derivative of the (sqrt of t/4t-3)

Final answer:

To say a shape has an area of 8 square inches means the shape covers 8 units of square inches. For similar shapes, the area comparison is the square of their scale factor; hence, if one shape's dimensions are twice another's, its area is four times larger.

Explanation:

When it is said that a shape has an area of 8 square inches, it means that the surface enclosed by the shape covers 8 units of square inches. In other words, you could fit 8 squares, each measuring 1 inch by 1 inch, inside the shape without overlapping or leaving any space inside the shape uncovered. To understand how the area of similar shapes compares, we can look into the problem involving two squares.

Marta has one square with a side length of 4 inches. A similar square has dimensions that are twice as large, meaning its side lengths are 8 inches. The area of the smaller square can be calculated as 4 inches x 4 inches, which equals 16 square inches. The area of the larger square would be 8 inches x 8 inches, resulting in 64 square inches. The ratio comparing the two areas is 64:16, which simplifies down to 4:1. This shows that the larger square's area is four times greater than that of the smaller square.

An area of 8 square inches means the shape covers a space equivalent to eight 1-inch by 1-inch squares.

The expected payback for betting $2 on red in a roulette game is -$0.62. This indicates an expected average loss, making it not a profitable bet.

The expected payback for betting $2 on red in a roulette game is -$0.62. This means that on average, you would expect to lose 62 cents per game if you play this game repeatedly over a long string of games. The expected value indicates an expected average loss, so it is not a profitable bet.

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Answer:

A) $204   B) $331.50

Step-by-step explanation:

For both scenarios, you just multiply the amount of hours worked by the amount per hour to find the total amount made.

Eugene earned $204 by tutoring for 12 hours and $331.50 for 19.5 hours, calculated by multiplying the number of hours by her hourly rate of $17.

Eugene earns money by tutoring athletes at Brooklyn University. The amount she earns can be calculated by multiplying the number of hours she tutors by the hourly rate.

Part A Calculation

For 12 hours of tutoring:
Amount Earned = Hourly Rate  imes Hours Tutored
Amount Earned = $17/hour  imes 12 hours
Amount Earned = $204

Part B Calculation

For 19.5 hours of tutoring:
Amount Earned = Hourly Rate  imes Hours Tutored
Amount Earned = $17/hour  imes 19.5 hours
Amount Earned = $331.50

1 mile = 5280 feet

5280 * 3/5 = 3168 feet more to go

Answer:

The rate of change of section A is 3 and rate of change of section B is 48.

Step-by-step explanation:

The given function is

[tex]h(x)=4^x[/tex]

Formula for average rate:

[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

Section A is from x = 0 to x = 1, the average rate of change of section A is

[tex]m_1=\frac{h(1)-h(0)}{1-0}=\frac{4-1}{1}=3[/tex]

Section B is from x = 2 to x = 3, the average rate of change of section B is

[tex]m_2=\frac{h(3)-h(2)}{3-2}=\frac{64-16}{1}=48[/tex]

Therefore rate of change of section A is 3 and rate of change of section B is 48.

[tex]m_1\times k=m_2[/tex]

[tex]3\times k=48[/tex]

[tex]k=12[/tex]

Therefore average rate of change of Section B is 12 times of Section A.

The given function is an exponential function and rate of change is not constant.

Answer:

y = -1/34 . x + 167/17

Step-by-step explanation:

The slope-intercept form of a linear equation is:

y = m.x + b

where,

m is the slope

b is the y-intercept

Line v is perpendicular to the graph of y = 34 x - 11. If 2 lines are perpendicular, the slope of one is the inverse and opposite of the other. Then, the slope of v is -1/34.

Line w is parallel to line v. When 2 lines are parallel, they have the same slope.

The equation of w is:

y = -1/34 . x + b

Lines b passes through the point (-6, 10). We can replace this ordered pair in the previous equation to find the value of b.

10 = -1/34 . (-6) + b

b = 167/17

The equation of w is:

y = -1/34 . x + 167/17

Answer:

18 just took the test

Answer:

Option C It will cost $42 for 28 binders

Step-by-step explanation:

Mrs. Santos determined that 15 binders would cost = $22.50

Therefore, 1 binder would cost = $1.50

Now we calculate each statement :

a. 18 binders will cost $12

= 18 × $1.50 = $27.00 (not correct)

b. 30 binders will cost $20

= 30 × $1.50 = $60.00 (not correct)

c. 28 binders will cost $42

28 × $1.50 = $42.00 (Correct)

d. 48 binders will cost $48

48 × $1.50 = $72.00 (not correct)

Option C It will cost $42 for 28 binders would be correct.

Answer:

Step-by-step explanation:

Given is a scatter plot and the regression line using least squares.

We are required to find out how many more goals a player will score for every additional hour of practice.

In other words, we are to find the slope of the regression line.

By taking two points on the line we can find slope of the line.

(1.5,2) and (6.5,6) are points on the line

Find slope using two point formula

Slope = [tex]\frac{y2-y1}{x2-x1} =\frac{6-2}{6.5-1.5} \\=\frac{4}{5}[/tex]

near slope is 3/4

Hence answer is option b.

On average, the goals a player scores for every additional hour of practice will be 3/4.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

We need to find out how many more goals a player will score for every additional hour of practice.

In other words, we have to find the slope of the regression line.

By taking two points on the line we can find the slope of the line.

Lets (1.5,2) and (6.5,6) are points on the line

So, the slope will be

Slope = y-y₁ / (x-x₁)

          = 6- 2 / 6.5 - 1.5

          = 4/5

Thus, the near slope is 3/4. Option B is correct.

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The area of the living room is approximately 238 square feet.

To find the area of the living room, we need to multiply its length by its width.

First, let's convert the dimensions from feet and inches to feet. We have:

Length: 12 feet + 4 inches = 12 + 4/12 = 12.33 feet

Width: 19 feet + 4 inches = 19 + 4/12 = 19.33 feet

Now, we can multiply the length and width to find the area:

Area = length × width = 12.33 feet × 19.33 feet = 238.1289 square feet

Rounding to the nearest whole square foot, the area of the living room is approximately 238 square feet.

Please help me with this problem.

The diagram shows the floor plan of a one-bedroom apartment. Find the area of the living room in square feet. Round to nearest square foot.

The dimensions of living room are 12' 4" x 19' 4"

On rounding off to nearest feet we get the area of the living room as 238 ft²

In the figure it is given that the dimensions of the living room are 12' 4" x 19' 4". This means that the dimensions are:

12 ft 4 in x 19 ft 4 in

To get the area in feet, we need to convert the dimensions into feet. This can be done by using the conversion factor that 1 foot = 12 inch

So, 12 ft 4 in can be converted into feet as follows:

[tex]12\ \text{ft}\ 4\ \text{in} = 12\ \text{ft}\ + \frac{4}{12}\ \text{ft} = 12.333\ \text{ft}[/tex]

19 ft 4 in can be converted into feet as follows:

[tex]19\ \text{ft}\ 4\ \text{in} = 19\ \text{ft}\ + \frac{4}{12}\ \text{ft} = 19.333\ \text{ft}[/tex]

Now to calculate the area we multiply the dimensions of the living room (as the living room is a rectangle and area of rectangle is product of its length and breadth):

[tex]area = 12.333 \times 19.333 =238.433889[/tex] ft²

On rounding of to nearest feet we get the area as 238 ft². So, the area of the living room is 238 ft²

If the graph has 1/3 length…

At least 20 minutes late: this would mean 20 minutes late or more.

20 or more minutes goes from 20 to 30. So that is a difference of 30 – 20 = 10. The distance of your rectangle is 10.

Length * width = (1/30) * 10 = 1/3 or 0.3333. The probability the friend is at least 20 minutes late is 0.3333.

The value of the integral is:  πcos(16)- πcos (81)

The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a  from a reference point and an angle from a reference direction.

Given:

∫∫ r sin(x²+y²)dA and 16≤x²+y²≤81.

Now,

x =rcosϕ

y=rsinϕ

I=r

Find the integration limits:

ϕ∈[0,2π]

16≤x²+y²≤81

16≤r² cos² Ф + r²sin² Ф≤81

16≤r²≤81

4≤r≤9

So, r∈[4,9]

Now,

∫∫ r sin(x²+y²)dA=

= [tex]\int\limits^9_4 {dr} \int\limits^{2\pi}_0 {rsin \;(r^{2}) } \, d\phi[/tex]

=2π [tex]\int\limits^9_4 {rsin \;(r^{2}) } \, dr[/tex]

Let r² = u

2rdr=du

Also, limit will change from 16 to 25.  

5→25

4→16

​

So,

= π[tex]\int\limits^{81}_{16} {sin \;(u) } \, du[/tex]

=−π|cos (u)∣[tex]^{81}_{16}[/tex]

= πcos(16)- πcos (81)

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​

The measure of the third angle is 50 degrees for the given triangle. The correct answer would be an option (A).

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbolΔ.

Let x be the measure of the third angle.

As we know that the sum of interior angles in the triangle is always 180 degrees.

So, as per the given question, we have

30° + 100° + x = 180°

130° + x = 180°

x = 180° - 130°

Apply the subtraction operation, and we get

x = 50°

Thus, the measure of the third angle is 50 degrees.

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Answer:

-5p-3

Step-by-step explanation:

use the distributive property