There are 5 cars to be displayed in 5 parking spaces, with all the cars facing the same direction. of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. if the cars are identical except for color, how many different display arrangements of the 5 cars are possible?

Since the value of the function is decreasing exponentially as x decreases ,

The function is of the form [tex] y=ae^{bx}+c,b>0 [/tex].

Since the curve passes through (0,6),

[tex] 6=ae^{0}+c,6=a+c [/tex],

Since the curve passes through (-1,0),

[tex] 0=ae^{-b}+c [/tex].

Since [tex] y=-3 [/tex] is a horizontal asymptote,

[tex] -3=ae^{-\infty}+c,c=-3 [/tex]

From the above 3 equations,

[tex] c=-3,a=9,9e^{-b}=3,e^b=3,b=\ln 3 [/tex].

Therefore, the required function is

[tex] y=9e^{\ln 3 x}-3\\
y=9*3^{ x}-3 [/tex].

It can be verified that the curve [tex] y=9*3^{ x}-3 [/tex] passes through [tex] (-2,-2) [/tex].

Answer:

A = { 9/2 π - 9 } in^2

Step-by-step explanation:

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To find the area of the segment, subtract the area of the triangle from the area of the sector.

To find the area of one segment formed by a square with sides of 6 inches inscribed in a circle, we need to find the area of the sector formed by the circle and subtract the area of the triangle formed by the diagonal of the square.

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Final answer:

The area of the quilt, which is a regular pentagon made from five congruent triangles, is 80 square inches, determined by multiplying the area of one triangle (16 inches) by five.

Explanation:

The area of the quilt which is in the shape of a regular pentagon can be determined by calculating the area of the five congruent triangles that make up the pentagon. Since each triangle has an area of 16 inches, we can find the total area by simply multiplying the area of one triangle by the number of triangles.

To calculate the total area of the quilt:

Therefore, the total area of the quilt is 80 square inches.

The radius of convergence of the maclaurin series is 1 unit.

It is given that maclaurin series  [tex]\rm \frac{2x}{(1+x^2)}[/tex]

It is required to find the radius of the convergence of the maclaurin series.

It is defined as the expansion of a function that provide the approximation of the given function at any point of function.

We have:

[tex]\rm \frac{2x}{(1+x^2)}[/tex]

To find the radius of convergence of the maclaurin series, we must find the roots of denominator hence:

[tex]\rm 1+x^2= 0\\\\\rm x^2 = -1\\\\[/tex]

From the complex number: the roots are imaginary:

[tex]\rm x_1 = i\\x_2 = -i[/tex]

i is the iota

and the distance from the origin (0,0) is 1.

Thus, the radius of convergence of the maclaurin series is 1 unit.

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We have been given that a park rangers notice a negative correlation between the number of available campsites in a park and the amount of litter on the park's trails.

We need to figure out the lurking variable that describes the given correlation.

Out of the given options, the most appropriate variable that describes that negative correlation between number of available campsites in the part and the amount of litter on the park's trails is number of visitors to the park.

The reason, why number of visitors to the park is the lurking variable for the given negative correlation, is that more the number of visitors, more the litter they produce and consequently, lesser the number of available campsites.

Answer:

5 and 1

1 is extraneous

Step-by-step explanation:

Correct options are Options B, D, E. The product of two rational expressions (a/b) and (x/y) is a rational expression, specifically the ratio of ax and by, or equivalently ax/by. Incorrect options include ay/bx and a/y(x/b).

To determine the product of two rational expressions (a/b) and (x/y), where b ≠ 0 and y ≠ 0, let's explore the given options. Here are the truths about the product:

The product is a rational expression: When you multiply two rational expressions, the result is also a rational expression. This follows from the definition of rational expressions, which are ratios of polynomials.

The product is the ratio of ax and by: Mathematically, multiplying the numerators and denominators of the two rational expressions gives us (ax)/(by).

The product is equivalent to ax/by: This restates the above ratio in a simplified expression form, confirming that the multiplication results in (ax)/(by).

As we can see, the other expressions mentioned (ay/bx, a/y(x/b), a/(y(x/b))) are not correct representations of the product. Correct options are Options B, D, E.

Complete question:

If a/b and x/y represent rational expressions and b0 and y0, what is true of their product? Select three options.

A. The product is equivalent to ay/bx

B. The product is a rational expression.

C. The product is equivalent to a/y(x/b)

D. The product is the ratio of ax and by.

E. The product is equivalent to ax/b(y)

Equation of an ellipse

→having center (0,0) , vertex ([tex](\pm a ,0)[/tex] and covertex [tex](\pm b ,0)[/tex] and focus [tex](\pm c ,0)[/tex] is given by:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2}=1[/tex]

As definition of an ellipse is that locus of all the points in a plane such that it's  distance from two fixed points called focii  remains constant.

Consider two points (a,0) and (-a,0) on Horizontal axis of an ellipse:

Distance from (a,0) to (c,0) is = a-c = [tex]F_{1}[/tex]

Distance from (-a,0) to (c,0) is = a + c = [tex]F_{2}[/tex]

[tex]F_{1} + F_{2} =[/tex] a -c + a +c

          = a + a

        = 2  a  →(Option A )

Answer:

The correct answer is Option A.

Step-by-step explanation:

Final answer:

The typist earns $121.50 per week by multiplying the charge per page ($0.90) with the daily page average (45 pages) and the number of days worked per week (3 days).

Explanation:

The question asks us to calculate the weekly earnings of a typist who charges $0.90 per page and averages 45 pages per day, working 3 days a week. To find the total weekly earnings, we can multiply the number of pages typed per day by the charge per page, and then multiply that result by the number of days worked in a week.

Multiply the number of pages (45) by the charge per page ($0.90): 45 pages × $0.90 = $40.50 per day.

Multiply the daily earnings by the number of days worked in a week (3): $40.50 × 3 days = $121.50 per week.

Therefore, the typist earns $121.50 per week.

The coefficients of the algebraic expression -2x² + 17 -15x + 7xy are -2, 17, -15 and 7

How to determine the coefficient of the expression

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

-2x² + 17 -15x + 7xy

Consider an expression represented as

Ax

Where A is a constant and x is the variable

The coefficient of the expression is A

Using the above as a guide, we have the following:

The coefficients of the algebraic expression are -2, 17, -15 and 7

Question

Which of the following gives all of the coefficients of the algebraic expression -2x^2 +17-15x+7xy

a. 2,  17, 15 and 7

b. -2, 17, -15 and 7

c. -2, -17, -15 and 7

d. -2, -17, 15 and 7

Answer:

It is $600

Step-by-step explanation:

hope it helps, murdle

The equation of the line through (-8,8) and (1,-10) is y = -2x - 8

Using the slope intercept form equation.

y = mx + b

where

m = slope

b = y-intercept

Therefore,

(-8,8) (1,-10)

m = -10  - 8 / 1 + 8 =  - 18  / 9 = -2

Therefore,

let's find b as follows:

(1, -10)

y = -2x + b

-10 = -2(1) + b

b = -10 + 2

b= -8

Therefore,

y = -2x - 8

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