PLEASE HELP ASAP!!!!

The shape below is a cuboid.
Find the length of AG to 2 d.p.

Answer:

it is the 3rd one to the bottem

o.7 - 0.31 = 0.39

Step-by-step explanation:

Ramon just substituted the 8.5 for the wrong variable. She must replace 8.5 for y-variable, because that's the right one for shoe size.

Based on the given conditions,

Ramona used the regression equation,

y = 444x - 21.29

The 8.5 is for shoes only, not for height.

Therefore, using 8.5 for the x-variable is incorrect because x denotes height and y denotes shoe size.

Ramon therefore simply changed the incorrect value to 8.5.

Because 8.5 is the proper value for the y-variable in terms of shoe size, she must replace it.

Therefore,

Ramon just substituted the 8.5 for the wrong variable. She must replace 8.5 for y-variable, because that's the right one for shoe size.

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This problem can be solved using the analytical one-term approximation method, but without specific details of the problem, it is not possible to provide a solution here.

As for whether this problem can be solved using lumped system analysis, it depends on the conditions of the problem. If the Biot number (Bi) is much smaller than 1 (Bi << 1), then lumped system analysis can be applied.

Otherwise, it might not be accurate to use the lumped system analysis, and you should rely on the analytical one-term approximation method or other numerical methods.

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Answer:

y=2500(0.85)^d

Step-by-step explanation:

Seeing as there are no option choices, I shall digress.

Because of a decrease of 15% each day, it means exponential decay. Using the formula y=a(1-r)^x, we have y=2500(1-0.15)^d -> y=2500(0.85)^d

Your function would thus be y=2500(0.85)^d

Answer:

The function that can be used is x = (2500 × 0.15)(number of days, or d)

Step-by-step explanation:

First we can create an equation to find this easier. We can say that x, or the number of infected students, is equal to (2500 × 0.15), since percentages are easily changed into decimals, and multiply that by the number of days or d.

The given vector field is not conservative.

Given: f(x, y) = (2xy y^(-2))i + (x^2-2xy^(-3))j. y > 0

We have to determine whether or not f is a conservative vector field. If it is, find a function f such that f = ∇f.

The vector field is called conservative if it is a gradient of a scalar function, called a potential function. The potential function of a conservative field is not unique; it is determined only up to a constant function.

Let's find the curl of vector field f, If curl f = 0, then f is conservative. Suppose curl f ≠ 0, then f is not conservative. We have,

curl f = (d/dx)i + (d/dy)j((x^2 - 2xy^(-3)) - (2xy y^(-2)))

= (d/dx)i + (d/dy)j(x^2 - 2xy^(-3) - 2xy^(-2))

= (d/dx)i + (d/dy)j(x^2 - 2xy^(-2)(y+1))

Now, The curl of the vector field is not zero, i.e., curl f ≠ 0. Therefore, the given vector field f is not conservative.

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Answer:

Step-by-step explanation:

What is the answer:

4(3x+2)-2=

12x + 8 - 2 =

12x + 6

Answer:

1.B

2.B

hope this helps

Answer:

B. 62mph

B. 55weeks

Step-by-step explanation:

496 ÷ 8 = 62

15weeks/3houses = x weeks/11houses

15 × 11 ÷ 3 =55weeks

good luck, i hope this helps :)

Answer:

d = st, d = 100 x 3

Step-by-step explanation:

distance = speed x time

distance = 100 x 3, therefore, distance = 300, but if you just want the equation, it is d = 100 x 3 or d = st

Step-by-step explanation:

d = 100 x 3.

d= 100n

where n = time the journey took.

The mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The mean-square end-to-end distance for the fractal line is as follows.⟨R2⟩ = ⟨(R(u)- R(v))^2⟩ for u = 0 and v = L where L is the length of the line.⟨R2⟩ = b²/L^2.D.L = b².L^(1-D).

Thus, the mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The radius of gyration Rg is defined as follows.

Rg² = (1/N)∑_(i=1)^N▒〖(R(i)-R(mean))〗²where N is the number of monomers in the fractal line and R(i) is the position vector of the ith monomer.

R(mean) is the mean position vector of all monomers.

Since the fractal dimension is D, the number of monomers varies with the length of the line as follows.N ~ L^(D).

Therefore, the radius of gyration for the fractal line is Rg² = (1/L^D)∫_0^L▒〖(b/v^(1-D))^2 v dv〗 = b²/L^2.D(1-D). Thus, Rg² = b².L^(2-D).

The ratio R²/Rg² is given by R²/Rg² = L^(D-2).

When D = 1, R²/Rg² = 1/L. When D = 1.7, R²/Rg² = 1/L^0.7. When D = 2, R²/Rg² = 1/L.

This provides information on mean-square end-to-end distance and radius of gyration for fractal line with a given fractal dimension.

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Answer: c

Feet

2

5

6

7

Inches

24

60

72

84

Step-by-step explanation: 1ft = 12 inches 2ft=24 inches 3ft= 36 inches etc

multiply ft by 12 to get inches

Answer:

i gotchuuu

Step-by-step explanation:

slope is 9/-2. this is because i used the slope formula y2-y1 over x2-x1. hope this helped :)

Answer:

3/2      3*5=15

3/2=1.5

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

so 8(2)=16=5x-4

5x=20

x=4

so B

A conclusion that can be made on the data collected from the public library is B. Non-fiction and science fiction represent over half of the selections.

When looking at the given data, we notice that the science fiction when summed up with the non - fiction section gives :

= 12 + 10

= 22

In terms of percentages of the number of people that data was collected from, the percentage is :

= 22 / 40 x 100 %

= 55 %

This shows that non -fiction and science fiction do indeed represent over half of the selections.

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Options for this question are:

A. Exactly 42% of the library patrons chose a mystery.

B. Non-fiction and science fiction represent over half of the selections.

C. Over 25% of the library patrons chose a science fiction book.

D. 136 total patrons can be expected to choose a non-fiction book.

The factorized form 16 - \((5y-2)^2\) is -1(5y+2)(5y-6)

The expression is

16 - \((5y-2)^2\)

The expression is a mathematical statement that consist of different variables, numbers and the arithmetic operators

The expression is

The expression is

16 - \((5y-2)^2\)

We know the identity

\((a+b)^2= a^2+2ab+b^2\)

Apply this identity on the expression

= 16 -( \(25y^2\)- 20y + 4)

Apply the distributive property

= 16 - \(25y^2\)+ 20y - 4

Subtract the like terms

= - \(25y^2\)+ 20y + 12

Take common term outside

= -1(\(25y^2\)- 20y - 12)

Split the middle term and apply factorization

= -1 (\(25y^2\)+ 10y -30y - 12)

Take common term outside

= -1 ( 5y(5y+ 2) -6(5y +2)

Take common term outside

= -1(5y+2)(5y-6)

Hence, the factorized form 16 - \((5y-2)^2\) is -1(5y+2)(5y-6)

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Answer:A unit rate is a comparison of two measurements, one of which has a value of ... The unit scale on a map may read \begin{align*}\frac{1}{2}\ inch=100 ... A line 4 inches long would represent an actual line of 800 feet. Unit scales and proportions can be used to calculate actual distances from maps, drawings, ...

Step-by-step explanation:

The total interest earned in 45 days is $9.79.

To find the interest earned in 45 days, we need to calculate the interest earned on both the CD and the savings account, and then add them together.

First, we are given that emergency fund is 4 times the monthly fixed expenses. So, the emergency fund equals:

= 4 x $1,328.90

= $5,315.60

1/2 of the emergency fund is placed in a 45-day CD at a 4.5% APR. The CD amount will be:

= $5,315.60 / 2

= $2,657.80

The CD interest will be calculated as:

= CD amount x (APR / 365) x days

= $2,657.80 x (0.045 / 365) x 45

= $7.47

The remainder of the emergency fund is placed in a regular savings account at a 3.2% APR is computed as

= $5,315.60 / 2

= $2,657.80

The interest on the Savings account is calculated as:

= Savings account amount x (APR / 365) x days

= $2,657.80 x (0.032 / 365) x 45

= $2.32

Now, total interest earned in 45 days is the sum of the CD interest and the savings account interest will be:

= CD interest + Savings account interest

= $7.47 + $2.32

= $9.79

Question solved "Your fixed expenses are $1,328.90/month and you saved 4 months' worth in an emergency fund. You plage half in a 45-day CD at a 4.5% APR and the remainder in a regular savings account at a 3.2% APR. How much total interest do you earn in 45 days?".

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The regions R and S in the first quadrant are bounded by specific graphs, and the task is to find the areas of these regions.

To determine the areas of regions R and S, we need to analyze the given graphs and apply integration techniques. Region R is bounded by the x-axis, the graph of y = f(x), and the vertical line x = a. To find the area of this region, we can integrate the function f(x) from x = 0 to x = a. The integral ∫[0,a] f(x) dx will yield the area of region R.

Region S, on the other hand, is bounded by the graph of y = g(x), the line x = a, and the line y = b. To find the area of this region, we first need to identify the points of intersection between the graphs. These points will help us determine the limits of integration. Once we have the appropriate limits, we can integrate the function g(x) from x = a to x = c, where c is the x-coordinate of the intersection point between the graphs of g(x) and y = b. The resulting integral ∫[a,c] g(x) dx will provide us with the area of region S.

By applying the fundamental theorem of calculus and appropriate limits of integration, we can evaluate these integrals and find the areas of regions R and S.

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When 100 ft of rope is out, the rate at which the boat is approaching the dock is 0 ft/min which means the boat is not moving towards the dock at that moment.

Let x represent the horizontal distance between the boat and the dock (in feet).

Let y represent the vertical distance between the boat and the pulley (in feet).

Since the rope is attached to the front of the boat, which is 10 feet below the level of the pulley, we have y = 10 ft.

The rate of change of the length of the rope, which is related to the distance between the boat and the dock, is dx/dt = 12 ft/min.

We want to find the rate at which the boat is approaching the dock, which is the rate of change of x with respect to time (dx/dt) when 100 ft of rope is out.

Now, let's set up the similar triangles between the boat, the pulley, and the dock.

x / y = (x + 100) / 100

Now, we can differentiate both sides of this equation with respect to time t:

d(x/y)/dt = d((x + 100) / 100)/dt

To solve for dx/dt, we need to differentiate x/y and (x + 100)/100 with respect to time.

Using the quotient rule, we have:

(dx/dt × y - x × dy/dt) / (y²) = (1/100) × (dx/dt)

Substituting y = 10 and dy/dt = 0 (since the pulley is fixed), we get:

(dx/dt × 10 - x × 0) / (10²) = (1/100) × (dx/dt)

10 × dx/dt = (1/100)×(dx/dt)

10 × dx/dt - (1/100) × dx/dt = 0

(1000/100 - 1/100) × dx/dt = 0

(999/100) × dx/dt = 0

dx/dt = 0

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Answer:

i. The description is sufficient to describe all cases of a circle.

ii. The description includes only necessary information to describe a circle.

iii. The description is a mathematically precise definition of a circle.

Step-by-step explanation:

A circle can be described as a plane shape bounded by circumference. It's circumference can be determined by: 2\(\pi\)r, where r is its radius.

Thus, it can be said that it contains equidistant (equal distant) points from a common central point called the center of the circle. This definition can be used to describe any circle.

Some of its parts are: diameter, radius, sector, semicircle etc.

Answer:

A,B,C

Step-by-step explanation:

The foil method is an effective method because you are able to successfully remember the other at which you multiply the brackets to open them using F.O.I.L, so its not only easy to remember but very good to use for quadratic, cubic and to an extent, polynomials.

The FOIL Method stands for First Outer Inner Last. This is a standard method for multiplying two binomials together. It is also a valid method for solving quadratic equations and simplifying expressions.

The FOIL method is a valid method because it helps to simplify complicated expressions, and it is easy to use. It is used to multiply two binomials together.

By following the steps, the user can easily find the product of two binomials. The steps are as follows:

The FOIL method is valid because it helps to simplify expressions by breaking them down into smaller parts. This makes it easier to see how the parts relate to each other and how they combine to create the final expression. It is a straightforward method, and it is easy to use.

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The line integral of f(x, y) along C is -1. Answer: none of the given options. We can parameterize the curve C as r(t) = (t, t) for t in the interval [0, π/2]. Then the line integral of f(x, y) along C is given by:

∫C f(x, y) ds = ∫[0,π/2] f(r(t)) ||r'(t)|| dt

where ||r'(t)|| is the magnitude of the derivative of r(t) with respect to t.

We can find r'(t) by taking the derivative of each component of r(t):

r'(t) = (1, 1)

Then ||r'(t)|| = sqrt(1^2 + 1^2) = sqrt(2).

Substituting everything into the line integral formula, we get:

∫C f(x, y) ds = ∫[0,π/2] (cos t + sin t) sqrt(2) dt

We can evaluate this integral by using the trigonometric identity cos t + sin t = sqrt(2) sin (t + π/4). Then we have:

∫C f(x, y) ds = ∫[0,π/2] (cos t + sin t) sqrt(2) dt

= sqrt(2) ∫[0,π/2] sin (t + π/4) dt

= sqrt(2) [-cos(t + π/4)] [0,π/2]

= sqrt(2) [-cos(π/4) + cos(3π/4)]

= sqrt(2) (-sqrt(2)/2 + 0)

= -1

Therefore, the line integral of f(x, y) along C is -1. Answer: none of the given options.

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The change in total revenue brought about by a 16 unit increase in Q is -1.5.

(a) (i) To differentiate y = 4x⁴ − 2x² + 28 with respect to x, we apply the power rule of differentiation. We have:
dy/dx = 16x³ - 4x

(ii) To differentiate f(x) = 1/x² + √x³ with respect to x, we can apply the chain rule of differentiation. We have:
f(x) = x⁻² + x³/²
df/dx = -2x⁻³ + 3/2x^(3/2)

(iii)(a) The slope of the function y = 3x² − 4x + 5 at x = 4 and x = 6 can be found by differentiating the function with respect to x. We have:
y = 3x² − 4x + 5
dy/dx = 6x − 4
At x = 4,
dy/dx = 6(4) − 4 = 20
At x = 6,
dy/dx = 6(6) − 4 = 32

(b) The second-order derivative of the function y = 3x² − 4x + 5 at x = 4 can be found by differentiating the function twice with respect to x. We have:
y = 3x² − 4x + 5
dy/dx = 6x − 4
d²y/dx² = 6
The second-order derivative at x = 4 is 6. The slope of the function at x = 4 is positive, so we would expect the second-order derivative to be positive.

(b) (i) The demand equation is given by: P = aQ⁻² + b
The marginal revenue function is the derivative of the total revenue function with respect to Q. The total revenue function is:
R = PQ
Differentiating both sides with respect to Q gives:
dR/dQ = P + Q(dP/dQ)
Since P = aQ⁻² + b,
dP/dQ = -2aQ⁻³
Substituting into the equation for dR/dQ, we have:
dR/dQ = aQ⁻² + b + Q(-2aQ⁻³)
dR/dQ = aQ⁻² + b - 2aQ⁻²
dR/dQ = (b - aQ⁻²)
Therefore, the marginal revenue function is:
MR = b - aQ⁻²

(ii) To calculate the marginal revenue when Q = 3b, we substitute Q = 3b into the marginal revenue function:
MR = b - a(3b)⁻²
MR = b - ab²/9
To find the change in total revenue brought about by a 16 unit increase in Q, we can use the formula:
ΔR = MR × ΔQ
where ΔQ = 16
ΔR = (b - ab²/9) × 16
To show that ΔR = -1.5, we need to use the given relationship a > 0 and b > 0. Since a > 0, we know that ab²/9 < b. Therefore, we can write:
ΔR = (b - ab²/9) × 16 > (b - b) × 16 = 0
Since the marginal revenue is negative (when b > 0), we know that the change in total revenue must be negative as well. Therefore, we can write:
ΔR = -|ΔR| = -16(b - ab²/9)
Since ΔQ = 16b, we have:
ΔR = -16(b - a(ΔQ/3)²)
ΔR = -16(b - a(16b/3)²)
ΔR = -16(b - 256ab²/9)
ΔR = -16/9(3b - 128ab²/3)
ΔR = -16/9(3b - 16(8a/3)b²)
ΔR = -16/9(3b - 16(8a/3)b²) = -16/9(3b - 16b²/9) = -16/9(27b²/9 - 16b/9) = -16/9(3b/9 - 16/9)
ΔR = -16/9(-13/9) = -1.5

Therefore, the change in total revenue brought about by a 16 unit increase in Q is -1.5.

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Answer:

it looks like you are trying to find x in this problem so x= -6

Answer:

Step-by-step explanation:

3 + 5x = 3x -9

-3  -3x   -3x  -3

2x = -12

2x/2 -12/2

X=     -6

Final Answer:  a. 160 lb

a . Load Limit is 4000 lb and number of passengers that are allowed is 25.

So maximum mean weight = (Total load limit)/(number of passengers)

maximum mean weight = 4000/25 = 160

Hence Maximum mean weight is 160.

b.

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional.

Occurrence to determine the conditional probability. P(A and B) = P(A) * P if A and B are two Independent events (B).

How can you calculate the likelihood of two occurrences, A and B, coming together?

The probability of their union, or the event that either A or B occurs, is equal to the total of their probabilities less the sum of their intersection if two occurrences A and B are not disjoint. P(A) + P(B) - P(A and B) (A and B).

The answer is then (0.28 + P(B) - (0.51 = 0.23).

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Answer:

C. 272

Step-by-step explanation:

Since we know 85% of the students participated last year we can assume the same amount will participate this year so to find the answer you simply do the total number of students (320) multiplied by 85% or .85 to get the best guess of how many students will participate this year.

Answer:

d

Step-by-step explanation:

-1*-2=2

2*5=10

Hope this helps!!!

Answer:

Given equation:

\(\sqrt{30-2x} =x-3\)

Square both sides:

\(\implies (\sqrt{30-2x})^2 =(x-3)^2\)

\(\implies 30-2x =(x-3)^2\)

Expand the right side:

\(\implies 30-2x =x^2-6x+9\)

Add \(2x\) to both sides:

\(\implies 30 =x^2-4x+9\)

Subtract 30 from both sides:

\(\implies x^2-4x-21=0\)

Factor:

\(\implies (x-7)(x+3)=0\)

Therefore,

\(x-7=0 \implies x =7\)

\(x+3=0 \implies x=-3\)

Substitute both values of \(x\) into the original equation to check:

\(x=7 :\)

\(\implies\sqrt{30-2(7)} =7-3\)

\(\implies 4=4\)

correct!

\(x=-3\)

\(\implies\sqrt{30-2(-3)} =-3-3\)

\(\implies 6 \neq =-6\)

incorrect!

Therefore, \(x=7\) is the only correct solution, and \(x=-3\) is the extraneous solution

**Extraneous solution: a root of a transformed equation that is not a root of the original equation**