Evaluate using the given values.

The probability that exactly 5 small businesses will fail during a given month 0.0037268.

The Poisson distribution would be used to calculate the likelihood that different counts of the same event will occur within a constrained time period. It is viewed as a discrete distribution since it evaluates counts. The distribution displays identical mean and dispersion values.

The pmf of the Poisson distribution is

[tex]p(x)=\frac{e^{\lambda} \lambda^{x}}{x!}[/tex]

The mean total number of small business failures λ=14

Let x represent the number of failed small businesses in a given month.

X~P(14)

X follows the Poisson distribution since the likelihood of failure stays constant for two months and the mean number of failures per month is 14.

The likelihood that precisely four small firms would fail in a given month must be calculated.

P(X=5)

[tex]P(X=5)= \frac{e^{14} \ 14^{5}}{5!}[/tex]

P(X=5)= 0.44721/5!

P(X=5)=0.0037268.

In a month there is 0.0037 that is 3.7% probability that a small business fail.

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Answer:

The slope of the perpendicular line is -2.

Step-by-step explanation:

A perpendicular line has a slope that is the negative inverse of the slope of the reference line.  The reference line in this problem is 3x-6y=144.

Let's rearrange this equation to standard slope-intercept form of y=mx+b, where m is the slope and b is the y-intercept (the valuue of y when x=0).

3x-6y=144

-6y=144-3x

-6y=-3x + 144

 y = (3/6)x + (144/-6)

 y = (1/2)x - 24

This line has a slope of (1/2) and a y-intercept of -24.  A line perpendicular to this will have a slope that is the negative inverse of (1/2).  This would be -2.  The new line will take form:

 y = -2x + b

We are not given b, and there is not enough information to calculate one, so let's assume a value of -24, so that it intersects the original line at (0, -24).  See the attached graph.

If you flip a coin 300 times, 150times would you expect it to land on

tails

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

There are three primary categories of algebraic expressions, including:

Numeral Expression.

Binary Expression

Expression of a polynomial.

Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.

Given

flip a coin = 300

So the coin have 2 sides , one side is head and other side is tail

300/2

=150

So the 150 times the tail will come  while Flip  a coin.

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Answer:

To determine whether (1, 5) is a solution of a given system, you need to substitute these values into the equations of the system and check whether the resulting statements are true.

For example, if the given system is represented by the equations y = 2x + 1 and y = x - 3, then you would substitute 1 for x and 5 for y in each equation and check whether the resulting statements are true.

Substituting these values into the first equation, we get:

5 = 2(1) + 1

5 = 2 + 1

5 = 3

This statement is not true, so (1, 5) is not a solution of this system.

On the other hand, if the given system is represented by the equations y = 2x + 1 and y = 5, then substituting the values (1, 5) into both equations would result in true statements, so (1, 5) would be a solution of this system.

I hope this helps! Let me know if you have any more questions.

Step-by-step explanation:

5 scoops of powder are combined with 8 glasses of water by Noah.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

Hence, 5 scoops of powder are combined with 8 glasses of water by Noah.

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A rectangle is constructed on a semicircle so that the length equals the diameter. The width of the rectangle is approximately 10.65 inches.

Generally, Let the width of the rectangle be x. Then the length of the rectangle is 3x.

The diameter of the semicircle is also the length of the rectangle, so it is 3x.

The area of the rectangle is x*(3x) = 3x^2. The area of the semicircle is (1/2)πr^2, where r is the radius of the semicircle. Since the diameter of the semicircle is 3x, the radius is (3x)/2. The area of the semicircle is (1/2)π((3x)/2)^2 = (9/8)πx^2.

The total area of the figure is the sum of the area of the rectangle and the area of the semicircle. We can set up the equation:

3x^2 + (9/8)πx^2 = 750

(21/8)πx^2 = 750

x^2 = 750/(21/8)*π

x = √(750/(21/8)*π)

To find the approximate dimensions of the rectangle, we can use the fact that pi is approximately 3.14. This gives us:

x = √(750/(21/8)*3.14)

= √(750/6.71)

= √(112.64)

= approximately 10.65 inches.

The width of the rectangle is approximately 10.65 inches. The length of the rectangle is 3 times the width, so it is approximately 31.95 inches.

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45%

You made a higher percentage of shots.

36/80*100 = 45%

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Answer: x=8,r=30

Step-by-step explanation:

Answer:

Yeah, they are not equal.

Step-by-step explanation:

Given statement,

→ -3 to the second power is not equal to (-3) to the second power.

Forming the equation,

→ -3² ≠ (-3)²

Let's check the equation,

→ -3² = (-3)²

→ -(3)² = (-3)²

→ -9 ≠ 9

→ LHS ≠ RHS

Hence, they are not equal.

a local winery bottles 14 different white wines. to help customers with their purchasing choice, the winery offers customers 5 white wine tasting samples free of charge 2002 many ways does a customer have to choose 5 different white wines to taste, using the concept of combination formula.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.

The combination formula is: n! / (n-r)! r! , where n is the total number of items (14 in this case) and r is the number of items being selected at once (5 in this case),

Plugging our numbers into the formula we get:

= 14! / (14-5)! 5!

= 2002

After simplifying, we get 2002.

So, there are 2002 ways of picking 5 different white wines to taste from a group of 14 local winery bottles.

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Answer:

x=2

Step-by-step explanation:

Remove parentheses

collect like terms

move constants to the right

calculate

divide both sides

Answer:

no

Step-by-step explanation:

The three angles of a triangle are 180, but the sum of the three angles in the figure is 200.so its impossible .

The perimeter can be calculated using the formulas 22x+23 and 2x+3x+17x+7+16.

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The surface of a shape's area is measured.

The total length of the four sides makes up the perimeter (P) of a rectangle. A rectangle has two equal lengths and two equal widths since its opposite sides are equal. The following is the formula for calculating a rectangle's perimeter: The formula for perimeter is length + length + width + width. P = l + l + w + w.

you want to add the variables of the same kind in this case

2x        

3x         7

17x       16

_________

22x  +     23

Therefore Two expressions for the perimeter would be 22x+23 and 2x+3x+17x+7+16

The complete question is : Write two expressions for the perimeter of the figure.

2x

7

3x

172

16

Note: The figure is not drawn to scale.

(a) Use all five side lengths.

perimeter - ] + + + +

(b) Simplify the expression from part (a).

perimeter =

Х

$ ?

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The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to  54.52 , 1.808, 3.2712 respectively.

As given in the question,

Let success be defined by health department inspection is passed by restaurant

Probability of success rate 'p' = 0.94

Value of ' 1 - p ' = 1 - 0.94

                         = 0.06

Number of owners of restaurant which are surveyed 'n' = 58

For the given binomial experiments calculation of the following distributions are:

Mean 'μ' = np

              = 58 × 0.94

              = 54.52

Standard deviation 'σ' = √ np (1 - p)

                                    = √ 58 × 0.94 × 0.06

                                    = √3.2712

                                    = 1.808

Variance 'σ²' =  np( 1 - p )

                     = 58 × 0.94 × 0.06

                     = 3.2712

Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.

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Answer:

( [tex]-\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] )  

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

Coordinates of midpoint are

( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )

~~~~~~~~~~~~~~~~~~~~

The figure is right triangle.

The circumcenter is the middle of the hypotenuse.

( - 2, 4 )

( 1 , - 1 )

( [tex]-\frac{1}{2}[/tex] , [tex]\frac{3}{2}[/tex] )

Step-by-step explanation:

I think it's y=x² +6 because this is a quadratic equation

Answer:

  a)  y = 16/x²

  b)  x = 4/5

Step-by-step explanation:

You want the equation for y in terms of x when y is inversely proportional to the square of x, and y is 16 when x is 1. Further, you want the value of x when y is 25.

The wording "inversely proportional to the square" means the form of the equation is ...

  y = k/x² . . . . . . where k is the constant of proportionality

The value of k can be found from the given (x, y) pair.

  k = x²y = (1)²(16) = 16

The equation is ...

  y = 16/x²

Solving for x gives ...

  x = √(16/y)

Then the value of x for y = 25 is ...

  x = √(16/25)

  x = 4/5

Check the picture below.

Answer:

9/10 =0.9

Step-by-step explanation:

We have been given to calculate 1 1/2 times 3/5 . First of all ,we shall convert 1 1/2 ( a mixed fraction form) to a proper fraction form .

1 1/2 is actually 1 + 1/2 =3/2

1 1/2 X 3/5  =3/2 X 3/5 =9/10

9/10  is actually 0.9

Therefore we have finally converted this into division sentence too

Answer:

-17

Step-by-step explanation:

replace x with 6

g(6)=-2(6)-5

g(6)=-12-5

g(6)= -17

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1/10  fraction of the circumference of the circle .

What is arc?

An arc is any straight line that connects two locations. The term "arc length" refers to an arc's length. An ordered pair of adjacent vertices is referred to as a graph arc in a graph.

                        Any section of the circle's circumference (other than the entire curve) is referred to as an arc.

C = 2πr

C - circumference of a circle

r - radius of a circle

r =  4

Then

C = 2π • 4 = 8π

Writing the fraction:

(4π/5)/8π = 1/10

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The height of the tree that produce a shadow of length 27.25 m is 10.18 m.

Height is the vertical distance between two points.

To calculate the height of the try, we use the formula of similar angle.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for H

Hence, the height of the tree is 10.18 m.

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The chance that a student is selected at random from the class who passed the exam and finished the assignment is 0.2105

Probability refers to potential. The occurrence of a random event is the subject. Probability values are limited to the range of 0 to 1. Its fundamental notion is that something is probable to occur. It is the proportion of favorable events to all other events.

A exam and an assignment were due on the same day in a math class with 19 pupils.

There were 14 students that finished the assignment, and 11 of them completed the test.

3 pupils both failed the exam and didn't finish the assignment.

Then the probability that a student is chosen randomly from the class passed the test and completed the homework will be

The number of the student who has done at least one assignment or passed the test is 19 - 3 = 16

n(A) = passes student

n(B) = given assignment

Then we have

n(A ∩B) = n(A) + n(B) - n (A ∪B )

n(A ∩B) = 11 + 14 - 16

n(A ∩B) = 9

Then the probability will be

P = 9C2 /19C2

P = 36/171

P = 0.2105

The probability that a student chosen randomly from the class completed the homework is 0.2105

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The two line segments after the reflection over the x-axis are vertical lines, and the same will be true for the third segment.

The rule for a reflection over the x-axis is given as follows:

(x,y) -> (x,-y).

Meaning that the x-axis remains constant, while the coordinates of the y-axis are changed.

The vertices of the original triangle will be attributed as follows:

A(1,1), B(4,1) and C(1,5).

Hence the vertices of the reflected triangle will be given as follows:

A'(1,-1), B'(4,-1) and C(1,-5).

Thus the lines are given as follows:

Hence there are three vertical lines.

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The value of the equation 3d/ac x 2ad/30 is ( d² / 5c )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

A = 3d/ac x 2ad/30   be equation (1)

On simplifying the equation , we get

A = 3d/ac x 2ad/30  

A = 6ad² / 30ac

On further simplification of the equation , we get

The value of A = 1/5 ( ad² / ac )

The value of A = 1/5 ( d²/c )

Therefore , the value of A is  ( d² / 5c ) or A = 1/5 ( d²/c )

Hence , The value of the equation 3d/ac x 2ad/30 is ( d² / 5c ) or

A = 1/5 ( d²/c )

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Answer:

384cm^2

Step-by-step explanation:

8x8x6 = 384

Answer:

Seagle =10

Dolphin =2.5

Penguin-flat =0

Shark = -2.5

Clownfish= -7.5

Octpus= -10

Step-by-step explanation:

Answer:

Step-by-step explanation:

The distance between each animal and the sea level is already shown in the image.

- for the seagull the vertical line with measurements of 0,5, 10 if you measure how high the seagull it would be 10 cm, how do I measure it? go from 0 to the height of the dolphin and you'll find the answer.

- for the dolphin, look at the vertical line with measurements of 0,5, and 10  how do I measure it? go from 0 to the height of the dolphin and you'll find the answer which would be 2cm.

you keep doing the same thing to the other animals the meters are shown on the image you have to measure from 0 and go up or down depending on where the animal is.

Answer: 6

Step-by-step explanation:

Answer:

y=n-3^2 is linear

Step-by-step explanation:

A linear equation is an equation between two variables that give a straight line with plotted on a graph.

The two variables used are "n" and "3^2"

When graphed, it forms a diagonal, straight line.