What is the area of the figure?

Sophia will ride 1 mile in 5 minutes

Answer: B

Step-by-step explanation: mm

To find the missing angle measure, we need to use the fact that the sum of angles in a triangle is 180 degrees. Let's denote the missing angle as x. We know that one angle is 38 degrees and another angle is 12.5 degrees.Therefore, the missing angle measure is 129.5 degrees.

By subtracting these two angles from 180 degrees, we get:

180 - 38 - 12.5 = 129.5

Without additional information, it is not possible to determine the remaining parts of the triangle. We would need the lengths of at least one side or the measures of other angles to solve for the missing parts.

The given information states that AC is equal to AB minus mzB. Without knowing the values of AB and mzB, we cannot determine the exact length of AC. We would need additional information to solve for the length of AC.Therefore, the missing angle measure is 129.5 degrees.

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Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.

I prefer Wills method because it is easier and less complicated.

Wills method:

(5x + 6x) - (2x - 1)

Subtract both 2x and -1

5x + 6x - 2x - - 1

5x + 4x + 1

In conclusion, Wills method is preferred when both methods are compared.

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If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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The signature of the Principal Investigator on the final proposal does not imply responsibility for the availability of funding or the financial aspects of the project.

The complete question should be What does the signature of the Principal Investigator on the final proposal NOT imply responsibility for?

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Answer:

1.8 in.

Step-by-step explanation:

Hi there!

1) Determine the radius of the base

\(V=\frac{1}{3} \pi r^2h\) where r is the radius of the base and h is the height of the cone

Plug in the known values (h=4.2, V=3.6)

\(3.6=\frac{1}{3} \pi r^2(4.2)\)

Isolate r; divide both sides by 4.2

\(\frac{3.6}{4.2} =\frac{1}{3} \pi r^2\\\frac{6}{7} =\frac{1}{3} \pi r^2\)

Multiply both sides by 3

\(\frac{6}{7}*3 =\pi r^2\\\frac{18}{7}=\pi r^2\)

Divide both sides by π

\(\frac{18}{7\pi }=r^2\)

Take the square root of both sides

\(\sqrt{\frac{18}{7\pi }} =r\)

2) Determine the diameter

Now that we have the radius, to find the diameter, multiply r by 2:

\(d=\sqrt{\frac{18}{7\pi }}*2\\d=1.8\)

Therefore, the diameter is 1.8 in. when rounded to the nearest tenth.

I hope this helps!

Answer:

1.8 in

Step-by-step explanation:

we know the equation for the volume of a cone is pi*r^2 h/3=3.6

pi r^2 *4.2=10.8

solve for r

r is about 0.9 so diameter is 1.8 in

Answer:

set y = 0 to get the x intercept,,,,,,,,,,   0 = 2x -3 =    x = 3/2 or 1.5

Step-by-step explanation:

Answer:

The sum of the series is: 749

Step-by-step explanation:

Given

\(a_1 = 8\)

\(a_{14} = 99\)

\(n = 14\)

Required

The sum of the series

This is calculated using:

\(S_n = \frac{n}{2}[a_1 + a_n]\)

Substitute 14 for n

\(S_{14} = \frac{14}{2}[a_1 + a_{14}]\)

\(S_{14} = 7[a_1 + a_{14}]\)

Substitute values for a1 and a14

\(S_{14} = 7[8 + 99]\)

\(S_{14} = 7*107\)

\(S_{14} = 749\)

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$99.931\\ r=rate\to 14\%\to \frac{14}{100}\dotfill &0.14\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (99.931)(0.14)(5)\implies I\approx 70\)

Answer: 81y^2

Step-by-step explanation: a^2-2ab+b^2=(a-b)^2 Plug values and solve.

2 cups you need to fill the jug to 4.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

It depends on the size and markings of the jug.

If we assume that the jug is divided into equal intervals and each interval represents an equal volume,

then we can say that filling the jug to the second interval means that the jug is 1/2 full.

To fill the jug to the fourth interval, we need to fill the remaining 2 intervals, which means we need to add another 2 cups of liquid.

So, the answer is 2 cups.

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The end behavior of the function f(n) = 3(n + 2)²(n - 3)(n - 2) is given as follows:

The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.

The function for this problem is given as follows:

f(n) = 3(n + 2)²(n - 3)(n - 2).

Considering the degree, the function can be interpreted as follows:

\(3n^4\)

(for the limit when the input goes to infinity we consider only the term with the highest degree).

The leading coefficient is positive and the exponent is even, hence the end behavior is given as follows:

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Answer:

40

Step-by-step explanation:

you have to find the multiplier that gets 3 to equal 60, that would be 20

therefore, you then multiply the numerator by 20 also and get 40

Answer:

4 cups of sugar require 14 cups of sugar

Step-by-step explanation:

Given 7/8 cup flour= 1/4 cup sugar

Required determine the cups of flour for 4 cups of sugar

Determine the cups of flour for 4 cups of sugar

First, we need to determine the unit rate for 1 cup of sugar.

This is done by multiplying both sides by 4

Next, we determine cup of flour for 4 cups of sugar.

This is done by multiplying both sides by 4

Hence;4 cups of sugar require 14 cups of sugar

I hope this helps! if it doesn't if you tell me what the options are I can try to help more.

Answer:825cm

Step-by-step explanation:550cm/2=275cm

275*3=825cm

The domain of the function, is : Domain → (- ∞ , + ∞) and the inverse of the function is y = 3 + √x.

Domain is the set of {x} - values for which a function {y - values} exists. It is one of the important parameter while defining the characteristics of a function.

Given is the function as -

f(x) = (x - 3)²

{ 1 } -

The domain of the function f(x) = (x - 3)².

The function has no undefined points. So, we can write the domain as -

Domain → (- ∞ , + ∞)

{ 2 } -

The inverse of the function f(x) = (x - 3)².

We have -

f(x) = (x - 3)²

y = (x - 3)²

x = (y - 3)²

y - 3 = √x

y = 3 + √x

Therefore, the domain of the function, is : Domain → (- ∞ , + ∞) and the inverse of the function is y = 3 + √x.

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To find the local and absolute maximum and minimum points of the function f(x) = (3/5)x^5 - 9x^3 + 2 on the closed interval [-4,5], we need to follow these steps:

a) Find all critical numbers (x-coordinates only):

To find the critical numbers, we need to identify where the derivative of the function is zero or undefined. Let's find the derivative of f(x) first:

f'(x) = 3x^4 - 27x^2

Now, set the derivative equal to zero and solve for x:

3x^4 - 27x^2 = 0

Factoring out a common factor of 3x^2, we get:

3x^2(x^2 - 9) = 0

This equation is satisfied when either 3x^2 = 0 or x^2 - 9 = 0.

For 3x^2 = 0, we have x = 0.

For x^2 - 9 = 0, we have x = -3 and x = 3.

Therefore, the critical numbers (x-coordinates) are 0, -3, and 3.

b) Find the intervals on which the graph is increasing (mark critical numbers):

To determine the intervals of increasing, we need to analyze the sign of the derivative on each side of the critical numbers. We create a sign chart for f'(x):

Interval (-∞, -3): Choose a test point x < -3, e.g., x = -4

f'(-4) = 3(-4)^4 - 27(-4)^2 = 768 > 0

The derivative is positive, indicating the graph is increasing.

Interval (-3, 0): Choose a test point x between -3 and 0, e.g., x = -1

f'(-1) = 3(-1)^4 - 27(-1)^2 = -24 < 0

The derivative is negative, indicating the graph is decreasing.

Interval (0, 3): Choose a test point x between 0 and 3, e.g., x = 1

f'(1) = 3(1)^4 - 27(1)^2 = -24 < 0

The derivative is negative, indicating the graph is decreasing.

Interval (3, ∞): Choose a test point x > 3, e.g., x = 4

f'(4) = 3(4)^4 - 27(4)^2 = 768 > 0

The derivative is positive, indicating the graph is increasing.

Therefore, the graph is increasing on the intervals (-∞, -3) and (3, ∞).

c) Find the intervals on which the graph is decreasing (mark critical numbers):

From the analysis above, we can see that the graph is decreasing on the intervals (-3, 0) and (0, 3).

d) Find all local maximum points:

To find the local maximum points, we need to examine the points where the graph changes from increasing to decreasing. By observing the sign changes in the derivative, we can identify potential local maximum points.

From our analysis in part b, we can see that the graph changes from increasing to decreasing at x = -3 and x = 0. Therefore, these are the local maximum points.

e) Find all local minimum points:

To find the local minimum points, we need to examine the points where the graph changes from decreasing to increasing. By observing the sign changes in the derivative, we can identify potential local minimum points.

From our analysis in part c, we can see that the graph changes.

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The odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Since Jenny won a charity raffle, and her prize will be randomly selected from the 9 prizes shown below, and the prizes include 7 rings, 1 camera, and 1 headset, to find the odds against Jenny winning a headset, and find the odds in favor of Jenny winning a headset, the following calculations must be performed:

· 1 headset out of 9 total prizes

· 1/9 = headset

· 1/9 x 100 = 11.11%

· 100 - 11.11 = 88.89%

Therefore, the odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Answer:

D

Step-by-step explanation:

Remember that for this kind of question, when f(x) is given as 3, then 3 is the y value of the point. So you must have a point whose value is (x,3)

There is only one point that does that. x = - 2

The answer is D

The width of the path is approximately 7.45 meters.

What is meant by width?

The width refers to the measurement of something from side to side, typically in a direction perpendicular to its length or height, such as the width of a door or the width of a piece of paper.

What is meant by meters?

Meters are a unit of measurement used to measure the length in the metric system. One meter is equal to 100 centimetres or approximately 3.28 feet. It is commonly used to measure distances, heights, and lengths.

According to the given information

The area of the pool is given by the product of its length and width:

18 × 30 = 540 square meters

The area of the entire region, including the pool and the path, is given by the product of the length and width of the outer rectangle:

(18 + 2x) × (30 + 2x)

Expanding this expression, we get:

540 + 36x + 60x + 4x²

Simplifying, we get:

4x² + 96x + 540

We are given that the area of the entire region is 1900 square meters:

4x² + 96x + 540 = 1900

Subtracting 1900 from both sides, we get:

4x² + 96x - 1360 = 0

Dividing both sides by 4, we get:

x² + 24x - 340 = 0

We can use the quadratic formula to solve for x:

x = (-24 ± √(24² - 4 × 1 × (-340))) / (2 × 1)

Simplifying, we get:

x = (-24 ± √(1216)) / 2

x ≈ -17.45 or x ≈ 7.45

Since the width of the path cannot be negative, we can ignore the negative solution.

Therefore, the width of the path is approximately 7.45 meters.

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The population increases by 1200 people each year starting from the base population of 28,000 in 2003.

To write an equation for the population, P, years after 2003, we can use the information given about the population growth.

We know that in 2003, the population was 28,000. Since the population has been growing linearly by 1200 people each year, we can express the growth rate as 1200 people per year.

Let's denote the number of years after 2003 as 'x'. Since the growth rate is constant, we can use the slope-intercept form of a linear equation to represent the population:

P = mx + b

Where:

P represents the population

m represents the slope (growth rate)

x represents the number of years after 2003

b represents the y-intercept (population in the base year)

In this case, the slope, m, is 1200 people per year, and the y-intercept, b, is 28,000 people in 2003.

Plugging in the values, the equation for the population, P, years after 2003 becomes:

P = 1200x + 28000

This equation represents the linear growth of the town's population, where the population increases by 1200 people each year starting from the base population of 28,000 in 2003.

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Answer:

Distributive Property

Step-by-step explanation:

It looks like you are multiplying the 6 to both the 3 and 8.

Answer:

x = 5

Step-by-step explanation:

8x + 9 + 7x + 6 = 90,

15x + 15 = 90,

15x = 75,

x = 5

Answer:

She was there for 3 hours.

Step-by-step explanation:

7.25-5= 2.25

2.25÷0.75=3

Answer:  26 and 1/4

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

24 divided by 6 is 4, subtract Doug, there were 3 friends