Sandy is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 4 km/h. After two hours, the velocity of the runner is 2 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 4 hours? (5 points)

The distance between Indy and Kokomo be in real life is given by the proportion A = 60 miles

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

Let the distance between Indy and Fort Wayne in map = 13 cm

Let the distance between Indy and Fort Wayne in real = 120 miles

And , let the distance between Kokomo and Indy map = 6.5 cm

So , the proportion is

120 / 13 = A / 6.5

Multiply by 6.5 on both sides , we get

A = 120 / 2

A = 60 miles

Hence , the distance is 60 miles

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There are either three or four brown bears, and brown bear > 2 is the inequality that best describes the circumstance.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

given, there are 4 bears. some are black and some are brown. there are fewer than 2 black bears.

Since,

Black bear < 2

mathematically it can be 0 or 1

the inequality that represents the number of brown bears> 4 - 2

brown bear > 2

theoretically, it could be 3 or 4

therefore, there are either 3 or 4 brown bears, and the inequality that represents the situation is brown bear > 2.

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Answer:

Step-by-step explanation:

Arleen has a gift card of the amount = $200

The total cost to rent the tiller for 4 days and a rake for $9

= ($35 × 4) + $9

= 140 + 9 = $149

A. Now the balance on the gift card = $200 - $149

                                                            = $51

B. Arleen have $51 in her gift card so she has enough to buy a wheelbarrow for $50.00.

An icosahedron is a symmetrical, solid shape with 20 triangular faces and 12 corners.

An icosahedron is a symmetrical, solid shape that has 20 faces. Each of these faces is an equilateral triangle. The structure of an icosahedron also includes 12 corners, where the faces meet. This geometric shape is an example of a regular polyhedron, one of the five Platonic solids, which are convex polyhedra with faces made of congruent regular polygons.

Answer:

so on the fourth bounce the ball will reach a height of 8 feet

Step-by-step explanation:

There is a common ratio of 2/3 between the height of the ball at each bounce so the bounce height from a geometric sequence 27,18,12 two-thirds of 12 is 8 so on the fourth bounce the ball will reach a height of 8 feet

To compare 29 feet and 9 yards, convert 9 yards to feet, which equals 27 feet. Since 29 feet is greater than 27 feet, 29 feet is longer.

To determine which length is longer between 29 feet and 9 yards, we need to convert one of the measurements to the same unit. We know that 1 yard is equal to 3 feet. Therefore, to convert 9 yards to feet:

Comparing the two lengths, 29 feet is longer than 27 feet.

Thus, 29 feet is the longer length.

The velocity of the bus is:

velocity (bus) = 36 miles / 40 min

velocity (bus) = 0.9 miles / min

Since the car is 1.5 times faster, so the velocity of the car is:

velocity (car) = 1.5 * 0.9 miles / min

velocity (car) = 1.35 miles / min

At the meeting point, the sum of the distance is equal to 36 miles. Therefore:

1.35 t + 0.9 t = 36

2.25 t = 36

t = 16 min

So they will meet after 16 minutes.

The problem given is a linear system of differential equations with initial conditions, but the system is not properly defined and appears to have a typo. Normally, such a system would be in the form x' = ax + by and y' = cx + dy, with initial conditions that would determine the particular solution.

This question is about solving a linear system of differential equations with initial conditions, specifically the system {x′y′==−5x+3y−18x+10y with the initial conditions x(0)=4 and y(0)=11. However, there seems to be a typo, as the system is not properly defined and doesn't make sense as written. Under normal conditions, such a system would be in the form x' = ax + by and y' = cx + dy, where a,b,c,d are constants and x' and y' are the derivatives of x and y respectively.

Additionally, the initial conditions x(0)=4 and y(0)=11 would serve to define the particular solution for the system of differential equations. Correcting and resolving such typos would be the first step in progressing towards a solution.

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The number of slices that Jay could make is equal to 28

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given here: Dimension of the roll= 10¹/₂ inches and length of each slice=3/8 inch

Thus the number of slices that Jay could make is = 10+ 1/2 /3/8

                                                                                  =21/2 × 8/3

                                                                                  =28

Hence The number of slices that Jay could make is equal to 28

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Answer: The thermometer is both accurate and precise

Step-by-step explanation: Hope this helped!!

Question 2 is 11 i am sure

A. First let us start with the linear model.

The equation is in the form of y = m x + b

Calculating for the slope m:

m = (309,587 – 50,000) / (2007 – 1997)

m = 25,958.7

Subsituting:

y = 25,958.7 x + b

Taking x = 1997, y = 50,000. Solve for b:

50,000 = 25,958.7 (1997) + b

b = -51,789,523.9

The complete equation is therefore:

y = 25,958.7 x - 51,789,523.9

B. The exponential model has the following form:

y = a b^x

where a and b are constants

Taking x1= 1997, y1 = 50,000; x2 = 2007, y2 = 309,587

50,000 = a b^1997

309,587 = a b^2007

Combining in terms of a:

50,000 / b^1997 = 309,587 / b^2007

b^2007 / b^1997 = 309,587 / 50,000

b^10 = 6.19174

b = 1.2

Substituting:

y = a 1.2^x

Solving for a:

50,000 = a 1.2^1997

a = 3.75 x 10^-154

The complete equation is:

y = 3.75 x 10^-154 * 1.2^x

To solve the system of equations, set the demand and supply equation equal to each other and solve for the unknown. Substitute Qd with Qs and solve for P.

We now have a system of three equations and three unknowns (Qd, Qs, and P), which we can solve with algebra. Since Qd = Qs, we can set the demand and supply equation equal to each other:

By substituting Qd with Qs, we get:

16 - 2P = 2 + 5P

From here, we can solve for P to find the value of the unknown.

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Final answer:

To multiply 6 x 298 using friendly numbers, you multiply 6 by 300 and then subtract 12, getting 1788. Using properties and mental math, you break 298 into 200 + 90 + 8, multiply each by 6, and add the results together to get the same answer, 1788. The second method is preferred for its accuracy and reinforcement of the associative property.

Explanation:

To multiply 6 x 298 using friendly numbers, we can adjust 298 to a number that is easier to multiply, such as 300. This method involves approximation for ease of calculation. Here's how it would look:

Using properties and mental math, we can use the distributive property to break 298 into more manageable numbers. Here's the step-by-step process:

I prefer the second method because it guarantees accuracy and still takes advantage of the associative property to simplify calculations without approximations. Additionally, this type of mental math helps to reinforce an understanding of multiplication as a series of simpler, added-together parts.

Answer:

1 unit shorter

Step-by-step explanation:

By plotting the given points in the coordinate plane,

We get a rectangle ABCD having vertices,

A(-1,6), B (3,6), C (3,1), D (-1,1)

By the distance formula,

Shorter side or width of the rectangle,

[tex]AB=\sqrt{(3-(-1))^2+(6-6)^2}=\sqrt{4^2+0}=4\text{ unit}[/tex]

Longer side or length of the rectangle,

[tex]BC=\sqrt{(3-3)^2+(1-6)^2}=\sqrt{5^2}=5\text{ unit}[/tex]

The difference between length and width,

[tex]BC - AB = 5 - 4 = 1\text{ unit}[/tex]

Hence, the width of rectangle is 1 unit less than the length.