Select ALL the correct answers.
A skateboard company tracks the sales of their short boards and long boards. The company's records show the sales of short boards decrease every three months as represented by expression A, where t is the number of years that the boards have been for sale.



The company's records show that the sales of long boards increase every four months as represented by expression B, where t is the number of years that the boards have been for sale.



Select the statements that give a correct interpretation of the above expressions.

Expression A grows at a rate of 5% every three months, while expression B decays at a rate of 12% every four months.
Expression A decays at a rate of 5% every three months, while expression B grows at a rate of 12% every four months.
Expression A has an initial value of 0.95, while expression B has an initial value of 1.12.
Expression A decays at 5% every three years, while expression B grows at a rate of 12% every four years.
Expression A has an initial value of 624, while expression B has an initial value of 725.

Erick just needed to open the compass more to create arcs that have a radius of more than half the length of the segment AB. Option C

The steps involved in constructing a perpendicular bisector are:

Thus, Erick just needed to open the compass more to create arcs that have a radius of more than half the length of the segment AB. Option C

The complete question

Eric was attempting to construct a perpendicular bisector to the segment AB with a compass and straight edge. Which of the below statements explains what Eric may have done wrong?

a. Eric should have started by putting the compass needle point at the midpoint of the segment AB.

b. On the second step, Eric should have placed the compass needle point where the first arc intersected the segment AB.

c. Erick just needed to open the compass more to create arcs that have a radius of more than half the length of the segment AB.

d. Erick didn’t do anything wrong he just needs to connect the opposite endpoints of each arc to finish the construction.

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Answer:

968 cargo boxes

Step-by-step explanation:

66/3 = 22

22 cargo boxes for each train car

22 * 44 = 968 cargo boxes total

The solution of Neumann problem, ∇²u= 0 if r < R , Uₙ (R,θ) = f(θ) is u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ) with boundary conditions uᵣ (r,θ) = ∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ) and

Aₙ=∫(f(θ)cosnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]

Bₙ=∫(f(θ)sinnθ /π nR⁽ⁿ⁻¹⁾)dθ, where θ∈[-π, π]

Given that

The solution of Numann problem

∇²u= 0 if r < R , Uₙ (R,θ) = f(θ)

Use polar co-ordinates (r,θ)

uᵣᵣ + 1/r uᵣ+ 1/uᵣ (uθθ) = 0 ,0 < r< R,

0 <θ <2π and ∂u/∂r(R,θ) = f(θ) is directional derivative

r²d²u/dr² + rdu/dr + d²u/dθ² = 0

Let , r = ε⁻ᵗ , u(r(t),θ)

uₜ = uᵣ(rₜ) = - e⁻ᵗ uᵣ

uₜₜ =( - e⁻ᵗ uᵣ )ₜ = ε⁻ᵗuᵣ + e⁻²ᵗ uᵣᵣ

= r uᵣ+ r²uᵣᵣ

Thus we have, uₜₜ + uθθ = 0

Let u(t,θ) = X(t)Y(θ)

Which gives X''(t)Y(θ) + X(t)Y"(θ) = 0

X"(t)/X(t) = - Y"(θ)/Y(θ) = λ

From Y"(θ) + λ Y(θ) = 0

We get, Yₙ(θ) = aₙ cosnθ + bₙ sinnθ

λ= n² , n =0, 1, ...

With these values of λn we solve,

X"(t) - n² X(t) = 0

If n = 0 , X₀(t) = c₀t + d₀

X₀(r) = -c₀log (r) + d₀

If n not equal to 0 then

Xₙ (t) = cₙeⁿᵗ + dₙ e⁻ⁿᵗ

Xₙ(r) = cₙ(r)⁻ⁿ + dₙ (r)ⁿ

We have u₀(r, θ) = X₀(r)Y₀(θ)

= a₀ ( - c₀(log r) + d₀)

uₙ(r,θ) = Xₙ(r) Yₙ(θ)

= (cₙ r⁻ⁿ+ dₙrⁿ)(aₙ cosnθ + bₙ sinnθ)

But u must be positive at t =0

So, cₙ = 0 ; n = 0,1,2....

u₀ (r,θ) = a₀ d₀

uₙ(r,θ) = dₙ rⁿ( aₙ connθ + bₙ sinnθ)

By superposition , we can write as

u(r,θ) = a'₀+ rⁿ(a'ₙ cosnθ + b'ₙ sinnθ)

Boundary conditions gives

uᵣ (r,θ)=∑n R⁽ⁿ⁻¹⁾(Aₙ cosnθ + Bₙ sinnθ) = f(θ)

the coefficients aₙ , bₙ for n ≥ 1 are determined are Fourier series for f(θ)

but a₀ is not determined from f(θ) therefore , it may take arbitrary value. By using Fourier series,

Aₙ= Integration of(f(θ)cosnθ dθ/π n R⁽ⁿ⁻¹⁾) where θ∈[-π, π]

Bₙ= Integration of (f(θ) sinnθ dθ/π nR⁽ⁿ⁻¹⁾) where θ∈[-π, π]

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Answer:

Step-by-step explanation:

.................8908989

Answer:

candidate b because it's mostly likely to have more people i think

Answer:

n x 40 = w

Step-by-step explanation:

The ratio of Gracie's rate of typing is 240 for every 6 min, but what about per minute?  You can divide 240 by 6 and get 40. It'll be easier that way.

sLet's use for example n = 9  we want to know how many words Gracie can type in nine minutes. Using the key 40 per minute we can use an expression n x 40 = w

which is now 9 x 40 = w    9 x 40 = 360

360 words can be typed in nine minutes.

The required equaiton to predict the number of words, w, Gracie can type in n minutes is w = 40n.

Rate of change is defined as the change in value with rest to the time is called rate of change.

here,
Gracie can type 240 words in 6 minutes.
Typing rate = words/time
Typing rate = 240 / 6  = 40 words per minute

Number words  = rate × time

According to the question, to predict the number of words, w, Gracie can type in n minutes.  
w = 40n

Thus, the required equaiton to predict the number of words, w, Gracie can type in n minutes is w = 40n.

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Answer:

6

Step-by-step explanation:

completing step 2 will land you at (8,0). you would just need to count up from there until you reach the line.

Answer:

7.0686

your welcome :D.

The concept is the Chi-square test, a statistical test for comparing observed results to expected results. The answer is option A.

The test statistic x^2 is equivalent to the test statistic Z. Homogeneity 2x2 The chi-square statistic (and the test) is equivalent to a two proportion test.

The chi-square test is a statistical test used to compare observed results to expected results.The purpose of this test is to determine whether the difference between the observed and expected data is due to chance or to the relationship between the variables being studied. The

Two Ratio Z-Test is a statistical hypothesis test used to determine whether two ratios are different from each other. When you run the test, the z-statistic is calculated from two independent samples, and the null hypothesis is that the two proportions are equal.

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Using the formula for the midpoint of the line with given points  A and B as the end points of the line, the coordinates of the point B is (6,-8).

To find the midpoint of a line segment, you must first find the coordinates of the two endpoints of the segment. Then, take the average of the x-coordinates and the y-coordinates to find the x and y coordinates of the midpoint. This can be done by adding the x-coordinates and y-coordinates of the two endpoints together and then dividing by 2.

What is the formula for finding the midpoint of a line segment?

The formula for finding the midpoint of a line segment is:

Midpoint = ( (x1+x2)/2 , (y1+y2)/2 )

Where (x1,y1) and (x2,y2) are the coordinates of the two endpoints of the line segment.

Using the given coordinates of point A(8,-6) and the midpoint M(7,-7) of the line,  and using the midpoint formula for a line AB,

Midpoint(M) = \((\frac{x1+x2}{2},\frac{y1+y2}{2} )\)

where x1, y1 are coordinates of point A , and x2, y2 are the coordinates of point B

so , (7,-7) = \((\frac{8+x2}{2} , \frac{-6+y2}{2})\)

equating the corresponding points,

7 =(8+x2)/2

therefore, x2 = 6

and , -7 = (-6+y2)/2

therefore , y2 = -8

Hence the coordinates of B is , (x2,y2 ) = (6,-8)

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In statistics, the risk of making an error is referred to as a significance level. A significance level represents the probability of making a Type I error, which occurs when a null hypothesis is rejected even though it is true.

The most common significance level used in statistical analyses is 0.05 or 5%. This means that there is a 5% chance of rejecting a true null hypothesis.

In general, the choice of significance level depends on the specific application and context of the statistical analysis.

The 5% significance level is commonly used in scientific research, particularly in the fields of medicine and psychology.

The choice of this level is based on a balance between the risk of making a Type I error and the risk of making a Type II error, which occurs when a null hypothesis is not rejected even though it is false.

A Type II error is often more serious than a Type I error since it may lead to incorrect conclusions about the relationship between variables or the effectiveness of a treatment or intervention.

A 5% significance level provides a reasonable balance between these two types of errors. However, in some situations, a higher or lower significance level may be more appropriate.

For example, in a clinical trial where the consequences of a Type II error are severe, a lower significance level may be used to reduce the risk of this type of error.

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-2b + 3 = b - 9

The value of b.

-2b - b = -9 - 3

or, -3b = -12

or, b = -12/-3

or, b = 4

The value of b is 4.

Answer:

b=4

Explanation:

1. Add 2b to each side:  3=3b-9

2. Add 9 to each side: 12=3b

3. Divide by 3: b=4

Answer:

The answer is A.

Step-by-step explanation:

Recall that the area for the circumference of a circle is: \(2\pi r\) or \(\pi d\), where r is the radius and d is the diameter.

We know that the diameter is 27 meters, so we can use the second equation.

Thus:

\(C=\pi d\)

\(C=(27)\pi\)

\(C \approx 84.8\)

Answer:

x/2 - 12

Step-by-step explanation:

let the number be x

half a number means x divide by 2. i.e x/2

when decreased by 12 means x/2 - 12

Answer:

3(6+4)

Step-by-step explanation:

A line segment that measures 92 millimeters in length can be drawn using scale.

Given that,

A line segment has to be drawn which has a measure of length 92 millimeters.

We know that,

10 millimeters = 1 centimeter

1 millimeter = 1/10 centimeters

92 millimeters = 92/10 = 9.2 centimeters

So it is enough to draw a line segment of length 9.2 centimeters.

In the scale, between a centimeter, there are 9 small lines which indicates the millimeters.

In between 9 and 10, there are 9 lines which indicates, 9.1, 9.2, 9.3, ....., 9.9 and after that is 10 cm.

So draw a line segment starting from 0 to 9.2.

Hence the line segment is drawn with scale.

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Answer:

{4.5}

Step-by-step explanation:

n - 4 /2 = 2/8

n -4 = 2 * 1/4

n -4 = 1/2

2n - 8 = 1

2n = 9

n = 4.5

Answer:

Step-by-step explanation:

\( = > \frac{n - 4}{2} = \frac{2}{8} \)

=> 8(n - 4) = 2 × 2

=> 8n - 32 = 4

=> 8n = 4 + 32

= 36

\( = > \frac{8n}{8} = \frac{36}{8} \)

=> n = 4.5 (Option "C") (Ans)

Answer:

\(y = C_1J_2(3\sqrt{x})+C_2Y_2(3\sqrt{x})\)

Step-by-step explanation:

\(x^{2} \dfrac{d^2 y}{dx^2} + x\dfrac{dx}{dy} + (x-1)y =0\)

Considering \(x=0\) ordinary point we could use Frobenius method assuming

\($y = \sum_{n=0}^{\infty} c_nx^n$\)

and consider the series representation given by the method to solve the equation. I think this way is harder.

In your case, It seems to have something to do with Bessel differential equation

\(x^2 y'' + x y' + (x^2-n^2) y = 0\)

that will have the same representation as the Frobenius method. To get the form \((x^2-n^2)\) as we have \( (x-1)\) in the given equation we can substitute \(x\) and take \(x = \dfrac{t^2}{9}\)

Thus,

\(\dfrac{dy}{dx} = \dfrac{3}{t}\dfrac{dy}{dt} \implies \dfrac{d^2y}{dx^2} = \dfrac{9}{t^2}\dfrac{d^2y}{dt^2}-\dfrac{9}{t^3}\dfrac{dy}{dt} \)

\($\implies \frac{1}{3^2}\left(t^2\frac{{d}^2y}{{d}t^2}+t\frac{{d}y}{{d}t}+(t^2-3^2)y\right) = 0$\)

The solution will have the format

\(y( x) = {C_1}{J_n}( x) + {C_2}{Y_n}( x )\)

such that

\(${J_n}( x ) = \sum\limits_{p = 0}^\infty {\frac{{{{( { - 1} )}^p}}}{{\Gamma ( {p + 1} )\Gamma ( {p + n + 1} )}} {{\left( {\frac{x}{2}} \right)}^{2p + n}}}$ \)

\(${Y_n}\left( x \right) = \frac{{{J_n}\left( x \right)\cos \pi n - {J_{ - n}}\left( x \right)}}{{\sin \pi n}}$ \)

and \(C_1, C_2\) are constants

And the order of the Bessel equation is \(n=2\)

In our case, we can just write

\(y(t) = C_1J_2(t)+C_2Y_2(t)\)

\(y = C_1J_2(3\sqrt{x})+C_2Y_2(3\sqrt{x})\)

Answer:

10.60305932

Step-by-step explanation:

Answer:

\( cos A = \frac{5}{13} \)

Step-by-step explanation:

The given triangle, ∆ABC is a right triangle.

To find cos A, we'd need to apply the trigonometric ratio formula, which is cos A = adjacent length/hypotenuse length

From the ∆ given,

AC = adjacent = 15,

BC = opposite = 36

We are not given the hypotenuse length AB.

==>Find the hypotenuse length AB, using the Pythagorean theorem formula:

c² = a² + b²

AB² = 15² + 36² = 225 + 1296 = 1521

AB = √1521

AB = 39

==>Find cos A:

cos A = adjacent/hypotenuse

\( cos A = \frac{adjacent}{hypotenuse} \)

Adjacent = AC = 15

Hypotenuse = AB = 39

\( cos A = \frac{15}{39} \)

\( cos A = \frac{5}{13} \)

Answer:

B. 30°

Step-by-step explanation:

Given in the question that triangle ABC  and similar to triangle XYZ where ∠A = 50° ,∠B=100° then its true to say by AA { Angle-Angle} similarity ;

if ΔABC ≅ ΔXYZ then

∠A =∠X  

∠B = ∠ Y

hence ; ∠C = ∠Z

Finding angle ∠C as ;

180°-{100+50}°

180°-150° = 30°

So angle ∠Z = 30°

A sequence of instructions that solves a problem is called an algorithm.

The hospital can get 4.15 milligrams from these three companies.

A linear equation is one in which the highest power of any variable is not more than 1. A linear equation in 2 variables can be solved by substitution method, if we have two simultaneous equations.

Here, we know that

Company A's supply of medicine = 1.7 mg

also, company A's supply = 2( B's supply - C's supply)

⇒ 1.7 = 2( B - C)

⇒ 1.7 = 2B - 2C .... (1)

Moreover, we are given that

A's supply = C's supply + 0.9

⇒ 1.7 = C + 0.9

⇒ 1.7 - 0.9 = C

⇒ 0.8 = C

Now, substituting the value of C in (1), we get,

1.7 = 2B - 2(0.8)

1.7 = 2B - 1.6

1.7 + 1.6 = 2B

⇒ B = 3.3/2

B = 1.65

Thus, the total supply from all three companies is (1.7 + 1.65 + 0.8) = 4.15 mg

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Answer:

11

Step-by-step explanation:

D+16/3=17 the steps?

1. D+16/3=17

Divide 16/3.

D+6 = 17

2. subtract 6 from both side.

D = 11.

Here is one solution to the puzzle:

Squares: 2, 8, 16

Circles: 5, 7, 14

Total: 26

You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.

An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.

Therefore, the correct answer is as given above

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Answer:

Brand A

Step-by-step explanation:

Brand A has a box of 25 forks for 1.99

Take the price per fork

1.99 /25 = .0796

              .08 per fork

Brand B has a box of 42 totals for 3.89

3.89 / 42

.092319048

.09 per fork

Answer:

20

Step-by-step explanation:

5 times 4 = 20