Exact value: 120 L
Approx. Value: 135 L

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 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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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

Answer:

the volume of the prism at the right is 56.7 cm³

Step-by-step explanation:

To find the volume of the prism at the right, we need to first find the area of the base, which is a triangle. The area of a triangle is given by A=21​bh

where A

is the area, b

is the base, and h

is the height of the triangle.

The base of the triangle is 4.2 cm and the height of the triangle is 3 cm. So, we can plug these values into the formula and get:

A=21​(4.2)(3)

A=6.3 cm2

Now that we have the area of the base, we can multiply it by the height of the prism, which is 9 cm. This will give us the volume of the prism:

V=B×h

V=6.3×9

V=56.7 cm3

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:

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.

If v = 4i and w = 2i + 5i, the angle between the vectors v and w is approximately 47.32 degrees.

To find the angle between two vectors, we can use the dot product formula, which relates the cosine of the angle between the vectors to their dot product and magnitudes. The dot product of two vectors v and w is given by:

v · w = |v| |w| cos(θ)

where |v| and |w| are the magnitudes of the vectors, and theta is the angle between them.

In this case, we are given the vectors v = 4i and w = 2i + 5j. We can compute their dot product as:

v · w = (4i) · (2i + 5j) = 8 + 0 = 8

We can also compute the magnitudes of the vectors as:

|v| = √((4² + 0²)) = 4

|w| = √((2² + 5²)) = √(29)

Substituting these values into the dot product formula, we get:

8 = 4 √(29) cos(θ)

Solving for cos(θ), we get:

cos(θ) = 2 / √(29)

Taking the inverse cosine of both sides, we get:

θ = cos⁻¹(2 / √(29)) = 47.32 degrees

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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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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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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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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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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 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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Answer:

(a) Christine will have to pay $400 in total interest.

(b) Christine will have to repay a total of $4400, including interest.

Step-by-step explanation:

(a) The interest charged on the loan is calculated as simple interest, which means that it is calculated as a percentage of the principal amount for each year. The interest rate is 5%, and the principal amount is $4000.

The total interest charged on the loan is:

Interest = Principal x Rate x Time

Interest = $4000 x 0.05 x 2

Interest = $400

Therefore, Christine will have to pay $400 in total interest.

(b) The total repayment amount is the sum of the principal and the interest charged on the loan.

Total repayment amount = Principal + Interest

Total repayment amount = $4000 + $400

Total repayment amount = $4400

Therefore, Christine will have to repay a total of $4400, including interest.

Answer:

Step-by-step explanation:

185

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 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 value of x in the similar triangle is 2 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, let's use the ratio to find the side length of x in the triangle.

Hence, the right angle triangle FHJ is similar to the right angle triangle GFJ. Using the similarity ratios,

GH / GF = GF / GJ

Hence,

GH = 9

GF = 3√11

GJ =  x + 9

9 / 3√11 = 3√11 / x + 9

cross multiply

9(x + 9) = (3√11)(3√11)

9x + 81 = 9(11)

9x + 81 = 99

9x = 99 - 81

9x = 18

divide both sides by 9

x = 18 / 9

x = 2

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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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[tex]\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ 2\log(6)-\log(9)\implies \log(6^2)-\log(9)\implies \log\left( \cfrac{6^2}{9} \right)\implies \log(4)[/tex]

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 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 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 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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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.