Write the arithmetic series 3+9+15+21+27 using summation notation

Answer:

y = 5x - 6

Step-by-step explanation:

1. In a linear equation, it is represented by y = mx + b

2. A line parallel to another has the same slope (m) but a different y-intercept (b)

3. So we know that it is y = 5x as the first half. However, we need to find the new y-intercept.

4. Let's plug in the point we know into the equation, and see what amount we are missing (the y-intercept)

5. y = 5(3)

6. y = 15, however, we know that y = 9. That's a difference of -6.

This shows us that the y-intercept is -6 making the full equation:

y = 5x - 6

We can check by putting the point back into the equation:

y = 5(3) - 6

y = 15 - 6

y = 9

This correlates with the original point, we have solved the equation.

The equations that can be used are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0

The given parameters are:

Length = y

Width = y - 5

Area = 750

The area of a rectangle is:

Area = Length * Width

So, we have:

y * (y - 5) = 750

Expand

y^2 - 5y = 750

Rewrite as:

y^2 - 5y - 750 = 0

Factorize

(y + 25)(y – 30) = 0

Hence, the equations that can be used are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0

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Complete question

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room?

It is a true statement that  it  is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.

A cubic equation is one in which the highest power of the variable present is 3. A quartic equation is one in which the highest power is 4. When we have a cubic or a quartic equation, the usual approach is to reduce the equation to a quadratic equation and solve by factorization.

Thus, it  is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.

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The absolve value function that models the ditch's vertical depth below ground level, is B. f(x) = -|x − 5| − 5

From the information given, it was stated that the ditch will be 5 feet deep at its lowest point. Also, x is the horizontal distance from the left edge of the ditch.

Now, the absolve value function that models the ditch's vertical depth below ground level will start with a (-) sign since it's below ground level. The appropriate function will be f(x) = = -|x − 5| − 5

In conclusion, the correct option is B.

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Step-by-step explanation:

ratio of ifran and Asim= I:A

2:3

rule of equation= TOTAL ratio=total amount

=(addition of the two ratios which are 2 and 3=5) and 1000

=5=1000

ratio of ifran(2)=? cross multiplication

=2×1000÷5

=400

=5=1000

ratio of Asim(3)=? cross multiplication

=3×1000÷5

=600

Answer:

Step-by-step explanation:

Irfan and Asim's ratio is 2:3, which means Irfan gets 2 parts while Asim gets 3. There are 5 parts in total, and this equals 10000. Let parts be p. [tex]5p=10000\\\\p=2000[/tex]

This means Irfan gets 2p = 4000 and Asim gets 3p = 6000.

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Using the binomial distribution, it is found that P(X = 2) = 0.0032.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

n = 15, x = 2, p = 0.5.

Hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{15,2}.(0.5)^{2}.(0.5)^{13} = 0.0032[/tex]

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Answer:

x = -4, 1

Step-by-step explanation:

Since we have a absolute value function here, we can tell there is goning to be multiple values.

First we will find x with the original function since we know |5| = 5.

Given f(x) = 5 = -2x-3,

[tex]2x-3 = 5 \\

-2x-3+3 = 5 + 3 \\

-2x = 8 \\

x = \frac{8}{ - 2} \\ = - 4[/tex]

Now we also know that |-5| = 5 as well (absolute value)

Given |-2x-3| = |-5|,

[tex] - 2x - 3 = - 5 \\ - 2x - 3 + 3 = - 5 + 3\\ - 2x = - 2 \\ x = \frac{ - 2}{ - 2} \\ = 1[/tex]

You can verifiy these 2 values by substituting them into the equation.

f(-4) = |-2(-4)-3|

= |8-3|

= |5|

= 5

f(1) = |-2(1)-3|

= |-2-3|

= |-5|

= 5

A modulus function is defined as a function that gives positive value for either a negative or positive argument. The values of x for given condition are -4 and 1.

A function in the form of f(x) = |x| is known as a modulus function. The graph of a modulus function is symmetric about y-axis.

The function is given as,

f(x) = |-2x-3|

which implies that f(x) = -2x - 3 for x > 0 and  f(x) = -(-2x - 3 )for x < 0

As per the question ,

Substitute the value of f(x) = 5, for both the cases to get the value of x as,

-2x - 3 = 5  and -(-2x - 3 ) = 5

=> x = -4 and x = 1.

Hence, the values of x obtained for the given condition are x =-4 and x = 1.

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Answer:

D. 4/7 = 24/28

Step-by-step explanation:

In any proportion, the value of the numerator and denominator does not change if is multiplied by the same value.  

We know that 4*6 = 24, so the numerator holds true.  However, 7*6 is 42.  In the same vein, 7*4 is 28, so the denominator would hold true.  However, 4*4 is 16.  Thus, the proportion has not been multiplied by the same value.  

In order to get 24/28 from 4/7, you would have to multiply by 6/4, which is not the same value.

Answer:

[tex]1.7x10^{4}[/tex]

Step-by-step explanation:

To divide the scientific notation, divide 5.1 to 3 then subtract the exponents of your ten - following the quotient rule.

5.1/3 = 1.7, then 9-5 = 4

final answer is [tex]1.7x10^{4}[/tex]

The total cost of the fencing is a function of the length of a side x (feet) is  10x + 14y.

The perimeter is made by adding the south, north, east, and west side.

Given that

The cost of fencing for the east and west sides is $7 per foot, and the cost of fencing for the north and south sides is only $5 per foot.

We have to find total cost of the fencing is a function of the length of a side x (feet).

The east and west fencing cost is $7/ft but the south and north fencing cost is $5/ft.

x = north and south fencing

y = the east and west sides, then you can get this equation.

Total cost= (south +north) × 5 + (east+ west) × 7

Total cost =(x + x) × 5 + (y+ y) × 7

Total cost = 5(2x) + 7(2y)

Total cost = 10x + 14y

Hence, the total cost of the fencing is a function of the length of a side x (feet) is 10x + 14y.

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The angle of X is 108°

Given,

XW ≅ YZ

∠Z = 72°

then ∠X = ?

Properties of trapezoid are:

We know that from the figure that ∠Z = ∠V & ∠W = ∠U

∵ Isosceles trapezoid rule

And sum of all the angles in a trapezoid = 360°

Now, 2 × 72 = 144

∴ 360 ₋ 144 = 216°

Now sum of other two angles = 216°

                              one angle = 216/2

                                               = 108°

Therefore the angle of ∠X is 108°

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The amount spent on promotion by the store on monthly sales of $86,600, when they are spending 14 percent on promotion is $12,124.

The percent signifies the hundredth part of the whole.

When informed that the promotion is 14 percent of the monthly sales of $86,600.

Therefore, to calculate the total amount spent on promotion, we calculate 14 percent of 86600.

Therefore, the total amount on promotion = 14% of $86,600 = $ (14/100 * 86,000) = $ (14*866) = $12,124.

Therefore, the amount spent on promotion by the store on monthly sales of $86,600, when they are spending 14 percent on promotion is $12,124.

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Answer:

[tex]\sf C. \quad \dfrac{1}{9}[/tex]

Step-by-step explanation:

Addition Law for Probability

[tex]\sf P(A \cup B)=P(A)+P(B)-P(A \cap B)[/tex]

Given:

  [tex]\sf P(A)=\dfrac{1}{3}=\dfrac{3}{9}[/tex]

  [tex]\sf P(B)=\dfrac{2}{9}[/tex]

  [tex]\sf P(A \cup B)=\dfrac{4}{9}[/tex]

Substitute the given values into the formula and solve for P(A ∩ B):

[tex]\implies \sf P(A \cup B) = P(A)+P(B)-P(A \cap B)[/tex]

[tex]\implies \sf \dfrac{4}{9} = \sf \dfrac{3}{9}+\dfrac{2}{9}-P(A \cap B)[/tex]

[tex]\implies \sf P(A \cap B) = \sf \dfrac{3}{9}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]

[tex]\implies \sf P(A \cap B) = \sf \dfrac{3+2-4}{9}[/tex]

[tex]\implies \sf P(A \cap B) = \sf \dfrac{1}{9}[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=P(A)+P(B)-P(A\cup B)[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{3}+\dfrac{2}{9}-\dfrac{4}{9}[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{3+2-4}{9}[/tex]

[tex]\\ \rm\leadsto P(A\cap B)=\dfrac{1}{9}[/tex]

The estimated total of 674, 692, 724, and 739 is: 2800.

To find the sum using clustering estimation technique first step is to round each number to the nearest 10s.

674 into 670

692 into 690

724 into 720

739 into 740

Second step is to add

Addition=670+690+720+740

Addition=2820

2820 to the nearest 100s is 2800.

Therefore the estimated total of 674, 692, 724, and 739 is: 2800.

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[tex]\sqrt[5]{3125e^{\frac{11\pi}{2}i}}\\=\\\sqrt[5]{3125}\sqrt[5]{e^{\frac{11\pi}{2}}i}\\\\=5e^{\frac{11\pi}{10}i}\\\\\boxed{5\left(\cos \left(\frac{11\pi}{10} \right)+i \sin \left(\frac{11\pi}{10} \right) \right)}[/tex]

The solutions to the equation on the given interval are;

x = π/4, 3π/4, 5π/4, 7π/4.

Given that;

4(sin x)² - 2 = 0

Add 2 to both sides and divide both sides 4

4(sin x)² - 2 + 2  = 0 + 2

4(sin x)²  = 2

(4(sin x)²)/4  = 2/4

(sin x)²  = 1/2

Square both sides

√((sin x)²)  = ±√(1/2)

sin x = ±√(1/2)

sin x = ±(√2)/2

Next, we solve for x

Not that 180° = π

x = sin⁻¹ ( (√2)/2 ) = 45° = 180°/4 = π/4

x = π/4

Since the sine function is positive in the first and second quadrant, we subtract the reference angle from π to find the solution in the second quadrant.

x = π - π/4

x = 3π/4

Now, we find the period of sin x

2π / |b|

We know that, the distance between a number and zero is 1

2π / 1

2π

Hence, period of sin x function is 2π, values will repeat every 2π radians in both direction.

Since sine function is negative in third and fourth quadrant,

x = 2π + π/4 + π

x = 5π/4

Now, add 2π to every negative angle to get a positive angle

x = 2π + ( - π/4 )

x = 2π×4/4 - π/4

x = ((2π × 8) - π ))/4

x = (8π - π)/4

x = 7π/4

Therefore, the solutions to the equation on the given interval are;

x = π/4, 3π/4, 5π/4, 7π/4.

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Parallel lines have the same slope, so since the slope of the given line is -74, the slope of the line we want to find is also -74.

Substituting into point-slope form,

[tex]y+2=-74(x-4)\\\\y+2=-74x+296\\\\\boxed{y=-74x+294}[/tex]

The ordinary annuity and annuity due as required in the task content are; $126,498.08 and $135, 431.43 respectively.

a) The amount which would be in the account in 25 years can be evaluated by means of the annuity factor obtained from the table under column 7% and row 25 years and hence, the value in 25 years would be; $2,000 × 63.24904

= $126,498.08.

b) For the annuity due case; the future value is;

= (1+0.07) × $2000((1+0.07)^(25) - 1)/0.07

= (1.07) × $2000(5.43-1)/0.07

= $135, 431.43.

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The odd functions are f(x)=x⁵-3x³+2x and f(x)=1÷x.

Given functions are f(x)=x³-x², f(x)=x⁵-3x³+2x, f(x)=4x+9 and f(x)=1÷x.

A function is said to be odd function if and only if: f(-x) = -f(x)

For every value of x in its domain.

1. f(x)=x³-x²

Substituting -x in this, we get

f(-x)=(-x)³-(-x)²

f(-x)=-x³-x²

From above we see that

f(-x)≠-f(x)

So, this function is not odd.

2. f(x)=x⁵-3x³+2x

Substituting -x in this, we get

f(-x)=(-x)⁵-3(-x)³+2(-x)

f(-x)=-x⁵+3x³-2x

f(-x)=-(x⁵-3x³+2x)

From above we see that

f(-x)=-f(x)

So, this function is odd

3. f(x)=4x+9

Substituting -x in this, we get

f(-x)=4(-x)+9

f(-x)=-4x+9

From above we see that

f(-x)≠-f(x)

So, this function is not odd.

4. f(x)=1÷x

Substituting -x in this, we get

f(-x)=1÷(-x)

f(-x)=-(1÷x)

From above we see that

f(-x)=-f(x)

So, this function is odd.

Hence, the function f(x)=f(x)=x³-x² is not odd, f(x)=x⁵-3x³+2x is odd, f(x)=4x+9 is not odd and f(x)=1÷x is odd.

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Answer:

B.) f(x)=x5-3x3+2x is odd

D.) f (x) = 1/ x is odd

Step-by-step explanation:

just did it on edg

Keiko have $31 in her wallet.

David have $25 in his wallet.

Tony have $50 in his wallet.

Keiko

Let x = the amount in Keiko’s wallet.

David

David has $6 less than Keiko .

x - 6

Tony

Tony has has two times what David has.

2(x - 6)

The total sum of their money = 106

Keiko

x + x - 6 + 2(x - 6) = 106

2x - 6 + 2x - 12 = 106

4x - 18 = 106

4x = 106 + 18

4x /4 = 124/4

x = 31

Therefore Keiko have $31 in her wallet.

David

x - 6

31 - 6 = 25

Therefore David have $25 in his wallet.

Tony

2(x - 6)

2(31 - 6)

2(25) = 50

Therefore Tony have $50 in his wallet.

To check your work out

31 + 25 + 50 = 106

The first expression is Contingency.

The second expression is Tautology.

The third expression is Contingency.

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra.

A sentence is called a contingency if its truth table contains at least one 'T' and at least one 'F. '

A statement is called a contradiction if the final column in its truth table contains only 0's.

A tautology is a statement that is always true.

The first expression is Contingency.

The second expression is Tautology.

The third expression is Contingency.

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Observe that the [tex]n[/tex]-th term in the sum is

[tex]\dfrac{n^2 + n(n+1) + (n+1)^2}{n^3(n+1)^3} = \dfrac{3n^2 + 3n + 1}{n^3 (n+1)^3} \\\\ ~~~~~~~~ = \dfrac{(n+1)^3 - n^3}{n^3(n+1)^3} \\\\ ~~~~~~~~ = \dfrac1{n^3} - \dfrac1{(n+1)^3}[/tex]

Then the sum telescopes, and we have

[tex]\displaystyle \sum_{n=1}^{9} \frac{n^2 + n(n+1) + (n+1)^2}{n^3 (n+1)^3} = \sum_{n=1}^{9} \left(\frac1{n^3} - \frac1{(n+1)^3}\right) \\\\ ~~~~~~~~ = \left(\frac1{1^3} - \frac1{2^3}\right) + \left(\frac1{2^3} - \frac1{3^3}\right) + \cdots + \left(\frac1{8^3} - \frac1{9^3}\right) + \left(\frac1{9^3} - \frac1{10^3}\right) \\\\ ~~~~~~~~ = \frac1{1^3} - \frac1{10^3} \\\\ ~~~~~~~~ = 1 - \frac1{1000} = \boxed{\frac{999}{1000}}[/tex]

The sum of the series is 999/1000 .

A series is a sequence of expression in a certain pattern.

The series of n terms is given

[tex]\rm \frac{1^2+1*2+2^2}{1^3*2^3} + \frac{2^2+2*3+3^2}{2^3*3^3} +...+\frac{9^2+9*10*10^2}{9^3*10^3}[/tex]

nth term of the series is given by

[tex]\rm T_n = \rm \dfrac{n^2 + n(n+1)+ (n+1)^2}{n^3*(n+1)^3}[/tex]

On simplification it can be written as

[tex]\rm T_n = \rm \dfrac{3n^2 + 3n+1}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{3n(n +1)+1}{n^3*(n+1)^3}\\\\\\T_n = \rm \dfrac{ (n +1)^3 - n^3}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{ 1}{n^3} - \dfrac{1}{(n+1)^3}[/tex]

The sum of terms from 1 to 9 is given by

∑  ( [tex]\rm \frac{ 1}{n^3} - \frac{1}{(n+1)^3}[/tex])

= [tex]\rm \dfrac{1}{1^3} - \dfrac{1}{2^3} + \dfrac{1}{2^3} - \dfrac{1}{3^3}+ .......... + \dfrac{1}{9^3} - \dfrac{1}{10^3}[/tex]

= (1/1³) - (1/10³)

= 999/1000

Therefore the sum of the series given is 999/1000

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Answer:

Step-by-step explanation:

Fundamental Theorem of Arithmetic is not a method for solving a system of equations.

A system of equations is a collection of two or more equations with a same set of unknowns.

The system of equation can be solved using the following method.

The graphing involves using graph to find the intersection of the system of equation.

Substitution method involves substituting one variable to another.

Therefore, Fundamental Theorem of Arithmetic is not a method for solving a system of equations

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Answer:

$100.8

Step-by-step explanation:

Discount=20% of 120 =24

Before tax: BP=120-24=96

After Tax BP=105% of 96=$100.8

Answer:

t=5.5

Step-by-step explanation:

The ball hits the ground when h = 0.

[tex]-16t^2 + 88t = 0 \\ \\ 2t^2 - 11t =0 \\ \\ t(2t-11)=0 \\ \\ t=0, 5.5[/tex]

However, as the answer must be positive, t=5.5

Entry ticket = $7

Gift shop money = $g

Maximum to spend = $30

Inequality => 7+g ≤ 30

Hope it helps!

The value of 1000 represent the initial population of bacteria in the study and the difference of 1200 and 1000 mean difference between the initial populations in the studies.

Exponential functions are are written as y(x) = abˣ

Here

a is the initial population

b is the rate of growth or decrease

x is the time taken

The Given exponential function is

[tex]\rm b_1(t) = 1200( 1.8 )^t\\\\b_2(t) = 1000 (1.8)^t[/tex]

From the standard equation of Exponential function

(a) a = 1200 and 1000 is the initial population of the bacteria

(b)The difference of 1200 and 1000 means the difference between the initial populations in the studies

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Answer:

b³

Step-by-step explanation:

The lowest common multiple of the expression is b². This because, taking out a factor of b, b ( b² + 6b ), taking out a factor of b², b² ( b + 6 ),

taking out a factor of ( b + 6 ), ( b + 6 ) b². As a result b² is only the option which is not a factor.