Is 70,509,733 divisible by 6?

Answer:

The third graph

Step-by-step explanation:

We can immediately eliminate the 1st and last graphs because they are decreasing, not increasing. It wouldn't make sense that the more classrooms there are, the fewer students. Y = 22x would be increasing in the graph.

Let's plug some x values into the equation first, to see where our points are at.

Plug 1 into x

Y = 22(1)

Y= 22

(1,22)

Plug 2 into x

Y = 22(2)

Y = 44

(2,44)

Plug 3 into x

Y = 22(3)

Y = 66

(3,66)

Plug 4 into x

Y = 22(4)

Y = 88

(4,88)

The second graph matches the coordinates, so it works, but it isn't a complete function graph. A function graph needs a line drawn through the points. The second graph isn't your answer.

Let's look at the third graph. The coordinates also match up with the graph and it has a line drawn through the points. It's an accurate function graph representing this scenario. Therefore, the third graph is your answer.

Have a lovely day! :)

Answer: the 2nd graph is what i got right on the test

Step-by-step explanation:

Shop Layout, in a scene shop, sheet lumber (such as lauan, plywood, masonite, and MDF) is commonly stored flat in an area that is at least  C. 4'x8'.

The most common size (area) for sheet lumber is  4 x 8 feet, about 32ft² or 2.97m².

Other areas that sheet lumber can occupy include 2 x 2 feet, 2 x 4 feet, 4 x 4 feet, and 4 x 10 feet.

This implies that sheet lumber does not usually come in the following sizes: 4'x6', 8'x8', and 6'x10'.

Length of sheet lumber = 8 feet

Width of sheet lumber = 4 feet

Area of sheet lumber = 32 ft² (8 x 4)

Thus, according to Shop Layout, in a scene shop, sheet lumber (such as lauan, plywood, masonite, and MDF) is commonly stored flat in an area that is at least  C. 4'x8'.

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The number of weeks that it takes to empty the lake is; 350/11 weeks

We are told that Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time.

Let w = number of weeks required to empty the lake

let the completed job = 1 (an empty lake)

Thus;

w/14 - w/25 = 1

Multiply through by 350 to get;

25w - 14w = 350

11w = 350

w = 350/11 weeks

Thus, the number of weeks that it takes to empty the lake is; 350/11 weeks

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This statement in the article is wrong because $2.69 is not the mean price ($2.81)

The prices from 5 gas stations surveyed are given as:

$2.79, $2.99, $2.69, $2.89, and $2.69.

There are no outliers in the dataset

So, the dataset can be summarized by the mean

The mean is

Mean = Sum/Count

So, we have

Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5

Evaluate

Mean = 2.81

The article quoted $2.69 as the typical price

This statement in the article is wrong because $2.69 is not the mean price ($2.81)

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Answer: 70

Step-by-step explanation:

7 days a week x 2 lawns = 14

14 lawns x 5 weeks = 70 lawns

Answer:

70 lawns

Step-by-step explanation:

If Bob mows lawns every day for 5 weeks this is how the equation would work:

2 * 7 = 14

14 * 5 = 70

I got the 7 because there's seven days per week.

The calculated division of the numbers 40 divided by 20 is 2

From the question, we have the following parameters that can be used in our computation:

40 divided by 20

When represented as an equation, we have

40 divided by 20 = 40/20

Divide 40 by 20

So, we have the following result

40 divided by 20 = 2

Using the above as a guide, we have the following:

the result is 2

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The mathematical expression of the statement is x - 15 <= 5

The statement is given as:

Hourly wage of $15 differs from the average by less than or equal to $5

Let the average hourly wage be x

So, we have:

Hourly wage of $15 differs from the average = x - 15

less than or equal to $5 => <=5

So, the expression is

x - 15 <= 5

Hence, the mathematical expression of the statement is x - 15 <= 5

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The maximum and minimum value of η at q = 10 and q = 85 respectively.

The demand equation is p = 190/ (q + 10) where 10 < 0 < 85.

η is the elasticity of demand.

Then, the elasticity of demand is given as:

η = ( dq/ dp) × ( p / q )

Now, we have p = 190/ (q + 10)

Therefore,

p ( q + 10 ) = 190

pq + 10p = 190

q = ( 190 - 10p ) / p

Now,

dq / dp = ( d/dp ) ( ( 190 - 10p ) / p )

dq / dp =  ( -190/ p² )

Substituting these values in the elasticity demand,

η = ( dq/ dp) × ( p / q )

η = ( -190/ p² ) × ( p / q )

η = ( -190/ pq )

η = ( -190/ [190 / (q + 10 ) ]q )

η = [ - ( q + 10 ) / q ]

| η | = | - ( q + 10 ) / q |

η =  ( q + 10 ) / q = 1 + 10/q

The critical point is when | η' | = 0.

η' = ( d / dq ) ( 1 + 10/q )

η' = - 10/ q²

- 10/ q² = 0

Hence, - 10/ q² is not defined.

Therefore, the function is not defined at q = 0.

Therefore, q = 0 is not a solution.

We have 10 ≤ q ≤ 85

The value of functions at the endpoint,

At q = 10,

η = ( 1 + 10/q )

η = ( 1 + 10/10 )

η = 1 + 1 = 2

At q = 85,

η = ( 1 + 10/q )

η = ( 1 + 10/85 )

η = 1.11764

Therefore, the absolute value of the elasticity of demand is maximum at q = 10.

The absolute value of the elasticity of demand is minimum at q = 85.

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The amount of gas in the tank is 13 1/3 gallons

The tank of the car holds 20 gallons of gas

The gasoline gauge shows 2/3 full

The amount of gas left in the tank can be calculated as follows

= 2/3 × 20

= 40/3

= 13 1/3

Hence there are 13 1/3 gallons of fuel left in the tank

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Using the Pythagorean theorem, the missing sides are:

1. 5

2. 13

3. √15

4. 3

The Pythagorean theorem is given as: c² = a² + b², where c is the longest side and a and b are the other two legs.

1. Missing side = √(3² + 4²) [Pythagorean theorem]

Missing side = 5

2. Missing side = √(12² + 5²) [Pythagorean theorem]

Missing side = 13

3. Missing side = √(4² - 1²) [Pythagorean theorem]

Missing side = √15

4. Missing side = √((√10)² - 1²) [Pythagorean theorem]

Missing side = √(10 - 1) = √9

Missing side = 3

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Answer:

A. 72°

D. 144°

E. 216°

Step-by-step explanation:

are you tempted to calculate the internal angles ?

that is, I guess, the trap set by your teacher here, and it would be the wrong approach.

nevertheless, quickly just as a reminder :

the sum of all internal angles in a polygon is

(n - 2)×180°

n being the number of sides.

in our case that is

(5 - 2)×180 = 3×180 = 540°

so, each internal angle is 540/5 = 108°.

but we are not turning at an edge or vertex. no, we are turning the pentagon around is central point.

we are running each vertex along a circle arc. the center of that circle being P.

after every 1/5 of the circle arc there is a vertex of the pentagon.

and whenever we rotate one vertex on top of the next one, we carry the pentagon visually onto itself.

so, instead of a full circle rotation we need only 1/5 of that :

360 / 5 = 72°

and with every additional 1/5 of the circle arc (or 72°) we get it again.

that means at

72°

144°

216°

288°

360°

the pentagon carries onto itself.

therefore, A, D and E are correct.

The angles that are vertical angles are:

<EBD and <ABC

<ABE and <CBD

When two straight lines intersect at a point, they form two pairs of angles that are directly vertically opposite each other. These pairs of angles are called the vertical angles.

Given the image below that shows two lines intersecting at point B, they form two pairs of angles that are directly vertically opposite each other, which are:

<EBD and <ABC

<ABE and <CBD

These two pairs of angles are called vertical angles.

Therefore, the angles that are vertical angles are:

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The dimensions of the concrete patio should be 23ft x 12ft x 0.5feet.

Since a rectangle is two-dimensional, while a cube is three-dimensional, the dimensions of the concrete patio include its length, width, and height or thickness.

The quantity of concrete required = 138ft³

The perimeter of the patio = 70 feet

Height = 6 inches or 1/2 foot or 0.5 ft

Perimeter = 2(L + W)

70 = 2(L + W)

L + W = 35 (70/2)

The possibilities for the length and width include 20 and 15, 25 and 10, and lastly, 23 and 12, which are also the two pair factors of 276.

Let L = 23 (the length is always longer than the width)

W = 12 (35 - 23)

Check:

Volume of concrete = 138ft³

Area = 276ft² (138ft³/0.5ft)

Two pair factors of 276 are 92 and 3, 46 and 6, 23 and 12, 2 and 138, and 1 and 276.

Given also that (23 + 12)2 = 70 (perimeter)

The dimensions that meet the two requirements are:

Length = 23 feet

Width = 12 feet

and Height = 0.5 feet

= 23 x 12 x 0.5 = 138

Thus, the dimensions of the concrete patio should be 23ft x 12ft x 0.5feet.

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Answer: They will need to sell 1,500,000 to break even.

12,000,000 / 8 is 1,500,000

Answer:

linear

Step-by-step explanation:

because they're are all in a vertical vay

Answer:

n = 4

Step-by-step explanation:

8 * n = 32

Solve for n

Divide each side by 8

8*n/8 = 32/8

n = 4

Step-by-step explanation:

we get the points with extreme values as the 0 points of the first derivative of the function.

h'(t) = 592 - 32/7 t = 0

592 = 32/7 t

4144 = 32t

t = 129.5 seconds

so, it will reach its max. height after 129.5 seconds.

The time that the ball reaches its maximum height is 129.5 seconds.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The height above the lunar surface (in feet) after ‘t’ seconds is given by the formula;

⇒ h =592t - 16/7t²

Now,

We have to find the derivative of above formula and equate to zero for the maximum time as;

⇒ h =592t - 16/7t²

⇒ h' =592 - 16/7 × 2t = 0

⇒ 592 - 32/7 t = 0

⇒ 32/7 t = 592

⇒ 32t = 592 × 7

⇒ 32t = 4,144

⇒ t = 4,144/32

⇒ t = 129.5 seconds.

Thus, The time that the ball reaches its maximum height is 129.5 seconds.

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Applying the distributive property, the solution of x for item c is given as follows:

x = (3a - 8 - b)/(a - b).

The distributive property is when the outside term multiplies each of the inside terms of an expression.

For example, in this problem:

Hence the solution for x of the expression is found as follows:

a(x - 3) + 8 = b(x - 1).

ax - 3a + 8 = bx - b

ax - bx = 3a - 8 - b

x(a - b) = 3a - 8 - b

x = (3a - 8 - b)/(a - b).

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Answer:

It is 41, 43, 47! :D

Step-by-step explanation:

The limit of the composite function is given as follows:

lim x->7 f(g(x)) = 2.

A limit is given by the value of function f(x) as x tends to a value.

From the graph of g(x), we have that the lateral limits at x = 7 are given as follows:

[tex]\lim_{x \rightarrow 7^-} = \lim_{x \rightarrow 7^+} = -2[/tex]

Hence:

lim x->7 f(g(x)) = f(lim x->7 g(x)) = f(-2).

Looking at the graph of f(x), we have that:

f(-2) = 2.

Hence:

lim x->7 f(g(x)) = 2.

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Let us understand the properties of Logarithms. In mathematics Logarithms are the inverse of exponential function. In the simplest case, the logarithm counts the number of times same factor in present in a repeated multiplication.

A logarithm of a number 'x' to a base 'y' is defined as:

[tex]log_y^x=z (y > 0)[/tex]

which represents [tex]y^{z} =x[/tex]

According to the properties of Logarithm :

Now let us solve the given problem:

[tex]2 log (x-y)=log x+ log y\\or,log(x-y)^2=log(xy)\\or,log(x^2+2xy+y^2)=log(xy)[/tex]

[tex]or,x^{2} +2xy+y^{2}=xy\\[/tex] ( taking anti-logarithms on both sides)

[tex]or,x^{2}+y^{2}=xy+2xy[/tex]

Now let us use the above equation to solve

Left Hand Side:

[tex]2 log(x+y)\\=log(x+y)^2\\=log(x^{2} +2xy+y^{2} )\\=log(x^2+y^2+2xy)\\=log(xy+2xy+2xy)\\=log(5xy)\\=log(5)+log(x)+log(y)[/tex]

=Right Hand side

Hence the statement is proved by using the properties of logarithm.

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Answer: 0

Step-by-step explanation:

because -2+-1 is -3. then -3+0 is just -3. lastly -3+1 = -2 and -2 + 2 = 0

The figure KLMN is being rotated by 90°, which is a rigid transformation, the true statements are therefore;

(D) Figure RSTU is congruent to figure KLMN

(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

The given parameters are;

In KLMN, KN||LM

The transformation applied to figure KLMN = A 90° clockwise rotation about point P.

The image of KLMN following the rotation transformation is Figure RSTU.

Please find attached a drawing of the possible diagram in the question obtained from a similar question online.

The options from the question are;

(A) [tex] \overline{ST}[/tex] is parallel to [tex] \overline{RU}[/tex]

(B) [tex] \angle R[/tex] is the same measure as [tex] \angle N[/tex]

(C) [tex] \overline{RS} [/tex] is the same length as \overline{MN}

(D) Figure RSTU is congruent to figure KLMN

(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

A rotation transformation is a rigid transformation, therefore;

The distances between any two points on the pre–image is the same as the distance between corresponding points on the image, which gives;

Figure KLMN [tex] is congruent to [/tex] Figure RSTU

Figure KLMN [tex] \cong [/tex] Figure RSTU

According to the postulate, Corresponding Angles of Congruent Figures are Congruent, we have;

[tex] \angle T \cong \angle M[/tex]

Which gives;

[tex] \angle T[/tex] = [tex] \angle M[/tex]

[tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

The correct options are therefore;

(D) Figure RSTU is congruent to figure KLMN

(E) [tex] \angle T[/tex] is the same measure as [tex] \angle M[/tex]

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1. The effects of each transaction on the individual items of the accounting equation are as follows:

Cash    $70,000 + (40,000) + (15,000) + (500) + 4,000 + (3,275) + 1,800 + (700) + (1,800) = $14,525

Accounts Receivable $2,800 - 1,800 = $1,000

Office Supplies $1,200

Equipment $10,000 + 15,000 + 1,700 = $26,700

Office Suites $40,000

Accounts Payable $1,200 + $1,700 + (700) = $2,200

Capital–L. Lopez $70,000 + 10,000 = $80,000

Dividends $3,275

Revenues $2,800 + 4,000 = $6,800

Advertising Expenses $500

Wages Expense $1,800

Total $2,300

2. The company's Net income is $4,500.

Net income = Revenue - Expenses

= $2,300 ($6,800 - $2,300).

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1. Use additions and subtractions within the table to show the dollar effects of each transaction on individual items of the accounting equation.

2. Determine the company’s net income.

Answer:

You can flip the second fraction and multiply the fractions so 3/5 * 15/3 = 3

Step-by-step explanation:

This process required 3 to be subtracted 5 consecutive times, so again we see that 15 ÷ 3 = 5. The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient.

Division is a simple operation in which a number is divided. It's easiest to think of it as a number of objects being divided among a certain number of people.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

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