A route between Guilford and Bath has a distance of 180 kilometres.
Dave drives from Guilford to Bath. He takes 3 hours.

Olivia drives the same route. Her average speed is 15 kilometres per hour faster than Dave's.
(a) How long does it take Olivia to drive from Guilford to Bath?
Give your
answer in hours and minutes

By taking the longer route, the amount of money Kelsey will save is $7.38.

To find out how much money Kelsey saves by taking the longer route, we need to calculate the total cost of each route and compare them.

For the shorter route, the total cost is the cost of gas plus the cost of tolls.
- The cost of gas is the distance traveled divided by the miles per gallon of the car, multiplied by the price of gas: (214 mi / 34.0 mpg)($3.29/gal) = $20.48
- The cost of tolls is $9.75
- So the total cost of the shorter route is $20.48 + $9.75 = $30.23

For the longer route, the total cost is just the cost of gas, since there are no tolls:
- The cost of gas is (236 mi / 34.0 mpg)($3.29/gal) = $22.85
- So the total cost of the longer route is $22.85

Now we can compare the two costs to find out how much money Kelsey saves by taking the longer route:
$30.23 (shorter route) - $22.85 (longer route) = $7.38

Therefore, Kelsey saves $7.38 by taking the longer route.

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The six primary sources of greenhouse gas emissions in the United States are:

2. The seven types of greenhouse gases of climate change are:

3. The four types of Machine learning are:

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ds/dt = sec(t)

To find the length of the curve, we need to find the arc length. The arc length of the curve r(t) is given by:

LENGTH = $\int_{0}^{1} \sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)} dt$

To find ds/dt, we can take the derivative of the above equation with respect to t:

$\frac{ds}{dt} = \frac{d}{dt} \sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}$

$\frac{ds}{dt} = \frac{6^2\cos(t)\sin(t) + 10\sin(t)\cos(t)}{\sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}}$

$\frac{ds}{dt} = \frac{16\sin(t)\cos(t)}{\sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}}$

$\frac{ds}{dt} = \frac{16\sin(t)\cos(t)}{\sqrt{1+tan^2(t)}}$

Thus, ds/dt = sec(t).

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Answer:So the common factor of the numerator and denominator is (x+7)(x+7) or (x+7)^2, and the simplified expression is (x+1)(x−1).

Step-by-step explanation:

To find the common factor of the numerator and denominator of the expression (x+1)(x+7)(x+7)(x−1), we need to factorize it completely.

(x+1)(x+7)(x+7)(x−1) = (x+1)(x−1)(x+7)(x+7)

Now we can see that the common factor of the numerator and denominator is (x+7)(x+7) or (x+7)^2.

Therefore, we can simplify the expression by dividing both the numerator and denominator by (x+7)^2:

(x+1)(x−1)(x+7)(x+7)/(x+7)(x+7) = (x+1)(x−1)

So the common factor of the numerator and denominator is (x+7)(x+7) or (x+7)^2, and the simplified expression is (x+1)(x−1).

So the area of one tile is 50 square inches. Therefore, the length of the triangle's base is 20 inches.

Area is a measure of the amount of space inside a two-dimensional (2D) shape or figure. It is usually measured in square units, such as square meters (m²) or square centimeters (cm²). The area of a shape is calculated by multiplying the length of one side or dimension of the shape by the length of another side or dimension. The resulting value represents the total number of square units that are contained within the shape.Area is an important concept in mathematics and is used in various fields, such as geometry, physics, and engineering. It helps in measuring and comparing the sizes of shapes and figures, and in determining how much material is needed to cover or fill a certain area.

Here,

The area of a parallelogram can be calculated as the product of its base and height. In the case of the given tile, the base and height are 10 inches and 5 inches respectively. Therefore, the area of one tile is:

Area of tile = Base x Height

Area of tile = 10 in x 5 in

Area of tile = 50 square inches

If the two tiles have the same area, then we can assume that the area of the triangle tile is also equal to 50 square inches (the area of one parallelogram tile that we calculated in the previous question).

The formula for the area of a triangle is:

Area of triangle = (1/2) x Base x Height

where the base is one of the sides of the triangle, and the height is the perpendicular distance from the base to the opposite vertex.

In this case, we know that the area of the triangle is 50 square inches and the height is 5 inches, so we can solve for the base as follows:

Area of triangle = (1/2) x Base x Height

50 = (1/2) x Base x 5

Base = (2 x 50) / 5

Base = 20

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Complete question:

An artist is using tiles in the shape of a parallelogram to make a mosaic. The tiles are in the shape of parallelogram with height as 5 inch and length as 10 inch. What is the area of one tile? if the two tiles have the same area, what is the length of the triangles base?

The answer is 2520 different 7-letter codes that can be made from the word CONCERN.

There are 7!/(2!2!) different 7-letter codes that can be made from the word CONCERN.

To find the number of different 7-letter codes that can be made from the word CONCERN,

we can use the formula for permutations of n objects with r identical objects:

P(n,r) = n!/(r1!r2!...rk!)

Where n is the total number of objects, r1, r2, ..., rk are the number of identical objects in each group, and n! is the factorial of n.

In this case, n = 7, r1 = 2 (for the two C's), and r2 = 2 (for the two N's). So, the formula becomes:

P(7,2,2) = 7!/(2!2!)

= (7*6*5*4*3*2*1)/((2*1)*(2*1))

= 2520

Therefore, there are 2520 different 7-letter codes that can be made from the word CONCERN.

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By calculating the Cost Per Point, it can be concluded that advertisers are paying such a premium to run an ad during a sporting event vs. normal primetime programming because sporting events have a larger and more engaged audience.

Cost per Point (CPP) is a measurement of cost efficiency that enables comparison between the cost of one advertisement to other advertisements. CPP is calculated by dividing the gross media cost by the gross rating point.

CPP = gross media cost / gross rating point

The household CPP for the Super Bowl, Men's NCAA Basketball Championship game, and NCIS can be calculated as follows:

For the Super Bowl:

CPP = $5.5 million / 45.0 = $122,222.22

For the Men's NCAA Basketball Championship game:

CPP = $1.0 million / 8.9 = $112,359.55

For NCIS:

CPP = $125,000 / 6.5 = $19,230.77

Comparing the CPP for the Super Bowl, Men's NCAA Basketball Championship game, and NCIS, it is clear that the Super Bowl has the highest CPP, followed by the Men's NCAA Basketball Championship game, and then NCIS.

Advertisers are paying such a premium to run an ad during a sporting event vs. normal primetime programming because sporting events have a larger and more engaged audience.

Sporting events, especially ones like the Super Bowl and the Men's NCAA Basketball Championship game, are highly anticipated and have a dedicated fan base. This means that advertisers have a better chance of reaching a larger audience and making a bigger impact with their ads during these events. Additionally, sporting events are often live, which means that viewers are less likely to skip through commercials. This guarantees that advertisers' messages will be seen by more people, making it worth the higher cost.

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The surface area of the prism is 840 square inches.

What is Prism?

A prism is a three-dimensional geometric shape that has two identical parallel bases and straight sides that connect the bases. The sides of a prism are typically rectangular, but can also be triangular or other polygonal shapes.

To find the surface area of the triangular prism, we need to find the area of the two triangular bases and the three rectangular faces.

Area of the triangular base:

The base is a right triangle with base 10 inches and height 24 inches. Therefore, the area of the base is:

(1/2) x base x height = (1/2) x 10 x 24 = 120 square inches.

Area of the rectangular faces:

The rectangular faces are all congruent, with dimensions of 10 inches by 20 inches. Therefore, the area of each rectangular face is:

length x width = 10 x 20 = 200 square inches.

There are three rectangular faces, so the total area of the rectangular faces is:

3 x 200 = 600 square inches.

Total surface area:

The total surface area of the prism is the sum of the areas of the two triangular bases and the three rectangular faces:

Total surface area = 2 x area of triangular base + 3 x area of rectangular face

= 2 x 120 + 3 x 200

= 240 + 600

= 840 square inches.

Therefore, the surface area of the prism is 840 square inches.

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Answer:

Step-by-step explanation:

(h)

[tex]KE= \frac{1}{2}mv^{2} \\KE=\frac{mv^{2} }{2} \\2KE=mv^{2}\\2KEm=v^{2} \\v=\sqrt{2KEm}[/tex]

(g)

[tex]s=\frac{(u+v)t}{2} \\2s=(u+v)t\\\frac{2s}{t}=u+v\\u= \frac{2s}{t}-v[/tex]

(i)

[tex]s=ut+\frac{1}{2} at^{2} \\s-ut=\frac{at^{2} }{2} \\2s-2ut=at^{2} \\\sqrt{2s-2ut}=at\\a=\sqrt{2s-2ut}-t[/tex]

(j)

[tex]\frac{pV}{T} =nR\\T=\frac{pV}{nR}[/tex]

(k)

[tex]a^{2} -b^{2} +c^{2} \\a^{2} +c^{2} =b^{2} \\b=\sqrt{a^{2} +c^{2} }[/tex]

(i)sinθ[tex]=\frac{a}{b}[/tex]

       θ=[tex]\frac{a}{sin(b)}[/tex]

Answer:

2.90

Step-by-step explanation:

One hundredth is 0.01. 2.89+0.01= 2.90.

Hope this helps, please mark brainliest!

By using technology, the value of r² is equal to; C. 0.32.

In Mathematics, a coefficient of determination (r² or r-squared) can be defined as a number between zero (0) and one (1) that is typically used for measuring the extent (how well) to which a statistical model predicts an outcome.

Based on the given data, the correlation can be determined by using an online graphing calculator as shown in the image attached below. Since the value of r is equal to -0.56, the coefficient of determination (r²) can be calculated as follows;

r² = (-0.56)²

r² = 0.3136 ≈ 0.32

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Complete Question:

A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and

their grade point average (GPA), y. The given data list the number of absences and GPAs for 15 randomly selected students.

Number of Absences

15

1

0

6

9

12

3

3

1

2

7

0

4

9

10

GPA

2.1

4.3

4.5

3.2

4.0

1.7

3.8

2.9

3.6

3.4

2.6

3.1

2.8

2.8

4.1

Using technology, what is the value of r²?

O-0.56

O-0.32

O 0.32

O 0.56

Answer:

No solution

Step-by-step explanation: no values of x

The input values are all the values of the x-coordinates and the output values are all the values of the y-coordinate corresponding the x-value: (0, 3), (2, 2), (-1, 1).

An ordered pair (a, b) is a pair of objects in mathematics. Because the ordered pair (a, b) differs from the ordered pair (b, a) unless a = b, the order in which the items occur in the pair is important. The unordered pair a, b, on the other hand, equals the unordered pair b, a.

Ordered pairs are sometimes known as 2-tuples, or sequences of length 2 (or, in computer science, sometimes, lists). 2-dimensional vectors are occasionally used to refer to ordered pairs of scalars.

The input values are all the values of the x-coordinates and the output values are all the values of the y-coordinate corresponding the x-value.

Some of the input, output pair are:

(0, 3)

(2, 2)

(-1, 1)

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The simplified result is (-x + 4)/(x^(2) - 16).

To add the given expressions, we need to combine the like terms in the numerator and keep the denominator the same since they are already common denominators.

The combined expression will look like this:

(7x + 10 - 8x - 6)/(x^(2) - 16)

Now we need to simplify the numerator by combining the like terms:

(-x + 4)/(x^(2) - 16)

This is the simplified expression. We cannot simplify it any further since there are no common factors between the numerator and denominator.

Therefore, the answer to the given question is (-x + 4)/(x^(2) - 16).

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Answer:

Slope would approximately be -1/8

Step-by-step explanation:

The first point that it looks like it touches would be (0,100) then from what I can see the next point would be (400,50). To get from the first point to the second, the slope would have to drop 1 block and move to the right 8 blocks. This means the slope would be -1/8

Answer:

AB and CD.

Step-by-step explanation:

To check if two sides of a quadrilateral are congruent, we need to find the length of each side. We can use the distance formula to calculate the length of each side:

AB = √[(1 - 4)^2 + (4 - 1)^2] = √(9 + 9) = 3√2

BC = √[(5 - 1)^2 + (1 - 4)^2] = √(16 + 9) = √25 = 5

CD = √[(1 - 1)^2 + (-2 - 1)^2] = √9 = 3

AD = √[(-3 - 1)^2 + (1 - (-2))^2] = √(16 + 9) = √25 = 5

Therefore, AB and CD have the same length and are congruent, while BC and AD have the same length and are congruent.

So the correct answer is AB and CD.

Answer:

Step-by-step explanation:

1. Solve for

x by simplifying both sides of the equation, then isolating the variable.

x= 3, −5

2. x by simplifying both sides of the equation, then isolating the variable.

x= −7, 1

Answer:

Two possible answers: 36 and 4m

Step-by-step explanation:

Changes is not specific, but we know it is a vertical change due to it saying elevation.

20+16=36m

20-16=4m

We don't know if the bird is going up or down.

Down is 4m and up is 36m

Answer:

look down

Step-by-step explanation:

let length be" x"

accroding to question

breadth= 2x/3

we know,

Area of rectangle= l × b

384=x × 2x/3

calculate

(a) The three points are:
(x,y) = ( 2.25 , -3.5 ) (smallest x-value)
(x,y) = ( 2.5 , -4 )
(x,y) = ( 2.75 , -4.5 ) (large x-value)

(b) The three points are:
(x,y) = ( -0.75 , -0.75 ) (smallest x-value)
(x,y) = ( -0.5 , -0.5 )
(x,y) = ( -0.25 , -0.25 ) (large x-value)

To find the three points that divide the line segment joining the given points into four equal parts, we need to use the formula for a point that divides a segment in a given ratio. The formula is:

(x,y) = ( (x1 + rx2)/(1+r) , (y1 + ry2)/(1+r) )

Where (x1,y1) and (x2,y2) are the given points, r is the ratio, and (x,y) is the point that divides the segment in the given ratio.

(a) For the given points (2,-3) and (3,-5), we need to find the points that divide the segment in the ratio 1:3, 2:2, and 3:1.

For the first point, we use the formula with r=1/3:
(x,y) = ( (2 + (1/3)*3)/(1+(1/3)) , (-3 + (1/3)*(-5))/(1+(1/3)) )
(x,y) = ( 2.25 , -3.5 )

For the second point, we use the formula with r=2/2:
(x,y) = ( (2 + (2/2)*3)/(1+(2/2)) , (-3 + (2/2)*(-5))/(1+(2/2)) )
(x,y) = ( 2.5 , -4 )

For the third point, we use the formula with r=3/1:
(x,y) = ( (2 + (3/1)*3)/(1+(3/1)) , (-3 + (3/1)*(-5))/(1+(3/1)) )
(x,y) = ( 2.75 , -4.5 )

So the three points are:
(x,y) = ( 2.25 , -3.5 ) (smallest x-value)
(x,y) = ( 2.5 , -4 )
(x,y) = ( 2.75 , -4.5 ) (large x-value)

(b) For the given points (-1,-1) and (0,0), we need to find the points that divide the segment in the same ratios as before.

For the first point, we use the formula with r=1/3:
(x,y) = ( (-1 + (1/3)*0)/(1+(1/3)) , (-1 + (1/3)*0)/(1+(1/3)) )
(x,y) = ( -0.75 , -0.75 )

For the second point, we use the formula with r=2/2:
(x,y) = ( (-1 + (2/2)*0)/(1+(2/2)) , (-1 + (2/2)*0)/(1+(2/2)) )
(x,y) = ( -0.5 , -0.5 )

For the third point, we use the formula with r=3/1:
(x,y) = ( (-1 + (3/1)*0)/(1+(3/1)) , (-1 + (3/1)*0)/(1+(3/1)) )
(x,y) = ( -0.25 , -0.25 )

So the three points are:
(x,y) = ( -0.75 , -0.75 ) (smallest x-value)
(x,y) = ( -0.5 , -0.5 )
(x,y) = ( -0.25 , -0.25 ) (large x-value)

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To solve this problem, we need to combine like terms and use the distributive property.

Here are the steps:

1. Combine like terms in the sum of m^(2) n+ mn^(2) + 2n^(2) and 2m^(3) n^(3)- mn^(2) + 5n^(2):
m^(2) n+ mn^(2) + 2n^(2) + 2m^(3) n^(3)- mn^(2) + 5n^(2) = 2m^(3) n^(3) + m^(2) n + 7n^(2)

2. Use the distributive property to subtract 7m^(3) n^(3)+ 2m^(2) n- n^(2) from the sum:
2m^(3) n^(3) + m^(2) n + 7n^(2) - (7m^(3) n^(3)+ 2m^(2) n- n^(2)) = 2m^(3) n^(3) + m^(2) n + 7n^(2) - 7m^(3) n^(3)- 2m^(2) n + n^(2)

3. Combine like terms:
-5m^(3) n^(3) - m^(2) n + 8n^(2)

Therefore, the answer is -5m^(3) n^(3) - m^(2) n + 8n^(2).

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The solutions to the given equations are x = 10 and m = 1.5.

Using the one-to-one property of logarithms, we can solve the given equations as follows:

First, we will solve the equation: 15.Ln(10−3x)=ln(−4x)
The one-to-one property of logarithms states that if logb(a) = logb(c), then a = c. Therefore, we can use this property to set the arguments of the logarithms equal to each other:

10 - 3x = -4x
Simplifying this equation gives:

10 = x

So the solution to the first equation is x = 10.

Next, we will solve the equation: 16.log4​(6−m)=log4​3(m)
Again, using the one-to-one property of logarithms, we can set the arguments of the logarithms equal to each other:

6 - m = 3m
Simplifying this equation gives:

6 = 4m
m = 6/4
m = 1.5

So the solution to the second equation is m = 1.5.

Therefore, the solutions to the given equations are x = 10 and m = 1.5.

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The answer of the given question based on the histogram of Investment Account Values the correct option is c) 63%.

Investment refers to act of allocating resources, like  money or time, with  expectation of generating income or profit in  future. In other words, it involves sacrificing something of a value in  present, in hope of obtaining something of the greater value in  future

Investments can be taken  in many forms, including stocks, bonds, mutual funds, real estate, and commodities, among others. The choice of investment depends on variety of factors, including investor's risk tolerance, financial goals, and the investment time horizon.

Based on the histogram of Investment Account Values provided, it appears that approximately 63% of investments have a value of $150 or less. This can be determined by adding up the percentage of investments in each bar up to and including the $150 bar.

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If $8000 is invested at 8% compounded continuously, the amount 8 years is $12,904.95.

To find out how long it will take $3,000 to grow to $20,000 if it is invested at 4% compounded monthly, we can use the formula A=P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we get:

20,000=3,000(1+0.04/12)^(12t)

Dividing both sides by 3,000, we get:

6.66667=(1+0.04/12)^(12t)

Taking the natural logarithm of both sides, we get:

ln(6.66667)=12t*ln(1+0.04/12)

Solving for t, we get:

t=ln(6.66667)/(12*ln(1+0.04/12))

t=41.2 years

So it will take approximately 41.2 years for $3,000 to grow to $20,000 if it is invested at 4% compounded monthly.

To find out the amount of $8,000 invested at 8% compounded continuously for 8 years, we can use the formula A=Pe^(rt), where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the number of years. Plugging in the given values, we get:


A=8,000e^⁰ ⁶⁴

A=12,904.95

So the amount of $8,000 invested at 8% compounded continuously for 8 years is $12,904.95.

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Answer:

38

Step-by-step explanation:

Interquartile Range

IQR = Q3 - Q1

Quartiles are the values that divide a list of numbers into quarters:

301, 301, 304, 309, 311, 328, 330, 341, 342, 343, 345

Hence,

Quartiles:

Q1 --> 304

Q2 --> 328

Q3 --> 342

And since, IQR = Q3 - Q1

Then,

342 - 304 = 38

As a result, the interquartile range for the data set is 38.

RevyBreeze

line e is parallel to line m because angle 1 + angle 2 = 180°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Represent the adjascent angle to angle 2 by x and adjascent angle to angle 1 by y

therefore ;

2 = y ( corresponding angles are equal)

1 = x ( corresponding angles are equal)

angle 1+y = 180 ( angle on a straight line)

angle 2 + x = 180

<1= 180-y

<2 = 180 -x

and both equations

< 1 +<2 = 180

therefore since < 1 +<2 = 180, then line e is parallel to line m

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The completely factored form of the given polynomial is 4(v-6)(v+2).

To factor the given polynomial, 4v^(2)-16v-48, we first need to factor out the constant, which is 4. This will give us:

4(v^(2)-4v-12)

Now, we can use the factoring method to factor the remaining polynomial, v^(2)-4v-12. We need to find two numbers that multiply to -12 and add to -4. These numbers are -6 and 2. So, we can write the polynomial as:

4(v-6)(v+2)

Therefore, the completely factored form of the given polynomial is 4(v-6)(v+2).

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The equation of the tangent plane to the surface z = ry at the point (2, 3, 6) is 2x + y – z = 16. The equation of the tangent plane to the surface 2x2 – 3xy -4x-7 = 0 at the point (1, -1, 2) is 2x – y + 3z = 2.

To obtain the equation of the tangent plane, we must first find the partial derivatives of the equation of the surface with respect to the coordinates x, y, and z. The partial derivative of the first surface with respect to x is r, and the partial derivative of the second surface with respect to x is 4x - 3y.

We can then use the equation of the tangent plane, which is: z - z0 = fx(x - x0) + fy(y - y0) + fz(z - z0), where z0, x0, and y0 are the coordinates of the given point, and fx, fy, and fz are the partial derivatives of the surface equation with respect to x, y, and z, respectively.

For the first surface, the equation of the tangent plane is:
z - 6 = r(x - 2) + 0(y - 3) + 0(z - 6)
=> z = rx + 6.

For the second surface, the equation of the tangent plane is:
z - 2 = 4x - 3y + 0(z - 2)
=> z = 4x - 3y + 2.

Therefore, the equation of the tangent plane to the surface z = ry at the point (2, 3, 6) is 2x + y – z = 16 and the equation of the tangent plane to the surface 2x2 – 3xy -4x-7 = 0 at the point (1, -1, 2) is 2x – y + 3z = 2.

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