What is the area of the parallelogram?
(-6.6)
(-9,-3)*
(-5-3)
(-2,6)

The formula for the sum of cubes of the first n natural numbers is:

(1³+2³+3³+ ... + n³) = (1 + 2 + 3 + ... + n)²

Let us consider:

A(n)=1³+2³+⋯+n³--------(1)

B(n)=(1+2+⋯+n)²---------(2)

Now plug the numbers in the above equations(1)&(2) then,we get:

A(1)=B(1)=1

A(2)=B(2)=9

A(3)=B(3)=36

A(4)=B(4)=100

A(5)=B(5)=225

So both A and B are polynomials of degree at most 4 on n, and they coincide at 5 points.

Hence A(n) = B(n) for all n.

In general, p(n) is a polynomial of degree d on n,

∑kn=1 P(k)

is defined as a polynomial of the degree of d+1 on n. This trick will help solve every single issue involving the summation of polynomials, and then find the value on d+2 points, and we will determine the sum for all n.

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The factor of 1 - 2.25x⁸ is (1 + 1.5x⁴) (1 - 1.5x⁴).

The correct option is C.

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.

Given:

An expression,

1 - 2.25x⁸.

Simplifying to the factored form.

1² - (1.5x⁴)²

= (1 + 1.5x⁴) (1 - 1.5x⁴)

Therefore, (1 + 1.5x⁴) (1 - 1.5x⁴) is the factored form.

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Answer: 4.8

Step-by-step explanation:

6.4 - 1.6 = 4.8

The system of equations is solved by graphing as shown in the image, where the solution is (1, 2).

A system of equations can be solved by graphing each line that represents each equation, then find the point where they both intercept.

Thus, the coordinates of the point where the two linear equations intercept will be the solution of the system of equations.

Given the system, 9x - 7y = -5 is the red line while -3x + 7y = 11 represents the blue line. Both intercept at (1, 2), which is the solution of the equations.

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Answer:

7cm²

Step-by-step explanation:

volume of a triangular prism=1/2×b×h×l

1/2×b×h=cross sectional area

84cm³=C.A×12

C.A=84/12

base area=7cm²

After resolving [tex](c+3)^{2}[/tex] , c = -3, and the approach is an example of the distributive property of equations.

Its simplest form has been thought to be the figure is probably smallest equivalent fraction. How or when to determine the basic form. Look for shared factors throughout the denominator and numerator. A fractional number can sometimes be checked to discover if it is a power of 2. A statement having two equal sides and an equal sign in the middle is referred to as a mathematical equation. Every variable's degree courses are listed in descending order as in general form of any equation. The formula for a linear equation is x + b = 0. The general form of a three separate linear equation is an x + b y + c = 0. (or something similar). Either conditioned equations or identities are categories for mathematics. An identity holds true for whatever value of the variables.

Given,

[tex](c+3)^{2}[/tex]

= by using formulas of [tex](a+b)^{2}[/tex]

by distributive property

[tex]c^{2}[/tex] + [tex]3^{2}[/tex] + 6c

= [tex]c^{2}[/tex] + 9 + 6c

= [tex]c^{2}[/tex] + 6c + 9 = 0

[tex]c^{2}[/tex] + 3c + 3c + 9 = 0

= c ( c + 3 ) + 3 ( c + 3)

= (c + 3 )(c+ 3)

c = - 3

After resolving [tex](c+3)^{2}[/tex], c = -3, and the approach is an example of the distributive property of equations.

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Answer:

B. 60

Step-by-step explanation:

Since the digits 1, 1, 1, 2, 2, 3 are repeated, we use the concept of permutations with repetition. In this case, we can choose the first digit to be any one of the three, the second digit to be any one of the three, and so on. Therefore, the total number of distinct 6-digit numbers that can be made is 3 × 3 × 3 × 3 × 3 × 3 = 729.

However, we need to exclude the numbers that start with a 0 (i.e., numbers like 011112 or 001122). Therefore, the final answer is 729 - 3 = 726, which is the number of 6-digit numbers that do not start with a 0. The number of 6-digit numbers that start with a 0 is 3 (111120, 111202, 112102), so the total number of distinct 6-digit numbers is 726 - 3 = 60.

Answer:

[tex]6 {}^{3x} [/tex]

Step-by-step explanation:

Given expression to us is ,

2^{-x} . 3^{-x} . 6^{2x} . 3^{2x} . 2^{2x}

We can rewrite it as ,

[2^{-x} . 2^{2x} ] [ 3^{-x} . 3^{2x}] . 6^{2x}

we know a^m . a^n = a^{m+n} , so ;

2^{-x +2x} . 3^{-x+2x} . 6^2x

simplify,

2^x . 3^x . 6^{2x}

we know a^m . b^m = (ab)^m , so ;

(2*3)^x . 6^{2x}

6^x . 6^2x

6^{x+2x}

6^{3x}

And we are done!

Answer:

[tex]6^{3x}[/tex]

Step-by-step explanation:

Given exponential expression:

[tex]2^{-x} \cdot 3^{-x} \cdot 6^{2x} \cdot 3^{2x} \cdot 2^{2x}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:[/tex]

[tex](2\cdot 3)^{-x} \cdot 6^{2x} \cdot (3 \cdot 2)^{2x}[/tex]

Multiply the numbers:

[tex]6^{-x} \cdot 6^{2x} \cdot 6^{2x}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]6^{(-x+2x+2x)}[/tex]

Therefore:

[tex]6^{3x}[/tex]

Answer:

the inequality y ≥ 0.8x + 1.5 accurately describes the relation between the duration of the hike (x) and the amount of water needed (y). This inequality means that for any duration of the hike (x), the amount of water needed (y) must be greater than or equal to 0.8x + 1.5.

Answer:

Step-by-step explanation:

3 liters of water for 4 hours of hiking.

A group of students and adults are going to the museum and have spent a total of $115 on tickets. Adult tickets cost $5 each and student tickets cost $3 each. There are 25 more students than adults in the group therefore the number of students are in the group are 35 and the number of adults in the group are 5.

This is referred to as the value of money that has been used up to produce something or deliver a service.

Since we were told that  Adult tickets cost $5 each and student tickets cost $3 then  $5 × 5 = $25 and $3 × 30 = $90. Therefore the total is $115.

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Answer: $14.22

Step-by-step explanation: 237*0.06

The simplified expression for this problem is given as follows:

[tex]43\sqrt{5} - 6[/tex]

The expression for this problem is defined as follows:

[tex]30\sqrt{5} + 13\sqrt{5} - 6[/tex]

To simplify the expression, we combine the like terms, which are the terms that have the same rational, thus:

[tex]30\sqrt{5} + 13\sqrt{5} = 43\sqrt{5}[/tex]

Combining along with the subtraction by 6, the complete simplified expression is given as follows:

[tex]43\sqrt{5} - 6[/tex]

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Answer: (x, y) = (5/4, 2).

The given system of equations is:

4x - y = 3

3x + y = 4

We can solve for x and y using either substitution or elimination method.

By substitution, we can solve for y in one of the equations and substitute that value into the other equation to solve for x.

Starting with 4x - y = 3, we can add y to both sides to isolate x:

4x = 3 + y

Then, we can substitute this expression for y into the second equation:

3x + (3 + y) = 4

Expanding the right side, we get:

3x + 3 + y = 4

3x + 3 = 4 - y

3x = 1 - y

x = (1 - y)/3

Now, we can substitute the expression for x into the first equation:

4((1 - y)/3) - y = 3

4(1 - y)/3 = 3 + y

4 - 4y/3 = 3 + y

1 - 4y/3 = y + 3

-3y/3 = -2

y = 2

Finally, we can substitute the value of y into one of the original equations to find x:

4x - 2 = 3

4x = 5

x = 5/4

So, the solution to the system of equations is (x, y) = (5/4, 2).

Answer:

300 cm^2

Step-by-step explanation:

An area of a triangle is b*h/2.

Therefore, plug in the base and height into the equation.

24cm * 25cm / 2 = area

600cm^2 / 2 = area

300cm^2 = area

The value of 2:3 can be written as a fraction: 2/3.

What is the ratio?

In mathematics, a ratio is a comparison of two quantities, often expressed as a fraction or using the colon (:) symbol. Ratios are used to indicate the relative size or amount of two or more things.

For example, the ratio of the length of a rectangle to its width can be expressed as a fraction, where the numerator represents the length and the denominator represents the width.

The ratio of hydrogen atoms to nitrogen atoms is 2:3.

This means that for every 2 hydrogen atoms, there are 3 nitrogen atoms in the container. The value of the ratio 2:3 is a way of expressing the relative quantity of hydrogen atoms to nitrogen atoms in a simplified form. It can also be written as a fraction: 2/3.

Hence, the value of 2:3 can be written as a fraction: 2/3.

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The required events E and H are not mutually exclusive, because they can both occur at the same time.So  D - No, because P(E∩H) = 0.20 is correct.

The events E and H are not mutually exclusive, because they can both occur at the same time. In other words, a student can have both brown eyes and brown hair.

The probability that a student has both brown eyes and brown hair, P(E∩H), can be found using the formula:

P(E∩H) = P(E) + P(H) - P(E or H)

where P(E) is the probability of having brown eyes, P(H) is the probability of having brown hair, and P(E or H) is the probability of having either brown eyes or brown hair.

Given that:

P(E) = 0.35

P(H) = 0.45

P(E or H) = 0.60

So,

P(E∩H) = 0.35 + 0.45 - 0.60 = 0.20

So, the answer is D - No, because P(E∩H) = 0.20.

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This means that the average sale price for a home in this sample was "$773" and that half the sales were for less than the median price of "$577", while half were more than the median price of "$577".

(a) To calculate the sample mean, we add up all the values and divide by the number of values:

x = (592 + 817 + 577 + 608 + 353 + 1,281 + 412 + 535 + 550 + 679)/10 = 7,727/10 = $773

The sample median is the middle value when all the values are ordered from smallest to largest:

353, 412, 535, 550, 577, 608, 592, 679, 817, 1,281

The median is 577.

This means that the average sale price for a home in this sample was $773 and that half the sales were for less than the median price of $577, while half were more than the median price of $577.

(b) If the 6th observation had been 985 rather than 1,281, the new mean would be calculated as:

x = (592 + 817 + 577 + 608 + 353 + 985 + 412 + 535 + 550 + 679)/10 = 7,610/10 = $761

The new median would still be $577.

(c) To calculate a 20% trimmed mean, we first need to find the two smallest and two largest observations, then remove them and take the average of the remaining values:

Two smallest: 353, 412

Two largest: 1,281, 817

Remaining values: 535, 550, 577, 608, 592, 679

The trimmed mean is (535 + 550 + 577 + 608 + 592 + 679)/6 = $592

(d) To calculate a 15% trimmed mean, we first need to find the three smallest and three largest observations, then remove them and take the average of the remaining values:

Three smallest: 353, 412, 535

Three largest: 817, 1,281, 679

Remaining values: 550, 577, 608, 592

The trimmed mean is (550 + 577 + 608 + 592)/4 = $576.

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Number of acres more there at Navajo Monument than at George Washington Carver Monument is 120.

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.

Given;

The area of navajo monument= 360acres

The area of George Washington Carver Monument = 240 acres

Now

More area navajo monument has =area of navajo monument -  area of George Washington Carver Monument

=360-240

=120

Therefore, the extra area navajo monument has is 120 acres.

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ac is congruent to pr because those sides correspond

l=7m

Step-by-step explanation:

here us the answer of the solution

The value of x in the given paralellogram is 12.

What is parallelogram?

"It is a quadrilateral with parallel opposite sides."

"The opposite angles of parallelogram are equal. "

For given question,

Two of the angles in a parallelogram measure 8x° and 7x°

The measure of an angle opposite to 8x° is also 8x°

In a similar manner, an angle opposite to 7x° is measured as 7x°.

So, we have the four angles of parallelogram as 8x°, 7x°, 8x°, 7x°

We are know that the total angle of a quadrilateral is 360°.

⇒ 8x° + 7x° + 8x° + 7x° = 360°

⇒ (5 + 7 + 5 + 7) x = 360

⇒ 30x = 360

⇒ x = 12

Therefore, the value of x is 15.

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Answer:

If we subtract 14 from both sides of the equation for RU, we get 6p = RU - 14, or 6p = RU - 14. We can then substitute this expression for 6p into the equation for ST to get:

ST = p + 31

ST = (RU - 14) + 31

Expanding RU, we get:

ST = RU - 14 + 31

ST = RU + 17

Since RU = 6p + 14, we can substitute this expression into the above equation to solve for p:

ST = 6p + 14 + 17

ST = 6p + 31

Finally, we can subtract 31 from both sides of the equation to find p:

ST - 31 = 6p + 31 - 31

ST - 31 = 6p

ST - 31 = 6p

p = (ST - 31) / 6

So, to find the value of p, we need to know the value of ST.

Answer:y=5/3 x-5

Step-by-step explanation: first find the y-intercept, when the x value is 0 that is the y intercept, then the equation becomes -3x=15, there you get

x=-5, then do the same to the other to get the x value so you get the points (0,-5), and (3,0) there you find the slope and plug in

]Answer:

The area of a rectangle is calculated by multiplying its length by its width. If the length of the rectangle is 7 and its width is 4x, the area can be found by performing 7 * 4x. The answer would be 28x square units, where x represents the unit of measurement.

Maryann needs to run 2 more laps to run on Sunday .

Lap can be referred as One complete trip around a race track οr from one end of a swimming pool to the other: Fοr example, Each lap of the track is 400 meters.

Given:

Maryann runs : 3/4-mile track

She runs  on Saturday: 8 1/2 laps = 17/2

Total miles to cover = 10 1/2 = 21/2

more laps does Maryann need to run on Sunday

= Total miles to cover - She runs  on Saturday

= 21/2 - 17/2

= 4/2

= 2

Hence , Maryann needs to run 2 more laps to run on Sunday .

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Answer:

C (51)

Explanation

The likelihood that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.

The probability that an event will happen or a claim will be correct is measured by statistical mechanics, a branch of mathematics. The possibility of an occurrence is a positive integer and 1, where about 0 represents how likely the event is to occur and value of 1 indicates certainty. A probability is a numerical illustration of the possibility that a specific activity will take place. Probabilities can also be expressed using percentages extending from 0% to 100% or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrences in a comprehensive set of equally likely choices that lead to a specific occurrence.

given

This is Z's pvalue for X = 98. So

Z = 98 -100 / 15

Z = -0.133

Z = -0.133 pvalue of 0.4470

The likelihood that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.

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Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. If a line is parallel to another line, it means they have the same slope. To find the slope of the line 7x - y = 3, we can rearrange it into slope-intercept form: y = 7x - 3. So, the slope of the line 7x - y = 3 is 7.

Since the line we want to find is parallel to 7x - y = 3 and has a slope of 7, the equation of the line can be written as y = 7x + b, where b is the y-intercept. To find b, we use the point (6, 3) as a solution:

y = 7x + b

3 = 7 * 6 + b

3 = 42 + b

b = -39

So, the equation of the line that passes through (6, 3) and is parallel to 7x - y = 3 is y = 7x - 39.

The eigenvalues of a matrix are roots of its characteristic polynomial using this we prove  that a square matrix and its transpose have the same characteristic polynomial.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.

Recall that the eigenvalues of a matrix are roots of its characteristic polynomial.

Hence if the matrices A and A Transpose have the same characteristic polynomial, then they have the same eigenvalues.

So we show that the characteristic polynomial pA(t)=det(A−tI) of A is the same as the characteristic polynomial p[tex]A^T[/tex] (t)=det(A ^T−tI)of the transpose [tex]A^T[/tex].

We have,

p[tex]A^T[/tex](t)=det([tex]A^T[/tex] −tI) =det([tex]A^T[/tex] −tI T )

=det((A−tI) [tex]A^T[/tex] )

=det(A−tI)

=pA(t)

Since I ^T =I

Since det([tex]B^T[/tex] )=det(B)for any square matrix B

Therefore, we obtain p[tex]A^T[/tex] (t)=pA(t), we conclude that the eigenvalues of A and [tex]A^T[/tex] are the same.

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