HELPPPPPP PLZZ!!!!!!!

The area of the sector with an angle of 30° and radius of 18 mi is 27π mi².

A sector is simply the portion of a closed region bounded by a circle enclosed by two radii and an arc.

Area of a sector is expressed as;

A = θ/360° × πr²

Given the data in the image;

Plug the given values into the above formula and solve for A.

A = θ/360° × πr²

A = 30°/360 × π × (18 mi)²

A = 1/12 × π × 324 mi²

A = 27π mi²

Therefore, the area of the sector is 27π mi².

Option B) 27π mi² is the correct answer.

Learn more about sector here: https://brainly.com/question/16367606

#SPJ1

To ensure that the function f(x)={ x+1,x^2+bx+c,1 is continuous on the entire real number line, we can choose any value of b and set c=1-b.

To ensure that the function f(x) is continuous on the entire real number line, we need to ensure that the two pieces of the function match at x = 1. That is, we need to find values of b and c such that:

x + 1 = x^2 + bx + c, at x = 1

Simplifying the right-hand side, we get:

1 + b + c = 2

We also need to ensure that the function is continuous at x = 1 for the second piece, which means that the limit of the function as x approaches 1 from either side must exist and be equal to the value of the function at x = 1. That is:

lim x->1^- (x^2 + bx + c) = lim x->1^+ (x + 1) = 2

Taking the left-hand limit, we get:

lim x->1^- (x^2 + bx + c) = 1 + b + c

So, we need to find values of b and c such that:

1 + b + c = 2, and lim x->1^- (x^2 + bx + c) = 2

Using the first equation, we can solve for c:

c = 1 - b

Substituting this into the second equation and simplifying, we get:

lim x->1^- (x^2 + bx + 1 - b) = 2

=> 1 + b + 1 - b = 2

=> 2 = 2

This equation is always true, regardless of the value of b, so any value of b will work as long as c is set to 1 - b. Therefore, we have:

b = any real number

c = 1 - b

So, to ensure that the function f(x) is continuous on the entire real number line, we can choose any value of b and set c = 1 - b.

To know more about Continuity of function:

https://brainly.com/question/21447009

#SPJ4

Answer: I belive the answer you are lookin for is  8x+2!

Step-by-step explanation:

First, we have to do 10x-5 - 2x +7

Then we have 8x + 2 ( our answer)

Answer:

28.0ft

Step-by-step explanation:

22/7= π= 3.142857143

circumference= πd

88= 3.142857143×d

d= 88/3.142857143

d=28.0ft

Answer:

m = 5

Step-by-step explanation:

Given

\(\frac{m-2}{6}\) = \(\frac{1}{2}\) ( multiply both sides by 6 to clear the fraction )

m - 2 = 3 ( add 2 to both sides )

m = 5

Answer:

4.1015659297

Explanation:

4.1015659297 is the number that you multiply by itself 3 times to get 69

Answer:

4.102

Step-by-step explanation:

there is no exact cube root of 69

The mean of the number of drivers expected not to be wearing seatbelts is approximately 4.35, the variance is approximately 15.62, and the standard deviation is approximately 3.95 and they expect to stop approximately 4.35 cars before finding a driver whose seatbelt is not buckled.

a. To find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts, we can model the situation using a geometric distribution.

Let's define a random variable X that represents the number of cars stopped until the first driver without a seatbelt is found. The probability of a driver not wearing a seatbelt is given as p = 0.23.

The mean (μ) of a geometric distribution is given by μ = 1/p.
μ = 1/0.23 ≈ 4.35

The variance (σ^2) of a geometric distribution is given by σ^2 = q/p^2, where q = 1 - p.
σ^2 = (0.77)/(0.23^2) ≈ 15.62

The standard deviation (σ) is the square root of the variance.
σ = √(15.62) ≈ 3.95


b. The expected number of cars they expect to stop before finding a driver whose seatbelt is not buckled is equal to the reciprocal of the probability of success (finding a driver without a seatbelt) in one trial. In this case, the probability of success is p = 0.23.

Expected number of cars = 1/p = 1/0.23 ≈ 4.35

To learn more about mean, variance and standard deviation go to:

https://brainly.com/question/30558769

#SPJ11

Answer:

3769.57 cm²

Step-by-step explanation:

Diameter = 98 cm

Radius = 98/2 = 49 cm

Area of Semi Circle = πr²/2

= 3.14 × 49 × 49/2

= 3769.57 cm²

So 3769.57 cm² is the answer

It is impossible to determine with certainty which number of pushups Bucky will never do in any game, as this depends on Bucky's physical abilities, training, and determination.

It is possible that Bucky may be able to do a very large number of pushups in a game, or he may not be able to do very many. It is also possible that there may be certain numbers of pushups that Bucky finds more challenging or difficult to do than others, but this would depend on his individual physical abilities and strengths. Ultimately, the number of pushups that Bucky will be able to do in any given game will depend on a variety of factors, and it is not possible to predict with certainty which numbers he will never do.

To learn more about the numbers, visit:

brainly.com/question/17429689

#SPJ4

Number of push-ups Bucky will never perform in any game is impossible to predict with confidence because it relies on Bucky's physical prowess, training, and willpower.

In a game, Bucky might be able to perform a lot of push-ups or he might not be able to perform many at all. It's also likely that Bucky will find some numbers of push-ups harder or more difficult to complete than others; however, this will depend on his particular physical prowess and capabilities.

In the end, Bucky's ability to do a certain number of push-ups throughout a game will rely on a multitude of variables, and it is impossible to say with certainty certain numbers he will never complete.

To learn more about physical ability link is here

brainly.com/question/12643225

#SPJ4

No, the lines cannot ever match up perfectly because there is always some sort of difference between them. The lines can have the same slope if they have the same change in y-values for a given change in x-values. The lines can also have the same y-intercept if they cross the y-axis at the same point.

No, there will never be a perfect alignment between the lines since there will always be a discrepancy of some kind. However, the lines can have the same slope and y-intercept. This is possible because the slope and y-intercept are determined by the equation of the line, and if two lines have the same equation, then they will have the same slope and y-intercept.

If the lines intersect the y-axis at the same location, they can also have the same y-intercept. This means that the two lines have the same value of b in the equation y = mx + b. This means that the two lines have the same slope and the same y-intercept.

To learn more about equation of the line link is here

brainly.com/question/21511618

#SPJ4

84. A basis for the solution space of the given homogeneous linear system is {(1, -1, 0), (-1, 0, 1)}. The dimension of the solution space is 2.85. A basis for the solution space of the given homogeneous linear system is {(2, -1, 0, 1), (-1, 2, 1, 0), (1, 0, 1, 3)}.

The dimension of the solution space is 3.86. A basis for the solution space of the given homogeneous linear system is {(2, 6, 1, 0), (-1, -3, 0, 1), (2, 6, 1, 0)}. The dimension of the solution space is 2.87. A basis for the solution space of the given homogeneous linear system is {(2, -1, 1)}. The dimension of the solution space is 1.

We will find the solution of each equation by using the elimination method.84. 2x1 - x2 + x3

= 0  x1 + x2

= 0  -2x1 - x2 + x3 = 0  Let's solve this linear system of equations in order to find the solution of x. x1 + x2 = 0 can be rewritten as

x2 = -x1.Substitute x2 = -x1 in equation 1 and 3.

2x1 - x2 + x3 = 0 becomes

2x1 + x1 + x3 = 0 which gives

3x1 + x3 = 0 or x3

= -3x1.-2x1 - x2 + x3 = 0 becomes

-2x1 + x1 - 3x1 = 0, and that simplifies to

-4x1 = 0. This implies x1 = 0.Now we have

x1 = 0 and

x3 = 0. x2 = -x1 = 0.

The dimension of the solution space is

2.85. 3x1 - x2 + x3 - x4

= 0  4x1 + 2x2 + x3 - 2x4

= 0

We will solve this linear system of equations by using the elimination method. This will result in the solution of

x.3x1 - x2 + x3 - x4 = 0 becomes

x4 = 3x1 - x2 + x3. Substituting x4 into the second equation, we obtain 4x1 + 2x2 + x3 - 2(3x1 - x2 + x3) = 0.

This simplifies to -2x1 + 3x2 - 4x3 = 0.

Now we have x4 = 3x1 - x2 + x3 and -2x1 + 3x2 - 4x3 = 0.

To get the basis for the solution space, we find all free variables. In this case, there are three free variables.

Let x1 = 1, x2 = 0, and x3 = 0, this gives (2, 0, 0, 3).

learn more about  homogeneous linear system

https://brainly.com/question/14783356

#SPJ11

Let be "x" and "y" the two positive numbers mentioned in the exercise.

You need to remember the following definitions:

- A Difference is the result of a Subtraction.

- A Product is the result of a Multiplication.

In this case, you know that their Difference is 12 and their Product is 693. So you can set up this System of Equations:

You can solve the System of Equation using the Substitution Method:

1. You can solve for the variable "x" from the first equation:

2. Substitute this new equation into the second original equation and simplify:

3. Now you have to solve for "y", in order to find its value:

- Rewrite the equation in this form:

Since it is the variable "y":

Then:

4. Use the Quadratic Formula to find the values of "y". The formula would be:

In this case:

Then, substituting values and evaluating, you get:

5. Since the numbers mentioned in the exercise are both positive, you must choose only the positive values. Therefore:

6. To find the value of "x", you have to substitute the value of "y" into the equation

Then:

7. Finally, you have to solve the Addition:

The answer is:

(a) Stability of Velocity of Money:

It is the extent to which the quantity theory of money holds in the short term. Velocity of money refers to the rate at which money changes hands or in other words it is defined as the number of times a unit of money is used in purchasing final goods and services in a given period of time.

(b) Importance of Stability of Velocity of Money in explaining Fisher's theory of demand for money:

According to Fisher, there is a direct relation between the volume of trade and the demand for money.

(c) Differences between Fisher's and Friedman's theory of the demand for money:Fisher's Theory of Demand for Money:It is based on the Quantity Theory of Money ,while Friedman's theory of the demand for money is based on the modern Quantity Theory of Money

a) In case, the velocity of money is unstable, then an increase in money supply may lead to a decrease in velocity of money leading to an insignificant effect on prices.

Whereas, in case, velocity is stable, then an increase in money supply will lead to an equivalent rise in prices. The stability of the velocity of money is critical for the Quantity Theory of Money.

b) According to him, the volume of trade is influenced by the quantity of money, and the velocity of money remains constant.

In other words, Fisher assumed the stability of velocity of money and believed that changes in the quantity of money lead to an equal proportionate change in the general price level. So, in order to validate Fisher's Quantity Theory of Money, velocity of money should be stable.

c) Fisher assumes that velocity of money is constant in the short-run, therefore, the only variable affecting the price level is the quantity of money.

Friedman's Theory of Demand for Money:

Friedman's theory of the demand for money is based on the modern Quantity Theory of Money. He has divided the demand for money into two components: Transactions demand for money and Asset demand for money. He also assumes that velocity of money is not constant rather it is stable in the long run. Friedman also included other factors which influence the

Learn more about demand at;

https://brainly.com/question/32703554

#SPJ11

Answer:

$3.00

Step-by-step explanation:

7.50/5 = 1.5

12/8 = 1.5

Since each song costs $1.50 each, multiply the cost by the number of songs.

1.50(2) = 3

$3.00

The probability of a typical driver who drives less than 10,000 miles per year having an accident in a year is 9.18%.

To calculate the probability of a driver who drives less than 10,000 miles per year having an accident, we can use the Z-score and the standard normal distribution.

First, we need to calculate the Z-score for a driver who drives less than 10,000 miles per year. The Z-score formula is:

Z = (X - μ) / σ

Where:

X is the value we want to calculate the Z-score for (10,000 miles per year),

μ is the mean (15,000 miles per year), and

σ is the standard deviation (3,750 miles per year).

Plugging in the values, we get:

Z = (10,000 - 15,000) / 3,750

Z = -1.333

Looking up the Z-score -1.333 in the standard normal distribution table, we find the probability to be approximately 0.0918 or 9.18%.

Therefore, the probability of a typical driver who drives less than 10,000 miles per year having an accident in a year is approximately 9.18%.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ4

The piecewise function in the graph is:

f(x) = -1  if x ≤ -5

f(x) = x - 1   if x > 3

First, on the left side we can see a constant function that ends at x = -5, so we can write that first part as:

f(x) = -1  if x ≤ -5

The second part is a line that starts at x = 3 (but does not contain it). It is a linear equation, and we can see the points (3, 2) and (4, 3), so the slope is 1.

y = x + b

To find the value of b, we can replace any of the points there:

2 = 3 + b

2 - 3  =b

-1 = b

Then the piecewise function is:

f(x) = -1  if x ≤ -5

f(x) = x - 1   if x > 3

Laern more about piecewise function:

https://brainly.com/question/3628123

#SPJ1

There are 15 different possibilities for the three whole numbers whose product is 120.

To find the different possibilities for the three whole numbers, we need to find all the ways we can multiply three whole numbers together to get 120, which is the product.

We can start by listing out the factors of 120:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

From this list, we can start trying out combinations of three numbers that multiply to 120. For example:

1 x 1 x 120 = 120
1 x 2 x 60 = 120
1 x 3 x 40 = 120
1 x 4 x 30 = 120
1 x 5 x 24 = 120
1 x 6 x 20 = 120
1 x 8 x 15 = 120
2 x 3 x 20 = 120
2 x 4 x 15 = 120
2 x 5 x 12 = 120
2 x 6 x 10 = 120
3 x 4 x 10 = 120
3 x 5 x 8 = 120
4 x 5 x 6 = 120

So there are 15 different possibilities for the three whole numbers that multiply to 120.
To find the different possibilities for the three whole numbers whose product is 120, we need to find the combinations of factors of 120.

Step 1: Find the prime factorization of 120.
\(120 = 2*2*2*3*5 (2^3 * 3 * 5)\)

Step 2: Identify the possible factors.
Using the prime factors, we can generate the different whole number factors for 120:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Step 3: Find the possible combinations of three whole numbers.
1. 1 × 1 × 120
2. 1 × 2 × 60
3. 1 × 3 × 40
4. 1 × 4 × 30
5. 1 × 5 × 24
6. 1 × 6 × 20
7. 1 × 8 × 15
8. 1 × 10 × 12
9. 2 × 2 × 30
10. 2 × 3 × 20
11. 2 × 4 × 15
12. 2 × 5 × 12
13. 2 × 6 × 10
14. 3 × 4 × 10
15. 3 × 5 × 8

Learn more about product here:

https://brainly.com/question/8849203

#SPJ11

Set of factors can be rearranged in six different ways, there are actually 60 possible ways to arrange the factors into three numbers.

The possible combinations of three whole numbers that result in a product of 120.

One way to approach this is to list all the factors of 120 and then group them into sets of three.

Another method is to use prime factorization.

120 as a product of its prime factors: 2 x 2 x 2 x 3 x 5.

The possible combinations of three factors, we can use a combination formula.
The formula for the number of combinations of n items taken r at a time is:

\(nCr = n! / (r! \times (n-r)!)\)
In our case, n = 5 (the number of prime factors), and r = 3 (the number of factors we want to choose).

So, the number of possible combinations is:
\(5C3 = 5! / (3! \times 2!) = (5 \times 4 \times 3) / (3 \times 2) = 10\)
There are 10 different possibilities for the three whole numbers that multiply to 120.

These are:
\(\(2 \times 2  \times 30, 2  \times 3  \times 20, 2  \times 4 \times 15, 2  \times 5  \times 12, 2  \times 6  \times 10, 3  \times 4  \times 10, 3  \times 5  \times 8, 4  \times 5  \times 6, 3  \times 2  \times 20, and  5  \times 2  \times 12.\)\)
The order of the factors does not matter, so\(2 \times 3 \times 20\) is the same as\(3 \times 2 \times 20\).

For similar questions on factors

https://brainly.com/question/25829061

#SPJ11

Answer:

f(x) / g(x) = 8^x / 9 --> B

Step-by-step explanation:

You just need to plug in the values

Answer:

B. 8^2/-9

Step-by-step explanation:

I think the first guy is right

Answer:

the area below the line is shaded

Step-by-step explanation:

Answer:

Starting at the origin and going up.

Step-by-step explanation:

Typically in geometry you want to start at the origin and move up to begin your first point, and move to either side for the second.

The number of rabbits that must be sold if they want to be fed for 15 more days is 150 rabbits.

In a farm, there is food to feed 300 rabbits for 60 days.

Let x be the number of rabbits that must be sold if they want to be fed for 15 more days.

From the given data, we have the following equation:

300 * 60 = (300 - x) * 75

The equation represents the amount of food for 300 rabbits that can last 60 days is equal to the amount of food for 300 - x rabbits that can last 75 days.

Solving for x, we get:

x = 150 rabbits

Hence, the number of rabbits that must be sold if they want to be fed for 15 more days is 150 rabbits.

For more such questions on rabbits, click on:

https://brainly.com/question/378897

#SPJ8

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

Learn more about circle here

brainly.com/question/11878555

#SPJ4

Option B "Perpendicular Lines"  is correct.

"Perpendicular Lines" are two lines that intersect at a right angle, forming 90-degree angles between them. Thus, Option B holds the truth.

Perpendicular lines are a fundamental concept in geometry and they are defined as two lines that meet at a right angle; forming four 90-degree angles. This means that the slopes of the two lines are negative reciprocals of each other. Perpendicular lines are important in many areas of mathematics and physics because they allow us to calculate angles, distances and other geometric properties.

Perpendicular lines are useful in many practical applications such as: architecture, engineering and construction. By understanding the properties of perpendicular lines, one can better understand the geometry of our world and solve real-world problems.

Learn more about Perpendicular lines brainly.com/question/1202004

#SPJ4

Answer: 48, 24, 8,

Step-by-step explanation:

The future value (A) is approximately 5610.2 for the given investment and annu $4000 for 5 years at 7% compounded annually

To find the compound amount and compound interest rate for the given investment, we can use the formula for compound interest:

(a) The compound amount in the account after 5 years can be calculated using the formula:

A = P(1 + r/n)^(nt)

Where A is the compound amount, P is the principal (initial investment), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Given that the principal (P) is $4000, the interest rate ® is 7%, and the interest is compounded annually (n = 1), and the investment is for 5 years (t = 5), we can plug these values into the formula:

A = 4000(1 + 0.07/1)^(1*5)

A = 4000(1 + 0.07/1)^(1*5)

= 4000(1 + 0.07)^(5)

= 4000(1.07)^(5)

≈ 4000(1.402551)

≈ 5610.20

Therefore, the future value (A) is approximately 5610.2

Calculating this expression will give us the compound amount after 5 years.

(b) The compound interest earned can be calculated by subtracting the principal from the compound amount:

Compound interest = Compound amount – Principa

This will give us the total interest earned over the 5-year period.

By evaluating the expressions in (a) and (b), we can determine the compound amount and the compound interest earned for the given investment.

Learn more about compound interest rate here:

https://brainly.com/question/30501640

#SPJ11

Answer:

12b=3b+75

Step-by-step explanation:

Answer:

12b=3b+75

Step by step equation

Answer:

\(\sf x = 1 + 2\sqrt{3}\)

Explanation:

In a right angle triangle, the hypotenuse is the longest side.

Here the given sides are (x + 1) cm, (x + 2) cm, (x + 4) cm.

where (x + 4) is the longest side among all the side lengths.

Apply Pythagoras theorem:

(leg 1)² + (leg 2)² = (hypotenuse)²

substitute values

\(\sf (x + 1)^2 + (x + 2)^2 = (x + 4)^2\)

\(\sf x^2 + 2x + 1 + x^2 + 4x + 4 = x^2 + 8x + 16\)

\(\sf x^2 + x^2 - x^2 + 2x + 4x - 8x + 1 + 4 - 16 = 0\)

\(\sf x^2 - 2x - 11 = 0\)

use quadratic formula

\(\sf \dfrac{-(-2)\pm \sqrt{(-2)^2 - 4(1)(-11)} }{2(1)}\)

\(\sf \rightarrow \dfrac{2\pm \sqrt{48} }{2}\)

\(\sf \rightarrow 1\pm \sqrt{48}\)

\(\sf \rightarrow 1\pm 2\sqrt{3}\)

\(\sf \rightarrow 1+ 2\sqrt{3} \:\ or \:\ 1 -2\sqrt{3}\)

\(\sf \rightarrow 4.46 \:\ or\:\ -2.46\)

As length can only be positive, the value of x will be 1 + 2√3.