Find the common difference of the sequence shown.

1/2, 1/4 , 0, ...

Answer:

1/3(n) - 3 < 6; n < 27

Step-by-step explanation:

" 3 subtracted from one third of a number"

= 1/3(n) - 3

given that this is less than 6:

1/3(n) - 3 < 6

1/3(n) < 6 +3

1/3(n) < 9

n < 27

Inequality and solution is  1/3(n) - 3 < 6 and n < 27.

The correct option is (A).

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given statement is : " 3 subtracted from one third of a number less than 6"

or, 1/3(n) - 3 < 6

or, 1/3(n) < 6 +3

or, 1/3(n) < 9

or, n < 27

Hence, Inequality and solution is  1/3(n) - 3 < 6 and n < 27.

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Answer:

17.325 liters

Step-by-step explanation:

Given

Muriatic acid needed by one hot tub = 165 ml

Total hot tubs: 105

So, in order to find the total quantity of muriatic acid, the quantity for one tub will be multiplied by total tubs

So,

Total quantity of muriatic acid: 105 * 165

= 17325 ml

Since we have to find the answer in liters.

1 liter contains 1000 milliliters.

So,

for 17325 ml

= 17325 / 1000 = 17.325 liters

Hence, Apollo Spas needs 17.325 liters of muriatic acid for all of the hot tubs ..

Answer:

17.325 liters

Step-by-step explanation:

Number of Apollo Spas Services= 105 hot tubs

Each hot tub needs Muriatic acid= 165 ml

We have to find the total liters of muriatic  acid

Total number of liters required = Number of hots cups× 165 ml

Total number of liters required= 105×165 ml

Total number of liters required= 17,325 ml

1ml = 1/1000 liters

Total number of liters required= 17.325 liters

Hence, the correct answer is 17.325 liters

Answer:

Yes

Step-by-step explanation:

Any relation is said to be a function , if and only if

i) every element of first ordered pair is mapped with some element of second ordered pair.

ii) every element in first ordered pair is mapped to only singe element from the ordered pair.

Here in this case we see that there is some value of y for every value of x Hence first condition satisfies.

Also , none of the value of x is mapped or resulting into a two different values of y

Hence both the conditions are fulfilled , there for it is a function.

Answer:

Step-by-step explanation:

8/12+8/11 needs to be converted, so the denominator (the bottom number) is the same. To do that, you can multiply them, so 12 x 11= 132

Now since you multiplied the bottom, you need to multiply the top of each equation.

88/132+96/132=184/132 or as a decimal, 1.3939393939....

Or a faster way is to just insert into a calculator 8 divided by 12 then add 8 divided by 11.

Answer:

16/23

Step-by-step explanation:

I added 12 and 11 and then I added 8 and 8

Answer:

See below.

Step-by-step explanation:

The common ratio = -10/4 = -5/2 and the first term is 4.

The sigma notation is:

n=6

∑       4(-5/2)^n-1.   (answer).

n=1

Answer:

[tex]\sum_{n=1}^{n=6} 4(\frac{-5}{2} )^{n-1}[/tex]  

Step-by-step explanation:

We are given the geometric series [tex]4 + -10+ 25+ -62.5+ 156.25+ -390.625[/tex]

General geometric series is of the form

[tex]a, ar, ar^2, ar^3, ar^4,\text{ and so on}[/tex], where a is the first term and r is the common ration.

The common ratio for given geometric series is [tex]\frac{\text{Second Term}}{\text{First Term}}[/tex] = [tex]\frac{-10}{4} = \frac{-5}{2}[/tex]

[tex]a = 4\\r = \frac{-5}{2}[/tex]

To write the series in summation form we use:

[tex]\sum_{k=0}^{k=n} a(r)^{k}[/tex]

Thus, the given geometric series is

[tex]\sum_{n=1}^{n=6} 4(\frac{-5}{2} )^{n-1}[/tex]

Option: C is the correct answer.

The ordered pair which will be found in the graph of the inverse function is:

C.  (0,-2) , (4,-1) , (8,0) , (12,1) , (16,2)    

We are given a table of values as:

       x                f(x)

     -2                 0

     -1                  4

      0                  8

      1                   12

      2                  16

i.e. the domain of the function is: {-2,-1,0,1,2}

and range of the function is: {0,4,8,12,16}

We now that for any function f(x) and it's inverse function the x and y value get interchanged i.e. the domain of the function f(x) becomes the range of its inverse function and the range of the function f(x) becomes the domain of the inverse function.

Hence, for any function with given ordered pair the inverse function will have ordered pair with x and y-value getting swapped.

i.e. if (-2,0) is an ordered pair of f(x)

then (0,-2) will be an ordered pair in the inverse function of f(x).

Hence, similarly all the ordered pairs could be obtained.

            The answer is:

             Option: C

First add 3 to both sides (what you do on one side you must do to the other). Since 3 is being subtracted, addition (the opposite of subtraction) will cancel it out (make it zero) from the right side and bring it over to the left side.

1 > s - 3

1 + 3 > s - 3 + 3

4 > s

For the graph will you have a empty or colored in circle?

If the symbol is ≥ or ≤ then the circle will be colored in. This represents that the number the circle is on is included.

If the symbol is > or < then the circle will be empty. This represents that the number the circle is on is NOT included.

Which direction will the ray go?

If the variable is LESS then the number then the arrow will go to the left of the circle.

If the variable is MORE then the number then the arrow will go to the right of the circle.

In this case your inequality is:

4 > s OR s < 4

aka 4 is greater then s OR s is less then 4

This means that the graph will have an empty circle and the arrow will go to the left of 4. Look at image below.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

[tex](-3,\ -3)\to x=-3,\ y=-3\\\\\text{Put the values of x and y to the equations and check equality:}\\\\x-5y=-12\\-3-5(-3)=-12\\-3+15=-12\\12=-12\qquad\bold{FALSE}\\\\x-5y=12\\-3-5(-3)=12\\-3+15=12\\12=12\qquad\bold{TRUE}\\\\3x+2y=-15\\3(-3)+2(-3)=-15\\-9-6=-15\\-15=-15\qquad\bold{TRUE}[/tex]

The system of linear equations has this point as its solution will be,x-5y=12 and 3x+2y=-15. Option C is correct.

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The solution to a system of linear equations is (-3, -3).

x = -3

y= -3

After putting the value one by one in the given equations;

A)

[tex]\rm x-5y=-12\\\\\ -3-5(-3)=-12\\\\-3+15=-12\\\\12\neq-12[/tex]

B)

[tex]\rm x- 5y =12\\\\ -3-5(-3)=12\\\\-3+15=12\\\\12=12[/tex]

[tex]\rm 3x+2y=-15\\\\3(-3)+2(-3)=-15\\\\ -9-6 =-15\\\\ -15=-15[/tex]

The system of linear equations has this point as its solution will be,x-5y=12 and 3x+2y=-15.

Hence, option C is correct.

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Answer:

The system has one solution

Step-by-step explanation:

we have

[tex]y=(0.5)^{x}[/tex] ----> equation A

[tex]y=6[/tex] -----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

There is only one  point of intersection

therefore

The system has one solution

see the attached figure

Answer:

D

Step-by-step explanation:

These I's are being used as sticks

lets say i have 40 sticks then i add 55 more sticks to them

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII + IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII If i were to reverse the sequence and use the 55 sticks and add 44 sticks to them it would be the same as me having 44 sticks and adding 55 more.

By commutative property, the following which is equal to 40 + 55 is Option(D) 55 + 40.

The commutative property is a math rule that says that the order in which we find the sum of the numbers does not change the sum up value of the numbers.

By the statement,

A + B = B + A , where A and B are any numbers

The original expression given is 40 + 55 .

Therefore by commutative property, the equivalent expression is -

40 + 55 = 55 + 40

Thus, by commutative property, the following which is equal to 40 + 55 is Option(D) 55 + 40.

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Answer:

3367 calls

Step-by-step explanation:

Number of calls made more than last year = 12,376 - 9009 = 3367

Answer:

[tex]\frac{4}{15}[/tex] of the pizza has both pepperoni and onions.

Step-by-step explanation:

As we know, [tex]\frac{2}{5}[/tex] of the pizza has pepperoni and [tex]\frac{1}{3}[/tex] of it is onions.

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

= [tex]\frac{6}{15}[/tex] + [tex]\frac{5}{15}[/tex]     (because you have to find like denominators when you add)

= [tex]\frac{11}{15}[/tex]

[tex]\frac{11}{15}[/tex] of the pizza have one topping.

The whole is 1, or [tex]\frac{15}{15}[/tex]. So,

[tex]\frac{15}{15}[/tex] - [tex]\frac{11}{15}[/tex] = [tex]\frac{4}{15}[/tex].

[tex]\frac{4}{15}[/tex] of the pizza have both pepperoni and onions.

Final answer:

Two-fifths (2/5) of the pizza has just pepperoni and one-third (1/3) has just onions. Since the sum of these portions exceeds one, we find the overlap by subtracting one from the sum (11/15 - 15/15), resulting in 4/15 of the pizza having both pepperoni and onions.

Explanation:

Cindi bought a sheet pizza for a party with some sections having different toppings. To find out what fraction of the pizza has both pepperoni and onions, we'll first consider the fractions of the pizza with individual toppings. Two-fifths (2/5) of the pizza has just pepperoni and one-third (1/3) has just onions. The sum of these fractions exceeds one, indicating an overlap which must be the part with both toppings.

To calculate the overlap, we add the fractions for just pepperoni and just onions:
2/5 + 1/3 = 6/15 + 5/15 = 11/15.

Since the total cannot exceed one whole pizza, the overlap - the portion with both toppings - is the amount that the sum of individual parts exceeds one. Therefore, we subtract one from the combined fraction:
11/15 - 1 (which equals 15/15) equals -4/15. This negative value is indicative of the overlap. Therefore, 4/15 of the pizza has both pepperoni and onions.

Answer:

B) (-⁷/₂, ³/₂)

Step-by-step explanation:

Midpoint equation: ( (x₁ + x₂)/2, (y₁ + y₂)/2 ), when the two points are (x₁, y₁) and (x₂, y₂).

Plug in: ( ⁽⁻⁶ ⁺ ⁻¹⁾/₂, ⁽⁻² ⁺ ⁵⁾/₂ )

Add: (-⁷/₂, ³/₂)

Answer:

B

Step-by-step explanation:

Using the midpoint formula

given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ [tex]\frac{1}{2}[/tex](x₁ + x₂), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]

let (x₁, y₁ ) = (- 6, - 2) and (x₂, y₂ ) = (- 1, 5)

midpoint = [ [tex]\frac{1}{2}[/tex](- 6 - 1), [tex]\frac{1}{2}[/tex](- 2 + 5)]

              = (- [tex]\frac{7}{2}[/tex], [tex]\frac{3}{2}[/tex] ) → B

Answer: C

Step-by-step explanation: The table represents absolute value

For this case we must find a function of the form:

[tex]y = f (x)[/tex]that complies with the relation of the table.

We note that for the first two values of x, the function yields the same value but with a positive sign.

So:

[tex]f (x) = | x |\\y = | -2 | = 2\\y = | -1 | = 1\\y = | 0 | = 0\\y = | 1 | = 1\\y = | 2 | = 2[/tex]

Answer:

Option C

Answer:

x = 1

Step-by-step explanation:

Given

5x - (4x - 1) = 2 ← distribute the parenthesis by - 1

5x - 4x + 1 = 2

x + 1 = 2 ( subtract 1 from both sides )

x = 1

Answer: B

Step-by-step explanation:

The function results [tex]f(x) = -3(x - 1)5 + 2[/tex]  after applying a sequence of transformations [tex]f(x) = x^5[/tex].

We have to determine, which function results after applying the sequence of transformations [tex]f(x) = x^5[/tex].

According to the question,

To find the sequence of the transformation of the given function following all the steps given below.

Function; [tex]f(x) = x^5[/tex]

                   [tex]f(x) = -3[(x )^5][/tex]

                   [tex]f(x) = -3(x)^5[/tex]

                    [tex]f(x) = -3(x-1)^5[/tex]

                    [tex]f(x) = -3(x-1)^5 +2[/tex]

Hence, The function results [tex]f(x) = -3(x - 1)5 + 2[/tex]  after applying a sequence of transformations [tex]f(x) = x^5[/tex].

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Answer:

1/21.

Step-by-step explanation:

To solve the problem 'How long would they take to do the job working together?'  you would work in fractions of the job done / minute:

1/21 + 1/28 = 1/x.

So for person 1 the expression is 1/21.

Final answer:

To find the length of the ladder, use the tangent of the angle of elevation. The height of the ladder is equal to the distance from the house multiplied by the tangent of the angle of elevation.

Explanation:

To find the length of the ladder, we can use the trigonometric relationship of the angle of elevation. The tangent of the angle of elevation is equal to the opposite side (height of the ladder) divided by the adjacent side (distance of the ladder from the house).

Tan(69°) = height/12 ft

height = 12 ft x tan(69°)

Using a calculator, we can determine that the height of the ladder is approximately 31.99 ft.

Answer:

B. 24 yd^2

Step-by-step explanation:

Let A denote the area of the smaller figure:

We can determine the ratio of both lengths and areas as:

3:5 :: A:40

As the areas of figures vary directly with their lengths and widths so the proportion will be direct proportion.

Converting into fractions will give us:

3/5 = A/40

Now we have to find the value of A for the area of smaller figure.

Cross multiplication will give us:

3*40 = 5A

=> 120 = 5A

=> 120/5 = 5A/5

So,

A = 24 yd^2

So, Option B is the correct answer ..

Answer:

A. 14.4 yd2

Step-by-step explanation:

Answer:

7,680

Step-by-step explanation:

I did 12% x 5 years and got 60

Then I decreased 19,200 by 60% to get 7,680

Hope this helps!

Answer:

8,680 years old

Step-by-step explanation:

The fossil is 8,680 years old if 35% of its carbon-14 remains.

Answer:

a=1 or a=5/6

Step-by-step explanation:

I'm going to attempt to factor 6a^2-a-5

a=6

b=-1

c=-5

Find two numbers that multiply to be a*c and add to be b.

a*c=-30                                   =-6(5)

b=-1                                          =-6+5

So replace -a with -6a+5a in the expression we started with

6a^2-6a+5a-5

now we factor by grouping

6a(a-1)+5(a-1)

(a-1)(6a-5)

Now let's solve the equation:

(a-1)(6a-5)=0

So a=1 or a=5/6

Answer:

4 units

Step-by-step explanation:

We have to calculate the distance between two points first to check the correct answer.

so,

The formula for distance is:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\Here\\(x_{1},y_{1})=(3,3)\\(x_{2},y_{2})=(7,3)\\Putting\ Values\\d=\sqrt{(7-3)^{2}+(3-3)^{2}}\\d=\sqrt{(4)^{2}+(0)^{2}}\\d=\sqrt{16+0} \\d=\sqrt{16} \\Taking\ Square\ Root\ will\ give\ us:\\d=4 units\\So\ the\ distance\ between\ two\ points\ is\ 4\ units ..[/tex]

Answer:

24

Step-by-step explanation:

Varies directly means that something constant times l equals V or V=kl where k is that constant.  

Plug in point given 288=k(12) and solve the constant of proportionality by dividing both sides by 12.

k=288/12=24

The graph is attached.

To solve the problem, we need to look for the characteristics of the line.

We can see that:

- The line has a positive slope since the coefficient of the linear term is a positive number (2).

- Since the line has a positive slope, the line is increasing.

From the line we can calculate the axis intercepts:

For the x-axis intercept, making "y" equal to 0, we have:

[tex]y=2x+1\\\\0=2x+1\\\\x=-\frac{1}{2}=-0.5[/tex]

We have that the x-axis interception point is located at the point (-0.5,0)

For the y-axis intercept, making "x" equal to 0, we have:

[tex]y=2x+1\\\\y=2*0+1\\\\y=1[/tex]

We have that the y-axis interception point is located at the point (0,1)

Also, we have a "less" symbol for the inequality, meaning that the shade that represents the solution of the inequality is located under the pointed line.

The graph of the inequality is attached.

Have a nice day!

Answer:

[tex]\large\boxed{y=2x^2+4}[/tex]

Step-by-step explanation:

The vertex form of a parabola:

[tex]y=a(x-h)^2+k[/tex]

(h, k) - vertex

We have the vertex at (0, 4) → h = 0 and k = 4.

Substitute:

[tex]y=a(x-0)^2+4=ax^2+4[/tex]

The point (-1, 6) is on the parabola. Put the coordinates of the point to the equation:

[tex]6=a(-1)^2+4[/tex]            subtract 4 from both sides

[tex]2=a\to a=2[/tex]

Finally:

[tex]y=2x^2+4[/tex]

Answer:

These kind of problem can be modeled by using the following equation

y = Po*e^(k*(t-to))

Where

Po = initial population

to = year of the initial population

y = Number of students at current year

k = constant rate of change

t = time in years

In 2012

695 = Po*e^(k*(2012 - 2012))

Po = 695

In 2016

825 = 695.e^(k*(2016-2012))

825/695 = e^(k*(4))

ln(825/695) = 4*k

k = ln(825/695) / 4

k = ln(825/695) / 4

k = 0.04287

in 2018

y = 695*e^(0.04287*(2018-2012))

y = 695*e^(0.04287*(6))

y = 695*e^(0.257)

y = 695*1.293

y = 898.85

approximately

899 students

Final answer:

The predicted school population in 2018, based on a constant rate of change, is 890 students. This is calculated by determining the annual rate of increase between 2012 and 2016 and applying it to the 2016 population.

Explanation:

To predict the population of the school in 2018, we need to calculate the constant rate of change between 2012 and 2016, and then apply that rate to extend the prediction to 2018. From 2012 to 2016, the school's population grew from 695 to 825 students. This is an increase of 825 - 695 = 130 students over 4 years.

The annual rate of change is thus 130 students
over 4 years = 32.5 students per year. To predict the population for 2018, we add twice the annual rate of change to the 2016 population (since 2018 is two years after 2016): 825 + (2 * 32.5) = 825 + 65 = 890 students.

Therefore, we can predict that the school population in 2018 will be 890 students.

The expression log 5 + log 2 can be combined using the property that the logarithm of a product is equal to the sum of the logarithms, which simplifies to log 10. Since log 10 is equal to 1, the solution to the expression is 1.

To solve the expression log 5 + log 2 using the logarithmic theorems, we can apply one of the fundamental properties of logarithms. Specifically, the logarithm of a product of two numbers is equal to the sum of the logarithms of those two numbers (log xy = log x + log y). Applying this property to our expression, we can combine the two logarithms as follows:

log 5 + log 2 = log (5 x 2)

Now, we can easily calculate the combined term:

log (5 x 2) = log 10

Since the base of the logarithm is not specified, we can assume it is 10 (common logarithm). Therefore, we can simplify further:

log 10 = 1

Thus, the solution to the given expression is 1.

Answer:

Option B

Step-by-step explanation:

. If a function is given in the form of f(x) = ax² + bx + c, then value of x is "input" and the value ... Now from the given table output values of the function are 8, 3, -5, -2 and 12. ... Therefore Option B

The area of the parking lot without considering the arena is determined to be 6518.75 square units.

To determine the parking lot area excluding the arena, the process involves multiple steps:

Parking Lot Area Calculation:

Utilize the formula A = B x H, where B is the base (100) and H is the height (75).

Compute A = 100 x 75, resulting in an initial parking lot area of 7500 square units.

Arena Area Calculation:

Employ the formula A = π r², where r is the radius (25) of the arena.

Calculate A = π x 25², yielding an arena area of 19625 square units.

Adjustment for Arena Area:

Observe the image indicating that the car park bisects the arena, cutting its area in half.

Subtract half of the arena's area from the parking lot area to obtain the adjusted area within the car park.

The adjustment equation is A = area - 0.5 x arena, where area is the parking lot area (7500) and arena is half of the arena's area (19625 / 2 = 981.25).

Final Result:

Perform the subtraction: A = 7500 - 981.25, yielding a final area of 6518.75 square units.

Therefore, the area of the parking lot without considering the arena is determined to be 6518.75 square units.