Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit (in dollars) of the product according to the following formula. y = 32(3p + 1)−2/5, p > 0
(a) What is the rate of change in sales volume when the price is $22? (Round your answer to three decimal places.) dy dp = -0.107 CORRECT ANSWER
(b) Interpret your answer to part (a). (Round your answer to the nearest whole number.) If the price increases $1, the sales volume will decrease by : ?

Answer:

A. x = -6

Step-by-step explanation:

-1/6x - 5 = 2/3x

add 1/6x to both sides:

-1/6x - 5 + 1/6x = 2/3x + 1/6x

-5 = 2/3x + 1/6x

common denominator on right side:

-5 = 4/6x + 1/6x

combine right side:

-5 = 5/6x

multiply both sides by 6/5:

(-5)(6/5) = (5/6x)(6/5)

-30/5 = x

reduce left side:

-6 = x

x = -6 (option a)

Answer: A) x=-6

Step by step explanation:

[tex]\boldsymbol{\sf{\dfrac{-1}{6}x-5=\dfrac{2}{3}x }}[/tex]

We calculate the multiplication expression.

    [tex]\boldsymbol{\sf{\dfrac{-1}{6}x-5=\dfrac{2}{3}x \iff \ -\dfrac{x}{6}-5=\dfrac{2}{3} x \iff -\dfrac{x}{6}-5=\dfrac{2x}{3} }}[/tex]

Eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.

     [tex]\boldsymbol{\sf{ -\dfrac{x}{6}-5=\dfrac{2x}{3} \iff \ -x-30=4x}}[/tex]

The variable is moved to the left and the symbol is changed.

    [tex]\boldsymbol{\sf{-x-30=4x \iff -x-30-4x=0}}[/tex]

We move the constant to the right side and change the sign.

    [tex]\boldsymbol{\sf{-x-30-4x=0 \iff -x-4x=30}}[/tex]

 [tex]\boldsymbol{\sf{-x-4x=30 \ < == We \ organize \ the \ equation== > \ -5x=30 }}[/tex]

             [tex]\bf{\underline{Change \ the \ sign \ on \ both \ sides \ of \ the \ equation.}}[/tex]

  [tex]\boldsymbol{\sf{-5x=30 \iff \ 5x=-30 \ < ==Split== > \ x=-\dfrac{30}{5}=\boxed{\boxed{\boldsymbol{\sf{-6}}}} }}[/tex]

We get the following answers:

A) The least square regression line is:

yi = 88.73 - 2.827(xi)

B) The slope  is β₁ = -2.827 and The intercept is β₀ = 88.73.

C) e*₆ = -0.6964, final grade is below average grade.

E) It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

we have Xi = No of absences

Yi = Final grade

The regression model is

Yi = β₀ +  β₁Xi + i

β₀ = y -  β₁x

we have n = 10, x bar = 4.5 , y bar = 76.01

cov(x,y) = -23.325 and var(x) = 9.1667

therefore,  β₀ = 88.73 and  β₁ = -2.827

A) Least square regression line is given by:

yi =  β₀+ β₁Xi

yi = 88.73 - 2.827(xi)

B) The slope  β₁ = -2.827 which means when no of absence is increased by 1 duty then the final grade will decrease by 2.827

The intercept  β₀ = 88.73 when there are 0 days absence the average grade is 88.73

C) Predicted graph for student who misses five class periods is

x = 5

y*5 = 88.73 - 2.827(5) = 74.5964

Hence for corresponding residual is:

e*₆ = 73.9 - 74.5964

e*₆ = -0.6964, final grade is below average grade.

D) please see graph

E) when student miss 15 class periods the final grade will be

X = 5

y* = 88.73 - 2.827(15)

= 46

It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

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Answer:

  A, B, C

Step-by-step explanation:

You want to know the correct descriptors of the given graph.

The solution to a system of equations is the set of points that satisfy all of the equations at once. On a graph, it will be the set of points where the graphs of the equations intersect.

Here the two lines cross at one point, hence there is one solution.

The point where the lines cross is approximately (3, -0.5). That makes (3, -0.5) a reasonable estimate of the solution of the system.

Answer: Brazil and Alaska

Step-by-step explanation

Take away Brazil's temperature from Alaska's to get your answer

81 - 23 = 58'F

To write the equation in exponential form we must follow certain rules:

1. Logarithm product rule -            log b ( x ∙ y) = log b ( x) + log b ( y)

2. Logarithm quotient rule -           log b ( x / y) = log b ( x) - log b ( y)

3. Logarithm power rule -               log b ( x y) = y ∙ log b ( x)

4. Logarithm base switch rule -     log b ( c) = 1 / log c ( b)

1. ㏒z(w) = p

Here all constants are taken to be positive and not equal to 1

z = base of the logarithmic function

z^p = w --------> (1)

This z^p = w is the exponential form of ㏒z(w) = p

2. ㏒(s) = r

Here all constants are taken to be positive and not equal to 1

e = base of the logarithmic function

e^r = s --------> (2)

This e^r = s is the exponential form of ㏒(s) = r

3. 7m = a

Here we have to write the equation in logarithmic form

㏒(7m) = log r

log(7m) - log r = 0

We know quotient rule :-

log b ( x / y) = log b ( x) - log b ( y)  --------(A)

Applying that same principle to our question by using this equation we have:

log (7m/r)

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The function f{ g(2) } is equivalent to for the functions f(x) = 2x² + 1 and g(x) = 3x - 5 is 3.

Given is that f(x) = 2x² + 1 and g(x) = 3x - 5.

We have to find -

f{g(2)}

Now -

g(2) = g(2) = 3 x 2 - 5 = 6 - 5 = 1

g(2) = 1

f{g(2)} = 2x² + 1 = 2 x 1 x 1 + 1

f{ g(2) } = 3

Therefore, the function f{ g(2) } is equivalent to for the functions f(x) = 2x² + 1 and g(x) = 3x - 5 is 3.

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Answer:

x = 6

Step-by-step explanation:

let x = the width

let x + 8 = the length

Area = w times l

84 = 14 x 6

width = 6

length = 6+8

           = 14

Answer:

Step-by-step explanation:

-7-9=-16

a) The equation of a vertical line is x = k, where k is the x-coordinate of the point where the line intersects the y-axis. In this case, the point where the line intersects the y-axis is (2, -65), so the equation of the line is x = 2. The slope of a vertical line is undefined, since it has no slope.

b) The equation of a horizontal line is y = k, where k is the y-coordinate of the point where the line intersects the x-axis. In this case, the point where the line intersects the x-axis is (-2, 4), so the equation of the line is y = 4. The slope of a horizontal line is 0, since it has no slope.

If the circumference of ABDE is 30 cm, then the length of the line DE is 6 cm.

The answer to the query is

ABDE's perimeter is 30 cm.

AB length is 12 cm.

Let DE ne length be "x"

Since DE and AB are parallel, the alternate interior angles theorem states that

∠ABE = ∠DEB and ∠BAD = ∠ADE.

Since AD is the angle that bisects ∠A,

∠DAB = ∠EAD

BE is the angle bisector of B, therefore

∠EBD = ∠ABE.

∠EAD = ∠ADE and ∠EBD = ∠BED as a result.

If AE = ED and ED = DB, the triangles ADE and EDB are therefore isosceles. AE = DE = DB = x, then.

Given that ABDE's perimeter is 30 cm,

therefore 12 + 3x = 30,

By finding the x,

=> 3x = 30 -12

=> 3x = 18

=> x = 6 cm.

Consequently, DE has a length of 6 cm.

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Answer: The voting district that contributed the most to the test statistic is District B.

Step-by-step explanation:

How do you calculate the contribution of each voting district to the test statistic?

The contribution of each voting district to the test statistic is calculated by taking the difference between the observed and expected values for that district, squaring it, and then dividing it by the expected value. In this case, the contribution for District A is (58-46.80)^2/46.80 = 2.68, the contribution for District B is (22-32.40)^2/32.40 = 3.34, the contribution for District C is (12-18)^2/18 = 2.00, and the contribution for District D is (28-22.80)^2/22.80 = 1.19. Therefore, District B contributed the most to the test statistic.

The chi-square goodness-of-fit test compares observed and expected values to determine if they are significantly different from each other. The test statistic is calculated by summing the squared differences between the observed and expected values, divided by the expected values. The larger the difference between the observed and expected values, the larger the contribution to the test statistic. In this case, District B had the largest difference between the observed and expected values, therefore it had the greatest impact on the overall test statistic.

District B contributed the most to the test statistic because it had the highest value in the "Components" column. The formula for the chi-square goodness-of-fit test is (Observed - Expected)^2 / Expected, and the resulting value for District B is 3.34, which is the highest of the four districts. Therefore, District B had the biggest deviation from the hypothesized proportions.

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Answer: Voting district B contributed the most to the test statistic.

Step-by-step explanation:

How do you determine each voting district's contribution to the test statistic?

By subtracting the observed value from the predicted value for each voting district, square rooting the result, and then dividing the result by the expected value, the contribution of each voting district to the test statistic is determined. In this instance, the contributions for Districts A, B, C, and D are as follows:

District A's contribution is (58-46.80)²/46.80 = 2.68; District B's contribution is (22-32.40)²/32.40 = 3.34; District C's contribution is (12-18)²/18 = 2.00; and District D's contribution is (28-22.80)²/22.80 = 1.19. As a result, District B was most responsible for the test statistic.

In order to assess if actual and expected values differ significantly from one another, the chi-square goodness-of-fit test compares observed and expected values. The test statistic is determined by multiplying the expected values by the total of the squared discrepancies between the actual and predicted values. The contribution to the test statistic increases as the gap between observed and predicted values widens. In this instance, District B's largest disparity between actual and predicted values had the biggest effect on the test statistic as a whole.

Due to having the highest value in the "Components" column, District B had the greatest impact on the test statistic. (Observed - Expected)² / Expected is the formula for the chi-square goodness-of-fit test, and the result for District B, which is the highest of the four districts, is 3.34.

District B therefore, showed the greatest departure from the predicted proportions.

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Number of people that use blogs to make a purchase are 24.75= 25 and number of people that never buy anything without reading a review first are 60.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given, 33% of millennials rely on blogs before making a purchase.

Eight out of 10 millennials never buy anything without reading a review first.

That means,

8 out of 10 is 80%.

In a sample size of 75 millennials:

To find the number of people that never buy anything without reading a review first:

80% of 75

80 x 75 / 100

= 6000/ 100

= 60

To find the number of people that use blogs to make a purchase:

33% of 75

33 x 75 / 100

= 2475/ 100

= 24.75

Therefore, the number of people are 24.75 and 60.

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The function represented by the series is [tex]$\quad f(x)=\frac{4}{1-x^2}$[/tex]

The interval of convergence of the series is ( - 1, 1 )

As per the question the given function is:

[tex]$$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k$$[/tex]

[tex]$$\sum_{n=0}^{\infty} a r^n=\frac{1}{1-r}$$[/tex]

[tex]$$\sum_{n=0}^{\infty} x^n=\frac{1}{1-x}$$[/tex]

[tex]$$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\frac{1}{1-\frac{x^2+3}{4}} \\& =\frac{1}{\frac{4-x^2-3}{4}} \\& =\frac{4}{1-x^2}\end{aligned}$$[/tex]

Thus, [tex]$\quad f(x)=\frac{4}{1-x^2}$[/tex]

[tex]$$\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k=\sum_{k=0}^{\infty} \frac{\left(x^2+3\right)^k}{4^k}$$[/tex]

[tex]$$\begin{aligned}L & =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)^{k+1}}{4^{k+1}} \frac{4^k}{\left(x^2+3\right)^k}\right| \\& =\lim _{k \rightarrow \infty}\left|\frac{\left(x^2+3\right)}{4}\right| \\& =\left|\frac{\left(x^2+3\right)}{4}\right|\end{aligned}$$[/tex]

The series will converge, if L<1

[tex]$$\begin{array}{ll} & \left|\frac{\left(x^2+3\right)}{4}\right| < 1 \\ & \frac{\left(x^2+3\right)}{4} < 1 \\ & x^2+3 < 4 \\\end{array}[/tex]

[tex]& x^2 < 1 \\[/tex]

 |x| < 1

 -1 < x < 1

Substitute the values of 'x' in the given function

At, x = - 1

[tex]\begin{aligned} \\\qquad \begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(-1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}\end{aligned}$$[/tex]

Also, at x = 1

[tex]$$\begin{aligned}\sum_{k=0}^{\infty}\left(\frac{x^2+3}{4}\right)^k & =\sum_{k=0}^{\infty}\left(\frac{(1)^2+3}{4}\right)^k \\& =\sum_{k=0}^{\infty}\left(\frac{4}{4}\right)^k \\& =\sum_{k=0}^{\infty} 1^k\end{aligned}$$[/tex]

Thus, the interval of convergence is ( - 1, 1 )

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The ordered pair that is NOT a solution to the equation y = 2x is (3, 8)

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

y = 2x

From the graph (see attachment), we have the following points:

A = (1, 2)

B = (2, 4)

C = (3, 8)

D = (5, 10)

The equation y = 2x means that

y is twice of x

In C = (3, 8), 8 is not twice of 3

Hence, the ordered pair that is NOT a solution is C = (3, 8)

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An ellipse's equation has its origin at its center, its foci on the y-axis, and its major axis at x2/16+y2/144, which is three times longer than its minor axis.

In mathematics, an ellipse is a planar curve with two focal points, where the total of the two distances from any point on the curve to the focal points is a constant.

It generalizes the shape of a circle, a unique variety of ellipse in which the two focus points coincide.

The eccentricity of an ellipse,  , which ranges from 0 (the limiting case of a circle) to 1 (the length of the ellipse), is used to determine how long it is (the limiting case of infinite elongation, no longer an ellipse but a parabola).

The area of an ellipse has a straightforward algebraic solution, while the perimeter (also known as circumference), for which integration is necessary to arrive at a precise answer, only has approximations.

According to our question-

M(X0|Y)   M(0|0)

(X-X0)^2/a^2 +(Y-Y0)^2/b^2=1

x2/a2+x2b2=1

a=4 b=3 .a=12

x2/16+y2/144

Hence, An ellipse's equation has its origin at its center, its foci on the y-axis, and its major axis at x2/16+y2/144, which is three times longer than its minor axis.

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Step-by-step explanation:

so, we have 1 position with 2 options (0 or 1).

and 6 positions with 10 options (0 to 9).

so, we have

2×10×10×10×10×10×10 = 2×10⁶ = 2,000,000

different identification numbers possible.

We state that a student correlates to a faculty member if somehow the student gets currently enrolled in some kind of a course taught by such faculty member in order to define a one to one relationship between the two sets. The correspondence a function.

The symbol for an ordered pair is (INPUT, OUTPUT): The relation denotes the connection between the input and output.

For the stated question-

We state that a student correlates to a faculty member if somehow the student gets currently enrolled in some kind of a course taught by such faculty member in order to define a one to one relationship between the two sets.

One student is related to one facility.

Thus, correspondence given forms a function.

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In a normal distribution, a data value located 1.1 standard deviations below the mean has Standard Score: z = -1.1

What is standard deviation?

In statistics, the quality deviation could be a live of the quantity of variation or dispersion of a group of values. an occasional variance indicates that the values tend to be about to the mean of the set, whereas a high variance indicates that the values area unit opened up over a wider vary

Main body:

The z score tells us the distance, in terms of standard deviation, the raw score is from the mean. Negative z values are below the mean, while positive ones are above the mean.

Something like z = 2.5 indicates we're 2.5 standard deviation units above the mean.

Something like z = -1.1 indicates we're 1.1 standard deviation units below the mean.

The value z = 0 itself is the center of the standard normal distribution (it's the mean mu).

The sigma value for the standard normal Z distribution is sigma = 1

sigma = population standard deviation

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The ordered pair for the vertices after the transformation will be:

Q' = (3, 5)

R' = (5, -1)

S'= (2, 0)

T' = (0, 3)

A geometric transformation is a function that maps points in a plane or space to other points in the same plane or space. Geometric transformations can be used to change the size, shape, orientation, or position of an object or image.

Given:  (Ry-axis T(2, 0))(QRST). That means we have a translation T(2, 0). This implies (x,y) → (x + 2, y + 0). Thus, the ordered pair for the vertices will be:

Q (x = 1, y = 5)

Q' = Q(x+2, y + 0) = (1+2, 5+0) = (3, 5)

R (x = 3, y = -1)

R' = R(x+2, y + 0) = (3+2, -1+0) = (5, -1)

S (x = 0, y = 0)

S' = S(x+2, y + 0) = (0+2, 0+0) = (2, 0)

T (x = -2, y = 3)

T' = T(x+2, y + 0) = (-2+2, 3+0) = (0, 3)

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Answer:

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

Simplify:

Answer:

[tex] \sf \red{c) \: 16} \: is \: the \: answer.[/tex]

Step-by-step explanation:

Given problem,

[tex] \sf →6 + \frac{3}{8} [/tex]

Changing error in problem,

[tex] \sf →6 \div \frac{3}{8} [/tex]

Let's solve the problem,

[tex] \sf →6 \div \frac{3}{8} [/tex]

[tex] \sf →6 \times \frac{8}{3} [/tex]

[tex] \sf → \frac{(6 \times 8)}{3} [/tex]

[tex] \sf → \frac{48}{3} [/tex]

[tex] \sf \: →16 \:[/tex]

Hence, the answer is 16.

A stock price will rise if demand for stock is greater than supply. So, the correct answer is option (d).

The stock price or share price is the amount of money it costs to buy shares in a company. Stock prices are not fixed and fluctuate based on market conditions. It is likely to go up if the company is viewed as good, and it is likely to go down if the company is not performing as expected. If there are more people who want to buy a demand than sell (supply ) it, the stock price will go up. Conversely, if more people want to sell than buy stocks, there will be more supply than demand and prices will fall. Understanding supply and demand is easy.

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Complete question:

A Stock Price Will Rise If:

a) Supply Of Stock Is Greater Than Demand

b)The Price-Earnings Ratio Is 10 Or Greater

c)Stock Yield Is Greater Than 8%

d) Demand For Stock is Greater Than Supply

e) None Of These.

Answer:

See below

Step-by-step explanation:

If I make x the scope of mix and y the quarts of water, my equation would be y = .125x

I can find the constant of Proportionally by y/x

Using points (4,.5) and (12,1.5)

(.5/4) = 0.125

(1.5/12) = 0.125

The equation would then be:

y = 0.125x

C see the graph provided from Desmos (a free graphing calculator).  as x Increases by 1, y increases by 0.125

y = 0.125x

y =.0125(20)

y = 2.5

For 20 scoops, I would need 2.5 quarts of water.

You can also see from the graph as 8 scoops, I would need 1 quart of water.

The polar coordinates of the points are: A(√29,68.1°),B(√45,-63.4°),C(√97,66.0°),D(√65,7.12°)

consider A=(2,5)

To find the polar coordinates we have the formula:

[tex]r=\sqrt{x^2+y^2} and tan^{-1} (\frac{y}{x} )----------(1)[/tex]

Assume that x=2,y=5 and substitute in equation(1)

r=√2^2+5^2 and tan^-1(5/2)

r=√4+25 and tan^-1(2.5)

r=(√29,68.1°)

For point B =(3,-6)

Assume that x=3,y=-6 and substitute in equation(1)

r=√3^3+(-6)^2 and tan^-1(-6/2)

r=√9+36 and tan^-1(-2)

r=(√45,-63.9°)

For point C=(-4,9)

Assume that x=-4,y=9 and substitute in equation(1)

r=√(-4)^2+9^2 and tan^-1(9/-4)

r=√16+81 and tan^-1(2.25)

r=(√97,66.0°)

For the point D=(-8,-1)

Assume that x=-8,y=-1 and substitute in equation(1)

r=√(-8)^2+(-1)^2 and tan^-1(-1/-8)

r=√64+1 ,7.12°

r=(√65,7.12°)

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Answer:

2 × 2 × 7

Step-by-step explanation:

start dividing by the lowest prime and work up until 1 is reached

28 ÷ 2 = 14

14 ÷ 2 = 7

7 ÷ 7 = 1

then

28 = 2 × 2 × 7 = 2² × 7

Answer:

the nth term is 2n

Step-by-step explanation:

notice how for each number of tiles, 2, 4, 6, 8, 10, they are all multiples of 2, so like ok 2 is definitely in the term, next check how n can fit. Well, since they are multiples, you multiply n by 2, now check to see if you dont need to add any values by the following method:

first number = 2,  then 2(1) = 2 if n = 1

second = 4, then (2)(2) = 4 if n = 2

its all the same for the rest. Each new diagram or tile structures represents n, so if n =1, then there are 2 tiles, if n = 4 there are 8 tiles and so on, which explains us why the nth term is 2n

The nth term formula for the number of square tiles in the nth figure is aₙ=2n.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

The given sequence is 2, 4, 6, 8, 10,.....

Here, a=2 and d=4-2=2

Substitute a=2 and d=2 in aₙ=a+(n-1)d, we get

aₙ=2+(n-1)×2

aₙ=2+2n-2

aₙ=2n

Therefore, the nth term formula for the number of square tiles in the nth figure is aₙ=2n.

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When you determine the number of months it takes to pay off a credit card and you get 24.35, payments, you have to round up.

You should understand that rounding up numbers or decimals involves writing it as a whole number

The question is given in months and we are not asked to state the weekly fractions.

24.35 is 24 months + .35*30=10 weeks

Now 24.35 in months is 24 months 10 weeks and 5 days

Hence payment is in months it should be 24 months only.

In conclusion you should not round it up.

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Hello,

The probability that both number generators generate the number 5 is (1/10) * (1/10) = 1/100 = 0.01 or 1%.

This is because the probability of an event occurring is the product of the probabilities of each event occurring independently. In this case, the probability of the first generator generating the number 5 is 1/10 and the probability of the second generator generating the number 5 is also 1/10, so the probability of both events occurring is (1/10) * (1/10) = 1/100.

----

Letss try using Pythagoras Theorem with

[tex]a+b+c=180\\21+28+c=180\\c=180-21-28\\c=131[/tex]

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The factorized expression of  5x³ + 40y⁶ is  5 ((x + 2y²) (x² - 2xy² + 4y⁴))

Factorisation of an algebraic expression means writing the given expression as a product of its factors. These factors can be numbers, variables, or an algebraic expression.

To the factor, a number means to break it up into numbers that can be multiplied to get the original number

According to the question,

We have to factorize the expression

5x³ + 40y⁶

Taking a Common factor 5 out ,

5 (x³ + 8y⁶)

Factoring the expression within the parenthesis we have:

5 ((x + 2y²) (x² - 2xy² + 4y⁴))

Now, we cant do further factor

Hence ,  The factored expression is given by:  5 ((x + 2y²) (x² - 2xy² + 4y⁴))

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