g(x)=-3x - 2
f(x) = 3x + 1
Find g(x) ÷ f(x)

Answer: 14a + 1

Step-by-step explanation:

( 7a x 3 - 2a - 2 ) + ( -5a + 3 )

( 21a - 2a - 2 ) + ( -5a + 3 )

21a - 2a - 2 - 5a + 3

14a + 1

Answer:

Step-by-step explanation:

The function B(n = 1 250 + 50 represents the price. B(n), to buy n pounds of watermelons. The function S(n) = 0.50n + 300 represents it price, s(n), to ship n pounds of watermelons. Which of the following functions can be used to find the total price. T(n), to buy and ship n pounds of water.

Answer:

slope=-1/5

Step-by-step explanation:

the slope is -1/5 because it falls 1 unit from one point before crossing 5 units and hitting another point.

Answer:

Hope this helps! have a good day. :)

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3(x−2)=2(x−3)

(3)(x)+(3)(−2)=(2)(x)+(2)(−3)(Distribute)

3x+−6=2x+−6

3x−6=2x−6

Step 2: Subtract 2x from both sides.

3x−6−2x=2x−6−2x

x−6=−6

Step 3: Add 6 to both sides.

x−6+6=−6+6

x=0

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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0.470

To calculate the mean of the sampling distribution of the sample proportion for those in the category unhappy or very unhappy, you should follow the steps given below:

Step 1: Identify the values.n = 459p = 0.47Step 2: Determine the mean of the sampling distribution of the sample proportion of customers who are unhappy or very unhappy.μ = p = 0.47. Therefore, the mean of the sampling distribution of the sample proportion for those in the category unhappy or very unhappy is 0.470 (rounded to three decimal places).Note: A mean is a statistical measure that is used to calculate the central tendency of a dataset. It is defined as the average of a dataset or a set of numbers. The mean can be calculated for both interval-scaled measures as well as proportion.

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The constant of proportionality of the given function of the graph would be 3 / 4.

The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.

Let the equation below which is shown in the graph:

y = kx ....(i)

where k is the constant of proportionality.

As per the given graph, take a point x = 4, and y = 3

Substitute the values x = 4, and y = 3 in the equation (i)

3 = k × (4)

4k = 3

k = 3 / 4

Thus, the constant of proportionality of the given function of the graph would be 3 / 4.

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after 1 year he will get : 800 + 800 x 3,5% = 800 x 1,035 = $828

after 2 years he will get : 828 x 1,035 = 800 x 1,035 x 1,035 = 800 x 1,035²

so

after 10 years he will get : 800 x 1,035¹⁰

Answer:

32=X becuase you said He subtracted 7 three times or thrice so we multiply that then add 11 because it was our remaining number from subtraction. so 32

Step-by-step explanation:

Given:

The equation is

\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\dfrac{\sqrt{3}}{2}\)

To find:

The solutions of given equation over the interval \([0,2\pi]\).

Solution:

We have,

The equation is

\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\dfrac{\sqrt{3}}{2}\)

\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\sin \dfrac{\pi }{3}\)

\(\sin\left(x+\dfrac{7\pi}{2}\right)=\sin (-\dfrac{\pi }{3})\)

If \(\sin x=\sin y\), then \(x=n\pi +(-1)^ny\).

Over the interval \([0,2\pi]\).

\(x+\dfrac{7\pi}{2}=4\pi-\dfrac{\pi }{3}\) and \(x+\dfrac{7\pi}{2}=5\pi+\dfrac{\pi }{3}\)

\(x=\dfrac{11\pi }{3}-\dfrac{7\pi}{2}\) and \(x=\dfrac{16\pi}{3}-\dfrac{7\pi}{2}\)

\(x=\dfrac{22\pi-21\pi }{6}\) and \(x=\dfrac{32\pi-21\pi }{6}\)

\(x=\dfrac{\pi}{6}\) and \(x=\dfrac{11\pi }{6}\)

Therefore, the two solutions are tex]x=\dfrac{\pi}{6}\) and \(x=\dfrac{11\pi }{6}\).

Answer:

C. π/6 & 11π/6

Step-by-step explanation:

If you graph the equation ( Sin (x+7π/2)=-√3/2) and look between 0 & 2π, you'll see that the lines intersect the x-axis at π/6 & 11π/6.

The amount of interest that the customer will pay is given as follows:

$31.88.

The balance of an account after t periods is given as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

Hence the interest accrued is given as follows:

I(t) = Prt.

The parameters for this problem are given as follows:

P = 2530.16, r = 0.00042, t = 30.

Hence the interest is given as follows:

I(30) = 2530.16 x 0.00042 x 30

I(30) = $31.88.

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The volume of the Parallelepiped with adjacent edges pq, pr,and ps = 136

Geometrically, the Scalar triple product:

\({\displaystyle \mathbf {a} \cdot (\mathbf {b} \times \mathbf {c} )} \mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})\)

is the (signed) volume of the parallelepiped defined by the three vectors given. Here, the parentheses may be omitted without causing ambiguity, since the dot product cannot be evaluated first. If it were, it would leave the cross product of a scalar and a vector, which is not defined.

Given three vectors, there is a product, called scalar triple product, that gives , the volume of the parallelepiped that has the three vectors as dimensions.

So,

Given : p(-2,1,0) , q(3,4,3), r(1,4,-1), s(3,6,4).

pq =  ( -2-3 ,1-4 ,0-3) = (-5,-3,-3)

pr= (-2-1, 1-4, 0+1) = (-3,-3,1)

ps= ( -2-3, 1-6, 0-4) = (-5,-5,-4)

pq = (-5  ,  -3  , -3)

pr = (-3,  -3,  1)

ps= (-5,  -5,  -4)

The scalar triple product is given by the determinant of the matrix (3×3)

that has in the rows the three components of the three vectors:

\(\left[\begin{array}{ccc}-5&-3&-3\\-3&-3&1\\-5&-5&-4\end{array}\right] \\\\-5(12+5)-3(12+5)-3(15-15)\\-5(17)-3(17)-3(0)\\-85-51\\-136\\\)

So, The volume never be negative then by applying vector

v = |-136|

v= 136

the volume of the parallelepiped with adjacent edges pq, pr,and ps = 136

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Answer:

Hope that this helps!!!

The negative square root of three is not included in the range since it correlates to negative radial distances.

The radial distance (r), which is always a non-negative value in polar coordinates, represents the distance from the origin to a point in the xy-plane.

The equation x2 + y2 = 3 denotes a circle with a radius of √3 and is centered at the origin. This equation can be expressed in polar coordinates as r2 = 3. It is impossible for r to be negative because it denotes the radial distance. Consequently, the range for r is 0 ≤ r ≤ √3.

Since it would correlate to negative radial distances, which are meaningless in the context of the issue and do not correspond to points inside the contained solid, the negative square root of three is excluded from the range.

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Answer:

-8

Step-by-step explanation:

because:

-8 is higher than -7 even though it is a negative and also if this is on paper question but if it is for homework or online and you have multiple goes at answering just guess

Answer:

A

Step-by-step explanation:

1 is linear with 138, and they must add to 180, so 180 - 138 = 42

Answer:

25

Step-by-step explanation:

Let's simplify this, while still doing it.

3 + 2(4 + 7)

3 + 2(11)

3 + 22

25.

the answer is 25!!

Answer:

The answer is 25

2(4+7)

8+14 + 3 = 25

Step-by-step explanation:

Construct validity and ecological validity are the two validities that are most often in a trade-off.

Construct validity and ecological validity are the two validities that are most often in a trade-off. Construct validity deals with how accurately a test measures what it is supposed to measure. On the other hand, ecological validity refers to how generalizable the findings are to real-world settings.

Researchers may prioritize one type of validity over the other in research studies. Construct validity is important when researchers want to make sure that their tests are measuring what they claim to be measuring. This requires a lot of control over the study setting, which can make it harder to have high ecological validity. Researchers might have to use laboratory settings or artificially manipulate the independent variable to increase construct validity at the cost of ecological validity.

Researchers may prioritize ecological validity when they want their findings to apply to real-world settings. This requires using a more naturalistic setting, which can make it harder to control all the variables, leading to lower construct validity. Thus, researchers often have to make a trade-off between construct validity and ecological validity when conducting studies.

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Answer:

expression is 20. +20...

The system of inequalities is

x + y ≥ 14

5x + 2.5y ≤ 60

Given, that Yaritza and her children went into a restaurant that sells hamburgers for $5 each and tacos for $2.50 each.

Yaritza has $60 to spend and must buy at least 14 hamburgers and tacos altogether.

As, x represents the number of hamburgers purchased and y represents the number of tacos purchased

Now, according to the question

x + y ≥ 14

as, she must buy at least 14 hamburgers and tacos altogether.

Now, 5x + 2.5y ≤ 60

as, she has $60 to spend.

So, we have two inequalities

x + y ≥ 14

5x + 2.5y ≤ 60

Hence, the system of inequalities for the given problem is

x + y ≥ 14

5x + 2.5y ≤ 60

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We are asked to estimate the arc length of the curve y = x sin(x) using Simpson's Rule with n = 10. Additionally, we need to compare our estimate with the value of the integral produced by a calculator.

To estimate the arc length using Simpson's Rule, we divide the interval [0, 27] into subintervals and approximate the integral using a weighted sum of function values. With n = 10, we have 10 subintervals of equal width.

First, we calculate the width of each subinterval: h = (27 - 0) / 10 = 2.7.

Next, we evaluate the function y = x sin(x) at the endpoints and interior points of the subintervals to obtain the function values.

Using Simpson's Rule formula, the arc length is approximated as:

Arc length ≈ (h/3) * [y0 + 4y1 + 2y2 + 4y3 + 2y4 + ... + 4y9 + y10],

where y0, y1, y2, ..., y10 represent the function values at the respective points.

By performing the calculations according to the formula, we obtain the estimated value of the arc length using Simpson's Rule with n = 10.

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To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.

The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.

The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.

Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.

Solving for b, we find b = 30.

Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.

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Answer:40

Step-by-step explanation: 40 present

Answer:

90%

Step-by-step explanation:

The maximum value of P is 20.68, which occurs when x = 1.67 and y = 1.07.

The optimal solution, we need to first graph the constraints and determine the feasible region.

The first constraint is 3x + 5y ≤ 12, which represents a line with a y-intercept of 2.4 and a slope of -3/5.

The second constraint is 6x + 2y ≤ 10, which represents a line with a y-intercept of 5 and a slope of -3.

Plotting these lines on a graph, we get:

The feasible region is the shaded region that satisfies both constraints and lies in the first quadrant.

Next, we need to evaluate the objective function at each corner point of the feasible region to find the maximum value of P.

The corner points are:

(0, 2.4)

(1.67, 1.07)

(1.43, 0)

(0, 0)

Evaluating P at each of these points, we get:

(0, 2.4):

P = 9.6

(1.67, 1.07):

P = 20.68

(1.43, 0):

P = 17.72

(0, 0):

P = 0

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Answer: D is the ans

Answer:

-18/35

Step-by-step explanation:

Answer:

4.5 gallons

Step-by-step explanation:

The formula to find  the total number of shaded triangles in the first 10 sierpinski triangles is Sn = (1 - 310)/(-2).

The Sierpiski triangle, also known as the Sierpiski gasket or Sierpiski sieve, is a fractal appealing fixed set with the general shape of an equilateral triangle that is subdivided recursively into smaller equilateral triangles. The name Sierpiski is derived from the Polish language. This is one of the simplest instances of self-similar sets, meaning it is a mathematically generated pattern that can be replicated at any magnification or reduction. It was initially built as a curve.

The Sierpinski triangle can be divided into three self-similar sections (n=3), each of which can then be enlarged by a factor of two (m=2) to produce the full triangle. N = md, where n is the number of self-similar pieces and m is the magnification factor, is the formula for dimension d.

The formula to find  the total number of shaded triangles in the first 10 sierpinski triangles is Sn = (1 - 310)/(-2).

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