Expand. (ab)to the 5th power

In option D the location of point P represents the probability of an event that is likely but not certain.

The likelihood that an event will occur is measured by its probability. In our example, the point P on the number line is exactly equally distant from both 0 and 1 in option A, demonstrating that this event is equally likely. The fact that the point P is close to 0 in option B indicates that it is extremely unlikely. Option C has the point P after the point 1, which makes it certain because any probability cannot be larger than 1, which demonstrates that the event is unavoidable. In Option D point P's proximity to 1 demonstrates that it is extremely likely but not certain.

The complete question is:

On which number line the location of point P represent the probability of an event that is likely, but not certain?

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The factored form and the vertex form of the given quadratic equation is given by :

Standard quadratic equation is  : ay²+ by + c

Factored form of the quadratic equation is : A ( y - p )( y - q ).

Vertex form of the quadratic equation is : A ( y - h )² + k .

As given in the question,

Let us consider the standard quadratic equation be :

ay²+ by + c

Example : 3x² + 15x  + 18

Factored form is :

= 3 (x² + 5x + 6 )

= 3 ( x² + 2x + 3x + 6 )

= 3 ( x + 2 )( x + 3 )

Standard factored form is :  A ( y - p )( y - q )

Let ( h ,k ) be the vertex of the quadratic equation ,

Vertex form is given by : A ( y - h )² + k

Therefore, the factored and the vertex form of the given quadratic equation is equal to

Standard quadratic equation is  : ay²+ by + c

Factored form of the quadratic equation is : A ( y - p )( y - q ).

Vertex form of the quadratic equation is : A ( y - h )² + k .

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For k = 2, the given system of equation contains no solution, hence represent parallel lines.

There are no solutions to a system with parallel lines. Observe that the slope of parallel lines is the same. The lines will have the same steepness with distinct intercepts when graphed. Since parallel lines will never connect, there is no solution to the problem.

When the graphs are parallel, a system of linear equations cannot have a solution.

For a system of equations representing parallel lines means they do not intersect, hence, have no solutions.

For a system of equations [tex]$a_1 x+b_1 y+c_1=0 ; a_2 x+b_2 y+c_2=0$[/tex] to have no solution, the condition to be satisfied is

[tex]$\frac{a_1}{a_2}=\frac{b_1}{b_2} \equiv \frac{c_1}{c_2}$$[/tex]

[tex]$\Rightarrow \frac{\mathrm{k}}{4}=\frac{-3}{-6} \equiv \frac{6}{150}$$[/tex]

For k = 2, the given system of equation contains no solution, hence represent parallel lines.

The complete question is:

The value of k, for which the system of equations k x-3 y+6=0,4 x-6 y+150 represent parallel lines is

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The value of x in the given ΔCSU is 17.7.

Given data :

m∠CSU = 10x + 3

m∠CUS = 30x - 13 x

The three angles form the triangle ΔCSU then the addition of them makes 180°.

ΔCSU = 180

m∠CSU = 10x + 3

10x + 3  = 180

10x  = 180 - 3

x = 177 / 10 = 17.7

So,

m∠CSU = 10x + 3

Applying the value of x

= 10 x 17.7 + 3

= 180

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Therefore, utilizing features like split middle term, the elements of the quadratic polynomial x2 + 4x + 3 are (x+3)(x+1).

A quadratic polynomial in a single variable is represented by the equation x ax2+bx+c=0. a 0. Since this polynomial is of second order, the Fundamental Theorem of Algebra guarantees that it has at least one solution. There are both simple and complex solutions. A quadratic equation is just that—quadratic. It has at least one word that has to be squared, as shown by this. One of the often used solutions for quadratic equations is "ax2 + bx + c = 0." where X is an undefined variable and a, b, and c are numerical coefficients or constants.

given

Given that: x2+4x+3

                  =x2+3x+x+3,       by split middle term

                  =(x2 +3x)+(x+3),    by group pair of terms

                  =x(x+3)+1(x+3),       by factor each binomials

                  =(x+3)(x+1),             by factor out common factor (x+3)

Therefore, utilizing features like split middle term, the elements of the quadratic polynomial x2 + 4x + 3 are (x+3)(x+1).

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Answer:

3rd option

Step-by-step explanation:

the perimeter is the sum of the 3 sides of the triangle.

To find the third side subtract the sum of the 2 known sides from the given perimeter, that is

third side

= 8x + 7 - (4x + 2x - 3)

= 8x + 7 - (6x - 3) ← distribute parenthesis by - 1

= 8x + 7 - 6x + 3 ← collect like terms

= 2x + 10

The length of third side of Triangle is 2x + 10.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A triangle has a perimeter of 8x + 7.

First side = 4x, second side = 2x - 3

As, Perimeter of Triangle =  side + side + side

8x + 7 = 4x + 2x - 3 +side

8x + 7 = 6x - 3 + side

side = 8x - 6x + 7 + 3

side = 2x + 10

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The feasible region corresponds to the area that lies below the line y = 2x and above the line y = -x + 220. The feasible region is the area which is above and on the line y = 2x, and below and on the line y = -x + 220.

In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).

x + y <= 220 (because the total area used for flowers and vegetables must be less than or equal to 220 square feet)

y >= 2x (because the area used for vegetables must be at least twice the area used for flowers)

We can graph these inequalities on a coordinate plane. The first inequality x + y <= 220 represents a line with slope -1 and y-intercept of 220, this line is the upper boundary of the feasible region. The second inequality y >= 2x represents a line with slope 1/2 and y-intercept of 0, this line is the lower boundary of the feasible region.

The feasible region corresponds to the area that lies below the line y = 2x and above the line y = -x + 220. The feasible region is the area which is above and on the line y = 2x, and below and on the line y = -x + 220.

This region is a triangle.

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The solution of the system of equations:

4x - 6y = 12

2x + 2y = 6

is the point (3, 0).

Here we want to solve the following system of equations:

4x - 6y = 12

2x + 2y = 6

To do it, we need to graph the two equations (just find two points on the lines and connect them with lines) on the same coordinate axis and find the points where the graphs intercept, these points of interception are the solutions of the system of equations.

The graph can be seen in the image below. There we can see that the solution is the point (3, 0)

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Answer: 17/6 or it could be 2.83 but the 3 is repeating

[tex]\cfrac{10}{4}+\cfrac{1}{3}\implies \cfrac{(3)10~~ + ~~(4)1}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{30+4}{12}\implies \cfrac{34}{12}\implies \cfrac{17}{6}\implies 2\frac{5}{6}[/tex]

On solving the provided question, we can say that Arc AB = Radius * Angle  AB = 9 x 2.164

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

Radians = π/180 * degree

0.0174 x 124 = 2.164 rad

Arc AB = Radius * Angle ( In Radians )

AB = 9 x 2.164

=> 19.47m

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Answer: the equation of the line that is parallel to y = 2x + 9 and passes through the point (5,-10) is y = 2x + 20

Step-by-step explanation:

A line that is parallel to another line will have the same slope (m). The slope of the line y = 2x + 9 is m= 2.

To find the equation of the line that is parallel to y = 2x + 9 and passes through the point (5,-10), we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

So, the equation of the line that is parallel to y = 2x + 9 and passes through the point (5,-10) is:

y - (-10) = 2(x - 5)

Simplifying the equation:

y = 2x + 20

So, the equation of the line that is parallel to y = 2x + 9 and passes through the point (5,-10) is y = 2x + 20

Answer:

y = 2x - 20

Step-by-step explanation:

General equation of a line is y = mx + b where m = slope and b = y-intercept

Parallel lines will have same slope but different intercepts

Given line: y = 2x + 9

Slope of this line is 2

Parallel line will have equation y = 2x + b

Since it passes through 5, 10 the value of y = - 10 must be the same as 2x+b for x = 5

Plugging in values:

- 10 = 2(5) + b

- 10 = 10 + b

-10-10 = b

b = - 20

So the equation of the line that is parallel to the line y=2x+9 and passes through the line (5,-10)

y = 2x - 20

Answer:

Step-by-step explanation:

(9)^-5/2 = (1/9)^5/2 = (1/59049)^(5/2) = 1/(59049)^(5/2) = 1/243^(5/2) = 1/243^(5/2) = 1/(3^5)^(5/2) = 1/3^(5*5/2) = 1/3^25/2 =1/3^(25/2) = 1/3^12.5 = 1/(3^12.5) =1/3^12.5 =1/43046721 = 1/43046721

Answer: The sequence is defined by the rule f(n) = 2n^2 + 4.

To find the first 4 terms of the sequence, we need to plug in the values of n into the rule and calculate f(n) for each value of n.

n = 1: f(1) = 2(1)^2 + 4 = 2 + 4 = 6

n = 2: f(2) = 2(2)^2 + 4 = 8 + 4 = 12

n = 3: f(3) = 2(3)^2 + 4 = 18 + 4 = 22

n = 4: f(4) = 2(4)^2 + 4 = 32 + 4 = 36

So, the first 4 terms of the sequence are 6, 12, 22, 36

Step-by-step explanation:

C. x*110 is the product of unknown number with 110.

What is meant by product?

In mathematics, a product is the outcome of multiplying two or more numbers together.

For eg. 5*4*3.

Step by step explaination:

A. x+110

This  statement does not satisfy the condition of question .

So, the given statement is wrong.

B. x-110

This  statement does not satisfy the condition of question .

So, the given statement is wrong.

C. x*110

This statement satisfy the condition of question .

As it states that product of unknown number with 110.

product=multiplication.

So, ths given statement is right.

D. x/110

This  statement does not satisfy the condition of question .

So, the given statement is wrong.

C.x*110 is the product of unknown number with 110.

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The P-value for this hypothesis test is 0.00215

The p-value hypothesis test gives a measure of how much evidence is present to reject the null hypothesis. The smaller the p-value, the higher the evidence against the null hypothesis.

Given that:

Null Hypothesis: mu1 = mu2

Alternative Hypothesis: mu1<mu2

Notice that the alternative hypothesis is a one-tailed test

Now, when a one-tailed alternative hypothesis is used, To obtain a one-tailed alternative probability value i.e p-value, we divide the result by two (2).

so, given output ( z=3.25, p=0.0043)

since its one-tailed test:

P-value for this hypothesis test = 0.0043/2 = 0.00215

Therefore, the P-value for this hypothesis test is 0.00215

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Answer:

lolololololololololololololololol

Answer

Step-by-step explanation:

Answer:

9 x 20 x 19 = 3420

6 x 18 x 21 x 19 x 20 x 1 x 20 x 9 x 14 x 7 = 15202857600

3420 x 15202857600 = 5199377299200

Therfore, the answer is 5199377299200.

Using probability theory, it can be concluded that the probability that he will roll at least two 1's is 2/27

Probability is a value used to measure the degree of occurrence of a random event.

P(A) = n(A) / n(S)  ,  where:

P(A) = probability of event A

n(A) = number of events A

n(S) = total number of sample

Now we take a look at the given problem. there are three fair dices in the experiment (n = 3).

Probability of events with no 1's, p(A):

p(A) = (number of sides other than one / total number of sides) ^ number of dice

= (5/6)³

= 125/216

The probability of events with exactly one 1, p(B):

p(B) = number of dice * probability of events with one 1 in one dice * probability of events other than 1's in two dices

= 3 * (number of sides other than one / total number of sides) ^ number of dice * (number of sides other than one / total number of sides) ^ number of dice

= 3 * (1/6)¹ * (5/6)²

= 75/216

Probability of events with at least two 1's, p(C):

p(C) = 1 - p(A) - p(B)

      = 1 - 125/216 - 75/216

      = 216/216 - 200/216

      = 16/216

      = 2/27

Thus, the probability that he will roll at least two 1's is 2/27

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The logarithm of 7 with base 7 is equal to 1, since any number to the power of 1 is equal to itself.

The logarithm of a number is the exponent to which a base number must be raised to produce that number. For example, the logarithm of 10 with base 2 is 3, since 2 to the power of 3 is equal to 10. In this case, the logarithm of 7 with base 7 is equal to 1, since any number to the power of 1 is equal to itself.

This is because logarithms have the property that logb b = 1. This means that the logarithm of a number with the same base as the number itself is always equal to 1. This is why, in the case of log7 7, the answer is 1.

Logarithms can be used to simplify mathematical equations, as logarithms of multiplication and division are equal to the sums and differences of the logarithms of the individual numbers. They are also used in many scientific and engineering applications, such as calculating the pH of a solution.

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By calculating the given expression , we get 5 as a final resultant.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers the use of letters or alphabets without specifying their real values. The basics of algebra taught us the way to express an unknown fee the use of letters consisting of x, y, z, and so on. those letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any fee that is placed earlier than and improved with the aid of a variable is a coefficient.

Given expression ,

32- (3^2 -1 ) + 20 / 2

So by using the BODMAS rule ,

32 - (3*3  -  1 ) + 20 / 2

23 - (9 - 1 ) + 10

23 - (8) + 10

23 - 18

23 - 18

= 5

Hence, By calculating the given expression , we get 5 as a final resultant.

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If Malik gets to work in 25 minutes, he must be driving 42 mph

We know that the formula of  the speed.

speed = distance/time

Given that Malik can drive to work in 30 minutes when driving 35 mph.

Let d represents the distance to work place.

Let s1 be the speed and t1 be the time.

here, s1 = 35 mph

and t1 = 30 minutes

          = 0.5 hours

Using formula of speed,

s1 = d/t1

d = s1 × t1

d = 35 × 0.5

d = 17.5 miles

We need to find the speed if he gets to work in 25 minutes.

Using the formula of the speed,

s = d/t

here, t = 25 minutes

          = 0.4167 hour

So, s = (17.5) / (0.4167)

s = 41.99

s ≈ 42 mph

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The complete question is

Malik's speed and time vary inversely. He can drive to work in 30 minutes when driving 35 mph. How fast is he likely driving if he gets to work in 25 minutes?

The length s of the circular arc is 6.75π units

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

A figure made by two intersecting lines or two rays extending from the same point is called an angle.The character ∠ is used to represent it. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life.

Formula for the length s of the circular arc when angle θ is in radians:

s=r θ

=> s= 9(3π/4)  = (9*3*π)/4 = 6.75π units

Thus, the  length s of the circular arc is 6.75π units

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Answer: a vertical line goes up and down

Answer: horizontal is left to right, vertical is up and down.

Step-by-step explanation: a horizontal line is the same direction as the horizon, a vertical line is perpendicular to the horizon

Answer:

72 cm

Step-by-step explanation:

you said that the width is is 36 and the length is 2x as long making it 36*2 which is 72

-6p³ + 14p² -6 is the final polynomial after all operations

In order to get final polynomial we nedd to complete all operations on different polynomials provided velow.

A polynomial is a mathematical expression involving a sum of powers in one or more variables with real or complex coefficients. It is a type of algebraic expression which can be of degree 0,1,2,3,..n. It is represented by a letter such as "P" or "f", with one or more variables such as x, y, z, etc. and coefficients, which are numbers or constants. The degree of a polynomial is the highest power of the variable in it.

-3p³ - 3p³ + 5p² + 2p² + 7p² - 3 - 3

=> -6p³ + 14p² -6

so the required polynomial is -6p³ + 14p² -6 which is obtained after all the operation on the numbers.

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In the given parallelogram and considering the information in the figure, we have:

i. m<MJL = 62^o

ii. <M = 67^o

iii. x = 3

A parallelogram is a figure which has a pair of its two opposite sides to be equal and parallel. It has some differentiating properties.

Considering the parallelogram and the information given in the figure, we have;

i. m<JLM + m<LMJ + m<MJL = 180^o

   51^o + 67^o + m<MJL = 180^o

              118 + m<MJL  = 180

  m<MJL = 180 - 118

                = 62^o

m<MJL = 62^o

ii. <M = 67^o    (opposite angles of a parallelogram are congruent)

iii. 4x = 12    (opposite sides of a parallelogram are equal)

     x = 12/ 4

        = 3

     x = 3

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The parallelogram have the values for:

angles m∠MJL = 62°, m∠M = 67° and x = 3

Considering the triangle JKL,

m∠JLK + 67° + 51° = 180° {sum of interior angles of a triangle}

m∠JKL = 180° - 118°

m∠JKL = 62°

m∠JKL and m∠MJL are alternate angles and are equal so;

m∠MJL = 62°

m∠KJM = m∠MJL + m∠KJL

m∠KJM = 62° + 51°

m∠KJM = 113°

m∠M and m∠KJM are adjacent angles so;

m∠M + 113° = 180°

m∠M = 180° - 113° {subtract 113° from both sides}

m∠M = 67°

side KJ is equal to LM, so;

4x = 12

x = 12/4 {divide through by 4}

x = 3

Therefore, the parallelogram have angles m∠MJL and m∠M to be 62° and 67° respectively, and the value of x is equal to 3.

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Bar charts or Column charts are best for data comparison. They are easy to read and widely used.

What is graph ?

A graph is a visual representation of data or information, often used to display and compare numerical values. Graphs are used to display data in a way that is easy to understand and interpret. They can be used to show trends, patterns, and relationships between different sets of data.

Bar charts or Column charts are the best types of graph to make comparisons of data. They are particularly useful when you want to compare the values of different categories or groups of data. A bar chart or column chart can be used to compare the values of multiple items within a single dataset, or to compare the values of different datasets. They are also easy to read and understand and they are widely used across different fields such as business, economics, social sciences, and statistics.

Bar charts or Column charts are best for data comparison. They are easy to read and widely used.

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Answer:

To predict when the brothers will have the same amount in their college accounts, we can set up an equation using the information given. Let x be the number of months from April.

We know that:

Nico's account balance = $2,000 + $50x

Noah's account balance = $1,600 + $100x

We want to find when the two balances are equal, so we can set the two equations equal to each other:

$2,000 + $50x = $1,600 + $100x

Now we can solve for x. Subtracting $1,600 from both sides gives:

$400 = $50x + $100x

Now we can combine like terms:

$400 = $150x

Finally, we can solve for x by dividing both sides by 150:

x = 2.67

This means that the brothers will have the same amount in their college accounts after 2.67 months or 2 months and 2 weeks.