Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?
A.2520 B.2880 C.1320 D.3250 E.3750

We can identify key terms in word problems that can tell use what math symbols or operations to use:

There are other key terms that can help us, including:

We're given:

11 is more than twice x:

Less than 44:

Combine all of these to get the inequality:

11 + 2x < 44

The required area is 10.3 square units.

Area of triangle= 12 /(a* b)

Area of a triangle using trigonometric area formula = 1/2( a * b) sin(c)

here, base = a , height = b*sin(c)

Given ,

Only the sine of the included angle, whose two side lengths are specified, can be used despite the two angle measurements that have been provided. The EF and DF sides of our triangle's angle, which measures 31 degrees, are also provided.

On putting the values given in the formula we get,

Area = 1/2* 8 * 5sin(31)

        = 20 * 0.51503807491

         ≈ 10.3

Therefore, the area of the triangle DEF is 10.3 square units.

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The inequality could be used to determine the number of subscriptions that Jennifer needs to sell is 2x+x≥90.

In mathematics, an inequality is a relationship that results from a non-equal comparison of two integers or other mathematical expressions. It is most typically used on a number line to compare the sizes of two numbers. There are several notations for various sorts of inequalities:

The symbol a < b indicates that an is less than b.

The symbol a > b indicates that an is greater than b.

These are known as strict inequalities, because an is strictly less than or strictly bigger than b. Equivalence is not allowed.

Given,

Carol intends to sell twice the number of magazine subscriptions as Jennifer..

And also given that,

Carol and Jennifer needs to sell at least 90 subscriptions in all

Let Carol sell 2x magazines then Jennifer sell x

So, they need to sell at least 90

x+2x ≥ 90

∴2x+x ≥ 90

Hence, the answer is  option 4

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The probability that is lower than 63 grams is 95%

Given that,

X~ Normal ( 67 grams, 5 grams ) , n = 5

=> E( x ) = 67 grams , Var( X ) =5 grams

* ~ Normal ( 67 grams , 1 grams )

We know that, if X~ Normal ( E ( x) = a . Val (x ) = b)

Then X~ Normal ( E(x) = a, √Var (x)/n = √b/n)

E(x) = a, Var (x)/ = √b/n

Probability that sample mean X , is blw 65 and 70 grams

P ( 65< X<70 ) =

= P(Z<1. 76 ) - P(Z≤-2.65)

Using standard normal table values represent area

left of the Z- score, we get

= 0.96080 - 0.00402

= 0 .95678

=0.9568

So,The probability that is lower than 63 grams is 95%

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The correct option for the t test for the difference between the means of 2 independent populations is sample variances are equal.

The Autonomous samples t Test analyzes the method for two free gatherings to decide if there is factual proof that the related populace implies are essentially unique. The Free samples t Test is a parametric test. This test is otherwise called: Free t Test.

The t test for the difference between the means of 2 independent populations when standard deviations are unknown, we must assume that sample variances are equal.

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The answer choice which represents an expression which is equivalent to the given expression; √-36 is; Choice D; 6i.

It follows from the task content that the expression which is equivalent to the given expression be determined.

Since the given expression is; √-36.

The square root of a negative number is undefined but can however be evaluated as follows;

√-36

= √-1 × √36

= √-1 × 6

However, the square root of -1; √-1 = i.

= 6i

Ultimately, the required equivalent expression is; Choice D; 6i.

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Answer:

  x +2y = -2

Step-by-step explanation:

You want the line perpendicular to 2x-y = 5 that passes through (6, -4).

The slopes of perpendicular lines are opposite reciprocals. This means the equation of the perpendicular line can be formed by swapping the coefficients of x and y, and negating one of them. We want the leading coefficient to be positive, so we choose our line's equation to be ...

  2x -y = constant . . . . . . . . . . original line

  x +2y = <some constant>

The constant must be chosen so the equation is true at the given point:

  x + 2y = (6) +2(-4) = -2

An equation for the perpendicular line is ...

  x +2y = -2

The answers to all subquestions would be

Part A: [tex]P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}[/tex], x= 0, 1, 2, 3, ..., 15.

Part B: P(X = 1) = 0.2312

Part C: P(X = 2) = 0.2656

Part D: P(X ≥ 2) = 0.6814

Part E: P(X = 0) = 0.0874

What is a binomial distribution?

The binomial distribution with parameters n and p in probability theory and statistics is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each with its own Boolean-valued outcome: success or failure.

Let X be the random variable.

The number of trials n = 15, P=0.15

X ~ Bin(n, p)

Part A:

      [tex]P(X=x)= {n \choose x} (p)^{x} (1-p)^{n-x}[/tex]

      [tex]P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}[/tex], x=0, 1, 2, 3,..., 15.

Part B:

    [tex]P(X=1)= {15 \choose 1} (0.15)^{1} (0.85)^{15-1}\\\\P(X=1)= {(15)} (0.15) (0.85)^{14}\\\\P(X=1)=0.2312[/tex]

Part C:

     [tex]P(X=2)= {15 \choose 2} (0.15)^{2} (0.85)^{15-2}\\\\P(X=2)= {(105)} (0.15)^2 (0.85)^{13}\\\\P(X=2)=0.2856[/tex]

Part D:

 [tex]P(X\geq 2)= 1-P(X < 2)\\\\P(X\geq 2)=1-P(X=0)-P(X=1)\\\\P(X\geq 2)=1-0.0873-0.3212\\\\P(X\geq2)=0.6814[/tex]

Part E:

  The probability of none of the children getting the disease will be

             [tex]P(X=0)= {15 \choose 0} (0.15)^{0} (0.85)^{15-0}\\\\P(X=0)= {(1)} (1) (0.85)^{15}\\\\P(X=1)=0.8734[/tex]

Hence,

Part A: [tex]P(X=x)= {15 \choose x} (0.15)^{x} (0.85)^{15-x}[/tex], x= 0, 1, 2, 3, ..., 15.

Part B: P(X = 1) = 0.2312

Part C: P(X = 2) = 0.2656

Part D: P(X ≥ 2) = 0.6814

Part E: P(X = 0) = 0.0874

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The equation represents the line that passes through (- 6, 7) and (- 3, 6) is  y = -1/3x +5

The slope-intercept form is just a means of formulating a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are clearly visible. This form is frequently referred to as the y = mx + b form. This line form is one of the most prevalent in algebra classes.

A line's slope-intercept form is y = mx + b, where m is its slope and b is its y-intercept.

The equation of the line which is passing through two points is:

y₂-y₁ / x₂-x₁

(6-7)/(-3+6)=-1/3

A line's slope-intercept form is y =mx +b, where m is the slope and b is the y intercept.

y = -1/3 x +b. We must now calculate b, the y intercept. To find b, plug one of the given points into the previous equation and solve for b.

6 = -1/3(-3) + b

b = 5

y = -1/3x +5

Therefore, the equation represents the line that passes through (- 6, 7) and (- 3, 6) is  y = -1/3x +5

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let m be the vector space of all 3x3 matrices, and let h be its subspace consisting of all a satisfying. The dimension of h will be  0 ≤ h ≤ 3

If m be the vector space , a subset h ⊆ m is a subspace of m if the ten axioms (L₁ , L₂ , L₃ , . . . . L₁₀) of m are satisfied on h but it suffices only two axioms to hold on h for h that are axioms of closure of h under two linear operations : the sum of vectors and their multiplication by scalars in the field F.

Let m is a vector space over a field F,  a subset h which is closed under the two linear operation of m : the vector addition and multiplication of vector by scalar .

L₁ (∀x , y ∈m) , x+ y∈ m ---------(1)

L₂ (∀λ ∈ F) ( ∀ x∈ m ) λx ∈m -------(2)

A subset h⊆ m which satisfy (1) and (2) is a subspace of v

Dimension of Vector space and a subspace :

According to linear algebra theorem,

The number of vectors in all the basis if finitely generated vector space m is the same. This number is just the dimension of subspace m : dim m .

If m is spanned then here, dim m = 3

h ⊆ subs m <===> dim h < dim m

If h is subspace of m and dim m = 3 then,

dim h = h with 0≤ h ≤3

If h is zero, the dimension of improper subspace , h = {0}

If dim h = dim m = 3 the h = m since any basis A of h is a basis of m too and conversely,

Hence , any vector m of all 3×3 matrices and h be its subspace , the dim h will be 0 ≤ h ≤ 3

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Answer:

y= mx+b

y= 4x+b

-1=4(1)+b

-1=4+b

-4 -4

-5=b

y = 4x -5

Step-by-step explanation:

The hypotheses are:

Null hypothesis: the average test scores are the same for the different teaching methods.

Alternative hypothesis: the average test scores are different for the different teaching methods.

To determine the degree of freedom for the F test: we must find two sources of variation such that we have two variances. The two sources of variation are: Factor (between groups) and the error (within groups) and add this up. Or use (N - 1). N is number in sample.

Hence we get the required answer.

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Yes , on degeneracy of an optimal basic feasible solution in one problem (primal) implies uniqueness of optimal solutions for the other(dual).

Degenerate Elementary Feasible Solutions:

Elementary feasible solutions where one or more of the elementary variables are zero.

Discrete Variable: A decision variable that can only accept integer values.

Feasible Solution: A solution that satisfies all constraints.

Yes, a linear programming optimization problem can have a degenerate optimal solution, but a dual problem has a unique optimal solution, but only if instead of the optimal solution there is a degenerate optimal solution.

Example: Suppose the main problem depends on

max (z) = x₁+x₂

x₁≤1

x₁+x₂≤1

x₁, x₂≥0.

The solution (1,0) is optimal and degenerate, but all solutions (a,1−a) for 0≤a≤1 are also optimal.

dual is min(z)= y₁+y₂

subject to

y₁+y₂≥1,

y₂≥1,

y₁,y₂≥0.

dual has a unique (degenerate) optimal solution (0,1). So, there are situations where there are mostly degenerate optima, but unique dual optima.

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There are four common types of transformations -

translation

rotation

reflection

 dilation.

The probability of selling more than radios is 0.07 when the probability of selling radios is from 0 to 5.

Given that,

In the picture we can see the full question.

We have to find what is the probability of selling more than 3 radios.

We know that,

In the picture there is a table

We have to first find the table then we get the probability of selling more than 3 radios.

First,

Given data is 100 weeks of sales data

Probability is number of weeks/ 100 weeks

x=0, number of weeks is 3

P=3/100=0.03

x=1, number of weeks is 20

P=20/100=0.2

x=2, number of weeks is 50

P=50/100=0.5

x=3, number of weeks is 20

P=20/100=0.2

x=4, number of weeks is 5

P=5/100=0.05

x=5, number of weeks is 2

P=2/100=0.02

The probability table we get,

x term are 0,1,2,3,4,5

P(x)    |0.03 | 0.2 |  0.5 |  0.2 |0.05| 0.02|

The probability of selling more than 3 radios is sum of the probability of selling 4 radios and 5 radios

P(x>3)=P(x=4)+P(x=5)

P(x>3)= 0.05+0.02

P(x>3)= 0.07

Therefore, The probability of selling more than radios is 0.07 when the probability of selling radios is from 0 to 5.

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Using Magnetic field,

a) Magnetic force acting on loop is 2.59 ×10⁻⁴ N

b) Torque acting on loop is zero.

We have given that,

Each side of square loop wire , L = 2.00 cm

Square loop carring current , I₂ = 0.230 A

Solenoid , has n= 30 turns/cm

Current Carrying in solenoid, I₁ = 15.0 A

Magnetic field inside solenoid , B = μ₀ n I₁

where, μ₀---> susceptibility of free space

μ₀ = 4π×10⁻⁷A/m

pulgging all known values in above formula,

B = (4π×10⁻⁷ A/m) 30 turn/cm × 100cm /1m (15.0 A)

= 5.6 ×10⁻² T

Now, the magnitude of magnetic force on one side of loop , F = B× L× I₂× sinθ

=> F = ( 5.6 ×10⁻² T )(0.02 m)(0.230 A) sin90°

=> F = 0.02599 × 10⁻² N

=> F = 2.59 ×10⁻⁴ N

The force acting on one side of loop lie in the plane of loop, are prependicular to the all sides and directed away from interior of the loop. Thus, these force strech the loop do tends to rotate it.

So, if loop is not rotate then there is not torque associated. Hence, Torque acing on loop is zero.

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Complete question:

A single-turn square loop of wire, 2.00 cm on each edge, carries a clockwise current of 0.230A. The loop is inside a solenoid, with the plane of the loop perpendicular to the magnetic field of the solenoid. The solenoid has 30.0 turns/cm and carries a clockwise current of 15.0 A. Find (a) the force on each side of the loop and (b) the torque acting on the loop.

Answer:

Step-by-step explanation:

Yes it is possible because of the working man solution of indigineous triangles in the diameter of a ml

to find the percentage we divide the number with the other number which wew take it as base and multiply with 100

let us under stande this with an example

we want to know what percentage is 5 of 10

so we divide 5 by 10 and multiply it with 100

i.e. (5/10)*100 = 0.5*100 = 50%

hence we can say that 5 is 50% of 10

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We divide a number by another number, using that other number as the base, then multiply the result by 100 to get the percentage that one number is of another.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

We place the percent symbol (%) next to the number to indicate that the number is a percentage.

For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

To get what percentage one number is of another:

We divide the number by another number, use that other number as the base, and multiply the result by 100 to determine the percentage.

Let's use an example to further understand this:

We're curious about what proportion makes up 5 of 10.

Consequently, we increase it by 100 and divide 5 by 10.

That is (5/10) × 100 = 0.5 × 100 = 50%

So, we can say that 5 is equal to 10 / 50%.

Therefore, we divide a number by another number, using that other number as the base, then multiply the result by 100 to get the percentage that one number is of another.

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The present age of the son is 12 years and the present age of the father is 36 years.

What is the age problem?

Age problems are algebra word problems that deal with the ages of people currently, in the past, or in the future.

Let the present age of the son be 'x'

Then, the present age of the father will be '3x'

According to the question,

The age of the son after 12 years = (x+12) years

And the age of the father after 12 years = 2(x+12) years

Therefore,

or, 3x+12=2(x+12)

or, 3x+12=2x+24

or, x=12

And, the father's age = 3*12 = 36 years

Hence, the present age of the son is 12 years and the present age of the father is 36 years.

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The probability that the drawn marble is green is 5/9.

What do you mean by an intersection in probability?

P(A∩B) denotes the probability of A and B occurring together, also known as the likelihood of A intersecting with B, or the likelihood of two occurrences occurring concurrently, or the probability of two events occurring simultaneously.

We define the intersection of two events as the set of all results that occur for any two events A and B. In other words, if both A and B happen, the intersection will happen. A and B are crossed when A∩B is used as a symbol.

Solution Explained:

Total number of white marbles = 6

Total number of black marbles = 2

Total number of green marbles = 10

Marbles in total = 6 + 2 + 10 = 18

A marble is drawn on random

Therefore, the probability of the marble being green P(G) = 10/18 = 5/9

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x=[tex]\frac{y+1o}{4}[/tex] is the solution of the eqution y=4x+10.

An liner equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

From the question  y=4x-10

add 10 both side

y+10=4x

Divide both side with 4

                x = [tex]\frac{y+1o}{4}[/tex]

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NOTE: The given question is incomplete on the portal. Here is the complete question.

Question: What is the solution to the system of equation y = 4x - 10 ?

Cubic units are used to measure volume. Length, width, and height formula for a rectangular prism that represents its volume: The lengths of a rectangular prism's three distinct dimensions (length, width, and height) are multiplied together to determine the volume of the object. So, V = lwh is one volume formula for rectangular prisms.

What is Volume?

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc. Volume is sometimes referred to as capacity.

What is rectangular prisms?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Length, width, and height formula for a rectangular prism that represents its volume: The lengths of a rectangular prism's three distinct dimensions (length, width, and height) are multiplied together to determine the volume of the object. A volume formula for rectangular prisms is as follows:

                                         V = lwh

The prism's base is a rectangle with the dimensions (l, w) and (h), and the height (h) is the separation between the two bases at a perpendicular angle.

Rectangular prism volume formula based on base area and height: The area of a rectangular prism's one side can be used to determine the prism's base, or area B. B divided by the prism's height will yield the dimension of the prism. Thus, the following is a second formula for a rectangular prism's volume:

                                    V = Bh

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Using disk scheduling algorithm,

Total distance ( head movement) for following algorithms is 120.

Disk Scheduling Algorithm

Disk scheduling is performed by the operating system to schedule I/O requests to arrive at the disk. Disk scheduling is also called I/O scheduling.

we have given that

Total cylinders on a disk drive = 100 , numbered from 0 to 99.

The queue order is 10, 20, 50, 70, 80 .

Current disk position = cylinder 40

Starting from current head position.

We have to calculate the total distance (head movement) for the following algorithm.

Since, disk moving towards zero.

Now , Total distance = |40-10| + | 10-0| + |0-20| +

|20-50| + |50-70| + |70-80|

= 30 + 10 + 20 + 30 + 20 + 10

= 120

Hence, the required distance is 120.

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The length in cm of any one of its interior diagonals is √14 D.

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Answer:

$189

Step-by-step explanation:

Calculate a unit rate (dollars per hour) then times by 9 hours. OR use a proportion. You will get the same answer.

dollars/hour

= $252/12hours

= $21/1hour

= 21 $/hr

21 × 9 = 189

Yoko will make $189 for 9 hours.

OR use a proportion.

$/hour = $/hour

252/12 = x/9

cross-multiply

12x = 252(9)

12x = 2268

divide by 12

x = 2268/12

x = 189

same answer!

The correct option is option( A).

Using the property of Obtuse Triangle, the triangle with sides { 8, 10, 14 } is an Obtuse Triangle.

Obtuse Triangle:

An obtuse triangle is a triangle with one interior angle greater than 90 degrees. In geometry, a triangle is represented as a closed 2D figure with three sides of equal or unequal length and three angles of equal or unequal measurements.

Obtuse triangle property:

we have given the sides of triangle so, we use the fourth property for check the triangle formed by given sides are obtuse triangle or not .

8² + 10² = 164; 14² = 196 -> obtuse

9² + 12² = 225; 15² = 225 -> not obtuse

10² + 14²= 296 ; 17²= 289 --> not obtuse

12² + 15² = 369; 19²= 361 --> not obtuse

Hence, the required triangle is triangle with sides 8, 10, 14.

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Complete Question:

which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle

A. 8, 10, 14

B. 9, 12, 15

C. 10, 14, 17

D. 12, 15, 19

Answer: the answer is A 8, 10, 14.

Step-by-step explanation: it show below.

Answer: 1 1/6

Step-by-step explanation:

(P.S: Everthing in italics are either fractions. mixed numbers, or numbers.

And there ya' go! The answer is 1 1/6! You're welcome!

According to the given mean and standard deviation values, we find out that the proportion of cold sufferers that experience symptoms for more than 8 days is equal to 0.129 or 12.9%.

It is given to us that -

Amount of time a person experiences cold virus symptoms are normally distributed with

a mean of 7.5 days

and, a standard deviation of 1.5 days

We have to find out the proportion of cold sufferers that experience symptoms for more than 8 days.

Now, from the given information, we have

Mean = μ = 7.5

Standard deviation = σ = 1.5

and, X = 8

Now, the proportion of cold sufferers that experience symptoms for more than 8 days can be represented as -

P(X > 8)

= P{[(X-μ)/σ] > [(8-7.5)/1.5]}

=P(Z>0.33)

Looking at the z-score values, we find out that

P(Z>0.33) = 0.129 = 12.9%

Thus, from the given mean and standard deviation values, we find out that the proportion of cold sufferers that experience symptoms for more than 8 days is equal to 0.129 or 12.9%.

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Answer: 92°

Step-by-step explanation:

The triangle is an isosceles triangle, since two sides are equal. That means the two opposite angles are also equal. Hence m∠N = m∠M = 44°.

Since all interior angles of a triangle adds up to 180°, m∠L can be calculated as:

[tex]180-2(44)=180-88=92[/tex]

The five things when two parallel lines are cut by a transversal are the corresponding angle, alternate interior angle, alternate exterior angle, consecutive interior angles, and alternate angle.

Here we have to find the five things that happen when two parallel lines are cut by a transversal.

When two parallel lines are cut by the transversal line it will form five angles.

Corresponding angle, alternate interior angle, alternate exterior angle, consecutive interior angles, and alternate angle.

From the given figure:

Corresponding angle:

∠1 and ∠5

∠2 and ∠6

∠3 and ∠7

∠4 and ∠8

consecutive angle:

∠3 and ∠6

∠4 and ∠5

alternate interior angle:

∠3 and ∠5

∠4 and ∠6

alternate exterior angle:

∠2 and ∠8

∠1 and ∠7

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