The sales S (in thousands of units) of a cleaning solution after x hundred dollars is spent on advertising are given by the following.
S = 10(1-ekx)
When $675 is spent on advertising 2900 units are sold.
(a) Complete the model by solving for k. (Round your answer to 4 decimal places.)
k =
(b) Estimate the number of units that will be sold if advertising expenditures are raised to $925.
units

The x - intercept is (25, 0) and the y - intercept is (0, 10).

What is intercepts?

The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.

Put y = 0 and work out x to find the x-intercept.

Set x = 0 and work out y to find the y-intercept.

Given: You are ordering shirts for the math club at your school.

Short-sleeved shirts cost $ 8 each.

Long-sleeved shirts cost $ 20 each. You have a budget of $ 200 for the shirts.

The equation 8 x+20 y=200 models the total cost,

where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.

To find the x - intercept plug y = 0 in the above equation.

⇒ 8x + 20(0) = 200

                8x = 200

                  x = 25

So, the point becomes, (25, 0).

To find y - intercept plug x = 0 in the above equation.

⇒ 8(0) + 20y = 200

              20y = 200

                  y = 10

So the point becomes, (0, 10).

Hence, the x - intercept is (25, 0) and the y - intercept is (0, 10).

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The amount the she had in her savings before the trip was $825.

Calculating amount

From the question, we are to calculate how much Janessa has in her savings before the trip

Let the amount she has in her savings before the trip be x

From the given information,

Janessa spent a third of her savings on airfare for a vacation"

That is,

She spent (1/3)x

The amount remaining after this time will be x - (1/3)x = (2/3)x

"She then spent another $300 on hotels"

The amount remaining after this time will be (2/3)x - $300

"If she has $250 left for meals and souvenirs"

That is,

(2/3)x - $300 = $250

Now, solve for x

(2/3)x - $300 = $250

(2/3)x = $250 + $300

(2/3)x = $550

x = $550 × 3/2

x = $825

Hence, the amount the she had in her savings before the trip was $825

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The polynomial is of degree 4, and the leading coefficient is -6.

A polynomial of degree N with a leading coefficient A and the zeros {x₁, x₂, x₃, ..., xₙ} (notice that we have as many zeros as the degree of the polynomial) is written as:

p(x) = A*(x - x₁)*...*(x - xₙ)

Here we have the polynomial:

g(x) -2*(3x + 4)*(x - 1)*(x - 3)²

We can expand this as:

g(x) = -2*(3x + 4)*(x - 1)*(x - 3)*(x - 3)

Think that as we have "two zeros" at x = 3.

So we have 4 factors, then the degree of the polynomial is 4.

To find the leading coefficient we just need to look at the term that comes by multiplying all the terms with "x", we will get:

-2*(3x)*x*x*X

-6*x⁴

The leading coefficient is negative.

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The required simplification of given function is [tex]\frac{(x-1)^{2}}{x-2}[/tex] and restriction on domain are x  ≠ 1, 2.

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

We have,

[tex]\frac{(x+3)(x-1)}{x-2}[/tex] ÷ [tex]\frac{x+3}{x-1}[/tex]

[tex]\frac{(x+3)(x-1)}{x-2}[/tex] × [tex]\frac{x-1}{x+3}[/tex]

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

For domain, Function should have solution should not be not defined.

For this, denominator must not equal to zero

Then, x -2 ≠ 0, x - 1  ≠ 0

x  ≠ 2, x  ≠ 1

Thus, option(3) [tex]\frac{(x-1)^{2}}{x-2}[/tex] x  ≠ 1,2 is correct.

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Answer:

  (b)  (x -1)²/(x -2), x ≠ -3, 1, 2

Step-by-step explanation:

You want to know the domain restrictions and the simplified form of ...

  [tex]\dfrac{(x+3)(x-1)}{(x-2)}\div\dfrac{x+3}{x-1}[/tex]

We can "invert and multiply", then cancel the common factor from numerator and denominator.

  [tex]\dfrac{(x+3)(x-1)}{x-2}\div\dfrac{x+3}{x-1}=\dfrac{(x+3)(x-1)}{x-2}\times\dfrac{x-1}{x+3}=\dfrac{(x+3)(x-1)^2}{(x+3)(x-2)}\\\\=\dfrac{(x-1)^2}{x-2}\qquad x\ne -3[/tex]

The values of x that must be excluded from the domain are those values for which any part of this expression is undefined. The expression is undefined when any denominator is zero: at x = 2 (left "factor"), at x = 1 (right "factor"), and at x = -3.

The factor (x +3) doesn't show up in the simplified form, but it is a "hole" in the graph of the original expression—a value of x where the function is not defined.

Here is a summary of what you get at the restricted values:

The simplified form with restrictions is ...

  [tex]\boxed{\dfrac{(x-1)^2}{x-2},\ x \ne -3,1,2}[/tex]

The probability that the randomly selected time interval is longer than 95 minutes while solving for the mean time of the eruptions is 0.3192.

mean of x = 85 minutes

σ = 21.25 minutes

x ~ N(σ², μ)

p(x < 95)

1-p(x≤95)

1 - p(z≤0.47)

Using the z table here

1-0.6808 = 0.3192

Probability of x > 95 = 0.3192

b. n = 20

from central limit theorem

1 - p (z < 2.1045)

1-0.99826 = 0.0174

1 - p (z < 2.58)

1-0.9951

= 0.0049

. What we can observe from these results is that as the sample increase is increasing from 1, 20 to 30, the probability keeps decreasing.e. The probability is very small so one has to be doubtful if they are a really the population mean or if it has to be more than that.

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It will take 54 days for Teri's account to earn an amount of $5000.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.

It is given by formula

A = [tex]p*e^{r*t}[/tex]

where:

A is final amount

p is principal amount

r is rate of interest and

t, is time period

Given: A= $5000, p=$1500, r=2.25% = 0.0225

To find: time period to get compounded amount

5000=1500×[tex]e^{0.0225*t}[/tex]

[tex]e^{0.0225t}[/tex] = [tex]\frac{10}{3}[/tex]

0.0225t = ㏑ ([tex]\frac{10}{3}[/tex])

t = 53.5099 ≈ 54 days  

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Answer:

18 Skittles and 7 Kit Kats

Linear system of equations in two variables

Step-by-step explanation:

We a linear system of two equations which can be solved simultaneously

Total pieces of candy equation
s + k = 25    [1]

Total cost equation
0.8s + 0.9k = 20.70   [2]

Multiply [1] by 0.80
0.80s + 0.80k =  20 [3]

Subtract [3] from [2]

0.80s + 0.90k = 20.70
             [tex]-[/tex]
0.80s + 0.80k =  20
[tex]\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots[/tex]
0.1k   = 0.70

k = 0.70/0.10 = 7

In [1]
[tex]s + 7 = 25\\\\s = 25-7\\\\s = 18\\\\[/tex]

Answer: 18 Skittles and 7 Kit Kats

Answer:

f(11) = 228

Step-by-step explanation:

The option that is a strict inequality is A. y>4

It should be noted that inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.

Inequalities involving < or ">" are considered "strict inequalities," whereas those involving "" or "" are not. If you "switch" the two sides of an inequality, you must then reverse the inequality symbol's direction. For example, because 4 5 is true, it follows that 5 > 4.

In conclusion, the correct option is A.

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Answer given in the screenshot below. ↓

To solve for x, we need to isolate x on one side of the equation. To do this, we can first move all the terms that do not contain x to the right side of the equation by adding 3x and 2 to both sides:

2x - 2 + 3x + 2 = -3x + 13 + 3x + 2

5x = -3x + 15

8x = 15

Dividing both sides by 8, we get:

x = 15/8

= 1.875

Therefore, the value of x is approximately 1.875.

The value of x in equation 2x-2= -3x+13 is 3

To solve this equation we need to find the value of x so that all x terms should be one side and all constants should be at ones side:

2x+3x=13+2

5x=15

Now divide both side with 5 then, we get:

5x/5=15/5

x=3

Therefore, the value of x is 3

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The value of w for the expression of angle 6w + 13 will be 13. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a quadrilateral has 4 sides. One angle of regular quadrilateral measures (6w+13).

The value of 'w' will be calculated as,

6w + 13 = 90

6w = 90 - 13

6w = 77

w = 12.83 or 13

Therefore, the value of w for the expression of angle 6w + 13 will be 13. The correct option is A.

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The equation represents the volume of the box as V = - 4s³ + 250s².

The correct option is option A

The volume of any object is the capacity. How much it can hold.

The formula of volume is a product of length, breadth and height.

Volume = L × B × H

Given:

The perimeter of the square base of side s plus height h = 250cm

as per the given question,

The perimeter of the square base of side s plus height h = 250cm

2( s + s ) + h = 250

2 (2s) + h = 250

4s + h = 250

We can express h in the terms of s as,

h= 250 - 4s

Volume = length X breadth X height

Volume = s × s × h

V = s² × h

V = s² × (250 - 4s)

V = 250s² - 4s³

The equation represents the volume of the box as V = - 4s³ + 250s².

The correct option is option A

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The probability of getting a Hybrid car = 3/14

The probability formula states that the ratio of favorable outcomes to all outcomes determines the likelihood that an event will occur.

The formula for the probability of an event is given by

P(E) = No of favorable outcomes/ total number of outcomes  

Here we have

The ratio of hybrid cars to gasoline-powered cars is 3:11

Let 3x and 11x be the number of hybrid cars and gasoline-powered cars
[ Since they are in 3: 11 ratio]  

Then total number of cars = 3x + 11x = 14x

From the given data,

Total number of cars = 280

=> 14x = 280

=>  x = 20

Number of Hybrid cars, 3x = 3(20) = 60

Here we select a car from a random experiment

Number of outcome = 280

Number of outcomes that we get Hybrid car = 60  

Thus the probability of getting a Hybrid car = [tex]\frac{60}{280}[/tex]

= [tex]\frac{6}{28}[/tex] =  [tex]\frac{3}{14}[/tex]  

Therefore,

The probability of getting a Hybrid car = 3/14

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Complete question:

The ratio of hybrid cars to gasoline-powered cars in the parking lot of a local office building is 3:11. if there are 280 cars in the lot and one is to be selected at random to get the reserved parking space nearest the building, find the probability the car selected is a hybrid. express your answer as a fraction.

The measure of PQ in the triangle is 28 units.

The line segment connecting the midpoints of  two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

Therefore, using the mid point theorem, Let find the measure of PQ.

ST = -22 + 9x

PQ = 9x - 8

The measure of PQ can be found as follows:

ST = 1 / 2 (PQ)

-22 + 9x = 1 / 2 × (9x - 8)

-22 + 9x = 9x - 8 / 2

cross multiply

2(-22 + 9x) = 9x - 8

-44 + 18x = 9x - 8

-44 + 8 = 9x - 18x

- 36 = - 9x

x = - 36 / - 9

x = 4

Therefore,

PQ = 9(4) - 8 = 36 - 8 = 28 units

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Answer:

The tree lights and the porch lights will blink together every 12 seconds.

Step-by-step explanation:

In order to determine when the two sets of lights will blink together, you must find the least common multiple (LCM) of the time periods for each set of lights. The LCM of 4 and 6 is 12, which means that the tree lights and the porch lights will both blink again after 12 seconds have passed. Therefore, they will blink together every 12 seconds.

By using the concept of circle, it can be concluded that-

Center = (1, 0) lies on x axis

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

What is a circle?

Circle is a two dimensional round figure in which every point on the circle maintains a fixed distance from a point known as the center of the circle and the fixed distance is called radius of the circle

The equation of circle is

[tex]x^2 + y^2 - 2x - 8 = 0.[/tex]

[tex]x^2 - 2x + 1 - 1-8+y^2 =0\\(x -1)^2 + y^2 = 9\\(x - 1)^2 + y^2 = 3^2[/tex]

Center = (1, 0) lies on x axis

Radius of the given circle is 3 units

Radius of x² + y² = 9 is 3

So, the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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The three quadratic equation with different maximum and/or minimum values are y = (x-4)² – 1, y = -(x-4)² + 1, and y = -3(x-4)² + 3.

Quadratic equation:

In math, quadratic equation is the algebraic equation of the second degree in x.

The general form of quadratic equation is

ax² + bx + c = 0,

where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0).

Given,

Here we need to find the three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.

As per the definition of quadratic equation, here we have to write the quadratic equation, that have the roots of 3 and 5,

Here the problem was going to call for two equations but then we have realized that it could be as simply as multiplying the a and c values by -1. Therefore, the equation are,

=> y = (x-4)² – 1,

=> y = -(x-4)² + 1,

=> y = -3(x-4)² + 3.

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The lowest cost per ounce is  12 ounces of soda which cost $0.72.

An 8-ounce of soda can costs $0.96, a 12-ounce soda can costs $0.72 and 32 ounces of a cup of soda costs $2.24.

The lowest cost per ounce can be calculated as follows:

For  8 ounces of soda can costs $0.96.

cost per ounces = 0.96 / 8

cost per ounce = 0.12 dollars per ounce

For  12 ounces soda can costs $0.72.

cost per ounces = 0.72 / 12

cost per ounce = 0.06 dollars per ounce

For  32 ounces soda can cost $2.24.

cost per ounces = 2.24 / 32

cost per ounce = 0.07 dollars per ounce

Therefore, the lowest is 12 ounces of a soda can.

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Answer:

slope 6

y intercept 4

y = 6x + 4

Step-by-step explanation:

The slope is the change in y over the change in x.  

Look at he two points (0,4) and (1,10)

The y started at 4 and went up to 10.  That is a distance of 6.

AT the same time, the x changes from 0 tp 1 (0,4) (1,10).  That is a distance of 1.

6/1 = 6

The y intercept is where the line crosses the y axis.  It crosses at (0,4).  4 is the y intercept

y = mx + b  Put the slope is for m and the y intercept for b

y = 6x + 4

The required integer to represent the loss on each play is -5m-5.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

During a football game, a team lost 10 yards on its first play and 20 yards on its third play.

To write an integer to represent the loss on each play:

Use -10 to represent losing 10 yards.

Use -20 to represent losing 20 yards.

Add both of the expression,

(-10) + (-20)

= -10 -20.

Whenever we add two negative values, the sum is negative.

(-10) + (-20) = -10 -20 = - 30

Let m be the required integer.

So, -5m-5  is the loss on each play.

Where m is the number of play.

Therefore, the required integer is -5m-5.

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Answer:

Below

Step-by-step explanation:

Angle 2     or  angle  HFE

Vertex is F

GF and  FE   are the sides of angle 1

These pairs of sets of numbers: (a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} ) ∅,{∅}  are  equal, not equal and not equal respectively

The given pairs of sets of numbers are

a) (1, 3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1} b) {{1}}, {1, {1}} c) Ø, {0}​

To determine the reasons for the answers we have

(a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1}

All the number are distinct elements without any repetition is the same in both sets.

This implies that the sets are equal

b) {{1}},{1,{1}}

From the second set of numbers, the number of elements is not the same in both sets. The number of elements in the two sets are 1 and 2.

This therefore means that the pair of numbers are not equal

c) ∅,{∅}

In the third set of numbers, the number of elements is not the same in both sets.

The number of elements in the pairs are 0 and 1 in each of the sets . This implies that the pair of sets of numbers are not equal

In conclusion these pairs of sets of numbers: (a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} ) ∅,{∅}  are  equal, not equal and not equal respectively

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Answer:

$1,136

Step-by-step explanation:

If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.

Now in the given figure, the side YD is similar and equal to the side OD so option C will be the correct answer.

Hence the information do you need to prove the triangles are congruent by SSS Will be YD ≅ OD.

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of hurricane.

In essence, atmospheric pressure is the force that the weight of the air above a particular point on the Earth's surface exerts at that location.

In other words, the weight of the air molecules as a whole determines the atmospheric pressure, which is produced by the air that surrounds the Earth.

Lower pressure is felt by air molecules at higher altitudes because there are fewer molecules pressing down on them from above, while higher pressure is felt by air molecules at lower altitudes because they are closer together and are under more pressure from molecules piled on top of them.

F(x) is the pressure in inches of mercury

It is given pressure 28 inches of mercury

Put F(x) equal to 28

F(x) = 0.48㏑(x+2) +27

28 = 0.48㏑(x+2) + 27

28-27= 0.48㏑(x+2)

1= 0.48㏑(x+2)

1/0.48= ㏑(x+2)

25/12= ㏑(x+2)

x+2= [tex]e^{\frac{25}{12} }[/tex]

x+2=8.03119

x=8.03119-2

x= 6.03119

x = 6(round off)

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Answer:

$40.63

Step-by-step explanation:

If the phone company charges $17.75 already, and each minute costs $0.13, then we can do an equation that looks something like this:

17.75 + (0.13 × 176) = total price

We need to figure out how much 0.13 multiplied by 176 is.

0.13 × 176 = 22.88

Now that we figured out that 0.13 multiplied by 176 is equal to 22.88, we need to add the monthly access fee.

22.88 + 17.75 = 40.63

The monthly cost will be $40.63.

For 45th set up 140 toothpicks  are required.

A progression of numbers in which the difference between any two succeeding numbers is always a fixed amount is known as arithmetic progression (AP). It also goes by the name Arithmetic Sequence.

given:

For First Figure, 8 toothpicks are used

For Second Figure, 11 toothpicks are used

For Third Figure, 14 toothpicks are used

So, we get the series 8, 11, 14, ...

Now, for n= 45

Using Arithmetic Progression

[tex]a_{45} = a+ (45- 1) d[/tex]

     = 8 + 44(3)

     = 140

Hence, for 45th set up 140 toothpicks  are required.

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The total number of different room designs is 1296.

According to the fundamental counting principle, if there are n ways to do one thing and m ways to do another, then there are n×m methods to accomplish both things.

Given that, there are 6 paint colors, 4 types of flooring, 6 different curtains, 3 furniture sets, and 3 light fixtures.

As per the basic principle of counting, the total number of different room designs is:
6 × 4 × 6 × 3 × 3

= 1296

Hence, the total number of different room designs is 1296.

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Answer: 7

Step-by-step explanation: 7+2