one mousetrap car contestant researched the speed of actual race cars. he found that when nascar drivers race on the phoenix international raceway they make 312 laps. in april 2009 the race that was held there lasted for about 3 hours. what was the approximate rate the racers were traveling one mouse trap car contestant research the speed of actual race cars he found that one NASCAR drivers race on the Phoenix International Raceway they make 312 laps in April 2009 the race that was held there lasted for about 3 hours what was the approximate right the races were traveling ​

The volume of concrete required for the first 12 steps is 132.6 cubic feet

Given data

the first step requires 1.7 cubic feet of concrete

the first 4 steps require a total of 17 cubic feet

the first term = a = 1.7

4th step =  n/2 ( 2a + ( n - 1 ) d )

d is common difference

n = number of terms

17 = 4/2 ( 2*1.7 + ( 4 - 1 ) d )

17 = 2( 3.4 + 3d )

8.5 = 3.4 + 3d

5.1 = 3d

3d = 5.1

d = 1.7

sum of AP at 12th step

12th = n/2 ( 2a + ( n - 1 ) d )

12th = 6( 2 * 1.7 + ( 12 - 1 ) * 1.7)

12th = 6 (3.4 + 11 * 1.7)

12th = 6 * 22.1

12th = 132.6 cubic feet

The volume of concrete required for the first 12 steps is 132.6 cubic feet

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The answers are given below:-

a) The exponential function is: [tex]y(t) = 500e^{-0.0117593}[/tex]

b) The rule is: [tex]y(t) = y(0)(\dfrac{358}{500})^{\frac{t}{8}[/tex]

c) The half-life of the element is of 16.599 days.

The mathematical expression  [tex]f(x) = e^x[/tex] denotes the exponential function. The phrase typically refers to the positive-valued function of a real variable, unless otherwise specified.

Following t days, the substance's amount's exponential function is given by:

[tex]y(t) = y(0)e^{-kt}[/tex]

For this problem, we have that:

y(0) = 500, y(8) = 358.

Hence we can solve for k as follows:

[tex]y(t) = y(0)e^{-kt}[/tex]

[tex]358=500e^{-8k}[/tex]

[tex]e^{-8k}=\dfrac{358}{500}[/tex]

[tex]lne^-8k}=ln0.716[/tex]

-8k = ln(0.716)

k = -ln(0.716)/8

k = 0.041759389.

Hence:

[tex]y(t) = 500e^{-0.0117593}[/tex]

For item b, 358/500 of the material is what is left over after each 8-day period, therefore f(t) = t/8, and the rule is as follows:

[tex]y(t) = y(0)(\dfrac{358}{500})^{\frac{t}{8}[/tex]

For item c, using the rule from item a, we have to find t for which y(t) = 0.5y(0), hence:

[tex]y(t) = y(0)e^{-0.0117593}[/tex]

[tex]0.5y(0)=y(0)e^{-0.0117593[/tex]

[tex]e^{-0.0117593}=0.5[/tex]

[tex]lne^{-0.0117593}=ln0.5[/tex]

-0.041759389t = ln(0.5)

t = -ln(0.5)/0.041759389

t = 16.599.

The half-life of the element is of 16.599 days.

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The length of the line segment IJ is 9.

In this question we find that the line segments IJ and JK are collinear, that is, part of one same line. By Euclidean geometry and algebra, we construct the following formula:

IK = IJ + JK        

IJ = IK - JK

If we know that IK = 19 and JK = 10, then the length of the missing line segment is:

IJ = 19 - 10

IJ = 9

The length of the line segment IJ is 9.

The statement is poorly formatted, correct form is shown:

The point J is on line segment IK. Given that JK = 10 and IK = 19, determine the length IJ.

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Answer:

1. 11,207.23

2. 11,285.58

3. 11,303.49

4. 11312.52

I don't know if the last one is correct

The Ferris wheel in discuss which has 15 cars that are equally spaced around the circumference as described rotates 24° between successive cars being at the bottom.

It follows from the task content that the Ferris wheel in discuss has 15 cars spaced around it.

Since the Ferris wheel in discuss is circular and has a total angle measure of 360.

Hence, the total angle rotated between successive cars can therefore be evaluated as;

Angle rotated = 360°/15

= 24°.

Ultimately, The Ferris wheel in discuss which has 15 cars that are equally spaced around the circumference as described rotates 24° between successive cars being at the bottom.

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Answer:

c = -4

Step-by-step explanation:

c³ = -64

∛c³ = ∛-64

c = -4

Check:

-4 *-4 * -4 = -64

The values of the unknown variables a,b,c,d,e and f is 8, 7, -3, 6, 1, and 2 respectively.

The code is 2 ( 7 + 6 ) + 8 ( 1 - ( - 3 ) ).

1.given that

[tex] x^4 . x^a = {x}^{12}[/tex]

we know the formula

[tex] a^m . a^n = {a}^{m+n}[/tex]

so, [tex] {x}^{(4+a)} = {x}^{12}[/tex]

if bases are equal then Powers will be equals.

then 4 + a = 12

a = 12 - 4

a = 8.

2. given that.

[tex] (y^b)/(y^5)= y^2[/tex]

we know the formula

[tex] a^m/a^n = {a}^{(m-n)}[/tex]

so, [tex] {y}^{(b-5)} = y^2[/tex]

when bases are equal then Powers will be equal.

b - 5 = 2

b = 2 + 5

b = 7

3.given that

[tex] 3^c = (1)/(27)[/tex]

so, [tex] 3^c = ( 1/3)^3 [/tex]

[tex] 3^c = {( 3/1)}^{-3} [/tex]

if bases are equal then Powers will be equals.

then c = -3.

4.given that

[tex] (m^3)^2 = m^d[/tex]

we know the formula

[tex] (a^m)^n = {a}^{m.n}[/tex]

[tex] m^6 = m^d[/tex]

if bases are equal then Powers will be equals.

then d = 6

5. given that

[tex] 7^0 = e[/tex]

e = 1

6. given that

[tex] {4}^{(-2) }. {4}^{9}. {4}^{(-5)} = 4^f[/tex]

we know the formula

[tex] a^m . a^n = {a}^{(m+n)}[/tex]

so, [tex] {4}^{(-2+9-5)} = 4^f[/tex]

if bases are equal then Powers will be equals.

then -7+9 = f

f = 2.

Hence, the values of the unknown variables a,b,c,d,e and f is 8, 7, -3, 6, 1, and 2 respectively.

The code is

f ( b + d ) + a ( e - c )

2 ( 7 + 6 ) + 8 ( 1 - ( - 3 ) ).

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Answer:

b is the answer

Step-by-step explanation:

b is the answer

The output of the equation after transformation is y=3x^2 - 1.

According to the statement

We have to find that the mathematical transformation.

So, For this purpose, we know that the

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

From the given information:

The details are:

y=3x^2 + 2 translated down three units

According to this it is clear that the there is decrease of the 3 numbers.

Then the equation become:

y=3x^2 + 2

After transformation of the 3 units then:

y=3x^2 + 2 -3

y=3x^2 - 1

Then the output gets the y=3x^2 - 1.

So, The output of the equation after transformation is y=3x^2 - 1.

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Step-by-step explanation:

the line is perpendicular to

y = 2x.

and it goes through the point (1, 2).

the point-slope form looks like

y - y1 = a(x - x1)

"a"being the slope, and (x1, y1) being a point on the line.

the slope-intercept form is

y = ax + b

"a" is again the slope, "b" is the y-intercept (the y value when x = 0).

as you can see, we need the slope of the new line in both cases.

then we will start with the point-slope form, and transform it into the slope-intercept form.

the slope of a line is generally the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

it is always the factor of x.

we can see it is 2 for the original line. that means 2/1.

a perpendicular slope is turning the x and y values upside down, and is flipping the sign.

so, in our case it is

-1/2

so, starting with the new slope and the point to create the point-slope form :

y - 2 = -1/2 × (x - 1)

and from there we transform into the slope-intercept form :

2y - 4 = -x + 1

2y = -x + 5

y = (-x + 5)/2 = -1/2 x + 5/2 = -1/2 × (x - 5)

all of the expressions in the last line are valid forms to write it.

option B. g(x)=-2, x<-2, option D. g(x)=-2x+6, x>1 and option E. g(x)=x/2+1 represent a piece of the function in given graph.

The graph of a function is a collection of all ordered pairs of the relation. These are usually represented as points in a Cartesian coordinate system. It is a relationship between an independent variable and a dependent variable. The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x).

Reasons are given below:

In first option that is g(x)=-2x, -2<x<0, we can see a negative sign which indicates that the graph should be downward (negative slope). Also, g(x)=-2x has no y-intercept therefore g(x)=-2x, -2<x<0 does not represent a piece of the function in given graph.

In second option that is g(x)=-2, x<-2, we can see a negative sign and no y-intercept which indicates that it is a horizontal line parallel to x-axis. Also given that x is less than -2, therefore the line should move away from y-axis to the left where lies more negative values. The given data matches the slope given in third quadrant. Hence, it represents a piece of function in given graph.

In third option that g(x)=x-2, -2<x<1, we can see that the function indicates that it has y-intercept at y=-2 and a slope of value 1(positive) which means it should move in upward direction and must cut y-axis at y=-2. The given data does not match with the graph given. Hence, it does not represent a piece of function in the given graph.

In fourth option that is g(x)=-2x+6, x>1, we can see negative sign therefore it should be downward and +6 indicates that it is  with y-intercept too. Hence the given data matches with the graph given and therefore it represents a piece of the function in the given graph.

In fifth option that is g(x)=x/2+1, -2<x<1. As we can see, x lies between -2 and 1, to understand let us assume x=2 then x/2=2/2=1. Therefore, the slope can start at x=1 and extend till -2. Hence, it represents a piece of the function in the given graph.

Therefore, Functions g(x)=-2, x<-2, g(x)=-2x+6, x>1 and g(x)=x/2+1 represent a piece of the function in the given graph.

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Answer:

$840.77

Step-by-step explanation:

The amount of the 1167 rupees he have to pay every month according to the interest rate.

According to the statement

We have to find that the monthly repayments.

So, For this purpose, we know that the

Interest rate is the annual rate that is charged for borrowing , expressed as a single percentage number that represents the actual yearly cost of funds over the term of a loan.

From the given information:

A couple buys furniture for R50 000. They put down a cash deposit of 20% and pay off the balance using a higher purchase agreement, over 4years. The institution charges interest of 10% p.a and monthly Insurance fee of R75.00.

Then

A couple buys furniture =  50,000

cash deposit of 20% = 20% of 50,000

cash deposit = 20/100*50,000

cash deposit = 0.2*50,000

cash deposit = 10000

Left money on which company put interest of 10% =50000 - 10,000

Left money on which company put interest of 10% = 40,000

Then

interest amount per year = 10% of  40,000

interest amount per year = 10/100*40,000

interest amount per year = 0.1*40,000

interest amount per year = 4000

It means interest paid by the customer in 4 years = 4000*4

It means interest paid by the customer in 4 years = 16000

Then

Total money he pays with interest rate in 4 years = 16000 +40,000

Total money he pays with interest rate = 56000

Then

The money he have to pay every month in 4 years = 56000/48

The money he have to pay every month in 4 years = 1167.

So, The amount of the 1167 rupees he have to pay every month according to the interest rate.

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Based on the fixed costs and the equilibrium point, the function for total costs would be TC = 300 + 100VC

The total cost that a company incurs for making a good or service is a combination of both the fixed cost and the variable cost.

The total variable cost is found as:

= Number of units produced x variable cost per unit

= 100 units x vc

= 100vc

The total cost would therefore be:

= Fixed cost + Total variable cost

= 300 + 100vc

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Answer:

C - 8.2*10^-2

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

10^-2 = 0.01

0.01 × 8.2 = 0.082

By solving inequality  [tex]x[/tex] ∈ [tex][-2,3)[/tex]

What is inequality?

A declaration of the relation in terms of greater, greater than or equal to, smaller, or less than or equal to between two numbers or algebraic expressions is known as inequality.

[tex]4\leq 3x+10 < 19[/tex]

Rearranging the above equation

[tex]\left \{ {{4\leq 3x+10} \atop {3x+10} < 19} \right.[/tex]

Subtracting 10 from the above equation

[tex]\left \{ {{4-10\leq 3x+10-10} \atop {3x+10-10 < 19-10}} \right[/tex]

[tex]\left \{ {{-6\leq 3x} \atop {3x < 9}} \right.[/tex]

Dividing the above equation by 3

[tex]\left \{ {{\frac{-6}{3}\leq \frac{3x}{3} } \atop {\frac{3x}{3} < \frac{3}{3} }} \right.[/tex]

[tex]\left \{ {{-2\leq x} \atop {x < 3}} \right[/tex]

[tex]-2\leq x < 3[/tex]

Therefore, by solving inequality we get  [tex]x[/tex] ∈ [tex][-2,3)[/tex]

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The value of the linear equation after multiplying is 8/xX.

According to the statement

We have to find that the value of the statement.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

The equation is a:

7+1/X (1/x)

Here we know that the X and x are the different variables.

Then

7+1/X (1/x)

Now add the terms which are possible then

8/X (1/x)

Now, multiply the terms which are possible to multiply

Then the equation become

8/xX.

So, The value of the linear equation after multiplying is 8/xX.

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The mistake is that in both numbers 0.304 and 0.340, 4 is in the tenth position following the point.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs is known as a mathematical expression. A place-value system gives a number's specific location within a series a value.

Karin's softball batting average is 0.304, whereas Cheryl's is 0.340. They have the same average, according to Karin.

Because the numbers 0.340 and 4 are in the tenth position, as opposed to 0.304 and 4, the values are different from one another.

He made a mistake in his estimation because both averages are equal.

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The points of the graph are (0,-2), (4,1) and they are drawn on the graph below. The graph of the equation y= (3/4)x – 2 is a straight line.

The totality of the points in the plane with the form (x, f(x)) that make up the graph of a function f. The graph of y = f is another name for the graph of f. (x). Thus, the graph of an equation serves as a particular illustration of the graph of a function.

The given equation is

f(x)= ¾ x-2

Put x=0 in the equation

y = (¾)(0)-2

y = -2

Put x=4 in the equation

y = (3/4) (4)-2

y = 3-2

y = 1

Graph the points of the function on a graph as given below

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The time that you will arrive in Nashville is 1:33.

From the information given, the person leaves Knoxville at 11:13, and the journey takes 2 hours and 20 minutes.

Therefore the time when the person will arrive will be the addition of the time given.

This will be:

= 11:13 + 2:20

= 1:33

Therefore, the person will arrive by 1:33.

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Answer:

There are thirteen 4 card hands are possible with a 52 card deck.

Answer:

Thirteen 4 card hands are possible with a 52 card deck

The sampling method used to get the sample is  Systematic sampling.

The variable type of color of cars around the gym is qualitative.

Sampling is the process of choosing a subset of people (a statistical sample) from a statistical population in order to estimate characteristics of the entire population. It is used in statistics, quality control, and survey technique. Statisticians try to get samples that are typical of the population under consideration.

The different sampling methods used are:

Now the given sample of the residents that were selected was every eighth car . Hence  Systematic sampling is used.

Disclaimer: Missing question stem: Identify the sampling method(simple , stratified, cluster, systemic).

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The value of the middle integer is 26

From the question, we are to determine the middle integer

From the given information,

"The sum of the squares of three consecutive positive integers is 2030"

Let the first integer be x,

Then the middle integer will be x + 1

and the third integer will be x + 2

Thus,

x² + (x +1)² + (x +2)² = 2030

x² + x² + 2x + 1 + x² + 4x + 4 = 2030

3x² + 6x + 5 = 2030

3x² + 6x + 5 - 2030 = 0

3x² + 6x - 2025 = 0

x² + 2x - 675= 0

Solve quadratically

x² + 27x - 25x - 675 = 0

x(x + 27) -25(x + 27) = 0

(x - 25)(x + 27) = 0

x - 25 = 0 and x + 27 = 0

x = 25 and x = -27

Since x is a positive integer,

x = 25

Thus,

The middle integer,

x + 1

= 25 + 1

= 26

Hence, the value of the middle integer is 26

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Step-by-step explanation:

A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function =S+16.950.60M, where M is the number of miles driven.

The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function =I+4.900.15M.

Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.

Answer:

Do you mean GCF? If so, it is 10.

If you mean factors that they have in common it is: 1,2,5 and 10.

Step-by-step explanation:

Factors of 70: 1,2,5,7,10,14,35,70

Factors of 110: 1,2,5,10,11,22,55,110

GCF is 10

Answer:

10

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

y = 3x-2        switch x's and y's    then solve for y

x = 3y-2

x+2 = 3y

y = (x+2) / 3    <===== this is  f^-1 (x)

Now you can try the one posted in the picture.....

Answer:

1.) ab × ac

a × (b + c)

2.) 6m + 8

2 (3m + 4)

3.) 27d²+8d³-15d4t

27d²+8d³- (15 × 4)dt

27d²+8d³- 60dt

4.) 27m²n³p5-20m5n²p

135m²n³p - 20m × 5n²p

135m²n³p - 100mn²p

The height of the tank is h = 216/s^2, the surface area is s^2 + 864/s and the value of s is ∛432

The given parameters are

Volume = 216

Base length = s

Height = h

The base shape is a square.

So, we have

Volume = s^2h

This gives

216 = s^2h

Divide through by s^2

h = 216/s^2

Hence, the height of the tank is h = 216/s^2

This is calculated as

A = s^2 + 4sh

So, we have

A = s^2 + 4 * s * 216/s^2

Evaluate

A = s^2 + 4 * s * 216/s^2

This gives

A = s^2 + 864/s

Here, we have

A = s^2 + 864/s

Differentiate

A' = 2s - 864/s^2

Set to 0

2s - 864/s^2 = 0

Divide through by s

2 - 864/s^3 = 0

So, we have

864/s^3 = 2

This gives

2s^3 = 864

Divide by 2

s^3 = 432

Take the cube root

s = ∛432

Hence, the value of s is ∛432

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