A formula is expressed as d=a(2+kt). Express k in terms of d, a and t

The time taken by Graham is approximately 4/127 hours, which is about 0.0315 hours or roughly 1 minute and 53 seconds, to drive one mile.

To find out how many hours Graham took to drive one mile,

simply divide the total time (1 1/3 hours) by the total distance (42 1/3 miles):

Total time = 1 1/3 hours

                 = 4/3 hours

Total distance = 42 1/3 miles

                        = 127/3 miles

Now, divide the total time by the total distance:

Time per mile

= (Total time) / (Total distance)

= (4/3 hours) / (127/3 miles)

Now, when you divide by a fraction, you can multiply by its reciprocal:

Time per mile

= (4/3 hours) × (3/127 miles)

= (4/127) hours per mile

Therefore, the total time Graham took approximately 4/127 hours to drive one mile.

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The approximate maximum height that the rocket reaches is 25 feet.

Function is a type of relation, or rule, that maps one input to specific single output. Given two function f(x) and g(x) can be written as f(X) + g(X). It is the sum of two functions similar to the addition of any two polynomial functions

+ x -7.

We are given that;

Initial velocity of the rocket= 40 feet per second.

The height of the rocket after t seconds is given by the formula:

h(t) = -16t^2 + v0t + h0

where v0 is the initial velocity (in feet per second) and h0 is the initial height (in feet).

Since the rocket is launched from the ground, its initial height is h0 = 0. Substituting this and v0 = 40 into the formula, we get:

h(t) = -16t^2 + 40t

To find the approximate maximum height that the rocket reaches, we need to find the vertex of the parabolic function h(t) = -16t^2 + 40t. The vertex occurs at the value of t that maximizes the height, which is given by:

t = -b/2a

where a = -16 and b = 40 are the coefficients of the quadratic function. Substituting these values into the formula, we get:

t = -40/(2*(-16)) = 1.25

Therefore, the rocket reaches its maximum height after approximately 1.25 seconds. To find the maximum height, we can substitute this value of t into the formula for h(t):

h(1.25) = -16(1.25)^2 + 40(1.25) ≈ 25 feet

Therefore, by the given function answer will be 25 feet.

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Answer:

The heat added to the system.

Step-by-step explanation:

Answer:

d its d

Step-by-step explanation:

Answer:

Circumference of the circle to the nearest hundredth is, 69.08 cm

Step-by-step explanation:

Circumference(C) of the circle is given by:

[tex]C = 2\pi r[/tex]            .....[1]

where,

r is the radius of the circle.

As per the statement:

middle of circle is 11 cm

⇒[tex]r = 11 cm[/tex]

use [tex]\pi = 3.14[/tex]

Substitute these in [1] we have;

[tex]C = 2 \cdot 3.14 \cdot 11 = 69.08 cm[/tex]

Therefore, the circumference of the circle to the nearest hundredth is, 69.08 cm

The circumference of a circle with a radius of 11cm is 69.08cm, rounded to the nearest hundredth.

To estimate the circumference of a circle using π (Pi), you need to know the diameter of the circle which is twice the radius. Since you've mentioned the circle has a middle (radius) of 11cm, the diameter is 22cm. The formula for the circumference of a circle is C = πd, where d is the diameter.

Using the given approximation of Pi (π = 3.14), you can calculate:

C = 3.14 × 22cm

C = 69.08cm

Therefore, the estimated circumference is 69.08cm, which can be rounded to the nearest hundredth as 69.08cm.

Answer:

There is moderate level of overlap between the two data sets.  

Step-by-step explanation:

Overlap of data sets.

We are given two data sets in the question.

We have to find the amount of overlap in data set 1 and in data set 2.

There are 8 data points in data set 1 as shown in the image.

There are 8 data points in the data set 2 as shown in the image.

Out of the 8 data points for both data set 1 and data set 2, 5 data points overlap each other on 6, 7, 8 and 9.

Thus, we could say there is moderate level of overlap between the two data sets.

Given is a rectangular trampoline with dimensions 15 meters by 18 meters.

A pad of uniform width is fixed about the boundary of trampoline such that total area becomes 340 square meters.

It says to find width of the pad that is placed around trampoline.

Let's assume the width of pad = 'x' meters.

Now Length of trampoline with pad would be, L = 2x + 15 meters.

And Width of trampoline with pad would be, W = 2x + 18 meters.

Given is the Total area = 340 square meters.

We know the formula for area of rectangle is given as follows :-

Area of Rectangle = Length x Width

⇒ 340 = (2x+15)·(2x+18)

⇒ 340 = 4x² + 66x + 270

⇒ 4x² + 66x + 270 - 340 = 0

⇒ 4x² + 66x - 70 = 0

⇒ 2x² + 33x - 35 = 0

⇒ 2x² + 35x - 2x - 35 = 0

⇒ x·(2x + 35) - 1·(2x + 35) = 0

⇒ (x - 1)·(2x + 35) = 0

⇒ (x - 1) = 0 or (2x + 35) = 0

x can't be negative number, so x = 1.

Hence, x = 1 meter is the width of the pad.

Answer:

The width of the pad is [tex]1\ m[/tex]

Step-by-step explanation:

Let

x----> the width of the pad

we know that

[tex](15+2x)(18+2x)=340[/tex]

Solve for x

[tex]270+30x+36x+4x^{2} =340\\ \\4x^{2}+66x-70=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=1\ m[/tex]

see the attached figure

Answer: Width of canvas = 9 inches

Area left for painting after painting the border = 70 square inches.

Explanation :

Since we have given that

Area of painting = 108 square inches

Length of canvas = 12 inches

As we know that

[tex]\text{Area of rectangle} = length\times breadth[/tex]

[tex]108=12\times breadth\\\\\frac{108}{12}=breadth\\\\9=breadth[/tex]

So, breadth of canvas = 9 inches .

Now, Chloe paints a 1 inch wide blue border on the canvas.

[tex]\text{So, remaining length left for painting after painting the border} = 9-1-1=9-2=7\text{ inches}[/tex]

[tex]\text{ Remaining breadth left for painting after painting the border }= 12-1-1=12-2= 10\text{ inches}[/tex]

[tex]\text{So , area of remaining portion }= length\times breadth \\\\ \text{ area of remaining portion }=7\times 10\\\\\text{ area of remaining portion }=70 \text{ square inches}[/tex]

Hence, remaining area = 70 square inches .

Answer:

9 and 70

Step-by-step explanation:

The width of the canvas is 9 inches. Chloe paints a 1-inch-wide blue border on the canvas. The area left for painting after painting the border is 70 square inches.

Answer:

$12 per hour

Step-by-step explanation:

To solve how much did Robin earned per hour you just have to do a simple equation, we know that he worked 9 weeks, and that each week he worked 40 hours, so you equation would look like this:

[tex]Income=(wageperhour)*(hours worked)[/tex]

The hours worked is just a math done by multiplying the weeks worked by the hours worked per week that would be:

[tex]Hours worked=Hours worked per week*weeks\\Hours worked=(40 hours)*(9 weeks)\\Hours worked=360 hours[/tex]

So now we just put the data into our equation

[tex]Income=(wageperhour)*(hours worked)\\$4320=(wageperhour)*(360)\\wage per hour=4320/360\\ Wage per hour= 12[/tex]

The discount is $3.00 Why?  You need to multiply the cost of the sweater by the discount as follows:

15x0.2=3

If a rectangular prism has a lenght of 8 inches and a width of 7 inches. The lateral area is 150 square inches then the height of the rectangular prism is 5 inches.

To find the height of the rectangular prism, we'll first find the formula for the lateral area of a rectangular prism and then solve for the height using the given lateral area.

The lateral area of a rectangular prism is given by the formula:

[tex]\[ \text{Lateral Area} = 2 \times (\text{Length} \times \text{Height} + \text{Width} \times \text{Height}) \][/tex]

Given that the length is 8 inches, the width is 7 inches, and the lateral area is 150 square inches, we can substitute these values into the formula and solve for the height:

[tex]\[ 150 = 2 \times (8 \times \text{Height} + 7 \times \text{Height}) \][/tex]

[tex]\[ 150 = 2 \times (8\text{Height} + 7\text{Height}) \][/tex]

[tex]\[ 150 = 2 \times 15\text{Height} \][/tex]

Divide both sides by 2:

[tex]\[ 75 = 15\text{Height} \][/tex]

Now, solve for the height:

[tex]\[ \text{Height} = \frac{75}{15} \][/tex]

[tex]\[ \text{Height} = 5 \text{ inches} \][/tex]

So, the height of the rectangular prism is 5 inches.

Answer: Total purchase price of this watch is $9300.

Step-by-step explanation:

Since we have given that

Retail price of watch = $8000

Rate of sales tax = 6%

Amount of sales tax becomes

[tex]\dfrac{6}{100}\times 8000\\\\=\$480[/tex]

Rate of excise tax = 10%

Amount of excise tax is given by

[tex]\dfrac{10}{100}\times 8000\\\\=\$800[/tex]

So, Amount of watch after sales tax becomes

[tex]\$8000+\$480+\$800\\\\=$9280[/tex]

Amount of additional shipping charge = $20

Amount of watch after additional shipping charge becomes

[tex]\$9280+20\\\\=\$9300[/tex]

Hence, Total purchase price of this watch is $9300.

We are given:  The cost of one flower bouquet =$ b.

The cost of one vase = $ v.

First florist bought: 2 flower bouquets and 2 vases.

2 *  cost of one flower bouquet + 2*cost of one vase = Total cost.

2b +2v = 12.50   ------------------------equation (1).

Second florist bought: 8 flower bouquets and 2 vases.

8 *  cost of one flower bouquet + 2*cost of one vase = Total cost.

8b +2v = 29.00    ------------------------equation (2).

Therefore, system of equations  we got is 2b +2v = 12.50  and 8b +2v = 29.00.

Subtracting first equation from second equation.

8b +2v = 29.00

-(2b +2v = 12.50)

____________________

6b = 16.50.

Dividing both sides by 6, we get.

b= 2.75.

Plugging b=2.75 in first equation we get

2(2.75) +2v = 12.50

5.50 +2v = 12.50

Subtracting 5.50 from both sides, we get

5.50-5.50 +2v = 12.50-5.50

2v = 7

Dividing both sides by 2, we get

v =3.50.

Therefore, cost of one flower bouquet is $2.75 and cost of one vase is $3.50.