Nicole is selling lemonade at her stand. She charges $0. 75 per pint. Mr. Terry buys 36 quarts; how much money does he owe Nicole?

a) The exponential function that gives the percent P is: P = (0.85)^x.

b) The percentage of light that will pass through a cloth that is 2.75mm thick is given as follows: 63.96%.

A decaying exponential function is defined as follows:

y = a(1 - r)^x.

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 1, r = 0.15.

Hence the function is:

y = (0.85)^x.

The percentage passing through a cloth that is 2.75 mm thick is given as follows:

y = (0.85)^2.75

y = 0.6396.

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After n years Alex will earn salary which can be expressed as $(1 + 0.03)^n * 35,000.

The total amount Alex has earned in his first year of his career is $35,000.

In the second year of his career, he gets a 3% raise, which is an increase of 3/100 * $35,000 = $1,050.

So his salary for the second year is $35,000 + $1,050 = $36,050.

In the third year of his career, he again gets a 3% raise, which is 3/100 * $36,050 = $1,081.50

So his salary for the third year is $36,050 + $1,081.50 = $37,131.50

We can see that for each year, his salary is increasing by a fixed percentage of the previous year's salary.

This pattern can be represented by the expression:

(1 + 0.03)^n * 35,000

Where n is the number of years since the start of his career. This expression gives the total amount Alex has earned in his first n years of his career.

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A. The variable is qualitative because it is a numerical measure is correct answer.

Any variable that isn't numerical is referred to as a qualitative variable or a category variable. It describes information that falls into a category. for instance: Eye color (variables include: blue, green, brown, hazel).

In statistics, qualitative variables are given nominal scales since they cannot be ordered on a numerical scale. Qualitative variables are exactly what the word "nominal" means: names. No ordering is either conceivable or inferred on a nominal scale (except for alphabetical ordering like New York, Washington, West Virginia or Chelsea, Edinburgh, London). In other words, data are classified according to a category on the nominal scale.

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The rate of change in this context refers to the change in the value of p, specifically between the peak and closing.This allows us to understand how much p changes on average between these two points in time.

It is a measure of how quickly or slowly the value of p is changing over time.

By calculating the average rate of change, we can understand the overall trend of the value of p and whether it is increasing or decreasing at a steady rate or if there are fluctuations.

This information can be useful for understanding the performance of a stock or investment, as well as predicting future trends.

Additionally, the rate of change can also help to identify any potential issues or opportunities within the market.

Overall, the rate of change provides a clear picture of the stock's performance over a certain period of time.

To calculate the average rate of change of p between peak and closing, we need to find the difference in p values (p(14) - p(8)) and divide that by the difference in time (14 - 8).

p(14) - p(8) = ? - ? = ?

(14 - 8) = ?

The average rate of change of p is ?/6.

The meaning of the rate of change in the context of this problem is the average change in the value of p per unit of time.

In this case, we are looking at the average change in p between the peak and closing, and expressing that change as a ratio of p(14) - p(8) to (14 - 8). This allows us to understand how much p changes on average between these two points in time.

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Note that where the diameter of the bicycles are 60 inches and 9 inches respectively, the rotation of each tire after traveling 600 feet would be:

Small Tire (9in Diameter ) =   188.4 Rotations.

Big Tire (60 in Diameter) = 3.2 rotations

Note that the above were arrived at using the knowledge of Circumference.

Note that the circumference in geometry is the perimeter of a circle or ellipse.

This is calculated using the formula:

C = 2πr

or

C = πD

Where C = Circumference

R = radius

D = Diameter which is 2r

π = 3.14

To arrive at how many rotations each tire did, we'd have to divide the distance traveled by the circumference of each tire.

For the Small Tire, the diameter is 9 feet.

Thus, the circumference of Small Tire = 3.14 * 9

= 28.26 feet

Thus, the rotations by the small tire is:

600/28.26

= 21.2314225053

[tex]\approx[/tex] 21.2feet

Applying the same process to the big tire, we have:

C =  3.14 * 60

C = 188.4

The rotations by the big tire =
600/188.4

= 3.1847133758

[tex]\approx[/tex] 3.2 feet.

Thus, the rotations  by each tire over 600ft is given as:

Big Tire = 3.2

Small Tire =  188.4 .

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Full Question:

See attached image.

Answer: t = 10.50c

Step-by-step explanation: The relationship between the number of climbs, c, and the total cost, t, is proportional. This means that the ratio of t to c is constant. One way to represent this relationship is through an equation of the form:

t = kc

where k is a constant of proportionality. In this case, we know that 5 climbs cost $52.50, so we can use this information to find the value of k:

52.50 = k(5)

k = 52.50/5 = 10.50

So the equation that represents the total cost, t, of c climbs is:

t = 10.50c

Where t is the total cost, c is the number of climbs and 10.50 is the constant of proportionality.

The required mean of the table is 32.71.

Mean: The formula is E(X)=μ=∑xP(x). where x represents the value of the random variable X, P(x) represents the corresponding probability, and the symbol Σ represents the sum of all products xP(x). Here we use the symbol μ for mean, since it is a parameter. Represents the population mean.

Mean=Total of household/Total number of dogs

⇒ [tex]\frac{(323+176+87+51+32+8+10)}{(0+1+2+3+4+5+6)}[/tex]=[tex]\frac{687}{21}[/tex]=32.71

Standard Deviation: Standard deviation is calculated as the square root of variance by determining the deviation of each data point from the mean. If the data points are far from the mean, there will be more variation within the data set. Therefore, the wider the data, the higher the standard deviation.

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The solution for linear equations given will be x=-1 and y=2 using substitution method.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now

Given 4x+3y=2 -->1

x-2y=-5 --->2

Using substitution method, In this method, first, solve the equation for one variable, and substitute the value of the variable in the other equation.

From 2,  x=2y-5

Put x=2y-5 in 1

4(2y-5)+3y=2

11y-20=2

y=22/11

y=2

Hence,

           x=2*2-5

             x= -1

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Answer:

C. gaining confidence

Mary's Tuesday distance is 1/8 times her Monday distance

On Monday Mary ran 1 3/5 miles

= 8/5

On Tuesday Mary ran 1/5 miles

Therefore the number of times her Tuesday distance was her Monday distance can be calculated as follows

1/5 ÷ 8/5

= 1/5 ×5/8

= 1/8

Hence her Tuesday distance was 1/8 times her Monday distance

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The distance between PQ : 7

    Given  points  P: (1,6)

                            Q : (7,2)

   distance between two points formula is : √(x2-x1)^2 + (y2-y1)^2

    (x1,y1)= (1,6)

    (x2,y2) = (7,2)

    therefore

                  =  √(7-1)^2 +(2-6)^2

                  = √36+16

                  = √52

                  = 7.211

The volume of the cuboid is 16 cubic yards.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

Given:

A cuboid with height 2 yards, length 2 yards and width 4 yards.

The volume of the cuboid,

= length x width x height

= 4 x 2 x 2

= 16 cubic yards.

Therefore, the volume is  16 cubic yards.

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How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out

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The numerical value of x and the measure of segment BC are 1 and 5 respectively.

Given that; B is a point between A and C.

Since B is between A and C

AC = AB + BC

8 = 3x + 5x

Solve for x

8 = 8x

8x = 8

x = 8/8

x = 1

Next, determine the measure of BC,

BC = 5x

Plug in x = 1

BC = 5( 1 )

BC = 5

Therefore, x equal 1 and the measure of BC is 5.

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False claims do not have to engage with previous theories in order to be effective. So it must contradict previous theories. So the option d is correct.

A tentative, verifiable explanation for a natural world phenomenon is what is known as a scientific hypothesis. The scientific method's foundational element is it.

It's sometimes referred to as a "informed guess" that was made using past knowledge and observation. Despite the fact that this is true, a hypothesis is a better guess.

Creating a hypothesis calls for active observation and background research, in contrast to making a "informed guess," which implies a random prediction based on one's expertise. A hypothesis is predicated on the fundamental tenet that no outcome is predetermined.

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Answer:

[tex]\dfrac{-8y}{y-3}[/tex]

Step-by-step explanation:

[tex]\sf \dfrac{49 - y^2}{6y^2 +42y}=\dfrac{7^2-y^3}{6y^2 +6*7y}\\\\[/tex]

                 [tex]\sf =\dfrac{(7+y)(7-y)}{6y(y + 7)}=\dfrac{(7+y)(7-y)}{6y(7+y)}\\\\\\=\dfrac{7-y}{6y}[/tex]

y² - 10y + 21

sum = -10

Product = 21

Factors = (-7) , (-3)   {(-7)*(-3) = 21  & (-7)+ (-3) = -10}

y² - 10y + 21 = y² - 7y - 3y + 21

                    = y(y - 7) - 3(y - 7)

                   = (y - 7) ( y - 3)

[tex]\sf \dfrac{49 -y^2}{6y^2 + 42y}*\dfrac{48y^3}{y^2 - 10y + 21}=\dfrac{7-y}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\[/tex]

                                         [tex]\sf = \dfrac{(-1)(y-7)}{6y}*\dfrac{48y^3}{(y-7)(y-3)}\\\\\\=\dfrac{(-1)*8y^2}{y-3}\\\\\\=\dfrac{-8y^}{y-3}[/tex]

The simplest form of the expression is given as 12 + 6√3.

We know that when we are asked to simplify in mathematics, they are asking us to write the expression in the simplest form that the expression can be in. In this case, we are to simplify 6/2 - √3.

Then we would now have to multiply the numerator and the denominator by the conjugate of the denominator such that we have;

6/2 - √3 * 2 + √3/2 + √3

12 + 6√3/4 +2√3 - 2√3 - 3

12 + 6√3/1

12 + 6√3

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Answer:

It will be straight line on x equal zero and y equal 6 horizontal straight line

John will be able to meet the goal of practicing piano for mentioned time on Saturday and Sunday.

Required amount of practice = [tex]2 \frac{1}{2} [/tex] hours

Required amount of practice = (2×2)+1/2

Required amount of practice = 5/2 hours

Required amount of practice = 2.5 hours

Practice performed on Saturday = [tex]1 \frac{1}{6} [/tex]

Practice performed on Saturday = (6×1)+1/6

Practice performed on Saturday = 7/6 hours

Practice performed on Sunday = [tex]1 \frac{1}{4} [/tex]

Practice performed on Sunday = (4×1)+1/4

Practice performed on Sunday = 5/4 hours

Combined practice performed = 7/6 + 5/4

Combined practice performed = 1.2 + 1.3

Performing addition

Combined practice performed = 2.5 hours

The performed practice is equal to the goal and hence he will meet the goal.

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The probability of selecting sticks with a boy's name is 8/13 and the probability of selecting sticks with a girl's name is 2/5.

Now, According to the question:

Formula to find the probability of an event:

"P(A) = n(A) / n(S)

where, n(A) is the number of favorable outcomes of an event A

n(S) is the total number of outcomes for an experiment"

"Information available from the question"

Total number of students are,

n(S) = 10 + 16

n(S) = 26

Let event A: selecting first stick with a boy name

n(A) = 16

So, the probability of a boy is,

P(A) = n(A)/n(S)

P(A) = 16/26

P(A) = 8/13

if the first stick is not replaced, then n(S) would be,

26 - 1 = 25

Let event A: selecting first stick with a boy name

n(B) = 10

So, the probability of a boy is,

P(B) = n(B)/n(S)

P(B) = 10/25

P(B) = 2/5

Therefore, the probability of selecting sticks with a boy's name is 8/13 and the probability of selecting sticks with a girl's name is 2/5.

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Answer:

Start at 1 on y-intercept and go down 2 units and right 1 unit

Step-by-step explanation:

First you have to graph your y-intercept (1) *which is the red dot in the graph I made for you*

Then you must use your slope (-2) to graph the rest

Since your slope is negative you have to go down from your y-intercept. In your case you are going down 2 units from your intercept. And since your slope is a whole number instead of a fraction you just go to the right 1 unit to make the coordinate (1,-1).

That is how you graph your equation.

I hope this helped!

We randomly take a card, if it is not a, then the probability that it is b, is 1/4.

We have to find the the probability that it is a card of b, if it is not a.

We have total number of cards = 20

The cards of a = 10

The cards of b = 5

The cards of c = 5

We don't select the card a, then;

The probability of choosing card b = The total number of card b/total number of cards

The probability of choosing card b = 5/20

The probability of choosing card b = 1/4

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The total amount spent by John is $37.78.

Given is that John goes to a restaurant and has a bill of 32.57. He uses a 10% off coupon on the cost of the meal. The tax is 8%. He leaves a tip of 18% on the amount before the coupon or tax is applied.

Amount left as a tip -

{t} = 18% of 32.57

{t} = 18/100 x 32.57

{t} = 5.87

Amount included in tax -

8% of 32.57

8/100 x 32.57

2.61

Billed amount after coupan is applied -

10% of 32.57

10/100 x 32.57

$3.26

Amount spend -

(32.56 - 3.26) + 2.61 + 5.87

$37.78

Therefore, the total amount spent by John is $37.78.

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The final cost of the laptop be if jamal buys it on saturday is $695.79

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

The new laptop is currently priced at $859

On saturday the store is giving a 25% discount off all laptops

Sales tax on final purchase=8.5%

Now, the final value on saturday be x

x*100/859=25

x=25*859/100

x=214.75

The value will be 859-214.75=644.25

8% of 644.25

x*100/644.25=8

x=8*644.25/100

x=51.54

Final cost= 644.25+51.54

=695.79

Therefore, the final cost after 8 percent sales tax will be $695.79

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The correct solution for the following system of Inequalities is (-1, 1) because it is on the darker region.

An equation is an expression that shows the relationship between numbers and variables.

Inequalities is used for the non equal comparison of these numbers and variables.

Let x represent the x axis and let y represent the y axis.

The solution to the system of linear equalities is the intersection of both inequalities which is the darker region.

The point that satisfies both inequalities as shown on the graph is (-1, 1) because it is on the darker region.

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Answer:

97 inches

Step-by-step explanation:

Using law of sines, we know that y/sin∠Y = z/sin∠Z.

Solve:

[tex]\frac{500}{sin117}[/tex] = [tex]\frac{z}{sin10}[/tex]

Therefore, z = (500/sin117)(sin10)

Enter this into a calculator to get:

z = 97.44495296, which rounds to 97 inches.

I hope this helps! :D

The coordinates of vertices after dilation by scale factor of 1.5 with center of dilation is D'(3,-3), E'(6,-3) and  F'(1.5,-6).

A dilation is just a transformation which enlarges or contracts the size of a figure. This means that the preimage and image are similar and are scaled up or down using a factor.

The vertices of the triangle are D(2,-2), E(4,-2), F(1,-4).

The origin-centered dilation with a scale factor of k is defined as,

(x,y) → (kx,ky)

As a result, dilation with a scale factor of 1.5 centered at the origin is defined as,

(x,y) → (1.5x,1.5y)

The image's vertices are

D(2,-2) → D'(3,-3)

E(4,-2) → E'(6,-3)

F(1,-4) → F'(1.5,-6)

Therefore the coordinates of vertices after the dilation by the given scale factor 1.5 is D'(3,-3), E'(6,-3) and  F'(1.5,-6).

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Answer: x = -8

Step-by-step explanation:

12 ( x + 10 ) = 24

First we divide the two sides of the exercise by 12.

[tex]\boldsymbol{\sf{x+10=\dfrac{24}{12} }}[/tex]

We divide 24 by 12..

x + 10 = 2

Subtract 10 from both sides.

x = 2 - 10

Subtract 10 from 2 to get. Since the number 10 is greater than 2, the result will be negative.

x = -8

Answer:

[tex] \sf \: x = - 8[/tex]

Step-by-step explanation:

Given equation,

→ 12(x + 10) = 24

Now the value of x will be,

→ 12(x + 10) = 24

→ 12(x) + 12(10) = 24

→ 12x + 120 = 24

→ 12x = 24 - 120

→ 12x = -96

→ x = -96 ÷ 12

→ [ x = -8 ]

Hence, the value of x is -8.