Given mn, find the value of x.
(5x+2)®
(4x+6)°
m

a)The probability of exactly 5 accidents will occur is 0.1008.

b) The probability of fewer than 3 accidents will occur is 0.42318.

It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12. Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.

Given,

Mean = 3

a) By using Poission probability formula,

P( X = 5) = e⁺³ (3)⁵/5!

P(X = 5) = 0.1008

The probability of exactly 5 accidents will occur is 0.1008.

b) fewer than 3 accidents will occur:

P( X <3) = e⁻³ (3)⁰ + e⁻³ (3)¹ + e⁻³(3)²

P( X< 3) = 0.4978 + 0.14936 + 0.22404

P( X < 3) = 0.42318

The probability of fewer than 3 accidents will occur is 0.42318.

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The number of pairs of the parallel lines after the rotation is 2

The transformation is described by

Rotation by 90° counterclockwise about vertex G

There are four types of transformation, and they are:

As a general rule of rotation:

When a shape, line or an angle is rotated, the size of the properties in the rotated figure remains unchanged

Before rotation, a rhombus has two pairs of parallel sides

This means that the parallel sides would remain parallel after rotation

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Answer:

B.

Step-by-step explanation:

If the soccer team is going to purchase only warm-up pants, then the greatest number of warm-up pants the team can purchase is 42, but if instead the soccer team is going to purchase only duffel bags, then the greatest number of duffel bags the team can purchase is 54.

Inequality, a relationship between two values/expressions that aren't equal to each other, is involved in solving this problem.

The soccer team's got $1,512 to purchase either all warm-up pants or all duffel bags. The cost of the warm-up pants is $36 each and the cost of the duffel bags is $28 each. Since you're asked to find the greatest numbers of each purchase, you'll need to write inequalities to figure out the answer.

The keyword here is "greatest number", so you can use the symbol ≤ for the inequalities. Therefore, 36x ≤ 1,512 is the inequality for finding the greatest number of warm-up pants and 28x ≤ 1,512 is the inequality for finding the greatest number of duffel bags.

The solutions to the first and second inequalities are, consecutively, x ≤ 42 and x ≤ 54, meaning the team can buy at most 42 warm-up pants or 54 duffel bags.

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Answer:

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

First, compare the negative numbers as they are smaller than positives since negatives are to the left from zero on the number line and positives are to the right.

Since - 15 is smaller than - 6, the least number is - 3:

Now compare the positives.

Therefore:

The complete order is:

Answer:

-3 < -6/5 < 1/6 < √7 < 45

Step-by-step explanation:

Now the values will be,

→ 1/6 = 0.17

→ -3 = -3

→ √7 = 2.65

→ -6/5 = -1.2

→ 45 = 45

Let's arrange in ascending order,

→ -3, -1.2, 0.17, 2.65, 45

→ -3, -6/5, 1/6, √7, 45

Hence, number -3 comes first.

Taking into account the definition of a system of linear equations, the number of 2-pointers and 3-pointers Sarah made is 2 and 3 respectively.

A system of linear equations is a set of equations relating two or more unknown values, the goal of which is to determine those values so that the equations are true.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y= 10

2x+3y= 24

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "x" from the first equation:

x= 10 - y

Replacing this expression in the second equation:

2×(10-y)+3y= 24

Solving:

2×10 -2y +3y= 24

20 -2y +3y= 24

-2y +3y= 24 - 20

y= 4

Remembering that x= 10 -y, you get:

x= 10 -4

x= 6

Finally, the number of 2-pointers Sarah made is 2 and the number of 3-pointers she made is 3.

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After solving the equation made for a triangle, the value of angle A will be equal to 21.

Simple polygons with three sides and three internal corners make up triangles. Being one of the fundamental geometric shapes, it is symbolized by the symbol and consists of three connected vertices.

As per the given data in the question,

Angle A is 13 less than angle C.

Let angle C is x then angle A is equal to (x - 13) and,

Angle B is 11 less than 4 times of angle C then,

B = 4x - 11

Add all the angles and equate them with 180.

(x -13) + (4x - 11 ) + x = 180

6x -24 = 180

6x = 180 + 24

x = 204/6

x = 34.

Substitute x = 34 in angle A

A = (x - 13)

A = 21.

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The distance from the origin to point P graphed on the complex plane is d = [tex]\sqrt{29}[/tex]

Given,

In the question;

From the figure,

To find the distance from the origin to point P graphed on the complex plane .

Now, According to the question:

To see the graph,

The point P lie on the x- axis and y - axis .

x = 2 and y = -5

We know the formula of distance,

Distance (d) = [tex]\sqrt{x^{2} +y^2}[/tex]

d = [tex]\sqrt{2^2 + (-5)^2}[/tex]

d = [tex]\sqrt{4 + 25}[/tex]

d = [tex]\sqrt{29}[/tex]

Hence, The distance from the origin to point P graphed on the complex plane is d = [tex]\sqrt{29}[/tex]

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a. The system of inequalities that best represent how much of the agricultural products of soybeans and corn the river barge can carry is

b. option A

c. The river barge can safely ship the agricultural products

information gotten from the question include

Corn weighs about 60 pounds per bushel

soybeans weigh about 90 pounds per bushel

A river barge can safely carry up to 4,500,000 pounds of cargo.

Let x = bushels of corn and y = bushels of soybeans.

a. From the statement, it can be deduced that the equation is

A. 60x + 90y ≤ 4,500,000, x ≥ 0, y ≥ 0

b. some interpretation on inequality

from the interpretation

the correct option is A (graph attached)

c. 60 * 24000 + 90 * 24000

= 3,600,000

The value is ≤ 4,500,000 hence the river barge can carry it

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a) since all the angles on the triangle are next to a given angle we just subtract the given angle from 180 to find the unknown angle

180-150=30=x

180-80=100=y

180-130=50=z

Sum of All triangles angles is always 180 degrees but we can still check

30+100+50

130+50=180

Now for the B triangle every angle is across from it like this means the triangle angle is equal to that

a= 40 degrees

b= 95 degrees

c= 45 degrees

And this also equal 180 degrees

Hopes this helps please mark brainliest

Answer:

1st Question Answer:

X=30

y=100

z=50

2nd Question Answer:

a=40

b=95

C=45

Step-by-step explanation:

1st Question : Since the angles of a straight line add up to 180 , we can subtract the degree of the angle given by 180 which gives us the answer . also we can make certain the angle is right because angles of a traingle add up to 180

2nd Question: Since the angles in the second question are parallel (which means they are the same) . we can easily find the answer . we can make sure the answer is right by using the same way ( angles of a triangle add up to 180)

Answer:

DEFG = (1/2)a^2

Step-by-step explanation:

tells us ∠FDG = 45° and ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90°!

So DFB- (1/2)(DF)(FB)=(1/2)a2

Main Answer:

The constant term of h(x) is 4x^3 - 16x^2 - 75x - 63\

Supportive Question and Answer:

What is an Algebraic Expression?

An expression that includes variables, constants, and algebraic operations is an algebraic expression in mathematics (addition, subtraction, etc.). Terms combine to form expressions.

Solution Explained:
Given,
h(x) = f(x).g(x)

h(x) = (x-7)(2x+3)^2

now, simplify,

(x-7)(2x +3)                                                    Expand the expression
           

(x-7)((2x)^2+2 X 2x X 3+3^2)                        Simplify the expression

(x-7)(2^2 X x^2 +2 X 2x X 3+3^2)                Calculate

(x-7)(4x^2+2 X 2x X 3 + 9)                            Mutiply

(x-7)(4x^2 + 12x + 9)                                       Expand the expression

x X 4x^2 + x X 12x + x X 9 - 7 X 4x^2 - 7 X 12x -7 X 9       Mutiply

4x^3 + 12x^2 + 9x - 28x^2 84x - 7 X 9           Calculate

4x^3 + 12x^2 + 9x - 28x^2 - 84x - 63                    Combine like terms

Hence, the constant term for h(x) is 4x-16x-75x 63.

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If the remainder is paid in equal monthly payments of $250. the number of month that the payments must be made is 24.

First step is to find the remainder after down payment

Remainder  = 6500-500

Remainder  = 6000

Now let find the number of monthly payment

Number of monthly payment = Remainder  / Monthly payment

Number of monthly payment = 6000 / 250

Number of monthly payment = 24

Therefore the monthly payment is 24.

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Answer:

(2.5×20)2=100 then square root of 100;

✓100=10

Hence answer is 10

Answer:

Step-by-step explanation:

1. Divide by -2 and thus flip the inequality

2. (n-5.5)<21/-2

3. Add 5.5 to both sides

4. n<-5

5.Check by plugging in any number less than -5 and see if the inequality is true

6. Example: plug in -10

Is -2(-10-5.5)>21?

Yes

31>21 your solution is n<-5

On solving the linear inequality −2(n − 5.5) > 21 for n, we get n < -5.

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'.

Given in the question,

-2(n - 5.5) > 21

Solving the inequality,

-2n + 11 > 21

-2n > 21 - 11

-2n > 10

-n > 5

n < -5

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The number of different sequences of stops that the driver can make is 24.

Permutation is simply used it illustrate the number of ways for a given information. The formula is illustrated as:

n! / (n – r)!

N is the number of things you are choosing from,

r is the number of items.

“!” is a factorial of a number

Since the delivery truck has 4 stops to make in a neighborhood, the sequences of stops will be:

= n! / (n – r)!

= 4!

= 4 × 3 × 2

= 24 stops.

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Answer:

Step-by-step explanation:

Yahweh’s

The measure of θ from the given trigonometric equation is 31°.

Given that, sin47°=cosθ and sinθ=cos(θ+16).

We know from geometry if the sum of two angles is 90°, then one angle is called the complement of the other.

The complementary angles are:

sinθ=cos(90-θ)

secθ=cosec(90-θ)

tanθ=cot(90-θ)

A) So, sin47°=cos(90°-47°)

⇒ sin47°=cos43°

Thus, θ=43°

B) sinθ=cos(θ+16)

⇒ sinθ=cos(43+16)

⇒ sinθ=cos 59°

⇒ sin(90-31)=cos 59°

Thus, θ=31°

Therefore, the measure of θ from the given trigonometric equation is 31°.

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x = y = 48 , by using angle sum property of triangle.

What are the properties of triangle?

A triangle's characteristics are:

1. Three sides, three angles, and three vertices make up a triangle.

2. A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.

3. Any two triangle sides can add up to a length that is longer than the third side.

4. The greatest side of a triangle is the side that faces the largest angle.

5. The sum of the triangle's internal opposite angles is equal to any of its outer angles. This is referred to as the triangle's outside angle property.

In the given triangle , two sides of the triangle are equal and we know angle opposite to equal sides are equal therefore both angle x and y are equal.

Now, Using angle sum property of triangle

x + y + 84 = 180 degree

x + x + 84 = 180

2x + 84 = 180

2x = 180 - 84

2x = 96

x = 96/2  

x = 48

Similary , y = 48 as x and y are equal.

Therefore, x = y = 48

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The true statement about the sentence 'sample of gas is enclosed in a container of fixed volume' are:

When a sample of gas is been enclosed in a container of fixed volume then then if the container temperature is been reduced then the kinetic energy of the gas will reduce.

Therefore the first and the third option are correct.

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To simplify the equations so that there would be no fractions, we

1. Multiply both sides by 8

2. Multiply both sides by 12

3. Multiply both sides by 10

4. Multiply both sides by 30

From the question, we are to determine what we could do first to each side of the equations so that there would be no fraction

1. (4x -4)/8 = (x +2)/4

Multiply both sides by the LCM of the denominators

The denominators are 8 and 4

The LCM of 8 and 4 is 8

Thus,

Multiply both sides by 8

8 × (4x -4)/8 = 8 × (x +2)/4

4x -4 = 2(x +2)

2. 3(4 - r)/6 = (4 + r) /4

Multiply both sides by the LCM of the denominators

The denominators are 6 and 4

The LCM of 6 and 4 is 12

Thus,

Multiply both sides by 12

12 × 3(4 - r)/6 = 12 × (4 + r) /4

2 × 3(4 - r) = 3(4 + r)

6(4 - r) = 3(4 + r)

3. (5q + 3)/10 = (q + 2)/5

Multiply both sides by the LCM of the denominators

The denominators are 10 and 5

The LCM of 10 and 5 is 10

Thus,

Multiply both sides by 10

10 × (5q + 3)/10 = 10 × (q + 2)/5

(5q + 3) = 2(q + 2)

4. 4(b - 7)/15 = (b + 3)/10

Multiply both sides by the LCM of the denominators

The denominators are 15 and 10

The LCM of 15 and 10 is 30

Thus,

Multiply both sides by 30

30 × 4(b - 7)/15 = 30 × (b + 3)/10

2 × 4(b - 7) = 3(b + 3)

8(b - 7) = 3(b + 3)

Hence, we will multiply both sides of the equation by 30

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The post-split market capitalization of Walnut Creek Inc. is $12995089.

Given that, Walnut Creek Inc. is going to do a revers stock split with a 3:4 ratio. The current price per share is $234.75 and the current number of outstanding shares is 38,750,000.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, 3+4 = 7

Now, 1/7 × 38,750,000

= 5535714 .29 shares

So, capitalization is 5535714 × 234.75

= $12995089

Therefore, The post-split market capitalization of Walnut Creek Inc. is $12995089.

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Answer: D

Step-by-step explanation:

The GCF of the number given as 45 and 27 is 9 and the factored expression is 9(5 - 3)

From the question, we have the following statement

The greatest common factor of 45 and 27

Rewrite the given expression as follows

This is represented using

45 and 27

Factor out 3 from the expression

So, we have the following representation

15 and 9 => Factored 3

Factor out 3 from the expression

So, we have the following representation

5 and 3 => Factored 3 * 3

So, we have

Factored = 3 * 3 = 9

This represents the GCF

So, the GCF is 9

In (a), we have

5 and 3 => Factored 3 * 3

This means that

45 - 27 = 3 * 3(5 - 3)

Evaluate the product

45 - 27 = 9(5 - 3)

Hence, the factored expression is 9(5 - 3)

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Answer:

[tex]y_{min}=-17[/tex]

[tex]y_{max}=15[/tex]

Step-by-step explanation:

Given function:

[tex]y=2x^2-12x+1[/tex]

The critical points are those values of x which make the derivative of the function zero.  

Differentiate the function:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=2 \cdot 2x^{2-1}-12x^{1-0}+0[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=4x-12[/tex]

Set the derivative to zero and solve for x:

[tex]\implies 4x-12=0[/tex]

[tex]\implies 4x=12[/tex]

[tex]\implies x=3[/tex]

To find the y-value of the critical point, substitute the found value of x into the function:

[tex]\implies 2(3)^2-12(3)+1[/tex]

[tex]\implies 2(9)-12(3)+1[/tex]

[tex]\implies 18-36+1[/tex]

[tex]\implies -18+1[/tex]

[tex]\implies -17[/tex]

Therefore, the critical point is (3, -17).

To find the endpoints of the function in the interval [0, 7], substitute x = 0 and x = 7 into the function:

[tex]\begin{aligned} x=0 \implies 2(0)^2-12(0)+1&=0-0+1\\&=1\end{aligned}[/tex]

[tex]\begin{aligned} x=7 \implies 2(7)^2-12(7)+1&=2(49)-12(7)+1\\&=98-84+1\\&=14+1\\&=15\end{aligned}[/tex]

Therefore:

Therefore the minimum y-value is -17 and the maximum y-value is 15 in the given interval [0, 7]

The minimum and maximum y value of the function is -17 and 15 respectively.

This is a basic problem in calculus.

Given function: [tex]y=2x^{2} -12x+1[/tex]

Step 1: First, let's find the derivative of the function

[tex]\frac{dy}{dx} = 2.2x^{2-1} -12x^{1-0} +0\\\frac{dy}{dx} = 4x-12[/tex]

Step 2: Equate the derivative with zero

4x-12=0

x=3

Therefore, x=3 is the critical value for x

Step 3: Find the critical value for y

[tex]y=2x^{2} -12x+1[/tex]

[tex]y=2\times3^{2} -12\times3+1\\y=-17[/tex]

Thus, the critical points for the function [tex]y=2x^{2} -12x+1[/tex] are (3,-17)

Step 4: Find endpoints using the given interval [0,7]

This can be done by substituting x1=0 and x2=7 simultaneously in the given function and finding y1 and y2.

For x1=0,

[tex]y1=2\times0^{2} -12\times0+1\\y1=0+0+1\\y1=1[/tex]

For x2=7,

[tex]y2=2\times7^{2} -12\times7+1\\y2=98-84+1\\y2=15[/tex]

Now, we have both critical points and endpoints.

Therefore, The minimum and maximum y value of the function is -17 and 15 respectively.

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