Tell what number you would add to each side of the inequality to solve the inequality.
f-2 ≤ 3
Add ___ to each side of the inequality

Answer: D.34 units

Step-by-step explanation:

What's happening is that every subtraction can be written as "addition of the opposite."

18-5 = 18 + (-5)

One reason this is done in the work you showed is that they're trying to show why you distribute the negative and the 1 into the parentheses, why you multiply everything in the parentheses by "-1" and not just 1.

The other reason is to later to be able to move the individual terms around, so you'll be able to combine like terms.

When you move terms around, the sign has to stay attached to the term, so writing all the subtractions as addition helps keep the sign attached.

Answer:

6x+10-3x=55

6x-3x=10+55

3x=65

65÷3=21.6

Answer:

D

Step-by-step explanation:

Break it into different shapes and find the areas. add the areas for the answer: D

9x4=36

9x20=180

9x2=18

36+180+18=234

Answer:

d

Step-by-step explanation:

((4*9)/2)+(4*9)+(9*20)

The first scenario described is an example of a retrospective cohort study.  The second scenario suggests a retrospective cohort study as well. The third scenario represents a cross-sectional study, where researchers conduct a survey among high school students to assess the prevalence of obesity and diabetes.

1. In the first scenario, a retrospective cohort study is conducted by tracking individuals over a 20-year period. The study begins in 1960 and collects data on cigar smoking practices. After 20 years, the participants are followed up to determine if they developed any cancers. This type of study design allows researchers to examine the long-term effects of smoking Cuban cigars.

2. The second scenario involves a retrospective cohort study as well. The objective is to study the long-term neurological effects of a discontinued anesthetic agent. The researchers identify patients who received the drug before it was discontinued and then assess the occurrence of subsequent neurological disorders. This study design allows for the examination of the relationship between exposure to the anesthetic agent and the development of neurological disorders.

3. The third scenario represents a cross-sectional study. Researchers aim to assess the prevalence of obesity and diabetes among high school students during their junior year. They conduct a survey to gather information on the students' current weight, diabetes status, and other relevant factors. A cross-sectional study provides a snapshot of the population at a specific point in time, allowing researchers to examine the prevalence of certain conditions or characteristics.

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Answer: ($2100+96d) + ($2755+116d)

               = $4855+212d

Answer:

The standard form of a circle's equation is (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius.

Step-by-step explanation:

Answer:

12 toppings

Step-by-step explanation:

To do this, we need to write an equation for each place, and then, equal both equations to solve for this.

Let's call "y" the price of the pizza, and "x" the number of toppings.

At Vincents, pizza costs 6.75 + 0.75 for each topping, so the equation here would be:

y = 6.75 + 0.75x  (1)

Now, at italian pizza, a pizza costs 6.15 + 0.80 per topping, so the equation:

y = 6.15 + 0.80x  (2)

Now, we don't need to know the actual price of the pizza, we only want to know how many toppings we need to add on both places, so the pizza has the same price. We have both equations, it's time to equal both of them:

Equalling (1) and (2) we have:

6.75 + 0.75x = 6.15 + 0.80x

Now, let's solve for x:

6.75 - 6.15 = 0.80x - 0.75x

0.6 = 0.05x

x = 0.6 / 0.05

x = 12

So the number of toppings to include in the pizza so the price is the same for both places, will have to be 12 toppings.

Answer:

12 toppings and the prize will be the same.

Step-by-step explanation:

Let

number of toppings = a

Medium pizza at Vincent's

cost  = 6.75 + 0.75a

Medium pizza at Original Italian Pizza

cost  = 6.15 + 0.80a

For the cost to be the same

6.75 + 0.75a = 6.15 + 0.80a

collect like terms

6.75 - 6.15 = 0.80a - 0.75a

0.6  = 0.05a

divide both sides by 0.05

a = 0.6/0.05

a = 12  

12 toppings and the prize will be the same.

Compound amount = $8867.39

compound interest = $1867.39

EXPLANATION

Given:

Principal(p) = $7000 Rate(r) = 0.12 Time(t) = 2 n= 4

We can calculate the compound amount(A) using the formula below:

Substitute the values and evaluate.

Hence, the compound amount = $8867.39

We proceed to find the compound interest.

A = P + I

⇒ I = A - P

= 8867.39 - 7000

=1867. 39

Therefore, the compound interest = $1867.39

In both scenarios, the total cost remains the same at $286.

Therefore, Max doesn't actually save any money by changing the scanning order.

Here, we have to calculate how much money Max saves by having the cashier scan the more expensive items first, we need to compare the two scenarios:

the original scanning order and the modified scanning order suggested by Max.

Original Scanning Order:

Shoe ($45) -> Jacket ($66) -> DVD player ($175)

Total cost = $45 + $66 + $175

                = $286

Modified Scanning Order:

DVD player ($175) -> Jacket ($66) -> Shoe ($45)

Total cost = $175 + $66 + $45

                = $286

In both scenarios, the total cost remains the same at $286.

Therefore, Max doesn't actually save any money by changing the scanning order.

The total amount paid remains unchanged regardless of the order in which the items are scanned.

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The statements that accurately compare the domain and range of the functions are: The domain of all three functions is all real numbers, The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.

The domain of a function refers to all the possible input values that make the function defined. For the quadratic function f(x) = 3x², there are no values of x that make the function undefined, so the domain of f(x) is all real numbers. To find the range of f(x), we can calculate the vertex of the parabola, which is (0,0). The range of f(x) is all real numbers greater than or equal to zero.

For the quadratic function f(x) = 3x², we can determine the vertex using the formula:

h = -b/2a

In this case, a = 3 and b = 0, so:

h = -0/2(3) = 0/6 = 0

The x-coordinate of the vertex is 0.

To find the y-coordinate, we evaluate the function at the vertex:

f(0) = 3(0)² = 0

So the vertex of the parabola is (0,0).

Since the coefficient of x² is positive, the parabola opens upwards, and the minimum value of the function occurs at the vertex. Therefore, the range of f(x) is all real numbers greater than or equal to zero.

For the rational function g(x) = 1/3x, the function is undefined when the denominator is equal to zero. Thus, we solve for the value(s) of x that make the denominator zero:

3x = 0

Dividing both sides by 3, we get:

x = 0

Therefore, the domain of g(x) is all real numbers except zero. The range of g(x) is all real numbers except zero, since the function cannot equal zero.

For the linear function h(x) = 3x, there are no values of x that make the function undefined. Thus, the domain of h(x) is all real numbers. The range of h(x) is also all real numbers, since the function is a straight line that passes through the origin and extend infinitely in both directions.

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Any graph that has a horizontal line at a period stays constant for a while.

In all cases, the function is moving right. If the function is moving right but the vertical axis remains constant, forming an horizontal line, the function is constant for that period.

Hence the graph in this problem shows that the height stays constant for a while because it has a horizontal line.

(the problem is incomplete as the graph is not given, but the explanation for a constant function is always this).

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18 ft is equal to 6 yards. A yard is one linear yards. "Yd" is the yard symbol. It is equivalent to three feet or 36 inches.

The majority of cloth is now sold by the linear yard. A linear yard is 36" long, with a width that varies depending on the cloth roll. Only the length of the material is considered when measuring in linear yards. To calculate square yards, multiply the length and width in yards. In a yard, there are 36 inches. The length of a yard of fabric is 36 inches. Calculating the amount of fabric required for a sewing job is a little more difficult than that, though. A yard of fabric is always one yard long, however the breadth varies depending on where you get it. Between 33 and 44 inches are the typical widths.

Add the conversion factor "0.33333333333278" to the number in feet.

So, 18 feet

= 18 × 0.33333333333278

= 5.99999999999 yards.

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The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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Step-by-step explanation:

6×(2.5)+1.5

15+1.5

16.5

or

f(x)= 6x+1.5

f(2.5)= 6(2.5)+15

f(2.5)=16.5

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To calculate the cost of each tile, we need to first determine the volume of each tile. The length and width of the tile are given as 16 inches, and the thickness is given as 1/4 inches, which can be converted to 0.25 inches. Therefore, the volume of each tile is 16 x 16 x 0.25 = 64 cubic inches.

Next, we need to determine the weight of gold in each tile. Since the density of gold is 11.17 ounces per cubic inch, the weight of gold in each tile is 64 x 11.17 = 715.68 ounces.

Finally, we can calculate the cost of each tile by multiplying the weight of gold by the price of gold per ounce. The price of gold is given as $1,303.80 per ounce, so the cost of each tile is 715.68 x $1,303.80 = $933,526.78. Rounded to the nearest dollar, each tile will cost $933,527.

In summary, each square tile made of solid gold and measuring 16 inches long and 1/4 inches thick will cost approximately $933,527. This cost is based on the density of gold, which is 11.17 ounces per cubic inch, and the price of gold, which is $1,303.80 per ounce.

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Answer:

48(42)-344=4n

1672=4n

n=418

Hope This Helps!!!

The ‘println’ statement is incomplete and missing the object reference. Additionally, the ‘a’ and ‘b’ variables are private and package-private respectively, making them inaccessible in the subclass.


The code attempts to create a final class named “first” with private and package-private variables ‘a’ and ‘b’. The constructor initializes these variables. However, in the subclass “second,” there is an incomplete ‘println’ statement missing the object reference and concatenation operator.

Moreover, the subclass is trying to access the private ‘a’ variable from the superclass, which is not allowed. Additionally, the package-private ‘b’ variable is inaccessible in the subclass because it is defined in a different package. To fix the errors, the 'println' statement should be corrected, and the accessibility modifiers of the variables should be adjusted accordingly.

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Decoding Forecast starting at 17:00Z:

Wind:

24014G23KT

Visibility:

5 statute miles

Weather:

Light rain showers

Clouds:

Overcast at 1500 feet

Temporary condition unknown.

The full decoded METAR report is:

Location:

KJAX (Jacksonville International Airport)

Date/Time:

10th at 23:20Z

Wind:

00000KT

Visibility:

More than 6 statute miles

Clouds:

Scattered at 3500 feet

Forecast starting at 11:00Z:

Wind:

00000KT

Visibility:

5 statute miles

Weather:

Mist

Clouds:

Broken at 1000 feet, Broken at 2000 feet

Forecast starting at 06:00Z:

Wind:

16003KT

Visibility:

2 statute miles

Weather:

Mist

Clouds:

Broken at 500 feet, Overcast at 1000 feet

Temporary condition between 08:00Z and 12:00Z:

Visibility:

1 statute mile

Weather:

Mist

Clouds:

Overcast at 300 feet

Forecast starting at 14:00Z:

Wind:

20010G18KT

Visibility:

More than 6 statute miles

Weather:

Showers in vicinity

Clouds:

Broken at 1500 feet, Overcast at 2500 feet

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If the Pascal's triangle row entries are 1,n,...,n,1 and the average is 2048 , then the value of n is  15  .

Let the number of entries in the row is = n + 1  .

Since the average of the entries is 2048,

So , the sum of the entries is = 2048 × (n + 1).

We know that the sum of the entries in a row of Pascal's Triangle is equal to 2ⁿ, so we have the equation as :

⇒ 2048 × (n + 1) = 2ⁿ ;

On simplifying ,

we get ;

⇒ n = -0.99975 and n = 15 .

Since the "n" cannot be in negative .So , n = 15   .

Therefore , the value of n is the  pascal's triangle is 15 .

The given question is incomplete , the complete question is

The entries in a certain row of Pascal's Triangle are 1,n,...,n,1 the average of the entries in this row is 2048. find  n  .

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Manuel deposits $4,000 at the beginning of each year for 15 years into a fund that earns 10% annually. Manuel awaits 11 more years from the time his 15th payment was made, and uses the accumulated amount in the fund to buy a perpetuity that pays an amount P every year, subject to 5% annual interest, with the first payment one year from the time of purchase. P is $6,602.38.

To find the amount P that Manuel will receive annually from the perpetuity, we need to calculate the accumulated amount in the fund after 15 years of deposits.

Given: Deposit amount per year (D) = $4,000 Number of years of deposits (n) = 15 Annual interest rate (r) = 10%

Using the formula for the future value of an ordinary annuity:

Future Value = D * ((1 + r)^n - 1) / r

Future Value = $4,000 * ((1 + 10%)^15 - 1) / 10% = $4,000 * (1.10^15 - 1) / 0.10

Now, we have the accumulated amount in the fund after 15 years. Manuel waits for 11 more years, and during this time, the accumulated amount grows at an annual interest rate of 5%. This accumulated amount will provide the perpetuity payment P.

Using the formula for the present value of a perpetuity:

Present Value = P / r

Present Value = Future Value * (1 + r)^-n

P / 5% = (Future Value) * (1 + 5%)^-11

Substituting the calculated Future Value:

P / 5% = ($4,000 * (1.10^15 - 1) / 0.10) * (1 + 5%)^-11

Now, we can solve for P:

P = (5% * $4,000 * (1.10^15 - 1) / 0.10) * (1 + 5%)^-11

P ≈ $6,602.38

Therefore, the amount P that Manuel will receive annually from the perpetuity is approximately $6,602.38.

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To find the response of the first-order system excited by the linear FM signal, follow these steps: use the difference equation, provide an initial condition for y[0], and compute y[n] for each value of n in the given range.

The response of a first-order system when excited by a linear FM signal. Here's a step-by-step explanation:
1. The first-order system is described by the difference equation y[n] = 0.8y[n-1] + 0.2x[n].
2. The system is excited by a linear FM signal x[n] = cos(2π(b/fs/n)n^2/3), where 0 ≤ n ≤ N.
To find the response of the first-order system to this input signal, we need to compute y[n] for each value of n from 0 to N.
3. Since y[n] depends on y[n-1], we need an initial condition for y[0]. If not given, we'll assume y[0] = 0.
4. Now, for each value of n from 1 to N, calculate y[n] using the difference equation and the input signal x[n]:
  y[n] = 0.8y[n-1] + 0.2*cos(2π(b/fs/n)n^2/3)
5. Repeat this calculation for all values of n within the specified range (0 ≤ n ≤ N) to obtain the system response y[n].
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Answer:

B)  73°

Step-by-step explanation:

m∠NMP = 180 -168 = 12

Sum of interior angles of ΔNMP = 180

m∠P = 180 - 95 - 12 = 73

The first four terms of an arithmetic sequence are 5, 9, 13, 17 and the nth term formula of this sequence is 4n+1.

To find the expression for the (n-1)th term, we need to substitute (n-1) into the nth term formula.

So, the nth term formula is 4n+1.

Substituting (n-1) for n, we get:

4(n-1)+1 = 4n-3

Therefore, the expression for the (n-1)th term of an arithmetic sequence is 4n-3.

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Factoring the sum or difference of cubes involves using specific formulas to simplify expressions.

The sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2), allow us to break down these expressions into more manageable factors.

To factor the sum or difference of cubes, you can use the following formulas:

Sum of Cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Cube difference: (a - b)(a - b)(a - b)(a - b)(a - b)

Sum of Cubes:

The sum of cubes formula states that the sum of two cubes, a^3 + b^3, can be factored into (a + b) multiplied by the quadratic expression a^2 - ab + b^2.

For example, let's factorize 8x^3 + 27:

We can identify a = 2x and b = 3, so using the sum of cubes formula:

8x^3 + 27 = (2x + 3)(4x^2 - 6x + 9)

Difference of Cubes:

The difference of cubes formula states that the difference between two cubes, a^3 - b^3, can be factored into (a - b) multiplied by the quadratic expression a^2 + ab + b^2.

For example, let's factorize 64y^3 - 125:

We can identify a = 4y and b = 5, so using the difference of cubes formula:

64y^3 - 125 = (4y - 5)(16y^2 + 20y + 25)

Factoring the sum or difference of cubes involves using specific formulas to simplify expressions. The sum of cubes formula, a^3 + b^3 = (a + b)(a^2 - ab + b^2), and the difference of cubes formula, a^3 - b^3 = (a - b)(a^2 + ab + b^2), allow us to break down these expressions into more manageable factors. Factoring such expressions can be useful in various algebraic calculations and simplifications.

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This is an exercise in solving problems involving quadratic functions, which is an important topic in mathematics and is used in many fields, including physics, engineering, and economics. In general, one seeks to find the critical points of a quadratic function, such as the vertex or the roots, to understand the behavior of the function in different situations.

To find the vertex of a quadratic function, we use the canonical form of the quadratic equation, which is f(x) = a(x - h)^2 + k, where (h, k) are the coordinates of the vertex. It is also possible to find the vertex using the formula -b/2a, which is derived from the general form of the quadratic equation.

In addition to finding the vertex, it is also common to find the roots of a quadratic function, which are the values of x where the function vanishes. This can be done using the general formula of the quadratic equation or by completing the square.

f(x) = 2(x + 8)² - 2

First we write the quadratic function in standard form.

Using (a + b)² = a² + 2ab + b², expand the expression.

   f(x) = 2(x² + 16x + 64) - 2

We distribute the 2 to the terms that are between the parentheses.

  f(x) = 2x² + 32x + 128 - 2 ⇒ subtract 2

  f(x) = 2x² + 32x + 126

Now we identify the coefficients a and b of the quadratic function.

a = 2, b = 32

We find the x-coordinate of the vertex by substituting a = 2 and b = 2 into x = - (b)/(2a).

     x = - (32)/(2 × 2) = - 32/4 = -8

     x = -8

Find the y-coordinate of the vertex by evaluating the function for x = -8.

   f(x) = 2(x + 8)² - 2, x = -8

  We substitute x = -8 in the equation.

    f(-8) = 2(-8 + 8)² - 2

The sum of two opposite numbers is equal to 0. The Inverse Property of Addition states that the sum of two opposite numbers is equal to 0.

f(-8) = 2 x 0² - 2

0 raised any positive power is equal to 0. We remember that a power represents a repeated multiplication of the base.

Therefore, the power 0² means that 0 is multiplied by itself 2 times, resulting in 0.

f(-8) = 2 × 0 - 2

Any expression multiplied by 0 equals 0.

f(-8) = 0 - 2

Removing the 0 does not change the value, so we remove it from the expression.

  f(-8) = -2

The vertex of the graph of the quadratic function is at (-8, -2).

  (-8,-2)

The vertex of the quadratic function f(x) = 28(x + 8)² - 2 is (-8,-2), the last option being correct.

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