The city is building a new roundabout in order to correct a traffic flow issue at some of its intersections. Due to safety regulations, the inner circle must have a diameter of 8 ft. When construction is complete, they plan to cover this area with grass. How much sod (grass) do they need to cover the inner circle of the roundabout?


Use 3.14 for π.


(If you manage to answer this in 3 sentences you get a virtual high five here's some sentence starters if needed, The formula for the area of a circle is ____________.The area of the roundabout about is _________ ft².This is how I found the area of the circle ________

a) The probability of picking at least one green marble is given as follows: 5/9, option D.

b) The expected number of repetitions with the same color is given as follows: 150 repetitions.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The number of outcomes in this problem is given as follows:

9.

The number of outcomes in which at least one green was picked is:

5.

Hence the probability is of:

p = 5/9.

3 outcomes had the same color, (G,G), (O,O) and (B,B), hence the probability is given as follows:

p = 3/9

p = 1/3

Out of 450 repetitions, the amount is given as follows:

E(X) =  1/3 x 450 = 150 repetitions.

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The measure of arc ZWX is 180 degrees.

Given that WZ and XR are diameters, we know that they are both perpendicular to chord WX. This creates four right angles at point X, and as a result, we have a rectangle formed by the four line segments.

Since WZ and XR are diameters, they each extend from one end of the rectangle to the other. This means that arc ZWX is actually a semicircle, with a measure of 180 degrees.

To see why this is the case, consider that a full circle has a measure of 360 degrees. Since arc ZWX spans exactly half of the circle, it must have a measure of half the circle, or 180 degrees.

In summary, the measure of arc ZWX is 180 degrees. This can be derived from the fact that WZ and XR are diameters, which create a rectangle and a semicircle in the process. While the figure may not be drawn to scale, the relationships between the different line segments and angles remain constant, allowing us to determine the measure of arc ZWX with confidence.

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If log 7 equals a and log 8 equals b then log 224 equals: E: none of the above.

Simplify the expression for log (224) by using:

log (ab) = log (a) + log (b) and log (a/b) = log (a) - log (b):

So,

log (224) = log ( 7 × 8 × 4)

= log (7) + log (8) + log (4)

Since log(4) = 0 (since 4 = 2^2)

Simplify

log(224) = log (7) + log (8) + log (4)

= log 7 + log 8

= a + b

Therefore the correct option is E.

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The mood of the argument is categorical and the figure is EIO. To determine the mood and figure of the given argument, we'll first identify the premises and conclusion, and then assign the appropriate categorical proposition to each statement.

The argument can be rewritten as:

Premise 1: Some dictators are not warmongers. (Some D are not W)
Premise 2: No dictators are egomaniacs. (No D are E)
Premise 3: Some egomaniacs are warmongers. (Some E are W)
Conclusion: Some dictators are not warmongers. (Some D are not W)

Now, let's assign the categorical propositions to each statement:
Premise 1: I (Some D are not W)
Premise 2: E (No D are E)
Premise 3: I (Some E are W)
Conclusion: O (Some D are not W)

The mood of the argument is IEO.

Next, we'll determine the figure by looking at the placement of the middle term (E) in the premises:
Premise 2: No D are E (subject-middle term)
Premise 3: Some E are W (middle term-predicate)

The figure is 1 because the middle term is the subject of one premise and the predicate of the other premise.

So, the mood and figure of the argument are IEO-1. Therefore, the correct answer is:

IEO - 1

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Answer:

2(p - 32)(p + 2)

Step-by-step explanation:

2p² - 60p - 128 ← factor out common factor 2 from each term

= 2(p² - 30p - 64) ← factor the quadratic

consider the factors of the constant term ( - 64) which sum to give the coefficient of the p- term (- 30)

the factors are - 32 and + 2 , since

- 32 × + 2 = - 64 and - 32 + 2 = - 30 , then

p² - 30p - 64 = (p - 32)(p + 2) , so

2p² - 60p - 128 = 2(p - 32)(p + 2)

The factors of a quadratic equation 2p² - 60p - 128 are (p - 4) and (p - 32).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

To factorize a quadratic equation of the form ax² + bx + c, we need to find two numbers that multiply to ac and add up to b. In this case, we have:

a = 2, b = -60, c = -128

The product of a and c is:

ac = 2 × (-128) = -256

We need to find two numbers that multiply to -256 and add up to -60. We can start by listing the factors of -256:

1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128, 256, -256

We can see that -16 and 16 are a pair of factors that multiply to -256. We can also see that -16 + 16 = 0, which is not what we want. We need factors that add up to -60, not to 0.

We can try the next pair of factors, -32 and 8. These multiply to -256 and add up to -24. This is closer to what we want, but we need factors that add up to -60.

We can try the next pair of factors, -64 and 4. These multiply to -256 and add up to -60. This is what we need, so we can use these factors to factorize the quadratic equation:

2p² - 60p - 128 = 2(p - 4)(p - 32)

Therefore, the factors of the quadratic equation are (p - 4) and (p - 32).

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The correct statement according to the zero product property is the one in option B.

The zero product property says that if the product of two numbers A and B is zero, then either A or (and) B are equal to zero.

Then if:

(x + 10)*x = 0

Then we have that either:

x = 0

or:

x + 10 = 0

x = -10

Then the correct option is B:

"Either x = 0 or x + 10 =0"

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Mandy's Candies sells an average of 68 pounds of fudge and 81 pounds of toffee each month. Option B

Using  a system of equations to solve this

Let f be the number of pounds of fudge sold each month, and

t be the number of pounds of toffee sold each month.

Then we have:

f + t = 149    (equation 1)

8.12f + 7.62t = 1169.38   (equation 2)

We can solve for f in equation 1:

f = 149 - t

Substituting this into equation 2, we get:

8.12(149 - t) + 7.62t = 1169.38

Simplifying and solving for t, we get:

1209.88 - 0.5t = 1169.38

0.5t = 40.5

t = 81

Substituting this back into equation 1, we get:

f + 81 = 149

f = 68

Therefore, Mandy's Candies sells an average of 68 pounds of fudge and 81 pounds of toffee each month.

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Answer:

The height of the new cylindrical tank is approximately 54.10 cm when rounded to two decimal places.

Step-by-step explanation:

Find the volume of the water in the original tank using the formula for the volume of a cylinder:

V1 = π(10.5cm)^2(20cm) ≈ 6939.25 cm^3

Since the amount of water is conserved, set the volume of the water in the new tank equal to V1:

V2 = π(10cm)^2(h)

π(10.5cm)^2(20cm) = π(10cm)^2(h)

Simplifying, we get:

4410 = 100h

h ≈ 44.10 cm

However, this is the height that the water would reach if it was poured into a cylinder with a radius of 10 cm. To find the actual height of the new tank, add the radius of the new tank (which is also 10 cm) to this height:

h_new = h + r = 44.10 + 10 = 54.10 cm

Therefore, the height of the new tank is approximately 54.10 cm when rounded to two decimal places.

1/2 is the probability that the number will add up to more than 4. Option C is correct

Probability is defined as the likelihood or chance that an event will occur.

Probability = Expected/Total

From the given spinner, the total outcome is expressed according to the permutation

For orange spin

3P2 = 3!
3P2  = 6

For green spin

4P2 = 4!/2!
4P2 = 12

If they are both spinned, the probability that the sum will be more than 4 are:

Expected (orange) = {(2,3)}

Expected (green) = {((1, 3), (3, 4) (2, 4), (2,3)}

Pr(number added is 4) = 1/6 + 4/12

Pr(number added is 4)  = 2+4/12

Pr(number added is 4)  = 1/2

Hence the probability that the number will add up to more than 4 is 1/2

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Answer:

6 units right

Step-by-step explanation:

To translate figure P onto figure Q, just translate the figure 6 units to the right.

For the given right angle triangle ABC  (A) option is the correct answer.

We have,

A right triangle, also known as a right-angled triangle, or more technically an orthogonal triangle, was originally known as a triangle, is a triangle with one right angle and two perpendicular sides. Trigonometry is based on the relationship between the sides and various angles of a right triangle.

What is the correct statement for right triangle ABC ?

Cos A = Sin ( 90˚- A )

Since at 90˚ Sine function convert into cosine function and (90˚- A) results in first quadrant where sine function is positive.

Therefore Cos A = Cos A

Hence the correct option is (a) option Cos A = Sin ( 90˚- A )

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complete question:

attached below.

Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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The area of the trapezium ABCD is 136 square cm

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

The image of the trapezium (see attachment)

The area of the trapezium ABCD is calculated as

Area = 1/2 * Sum of opposite sides * Height

When the given values are substituted in the above equation, we have the following equation

Area = 1/2 * (14 + 20) * 8

Evaluate the sum

Area = 1/2 * 34 * 8

Evaluate the products

Area = 136

Hence, the area of the trapezium ABCD is 136 square cm

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Nakeisha sold 8 lollipops and 5 fruit snacks to make a total of $18.25.

Let's fix this issue using a set of equations. Assume that x is the quantity of lollipops sold and y is the quantity of fruit snacks sold.

Then we have two equations based on the information given:

x + y = 13.(Total number of fruit snacks and lollipops sold)

1.5x + 1.25y= 18.25 (total amount of money earned)  

To solve for x and y, we can use the substitution method :

x + y = 13 (equation 1)

1.5x + 1.25y = 18.25 (equation 2)

From equation 1, we have x = 13 - y. Substituting this into equation 2, we get:

1.5(13 - y) + 1.25y = 18.25

Simplifying and solving for y, we get

19.5 - 0.25y = 18.25

-0.25y = -1.25

y = 5

Nakeisha therefore sold 5 fruit treats. We may change y = 5 into equation 1 and solve for x to get the quantity of lollipops sold:

x + 5 = 13

x = 8

Therefore, Nakeisha sold 8 lollipops and 5 fruit snacks to make a total of $18.25.

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The value of length JK is 11

A tangent is a straight line that touches any part of the circumference. A circumference is the outer body of a circle.

A theorem of tangency states that if lines comes from thesame point of a circumference and meet at a point , then the lines are equal.

Therefore we can say that;

JA = JB = 5

AL = LC = 9

CK = LK - LC

= 15 -9

= 6

BK = LK = 6

therefore ;

JK = BK + JP

= 6+5

= 11

Therefore the value of JK is 11

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Answer: 4140, 4060, and 4109

Step-by-step explanation:

4140: looking at the tens place (4) it is less than 5 so it rounds to 4100

4060: the tens place (6) is bigger than 5 so you add a 1 to the hundreds place everything behind it becomes a 0. and equal to 4100.

4109: everything behind becomes a 0

Correct answers -

a.Rate of change of water in the pool at t= 5 hours

b. Total volume of water in the pool at t=10 hours

c. Average rate of change of water in the pool = 389.31 gallons/hour

To answer the given questions, let's go step by step:

a. To find the rate of change of water in the pool at t=5 hours, we need to calculate the difference between the rate of water being pumped into the pool and the rate of water leaking from the pool at that specific time.

Rate of change of water in the pool at t=5 hours = P(5) - L(5)

P(5) = 1170 gal/hour (given)

L(5) = [tex]0.3e^5[/tex] gal/hour (given)

Substituting the values into the equation:

Rate of change of water in the pool at t= 5 hours = 1170 - [tex]0.3e^5[/tex]

b. To write an integral expression to calculate the total volume of water in the pool at t=10 hours, we need to integrate the rate of water being pumped into the pool over the time interval [0, 10] and subtract the integral of the rate of water leaking from the pool over the same interval.

Total volume of water in the pool at t=10 hours = ∫[0,10] P(t) - ∫[0,10] L(t) dt

P(t) = 1170 gal/hour (given)

L(t) = [tex]0.3e^t[/tex] gal/hour (given)

Calculating the integrals:

∫[0,10] P(t) dt = ∫[0,10] 1170 dt = 1170t | [0,10] = 1170 × 10 - 1170 × 0 = 11700 gallons

∫[0,10] L(t) dt = ∫[0,10] 0.3[tex]e^t[/tex] dt = 0.3 ∫[0,10] [tex]e^t[/tex]dt = 0.3 ([tex]e^t[/tex]) | [0,10] = 0.3 × ([tex]e^{10} - e^0[/tex]) ≈ 0.3 × (22025 - 1) ≈ 6606.9 gallons

Total volume of water in the pool at t=10 hours = 11700 - 6606.9 ≈ 5093.1 gallons

c. To find the average rate of change of water in the pool over the 10 hours, we need to divide the change in volume by the time interval.

Average rate of change of water in the pool = (Change in volume) / (Time interval)

Change in volume = Total volume of water in the pool at t=10 hours - Initial volume of water in the pool

Change in volume = 5093.1 - 1200 = 3893.1 gallons

Time interval = 10 hours

Average rate of change of water in the pool = 3893.1 / 10 = 389.31 gallons/hour

d. To find the absolute maximum volume of water in the pool over the interval [0,10], we need to find the maximum value of the volume function within that interval.

To determine this, we can find the critical points by setting the derivative of the volume function equal to zero and check the endpoints of the interval.

Since the volume function is not provided, we cannot directly find the absolute maximum volume without additional information.

Final answers-

a.Rate of change of water in the pool at t= 5 hours

b. Total volume of water in the pool at t=10 hours

c. Average rate of change of water in the pool = 389.31 gallons/hour

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The value of x such that f(x) = -24 is given as follows:

x = -3.

The exponential function in the context of this problem is defined as follows:

[tex]f(x) = -3(0.5)^x[/tex]

The numeric value of the function is given as follows:

f(x) = -24.

Hence we can equal the definition to -24 to obtain the value of x, as follows:

[tex]-3(0.5)^x = -24[/tex]

[tex]0.5^x = 8[/tex]

We have that:

Hence:

[tex]2^{-x} = 2^3[/tex]

x = -3.

Which is the solution to the exponential function in this problem.

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Answer:

10.6

Step-by-step explanation:

To find out how long the person must leave the money in the bank until it reaches $22,600, we can use the formula for compound interest:

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

Where:

A = the final amount (22600 dollars in this case)

P = the principal amount (9500 dollars)

r = the annual interest rate (5.75% expressed as 0.0575)

n = the number of times the interest is compounded per year (in this case, annually, so n = 1)

t = the time in years

Substituting the given values into the formula, we have:

22600 = 9500(1 + 0.0575/1)^(1*t)

Simplifying:

2.3789 = (1.0575)^t

To solve for t, we take the logarithm of both sides:

log(2.3789) = log((1.0575)^t)

Using logarithm properties, we can bring the exponent down:

log(2.3789) = t * log(1.0575)

Now, we can solve for t by dividing both sides of the equation:

t = log(2.3789) / log(1.0575)

Using a calculator, we find:

t ≈ 10.6

Therefore, the person must leave the money in the bank for approximately 10.6 years to reach $22,600.

The first term of an A.P is 14 and the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. The 3rd term of the A.P is 70/11.

The first term of an A.P is 14. Let the common difference be d. Then the second term of the A.P is given by 14 + d. Similarly, the third term of the A.P is given by 14 + 2d.

The third term of the A.P.Solution:

Sum of the first 5 terms of the A.P can be expressed as:

5/2 [2a + (5 - 1) d] = 5/2 [2(14) + 4d] = 35 + 10d

Sum of the first 10 terms of the A.P can be expressed as:

10/2 [2a + (10 - 1) d] = 10/2 [2(14) + 9d] = 70 + 45d

According to the question, the sum of the first five terms and the first ten terms are equal in magnitude but opposite in sign. It can be written as follows: 35 + 10d = - (70 + 45d)

Simplifying the above equation, we get:

55d = -105⇒ d = -105/55 = -21/11

Substituting the value of d in 14 + 2d, we get:

14 + 2d = 14 + 2(-21/11) = 14 - 42/11= 112/11 - 42/11= 70/11

Hence, the third term of the A.P is 70/11.

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The steps correcting the error;

Step 1: Convert the mixed fraction to improper fractions

Step 2: Find the lowest common  factor

27/8

A fraction can be defined as the part of a whole number, variable or element.

The different types of fractions are;

From the information given, we have that;

10 1/4 - 6 7/8

First, convert the mixed fractions to improper fractions, we have that;

Multiply the numerator of the fraction by the whole number then add the numerator

41/4 - 55/8

Find the LCM

82 - 55 /8

subtract the value

27/8

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Answer:

25.54

Step-by-step explanation:

SOH CAH TOA

           v            

   Cos 0 = [tex]\frac{adj}{hyp}[/tex]

-------------------------------------------

11.

Cos 20° = [tex]\frac{adj}{hyp}[/tex]

Cos 20° = [tex]\frac{24}{x}[/tex]

*Rearrange*

[tex]x[/tex] = [tex]\frac{24}{Cos 20}[/tex]

*Cos 20° = 0.9397*

[tex]x[/tex] = [tex]\frac{24}{0.9397}[/tex]

[tex]x[/tex] = 25.5400659785

Nearest tenth: 25.54

Answer:

1

You're welcome!

A coefficient is a constant which stands in front of a variable

For example, the coefficient of 3x is 3.  

Or, the coefficient of 9xy is 9

Same with 2x^2*z.  2

In this case, because there is nothing visible, the coefficient is 1.

The better statistics to compare the distribution are given as follows:

A. Mean and standard deviation.

The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.

The standard deviation of a data-set is calculated as square root of the sum of the differences squared between each observation and the mean of the data-set, divided by the cardinality of the data-set.

These two measures should be used as both distributions in this problem are symmetric, meaning that they do not contain outliers.

If the distribution contained outliers, then the median and the IQR should have been used.

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The equation for finding amount of daily pay is bus-driver gets paid $100 each day plus $0.20 per kilometer, "k" is p = 100 + 0.20k.

The equation for finding the amount of daily pay, "p", in the given situation would be : p = 100 + 0.20k,

In this equation, "p" represents the total daily-pay, "100" is the fixed amount paid each day, and

"$0.20" is the rate per kilometer. "k" represents the number of kilometers driven on that day.

To calculate the daily pay, you add the fixed amount of $100 to the product of the rate per kilometer and the number of kilometers driven on that day.

Therefore, the required equation is p = 100 + 0.20k.

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The given question is incomplete, the complete question is

Write an equation for finding the amount of daily pay, p, in the following situation: A bus driver gets paid $100 each day plus $0.20 per kilometer, "k".

Answer:

a) It would have taken 1 person 14 days to do this amount of work.

b) It would take 1 person 56 days to finish building this house extension.

We know that 1 person can build a house extension in 70 days. This means that in 1 day, 1 person can do 1/70 of the work. In 7 days, 2 people can do 2 * 7 * 1/70 = 2/10 of the work. This means that 1 person can do 1/10 of the work in 7 days. To finish the remaining 8/10 of the work, 1 person would need 7 * 8 = 56 days.

Step-by-step explanation:

To determine the number of offspring with skin darker than their parents, we need more information about the specific genetic inheritance patterns and traits involved.

The answer depends on factors such as the dominance or recessiveness of genes controlling skin color, the genotype of the parents, and the specific combination of alleles passed on to the offspring.

Without additional information, it is not possible to provide an accurate count of the number of offspring with darker skin. Genetic inheritance is a complex process that involves multiple genes and interactions, making it necessary to consider specific genetic traits and their inheritance patterns to determine the outcome.

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The time taken to triple the principal investemet for an interest compounded semi-annually is approximately 267 months.

The formula accrued amount in a compounded interest is expressed as;

[tex]A = P( 1 + \frac{r}{n})^{(nt)}[/tex]

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

P = principal amount (initial investment) = $2000

A = final amount (triple the initial investment) = 3 × $2000 = $6000

r = interest rate per period = 5%

n = number of compounding periods per year n = 2

t = time in years = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05

Plug the given values into the above formula and solve for time taken t.

[tex]A = P( 1 + \frac{r}{n})^{(nt)}\\\\t = \frac{In(\frac{A}{P}) }{n(In( 1 + \frac{r}{n}) } \\\\t = \frac{In(\frac{6000}{2000}) }{2(In( 1 + \frac{0.05}{2}) } \\\\t = 22.246\ years \\\\t = 267\ months[/tex]

Therefore, the time taken is approximately 267 months.

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a+c = b+d , because angle c = angle b and a = d

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

Angles on parallel lines can be alternate, corresponding or verically opposite to each other. And when they have these properties, the angles are equal to reach other.

b = c , since b+y = 360 and c+y = 360

and also a + x = 180

d + x = 180

therefore a = d

Therefore;

in b+d , we can substitute c for a and b for c

therefore b+d = a+c

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Answer:

The price would be 7.20

Step-by-step explanation: