A sports center offers party packages. They advertise a flat rate of $325 for the first 10 guests. They charge $15 per person for each additional guest. A formula for the cost of the party is:

C = 325 + 15p
where p is the number of guests more than 10. (For example, if 12 people come to the party, p = 2.) Suppose you want to have a huge birthday celebration this year. However, you have budgeted $600 for your party. How many guests can you invite if you decide to have your party at this sports center?

The solution to the system of equations for this problem is given as follows:

(11.59, 479).

The system of equations for this problem is defined as follows:

The solution for x is obtained when the two equations are equal, hence:

14.3x + 318 = 3.6x + 442

10.7x = 124

x = 124/10.7

x = 11.59.

Applying the substitution in any of the equations, the solution for y is obtained as follows:

y = 3.2(11.59) + 442

y = 479.

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The area of the rectangle represented as the sum of cubes is x³ + 3³

An equation is an expression showing the relationship between numbers and variables.

The sum of cubes of a polynomial is in the form a³ + b³ while A the difference of cubes of a polynomial is a³ - b³

The area of rectangle = length * width

From the diagram, length = x² - 3x + 9; width = x + 3, hence:

The area of rectangle = length * width = (x² - 3x + 9)(x + 3)

Area = x³ - 3x² + 9x + 3x² - 9x + 27 = x³ + 27

Area = x³ + 3³

The area of the rectangle is x³ + 3³

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The value of an irrational numbers are,

⇒ √28

⇒ √11

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 numbers are,

⇒ √100

⇒ √28

⇒ √11

⇒ 2.78⁻⁻⁻

Now, We know that;

An irrational number is a number that cannot be expressed as a fraction for any integers.

Hence, We get;

The correct value of an irrational numbers are,

⇒ √28

⇒ √11

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a) The Corresponding minimum UGPA = 3.70

b) The range of middle 50% values will be: (3.28, 3.52).

What is the z-score?

A z-score (also known as a standard score) is a measure of how many standard deviations an individual data point is from the mean of a distribution. A z-score is calculated by subtracting the population mean from an individual data point, and then dividing that number by the population standard deviation.

a) z score corresponding to top 5% area = 1.645

Hence,

Corresponding minimum UGPA = 3.40 + 1.645*0.18 = 3.70

b) z score corresponding to middle 50% area = -0.67, 0.67

Hence,

The range of middle 50% values will be:

(3.40 - 0.67*0.18, 3.40 + 0.67*0.18)

(3.28, 3.52)

Hence,

a) The Corresponding minimum UGPA = 3.70

b) The range of middle 50% values will be: (3.28, 3.52).

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47 percent of the sandwiches had turkey.

Find the whole amount of what you're looking for to get a percentage of.

To calculate the percentage, divide the number.

Add 100 to the value.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the sign "%" or just "percent" or "pct." For instance, 35% is equal to the fraction 0.35 or the decimal 0.35.

The value of the number out of 100 is the proportion of the number. For instance, there are 26 females and 24 boys in a class. As a result, 52 out of 100 students in the class are females, or 52% of the class.

The Latin word "per centum," which meaning "by the hundred," was the source of the English word "percentage." Percentages.

According to our question

47+53= 100%,

So 1= 1%

= 47x1= 47, So it equals 47%.

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The values of maximum and minimum values are  11i + 3 and √5+ 3 .

Function can be defined in which it relates an input to the output. Functions are relationships in mathematics where each input has a particular output. Functions are often used in science and mathematics. In this section, we will learn the definitions of functions, various kinds of functions, and properties, along with examples to help us understand.

Given,

The function is f(x) = √x+3.

We have to find the maximum and minimum values on the interval [-11,5]

So,

f'(x) = 1/2√x

As when,

f'(x) = 0

has no solution than,

f(-11)  =  √-11 + 3

= 11i + 3

f(5) = √5+ 3 .

Therefore, The values of maximum and minimum values are 11i + 3 and √5+ 3 .

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The journal entries required on February 28, 2021, for Selkirk Company to accrue interest and to record the discounting are as follows:

Debit Interest Receivable $225

Credit Interest Revenue $225

Debit Cash $15,048

Debit Interest Expense $177

Credit Note Receivable $15,000

Credit Interest Receivable $225

When a note receivable is discounted, the following steps are followed:

February 28, 2021

Interest Receivable $225 Interest Revenue $225

Cash $15,048 Interest Expense $177 Note Receivable $15,000 Interest Receivable $225

Note receivable = $15,000

Interest = 9%

Maturity period = 6 months (Jan 1, 2021, to July 1, 2021) or 180 days

Discount date = February 28, 2021

Maturity value = $15,675 ($15,000 + $15,000 x 9% x 6/12)

Discount = $627 ($15,675 x 12% x 120/360)

Proceeds = $15,048 ($15,675 - $627)

Accrued interest = $225 ($15,000 x 9% x 60/360)

Note's carrying value on February 28, 2021, = $15,225 ($15,000 + $225)

Interest expense = $177 ($15,048 - $15,225)

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The integral[tex]∫20(45t^3-34t^2+25t)dt[/tex] can be evaluated by using the power rule of integration, which states that the derivative of x^n is [tex]nx^(n-1)[/tex]. This rule can be applied to each term of the integral separately.

The first step is to integrate [tex]∫20(45t^3-34t^2+25t)dt[/tex] with respect to t. By using the power rule, we can find the antiderivative of each term inside the parentheses:

[tex]∫45t^3 dt = (45/4)t^4 + C[/tex]  (the antiderivative of 45t^3 is (45/4)t∧4)

[tex]∫34t^2 dt = (34/3)t^3 + C[/tex] (the antiderivative of 34t^2 is (34/3)t∧3)

[tex]∫25t dt = (25/2)t^2 + C[/tex] (the antiderivative of 25t is (25/2)t∧2)

Now, we can substitute these results back into the original integral:

[tex]20(∫45t^3 dt - ∫34t^2 dt + ∫25t dt) = 20((45/4)t^4 + (34/3)t^3 + (25/2)t^2) + C= 20(15t^4-11t^3+25t^2) + C[/tex]

So, the evaluated integral for [tex]∫20(45t^3-34t^2+25t)dt[/tex] is [tex]20(15t^4-11t^3+25t^2) + C.[/tex]

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Answer:

7 and 40

Step-by-step explanation:

for you to get the next number you have to add 7 to that number...then add 1 to the number you have gotten then continue like that

eg: to get 8 you had to add 7 to 1 now to get the next number add 1 to 8 to get 9 then add 7 to 9 to get 16 then continue like that

The new points of the trapezoid are P'(4, -8), Q'(8, -8), R'(8, 4) and S'(-8, 4)

An equation is an expression relating two or more numbers and variables.

Dilation is the increase or decrease in size of a figure by a scale factor. The rule for dilation is:

(x, y) ⇒ (kx, ky)

The vertices of the trapezoid is P(1, -2), Q(2, -2), R(2, 1) and S(-2, 1)

If the trapezoid is dilated by a scale factor of 4 about the origin, the new points are:

P'(4, -8), Q'(8, -8), R'(8, 4) and S'(-8, 4)

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The one-sided limit that does not exist is given as follows:

lim x -> -6^- f(x).

A one sided limit will not exist when it is outside the domain of the function.

The domain of a function is composed by the set of all the input values of the function, hence on the graph it is given by the values of x.

For this problem, the domain is then given as follows:

-6 ≤ x ≤ 8.

To the left of -6, the function is not defined, hence the one-sided limit that does not exist is given as follows:

lim x -> -6^- f(x).

Meaning that the correct option is given by the last option.

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Answer: x = -8/3

Step-by-step explanation:

7 = 3(5+x)

3(5+x)=7

apply the distributive property

15+3x=7

rearrange the variables to  the left side of the equation

3x=7-15

3x=-8

divide on both sides

x=-8/3

Answer:

x = -8/3

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 7 = 3(5 + x)

Then the value of x will be,

→ 7 = 3(5 + x)

→ 7 = 3(5) + 3(x)

→ 7 = 15 + 3x

→ 7 - 15 = 3x

→ -8 = 3x

→ 3x = -8

→ [ x = -8/3 ]

Hence, the value of x is -8/3.

The shape that results from a plane passing through a cone that is perpendicular to the base is a B. Circle

A circle intersects a cone when a plane passes through it perpendicular to the base. This is due to the plane cutting through the cone's circular cross-section at a 90-degree angle to the base of the cone.

As a result, if the plane were to be slanted or angled, the intersection would have the shape of an ellipse, which is a circle that has been flattened.

This is due to the fact that an ellipse is the shape created when a plane crosses a cone at an angle other than perpendicular to the base.

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Answer:

the third one

Step-by-step explanation:

an open circle means it does not include that number. therefore, it needs to be x is less than -2. a closed circle means it includes that number. therefore, x is greater than or equal to 4

Answer: 1. 7a 2. 5r 3. 8y+4 4. 12m-7 5. 7u+5 6. 8q+6 7. 3w+5x 8. 4j + 4k 9. 5d+6

Step-by-step explanation: Add the coefficients of the terms with same variables. ex. 5a+4a+7... 5a and 4a have same variable which is a so add the 5 and 4 and you get 9a and the 7 doesn't match so leave it out and you get 9a + 7

Answer:

1) 7a

2) 5r

3) 8y +4

4) 12m-7

5) 7u+5

6) 8q+6

7) 3w+5x

8) 4j +4k

9) 5d+6

Step-by-step explanation:

you just add or subtract the number with the same letter after it (if there is no letter just leave it as is, unless there are two or more numbers with no letter after, then add or subtract as normal)

Answer:

A)  6x - 27

Step-by-step explanation:

Given expression:

[tex]-9(x + 3) + 15x[/tex]

Apply the distributive property:

[tex]\implies -9 \cdot x -9 \cdot 3+15x[/tex]

[tex]\implies -9x -27+15x[/tex]

Collect like terms:

[tex]\implies -9x+15x -27[/tex]

Combine like terms:

[tex]\implies 6x -27[/tex]

Answer:

[tex] \sf \: a) \: 6x - 27[/tex]

Step-by-step explanation:

Now we have to,

→ simplify the given expression.

The expression is,

→ -9(x + 3) + 15x

Let's simplify the expression,

→ -9(x + 3) + 15x

→ -9x - 27 + 15x

→ (-9x + 15x) - 27

→ (6x) - 27

→ 6x - 27

Hence, the answer is 6x - 27.

Answer:

[tex]j = \dfrac{9}{2} = 4,5 \\\\\\k = 2[/tex]

Step-by-step explanation:

I am working on the assumption that the figure shown is a parallelogram, otherwise my answer will not be valid

The diagonals of a parallelogram bisect each other

In the above figure, the top left-bottom right diagonal is bisected by the top right  - bottom-left diagonal

This means

[tex]3j = 5j - 9[/tex]

Subtract 5j from both sides:

[tex]3j - 5j = -9[/tex]

[tex]-2j = -9[/tex]

[tex]j = \dfrac{-9}{-2} = \dfrac{9}{2} = 4,5 \\[/tex]
I am not sure if you want it in fraction or decimal

Similarly

[tex]k + 10 = 6k\\\\[/tex]

Subtract k from both sides:
[tex]10 = 6k-k\\\\\\10 = 5k\\\\\\\textrm{Switching sides,}\\5k = 10\\\\k = \dfrac{10}{5} = 2\\\\[/tex]

The  probability of selecting a boy then a girl is 24/91

Probability is defined as the chance of occurrence of an event

E.  It is the ratio of the number of required outcome over the total of all possible outcomes in an even.

the given parameters that will help us to determine the probabilities are

The probability of the event is

P(E) = Pr(B) Then Pr(G)

Pr(E) = 8/14 *6/13

Simplify the fractions to have  48/182

= 24/91

Conclusively the selection is 24/91

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Answer:

Out of all possible choices you've shown, I'd say the best answer would be C

Step-by-step explanation:

Angles in parallel lines are formed when two parallel lines intersect with another line known as a transversal. So here ∠y is 40° and ∠z is 140°.

We know that sum of angles over a straight line is 180°

So here ∠x + 140° = 180°

So ∠x = 180 - 140

Therefore ∠x = 40°

So in this figure ∠x = ∠y , Since they are corresponding angles are equal.

Therefore ∠y = 40°

So ∠z will be 140° . Since ∠y = 40° its opposite angle will also be 40°.

So ∠z + 40° = 180°

Therefore ∠z = 140°

So the angles ∠y = 40° and ∠z = 140°.

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Upon solving the decimals, The expression which is equivalent to 0.125 are -12.5 ÷ 10²⇒ 0.125 and 1,250 ÷ 10⁴ ⇒ 0.125.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

Decimal fractions and recurring (repeating or non-terminating, like) decimals are the three different sorts of decimals (a.k.a. converting a decimal into a fraction whose denominator is a power of ten).

1.25 ÷ 10       ⇒ 0.125

Upon solving the decimals,

12.5 ÷ 10²       ⇒ 0.125

0.125 ÷ 100    ⇒ 0.00125

1,250 ÷ 10⁴     ⇒ 0.125

12.5 ÷ 1           ⇒ 12.5

125 ÷ 1,000    ⇒ 0.0125

The expression which is equivalent to 0.125 are -

12.5 ÷ 10²       ⇒ 0.125

1,250 ÷ 10⁴     ⇒ 0.125

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Answer: It will take 7 more years for George’s sister to be taller than him.

Step-by-step explanation:

Answer:

Step-by-step explanation:

7 years

Answer:

Step-by-step explanation:

A typical geometric sequence can be represented as

c

0

a

,

c

0

a

2

,

⋯

,

c

0

a

k

and a typical arithmetic sequence as

c

0

a

,

c

0

a

+

Δ

,

c

0

a

+

2

Δ

,

⋯

,

c

0

a

+

k

Δ

Calling

c

0

a

as the first element for the geometric sequence we have

⎧

⎪

⎨

⎪

⎩

c

0

a

2

=

c

0

a

+

2

Δ

→

First and second of GS are  the first and third of a LS

c

0

a

+

3

Δ

=

10

→

The fourth term of the linear sequence is 10

5

c

0

a

+

10

Δ

=

60

→

The sum of its first five term is 60

Solving for

c

0

,

a

,

Δ

we obtain

c

0

=

64

3

,

a

=

3

4

,

Δ

=

−

2

and the first five elements for the arithmetic sequence are

{

16

,

14

,

12

,

10A typical geometric sequence can be represented as

c

0

a

,

c

0

a

2

,

⋯

,

c

0

a

k

and a typical arithmetic sequence as

c

0

a

,

c

0

a

+

Δ

,

c

0

a

+

2

Δ

,

⋯

,

c

0

a

+

k

Δ

Calling

c

0

a

as the first element for the geometric sequence we have

⎧

⎪

⎨

⎪

⎩

c

0

a

2

=

c

0

a

+

2

Δ

→

First and second of GS are  the first and third of a LS

c

0

a

+

3

Δ

=

10

→

The fourth term of the linear sequence is 10

5

c

0

a

+

10

Δ

=

60

→

The sum of its first five term is 60

Solving for

c

0

,

a

,

Δ

we obtain

c

0

=

64

3

,

a

=

3

4

,

Δ

=

−

2

and the first five elements for the arithmetic sequence are

{

16

,

14

,

12

,

10

The required equation is y=x/3+3

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here the line passes through the points (3,4) and (0,3)

Thus the slope intercept form of the line passing through these points is

y=x/3+3 where m=4-3/3-0 is the slope of the line

Hence, The required equation is y=x/3+3

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The average rate of change from the sixth to the fourteenth hours indicates that, on average, 15 fewer pairs of shoes were sold every hour.

A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).

given

slope = y2- y1 / x2 - x1

= -120/8  = -15

( 6 , 120 )

( 14 , 0 )

The average rate of change from the sixth to the fourteenth hours indicates that, on average, 15 fewer pairs of shoes were sold every hour.

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The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].

Miller Indices of Direction Vector:

The Miller indices of direction are rationalized components of the direction vectors taken in all crystallographic directions. They are indicated by [[u v w ]]. They are always defined as the smallest integers, so if they occur in fractional or decimal form, we need to convert them into the smallest integral value by algebraic manipulation.

The indices of direction 1.

Let the length of direction 1 along the x-axis be X units. The length of the vectors along the y and z axes is 0.

[ X 0 0 ]

⇒ [tex]\left[\begin{array}{ccc}0&0&0\\X'&X'&X'\\\end{array}\right][/tex]

Divide each length by X to convert it into the smallest integer.

⇒ [1 0 0]

And, this is the Miller indices of the direction vector 1.

So, the Miller indices of the direction vector 1 are [ 1 0 0].

Direction 2

The indices of direction 2.

Let the length of direction 2 along the x-axis be X units. The length of the vector along the y and z axes are 0.

[ 0.2 0 0.3 ]

⇒[ 2 0 3 ]

Multiply each fractional length by 10 to convert it into the smallest integer.

So, the Miller indices of the direction vector 2 are [ 2 0 3].

Therefore, The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].

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The equation formed by the sentence is 9b - 7 = 8.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Let the variable be b

By the given sentence we get the equation

9b - 7 = 8

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Answer:

[tex]\frac{35}{12}[/tex]

Step-by-step Explanation:

The tangent of an acute angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Sawyer lives 12.7 km farther from the soccer field.

Jabar lives 5 miles from the soccer fields, Sawyer lives 12.7 km from the same soccer fields .

The person that lives farther form the soccer field can be calculated as follows;

Let's convert Jabar distance from the soccer field to km.

1 miles = 1.60934

5 miles = ?

cross multiply

distance of Jabar from the soccer field = 5 × 1.60934

distance of Jabar from the soccer field = 8.0467 km

Therefore, jabar lives 8.0467 km from the soccer field.

Hence, Sawyer lives 12.7 km farther from the soccer field.

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