λ represents the average rate, and the expected number of events in a given time frame for the ____________ distribution.


A. Poisson

B. normal

C. binomial

D. geometric

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First find the area of the sector.

For that, use this equation:

area = [tex]\frac{x }{360} * \pi r^{2}[/tex]

where 'x' is the angle and 'r' is the radius

Sub the values in

area = [tex]\frac{56}{360} * \pi15^2[/tex]

Solve:

area = [tex]35\pi[/tex]

It is easier to keep it in terms of pi until the end

Now, calculate the area of the triangle within the sector

area = 1/2 ab x sinC

where 'a' and 'b' are the radius (side lengths) and C is the angle

thus,

area = 1/2(15 x 15) x sin(56)

area = 93.27 (to 2 d.p)

Now subtract the area of the triangle from the area of the sector

[tex]35\pi[/tex] - 93.27 = 16.6857

This would give you a final answer of 16.69 units^2

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Answer:

187

Step-by-step explanation:

A number m is such that when it is divided by 30, 36 and 45 the remainder is always 7.

We should first find the LCM of 30, 36 and 45

We get that the LCM of the three numbers is 280 (working attached).

So now;

[tex]\frac{180}{30}[/tex] = 6

[tex]\frac{180}{36}[/tex] = 5

[tex]\frac{180}{45}[/tex] = 4

But we need a number that leaves a remainder of 7 so we add 7 to 180 to get; 180 + 7 = 187.

The equation of line which is perpendicular to the line FG is

y = -2x -3.

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

[tex](y -y_{1}) = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } (x-x_{1} )[/tex]

If [tex]m_{1}[/tex] be the slope of one line, then the slope of the perpendicular line is [tex]\frac{-1}{m_{1} }[/tex].

The slope intercept form of the line is given by  y = mx + b

Where, m is the slope of a line.

According to the given question

We have a line FG and the coordinates of points F and G are (-5,1) and (9,8) respectively.

Therefore, the slope of the line FG = [tex]\frac{8-1}{9+5}=\frac{7}{14} =\frac{1}{2}[/tex]

⇒ The slope of the line which is parallel to line FG is -2

Now, from the given option of the equation of line , y = -2x -3 has a slope of -2 .

Hence, the equation of line which is perpendicular to the line FG is

y = -2x -3.

Learn more about the equation of a perpendicular line here:

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Answer:

x = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given

[tex]\frac{3}{4(x+2)}[/tex] = [tex]\frac{x}{x+2}[/tex]

multiply numerator/ denominator of [tex]\frac{x}{x+2}[/tex] by 4, thus

[tex]\frac{3}{4(x+2)}[/tex] = [tex]\frac{4x}{4(x+2)}[/tex]

Since the denominators are common , equate the numerators, that is

4x = 3 ( divide both sides by 4 )

x = [tex]\frac{3}{4}[/tex]

Answer:

Hey there!

Angle QRS is 70, and since it is located on the circle, we have a useful formula. If 141x-1 is called y, then 70 is half of that.

Thus, we have 141x-1=140

141x=141

x=1

Hope this helps :)

Answer:

$45

Step-by-step explanation:

find the hire purchase price: 12 months x $30 = $360 + $35 deposit = $395

difference: 395 - 350 = $45

Answer:

A

Step-by-step explanation:

The line from the vertex to the base is a perpendicular bisector and divides the isosceles triangle into 2 right triangles.

Using Pythagoras' identity in either of the 2 right triangles, then

([tex]\frac{1}{2}[/tex] x )² + 3² = ([tex]\sqrt{45}[/tex] )²

[tex]\frac{1}{4}[/tex] x² + 9 = 45 ( subtract 9 from both sides )

[tex]\frac{1}{4}[/tex] x² = 36 ( multiply both sides by 4 to clear the fraction )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12 → A

Answer:

Please find the attached the required inequality graph

Step-by-step explanation:

Given that inequality is 2.5 ≤ x ≤ 4.5, we have;

The region in the given inequality is the region between 2.5 and 4.5 inclusive

Therefore, to represent 2.5 ≤ x ≤ 4.5 on the number line, we have;

A closed circle (representing the less than or equal to inequality symbol, showing inclusiveness) at 2.5, another closed circle at 4.5 (representing the less than or equal to inequality symbol, showing inclusiveness) and the region between 4.5 and 2.5 shaded.

Answer:

Step-by-step explanation:

To find x we use tan

tan∅ = opposite / adjacent

From the question

The adjacent is x

The opposite is 30

So we have

tan 25° = 30/x

x tan 25 = 30

Divide both sides by tan 25

x = 30/tan 25

x = 64.34

x = 64 to the nearest tenth

Hope this helps you

Answer:

the second one........the shape of the conic section os circle

Answer:

25x  ²−49y ²

Step-by-step explanation:

We need to find product of (5x+7)(5x−7y)

By using identity (a+b)(a−b)=a −b  ²

We have a=5x,b=7y

Thus (5x+7y)(5x−7y)=(5x)  ²−(7y)  

let me know if it was helpful

25x² - 49y²

Step-by-step explanation:

To Find:

The product of (5x - 7y)(5 x + 7)

How to solve:

Just need to use the formula of a² - b² = (a+b)(a-b)

let's assume a = 5x and b = 7x

Solution:

(5x - 7y)(5 x + 7) = (5x)² - (7y)²

= 25x² - 49y²

Hence required answer is 25x² - 49y².

Answer:

18- 14+8=3x

4+8=3x

12=3x

12/3=2x/3

x=4

Answer:

2/3, -8, -1/6, 4.

Step-by-step explanation:

Step-by-step explanation:

The rational root theorem states that if the leading coefficient is taken to be an and the constant coefficient is taken to be a0 the possible roots of the equation can be expressed as :

Now, from the given options, the possible choices can be :

A, B, C and E

D can be there because after taking any pair the rational root can't be 3

F can't be possible because an does't have 4 in its factors so denominator cannot be 4.

======================================================

Work Shown:

A = area of trapezoid RSTU

A = height*(base1+base2)/2

A = ST*(UT+RS)/2

A = 14*(5+10)/2

A = 105 square cm

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

B = area of rectangle PQWV

B = length*width

B = WV*PV

B = 7*2.5

B = 17.5 square cm

If you're curious how I got PV = 2.5, you basically cut PT = 10 in half twice. So you go from 10 to 5, then from 5 to 2.5; which works because we have a bunch of midpoints.

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

C = total shaded area

C = A + B

C = 105 + 17.5

C = 122.5

Answer:

Step-by-step explanation:

REcall that f(x) is a polynomial whose one of its roots is -3+i. The fundamental algebra theorem states that any polynomial of degree n has n complex roots. In the real case, it can be also interpreted as any polynomial can be factored in factors of degree at most 2.

Consider that given a polynomial of degree 2 of the form [tex]ax^2+bx+c[/tex] the solutions are given by

[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]

In this case, the fact that x is real or complex depends on the number [tex]b^2-4ac[/tex] which is called the discriminant. When this number is negative, we have that x is a complex root. Let say that [tex]b^4-4ac<0[/tex] and that [tex]\sqrt[]{b^4-4ac}=di[/tex], so the roots are given by

[tex] x_1 = \frac{-b + di}{2a}, x_2 = x_1 = \frac{-b - di}{2a}[/tex]

this means that, whenever we have a complex root, the other root is the complex conjugate. Recall that the complex conjugate of a complex number of the form a+bi is obtained by changing the sign of the imaginary part, that is a-bi.

So, in our case since -3+i is a root, then -3-i necessarily is another root.

If -3 + i is a root then -3 - i is too.

Therefore, the answer is -3 - i

Answer:

150

Step-by-step explanation:

Answer:

150  =  half of 300

± 180

230

soooo 230 students

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

c is the correct answer

Step-by-step explanation:

Answer/Step-by-step explanation:

a. Unknown side, b, using the Pythagorean theorem is solved as shown below.

[tex] b^2 = c^2 - a^2 [/tex]

[tex] b^2 = 45^2 - 27^2 [/tex]

[tex] b^2 = 1,296 [/tex]

[tex]b = \sqrt{1,296}[/tex]

[tex] b = 36 [/tex]

Unknown side, b, = 36 km

b. Perimeter of the triangle = sum of all the sides of the ∆ = [tex] 36 + 45 + 27 [/tex]

[tex] perimeter = 108 km [/tex]

c. Area of triangle = ½*base*height

where,

Base = 36 km

Height = 27 km

[tex] Area = \frac{1}{2}*36*27 [/tex]

[tex] Area = 18*27 [/tex]

[tex] Area = 486 km^2 [/tex]

Answer:

The triangle inequality states that the sum of the lengths of the two shortest sides of a triangle must be greater than the length of the largest side. Because 4 + 12 > 17 is not a true statement, the answer is "This triangle does not exist because the sum of 4 and 12 is less than 17."

Answer:

This triangle does not exist due to the fact that the sum of 4 and 12 is less than 17

Step-by-step explanation:

The triangle formaction rule states that the 2 smaller sides must be able to combine and be greater than the greatest side.

Triangle

Sides - 3, 4, 5

3+4=7

Meaning the two smaller sides add up to because greater than 5.

Non-Triangle

Sides - 5, 6, 13

5+6=11

This means that this is not a triangle because the smaller sides ‘5 and 6’ do not add up to become greater than 13.

Gemma’s Triangle

Sides - 4, 12, 17

4+12=16

Hence, Gemma‘s figure is not a triangle because the 2 smaller sides ‘4 and 12’ don‘t add up to be greater than 17.

Answer:

a) Because the confidence interval  does not include  0​ it appears that there

is  a significant difference between the mean level of hemoglobin in women and the mean level of hemoglobin in men.

b)There is​ 95% confidence that the interval from  −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2

c)   1.62 < μ1−μ2< 1.76

Step-by-step explanation:

a) What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in​ men?

Given:

95% confidence interval for the difference between the two population​ means:

−1.76g/dL< μ1−μ2 < −1.62g/dL

population 1 =  measures from women

population 2 =  measures from men

Solution:

a)

The given confidence interval has upper and lower bound of 1-62 and -1.76. This confidence interval does not contain 0. This shows that the population means difference is not likely to be 0. Thus the confidence interval implies that the mean hemoglobin level in women and the mean hemoglobin level in​ men is not equal and that the  women are likely to have less hemoglobin than men. This depicts that there is significant difference between mean hemoglobin level in women and the mean hemoglobin level in​ men.

b)  

There is​ 95% confidence that the interval −1.76 g/dL<μ1−μ2<−1.62 g/dL actually contains the value of the difference between the two population means μ1−μ2.

c)

If we interchange men and women then

                                          1.62 g/dL<μ1−μ2<1.76 g/dL.

There is a significant difference between the mean level of hemoglobin in women and in men.

The confidence interval of the mean is given as:

[tex]-1.76 g/dL < \mu_1-\mu_2 < -1.62 g/dL[/tex]

The above confidence interval shows that the confidence interval is exclusive of 0.

This means that 0 is not part of the confidence interval

Since the confidence interval is exclusive of 0, then there is a significant difference between the mean level of hemoglobin in women and in men.

Read more about confidence intervals at:

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Hey Mate !

Your Answer is given in the snip below !!

Please do mark me as brainliest !!!

(ANSWER=  (D)   [tex]\frac{1}{6}[/tex] )

Explanation

Answer:

You have a standard number cube.

What is the probability of rolling a number less than 3, and then rolling a prime number?

D. 1/6

Answer:

Step-by-step explanation:

Given,

x = 2

y = - 4

Now, let's solve:

[tex] \frac{1}{ {2}^{ - 2} \: {x}^{ - 3} \: {y}^{5} } [/tex]

plug the values

[tex] \frac{1}{ {2}^{ - 2} \: {(2)}^{ - 3} \: {( - 4)}^{5} } [/tex]

A negative base raised to an odd power equals a negative

[tex] \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {( - 4}^{5}) } [/tex]

Determine the sign of the fraction

[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {4}^{5} } [/tex]

Write the expression in exponential form with a base of 2

[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {2}^{10} } [/tex]

Calculate the product

[tex] - \frac{1}{ {2}^{5} } [/tex]

Evaluate the power

[tex] - \frac{1}{32} [/tex]

Hope this helps...

Best regards!!

Answer:

1,325

Step-by-step explanation:

30 /2

= 155,000 - 245(15)

= 5,000 - 3,675

= 1,325

Answer:

1,325

Step-by-step explanation:

Hi,

Answer:

[tex]Angle=\frac{pi}{4}[/tex] = π/4 = 45°

Have a good day.

Answer:

in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves working together.

Step-by-step explanation:

If Maya rakes the leaves in x minutes, then, in one minute she rakes [tex]\frac{1}{x}[/tex] leaves.

In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes [tex]\frac{1}{y}[/tex] leaves.

Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: [tex]\frac{1}{x}+ \frac{1}{y}[/tex]

Now, to simplify this expression:

[tex]\frac{1}{x}+ \frac{1}{y} =\frac{y+x}{xy}[/tex]

Thus, in one minute they rake [tex]\frac{y+x}{xy}[/tex] leaves.

Answer:

D. Decision support systems

Step-by-step explanation:

Operation Support System, sometimes referred to a group of computer programs that is used by the communications service provider for carrying out various operations or functions, such as monitoring, controlling, analyzing and managing a telephone or computer network.

It is often used by professionals such as Network planners, service designers, operations, architects and engineering teams in the service provider.

There are however, types of Operation Support System which are being used for different and specific purpose. They are classified into the following categories:

1. Transaction Processing Systems

2. Process control system

3. Enterprise collaboration system

4. Enterprise Resource

Hence, from the question above, the DECISION SUPPORT SYSTEM is not classified as Operation Support System.

Answer:

2) 30, 70, 80

Step-by-step explanation:

Well there has to be 3 angles that all add up to 180°.

1)

100+130+130

=360

2)

30+70+80

= 180

3)

25+3+35

=63

4)

45 + 105 + 120

=150

150+120

270

Answer:

70 degrees

Step-by-step explanation:

(360 - 90 - 130)/2=70

Answer:

First option is the correct option.

Step-by-step explanation:

[tex] \frac{2x + 5}{ {x}^{2} - 3x } - \frac{3x + 5}{ {x}^{3} - 9x } - \frac{x + 1}{ {x}^{2} - 9 } [/tex]

Factor out X from the expression

[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x( {x}^{2} - 9)} - \frac{x + 1}{ {x}^{2} - 9} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] , factor the expression

[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x(x - 3)(x + 3) } - \frac{x + 1}{(x - 3)(x + 3)} [/tex]

Write all numerators above the Least Common Denominators x ( x - 3 ) ( x + 3 )

[tex] \frac{(x + 3) \times (2x - 5) - (3x + 5) - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]

Multiply the parentheses

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - (3x + 5) - x(x + 1)}{x(x - 3)(x + 3)} [/tex]

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]

Distribute -x through the parentheses

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x }{x(x - 3)(x + 3)} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex] , simplify the product

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x}{x( {x}^{2} - 9)} [/tex]

Collect like terms

[tex] \frac{ {x}^{2} + 7x + 15 - 5}{x( {x}^{2} - 9)} [/tex]

Subtract the numbers

[tex] \frac{ {x}^{2} + 7x + 10}{ x({x}^{2} - 9)} [/tex]

Distribute x through the parentheses

[tex] \frac{ {x}^{2} + 7x + 10}{ {x}^{3} - 9x} [/tex]

Write 7x as a sum

[tex] \frac{ {x}^{2} + 5x +2x + 10 }{ {x}^{3} - 9x } [/tex]

Factor out X from the expression

[tex] \frac{x(x + 5) + 2x + 10}{ {x}^{3} - 9x} [/tex]

Factor out 2 from the expression

[tex] \frac{x( x + 5) + 2(x + 5)}{ {x}^{3} - 9x } [/tex]

Factor out x + 5 from the expression

[tex] \frac{(x + 5)(x + 2)}{ {x}^{3} - 9x } [/tex]

Hope this helps...

Best regards!!

The difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

The expression is given as:

[tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex]

Factorize the denominators

[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x^2 - 9)} - \frac{x + 1}{x^2 - 9}[/tex]

Apply the difference of two squares to the denominators

[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x - 3)(x + 3)} - \frac{x + 1}{(x - 3)(x + 3)}[/tex]

Take LCM

[tex]\frac{(2x + 5)(x + 3) - 3x - 5 -x(x + 1) }{x(x - 3)(x + 3)}[/tex]

Expand the numerator

[tex]\frac{2x^2 +6x + 5x + 15 - 3x - 5 -x^2 - x }{x(x - 3)(x + 3)}[/tex]

Collect like terms

[tex]\frac{2x^2 -x^2 - x +6x + 5x - 3x+ 15 - 5 }{x(x - 3)(x + 3)}[/tex]

Simplify

[tex]\frac{x^2+7x+ 10 }{x(x - 3)(x + 3)}[/tex]

Factorize the numerator

[tex]\frac{(x+5)(x+ 2) }{x(x - 3)(x + 3)}[/tex]

Expand the denominator

[tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

Hence, the difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

Read more about equivalent expressions at:

https://brainly.com/question/2972832

Step-by-step explanation: A term can be a number, a variable, or a number times one or more variables.

So in this expression, the terms are +2n, +5, -3p, and +4q.

This means that there are 4 terms.

The answer is D - 4 :)