product obtained from the reaction or process, typically measured in grams or moles. It represents the actual amount of product obtained in the laboratory.

The theoretical yield, on the other hand, is the maximum amount of product that can be obtained based on stoichiometry and other factors. It is calculated using balanced chemical equations and the starting amounts of reactants.

By dividing the actual yield by the theoretical yield and multiplying by 100, we get the percent yield, which is expressed as a percentage.

This value provides insight into the efficiency of the reaction or process, with a higher percent yield indicating a more efficient conversion of reactants into products.

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Answer:

sali's speed was 18.75 km/h

Step-by-step explanation:

Jane took 3.5 hours to cycle the 63 km.

As,   , so the speed of Jane will be:  

Suppose, the speed of Sali is   km/h

Sali caught up with Jane when they had both cycled 30 km.

So, the time required for Jane to cycle 30 km  and the time required for Sali to cycle 30 km  

Given that, Sali started to cycle 4 minutes or  after Jane started to cycle. So, the equation will be.......

Answer:

8 meters per second.

Step-by-step explanation:

To find how many meters the cheetah travels per second, we need to divide 56 by 7.

This gives us 8, with no remainders, and our answer.

Answer:

27m/s

Step-by-step explanation:

distance(s) = 56m

Time(t) = 7sec

Speed(u) = ?m/s

using the formula

S = ut + ½at²

56 = 7u + ½ × 10 × 7²

56 = 7u + 5 × 49

56 = 7u + 245

7u = 245 – 56

7u = 189

u = 189/7

u = 27m/s

i hope i helped

(x² + 9x - 1)/((x - 4)(x² + 1)) = A/(x - 4) + (Bx + C)/(x² + 1)

x² + 9x - 1 = A(x² + 1) + (Bx + C)(x - 4)

∫(x² + 9x - 1)/((x - 4)(x² + 1)) dx = ∫(A/(x - 4) + (Bx + C)/(x² + 1)) dx

To evaluate the integral, we can use the method of partial fractions. First, we factor the denominator as (x - 4)(x² + 1). The next step is to express the fraction as a sum of simpler fractions with unknown constants as numerators. Let's assume the partial fraction decomposition is given by:

(x² + 9x - 1)/((x - 4)(x² + 1)) = A/(x - 4) + (Bx + C)/(x² + 1)

To find the values of A, B, and C, we can equate the numerators:

x² + 9x - 1 = A(x² + 1) + (Bx + C)(x - 4)

Expanding and comparing the coefficients of like terms, we can solve for A, B, and C. Once we have the partial fraction decomposition, we can integrate each term separately.

The integral becomes:

∫(x² + 9x - 1)/((x - 4)(x² + 1)) dx = ∫(A/(x - 4) + (Bx + C)/(x² + 1)) dx

Integrating each term individually, we obtain the final result.

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Answer:

Mean: 33.3

SD: 32.8

Step-by-step explanation:

Answer:

a₁₀ = 239

Step-by-step explanation:

Substitute n = 10 into the nth term rule , that is

a₁₀ = 2(10)² + 4(10) - 1

    = 2(100) + 40 - 1

    = 200 + 39

   = 239

Answer:

f(n) = 4 x 2^(n-1)

Step-by-step explanation:

The general form of a geometric sequence is given by:

an = ar^(n-1)

where a is the first term, r is the common ratio, and n is the term number.

Using the given sequence, we can find the values of a and r:

a = 4

r = 8/4 = 2

Therefore, the function that generates this sequence is:

f(n) = 4 x 2^(n-1)

For example, when n = 1, f(1) = 4 x 2^(1-1) = 4 x 1 = 4, which is the first term of the sequence. When n = 2, f(2) = 4 x 2^(2-1) = 4 x 2 = 8, which is the second term of the sequence, and so on.

Answer:

$6

Step-by-step explanation:

We have: The cost of a taxi ride is represented by the function c(m)=2m+4

Plug 1 mile into "m" of the function c(m)=2m+4

So, we have c (1) = 2 ˣ 1 + 4 = 6

Thus, The cost per mile of the cab is $6.

Answer:

It is 2

Step-by-step explanation:

I took the test

Answer:

How do you know something is in motion? Well, when something moves, it changes location. On the

other hand, things that don't move, don't change location. In this activity, you will observe objects

that are in motion, and some that are not.

Step-by-step explanation:

How do you know something is in motion? Well, when something moves, it changes location. On the

other hand, things that don't move, don't change location. In this activity, you will observe objects

that are in motion, and some that are not.

Answer:

75

Step-by-step explanation:

Answer:

r=11

Step-by-step explanation:

10r - 20 = 5r + 35

-5r. -5r

---------------------------

5r - 20 = 35

+20 = +20

---------------------------

5r = 55

------------

5r. 5

r=11

Answer:

(B) 1 unit cube and 75 smaller cubes of volume fraction 1 over 125 cubic inch each

Step-by-step explanation:

By ''ASA postulate'' or theorem can be used to prove that triangle XYZ and Triangle LYZ are congruent.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Two triangles XYZ and Triangle LYZ are shown in figure.

Now,

From triangle XYZ and Triangle LYZ;

⇒ YZ = ZY ( Common side )

⇒ ∠ YXZ = ∠ YLZ  

( By definition of isosceles triangle)

⇒ ∠ YZX = ∠ YZL

(Right angles)

Hence, By ''ASA postulate'' or theorem can be used to prove that triangle XYZ and Triangle LYZ are congruent.

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The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Answer:

25y+27x

Step-by-step explanation:

You cannot factor this any further

Yes, the given transformation is found to be  linear.

To determine if a transformation is linear, we need to check two conditions: preservation of addition and preservation of scalar multiplication.

For the preservation of addition, let's consider two arbitrary vectors u and v in R^2.

The transformation Lwt translates each vector up by 3 units.

Therefore,

Lwt(u+v) = (u+v) + (3,3)

= (u + (3,3)) + (v + (3,3))

= Lwt(u) + Lwt(v).

For the preservation of scalar multiplication, let's consider an arbitrary vector u in R^2 and a scalar c. The transformation Lwt translates the vector u up by 3 units.

Therefore,

Lwt(cu) = cu + (3,3)

= c(u + (3,3))

= cLwt(u).

Since both conditions hold true, the transformation Lwt is linear.

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If 3 metres of material costs £1.56, the cost of 5 metres of the material is  £2.6

The cost per unit of an item is represented by the unit price.

To determine the unit price of an item, we divide the price of a specific number of units by the number of units.

If 3 metres of material costs £1.56 this means that the unit price will be

= 1.56 / 3

= 0.52

for 5 metres of the material

= 0.52 * 5

= £2.6

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Answer:

y = 1

Step-by-step explanation:

6= 2(y+2)   Multiply 2*y and 2 *2

6 = 2y + 4    

6 - 4 = 2y

2 = 2y    -   Divide 2 and 2

y = 1

Answer:

yeah the person is right it is y=1

Step-by-step explanation:

Answer: 431 664.685 m2

Step-by-step explanation:

The point that should an open circle be drawn exists (0, 0).

The first equation in the system is f(x) = -x, for x < 0.  

This means when x=0, f(x) = f(0) = 0.

Since we have the inequality x<0, this means at the point (0, 0),

the point will be open and not filled in.

Therefore, the correct answer is option b) (0, 0).

The complete question is:

The function f(x) is to be graphed on a coordinate plane

At what point should an open circle be drawn?

a) (–1, 0)

b) (0, 0)

c) (0, 1)

d) (1, 0)

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Answer:

a^2+3a+2

Step-by-step explanation:

(a+1)(a+2)

a(a+2)+1(a+2)

a^2+2a+a+2

a^2+3a+2

Answer:

x  =  − 2

Step-by-step explanation:

Suppose that \(A1 ∩ A2\)is path-connected. If each of the subspaces A1, A2, and A1 ∩ A2 is simply connected, then the quotient space X / A1 ∼ A2 is simply connected too.

Given a quotient space et p which is obtained by identifying the north and south poles of two spheres s2 to a single point.

Let's find the value of p.The quotient space et p can be visualized as shown below:Quotient Space et pThis space et p has the structure of the cone C(A) over the 1-dimensional CW complex

A obtained from two 0-cells and one 1-cell connecting them with attaching maps

as shown below:

In our case, the spaces A1, A2, and A1 ∩ A2 are s2, s2, and S1, respectively. Both s2 and S1 are simply connected, since they are homotopy equivalent to a point. Since S1 is path-connected, we can apply the above proposition to conclude that et p is simply connected.Therefore, the value of p is 1 since the fundamental group of et p, π1(et p), is trivial.

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Answer:

Step-by-step explanation:

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