12 pointsss !!
What is the domain for the piece of the function
represented by f(x) = x + 1?

Answer:

Step-by-step explanation:

18 * 10 - 8 * 4    (remember pemdas)

180 - 32 =

148 cm²

Answer:

Check the table.

Step-by-step explanation:

For edmentum.

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

The rectangular prism has a greater volume than the Cylinder.

Since the rectangular prism has a greater volume than the cylinder because the rectangular prism fully occupies the space within its boundaries, while the cylinder has empty space above and below it.

The cylinder is rounded shape leaves gaps between its curved surface and the boundaries of the rectangular prism.

Therefore, the rectangular prism could hold more volume than the cylinder as it utilizes the entire space within its shape efficiently.

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Answer:

The answer should be 55.3

Step-by-step explanation:

because 6.5 × 8.5 = 55.25. and that rounded is 55.3. :>> hope this helpss!

the answer is D

The figure can be divided into a rectangle and 2 triangles

Answer:

3 feet would cost 9 dollars

Step-by-step explanation:

The total cost of the 3 feet lace is $9 and this can be determined by using the arithmetic operations and the given data.

Given :

The following steps can be used in order to determine the total cost of the 3 feet lace:

Step 1 - The arithmetic operations can be used in order to determine the total cost of the 3 feet lace.

Step 2 - According to the given data, one foot of lace costs 3 dollars.

Step 3 - So, let the total cost of the 3 feet lace be 'a'. So, the value of 'a' can be calculated as:

\(a = 3\times 3\)

\(a = \$9\)

The total cost of the 3 feet lace is $9.

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Answer:

10

Step-by-step explanation:

Total pizza topped with pepperoni, sausage or pepperoni and sausage = 33

Number of pizzas with pepperoni = 29

Number of pizzas with pepperoni and sausage = 15

Pizza with pepperoni only = 29 - 15 = 14

Pizza with sausage only = 33 - 29 = 4

Pepperoni only than sausage only :

14 - 4 = 10

please see the explanation.

\(Thereare\ \ \ \ \ \left[\begin{array}{ccc}3.zero,&5\ one.&\\6\ tno,&5\ three.&\\7\ four,&4\ tire.&\end{array}\right]\)

\((c).\ the\ most\ common\ is\ 4\)

\([Be\ carepucs\)

I hope this helps you

:)

Floyd needs 33 matches to make a rectangle with a length of 20 matches.

To find out how many matches Floyd needs to make a rectangle with a length of 20 matches, we can observe a pattern in the given information.

From the given data, we can see that as the length of the rectangle increases by 4 matches, the number of matches used increases by 8. This means that for every additional 4 matches in length, Floyd requires 8 more matches.

Using this pattern, we can calculate the number of matches needed for a rectangle with a length of 20 matches.

First, we need to determine the number of 4-match increments in the length of 20 matches. We can do this by subtracting the starting length of 3 matches from the target length of 20 matches, which gives us 20 - 3 = 17.

Next, we divide the number of 4-match increments by 4 to determine how many times Floyd needs to add 4 matches. In this case, 17 ÷ 4 = 4 with a remainder of 1.

Since Floyd requires 8 matches for each 4-match increment, we multiply the number of increments by 8, which gives us 4 × 8 = 32 matches.

Finally, we add the remaining matches (1 match in this case) to the total, resulting in 32 + 1 = 33 matches needed to reach a length of 20 matches.

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Answer:

K What's the problem?

Step-by-step explanation:

The various answers to the question are:

a)

A number of extension lines needed to accommodate $90 in calls immediately:

Use the calculation for busy k servers.

\($$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$$\)

The probability that 2 servers are busy:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

Hence, two lines are insufficient.

The probability that 3 servers are busy:

Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$\)

Thus, three lines are insufficient.

The probability that 4 servers are busy:

Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$\)

Generally, the equation for is  mathematically given as

To answer 90% of calls instantly, the organization needs four extension lines.

b)

The probability that a call will receive a busy signal if four extensions lines are used is,

\(P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$\)

Therefore, the average number of extension lines that will be busy is Four

c)

In conclusion, the Percentage of busy calls for a phone system with two extensions:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.

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The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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Answer:

Its B

Step-by-step explanation:

The derivatives for this problem are given as follows:

a) \(f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}\)

b) \(f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}\).

The derivative of the sum is the sum of the derivatives.

In this problem, the function is:

\(f(x) = 4\cos{x} + \ln{(x + 1)}\)

Using a derivative table for the derivatives of the cosine and the ln, the derivative of the function is:

\(f^{\prime}(x) = (4\cos{x})^{\prime} + (\ln{(x + 1)})^{\prime}\)

\(f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}\)

What is the product rule?

The derivative of the product is given as follows:

\((f(x) \times g(x))^{\prime} = f^{\prime}(x)g(x) + g^{\prime}(x)f(x)\)

In this problem, we have that:

Hence the derivative is:

\(f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}\).

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It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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Answer:

Step-by-step explanation:

If we input 4 into g(x) = 3(x/2), we get:

g(4) = 3(4/2) = 3(2) = 6

Therefore, the output of g(4) is 6.

The equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

We know that the method to find the axis of the symmetry of the parabola is given by:

x = - b / 2 a

We have the general equation of the parabola as:

y = a x² + b x + c

We have the equation of the parabola as:

y = - 4 x² + 24 x - 35

Comparing from this equation, we get that:

a = - 4

b = 24

c = - 35

Now, substituting the values, we get that:

x = - 24 / 2 (- 4)

x = - 24 / - 8

x = 24 / 8

x = 3

Therefore, the equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.

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Answer:

See below, please!

Step-by-step explanation:

\(\frac{11(8+14)}{5}\). Use PEMDAS. Sum of 8 and 14 is 22, multiply that by 11, and then divide by 5. Your answer is 48.4.

Hope this helped!

Answer:

3(x)+2

Step-by-step explanation:

2(5)+6 = 16

3(5)+2 = 17

4(5)-5 = 15

5(5)-10 = 15

Answer:

slope = 4

points on graph = (0,0), (1,4)

Step-by-step explanation:

line going through quadrants 1 and 3. Straight line.

Answer:

---------------------------------

Real distance is 4.4 miles and on the map it is 8 inches.

The scale is:

or

The length of the AC is x^2  + 4x  - 12.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given :

In Parallelogram ABCD, diagonals AC and BD intersect at point E.

such that

AE = x^2 - 12,

CE = 4x

We know that the diagonal of a parallelogram bisect each other.

x^2 - 12 = 4x

x^2  - 4x  - 12= 0

(x-6)(x-2) = 0

Hence, the value of x = 6, 2.

AC = AE + CE = x^2  + 4x  - 12.

The length of the AC is x^2  + 4x  - 12.

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Step-by-step explanation:

3/4:2/5=3/4×5/2=15/8

3/8 ÷ 2/12=3/8 ×12/2=36/16=9/4

Comparing the three in their simplest form we have the smallest ratio as 3 to 4.

A mathematical phrase that compares two values is called a ratio. It is written as the product of the division of two different quantities. As in 2:1 or 2/1, ratios are frequently expressed as a fraction or with a colon.

Mathematicians employ ratios in many different contexts, such as arithmetic, algebra, and geometry. They are used to compare amounts, identify equivalent values, and resolve proportional and rate-of-change issues.

Convert the ratios in their simplest form:

3 to 4 can be simplified by dividing both terms by their greatest common factor, which is 1. Therefore, 3 to 4 is already in its simplest form.

10 to 12 can be simplified by dividing both terms by their greatest common factor, which is 2. So, 10 to 12 simplifies to 5 to 6.

2 to 1 is already in its simplest form.

Thus, comparing the three we have the smallest ratio as 3 to 4.

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Answer:

1 adult ticket and 7 student tickets were purchased

Step-by-step explanation:

let a represent number of adult tickets purchased and s the number of student tickets purchased, then

a + s = 8 ( subtract s from both sides )

a = 8 - s → (1) ← based on total tickets purchased

10.5a + 7.25s = 61.25 → (2) ← based on cost of tickets

substitute a = 8 - s into (2)

10.5(8 - s) + 7.25s = 61.25

84 - 10.5s + 7.25s = 61.25

84 - 3.25s = 61.25 ( subtract 84 from both sides )

- 3.25s = - 22.75 ( divide both sides by - 3.25 )

s = 7

substitute s = 7 into (1)

a = 8 - 7 = 1

that is 1 adult ticket and 7 student tickets were purchased

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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The function that represents an exponential function is the 4th graph and it can be modeled as y = aeᵇˣ.

The exponential functions are written in the form of y = aeᵇˣ, where the output y increases exponentially for the input x.

In the first graph, the graph is of a parabola, and the function which represents this kind of graph is a quadratic equation, therefore, this graph represents a parabolic equation. It is given by the function, y=ax²+bx+c or y=a(x-h)²+k

For the 4th graph, (Green), In the fourth graph, the graph represented is the graph of an exponential function, and it can be modeled as, y = aeᵇˣ

Hence, the function that represents an exponential function is the 4th graph and it can be modeled as y = aeᵇˣ.

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11. The exponential function that models the growth is as follows:

Where t is the time in hours. In this case, if we double the population we have to:

y = 5000 x 2 = 10000

Therefore, substitute y = 10000 in the function and solve for t:

Divide both sides by 5000:

Apply the laws of exponents:

Solve for t:

Answer: B. 4.7 hours