What is the circumference of this circle?
r=3


A.
6π
B.
3π
C.
9π
D.
36π
E.
None of the above

\(\bold{n\equiv 91a+40b\ mod \ 130}\)

Given that a is the remainder when n is divided by 10. Then, \(n\equiv a\ mod 10\)

Also b is the remainder when n is divided by 13 i.e., \(n\equiv b\ mod 13\)

Then by Division algorithm, there are integers k and m such that n = a + 10k and n = b + 13m

These two equations are equivalent to

13n = 13a +130k and 10n = 10b + 130m

Adding these two equations, 23n = 13a + 10b + 130(k + m)

⇒ \(23n\equiv 13a+10b\ mod\ 130\)

gcd (23,130) = 1

So 23 has an inverse modulo 130.

Therefore, \(n\equiv 23^{-1} (13a+10b) \ mod\ 130\)

Applying Euclidean algorithm for 130 and 23,

130 = 23 x 5 + 15

23 = 1 x 15 +8

15 = 1 x 8 +7

8 = 1 x 7 + 1

Therefore, 1 = 8 - 7 = 8 - (15 -8 ) = 2 x 8 - 15 = 2( 23 - 15 ) - 15

                    = 2 x 23 -3 x 15 = 2(23) -3(130-5x23) =17(23) -3(130)

So inverse of 23 = 17

So, \(n\equiv 17 (13a+10b) \ mod\ 130\equiv 221a +170b \ mod \ 130 \equiv \bold{91a+40b \ mod\ 130}\)

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Answer:

242

Step-by-step explanation:

Answer:

242

Step-by-step explanation:

Given

9a² + 2b² ← substitute a = 4 and b = 7

= 9(4)² + 2(7)²

= 9(16) + 2(49)

= 144 + 98

= 242

Answer:

g=12

Step-by-step explanation:

divide both sides by 13

13g=156

g=156/13

g=12

Answer:

The selling price of the bag is $22.5

Step-by-step explanation:

Buying Price = $25,

Selling Price = ?

Since they sold it at a loss of 10%,

So, they sold it for a price 10% less than the buying price,

or at 90% or 0.9 of the buying price,

so,

Selling Price = (0.9)(25) = $22.5

Answer:

Step-by-step explanation:

Answer:

73

Step-by-step explanation:

Oh wow

Ur Beautiful!

The measure of the angle N is 17 degrees

From the information given in the parallelogram, we have the angles written as;

m<N = 3y + 8

m<M = 6y - 1

m< P = 6x

m< L = 5x + 9

Then, we can say that;

m< M = m<N

Substitute the values, we get;

6y - 1 = 3y + 8

collect the like terms

6y - 3y = 8 + 1

add the values

3y =9

Divide both sides by the coefficient of the variable, y , we have;

y = 9/3

Divide the values

y = 3

Then, m<N = 3y + 8 = 3(3) + 8 = 17 degrees

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Answer:

y= -3x + 7:)

Step-by-step explanation:

Hope this helps!

Answer:

y = - 3x + 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 3 , thus

y = - 3x + c ← is the partial equation

To find c substitute (4, - 5) into the partial equation

- 5 = - 12 + c ⇒ c = - 5 + 12 = 7

y = - 3x + 7 ← equation of line

Answer:

-7 = y

Step-by-step explanation:

3x=y-5

Let x = -4

3(-4) = y-5

-12 = y-5

Add 5 to each side

-12 +5 = y-5+5

-7 = y

Given

A stock market broker lists a stock with an expected growth of 9.84% and a margin of error of £ 1.08%. What is the minimum expected growth percent for that stock?

Solution

The final answer

The minimum expected is 8.76% Euros

The Laplace transform of a+bt+c is (a/s) + (b/s^2) + (c/s). The Laplace transform of A cos(t+Bsin(t)) is (s/(s^2+B^2)) (A cos(φ) + (B/sin(φ)) A sin(φ)), where φ = arctan(B/s).

For a function f(t), the Laplace transform F(s) is defined as ∫[0, ∞) e^(-st) f(t) dt, where s is a complex number.

To find the Laplace transform of a+bt+c, we use linearity and the Laplace transform of elementary functions:

L{a+bt+c} = L{a} + L{bt} + L{c} = a/s + bL{t} + c/s = a/s + b/s^2 + c/s

Therefore, the Laplace transform of a+bt+c is (a/s) + (b/s^2) + (c/s).

B. To find the Laplace transform of A cos(t+Bsin(t)), we use the following identity:

cos(t + Bsin(t)) = cos(t)cos(Bsin(t)) - sin(t)sin(Bsin(t))

Then, we apply the Laplace transform to both sides and use linearity and the Laplace transform of elementary functions:

L{cos(t + Bsin(t))} = L{cos(t)cos(Bsin(t))} - L{sin(t)sin(Bsin(t))}

Using the formula L{cos(at)} = s/(s^2 + a^2), we get:

L{cos(t + Bsin(t))} = (s/(s^2+B^2)) L{cos(t)} - (s/(s^2+B^2)) L{sin(t)}

Using the formula L{sin(at)} = a/(s^2 + a^2), we get:

L{cos(t + Bsin(t))} = (s/(s^2+B^2)) (1/s) - (B/(s^2+B^2)) (1/s)

Simplifying, we get:

L{cos(t + Bsin(t))} = (s/(s^2+B^2)) (A cos(φ) + (B/sin(φ)) A sin(φ)), where φ = arctan(B/s)

Therefore, the Laplace transform of A cos(t+Bsin(t)) is (s/(s^2+B^2)) (A cos(φ) + (B/sin(φ)) A sin(φ)), where φ = arctan(B/s).

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The hypothesis test suggests that there is not enough evidence to reject the claim made by the social media company that over 1 million people log onto their app daily, as the  t-value (-1.732) is less than the critical value (-2.429).

Null hypothesis, The true mean number of people who log onto the app daily is equal to or less than 1 million.

Alternative hypothesis, The true mean number of people who log onto the app daily is greater than 1 million.

Level of significance = 1%

We can use a one-sample t-test to test the hypothesis.

t = (X - μ) / (s / √n)

where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the values, we get

t = (998,946 - 1,000,000) / (23,876 / √65)

t = -1.732

Using a t-distribution table with 64 degrees of freedom and a one-tailed test at a 1% level of significance, the critical value is 2.429.

Since the calculated t-value (-1.732) is less than the critical value (-2.429), we fail to reject the null hypothesis. There is not enough evidence to support the claim that more than 1 million people log onto the app daily.

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The equations that represent the information given in the problem are  r + a = 5 and 3r + 6a = 20 respectively. The correct options are (b) and (c).

A system of linear equations is a group of  equations having same number of variables and degree.

For the n number of variables n number of equations are required.

On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.

The total weight of mixture is 5 pound.

And, the cost per pound is $4.

Then, the cost of a bag of 5 pound is 4 × 5 = $20.

Suppose the amount of raisin in 5 pound bag be r and that of almond be a.

Now, the equation for the total amount of raisin and almond is given as,

r + a = 5

And, for the cost of the 5 pound bag it is given as,

3r + 6a = 20

Hence, the equations to justify the given case are r + a = 5 and 3r + 6a = 20 respectively.

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Answer: Hello

Step-by-step explanation:

a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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Answer:

h = 61.83 feet

Step-by-step explanation:

length of string from Hector to kite = c = 86 feet.

and 4 feet off the ground.

angle A = 42° 15' 30"

req'd:  how high is the kite?

angle A = 42° + 15' (1° / 60') + 30"(1° / 3600'')

angle A = 42.26

to get the side a (height of kite) 4 feet above ground: use Sin(A) = opp / hyp

Sin(A) = a / c

Sin(42.26) = a / 86

a = Sin(42.26) * 86

a = 57.83 feet

therefore, the height of the kite from the ground = h = 57.83 + 4

h = 61.83 feet

All parabolas have A. One increasing and one decreasing interval .

A parabola is a U-shaped curve that can either be concave up or concave down. If the parabola is concave up (like the letter "U"), it has a minimum point and is increasing to the left and decreasing to the right.

If the parabola is concave down (like an upside-down "U"), it has a maximum point and is decreasing to the left and increasing to the right. Therefore, all parabolas have at least one interval of increase and one interval of decrease.

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From the above explanation, we can conclude that the required interval for which the Mean Value Theorem guarantees a\($c belongs (a,b)$\) such that \(f′(c)=4$ is $[2,4]$\).

Given that\($f(x)$\) is a continuous function on \($[a,b]$\) and differentiable on \($(a,b)$\) such that \($f(b)=10,f(a)=2$\).

We need to find the interval [a,b] for which the Mean Value Theorem guarantees a c∈(a,b) such that f′(c)=4.

The Mean Value Theorem states that for a function $f(x)$ that satisfies the following conditions:

a)\($f(x)$\) is continuous in the interval \($[a,b]$\).

b) \($f(x)$\) is differentiable in the interval\($(a,b)$\).

c)\($f(a) = f(b)$\) Then there exists a number \($c$\) in the interval \($(a,b)$\) such that \($f'(c) = \frac{{f(b) - f(a)}}{{b - a}}$\) Now we have \($f(b)=10$\) and \(f(a)=2$.\)

Therefore, \($f'(c)=\frac{10-2}{b-a}=\frac{8}{b-a}$\) It is given that \($f'(c) = 4$\)

. Therefore we have \($\frac{8}{b-a} = 4$\)

.This gives us \($b - a = 2$\)

Or, \($a = b - 2$\) Therefore, the required interval is [2,4].

the correct answer is option (C) [2,4].

The given question is related to the Mean Value Theorem. The Mean Value Theorem is used to find out a point in the given interval where the slope of the tangent of the curve is equal to the average rate of change of the function. Here, we have been given a function $f(x)$ that is continuous in the interval \($[a,b]$\) and differentiable in the interval \($(a,b)$\).

We need to find the interval \($[a,b]$\) for which the Mean Value Theorem guarantees a $c∈(a,b)$ such that\($f′(c)=4$\).

We have used the Mean Value Theorem formula and solved the equation to obtain \($b - a = 2$\).Therefore, the required interval is \($[2,4]$\).

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The value of the given ratio for triangle ACE and BCD include the following:

1.)25/16

2.)10/7

3.) 1

4.) 14/19

5.) 4/5

6.) 4/1

7.) 16/5

8.) 29/45

In order to calculate the ratio, the value of the missing parts of the triangle should be calculated such as line BD, and CE, by the use of Pythagorean formula.

The Pythagorean formula = c² = a² + b²

For first triangle:

BC = a = 20

CD = b = 14

BD = c = ?

C² = 20²+14²

c² = 400+196

c² = 596

C = √596

C = 24 = BC

The ratio of the given sides of the triangle include the following:

1.) = AC = 20+5 = 25; CE = 25/16

2.) BC:CD = 20/14 = 10/7

3.) BD:AE = 24/24 = 1

4.) CD:CE = 14/19

5.) BC:AC = 20/25 = 4/5

6.) BC:AB = 20/5 = 4/1

7.) CD:DE = 16/5

8.) perimeter of BCD = 20+14+24 = 58; perimeter of ACE =25+24+21 = 70

The ratio of perimeter of BCD:ACE = 58/70 = 29/45

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Answer:

1. Median

2. Altitude

3.  Altitude

4. Neither

Step-by-step explanation:

Median- splits the side into two congruent parts

Altitude- Makes a right  angle

1. Splits the side. Median

2. Makes a right angle. Altitude

3.  Makes a right angle. Altitude

4. Doesn't make a right  angle or split the sides. Neither

Answer:

254.34 m²

Step-by-step explanation:

The formula used to find the area of a circle is π · r².
The radius of a circle is half of it's diameter.
Using the given values, we can solve:

3.14 · 9²

3.14 · 81

= 254.34 m²

hope this helps!

Answer:

Area = 254.469004940773 m²

Step-by-step explanation:

formula : (area of a circle)

Area = π × r²

where r is the radius of the circle

\(\large \text r = \frac{\large \text Diameter \ of \ the \ circle }{2} = \frac{18}{2} =9\ m\)

then

Area = π × 9²

        = π × 81

        = 254.469004940773 m²

The single simplified fraction is (m + n)(p + m) / 2m.

To simplify the expression

\((3m^2 - 3n^2) / (m^2 + mp)÷ (6m - 6n) / (p + m)\)

we need to invert the second fraction and multiply by the first.

\((3m^2 - 3n^2) / (m^2 + mp) \times (p + m) / (6m - 6n)\)

We can then factor out a 3 from the numerator and the denominator, and cancel out the (m - n) terms. 3(m + n)(m - n) / 3m(m - n) x (p + m) / 6(m - n)

Simplifying further, we can cancel out the 3's and the (m - n) terms. (m + n) / m x (p + m) / 2

The simplified expression is (m + n)(p + m) / 2m.

To simplify the given expression, we invert the second fraction and multiply it by the first. Then we factor out common terms and cancel out like terms. We simplify the expression to obtain the single fraction (m + n)(p + m) / 2m.

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Item response theory is to latent trait theory as observer reliability is to inter-scorer reliability.

Reliability in a broad statistical sense is synonymous with consistency.

Item response theory (IRT) is a statistical framework used to model the relationship between the latent trait being measured and the observed responses to test items. It provides a way to estimate an individual's level on the latent trait based on their item responses.

The Observer reliability also known as inter-scorer reliability, is a measure of consistency or agreement among different observers or scorers when assessing or rating a particular phenomenon.

Both measures are concerned with the reliability or consistency of measurements but in different contexts and with different focal points.

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The missing side of the right angle triangle using pythagoras theorem is; A: 8

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

From the diagram, if the missing side is x, then we can say that;

x = √(17² - (7.5 * 2)²)

x = √(289 - 225)

x = √64

x = 8

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Mathematics focuses on geometry, numbers, and form. For such, axioms and definitions are needed to describe the study's subjects. On the basis of those definitions and axioms, properties are proved using logic.

Mathematical logic help you in using a phone, sending a fax, or operating a vehicle and many other things.

Logic models are composed of mathematical constructs. When it comes to supporting its conclusions, mathematics employs logic. The "science" of reasoning is logic. It deals with arguments, hence learning what constitutes a strong argument is a need for becoming a logician.

Logic can also be applied in everyday conversation about non-mathematical subjects. The amount of reasoning required is typically much more for mathematical inquiries than for non-mathematical ones.

Therefore, logic is a technique that mathematicians (as well as other individuals) employ when it comes to supporting their claims. Proof involves logic.

Mathematical logic has a direct impact on our daily life now more than ever. I'm not only referring to the marks pupils receive or the number of required mathematical subjects. I'm referring to using a phone, sending a fax, or operating a vehicle. I'm referring to making a home, purchasing medication for your family, and enjoying music.

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The probability of a student doing well on an exam given that they spend time reading is approximately 0.983 or 98.3%.

To calculate the probability of a student doing well on an exam given that the student spends time reading, we need to use conditional probability.

Let's denote:

P(R) as the probability of a student spending time reading (P(R) = 0.59),

P(E) as the probability of a student doing well on an exam (P(E)),

P(E|R) as the probability of a student doing well on an exam given that they spend time reading (P(E|R) = 0.58).

The formula for conditional probability is:

P(E|R) = P(E and R) / P(R).

Given that P(E and R) = 0.58 (the probability of a student doing well on an exam and spending time reading) and P(R) = 0.59 (the probability of a student spending time reading), we can substitute these values into the formula:

P(E|R) = 0.58 / 0.59 = 0.983.

Therefore, the probability of a student doing well on an exam given that the student spends time reading is approximately 0.983 or 98.3%.

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Answer:

false

Step-by-step explanation:

860 divided by 2 is 430 NOT 480

The number of ways to select a committee of four persons from a club consisting of six distinct men and seven distinct women, where the committee must include at least one woman, is given by the expression 7C1 × 6C3 + 7C2 × 6C2 + 7C3 × 6C1 + 7C4.

To determine the number of ways to form the committee, we can consider two cases: one with exactly one woman selected and another with more than one woman selected.

Case 1: Selecting exactly one woman: There are seven choices for selecting one woman and six choices for selecting three men from the remaining six men. The total number of combinations for this case is 7C1 ×6C3.

Case 2: Selecting more than one woman: We need to consider combinations with two women and two men, three women and one man, and all four women. The total number of combinations for this case is 7C2 × 6C2 + 7C3 × 6C1 + 7C4.

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Answer:

$89100

Step-by-step explanation:

Given data

Each trimester costs=$1,450

time taken to complete degree= 2 years

In 1 years, she will pay = 14500*3=  $43500

In 1 years, she will pay =$43500*2=  $87000 in tuition

The average costs for books each trimester is 350$

In 1 years, she will pay =  350*3=  $1050

In 1 years, she will pay =$1050*2=  $2100 for books

In all she will pay

87000+2100=$89100

Answer:

$10,800

Step-by-step explanation: