What is the radius of a circle what circumference is 44cm


A. 42cm
D. 24cm
B. 48cm
C. 12cm​

Answer:

Step-by-step explanation:

Comparing the three in their simplest form we have the smallest ratio as 3 to 4.

A mathematical phrase that compares two values is called a ratio. It is written as the product of the division of two different quantities. As in 2:1 or 2/1, ratios are frequently expressed as a fraction or with a colon.

Mathematicians employ ratios in many different contexts, such as arithmetic, algebra, and geometry. They are used to compare amounts, identify equivalent values, and resolve proportional and rate-of-change issues.

Convert the ratios in their simplest form:

3 to 4 can be simplified by dividing both terms by their greatest common factor, which is 1. Therefore, 3 to 4 is already in its simplest form.

10 to 12 can be simplified by dividing both terms by their greatest common factor, which is 2. So, 10 to 12 simplifies to 5 to 6.

2 to 1 is already in its simplest form.

Thus, comparing the three we have the smallest ratio as 3 to 4.

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The data set (B) could be represented by the shown box plot.

A box and whisker plot (also known as a box plot) expresses a five-number summary of a set of data: lowest, lower quartile, median, upper quartile, and maximum.

The box plot is given in the question as shown, as per the data :

Minimum = 41

First quartile Q1 = 43

Median = 44

Third quartile Q3 = 48

Maximum = 50

According to set (B), we have:

41, 42, 43, 43, 43, 45, 47, 48, 50, 50

Here, Minimum = 41

First quartile Q1 = 43

Median = (43+45/2) = 44

Third quartile Q3 = 48

Maximum = 50

Therefore, the data set (B) could be represented by the shown box plot.

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The required monthly payment to accumulate $28,000 in 12 years at a rate of 5.4% compounded monthly for an annuity is approximately

To find the required monthly payment to accumulate $28,000 in 12 years at a rate of 5.4% compounded monthly, we can use the formula for the future value of an ordinary annuity:

FV = P * (1 - (1 + r)⁺ⁿ) / r,

where:

FV is the future value of the annuity ($28,000),

P is the monthly payment we want to find,

r is the monthly interest rate (5.4% / 12 = 0.0045),

n is the total number of payments (12 years * 12 months = 144).

Plugging in the values, we have:

28000 = P * (1 - (1 + 0.0045)⁺¹⁴⁴) / 0.0045.

28000 = P * (1 - 0.5239) / 0.0045.

28000 = P * (0.4761) / 0.0045.

28000 = P * 105.8107.

p = 264.6235

P ≈ $264.62 (rounded to 2 decimal places)

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Answer:

a-25

b-243

5^3 = 125/3 = 25

3^6 = 729/3 = 243

Explanation:

Step 1. We are given the expressions for u(x) and v(x):

The first two parts of the problem consist of finding the derivative of these two expressions: u'(x) and v'(x).

Step 2. To derivate u(x) we use the following rule:

which means that in this case:

Step 3. To derivate v(x) we use the following rule:

In our case n=14, therefore, the derivative is:

simplifying the exponent:

Step 4. Now, to solve the third part of the problem, we consider the definition of f(x) given in the statement:

And to find the derivative of this function f'(x) or f', we use the quotient rule,

We already know u and v from the given definitions, and we found u' and v' in 2 and 3.

So now, we substitute the known values into the quotient rule formula:

Step 5. The last step is to simplify our result. We start by simplifying the exponent in the denominator:

and to simplify further, divide both the numerator and denominator by x^13

And that is the simplified solution.

Answer:

Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

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Jacob and Monod's unified hypothesis of gene regulation states that transcription of genetic information is regulated specifically at the level of initiation.

This involves the concept of operons, which are clusters of contiguous genes under the control of a single regulatory element. They proposed that transcription could be regulated by either activators or repressors, which bind to the regulatory element of the operon to either promote or inhibit transcription. In addition, they proposed that some regulatory elements are regulated by operators, which are small DNA sequences located between the promoter and the structural gene. The operator acts as a switch, binding either activators or repressors to control the expression of the structural gene. As such, Jacob and Monod's hypothesis provides a unified model for how genes are regulated in the cell, providing a way to explain the expression of multiple genes at the same time.

In summary, Jacob and Monod's unified hypothesis of gene regulation states that transcription is regulated specifically at the level of initiation, repressors and operators regulate messenger RNA, and operons contain regulatory elements that control the expression of contiguous genes. All of these statements are part of the hypothesis.

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Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

Answer:

tan²Θ

Step-by-step explanation:

simplify the expression using the identities

secΘ = \(\frac{1}{cos0}\)

tan²Θ = sec²Θ - 1

then

\(\frac{cos0-cos^30}{cos^30}\) ( divide each term on the numerator by cos³Θ

= \(\frac{cos0}{cos^30}\) - \(\frac{cos^30}{cos^30}\)

= \(\frac{1}{cos^20}\) - 1

= sec²Θ - 1

= tan²Θ

Answer:

\(\tan^2(\theta)\)

Step-by-step explanation:

Assuming this is

\(\dfrac{\cos(\theta)-cos^3(\theta)}{cos^3(\theta)}\)

Trig identities used:

\(\sin^2(\theta)+\cos^2(\theta)=1 \implies 1-\cos^2(\theta)=\sin^2(\theta)\)

\(\dfrac{\cos(\theta)-cos^3(\theta)}{cos^3(\theta)}\)

\(=\dfrac{\cos(\theta)(1-cos^2(\theta))}{cos^3(\theta)}\)

\(=\dfrac{1-cos^2(\theta)}{cos^2(\theta)}\)

\(=\dfrac{sin^2(\theta)}{cos^2(\theta)}\)

\(=\tan^2(\theta)\)

The amount of time that it takes to run around the baseball field is 120 seconds.

We have,

The given rate is 8 feet per second.

radius is 250 feet.

The measure of arc is 40% of radius of circle is 175 feet.

Now, Circumference of a circle = 2πr.

and, the length of arc is

= 40% of 2×3.14×175

= 40% of 1099

= 40/100 ×1099

= 0.4×1099

= 439.6

≈ 440

So, Total perimeter = 250+250+440

                                 = 940 feet

and, Number of seconds = 940/8

                                         = 117.5

Thus, the time taken 120 second.

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Answer:

64

Step-by-step explanation:

Answer:

a. For the function:

f(x) = { sin x/3, if x ≤ π

{ x√3/2π, if x > π

I. To find lim f(x) as x approaches π from the negative side, we need to evaluate f(x) for values of x that are slightly less than π. In this case, since sin(x/3) is a continuous function, we can simply evaluate it at x = π:

lim f(x) as x approaches π- = f(π-) = sin(π/3) = √3/2

II. To find lim f(x) as x approaches π from the positive side, we need to evaluate f(x) for values of x that are slightly greater than π. In this case, we can simply evaluate the other part of the piecewise function at x = π:

lim f(x) as x approaches π+ = f(π+) = π√3/2π = √3/2

III. To find lim f(x) as x approaches π, we need to check whether the left-hand and right-hand limits are equal. In this case, since both the left- and right-hand limits exist and are equal, we have:

lim f(x) as x approaches π = √3/2

b. For the function:

f(x) = (x^2 - 36)/√(x^2 - 12x + 36)

I. To find lim f(x) as x approaches 6 from the negative side, we need to evaluate f(x) for values of x that are slightly less than 6. In this case, we can substitute x = 6 - h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6- = lim f(6 - h) as h approaches 0

Substituting x = 6 - h into the function, we get:

f(6 - h) = [(6 - h)^2 - 36]/√[(6 - h)^2 - 12(6 - h) + 36]

= [h^2 - 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 - h) = h(h - 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 - h) as h approaches 0+ = lim h(h - 12)/h as h approaches 0+ = lim (h - 12) as h approaches 0+ = -12

II. To find lim f(x) as x approaches 6 from the positive side, we need to evaluate f(x) for values of x that are slightly greater than 6. In this case, we can substitute x = 6 + h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6+ = lim f(6 + h) as h approaches 0

Substituting x = 6 + h into the function, we get:

f(6 + h) = [(6 + h)^2 - 36]/√[(6 + h)^2 - 12(6 + h) + 36]

= [h^2 + 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 + h) = h(h + 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 + h) as h approaches 0+ = lim h(h +

Step-by-step explanation:

Answer:

Your answer is 12.8

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Answer:

A

Step-by-step explanation:

area = length x width

= (2a^2+4a-5)(3a)

= 6a^3 + 12a^2 - 15a

9.  The stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. The stamp duty payable on a property with a purchase price of K150,000 is K7,500.

To calculate the stamp duty payable on properties with a purchase price of K45,000 and K150,000, we need to apply the corresponding rates of stamp duty based on the given information.

Given:

Value of Property:

Up to K35,000: Stamp Duty Rate - 2%

K35,000 to K70,000: Stamp Duty Rate - 3%

K70,000 to K140,000: Stamp Duty Rate - 4%

Over K140,000: Stamp Duty Rate - 5%

9. Calculate the stamp duty payable on properties whose purchase price is K45,000:

Since the purchase price of K45,000 falls within the range of K35,000 to K70,000, the stamp duty rate applicable is 3%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K45,000 * 3%

= K45,000 * 0.03

= K1,350

Therefore, the stamp duty payable on a property with a purchase price of K45,000 is K1,350.

10. Calculate the stamp duty payable on properties whose purchase price is K150,000:

Since the purchase price of K150,000 is above K140,000, the stamp duty rate applicable is 5%.

Stamp Duty Payable = Purchase Price * Stamp Duty Rate

= K150,000 * 5%

= K150,000 * 0.05

= K7,500

Therefore, the stamp duty payable on a property with a purchase price of K150,000 is K7,500.

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Answer:

Neither

Step-by-step explanation:

The image below shows that the lines aren’t parallel. They instead, intersect, but they are not perpendicular. So it’s neither.

Hope this helps! :)

We are given the following information

Mean ATM withdrawal = μ = $67

Standard deviation of ATM withdrawal = σ = $35

Sample size = n = 50

The probability of obtaining a sample mean withdrawal amount between $70 and $75 is given by

To find the solution to the system of equations represented by the two lines based on the given tables of ordered pairs, you can follow these steps:

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Answer:

hope it helps you

Step-by-step explanation:

The right polar decomposition of a matrix A ∈ Cm×n m ≥ n has the form A = UP where U ∈ Cm×n is a matrix with orthonormal columns and P ∈ Cn×n is positive semi-definite. Definition 2.2 (Left Polar Decomposition).

The given relation is

(14, 15), (5,7), (3, 10), (11, 1), (5.8)

Here consider the pair (5,7) and (5,8)

Input 5 gives two outputs 7 and 8

But function has exactly one output for one input.

Hence this relation is not a function.

Answer:

<

Step-by-step explanation:

The bars on either side of 81.48 are the absolute value symbol.

The absolute value of a number is its positive numerical value.

\(\implies |81.48| = 81.48\)

\(\boxed{\begin{minipage}{5.3cm}\underline{Inequality symbols}\\\\$ < $ means "less than"\\$ > $ means "more than"\\$\leq $ means "less than or equal to"\\$\geq $ means "more than or equal to"\end{minipage}}\)

A negative number is always less than a positive number.

\(\implies -88.48 < |81.48|\)

Therefore, the sign that makes the statement true is "<".

Answer:

-88.48 < ∣81.48∣

Step-by-step explanation:

The given equation is,

→ -88.48 ? ∣81.48∣

The sign which we use will be,

→ -88.48 ? ∣81.48∣

→ -88.48 < 81.48

Hence, the sign we use is (<).

9514 1404 393

Answer:

  1.8%

Step-by-step explanation:

The effective rate can be found using the simple interest formula.

  I = Prt . . . interest of principal P at annual rate r for t years

  r = I/(Pt) . . . . solve for r

Using the given numbers, we have ...

  r = 243/(4500·3) = 0.018 = 1.8%

The annual interest rate was 1.8%.

Taking point (0,-2) of graph one and replacing in the equation;

2x+3y=6

2(0)+3(-2)=6

-6=6

So graph isn't the required graph.

Taking point (0,2) of graph 2;

2x+3y=6

2(0)+3(2)=6

6=6

So, graph 2 is the required graph.

Answer:

nice

Step-by-step explanation:

8

In this pattern, we have 4 12 then 20.

We can see that the difference 4 and 12 is 8.

Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.

Explanation

Since the mean is 71 inches and a standard deviation of 4.5 inches.

Using the empirical rule

Firstly, for one standard deviation

68% of people have heights between 66.5 and 75.5.

We will check then check for two standard deviations

95% of people will have height between 62 and 80.

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

\(\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2\)

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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Matching of the statements with their respective linear equations are:

1) The line contains (0, -8) and a slope of 3/2: y = ³/₂x - 8

2) A line that contains the point (0, -2) and (4, 0): 2y - x = -4

3) y-intercept is (0, -2) and slope is -3/4: y = -³/₄x - 2

4) A line that has a slope of 5/3 and a y-intercept of -4: 5x + 3y = -12

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

1) The line contains (0, -8) and a slope of 3/2

The only option that even has a slope of 3/2 is option B with the equation: y = ³/₂x - 8

2) A line that contains the point (0, -2) and (4, 0)

The only one that fits this is option C with the equation:

2y - x = -4

3) y-intercept is (0, -2) and slope is -3/4.

This means the only equation that matches it is:

y = -³/₄x - 2

4) A line that has a slope of 5/3 and a y-intercept of -4.

This means the only equation that matches it is:

5x + 3y = -12

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Answer:

8 miles

Step-by-step explanation: