what is the quotient of 3/4÷1/5​

The given sequence is geometric, with a common ratio of -5.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 2, -10, 50, -250, ....

We can observe here: [tex]\frac{-10}{2}=\frac{50}{-10}=\frac{-250}{50} = -5[/tex], hence following the condition required for a sequence to be geometric.

Hence, The given sequence is geometric, with a common ratio of -5.

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28.1 amu is the atomic weight of x.

What is atomic weight defined as?

The term "atomic weight" refers to an atom's overall weight. With the addition of a small amount from the electrons, it is roughly equal to the sum of the protons and neutrons.

What does atomic weight vs. atomic mass mean?

The atomic weight of the element will be a weighted average of the isotopes based on the relative abundance:

(27.977 x 0.9221) + (28.976 x 0.0470) + (29.974 x 0.0309

) = 25.798 + 1.362 + 0.926

= 28.08 = 28.1 amu

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The probability of spinner pointer landing on blue color region is equal to 1/3 .

As given in the question,

Total colors in the spinner is equal to 6

Each color is 2 times

Total number of colored region =6

Number of blue region = 2

Probability of pointer landing on blue color region denoted by P(B)

Probability is

= ( Total number of favourable outcomes) /  (Total number of outcomes )

⇒ P(B) = 2 / 6

⇒ P(B) = 1 /3

Therefore, the probability of spinner pointer landing on blue color region is equal to 1/3.

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The two legs of the right isosceles triangle are both [tex]\frac{11\sqrt{2} }{2}[/tex]

Since two of the angles in this triangle are 45 degrees and it has a 90 degree angle. It is a right isosceles triangle. An isosceles triangle has two sides the same, which have to be the two legs in this triangle because a triangle can not have two hypotenuses.

According to the Pythagorean Theorem:

[tex]a^{2}+b^{2} =c^{2}[/tex]

where a and b are the legs and c is the hypotenuse.

Since two legs in this right triangle are the same , the formula can be altered to be:

[tex]a^{2}+a^{2} =c^{2}[/tex]

[tex]2a^{2} =c^{2}[/tex]

Putting the value of c is 11

[tex]2a^{2} =11^{2}\\ \\ 2a^{2} = 121\\ \\a^{2} = \frac{121}{2\\}\\ a =\sqrt{\frac{121}{2} }[/tex]

[tex]a =\frac{121}{\sqrt{2} }\\ \\a =\frac{11\sqrt{2} }{2}[/tex] ~ [tex]7.78[/tex]

Hence, The two legs of the right isosceles triangle are both [tex]\frac{11\sqrt{2} }{2}[/tex]

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Using proportions, it is found that Chris made the most money in the week.

The rates for Michelle's works are missing, as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Chris's salary is given by the sum of the base plus commissions, hence:

C = 250 + 0.015 x 1500 = $272.5.

Michelle's salary is given as follows, considering she is paid double the hourly rate for the holiday:

M = 12 x 2 x 6.50 + 10 x 5 = $206.

Alex salary's is found as follows, considering the rate and the hour and a half for the weekend:

A = 5 x 1.5 x 7 + 7 x (6 + 5.75 + 4.5 + 6.75 + 5.5) = $252.

Hence Chris made the most money in the week.

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Answer: $110

Step-by-step explanation: 50+10*6=50+60=110

Computing the sum of the first term in the arithmetic series is relatively straightforward. Just add these values ​​together. However, adding, say, the first 100 words creates more problems. Instead of manually summing all these terms, mathematicians devised an arithmetic progression formula that efficiently computes the sum of the arithmetic progression.

a1 =-6

S50 = -5150

an=?

Sn=n(a1+an)/2

So, to find an

((2*sn) /n)-a1=an

((2*-5150) /50) -(-6)=an

An=200

D=-194/49

Here the first term a=-6,

Common difference d=-3.96

We know that,

f(n)=a+(n-1)d

f(50)=-6+(50-1)(-3.96)

=-6+(-193.99)

=-199.99

We know that,

Sn=n2[2a+(n-1)d]

∴S50=502⋅[2(-6)+(50-1)(-3.96)]

=25⋅[-12+(-193.99)]

=25⋅[-205.99]

=-5149.78

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She will share 513 candies, each students will receive 27 candies and the amount remaining is 13.

She has 526 pieces of candy that she wants to share with the 19 students in her class.

She makes sure that each classmate gets the same amount of candy.

This means each person or student gets the same or equal amount of candy.

let

x = amount of candy each student gets.

Therefore, the total amount of candy she shared is 526 pieces and the total number of students is 19.

Hence,

x =  amount of candy each student gets = 526 / 19

x =  amount of candy each student gets = 27.6842105263

x =  amount of candy each student gets = 27

Therefore, she will share 513 candies, each students will receive 27 candies and the amount remaining is 13.

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Step-by-step explanation:

so, f(x) = 3x

now, this is reflected around the x-axis.

points that were n units above the x-axis are now n units below the x-axis and vice versa.

so, the functional values start the same in their size, but their sign flips. for every point.

that means,

g(x) = -f(x) = -3x

Congruent radii are found in congruent circles. Concentric circles share a common center.

Congruent circles contain congruent radii. Concentric circles all have the same center. A central angle has a center vertex and circle endpoints.

The distances OA and OB are both equal to the radius of the circle because all points on the circle are equidistant from O. OA = OB, to put it another way.

According to the definition of line segment congruence, segments OA and OB are congruent. This is known as the "wheel theorem," because it is responsible for the operation of wheels.

Because all points on a circle are the same distance from the center, and circle radii have one endpoint on the circle and one at the center, all circle radii are congruent by definition. Every circle has an outer diameter.

Congruent circles contain congruent radii (the plural of radius). Concentric circles all have the same center.

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Answer:

102.9 m

Step-by-step explanation:

The shortest distance from A to C would be diagonally from A to C.

This comprises:

The length of the diagonal between A and C can be calculated using Pythagoras Theorem:

[tex]\begin{aligned}c^2&=a^2+b^2\\\implies \sf AC^2 & = \sf AB^2+AD^2\\\sf AC^2 & = \sf 50^2+80^2\\\sf AC^2 & = \sf 2500+6400^2\\\sf AC^2 & = \sf 8900\\\sf AC & = \sqrt{\sf 8900}\\\sf AC & = \sf 94.33981132\;m\end{aligned}[/tex]

Subtract the diameter of the circular path from this to calculate the sum of the lengths of the straight paths.

[tex]\implies \sf 94.33981132-15=79.33981132\;m[/tex]

To calculate the length of the circular part of the path, find half the circumference of the central circle:

[tex]\begin{aligned}\implies \textsf{Half the circumference} & = \sf \dfrac{1}{2} \pi d\\& =\sf \dfrac{1}{2} \pi (15)\\& =\sf 23.5619449\;m\end{aligned}[/tex]

Therefore, the shortest distance from A to C across the park is:

[tex]\begin{aligned} \implies \textsf{Shortest distance} & = \sf 79.33981132+23.5619449\\& = \sf 102.9017562\\& = \sf 102.9\;m\;(nearest\:tenth)\end{aligned}[/tex]

The translation is show below

What is translation in mathematics?

A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. When executing a translation, the original object is referred to as the pre-image, and the item following the translation is referred to as the image.

Let the coordinates be L (2, 5), M (4, 6), N (3, 7)

Follow the translation rule as (x-2, y+4), which shifts the triangle LMN to L'M'N' as L' (0, 9), M' (2, 10), N' (1, 11).

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The given pattern forms an Arithmetic progression.

Complete pattern is 144,132,120,108,96,84,72,....

As the given series is in A.P.

⇒ a5 = a + (n - 1)d

⇒ a5 = 144 + (4)d

⇒ a5 = 144 +4 (-12)

⇒ a5 = 144 - 48

⇒ a5 = 96

⇒ a6 = 144 + (6 - 1)d

a6 = 84

⇒ a7 = 144 + (7 - 1)d

a7 = 144 + 6d

a7 = 72

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Option 2, 8.3% p.a. compounded quarterly will provide the best return on the investment over a time period of 5 years.

Let's say you want to invest Rs 8000.

The formula for compound interest is given as:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where P is the principal amount, r is the interest rate, n is the number of times interest is applied, and t is the number of time periods elapsed.

For option 1,

P = 8000

r = 8.2% = 0.082

As the interest compounded annually.

n = 12

t = 5 years

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

[tex]A=8000( 1 + \frac{0.082}{12})^{12 \times 5}[/tex]

[tex]A=8000(1+0.00683)^{60}\\A = 8000(1.00683)^{60}\\A=8000 \times 1.5047\\[/tex]

A = Rs. 12037.74

For option 2,

8.3% compounded quarterly.

Quarterly means once three months.

There are four quarters in one year.

Therefore, n = 4 × 5 = 20

P = 8000

r = 8.3% = 0.083

t = 5

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

[tex]A=8000(1+\frac{0.083}{20})^{20 \times 5}\\[/tex]

[tex]A=8000(1+0.00415)^{100}\\A=8000(1.00415)^{100}\\A=8000 \times 1.51307\\[/tex]

A = Rs. 12104.566

Hence, option 2 will provide you with the best return on your investment.

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Answer: The answer should be A.

Step-by-step explanation: 1/2 x -16 = -8

By elimination, the solution of the system of equations, 2w + 5y = -24 and 3w - 5y = 14, is (w, y) = (-2 , -4).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in w and y, a variable should be eliminated by adding/subtracting the two equations.

Adding the two equations will eliminate the variable y.

2w + 5y = -24     (equation 1)

3w  - 5y = 14     (equation 2)

5w + 0y = -10

w = -2

Substitute the value of w to any of the two equations and solve for y.

2w + 5y = -24     (equation 1)

2(-2) + 5y = -24

5y = -24 + 4

5y = -20

y = -4

Hence, the solution of the system of equations is (w, y) = (-2 , -4).

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The ratio of the volume of the large cylinder to the volume of the small cylinder is 3:1.

We are given height of cylinders and the information that both the cylinders are same. So, the radius of cylinders will be same.

The formula for calculation of volume of cylinder is -

Volume = πr²h, where r is radius and h is height.

Ratio of the volume of the large cylinder to the volume of the small cylinder= πr²h(large):πr²h(small)

Ratio = πr²75:πr²25

Cancelling πr² from both numerator and denominator as it is common in both

Performing division by 25 to find the ratio

Ratio = 3:1

Hence, the ratio of the volume of the large cylinder to the volume of the small cylinder is 3:1.

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Answer:

r = 3

Step-by-step explanation:

Slope-intercept form of a linear equation:

[tex]\large\boxed{y=mx+b}[/tex]

where:

Given:

Substitute the given slope and point into the formula and solve for b:

[tex]\begin{aligned}y & = mx+b\\\implies -3 & = \dfrac{6}{5}(-2)+b\\-3 & = -\dfrac{12}{5}+b\\-3 +\dfrac{12}{5} & = b\\\implies b & = -\dfrac{3}{5}\end{aligned}[/tex]

Substitute the given slope and found value of b into the formula to create an equation for the line:

[tex]\boxed{y=\dfrac{6}{5}x-\dfrac{3}{5}}[/tex]

Substitute the point (r, 3) into the equation and solve for r:

[tex]\begin{aligned}y & = \dfrac{6}{5}x-\dfrac{3}{5}\\\implies 3 & = \dfrac{6}{5}r-\dfrac{3}{5}\\5 \cdot 3& = 5 \cdot \left(\dfrac{6}{5}r-\dfrac{3}{5}\right)\\15 & = 6r-3\\15+3&=6r-3+3\\ 18 & = 6r\\\dfrac{18}{6} & = \dfrac{6r}{6}\\3 & = r\\ \implies r & =3\end{aligned}[/tex]

Solution

Therefore, the value of r is 3.

When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.

When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0. In addition to being the length of the perpendicular that is drawn from the point to the x-axis, it is the value of y at the coordinates (x, y). It is, in other words, the vertical distance between the point and the x-axis.

An address that aids in locating a spot in two dimensions of space are the X and Y coordinates. Any point in the coordinate plane is denoted by the coordinates (x, y), where the x value represents the point's location in relation to the x-axis and the y value represents its position in relation to the y-axis.

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There are 402.28 in2 of pasta in the container.

The mathematical branch is known as algebra deals with symbols and the rules governing their manipulation. These characters, which are now expressed as Latin and Greek letters, stand for variables, or quantities without set values, in elementary mathematics.

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.

The radius of cylinder (r) = 3.2 inches

Height of cylinder (h) = 14 inches

Height of pasta = 14 – 1.4 = 12.5 inches

Pasta in container = 22/7*(3.2)2*12.5

=402.8 in2

Hence, the container carries 402.8 in2 of pasta in it.

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 The result of the evaluation of the series described by:

∑ = 3755.5

The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.

A series is the summation of a set of numbers or sequences.

The equation for this type of problem is:

∑ = n(a1 + an)/2

 Our values are:

1765,1414,1063, ........ ,-692

1765 - 351X = -692

351X = 1765 + 692

X = 7

∑ = 7(1765 - 692)/2

∑ = 3755.5

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In Δ JLP, m ∠ JMP = 3x - 6, JK = 3y - 2, and LK = 5y - 8 then the value of x = 32.

In geometry, an altitude is a line that passes through two very specific points on a triangle: a triangle's vertex, or corner, and its opposite side at a right, or 90-degree, angle. The base is the opposite side. Triangles have three vertices and three opposite sides in common.

A triangle's altitude is the perpendicular drawn from the triangle's vertex to the opposite side. The altitude, also known as the triangle's height, forms a right-angle triangle with the base.

Since JM is at an altitude of ΔJLP, m ∠ JMP = 90

3x - 6 = 90

simplifying the above equation we get

3x = 96

Dividing both sides of the equation by 3, we get

x = 32

The value of x = 32.

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Answer:

a = 3 [tex]\frac{1}{3}[/tex] or [tex]\frac{10}{3}[/tex]

Step-by-step explanation:

Since [tex]f(2)=g(2)[/tex], [tex]2a*2-6=2^2+a[/tex].

Now let's solve for [tex]a[/tex]:

Simplify: [tex]4a-6=4+a[/tex]

Add 6 to both sides: [tex]4a=4+a+6[/tex]

Simplify: [tex]4a=10+a[/tex]

Subtract a from both sides: [tex]3a=10[/tex]

Divide both sides by 3: [tex]x=\frac{10}{3}[/tex]

Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so a function's mirroring is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.

The function's reflection should be similar in size and shape to the original position.

f(x)=3x; y-axis

(consult the pictures attached below)

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Answer:

15.6

Step-by-step explanation:

Find the difference between coordinates:

(x2-x1) = (4 - -7) = 11

(y2-y1) = (3 - -8) = 11

Square the results and sum them up:

(11)2 + (11)2 = 121 + 121 = 242

Now Find the square root and that's your result:

Exact solution: √242 = 11√2

Aprox solution: 15.5563

Rounded to nearest tenth: 15.6

For the absolute value equation |2 x+1|-14=9

x = 11

Given, absolute value equation is

|2 x+1|-14=9

|2 x+1|-14 + 14 = 9+14

2x + 1 = 23

2x + 1-1 = 23-1

2x = 22

x = 11

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By elimination, the system of equations, 6x - 2y = 11 and -9x + 3y = 16, has no solutions.

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.

Multiply first equation 1 by 3 and equation 2 by -2.

6x - 2y = 11 ⇒ 18x -6y = 33     (equation 1)

-9x + 3y = 16 ⇒ 18x - 6y = -32     (equation 2)

Since the new equation of the two equations have the same coefficients, but different constants, then the two lines are in parallel.

Hence, the system of equations has no solutions.

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Answer:

The last one.

Step-by-step explanation:

2(x + 3)

= 2*x + 2*3

= 2x + 6.

Arithmetic progression AP is the given sequence of 3,7,11,15, ............ The common difference is found to be (d = 4).

The difference between two numerical orders in Arithmetic Progression (AP) is a constant value. Another name for it is Arithmetic Sequence.

Then we'd come across some key terms in AP, which are denoted as:

Some AP formulas are as follows:

Now, for the given sequence is   3,7,11,15, ...........

Let us suppose the first term is'a₁' = 3.

Let us suppose 'a₂' = 7 is the second term.

Let us suppose the third term is 'a₃' = 11.

Let us suppose the fourth term be 'a₄' = 15.

d = a₂ - a₁      

Substitute the values;

d = 7 - 3 = 4     ........(equation 1)

Now consider the other set;

d = a₃ - a₂    

d = 11 - 7 = 4      .......(equation 2)

As a result, both equations are equal. It means that the common difference is the same, which is (d = 4).

Therefore, the asserted sequence is discovered to be in AP, and the value of a common difference is discovered to be (d = 4).

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power of 3 is zero

Solution:

87499

Prime Number :

A prime number is a whole number greater than 1 whose only factors are 1 and itself. An element is a real number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Numbers that have more than two factors are called composite numbers.

Factorization:

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler things of the same kind

Factorization may also refer to more general decompositions of a mathematical object into the product of smaller or simpler objects. For example, every function may be factored into the composition of a surjective function with an injective function. Matrices possess many kinds of matrix factorizations. For example, every matrix has a unique LUP factorization as a product of a lower triangular matrix L with all diagonal entries equal to one, an upper triangular matrix U, and a permutation matrix P; this is a matrix formulation of Gaussian elimination.

Factorization of the number = 87499

= 87499

= 5147*17

=5147*7*1

power of 3 is zero

5147 is the prime number  

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