Look at the graph below. What is the slope of the line?

A. - 1/2
B - 2
C. 1/2
D. 2

Answer:

Step-by-step explanation:

Given that:

t          0           1              2          3            4            5           6            7

A'(t)    0.91       0.83       0.76     0.69       0.62      0.58      0.48      0.44

a)  \(\Delta x = \dfrac{5-0}{5}\)

\(\Delta x = 1\)

\(L_ 5= \Delta x ( (A'(0)+A'(1)+A'(2)+A'(3)+A'(4)) \\ \\ = 1 (0.91 + 0.83+ 0.76 +0.69 + 0.62 ) \\\\ L_5 =1( 3.81) \\ \\ \mathbf{L_5 = 3.81}\)

\(R_ 5= \Delta x ( (A'(1)+A'(2)+A'(3)+A'(4)+A'(5)) \\ \\ = 1 ( 0.83+ 0.76 +0.69 + 0.62 +0.58) \\\\ R_5 =1( 3.48) \\ \\ \mathbf{R_5 = 3.48}\)

The true statement:

\(Since, R_5 = 3.48 \ and \ L_5 = 3.81; \\ \\ Then : R_5 \le \int \limits ^5_0 A'(t) dt \le L_5\)

Answer:

W = 10

Step-by-step explanation:

W / 5 + 20 = 22

W / 5 - 20 = 22 - 20

W / 5 = 2

W * 5 = 2 * 5

W = 10

Step-by-step explanation:

\( \frac{w}{5} + 20 = 22 \\ \\ \frac{w}{5 } = 22 - 20 \\ \\ \frac{w}{5} = 2 \\ \\ w = 5 \times 2 \\ \\ w = 10\)

The steps Sergey could use to solve the quadratic equation by completing the square is 5(x2 + 4x) = –7

We should know that in completing the square method both sides of the equation are made perfect squares.

The given equation is 5x²+20x-7=0

Solving this equation by completing the square method we have

5(x²+4x+4)=-7

This means that (x+2)=±√27/5

Simplifying further we have

5(x²+4x)=7

Then expanding to make ²HS a perfect square we have

5(x²+4x+4)=7+20

This means that 5(x²+4x)=-7

Therefore the step he could use is 5(x²+4x)=-7\

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Answer:

Forest A will have 6 more trees.

Step-by-step explanation:

The number of trees in Forest A is represented by the function:

\(A(t)=72(1.025)^t\)

And Forest B is represented by:

\(B(t)=63(1.029)^t\)

And we want to determine which forest will have the greater number of trees after 20 years.

So, evaluate both functions for t = 20. For Forest A:

\(\displaystyle \begin{aligned} A(20)&=72(1.025)^{20} \\ &=117.9803...\\ &\approx 118 \text{ trees} \end{aligned}\)

And for Forest B:

\(\displaystyle \begin{aligned} B(20) &= 63(1.029)^{20} \\ &=111.5958... \\ &\approx 112 \end{aligned}\)

Therefore, after 20 years, Forest A will have 6 more trees.

Answer: Height = 20 inches, Width = 36 inches

Step-by-step explanation:

Let the height be \(h\) and the width be \(h+16\).

Using the formula for the perimeter of a triangle,

\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)

Answer:

the answer is 67.4545454545

Step-by-step explanation:

Answer:

Camillo will spend $48.75 dollars

Step-by-step explanation:

Since the better buy cost $1.95 we multiply.

1.95 * 25 = 48.75

So, the answer is 48.75

Hope this helps! :)

Step-by-step explanation:

Given,

-2x + 3y = -9 ------- (eqⁿ 1)

4x - 6y = 2 ----------- (eqⁿ 2 )

now,

multiply eqⁿ 1 by 2

so we got,

-4x + 6y = -18 -------- (eqⁿ 3)

now,

subtract eqⁿ 2 from eqⁿ 3

we got,

-8x = -16

x = -16/-8

x = 2,

so , after putting values in the eqⁿ 2

we got,

4(2) - 6y = 2

8 - 6y = 2

6y = 2 - 8 = 6

y = 6/6

y = 1

x = 2 and y = 1

hope this answer helps you dear...take care!

Answer:

Radius = 5.996958 (They probably just want “6”).

Step-by-step explanation:

9.42x4=37.68 (perimeter)

Perimeter=2\(\pi\)r

37.68÷2\(\pi\)=r

5.996958=r

The scatter plot shows a [positive linear] association.

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a positive linear association.

Hence, the association is a positive linear association.

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Answer: To find the percent increase in population, I used the following formula:

percent increase = (new value - old value) / old value * 100

In this case, the old value was the population from a decade ago (4360), and the new value was the current population (6590). So plugging these values into the formula, we get:

percent increase = (6590 - 4360) / 4360 * 100

percent increase = 51.38%

So the population of Placerville increased by approximately 51.38% over the past decade. The population of Placerville has increased by (6590 - 4360) = 2230 people over the past decade.

Step-by-step explanation:

Answer: It seems that it is 2/6 since the multiples of 3 are 3,6. Because there are two, the simplified answer is 2/6 or 1/3.
Since there is no 2/6 the best answer is 1/3

Step-by-step explanation:

Evaluate the expression with the given value of x. This is, replacing the x for the given value in the expression and solving it.

Answer:

17

Step-by-step explanation:

\(h(x) =x^2 +1\\k(x)=x-2\\\\3h(2)+2k(3)\\\\h(2)= ?\\k(3)=?\\\\h(2) = (2)^2 +1\\= 4+1\\h(2)=5\\\\\\k(3)= 3-2\\k(3) = 1\\\\3h(2) +2k(3)\\\\= 3(5)+2(1)\\=15+2\\3h(2)+2k(3) = 17\)

5, 9, and 17

Step-by-step explanation:

Answer:$53

Step-by-step explanation:

Answer:

He is not correct

2 boxes of eggs =1.30+1.30=2.60

1 bottle of juice cost=£2.60

2.60+2.60=£5.20

£10.00-0.90p=£9.10

9.10-5.20=£3.90

3.90/3=£1.30

1.30+1.30+1.30=£3.90

5.20+3.90=£9.10

Step-by-step explanation:

Answer: 8 books

Step-by-step explanation:

y= how much shelf space take up (inches)

x= # of books

y=2x

in this situation 16=y

16=2x

divide both sides by 2

8=x

16cm this answer for the quetion

Answer:

2

Step-by-step explanation:

x*x*x=8

2*2*2=8

Answer:

5

Step-by-step explanation:

if 17y-8=9, then you could say that 17y=17, by adding 8 to both sides.

So, y=1

Then, plug that value into the new equation 6y-1.

You recieve 6(1)-1

Therefore, the value of the new equation is 5

Answer: they have the same number in them for example -4 and 4

Step-by-step explanation:

Between the 5 and 7  is the answer

Answer:

They are the same.

Step-by-step explanation:

According to the commutative property, switching the order of this will not change the outcome.

Answer:

100 units.

Step-by-step explanation:

I am assuming that C is the cost.

You Can form the quadratic equation: 10530=x^2+5x+30. You put the left side to zero by subtracting 10530: x^2+5x+30-10530=0. You will get that x^2+5x-10500. You can use the quadratic formula or factoring. The factors that multiply to 10530 and add up to 5 is 105 and -100. You group: (x+105)(x-100)=0, you then use the zero-product property: x+105=0, x-100=0.

you get that x=100, -105. The number of units cant be negative, so x must be 100.

Answer:

Step-by-step explanation:

68000+6.75b>82000+5.5b. subtract 5.5b from both sides

68000+1.25b>82000. subtract 68000 from both sides

1.25b>14000. divide both sides by 1.25

b>11200

So she must sell more than 11500 books to make more with second publisher.

Answer:

Grapgical charts and data plots

Step-by-step explanation:

Step-by-step explanation:

Answer:

The measurement of the angle is 74.65

Step-by-step explanation:

We have the adjacent and hypoteneuse; the trig function will be cosine

\(cos^{-1}(\frac{9}{34})\\\\=74.650\)

Answer:

75°

Step-by-step explanation:

cos x = \(\frac{9}{34}\)

cos x = 0.2647

cos\(^{-1}\) ≈ 74.65

Answer:

22 1/2

Step-by-step explanation:

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

A. Negative correlation

B. Data isn't given

Step-by-step explanation:

A. A positive correlation occurs when variables that are related(not zero correlation)increase together, in other words variable a(independent variable) increases and makes variable b(dependent variable) increase too. There will be a negative correlation if the opposite happens, that is when variables that are related go in opposite directions, one increases while the other decreases. We observe from what we are told that a negative correlation occurs here since death rate from fires has likely(assumed) decreased as smoke detectors have increased.