the 4 winning numbers in a swimming club lottery were called out as follows the 1st number is the square root of 576 the 2nd number is a multiple of 8 between 30 and 39 the 3rd number is the cube of 3 the 4th number is the largest prime number less than 40 what we’re the 4 winning numbers?

If the account balances were taken from the adjusted trial balance for Urgent Messenger Service, a delivery service firm, for the fiscal year ended November 30, 20Y1: The income statement is $186,750.

Income statement can be defined as the statement that help to shows the revenue and expenditure a company or an organization. When preparing income statement when the revenue amount is greater that the expenses the end result will be net income and in a situation were the expenses is higher than the revenue the end result will be net loss.

Now let prepare the income statement

Urgent Messenger Service Income Statement For the Year Ended November 30, 20Y1

Revenue:

Fees earned $724,500

Expenses:

Salaries expense $393,100

Rent expense $75,000

Utilities expense $41,200

Supplies expense $6,150

Insurance expense $5,000

Miscellaneous expense $6,650

Total expenses $537,750

Net income  $186,750

($724,500 - $537,750 )

Therefore the income statement is the amount of $186,750.

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The complete question is:

The following account balances were taken from the adjusted trial balance for Urgent Messenger Service, a delivery service firm, for the fiscal year ended November 30, 20Y1:

Depreciation Expense $10,650

Fees Earned 724,500

Insurance Expense 5,000

Miscellaneous Expense 6,650

Rent Expense 75,000

Salaries Expense 393,100

Supplies Expense 6,150

Utilities Expense 41,200

Prepare an income statement.

Answer:

193 is it I'm not lying

Step-by-step explanation:

The inequality is given to be:

Recall the Absolute Rule:

Applying this to the inequality, we have:

or

Therefore, the solution to the inequality is:

Answer:

11 nickels . Are in a doldollar

Step-by-step explanation:

The most appropriate choice for function, domain and range of a function will be given by

Domain of the given function is [tex]\mathbb{R}[/tex], the set of real numbers

Range of the given function is [tex]\mathbb{Z}[/tex], the set of integers.

What is Function, Domain and Range of a function?

Function

A function from A to B is a rule that assigns to each element of A a unique element of B

Domain of a function

Domain of a function is the set of  values for which the function is defined.

Range of a function

The set of values obtained on putting the values of the domain is called the range of a function.

Here,

Domain of [tex]y = [x] + 2[/tex]

[tex][x][/tex] is defined for all [tex]x[/tex] ∈ [tex]\mathbb{R}[/tex], the set of real numbers

Domain of the given function is [tex]\mathbb{R}[/tex], the set of real numbers

[tex][x][/tex] is the greatest integer not exceeding [tex]x[/tex]

So [tex][x][/tex] [tex]+ 2[/tex] gives only integer values

So Range of the given function is [tex]\mathbb{Z}[/tex], the set of integers.

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Given a figure of a right trapezoid

The bases are the sides, 4 and 6

And the height = 4

The area of the trapezoid = 1/2(sum of the bases) times the height

So, the area =

So, the answer will be: Area = 20 unit²

A 22-inch piece of steel is divided into three parts, the length of 1st 2nd and 3rd piece are 3 inch,6 inch and 13 inch.

Given that,

A 22-inch piece of steel is divided into three parts, the second of which is twice as long as the first and the third of which is one inch longer than the first.

We have to find the parts' lengths.

Let us take, the length of the first piece is x inch.

Then the length of the second piece is 2x.

Then the length of the third piece is 4x + 1 inch.

We know total length of the steel is 22 inch.

We can write as,

x + 2x + 4x + 1 = 22

7x = 21

x = 3.

Then, the length of the first piece is 3 inch.

Then the length of the second piece is 2×3=6 inch.

Then the length of the third piece is 4×3 + 1=12+1=13 inch.

Therefore, the length of 1st 2nd and 3rd piece are 3 inch,6inch and 13 inch.

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Answer:

Step-by-step explanation:

First we have to consider the initial and final velocities to calculate the average acceleration:

v_i= - \Big[ 1.10\frac{m}{s}\Big]\widehat{i} \\ v_f= \Big[ 11.5\frac{m}{s}\Big]\widehat{j} \\ \implies \Delta v=v_f-v_i \\ \implies \Delta v= [ 1.10\frac{m}{s}]\widehat{i} +[ 11.5\frac{m}{s}]\widehat{j} \text{ in an average time } \Delta t=1.40\,s.v

i

​

=−[1.10

s

m

​

]

i

v

f

​

=[11.5

s

m

​

]

j

​

⟹Δv=v

f

​

−v

i

​

⟹Δv=[1.10

s

m

​

]

i

+[11.5

s

m

​

]

j

​

 in an average time Δt=1.40s.

With the information we can calculate the average acceleration in terms of the x- and y-components:

a=\Delta v/\Delta t= \dfrac{[ 1.10\frac{m}{s}]\widehat{i} +[ 11.5\frac{m}{s}]\widehat{j}}{1.40\,s} \\ \text{ } \\ \implies a= \big[ 0.786\frac{m}{s^2}\big]\widehat{i} + \big[ 8.214\frac{m}{s^2} \big]\widehat{j}a=Δv/Δt=

1.40s

[1.10

s

m

​

]

i

+[11.5

s

m

​

]

j

​

​

⟹a=[0.786

s

2

m

​

]

i

+[8.214

s

2

m

​

]

j

​

The standard equation of a circle is given by:

where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

For:

Rewrite the equation as:

We can conclude it is a circle with center at (-3,-1) and radius of 4

The number of weeks for your friend's savings to be same as your savings does not exist

The given parameters are:

Your savings account

Initial amount = $100

Weekly savings = $40

Your friend's savings account

Initial amount = $80

Weekly savings = $10

The equation that represents the amount in the account after w weeks is represented as

Amount = Initial amount + Weekly savings x Number of weeks

This gives:

You: Amount = 100 + 40x

Your friend = 80 + 10x

The above equations are linear equations

When the amounts are equal, we have

100 + 40x = 80 + 10x

This gives

30x = -20

Divide

x = -2/3

The number of weeks cannot be negative

Hence, your friend's savings will never be up to your savings

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Possible question

You have $100 in a savings accoun and save an additional $40 each week. Your friend has $80 in a savings account and saves and addtional $10 each week.

When will you and your friend have the same amount?

Answer: 80.7%

Step-by-step explanation: COGS (beverage and food costs) = $68,555

$68,555 is 80.6529412% of $85,000 rounded to the nearest tenth is 80.7%

Answer: b

Step-by-step explanation:

The number of dollars Jada and Kelly each have now is $18 and $15.

Given:

Ratio of the number of dollars Jada has to the number of dollars Kelly has = 4:7

Changed ratio after Kelly gives Jada $6.00 = 6:5

Let the number of dollars Jada and Kelly have be 4x and 7x.

Kelly gives Jada $6.00,

So,

Number of dollars Jada has now is $(4x + 6).

Number of dollars Kelly has now is $(7x - 6).

The ratio of the number of dollars is changed to 6:5.

⇒ [tex]\frac{4x + 6}{7x -6} = \frac{6}{5}[/tex]

⇒ 5(4x + 6) = 6(7x - 6)

⇒ 20x + 30 = 42x - 36

⇒ 42x - 20x = 30 + 36

⇒ 22x = 66

⇒ x = 3

Number of dollars Jada has now = (4x + 6) = $18

Number of dollars Kelly has now = (7x - 6) = $15

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SOLUTION:

Case: Simple Interest

Method:

Simple Interest, I

Where

P= $500

R= 7.5% or 0.075

I= $225

Therefore, Time T

Final answer:

6 years

Answer:Explanation:

(a)$10,488

(b)$12,218.

• ric;' Monthly Salary = $1,730

• Percentage commision = 12%

Part A

f Eric 's sales were $87,400 for last month, his amount of commission will be:

Eric's amount of commission is $10,488.

art B

Eric's gross pay will be the sum of his monthly salary and commission.

Eric's gross pay is $12,218.

Dependent events: The likelihood of one event happening influences the likelihood of the other event happening.

When the result of one event affects the result of another, two events are said to be dependent events.

The likelihood of two connected events is the sum of the probabilities of the occurrences X and Y that happen after X.

The likelihood of one event does influence the likelihood of the other happening.

For instance, the likelihood of drawing another King decreases if you remove a King from a deck of cards without replacing it.

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The change between the morning and afternoon temperature is 2.7.

It should be noted that temperature simply means the degree of hotness as well as the coldness that is in a particular body

In this case, the temperature was -2 1/2 in the morning . by the afternoon the temperature was 0.2.

The change between the temperature will be:

= 0.2 - (- 2 1/2)

= 0.2 + 2.5

= 2.7

The temperature change is 2.7.

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Step 1

Given;

Step 2

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles and squares of any side length are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Thus, the answer is;

Answer:

Since two angles of the triangle have the same measure, the triangle is an isosceles triangle.

Let one angle be a variable (eg: x) so we can form expressions and solve.

Let the first and second angle be x°.

Form an expression for the third angle using the information given.

Third angle = (x + 21)°

Since sum of angles in a triangle is 180°, we can form an equation.

x + x + (x + 21) = 180

Simplify and solve for x.

3x + 21 = 180

3x = 159

x = 53

Largest angle is the third angle.

Substitute x into the expression to find the value.

Third angle = 53 + 21

= 74°

First I will define what prime factor means

Prime factors of 42 are the factors of 42 that are prime

Prime numbers are those numbers that have two factors; 1 and itself

Factors of 42 are those numbers that can go into 42 without remainder

So let's list out the factors of 42, they are;

Factors of 42 = 1, 2, 3, 6, 7, 14, 21 and 42

Now among these factors, we will list out the ones that are prime, they are the prime factors

That is;

Prime factors of 42 = 2, 3, and 7

To express 42 as a product of it's prime factors, we have 2 ways of doing this

The first method is; To keep dividing 42 by the smallest prime factors

42 = 2 x 3 x 7

The second method is;

Therefore, the prime factorization of 42 = 2 x 3 x 7

The prime factorization of 42 is 2 × 3 × 7.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

The positive pair factors of 42 are (1, 42), (2, 21), (3, 14), and (6, 7).

The negative pair factors of 42 are (-1, -42), (-2, -21), (-3, -14), and (-6, -7).

The 42 factors that are prime are known as the prime factors of 42.

Prime numbers are those with just themselves and factor 1 as their factors.

The numbers that can round to 42 without leaving a remainder are known as 42 factors. Let's enumerate the 42 factors, which are as follows:

1, 2, 3, 6, 7, 14, 21, and 42 are factors of 42.

We shall now list the prime factors among them, they are the prime factors. which is;

42 has prime factors of 2, 3, and 7.

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We can replace x with any real number, positive or negative. We can also plug in x = 0. There aren't any restrictions to worry about with the input.

Examples:

Plug in x = 2 to get f(2) = 2(1/10)^2 = 0.02

Plug in x = -2 to get f(-2) = 2(1/10)^(-2) = 200

Plug in x = 0 to get f(0) = 2(1/10)^(0) = 2

The domain of the given function is "All real numbers". So, option D is correct.

The domain of a function is the set of possible values as inputs to the function. The Domain of the exponential function is the set of all real numbers represented by R.

here, we have,

Finding the domain of the given function:

The given function is f(x) = 2×

Since this function has the variable x in the exponent, this is an exponential function.

So, its inputs are of all real numbers. And the domain is {x:x ∈ R}.

Thus, option D is true.

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The bottle of 40 tablets will contain 420 milligrams of tablets.

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

Given that a multivitamin tablet contains 10.5 mg of calcium and there are 40 tablets in the bottle. The total amount of the tablets in the bottles will be calculated as:-

Total tablets = 10.5 mg x 40

Total tablets = 420 mg

Therefore, a bottle of 40 tablets will contain 420 milligrams of tablets.

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In this Matrix A= [-2     -3

                              3    12]

the matrix of A - 1 is

[-4/5    -1/5

 1/5    2/15]

According to the question, given that

[-2    -3

3     12 ]  ^ -1

First, we find the determinant

-2 * 12  - (-3 *3) = -24 - (-9) = -24 +9 = -15

Multiply 1 over the determinant by The matrix with the -2 and 12 switched and negate the -3 and the 3

1/-15 [12      3

         -3      -2 ]

after multiply by 1/ - 15, we get

[-4/5       -1/5

 1/5       2/15]

Therefore, In given Matrix A, after solving we get the value A- 1 is

[-4/5       -1/5

1/5       2/15]

Matrix

If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “m × n.” For example,

Matrix.  [ 5   6    3

               -2    3    2 ]

is a 2 × 3 matrix. A square matrix of order n have n rows and n columns. Ordinary numbers can be thought of as 1 1 matrices, making the number 3 the matrix [3]A row vector is a matrix with one row and n columns, and a column vector is a matrix with one column and n rows.

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From the question, we were asked that how many 42 inches wide panels must be bolted together to create a 28 feet wall.

First let's covert the two measurement to same unit.

So, lets convert 42 inches into feet.

Recall, 1 foot will give 12 inches

42 inches will be:

42/12 = 3.5 feet

Therefore, the wide wall that must be bolted together to create a 28 feet wall is:

= 28/3.5

= 8 feet.

[tex]a < 8 -+ 6 \\ =a < 14[/tex]

The second option is the answer.

The value of absolute inequality will be given by 0.002 ≥ |x-3|.

Inequality may be defined as the expression which shows unequal behavior between two entities while absolute inequality expression includes inequality along with an absolute value. For example, |x| > 3, |x| <3, |x| ≤3 or |x| ≥3. Now, let us assume the length of the part in the question as x. Since, the desired length is given as 3mm and also the parts are within 0.002 mm of the desired specifications.

Therefore, the maximum length of the part can be = 3 + 0.002

and the minimum length of the part can be = 3 - 0.002

Therefore, we can write the inequality as

3 - 0.002 ≤ x ≤ 3 + 0.002

⇒ 3 - 0.002 ≤ x and x ≤ 3 + 0.002

⇒ -0.002 ≤ x-3 and x-3 ≤ 0.002

⇒ 0.002 ≥ -(x-3) and x-3 ≤ 0.002 (Because a > b ⇒ -a<-b)

⇒ 0.002 ≥ | x - 3 |

Thus, the required absolute inequality is 0.002 ≥ |x-3|.

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Answer:

A: |x - 3| ≤ 0.002

Step-by-step explanation:

Answer:

  x -3y -3z = 0

Step-by-step explanation:

You want to write "City A has three times as many people as cities B and C combined" as an equation in standard form, letting x, y, z, w represent the populations of cities A, B, C, D, respectively.

The populations of cites B and C combined can be expressed by ...

  y +z

Three times the combined population is then ...

  3(y +z)

This is equal to the population of city A, so we can write ...

  x = 3(y +z)

This equation is in standard form when all of the variable terms are on one side of the equal sign, and the expression is simplified.

  x -3(y +z) = 0 . . . . . . . subtract the right side expression

  x -3y -3z = 0 . . . . . . . eliminate parentheses; standard form

Answer:

-3.15

Step-by-step explanation:

3/4 converted to a decimal is .75 so .75 + -3.9 is -3.15

Hope this helps! <3

Answer:

5(4 + 1).

Step-by-step explanation:

[tex]{ \rm{(30 \div 2) + 10 = 15 + 10}} \\ [/tex]

- Factorise out 5;

[tex]{ \tt{ = 5(3 + 2)}} \\ \\ = { \tt{5(4 + 1)}}[/tex]