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The particular number from the given equation is 10.

Given that, 120 was divided by a particular number.

Let the particular number be x.

Here, 120/x

7 was taken from the quotient

120/x -7

The  difference was multiplied by 5.

5(120/x -7)

Giving a product of 25

5(120/x -7)=25

120/x -7=5

120/x=12

120=12x

x=120/12

x=10

Therefore, the particular number from the given equation is 10.

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The expression -2/5 . 12 is equivalent to the expression (a) 2 . (-12/5)

From the question, we have the following parameters that can be used in our computation:

-2/5 . 12

The above statement is a product expression that multiplies the values of -2/5 and 12

So, we have

-2/5 . 12 = -24/5

This is  because we are multiplying the factors

Next, we ave

(a) 2 . (-12/5) = -24/5

(a) -2/12 . (1/5) = -2/60

This means that the value of the expression is equivalent to (a) 2 . (-12/5)

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Answer:

-3/7

Step-by-step explanation:

-7/3 × ? = 1

-7/3 × -3/7 = 1

you see how both the three's and Steven's canceled out resulting in one as the answer. also it has to be a negative 3/7 since two negative signs in multiplication result in a positive sign.

The result of carrying out the addition operation on the given fractions, 9/-8 + -2/5, is -61/40.

From the question, we are to determine the sum of the given fractions

From the given information,

The fraction are 9/-8 and -2/5

We are to carry out the addition operation on the fractions

The addition operation can be carried out on the fractions as follows:

9/-8 + -2/5

First, find the LCM of 8 and 5

The LCM of 8 and 5 is 40

Then,

We can write that

(-45 + -16)/40

= (-45 - 16)/40

= (-61)/40

= -61/40

Hence, the result of adding the fractions is -61/40

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The exact values of x for x² - 8x - 5 = 0 are x = 4 + √21 or x = 4 - √21

To solve for x in the equation x² - 8x - 5 = 0, we can use the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

Using this formula, we can identify the values of a, b, and c in the equation x² - 8x - 5 = 0.

Here, a = 1, b = -8, and c = -5.

Substituting these values into the formula, we get:

x = (-(-8) ± √((-8)² - 4(1)(-5))) / 2(1)

Simplifying this expression, we get:

x = (8 ± √(64 + 20)) / 2

x = (8 ± √84) / 2

Now, we can simplify the square root of 84 as 2√21:

x = (8 ± 2√21) / 2

We can further simplify this expression by factoring out 2 from the numerator:

x = 2(4 ± √21) / 2

Canceling out the 2s, we get:

x = 4 ± √21

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Answer:

Balance Sheet:

Cash Assets ($)

Checking account: $2,000

Liabilities ($)

Student loans: $10,000

Credit card(s) balance(s): $500

Total Assets: $2,000

Total Liabilities: $10,500

Net Worth: Total Assets - Total Liabilities

Net Worth: $2,000 - $10,500

Net Worth: -$8,500

Therefore, Rosa's total assets are $2,000, her total liabilities are $10,500, and her net worth is -$8,500. This indicates that her liabilities exceed her assets, and she has a negative net worth.

Step-by-step explanation:

r = 4 m

d = 2 × r

d = 2 × 4

d = 8 m = s

Area of square = s × s

= 8 × 8

= 64 m²

Area of circle = πr²

= 3.14 × 4 × 4

= 50.24²

Area of colored region = A. Square - A. Circle

= 64 - 50.24

= 13.76 m²

The monthly income of the first person is $600.

Given that, the average monthly income of three persons is RS 3,600.

The income of the first is 1/5 of the combined income of the other two.

Here, Let income of the first be A, let income of the second be B and let Income of the third be C.

A+B+C=3600 -----(i)

Income for the first person = 1/5(B+C) -----(ii)

Substitute equation (ii) in equation (i), we get

(B+C)/5 +B+C =3600

B+C+5B+5C=3600×5

6B+6C=18000

6(B+C)=18000

B+C=3000 ------(iii)

Substitute (iii) in equation (i), we get

A=$600

Therefore, the monthly income of the first person is $600.

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Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.

An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.

Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.

Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.

Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.

In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.

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Answer:

Step-by-step explanation:

185

Answer:

Since the figures are similar, their corresponding side lengths are proportional.

Let x be the scale factor between the larger and smaller figures. Then, the volume of the larger figure is x^3 times the volume of the smaller figure.

We can set up an equation to solve for x:

2500 = x^3 * 160

Divide both sides by 160:

x^3 = 2500/160

x^3 = 15.625

Take the cube root of both sides:

x = 2.5

So, the scale factor between the larger and smaller figures is 2.5.

Since surface area is proportional to the square of the scale factor, we can set up another equation to solve for the surface area of the smaller figure:

S.A. of smaller figure / S.A. of larger figure = (scale factor of smaller figure)^2 / (scale factor of larger figure)^2

Solving for the surface area of the smaller figure:

S.A. of smaller figure / 1400 = 2.5^2 / 1^2

S.A. of smaller figure / 1400 = 6.25

S.A. of smaller figure = 6.25 * 1400

S.A. of smaller figure = 8750

Therefore, the surface area of the smaller figure is 8750 meters squared.

Step-by-step explanation:

The requreid match of each conic section has been shown below.

For a general quadratic polynomial of the form Az² +By+Cz+Dy+E=0

Ellipse: A and B have different signs.

Parabola: A = 0 or B = 0, but not both.

Circle: A and B have the same value, and this value is not zero.

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The mass of the sample before one hour is negative 7.

Given that:

Mass of the first sample, m₁ = 8x + 1

Mass of the second sample, m₂ = 2x - 5

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The number of hours when the mass of the samples is the same. Then we have

m₁ = m₂

8x + 1 = 2x - 5

6x = - 6

x = - 1

The mass of the sample before one hour is calculated as,

m₁ = 8(-1) + 1

m₁ = - 8 + 1

m₁ = - 7

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The graph of the rational function is attached in the solution.

Given is a rational function we need to graph it,

h(x) = [tex]\frac{2x}{x^2-2x+1}[/tex]

So,

Finding the coordinates by putting the values of x and finding the corresponding values of h(x), the plot them on the graph and join, the curve obtained will be the graph of the function.

Hence, the graph is attached.

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____________________________________

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Answer: 49.2 feet

Step-by-step explanation:

The given equation h = -16t^2 + 56t represents the height of a football kicked by Lauren as a function of time t in seconds.

In the context of the problem, the vertex of the parabolic function (-16t^2 + 56t) represents the point at which the football reaches its maximum height. The vertex of a parabola is the point where the function reaches its highest or lowest value, and it is given by the coordinates (h, t) in this case.

Interpreting the coordinates of the vertex in context, the h-coordinate represents the maximum height of the football, while the t-coordinate represents the time at which the football reaches that maximum height. So, if we determine the vertex of the given function, we can interpret the maximum height and the time it occurs.

The formula for the x-coordinate (t) of the vertex of a quadratic function in the form y = ax^2 + bx + c is given by t = -b/2a. Comparing this with the given equation, we can identify that a = -16 and b = 56.

Plugging in the values of a and b into the formula, we get:

t = -56 / (2 * -16)

t = -56 / -32

t = 1.75

So, the t-coordinate of the vertex is 1.75 seconds, which represents the time at which the football reaches its maximum height.

To find the h-coordinate of the vertex, we can substitute the value of t we found (1.75) into the given equation:

h = -16(1.75)^2 + 56(1.75)

h = -16(3.0625) + 98

h = -48.8 + 98

h = 49.2

So, the h-coordinate of the vertex is 49.2, which represents the maximum height of the football in feet.

In conclusion, the coordinates of the vertex (49.2, 1.75) in the given context represent the maximum height (49.2 feet) of the football and the time (1.75 seconds) at which the football reaches its maximum height after being kicked by Lauren.

The linear function is solved and the output is y = -3n + 8

Given data ,

Let the linear function be represented as A

Now , the value of A is

The table of inputs = { 1 , 2 , 3 , 4 , n }

The table of outputs = { 5 , 2 , -1 , -4 , a }

So , the first point is P ( 1 , 5 ) and second point is Q ( 2 , 2 )

Slope m = ( 5 - 2 ) / ( 1 - 2 )

m = -3

And , the equation of line is y - 5 = -3 ( x - 1 )

Adding 5 on both sides , we get

y = -3x + 8

Now , when the input is n , the output is

y = -3n + 8

Hence , the equation is y = -3n + 8

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The test Statistic and the critical value is 20.692 and 15.308 respectively.

Given that,

Null and Alternative hypothesis,

Null hypothesis: H₀ = 5.7

and Alternative hypothesis: H₁ < 5.7

∴

Test Statistic =

x² = (n-1)s²/σ², where s is the standard deviation = 4.9 and n sample size = 29,

= 28 × 4.9² / 5.7²

= 20.692

The critical value of the left tailed test at significance level 0.025 and df = 28,

x²(critical) = x²(1-α), (n-1) = x²(0.975, 28)

= 15.308

Hence, the test Statistic and the critical value is 20.692 and 15.308 respectively.

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The walkway is 11 feet 6 inches long.

To find the length of the walkway, we need to add the lengths of the two boards.

The first board is 6 feet 11 inches long, which can be written as 6 + 11/12 feet using the fact that there are 12 inches in a foot.

The second board is 5 feet 7 inches long, which can be written as 5 + 7/12 feet.

Now we can add the lengths of the two boards:

6 + 11/12 feet + 5 + 7/12 feet

= 11 + 6/12 feet

=11 + 1/2 feet

Therefore, the walkway is 11 feet 6 inches long.

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The estimated regression equation for these data is ŷ = 0.69x + 2.15

From the question, we have the following parameters that can be used in our computation:

Observation 1 2 3 4 5 6 7 8 9

xi 2 3 4 5 7 7 7 8 9

yi 4 5 4 6 4 6 9 6 11

Using a graphing tool, we have the following calculation summary

Regression Equation: ŷ = bX + a

Where

b = SP/SSX = 31.22/45.56 = 0.68537

a = MY - bMX = 6.11 - (0.69*5.78) = 2.15122

So, we have

ŷ = 0.68537x + 2.15122

Rounding the numerical values to two decimal places, we have

ŷ = 0.69x + 2.15

Hence, the estimated regression equation for these data is ŷ = 0.69x + 2.15

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Answer: C. Stephanie who is buying a new vehicle and has a FICO score of 780.

Step-by-step explanation: The Annual Percentage Rate (APR) is the interest rate charged on a loan.  Lenders consider various factors when determining the APR, including the borrower's credit score and the type of vehicle being financed.

In this scenario, Stephanie has a FICO score of 780, which indicates a strong credit history and responsible financial behavior.  Lenders generally view higher credit scores as an indication of lower credit risk.  As Stephanie is buying a new vehicle, lenders may consider this a lower-risk loan compared to financing a used vehicle.

Lower credit risk and the lower risk associated with financing a new vehicle are factors that could result in Stephanie being offered a lower APR compared to Tyler (option A), who is buying a used vehicle, and Daniel (option B), who has a lower FICO score of 600.

It's important to note that other factors, such as the lender's policies, market conditions, and individual loan terms, can also influence the APR offered to borrowers.

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The numerical expression 4√5 in the rational exponents will be [tex]4\cdot \left ( 5 \right)^\frac{1}{2}[/tex].

Given that:

Numerical expression: 4√5

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The expression is also written as,

[tex]\rightarrow 4 \sqrt5\\\\\rightarrow 4 \cdot \left ( 5 \right)^\frac{1}{2}[/tex]

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The LSA of prism is  157  square feet.

The TSA of prism is  169.738  square feet

We have,

Height = 10 feet

Area of base = 20 square feet

So, area of pentagonal base = 1/4 √5 (5 + 2√5) a²

20 = 1/4 √5 (5 + 2√5) a²

a = 3.14

Now, LSA of prism

= 5bh

= 5(3.14)(10)

= 157  square feet

and, TSA of prism

= 5 x 2(20)/ 15.7  + 157

= 169.738 square feet

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The number is given as follows:

x = -3.

The variable representing the number is given as follows:

x.

The product of 3 and the number is given as follows:

3x.

Twenty less than the product of 3 and the number is:

3x - 20.

The entire expression is equivalent to -29, hence the value of x, representing the number, is obtained as follows:

3x - 20 = -29

3x = -9

x = -3.

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Eli's statement is incorrect. Since $10 is greater than $5, we cannot round $110 to $100 when rounding to the nearest 10.  

To determine if Eli is correct, we need to add the amount of cash he has with the value of his gift card;      

$38 + $72 = $110

Since Eli says that he has about a $100 when he rounds to the nearest 10, we need to check whether $110 rounds to $100 or not. To round to the nearest 10, we look at the last digit of the number, which is 0 in this case. If the last digit is 5 or greater, we round up to the next multiple of 10. If the last digit is less than 5, we round down to the previous multiple of 10.

Since the last digit of $110 is 0, we don't need to round up or down. $110 is already a multiple of 10. Therefore, Eli is incorrect in saying that he has about a $100 when he rounds to the nearest 10. He actually has $110.  

Alternatively, we can check if $110 is within $5 of $100, which is the threshold for rounding to the nearest 10.

$110 - $100 = $10

Therefore, Eli's statement is incorrect.

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