What is the average Rate of Change for the function f(x) = x ^ 2 + 7x - 4 over the interval [0, 2]

Answer:

I would say that the travling time is 3.5 hours and the Stationary time would be 2.5 hours.

Step-by-step explanation:

I'm sorry if I'm worng, (Can I get brainliest??)

Answer:

\(V=122.5in^3\)

Step-by-step explanation:

The volume of a right circular cone is given by:

\(V=\frac{\pi r^2h}{3}\)

where r is the radius of the circle and h is the height of the cone, and \(\pi\) is a constant \(\pi=3.1416\).

According to the problem the height is:

\(h=8.1 in\)

and we don't have the radius but we have the diameter, which is useful to find it. We just divide the diameter by 2 to find the radius:

\(r=\frac{d}{2}=\frac{7.6in}{3}=3.8in\)

Now, we can find the volume by substituting all the known values:

\(V=\frac{\pi r^2h}{3}\)

\(V=\frac{(3.1416)(3.8in)^2(8.1in)}{3} \\\\V=\frac{(3.1416)(14.44in^2)(8.1in)}{3} \\\\V=\frac{367.454in^3}{3} \\\\V=122.485\)

Rounding the volume to the nearest tenth of cubic inch we get:

\(V=122.5in^3\)

Answer:

4:6

Step-by-step explanation:

4:6

8:12

12:18

16:24

Answer:

2:4

Step-by-step explanation:

The equation of the shifted line is y = x + 2

From the question, we have the following parameters that can be used in our computation:

y = x

Shift left 2 units

To shift the equation y = x to the left by 2 units, we can replace x with (x + 2) in the equation.

i.e. (x. y) = (x + 2, y)

So, we have the new equation to be y = x + 2

This is the same line as the original equation but shifted 2 units to the left.

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Answer:

No.

It doesn’t pass through the origin point.

Step-by-step explanation:

Remember that for a graph to represent a proportional relationship, it must meet the following three criteria:

Our graph is indeed a line.

It is also not vertical or horizontal.

However, it does not pass through the origin point (0, 0).

Therefore, this graph is not a proportional relationship.

Answer:

1260cm^2

Step-by-step explanation:

15 times 12 = 180

180 times 7 = 1260

Answer:

The total surface area is given by: base area + 4 * triangular face area

Substituting the values we calculated: 52441 + 4 * 10424.4 ≈ 91588.4 square meters.

Therefore, the surface area of the square pyramid is approximately 91588.4 square meters.

Answer:

1,497.06  

Step-by-step explanation:

1,397.26 in gas, cuz 52 weeks in a year (sorry if I multiplied wrong), and $99.80 for oil, cuz 12 months in a year. So the total is 1,497.06

Answer:

$1497.56

Step-by-step explanation:

There are 52 weeks in a year.

$26.88 * 52 = $1397.76

Alma pays $24.95 every 3 months on oil so she does this 4 times a year.

$24.95 * 4 = $99.8

$1397.76 + $99.8 = $1497.56

Answer:

50*32=16.00

Step-by-step explanation:

Answer:

2 1/5 acres

Step-by-step explanation:

I'm guessing you want to find the area of an equally sized section. If so, you can divide the total of 8 4/5 by 4.

Convert to an improper fraction. 8*5 = 40+4= 44/5

Dividing is the same as multiplying by the reciprocal.

44/5 * 1/4 = 44/20

or 2 4/20 -> 2 1/5 acres

The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)

D = 5 units.

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Answer:

69+3devide 8 = 9 hours laura spend on bout

Answer: Laura can spend up to 9 hours in the boat.

Step-by-step explanation:

Lets say that T represents the number of hours.

1. Set up an equation to represent the situation.

2. Add the discount to the amount of money Laura wants to spend.

3. Divide the sum by the cost per hour to get your answer.

=> 8t - 3 ≤ 69

=> 8t ≤ 72

=> t ≤ 9

I might be wrong but I hope this helps :’)

The rate of each group was 1.86 mph and 3.36 mph.

Given that the two towns are 1150 miles apart.

A group of hikers from each town meet after a total hiking time of 220 hours.

One group travels 1 1/2 mile per hour slower than the other​ group,

We need to find the rate of each group,

So, let use consider, distance travelled by one group = x miles,

Therefore, second group travelled = 1150 - x miles.

Rate of first group = y mph

Rate of second group = y - 3/2 mph

Rate = distance / time

So,

y = x / 220

x = 220y.............(i)

Similarly,

y-3/2 = 1150 - x / 220

220y - 330 = 1150 - x

Using eq (i)

220y - 330 = 1150 - 220y

440y = 1480

y = 3.36

y - 3/2 = 1.86

Hence the rate of each group was 1.86 mph and 3.36 mph.

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Answer:

5%

Step-by-step explanation:

33/650=0.0507

0.0507*100=5.07

Answer:

$135

Step-by-step explanation:

Given data

Principal= $1,500

Time= 18 months = 1.5 years

Rate= 6%

The formula for simple interest is given as

SI= PRT/100

Substiute

SI= 1500*6*1.5/100

SI= 13500/100

SI= $135

Hence the simple interest after 18months(1.5 years) is $135

Answer:

24

Step-by-step explanation:

The formula for area of any triangle is (length * width) * 1/2. This makes the angle of 90 degrees irrelevant.

6 x 8 = 48

48 / 2 = 24

Student A's strategy of reading a consistent number of pages each day will enable them to finish the book in 20 days.

On the other hand, Student B's strategy of gradually increasing the number of pages read each day will result in a longer duration to complete the book.

Student A plans to read a consistent 25 pages each day, while Student B plans to start with 2 pages and increase the number of pages read by 50% each day after the first day.

Let's analyze the outcome of these two strategies.

For Student A:

Since the book has 500 pages and Student A reads 25 pages per day, the total number of days required to finish the book can be calculated as:

Total days = 500 pages / 25 pages per day = 20 days

Therefore, Student A will finish reading the book in 20 days by consistently reading 25 pages each day.

For Student B:

On the first day, Student B reads 2 pages.

From the second day onward, the number of pages read increases by 50% each day.

Let's see the pattern:

Day 2: 2 pages

+ 50% (2 pages) = 3 pages

Day 3: 3 pages + 50% (3 pages) = 4.5 pages

Day 4: 4.5 pages + 50% (4.5 pages) = 6.75 pages

We can observe that the number of pages read increases each day but with diminishing increments due to the 50% increase.

As a result, Student B will take longer to read the book compared to Student A.

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An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

times them

Step-by-step explanation:

all the numbers

Answer:

The equation of line in point-slope form is: \(y-7 = -7(x+5)\)

Step-by-step explanation:

Given points are:

(x1,y1) = (-5,7)

(x2,y2) = (-4,0)

Point slope form of equation is given by:

\(y-y_1 = m(x-x_1)\)

Here m is the slope

The slope is calculated using the formula:

\(m = \frac{y_2-y_1}{x_2-x_1}\)

Putting the values we get

\(m = \frac{0-7}{-4+5}\\m = \frac{-7}{1}\\m = -7\)

Putting in the equation we get

\(y-y_1 = -7(x-x_1)\)

Putting (-5,7) in the equation

\(y - 7 = -7\{x-(-5)\}\\y-7 = -7(x+5)\)

Hence,

The equation of line in point-slope form is: \(y-7 = -7(x+5)\)

Answer:

Step-by-step explanation:

Answer:

$37

Step-by-step explanation:

12 * 6 -35 = $37

Answer: $75

Step-by-step explanation: If interest earned on an account in 2 years is $15, then after 10 years, the interest would be $75.

We can know this because, if we divide $15 by 2, we get the amount of interest the account makes in 1 year.

15/2 = $7.50. The account makes $7.50 interest pear year.

We want to know how much interest the account will make in 10 years, simply multiply 7.50 by 10.

$7.50 x 10 = $75 in 10 years.

Step-by-step explanation:

tossing 2 coins at the same time, or one coin twice is the same scenario.

anyway, a probability is always the ratio

desired cases / all possible cases

when having 2 coin tosses, there are 2×2 = 4 total possible results (each toss has 2 possibilities, so 2 tosses have them 2×2 = 4 possibilities) :

head head

head tails

tail head

tail tails

how many of these 4 possible cases show at least one head ?

3 : head-head, head-tails, tails-head

so the probability to get at least one head is

3/4 = 0.75

formally calculated we would get this by saying either

this is NOT 2 times tail.

the probability of 2 times tails is

1/2 × 1/2 = 1/4 = 0.25

the probability for NOT 2 times tails is then

1 - 0.25 = 0.75

or by saying

this is either heads on the first coin and tails on the other, or tails on the first coin and heads on the other, or heads on both.

the probability of heads on the first and tails on the other coin is

1/2 × 1/2 = 1/4

the probability of tails on the first and heads on the other coin is

1/2 × 1/2 = 1/4

the probability of heads on both coins is

1/2 × 1/2 = 1/4

so, the total probability of all 3 cases is

1/4 + 1/4 + 1/4 = 3/4 = 0.75

you see : for an exclusive "or" condition we add the probabilities. for an exclusive "and" condition we multiply the probabilities.

Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20..

To estimate the value of the vehicle after 4 years, we can use the given equation A = 39500(0.86)^t, where A represents the value of the vehicle and t represents the number of years.

Substituting t = 4 into the equation:

A = 39500(0.86)^4

A ≈ 39500(0.5996)

A ≈ 23726.20

Rounding to the nearest cent, the estimated value of the vehicle after 4 years is approximately $23,726.20.

This estimation is based on the assumption that the vehicle's value decreases by 14% each year. The equation A = 39500(0.86)^t models the exponential decay of the vehicle's value over time. By raising the decay factor of 0.86 to the power of 4, we account for the 4-year period. The final result suggests that the value of the vehicle would be around $23,726.20 after 4 years of ownership.

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The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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