The winner of the 1998 Peoria 500 (mile) race was Serge Bologna, with an average rate
of 123.362 mi per hr. What was his time (to the nearest thousandth of an hour)?

The exponential function that is represented by the graph is f(x) = 2(2x).

This is because the graph shows a function with a base of 2 and an exponent of x. The function f(x) = 2(2x) has a base of 2 and an exponent of x, so it matches the graph.

To verify this, we can plug in some values of x into the function and see if they match the points on the graph. For example, when x = 0, the function gives us f(0) = 2(2^0) = 2(1) = 2, which matches the point (0, 2) on the graph. Similarly, when x = 1, the function gives us f(1) = 2(2^1) = 2(2) = 4, which matches the point (1, 4) on the graph.

Therefore, the correct answer is f(x) = 2(2x).

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12.3 hours or 12 hours and 18 minutes.

This suggests that Desmond's family has decreased their TV-watching time by 12.3 hours in the past week.

This can be expressed numerically as 12.3 hours, or 12 hours and 18 minutes.

To calculate this, we can subtract 17.7 hours from 30 hours:

Last week: 30 hours of TV

This week: 17.7 hours of TV

30 hours - 17.7 hours = 12.3 hours

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In the given situation the required area of the polygon is 258ft².

A polygon is a closed polygonal chain made up of a finite number of straight-line segments and is a type of planar figure in geometry.

A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.

A polygonal circuit's segments are referred to as its edges or sides.

Like other concepts in geometry that they created, the word "polygon" is Greek in origin. It merely denotes a lot of (poly) angles (gon).

There cannot be any bends, gaps, or openings in the shape of a polygon.

So, an object's area is how much space it takes up in two dimensions.

A rectangle's area is calculated as follows:

Area = length * breadth

Now, calculate the area as follows using the formula:

Area = [18 * (21 - 12)] + (12 * 8) = 258 ft²

Therefore, in the given situation the required area of the polygon is 258ft².

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In this polygon, all angles are right angles. What is the area of this polygon? Enter your answer in the box. ft² Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle. The left side of the figure is 18 ft, the bottom side of the figure is 21 ft, the right side of the figure is 8 ft, and the top part of the horizontal rectangle to the right of the vertical rectangle is 12 ft.

Answer:

Below

Step-by-step explanation:

Definition of density is  mass / volume = 1250 g / (5 x14x7) = 2.55 gm/cm^3

12.6 is the measure of the value of x

The given diagram is a right triangle and we need to determine the measure of value of 'x'.

First, we need to determine the measure of the height using the trigonometry identity;

cos55 = h/45

h = 45cos55

h = 25.81

Determine the measure of 'x'

tan 64 = h/x

x = h/tan64

x = 25.81/tan64

x = 12.6

Hence the measure of the value of x from the fiigure is 12.6

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The solutions of the system of inequalities are:

(0, 3)

(6, 2)

Here we have the graph of a system of inequalities, the solutions are all the points on the area where the two shaded regions intercept (it would be on the purple area).

And we can see that one line is solid, the points on that line are solutions, the other line is dashed, the points on that line are not solutions.

Then the points that are solutions are:

(0, 3)

(6, 2)

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As a result, it will take around 4.9 hours for the quantity of medicine remaining in the body to decline to 0.25 milligrams.

In mathematics, an exponent (also known as power or index) is a number that indicates how many times a base number is multiplied by itself. It is written as a superscript to the right of the base number. For example, in the expression 2³, 2 is the base number and 3 is the exponent. The exponent 3 indicates that the base number 2 is multiplied by itself 3 times, resulting in the value 8. Exponents are a shorthand notation for repeated multiplication and are used in many areas of mathematics and science.

Here,

The given model for the amount of the drug left in the patient after t hours is:

A(t) = 25e*(0.354t)

We need to find the time t when the amount of the drug left in the patient is 0.25 milligrams. So we can set A(t) = 0.25 and solve for t:

0.25 = 25e*(0.354t)

Dividing both sides by 25, we get:

0.01 = e*(0.354t)

Taking the natural logarithm of both sides, we get:

ln(0.01) = 0.354t

Simplifying, we get:

t = ln(0.01)/0.354 ≈ 4.9 hours

Therefore, it will take about 4.9 hours for the amount of the drug left in the patient to drop to 0.25 milligrams.

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The solution is, the length of MP = 9.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

from the given figure we get,

MPN is a right angled triangle,

by using Pythagorean theorem, we get,

here, height = 12

hypotenuse = 15

so, base = MP

              = √15²  - 12²

              =√81

              =9

Hence, The solution is, the length of MP = 9.

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Answer: The slope of the line between the points (-5, -4) and (1,-3) is 1/6 = 0.1667.

Step-by-step explanation:

To calculate the slope between two points, we apply the following formula:

[tex]\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff \ m=\dfrac{y_2-y_1}{x_2-x_1} }}[/tex]

where m is the slope of the line.

We identify the points:

     [tex]\boldsymbol{\sf{\diamond x_1=-5 \ \ \ \ \diamond y_1=-4 \ and \ x_2=1 \ \ \ \ \diamond y_2=-3 }}[/tex]

We substitute these points in the formula and solve:

          [tex]\boldsymbol{\sf{m=\dfrac{-3-(-4)}{1-(-5) }=\dfrac{1}{6}=0.1667 }}[/tex]

The slope of the line between the points (-5, -4) and (1,-3) is 1/6 = 0.1667.

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The value of x when we solve the equation 6/ -4.5 = 8/4x is x = - 1.5.

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. Another well formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's equivalents in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French.

The given equation is:

6/ -4.5 = 8/4x

Using the method of cross multiplication or butterfly method of multiplication we have:

6(4x) = (8)(-4.5)

24x = -36

x = -1.5

Hence, the value of x for the equation 6/ -4.5 = 8/4x is x = - 1.5.

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The required, we need to pay $0.132 in tax on the item that cost $3.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
To calculate the amount of tax, we need to multiply the cost of the item by the tax rate. The tax rate is 4.4% or 0.044 as a decimal.

So, the amount of tax on the item is:

0.044 × $3 = $0.132

Therefore, we need to pay $0.132 in tax on the item.

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Applying the AA Similarity theorem:

AC = 10

AB = 20

If two triangles have two corresponding congruent triangles they are similar to each other according to the AA Similarity theorem, which means their corresponding sides are proportional.

Triangles DCE and ACB are similar to each other by AA Similarity theorem, therefore:

AC/CE = BC/CD

Substitute:

AC/8 = 15/12

AC = (15 * 8)/12

AC = 10

Also,

AB/16 = 15/12

AB = (16*15)/12

AB = 20

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Answer:

To solve the system of linear equations:

x_1 + 3x_2 = 1 ...(1)

2x_1 + 5x_2 = 3 ...(2)

We can use the method of elimination to eliminate one of the variables. To do this, we multiply equation (1) by 2, and subtract it from equation (2), as follows:

2(x_1 + 3x_2 = 1) => 2x_1 + 6x_2 = 2 ...(3)

2x_1 + 5x_2 = 3 ...(2)

(2x_1 + 6x_2 = 2) ...(3)

-x_2 = 1

Thus, we have found that x_2 = -1.

We can substitute this value of x_2 into either equation (1) or (2) to solve for x_1. Let's use equation (1):

x_1 + 3(-1) = 1

x_1 - 3 = 1

x_1 = 4

Therefore, the solution to the system of linear equations is x_1 = 4, x_2 = -1.

So the solution set is {(4, -1)}.

The time series data should show a. trend b. cyclical c. seasonal, so the correct answer is d. all of the options are correct.

Time series data refers to a collection of data points that are measured over time at regular intervals. The time series data could refer to various metrics such as sales, revenue, foot traffic, website traffic, inventory levels, and other relevant business metrics that change over time.

By analyzing time series data, businesses can gain insights into trends, patterns, and other factors that can affect their operations.  

Time series can be used for forecasting. By analyzing past trends and patterns, businesses can make predictions about future performance and take proactive measures to achieve their goals.  

Since the time series will follow the trend, have multiple choices, and will be cyclical and it will analyze the patterns over time periods seasonally.

Therefore,

The time series data should show a. trend b. cyclical c. seasonal, so the correct answer is d. all of the options are correct.

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With the original price at 25 units , he paid 23 units and d(25) means the price he paid when the original price is 25 units.

Phil works at a department store and gets an employee discount. The price he pays can be modelled by the function d(c) = c - 0.08c , where c is the original price of the item.

Therefore, let's find d(25) and describes what it means.

Hence,

d(c) = c - 0.08c

where

Therefore,

d(25) = 25 - 0.08(25)

d(25) = 25 - 2

d(25) = 23

Therefore, d(25) is the price he paid when the original price is 25 units. Therefore, he paid 23 units

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The sinusoidal function is y = sin(2/3x) - 5

The general form of a sinusoidal function is given by:

y = A sin(Bx + C) + D

where:

We know that the period is 3π and the amplitude is 1.

So, we have

A = 1

B = (2π)/(3π) = 2/3

So, we have

y = sin(2/3x + C) + D

The point (-3π/2, -5) implies that, the function is shifted down by 5 units

So, we have

y = sin(2/3x) - 5

Hence, the function is y = sin(2/3x) - 5

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The monthly cost for 39 minutes of calls is $14.30.

Let's start by using the given information to find the slope and y-intercept of the linear function that gives the monthly cost in terms of the total calling time. We can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

Using the points (34, 14.69) and (57, 17.68), we get:

m = (17.68 - 14.69) / (57 - 34) = 0.09

To find the y-intercept, we can use the point-slope form with either of the two points:

y - 14.69 = 0.09(x - 34)

y - 14.69 = 0.09x - 3.06

y = 0.09x + 11.63

So the monthly cost (y) is a linear function of the total calling time (x) with a slope of 0.09 and a y-intercept of 11.63.

To find the monthly cost for 39 minutes of calls, we simply substitute x = 39 into the equation:

y = 0.09(39) + 11.63 = 14.30

Hence, the monthly cost for 39 minutes of calls is $14.30.

What is cost price ?

Cost price refers to the amount of money that is paid to purchase an item or produce a good. It includes all the costs incurred in the production or acquisition of an item, such as the cost of raw materials, labor, and other expenses. Cost price is important for businesses because it helps determine the profit margin on a product, which is the difference between the selling price and the cost price. A business needs to set a selling price that covers the cost of producing or acquiring a product and leaves room for profit.

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Step-by-step explanation:

let length and width be increased by x>0

(10+x)(5+x)=6×10×5

50+10 x+5x+x²=300

x²+15x-250=0

x²+25 x-10x-250=0

x(x+25)-10(x+25)=0

(x+25)(x-10)=0

x=-25(rejected),10

so x=10

The trigonometric ratios are given as follows:

a) cos(y) = -0.94.

b) sin(x) = 0.94.

The tree bisects an angle into two equal angle measures, one of which is of 70º and the other of which is of x.

Hence the measure of x is given as follows:

x = 70º.

The sine is given as follows:

sine of 70 degrees = 0.94.

The sum of the measures of the internal angles of a triangle is of 180º, hence the missing internal angle is of 20º.

An internal angle is supplementary with it's external angle, hence the value of y is given as follows:

y = 180 - 20

y = 160º.

Then the cosine is of:

cosine of 160 degrees = -0.94.

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The union member worked 176 hours during the month of March.

Dues are the payment or obligation required by law or custom, it is like a monthly payment, fees or charges made by organizations.

Let h be the number of hours worked during the month of March by the union member.

According to the problem statement, the union charges monthly dues of $5.00 plus $0.15 for each hour worked during the month.

So, the total dues for the month of March can be expressed as -

Total dues = $5.00 + $0.15 x h

It is also given that the union member's dues for March were $31.40.

Set up an equation using this information as follows -

$31.40 = $5.00 + $0.15 x h

To solve for h, isolate the variable on one side of the equation.

Start by subtracting $5.00 from both sides -

$31.40 - $5.00 = $0.15 x h

Simplifying the left side gives -

$26.40 = $0.15 x h

To solve for h, divide both sides by $0.15 -

h = $26.40 / $0.15

h = 176

Therefore, the number of hours is 176.

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The transformations that are needed to graph the given function is

Shrink the graph vertically by a factor of 3.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

f(x) = x²

g(x) = x² - 3

We see that,

f(x) → g(x)

There is a vertical shrink by a factor of 3.

Thus,

There is a shrinking vertically of f(x) by a factor of 3.

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Answer: The answer is 6.

Step-by-step explanation:

The index value of 99.2 in 1980 mean Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992, the correct option is D.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

Years, prices, prices as a percentage of 1990 price, price index 1990=100

Now,

The given table shows the average gasoline prices per gallon for various years, as well as the price index for each year, with 1990 being the reference year with a price index of 100. The price index measures the change in the price of gasoline relative to the price in 1990. Therefore, the price index value of 99.2 for 1980 means that the average gasoline price in 1980 was 0.992 times the price of gasoline in 1990.

It is important to note that the gas price index does not directly measure the cost per gallon of gas. Rather, it is a measure of the change in gasoline prices over time, with a reference year (in this case, 1990) used as a baseline.

Therefore, by ratio the answer will be  Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992.

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Answer:

The subtraction expression to determine the change in temperature is:

-11 °C - (-6 °C)

Simplifying the expression:

-11 °C + 6 °C

The change in temperature is -5 °C.

Therefore, the probability that the first number divided by the second number is greater than zero is 1/3.

In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and expressing how likely it is that a particular outcome will occur. Probability theory is used in a wide range of fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It is used to model and analyze random phenomena, make predictions, and estimate the likelihood of certain outcomes.

Here,

Since we are returning the first tile to the bag before selecting the second one, the two selections are independent of each other.

There are two cases to consider:

Case 1: We select a positive number on the first draw.

The probability of selecting a positive number on the first draw is 2/3, since there are two positive numbers (-12 and 1) out of a total of three tiles.

Regardless of what number we select on the first draw, there is only one negative number (-2) in the bag, so the probability of selecting a negative number on the second draw is 1/3.

Therefore, the probability of selecting a positive number on the first draw and a negative number on the second draw (which results in a quotient greater than zero) is:

(2/3) x (1/3) = 2/9

Case 2: We select the negative number (-2) on the first draw.

The probability of selecting the negative number (-2) on the first draw is 1/3.

In this case, we must select the positive number on the second draw in order for the quotient to be greater than zero. There is only one positive number (1) in the bag, so the probability of selecting it on the second draw is 1/3.

Therefore, the probability of selecting the negative number (-2) on the first draw and the positive number on the second draw (which results in a quotient greater than zero) is:

(1/3) x (1/3) = 1/9

Since these are the only two cases that satisfy the condition, the overall probability is the sum of the probabilities of these two cases:

2/9 + 1/9 = 3/9 = 1/3

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The boys agreed that each person would earn the same amount after Curran was reimbursed the money he spent on gas. After a week of work, the boys were paid a total of $177. thus each boy earned $88.50.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Let's denote the amount each boy earns by x.

According to the given information, Curran spent $20 for gas, which he should be reimbursed for. This means that the total revenue of the business was $177 + $20 = $197.

Since each person earns the same amount, we can set up an equation:

2x + $20 = $197

Simplifying and solving for x, we get:

2x = $177

x = $88.50

Therefore, each boy earned $88.50.

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Answer: 1/52 or 1.923%

Step-by-step explanation:

Due to the fact that the standard deck of 52 cards has 4 Kings then out of 52 is 1 that is going to be a black card. Hence the 1/52 as for the 1.923% is the percentage form of 1/52 for either or you need.

Answer:

The efficiency of the ACB radio is 68%.

Step-by-step explanation:

here is a step-by-step explanation of how to calculate the efficiency of the ACB radio:

Recall that the efficiency of a radio is the ratio of the power delivered to the antenna to the input power, expressed as a percentage.

Identify the given values: we are told that the ACB radio is rated at 7.5 watts, and it delivers 5.1 watts to the antenna.

Plug in the values to the efficiency formula: Efficiency = (Power delivered to the antenna / Input power) x 100%. Using the given values, we get: Efficiency = (5.1 / 7.5) x 100%.

Perform the division: 5.1 divided by 7.5 equals 0.68, or 68% when multiplied by 100%.

Round the answer: The prompt asks for the answer to be rounded to two decimal places, so we get 0.68 rounded to two decimal places is 0.68.

State the answer: The efficiency of the ACB radio is 68%.

the total area of all four square faces:  4 x 60.5 cm² = 242 cm²

To find the surface area of a rectangular prism, we need to calculate the area of each of its six faces and then add them up.

The two rectangular faces are congruent, so we only need to calculate one of them and multiply by 2.

The area of one rectangular face is:

6 cm x 5.5 cm = 33 cm²

Multiplying by 2 gives us the total area of both rectangular faces:

2 x 33 cm² = 66 cm²

The other four faces are also congruent, so we only need to calculate one of them and multiply by 4.

The area of one of the square faces is:

11 cm x 5.5 cm = 60.5 cm²

Multiplying by 4 gives us the total area of all four square faces:

4 x 60.5 cm² = 242 cm²

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