A caterer charges $150 dollars plus $15 per person served. The total cost is represented by the function y=15x+150 where y is the total cost and x is the number of guests. If Tatiana invites 200 people to a catered event, how much will it cost?



$

Answer:

I did the math there is no answer

Answer: If x<0, the identity does not always hold.

Step-by-step explanation:

If \(0 < \theta < \frac{\pi}{2}\), let \(\arctan x=\theta\), implying \(x=\tan \theta\), and vice versa.

We know that \(\tan \left(\frac{\pi}{2}-\theta \right)=\cot \theta=\frac{1}{\tan \theta}\), so this means that if we let \(\tan \theta=x\)

\(\tan \left(\frac{\pi}{2} -\theta \right)=\frac{1}{x}\\\frac{\pi}{2}-\theta=\arctan \left(\frac{1}{x} \right)\\\theta+\arctan \left(\frac{1}{x} \right)=\frac{\pi}{2}\)

Substituting back, we obtain that \(\arctan (x)+\arctan \left(\frac{1}{x} \right)=\frac{\pi}{2}\), as required.

The term Exponential decay in mathematics explains as a process of a constant percentage rate reduction in an amount over time.

In elementary mathematics, the graph designates a plot or a function graph. A graph is a set of points and the connections between some subset of those points (which may be empty).

Asymptote, An object that serves as the limit of another line or curve in mathematics.

y-intercept is (0, −2) means x = 0 and y = -2

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The domain of function f(x) is given as follows:

{x | 1 ≤ x < 5}.

The values of x of the function given at the end of the answer are as follows:

Hence the domain is given as follows:

{x | 1 ≤ x < 5}.

The function is given by the image presented at the end of the answer.

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Answer:

A - {x | 1 < x < 5}

Step-by-step explanation:

took the Quiz

Answer: 2.5

Step-by-step explanation: If you do 5/8 divided by 1/4 in the calculator it is 2.5.

Answer:

what question?...........

A formula without free variables is a formula that does not contain any variables that are not quantified.

Sentences are commonly referred to as formulas devoid of any unrestricted variables. These statements hold a truth value independent of the variable values, hence the reason.

Open formulas are frequently referred to as formulas with free variables. These are not actually declarations; instead, they are arrangements that can transform into declarations by allotting definite values to the independent variables.

Formulas without free variables are often easier to work with than formulas with free variables.

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Answer:

1-2x

Step-by-step explanation:

\((7+2x)-(4x+6)=7+2x-4x-6=1-2x\)

Answer:

D. $63.00 for 5 hours

Step-by-step explanation:

The actual cost to rent the boat per hour is $12.75 when you multiply all the other hours by 12.75 it equals the correct amount except for (D) 5 ×12.75 = 63.75

Answer:

g: games; r: rides

1.5g + 2.5r = 16.5

g = 2r

Step-by-step explanation:

g: # of games played

r: # of rides ridden

total amount spent:  1.50g + 2.50r = 16.50

relationship of games to rides: g = 2r

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of (2a - 13) ÷ b/15 when a = -2/5 and b = -8.25 is  \(25\frac{75}{825}\)

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(2a - 13) ÷ b/15

The value of (2a - 13) ÷ b/15 when a = -2/5 and b = -8.25.

= (2a - 13) ÷ b/15

= (2 x (-2/5) - 13) ÷ -8.25 / 15

= (-4/5 - 13 ) ÷ -8.25 / 15

= (-4 - 65) / 5 ÷ -8.25 / 15

= -69/5 ÷ -8.25/15

= -69/5 x -15/8.25

= 69 x 3 / 8.25

= 207 / 8.25

= 20700/825

We will write this in a mixed fraction.

= \(25\frac{75}{825}\)

Thus,

The value of (2a - 13) ÷ b/15 when a = -2/5 and b = -8.25 is  \(25\frac{75}{825}\)

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Answer:

A

Step-by-step explanation:

5.7(3) can be expressed as a fraction

(573 -57)/90

516/90

The missing fourth vertex needed to create a rectangle is (25, 3) option D.

Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.

Here, the width of one side of the rectangle;

⇒ +3 - (-6) = 9 unit                (left side y-coordinates)

Similarly the length of the rectangle;

⇒ 25 - (-15) = 40 unit             (up-side x-coordinates)

Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)

So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:

⇒ (25, -6+9) = (25, 3)

⇒ (-15+40, 3) = (25, 3)

Therefore, the missing fourth vertex is (25, 3)

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Answer:

4.6

Step-by-step explanation:

the first equation will be y=1.2x+4.6

the second will be y=0.8x+54.6

then i plugged the system of equations and that was where they met at :)

Answer:

for sure B

Step-by-step explanation:

The  fraction of the total books about mammals is 7/18

Let the total number of books in the school be 1 whole , ie 12/12( since we are dealing with fractions)

Number of science books =7/12

Number of mammals books =2/3 of science books

=2/3  x 7/12=14/36 = 7/18

Since the total books are 12/12 which is also =1 whole

Then the fraction of total books that are about mammals are 7/18 x 1 whole =7/18

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Using simple interest, it is found that:

12. The loan matured after 6 years.

13. The actual interest rate was of 12%.

Simple interest is used when there is a single compounding per time period.

The amount of interest after t years in is modeled by:

\(I(t) = Prt\)

In which:

Question 12:

The parameters are: P = 2000, r = 0.06, I = 720, hence:

\(I(t) = Prt\)

\(720 = 2000(0.06)t\)

\(t = \frac{720}{2000 \times 0.06}\)

\(t = 6\)

The loan matured after 6 years.

Question 13:

The parameters are: t = 5, P = 4000, r = 0.11.

Hence:

I = 4000 x 0.11 x 5 = 2200.

$200 more was charged in interest, hence I(5) = 2400, and:

\(I(t) = Prt\)

\(2400 = 4000(5)r\)

\(r = \frac{2400}{20000}\)

\(r = 0.12\)

The actual interest rate was of 12%.

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The graph of g(x) is on the image at the end, and the correct option for the transformation is B.

We define a horizontal dilation of scale factor k as:

g(x) = f(k*x)

if k > 1, we have a stretch.

if  0 < k < 1, we have a shink of scale factor 1/k

Here we have:

g(x) = f (5x) = 5x - 4

We can notice that k = 5, then we have a stretch, thus, the correct option is B.

The graph of function g(x) can be seen in the image at the end.,

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Answer:

n-7

Step-by-step explanation:

Seven fewer than a number means that you just subtract 7 from the original number.

Answer:

-63

Step-by-step explanation:

2 - make a positive e.g 1--1=2

Answer:

-63

Step-by-step explanation:

43 - __ = 106

We can subtract 43 from 106:

106 - 43 = 63

So, if we make 63 negative:

43 - (-63) = 106

Since you're subtracting with a negative, you'll flip the signs:

43 + 63 = 106.

So, the answer is -63.

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

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Multiplication of the given matrix is not possible by definition of matrix multiplication.

Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Expression for multiply,

⇒ [4, 0, -1, 2, -3, -1] x [0, 1, -3, 1]

Since, We can see that;

First matrix have order 1 x 6

And, Second matrix have order 1 x 4

We know that;

Matrix multiplication is possible when number of column in first matrix is same as number of rows in second matrix.

Hence, By given matrices we get;

Number of column in first matrix (6) ≠ number of rows in second matrix (1)

So, Multiplication of the given matrix is not possible by definition of matrix multiplication.

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Answer:

y=-1/2x+4

Step-by-step explanation:

y=mx+b

where m=slope and b=y-intercept

so

y=-1/2x+4

Answer:

See image

Step-by-step explanation:

The angles of ΔABC are ∠A = 40.86° , ∠B = 69.57°, and ∠C = 69.57° (rounded to two decimal places)

What are the angles of triangle?

To find the angles of  ΔABC, we can use the Law of Cosines and the Law of Sines. The Law of Cosines relates the sides and angles of a triangle, and states that for any triangle ABC with sides a, b, and c and angles A, B, and C opposite the respective sides:

c² = a² + b²- 2ab cos(C)

b² = a² + c² - 2ac cos(B)

a²= b² + c² - 2bc cos(A)

The Law of Sines relates the sides and angles of a triangle and states that:

sin(A)/a = sin(B)/b = sin(C)/c

Using the given values, we can solve for the angles:

a = 24 ft, b = 21 ft, c = 21 ft

c² = a² + b² - 2ab cos(C)

(21)² = (24)² + (21)² - 2(24)(21) cos(C)

441 = 1053 - 1008 cos(C)

cos(C) = (1053 - 441) / (2 * 24 * 21)

cos(C) = 0.3541667

C = \(cos^{-1(0.3541667)}\)

C = 69.57° (rounded to two decimal places)

b² = a² + c² - 2ac cos(B)

(21)² = (24)² + (21)² - 2(24)(21) cos(B)

441 = 1053 - 1008 cos(B)

cos(B) = (1053 - 441) / (2 * 24 * 21)

cos(B) = 0.3541667

B = \(cos^{-1(0.3541667)}\)

B = 69.57° (rounded to two decimal places)

A = 180 - B - C

A = 180 - 69.57 - 69.57

A = 40.86° (rounded to two decimal places)

Therefore, the angles of ΔABC are ∠A = 40.86°, ∠B = 69.57°, and ∠C = 69.57° (rounded to two decimal places).

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Answer:

Substitution means that we need to replace some of the variables by the given values.

1)  t = rs*(s + 1)      (if r=4 and s=5)

So we just need to replace r by 4 and s by 5 in the equation.

t = 4*5*(5 + 1) = 20*6 = 120

t = 120

2)  k = 6 - 5q/2g     (if q=3 and g=8)

We need to replace q by 3, and g by 8.

k = 6 - (5*3)/(2*8) = 6 - 15/16 = 5.167

k = 5.167

3) p = a + b - 2c   (if a = 2, b = -1, c = 5)

Replacing the variables we get:

p = 2 + (-1) - 2*(5)

p = 2 - 1 - 10 = -9

p = -9

4) I = 1/x - 2/y + z   (if x = 4, y = 6, and z = 2/3)

Replacing the variables we get:

I = 1/(4) - 2/(6) + (2/3)

I = 1/4 - 2/6 + 2/3 =  1/4 - 1/3 + 2/3

I = 1/4 + 1/3 = 3/12 + 4/12 = 7/12

I = 7/12 = 0.583

Answer: n2.4

Step-by-step explanation:

Average age=6⋅1+4⋅2+3⋅3+5⋅46+4+3+5=4318=2.38888...=2.4

The average age of a child attending this daycare is 2.4 years old.

Answer: 2a < 2b

Step-by-step explanation:

We are given a statement:

a < b and b < c, then 2a ____ 2b

We can use simple numbers that make the statement true.

Where,

a = 2

b = 3

c = 4

Now lets plug it in.

2 < 3 and 3 < 4, then 2(2) ____ 2(3)

and lets simplify:

2 < 3 and 3 < 4, then 4 ____ 6

We can see that 4 is less than 6,

so as a is less than b, 2a is less than 2b.

The only thing changing is the coefficient being multiplied by the variables a and b.

9514 1404 393

Answer:

  Marsha and Anthony

Step-by-step explanation:

Here a negative bank balance represents a debt. The larger the magnitude of the negative number, the more debt it represents. A positive bank balance corresponds to no debt.

Anthony and Marsha -- no debt . . . . smallest debt

Sara -- $90 in debt . . . . smallest non-zero debt

Sean -- $208 in debt

On those with non-zero debt, Sara has the smallest debt. Overall, Anthony and Marsha have the smallest debt: zero debt.

The amount of coverage that you will have on the contents of your home would be = $68,750

The total amount of money that was insured for the house = $125,000

The percentage of insurance that was left for the contents of the house = 55% of insurance.

That is;

= 55/100 × $125,000

= 6875000/100

= $68,750.

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\(\cfrac{3}{5}\div\cfrac{3}{7}\implies \cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{5}\cdot \cfrac{7}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{7}{5}\implies 1\frac{2}{5}\)