Daniel has 120 dollars in the bank. He is earning 3.5% compound interest each month. How much money will he have in the bank in one year?

The domain, range, x-intercept, or y-intercept of g(x) = f(x + 4) + 8. The features of g depend on the corresponding features of f.

Given the function g(x) = f(x + 4) + 8, let's examine its features:

Domain:

The domain of the function g will be the same as the domain of the function f, which depends on the restrictions or constraints of f.  However, it is important to note that shifting the input by 4 units (x + 4) does not inherently change the domain unless there are specific restrictions imposed by f.

Range:

Similar to the domain, the range of the function g will depend on the range of the function f.

x-intercept:

The x-intercept of a function is the point where the graph intersects the x-axis, meaning the y-coordinate is zero (y = 0). To find the x-intercept of g(x), we set g(x) = 0 and solve for x.

0 = f(x + 4) + 8

By subtracting 8 from both sides:

-8 = f(x + 4)

Since the exact value of x that makes f(x + 4) equal to -8. The x-intercept will depend on the behavior of f.

y-intercept:

The y-intercept of a function is the point where the graph intersects the y-axis, meaning the x-coordinate is zero (x = 0). To find the y-intercept of g(x), we substitute x = 0 into the function:

g(0) = f(0 + 4) + 8

g(0) = f(4) + 8

Again, the specific value of f(4) will depend on the behavior of the function f.

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La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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The best estimate of how much she will spend on movies and eating out is given as follows:

$162.

The best estimate of how much she will spend on movies and eating out is obtained applying the proportions in the context of the problem.

The percentages associated with movies and eating out are given as follows:

The amount that she has left is given as follows:

$300.

Hence the best estimate of how much she will spend on movies and eating out is obtained as follows:

(0.3 + 0.24) x 300 = 0.54 x 300 = $162.

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Answer: 2 ft.

Step-by-step explanation:
|-20| = 20, |-22| = 22
22 - 20 = 2

Answer:

A=11,13,17,19 B=12,18 None=10,14,16,19 Both=15

Step-by-step explanation:

11,13,15,17,19 are all odd so they go in A

12,15,18 Are all multiples of 3 so they go in B

10,14,16,19 Are not classified so they go outside of the diagram but inside E

15 is odd and a multiple of 3 so put it in the center and not with A and B

Answer:

A. This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.

Step-by-step explanation:

2x^3 + 4x^2 + 2x

First factor out the GCF

2x ( x^2 + 2x +1)

Then factor the inside by either using grouping or recognizing that this is a perfect square  a^2 + 2ab + b^2 = ( a+b) ^2

2x ( x^2 + 2 * x * 1 + 1^2)

2x ( x+1) ^2

Answer:

A. This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.

Step-by-step explanation:

2x^3+4x^2+2x

factor common term 2x

= 2x (x² + 2x + 1)

then factor x² + 2x + 1 to (x + 1)(x + 1)

= 2x (x + 1)(x + 1)

refining the equation

= 2x (x + 1)²

Answer:

$942.48

Step-by-step explanation:

Your area of the pool is correct, 278.54 m².

Now multiply the area of the pool by the cost of tile per square meter.

$12/m² × 278.54 m² = $942.48

Answer: x(15x)

Step-by-step explanation:

Answer:

12.5 inches

Step-by-step explanation:

We use proportion to calculate the scale drawing

27 feet = 5 inches, so

67.5 feet = more inches (we know that it would be bigger than 5 inches)

We then put the bigger number on top and crossmultiply by saying:

67.5 over 27 × 5

Your answer should come out as 12.5 inches.

The value of tan 2π/3 without calculator is -√3.

The value of tan 2π/3 without calculator is calculated by applying trig identities as follows;

the value of π = 180 degrees

So we can replace the value of π in the function with 180 degrees as follows;

tan ( 2π / 3) = tan (2 x 180 / 3)

tan (2 x 180 / 3) = tan (2 x 60)

tan (2 x 60) = tan (120)

tan (120) if found in the second quadrant, and the value will be negative since only sine is positive in the second quadrant.

tan (120) = - tan (180 - 120)

= - tan (60)

= -√3

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The expression can be rewritten by given term as;  3^15

We need to simplify the expression below:

(3^2 x 3^3)^3

Remember that we can add these exponents, so we get:

(9 x 9)^3 = 81^3

Then we can rewrite this as:

531441

Takin the product between the exponents we will get:

(3^5)^3

Thus, the solution is 3^15

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The number of possibilities for 8 of 37 servers to fail is 38608020

From the question, we have

Total number of servers, n = 37

Numbers to servers that fail, r = 8

The number of ways for 8 serves to fail is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 37 and r = 8

Substitute the known values in the above equation

Total = ³⁷C₈

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 37!/29!8!

Evaluate

Total = 38608020

Hence, the number of ways is 38608020

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Explanation

Parallel lines are two lines that always maintain the same distance and if they were extended towards infinity they would never touch. these are characterized by never touching while pointing in the same direction.

Answer:

0

Step-by-step explanation:

By the remainder theorem, this is the same as finding f(-1/2), which is equal to 0.

The most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year. Option B

Based on the given equation y = 195(1.10)^x, where x represents the number of years since 2005 and y represents the number of Salad Supreme restaurants, we can draw the following conclusions:

A. Salad Supreme had 110 restaurants in 2005: This conclusion is not supported by the given equation.

B. Salad Supreme is increasing the number of restaurants by 10% each year: This conclusion is supported by the equation.

C. Salad Supreme is increasing the number of restaurants by 195 each year: This conclusion is not supported by the equation.

D. Salad Supreme is increasing the number of restaurants by 110% each year: This conclusion is not supported by the equation. The growth factor of 1.10 (or 10%) indicates a 10% increase each year, not 110%.

Therefore, the most reasonable conclusion based on the given information is: Salad Supreme is increasing the number of restaurants by 10% each year.

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Answer:

50

Step-by-step explanation:

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

4x^2 - 12x + 9

Explanation:

(2x - 3)^2

(2x - 3)(2x - 3)

2x(2x - 3) -3 (2x - 3)

4x^2 - 6x - 3 (2x - 3)

4x^2 - 6x - 6x + 9

4x^2 - 12x + 9

Answer:

25 ; 35

Step-by-step explanation:

Given :

____________For __ Against __ No Opinion

21-40 years _________20 _______5

41-60 years ___20 ______________20

Over 60 years _55____ 15________ 5

Given that :

40% of 21-40 are against

Then :

40% = 20

To a obtain 100% of 21 - 40

40% = 20

100% = x

Cross multiply

0.4x = 20

x = 20/0.4

x = 50

100% of 21 - 40 = 50 people

For = 50 - (20 + 5)

= 50 - 25

= 25

2.)

Total who have no opinion :

(5 + 20 + 5) = 30

30 = 15%

Total number surveyed will be , x :

30 = 15%

x = 100%

Cross multiply :

0.15x = 30

x = 30/0.15

x = 200

Number of 41 - 60 against an increase, y:

(25 + 20 + 5 + 20 + y + 20 + 55 + 15 + 5) = 200

165 + y = 200

y = 200 - 165

y = 35

Answer: 72.36

Step-by-step explanation:

To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.

The initial amount of salt in the bowl was 59.16 grams.

Omar added 13.2 grams of salt to the bowl.

To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36

Therefore, the bowl contains 72.36 grams of salt now.

For the given logarithmic function, we have:

domain: (4, ∞).

range: (-∞, ∞).

For a function y = f(x), the domain is the set of the possible input values, and the range is the set of the possible output values.

Here we have the function:

f(x) = log(x - 4) - 3

First, we know that the range of logarithmic functions is the set of all real numbers.

We also know that the argument of logarithmic functions can only be larger than zero.

So the domain is defined by x > 4.

Then we have:

domain: (4, ∞).

range: (-∞, ∞).

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Answer:

here are the cordinates you need to mark :

Step-by-step explanation:

(1,15) : 1x,15y

(2,20) : 2x,20y

(3,35) : 3x,35y

(4,45) : 4x,45y

(5,70) : 5x,70y

Hope this helps :)

The distance from Maria's desk to Monique's desk is  \(2\sqrt{13}\)

Given,

In the question:

Maria's desk is located at (2, −1), and Monique's desk is located at (−2, 5).

To find the  distance from Maria's desk to Monique's desk.

Now, According to the question:

We know that :

The formula of Distance:

\(\sqrt{(x_{2} -x_{1} )^2+(y_{2}-y_{1} )^2}\)

Substitute (2, -1) and (-2, 5) into distance formula:

\(\sqrt{(-2-2)^2+(5+1)^2}\)

Calculate:

\(\sqrt{(-4)^2+(6)^2}\)

\(\sqrt{16+36}\\ \\\sqrt{52}\)

= \(2\sqrt{13}\)

Hence, The distance from Maria's desk to Monique's desk is  \(2\sqrt{13}\)

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Answer: square root of 52

Step-by-step explanation:

did the practice test

The correct option is that C. Carmen disagreed and said, "No, the answer is 72x^12"

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

It should be noted that when dividing exponents with same base, we will subtract the powers and when multiplying them, we will add the powers.

Here, the study team was discussing how to multiply 6x^10 by 12x^2. Therefore, this will be:

= 72 × x^(10 + 2)

= 72x^12.

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Answer:

5x^3-2

\(ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2\)

Explanation:

The two terms are \(5x^3\) and \(2\). Terms are separated by either a plus or minus.

We can write it as \(5x^3+(-2)\) which is an equivalent form. Here the two terms are \(5x^3\) and \(-2\). This is because adding a negative is the same as subtracting.

The coefficient is the number to the left of the variable.

The degree is the largest exponent, which helps form the leading term.

The third degree polynomial written above is considered a cubic binomial. "Cubic"  refers to the third degree, while "binomial" means there are 2 terms.

We can write something like \(5x^3\) as 5x^3 when it comes to computer settings.

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

Let's find the mean, median, and mode for each set of numbers:

Set: 40, 38, 29, 34, 37, 22, 15, 38

Mean: To find the mean, we sum up all the numbers and divide by the total count:

Mean = (40 + 38 + 29 + 34 + 37 + 22 + 15 + 38) / 8 = 273 / 8 = 34.125

Median: To find the median, we arrange the numbers in ascending order and find the middle value:

Arranged set: 15, 22, 29, 34, 37, 38, 38, 40

Median = (29 + 34) / 2 = 63 / 2 = 31.5

Mode: The mode is the number(s) that appear(s) most frequently in the set:

Mode = 38 (appears twice)

Set: 26, 32, 12, 18, 11, 14, 21, 12, 27

Mean: Mean = (26 + 32 + 12 + 18 + 11 + 14 + 21 + 12 + 27) / 9 = 173 / 9 ≈ 19.222

Median: Arranged set: 11, 12, 12, 14, 18, 21, 26, 27, 32

Median = 18

Mode: No mode (all numbers appear only once)

Set: 3, 3, 4, 7, 5, 7, 6, 7, 8, 8, 8, 9, 8, 10, 12, 9, 15, 15

Mean: Mean = (3 + 3 + 4 + 7 + 5 + 7 + 6 + 7 + 8 + 8 + 8 + 9 + 8 + 10 + 12 + 9 + 15 + 15) / 18 ≈ 8.611

Median: Arranged set: 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10, 12, 15, 15

Median = 8

Mode: Mode = 8 (appears 4 times)

Mean: 34.125, Median: 31.5, Mode: 38

Mean: 19.222, Median: 18, No mode

Mean: 8.611, Median: 8, Mode: 8

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Answer:

θ =  60 degrees

If needed in radians:

θ = π/3

Step-by-step explanation:

2cos(θ) = 1

We are solving for theta.

We can divide 2 on both sides.

2cos(θ) = 1

/2             /2

cos(θ) = 1/2

Now we can use Inverse of cosine to isolate theta.

θ \(= cos^-^1(1/2)\)

θ =  60 degrees

If needed in radians:

θ = π/3