write the statement using absolute value notation:
the distance between x and 4 is 3

In fraction,

175% = 35/20

In mixed fraction,

175%  = [tex]1\frac{15}{20}[/tex]

In simplest form,

175%  = 1.75

The given percentage is,

175%

Now to write it into fraction,

Divide it by 100 we get

175% = 175/100

         = 35/20

Thus,

175% = 35/20

Now divide 35 by 20 to write it into mixed fraction

20  ) 35 ( 1

     - 20

     ___

        15

Hence in simple fraction

175%  = [tex]1\frac{15}{20}[/tex]

Now again proceed the division,

20  ) 35 ( 1.75

     - 20

     ___

        15  0

      - 14 0

     _____

           10 0

         - 10 0

           ____

               x

Hence in simplest form,

175%  = 1.75

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Answer:

Option C. (n + 1)/(n +2).

Step-by-step explanation:

The given sequence is 2/3, 3/4, 4/5, 5/6, 6/7.

and we have to find the general term of the given sequence.

Since first term of the sequence is 2/3

So numerator can be represented as (n + 1) and the denominator as (n + 2)

Therefore the general term will be (n + 1)/(n + 2)

Option C is the answer.

Answer:

Step-by-step explanation:

Yes

Answer:

its c on edge babes, yw <3

Step-by-step explanation:

Grant should remove approximately 7.33 gallons of water to obtain a 24% ammonia solution from the initial 16% ammonia solution.

Let x be the number of gallons of water that Grant needs to remove.

The equation you can use to represent this situation is based on the principle of maintaining the amount of ammonia in the solution:

The amount of ammonia in the original solution = The amount of ammonia in the final solution

The amount of ammonia in the original solution is the product of the initial concentration (16%) and the initial volume (22 gallons).

The amount of ammonia in the final solution is the product of the desired concentration (24%) and the final volume (22 - x gallons, where x is the amount of water removed).

So, the equation becomes:

0.16 * 22 = 0.24 * (22 - x)

Now, you can solve this equation for "x" (the number of gallons of water to remove) to achieve the desired concentration:

0.16 * 22 = 0.24 * (22 - x)

3.52 = 5.28 - 0.24x

Now, isolate the variable "x" by subtracting 3.52 from both sides:

0.24x = 5.28 - 3.52

0.24x = 1.76

Now, divide both sides by 0.24 to solve for "x":

x = 1.76 / 0.24

x ≈ 7.33

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The solution to the first problem is that Julia can watch up to 3.5 more hours of TV this week. The solution to the second problem is that you need to watch 30 more movies to earn a free movie pass. An example of an equation with infinitely many solutions is x = x.

19. To represent this scenario as an inequality, we let T be the amount of television Julia can still watch this week. Since she can watch no more than 5 hours per week and she has already watched 1.5 hours, we subtract 1.5 from 5. So we have the inequality T + 1.5 <= 5. Subtracting 1.5 from both sides gives us the inequality T <= 3.5. So Julia can watch 3.5 more hours of TV this week.

20. Let m be the number of movies you need to watch to get a free movie pass. Each movie gives you 2 advantage points and you currently have 40 points. The equation to model this situation is 2m + 40 = 100. Subtracting 40 from both sides gives 2m = 60. Dividing by 2 gives m = 30. So you need to watch 30 more movies to get a free movie pass.

21. An equation with infinitely many solutions is one where all the terms on one side can be made identical to all the terms on the other side. A simple example is x = x. For every value of x, the equation holds, meaning it has an infinite number of solutions.

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By applying the PEMDAS rule, the coefficient of x is equal to 7.

In Mathematics and Euclidean Geometry, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.

Based on the information provided, we have the following mathematical expression:

[tex]10x^2+8x-6x^3+4x^2+12x^3-x+20\\\\12x^3-6x^3+10x^2+4x^2+8x-x+20\\\\6x^3+14x^2+7x+20[/tex]

In this context, we can reasonably and logically deduce that the coefficient of x is 7.

Complete Question:

When this polynomial is simplified, what is the coefficient of x?

[tex]10x^2+8x-6x^3+4x^2+12x^3-x+20[/tex]

Final answer:

The number that, when multiplied by itself 4 times equals 81, is 3, as 3 to the fourth power (3^4) is 81.

Explanation:

To find what number multiplied by itself 4 times equals 81, we need to find the fourth root of 81. The fourth root is the same as raising a number to the 0.25 power. To calculate manually, we may take two square roots in succession, since the square root of a number squared is the original number. The square root of 81 is 9, and the square root of 9 is 3, thus the fourth root of 81 is 3. Indeed, 34 = 3 × 3 × 3 × 3 = 81.

In the diagram, the pair of angles ∠1 and ∠7 form a pair of alternate exterior angles.

Here is the reason:

Within the graph, ∠1 and ∠7 are on the inverse sides of transversal t and exterior lines a and b. Subsequently, they are a combination of substitute outside points.

The other answer choices are not correct since:

Final answer:

The question is about solving a system of equations to find the number of nickels and dimes in a piggy bank, given a total amount and quantity of coins. The solution involves using either the substitution or elimination method to find the values of the two variables representing nickels and dimes.

Explanation:

The question involves solving a system of equations to find the number of nickels and dimes in Keana’s piggy bank. Given the total amount is $4.30 and there are 59 coins in total, we can set up the following equations:

Let N represent the number of nickels and D the number of dimes.

The value equation is 0.05N + 0.10D = 4.30 or 5N + 10D = 430

The quantity equation is N + D = 59.

To solve these equations, we will use the substitution or elimination method. First, solve the quantity equation for one variable, for example, N = 59 - D. Then, substitute this expression for N in the value equation and solve for D. After finding D, substitute its value back into any of the original equations to find N. The sum of the digits in the number of nickels in Keana's bank is then found by adding together the digits of N.

we get,  5(59 - D) + 10D= 430

295 - 5D + 10D = 430

5D = 135 , Therefore D = 27

and N = 59 - D = 59 - 27 = 32.

To find the sum of the digits in the number of nickels (n=32), we add the digits 3+2=5

Therefore, the sum of the digits in the number of nickels in Keana’s bank is 5.

The correct option is:

4(3x² + 1)(x – 5)

To find the completely factored form of the expression 12x³ – 60x² + 4x – 20, we can first factor out the greatest common factor, which is 4.

4(3x³ – 15x² + x – 5)

Next, we can factor the quadratic expression 3x³ – 15x² + x – 5 by grouping:

4[3x²(x – 5) + 1(x – 5)]

4(3x² + 1)(x – 5)

Therefore, the completely factored form of 12x³ – 60x² + 4x – 20 is:

4(3x² + 1)(x – 5

So, the correct option is:

4(3x² + 1)(x – 5)

Answer:

Option 2 is correct.

Step-by-step explanation:

In the given graph x-axis represents the numbers and y-axis represent the frequency.

Number         Frequency              Cumulative frequency

100                        14                              14

200                       6                               20   (20<36)

300                       18                              38  (38>36)

400                       12                              50

500                       2                               52

600                       12                              64

700                       8                               72

Total                     72          

Mode is the number which has highest frequency. From the above table it is noticed that the highest frequency is 18 at 300. Therefore mode of the data is 300.

Sum of frequency is 72, which is an even number.

[tex]Median=\frac{n}{2}\text{th term}[/tex]

[tex]Median=\frac{72}{2}\text{th term}[/tex]

[tex]Median=36\text{th term}[/tex]

We have to find the number whose cumulative frequency is more than 36 but preceding cumulative frequency is less than 36.

Median of the graph is 300.

Since the value of median and mode are same, therefore

[tex]median=mode[/tex]

Option 2 is correct.

P = the principal

t = 25 years the time in years

r = 0.0525 or 5.25% annual rate

m = 1 compounding periods per year

i = 0.0525 or 5.25% interest rate per period

n = t*m = 25 total number of compounding periods

A = $75,000 future value

A = P(1 + i)^n

P(1 + i)^n = A

P(1 + 0.0525)^25 = 75000

by solving we find:

P = $20,869.34

Answer: The explicit rule for the sequence will be

[tex]a_n=15.5-2.5n[/tex]

Step-by-step explanation:

Since we have given that

[tex]13,10.5,8,5.5,3,0.5.....[/tex]

Here,

a = first term = 13

d = common difference

[tex]a_2-a_1 = 10.5-13=-2.5[/tex]

Since it forms an A.P. ;

[tex]a_n=a+(n-1)d\\\\a_n=13+(n-1)(-2.5)\\\\a_n=13-2.5n+2.5\\\\a_n=15.5-2.5n[/tex]

Hence, the explicit rule for the sequence will be

[tex]a_n=15.5-2.5n[/tex]

Answer:

[tex]a_n[/tex]  [tex]= 15.5-2.5n[/tex]

Step-by-step explanation:

we know that

The standard form of the equation of the line is

[tex] Ax + By = C [/tex]

we have

[tex] y = \frac{1}{6}x + 4 [/tex]

Multiply by [tex] 6 [/tex] both sides

[tex] 6y = x+24 [/tex]

Subtract x both sides

[tex] -x+6y = 24 [/tex]

therefore

the answer is

the equation of the line in standard form is equal to

[tex] -x+6y = 24 [/tex]

c The probability that event A occurs, given that event B occurs, is 83%.

To find the arithmetic means in the given sequence, we fill in the missing numbers using the average of the numbers before and after them. The arithmetic means in the given sequence are 160, 175, and 190.

To find the arithmetic means in the given sequence, we need to fill in the missing numbers.

Given sequence: 145, __, __, __, 205.

The arithmetic mean is the average of two numbers. We can find the missing numbers by taking the average of the numbers before and after them.

First, let's find the missing number between 145 and 205. The average of 145 and 205 is 175. So, the missing numbers are:

145, 175, 175, 175, 205.

To find the last missing number, we can take the average of the two numbers after it: (175 + 205) / 2 = 190.

So, the arithmetic means in the given sequence are 160, 175, and 190.

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The question requires solving various problems involving projectile motion, a physics topic, using kinematic equations and algebraic techniques to determine height, flight time, and impact speeds.

The question involves calculating various aspects of projectile motion, which is a topic in physics. In these problems, equations of motion are used to determine the maximum height, time of flight, and speed at impact of objects thrown or released from certain heights.

Example Calculations

Each of these problems requires an understanding of the kinematic equations for vertical projectile motion and the ability to apply algebraic and calculus techniques.

The final equation is vf = [tex]\frac{(m1v1 + m2v2)}{(m1 + m2)}[/tex]

The given equation represents the conservation of momentum, which can be written as :

m1v1 + m2v2 = (m1 + m2) vf

To solve for vf, follow these steps :

Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.

The Laplace transform of the given function is,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]

Laplace transformation is the transformation in the integral form which convert a function of a real variable to a complex variable.

Given information-

The function given in the problem is,

[tex]t^{2}\sin(2t)[/tex]

By the Laplace transform we can write that,

[tex]L[t^{2}\sin(2t)]=(-1)^2\dfrac{d^2}{ds^2}L(\sin 2t)\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\;\dfrac{d}{ds}\dfrac{2}{s^2+4}\\L[t^{2}\sin(2t)]=\dfrac{d}{ds}\left [\dfrac{-4s}{(s^2+4)^2} \right ]\\[/tex]

Solve further to get the final result,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{(s^2+4)^2(-4)+4s(s^2+4)\times2s}{(s^2+4)^2} \right ]\\[/tex]

Simplify the above equation as,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]

Hence, the Laplace transform of the given function is,

[tex]L[t^{2}\sin(2t)]=\left [\dfrac{4(3s^2-4)}{(s^2+4)^2} \right ]\\[/tex]

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