Find limit for given function.

Answer:  A=a2

Here are the steps to finding the square root using factoring:

Find the factors. Factors are the numbers you multiply to find the total under the square root symbol. ...

Separate the factors into their own square roots. ...

Solve for the individual squares. ...

Finish solving the equation.

The correct answers are:

• 3642yd² explanation on bottom.

The given options represent the possible answers for the area of the square. To find the correct answer, we need to look for the option that matches the given area. The area is given in square units of yards, which means the answer will also be in square yards. Out of the given options, only "3642yd²" matches the given area of 3642 square yards. Therefore, the correct answer is "3642yd²".

• Another way to get the answer.

The given image shows a square with four sides equal in length. The area of a square is equal to the product of its sides. Among the given options, the area of the square is either 7242 yd², 36 yd², 72 yd², or 3642 yd². To determine the area of the square, we need to identify the correct measurement of its side, which is equal to 6 yd. We can then use the formula A = s², where A is the area and s is the length of each side, to find that the area of the square is 36 yd².

The requried, difference in monthly pension payments is the second offer pays $64.50 more per month. Option B is correct.

To calculate the monthly pension payment for the second offer, we need to know the number of years of service the welder plans to work at each company. Let's assume the welder plans to work for 18 years at each company (the same number of years used for the first offer).

For the first offer, the monthly pension payment is given as $1,893.

For the second offer, the pension rate is 1.5% per year of service, so the total pension rate after 18 years of service is:

1.5% * 18 = 27%

The monthly pension payment is calculated as a percentage of the average annual wage, which is $87,000 for the second offer. So the monthly pension payment for the second offer is:

27% * ($87,000 / 12) = $1,956.25

The difference in monthly pension payments is:

$1,956.25 - $1,893 = $64.50

So the answer is that the first offer pays $63.25 less per month than the second offer. Rounded to the nearest 10 cents, the answer is that the second offer pays $64.50 more per month than the first offer.

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The distance between the points (-3, -3) and (-6, 1) is 5 units

We know that the distance formula between two points (x₁, y₁) and (x₂, y₂) is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

We need to find the distance between the points (-3, -3) and (-6, 1)

Let us assume that (x₁, y₁) = (-3, -3)

and (x₂, y₂) = (-6, 1)

Using above distance formula, the distance between the points (-6,7) and (-1,1) would be,

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(1 - (-3))² + ((-6) - (-3))²]

d = √[(1 + 3)² + (-6 + 3)²]

d = √[(4)² + (-3)²]

d = √[16 + 9]

d = √(25)

d = 5 units

This is the required distance.

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Answer:

Let's represent the width of the flag with 'w'. Then, according to the problem, the length would be 'w + 90'.

We know that the perimeter of a rectangle is given by:

P = 2(length + width)

Substituting the values from the problem, we get:

500 = 2(w + w + 90)

Simplifying, we get:

250 = 2w + 90

2w = 160

w = 80

So, the width of the flag is 80 feet.

And the length of the flag would be:

w + 90 = 80 + 90 = 170 feet.

In the given problem, solving using the given formula, after ten years, the value of the annuity in which you put $10,000 at a 4% annual interest rate is roughly $14,802.42.

The given formula to solve the problem is fv=P(1+r)n.

Where:

P = $10,000 (the principal)

r = 0.04 (the annual interest rate)

n = 10 (the number of years)

Furthermore, plugging in the values into the formula, we have:

fv = P(1+r)^n

= $10,000(1+0.04)^10

= $14,802.42 (rounded to two decimal places)

In conclusion, the ten-year value of a annuity of $10,000 with a 4% annual interest rate will approximately be $14,802.42.

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Answer:4/3

Step-by-step explanation:48/36

The slope of the least-squares regression line for math is 0.68 and for English is 0.68. Then the correct option is A.

Given that:

English (x)    450    470   510   520   540   570   590   620   670   680

Math (y)        490    480  500   580  550   540    610    590  620   650

The slope of the least-squares regression line represents the rate of change between two variables. To find the slope of the line, we need to use linear regression analysis.

The slope of the line turns out to be 0.68, which means for each additional point in the English score, the math score is predicted to increase by 0.68 points.

Therefore, the correct answer is:

0.68, which means for each additional point in the English score, the math score is predicted to increase by 0.68 points.

Thus, the correct option is A.

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Step-by-step explanation:

(212900 + 213500) ÷ 2

426400/2 = 213200

The number exactly halfway between 212,900 and 213,500 is 213,200.

Finding the number that is halfway between two given values is a fundamental concept in mathematics, and it involves a simple calculation using basic arithmetic.

To find the number that is exactly halfway between two values, you need to add the two values together and then divide the sum by 2.

In this case, 212,900 + 213,500 = 426,400.

Dividing 426,400 by 2 gives us 213,200, which is the number exactly halfway between the two given values.

Therefore, 213,200 is the answer to the question.

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Answer: 10 feet wide

Step-by-step explanation:

If there is 50 feet long on either side, then the perimeter of the length is 100 feet.  That would mean that there is 20 feet left. If there is 20 feet for 2 sides, we would divide that in half. 20 / 2 = 10.

So, for all of the tiles to be used, the pool would have to be 10 feet wide.

The condition of equal variability of residuals across all values of the predictor variable (homoscedasticity) does not appear to be satisfied.

Based on the residual plot, the condition for inference for the slope of the regression line that does not appear to be satisfied is the assumption of constant variance (also known as homoscedasticity).

This condition states that the variability of the residuals should be roughly the same at all levels of the predictor variable (in this case, the number of people in the dining party).
If the residual plot shows a pattern, such as a widening or narrowing of the points, it indicates that the constant variance assumption might not hold.

This could affect the accuracy of the linear regression analysis and the validity of the conclusions drawn from it.

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The value k of the exponential growth rate will be 0.045.

Given that:

$228 in 1975

$472 in 1986

Let 'x' be the number of years and 'y' be the selling price. Then the equations are given as,

[tex]\rm 288 = P_o \times e^{k *1975} \ \ \ \ \ \ ...(1)\\\\\rm 472 = P_o \times e^{k *1986} \ \ \ \ \ \ ...(2)[/tex]

From equations (1) and (2), then

[tex]e^{k(1986 - 1975)} = \dfrac{472}{288}\\\\e^{k(1986 - 1975)} = 1.63889[/tex]

Take log on both sides, then

k x (11) = ln 1.63889

k = 0.494/11

k = 0.045

The value k of the exponential growth rate will be 0.045.

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Answer:

Step-by-step explanation:

The maximum and minimum values of f(x, y, z) subject to the given constraint can be found by substituting the values of x, y and z in the function f(x, y, z).

What is function?
Function is an operation that takes one or more inputs and produces an output, or a set of outputs, depending on the type of function. Functions are commonly used in mathematics and computer science, and are essential for solving a wide range of problems.

We are given a function f(x, y, z) = xyz and the constraint x2 + 2y2 + 3z2 = 96. To find the maximum and minimum values of f(x, y, z) subject to the given constraint, we can use the method of Lagrange multipliers.

Let λ be the Lagrange multiplier. Then, the Lagrange function is given by:

L(x, y, z, λ) = xyz + λ (x2 + 2y2 + 3z2 - 96)

We will now calculate the partial derivatives of L with respect to x, y, z and λ.

∂L/∂x = yz + 2xλ = 0
∂L/∂y = xz + 4yλ = 0
∂L/∂z = xy + 6zλ = 0
∂L/∂λ = x2 + 2y2 + 3z2 - 96 = 0

Solving the above equations, we get:
2xλ = -yz
4yλ = -xz
6zλ = -xy
x2 + 2y2 + 3z2 = 96

Substituting the values of λ in the first three equations, we get:
2x(-xz/4y) = -yz
2x2z/4y = -yz
x2z/2y = -yz

From the fourth equation, we get:
x2 + 2y2 + 3z2 = 96

Substituting the values of x2, y2 and z2 from the above equation in the fifth equation, we get:
(96 - 2y2 - 3z2)z/2y = -yz
96z/2y - yz - 3z3/2y = 0

Solving for z, we get:
z = (96/4y) ± √(962/16y2 - 3y2)

Substituting the values of z from the above equation in the fourth equation, we get:
x2 + 2y2 + 3 (96/4y)2 ± √(962/16y2 - 3y2)2 = 96

Solving for y, we get:
y = ±√(96/14 - 3z2/2)

Substituting the values of y from the above equation in the third equation, we get:
x = ± 2z √(14z2/96 - 1/3)

Hence, the maximum and minimum values of f(x, y, z) subject to the given constraint can be found by substituting the values of x, y and z in the function f(x, y, z).

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The value of [tex]x _{238} = 111.1875 _{238}[/tex] for the given equation in congruence.

Congruence is an equivalence relation that is applied to compare numbers in discrete or modular arithmetic. If the difference between two numbers, a and b, is divisible by n, then the two numbers are said to be congruent modulo n (abbreviated as a b mod n). In other words, when a and b are divided by n, the remainders are equal. A key idea in number theory, congruence has a wide range of uses in domains like computer science and encryption.

For the given expression we have:

[tex]2142 . x _{238} = 442 _{238}\\x _{238} = 442 _{238} / 2142 _{238}\\x _{238} = 111.1875 _{238}[/tex]

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Answer: Your answer is 23.5in²

Hope it helped :D

Good Luck!

Answer:

Step-by-step explanation:

You want the x-coordinates of the absolute extrema of the function f(x) = 5x² -8x +7 on the interval [0, 8].

The absolute extrema of a function on an interval will lie at the ends of the interval or at a turning point within the interval.

For a quadratic ax²+bx+c, the turning point is at x=-b/(2a). For the given function, the turning point is at ...

  x = -(-8)/(2·5) = 0.8

This lies within the interval, and represents the location of the absolute minimum of this function whose graph opens upward.

The graph of the function is symmetrical about the vertical line through the turning point. The function increases as x-values are farther from the turning point, so the end of the interval farthest from x = 0.8 will be the location of the absolute maximum. That is at x = 8.

The absolute minimum at x = 0.8; the absolute maximum is at x = 8.

The length of the lake is solved to be

The length of the lake is solved by subtraction of length obtained using angle of depression of 68 degrees from the length obtained solving using angle of depression of 32 degrees

Using angle of depression of 68 degrees

The complimentary angle is 22 degrees

sin 22 = length / 250

length = sin 22 x 250

length = 93.65

Using angle of depression of 32 degrees

The complimentary angle is 58 degrees

sin 58 = length / 250

length = sin 58 x 250

length = 212.01

The length of the lake

= 212.01 - 93.65

= 118.36 m

= 118 m to the nearest m

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Answer: 94.2

Step-by-step explanation:

30 x 3.14

For a more accurate answer, multiply by the π symbol

30 x π = 94.25

The attributes, measurements used, and observations of the data are given below as per the average age of the score.

Attributes:

The table is given in the attached image below.

Measurements used:

Number of players (count)

Average score per game (mean)

The average age of players (mean)

Observations:

There are six basketball teams denoted by A, B, C, D, E, and F.

Team A has 12 players, with an average score per game of 74 and an average age of 13.5.

Team B has 15 players, with an average score per game of 50 and an average age of 12.8.

Team C has 14 players, with an average score per game of 63 and an average age of 12.2.

Team D has 17 players, with an average score per game of 38 and an average age of 13.1.

Team E has 11 players, with an average score per game of 51 and an average age of 12.7.

Team F has 16 players, with an average score per game of 60 and an average age of 11.

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To simplify the expression, we need to rationalize the denominator:

7_4√3 + 1 ÷ 7_4√3

= (7_4√3 + 1) ÷ 7_4√3 (since division is the same as multiplication by the reciprocal)

= (28 + 4√3 + 1) ÷ 28 (multiplying the numerator and denominator of the first fraction by the conjugate of the denominator)

= (29 + 4√3) ÷ 28

So the simplified expression is (29 + 4√3) ÷ 28.

Answer:

0.29    

Step-by-step explanation:

Knowing that the shaded angle is 106 degrees, and a circle's angle total is 360 degrees, we will know what fraction of the circle is shaded by dividing the shaded region's angle by the angle of an entire circle:

106/360 = 0.29              

The fraction of the circle that is shaded is also the probability that a randomly selected point within the circle falls in the shaded region since we just divided the desired outcome by all of the possible outcomes.

According to Daniel's theory, 18 customers would buy a toaster that costs $750.

If the popularity of a toaster is inversely proportional to its cost, we can set up a proportion as:

popularity of toaster 1 / cost of toaster 1 = popularity of toaster 2 / cost of toaster 2

Let's let x be the number of customers who would buy a toaster that costs $750.

We can write:

12 / 500 = x / 750

Simplifying:

12(750) = 500x

9000 = 500x

x = 18

Therefore, according to Daniel's theory, 18 customers would buy a toaster that costs $750.

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Answer:

x=5

Step-by-step explanation:

Add 4 to both sides to eliminate the constant term on the left side.

53x​−4+4=−6+x+4

53x​=−2+x

Multiply both sides by 5 to clear the fraction on the left side.

5×53x​=5×(−2+x)

3x=−10+5x

Subtract 3x from both sides to collect the variable terms on the right side.

3x−3x=−10+5x−3x

0=−10+2x

Add 10 to both sides to eliminate the constant term on the right side.

0+10=−10+2x+10

10=2x

Divide both sides by 2 to get the value of x.

210​=22x​

5=x

Step-by-step explanation:

3/5  x  -4 = -6 + x       add 6 to both sides of the equation

3/5 x + 2 = x               subtract 3/5 x from both sides

2 =  2/5 x                   multiply both sides by  5/2

5/2 * 2  = x = 5

4g to 3.5g written as a fraction in simplest form is equal to 8/7.

In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In this exercise, you are required to determine the ratio as a fraction in simplest form. Therefore, we would multiply both the numerator and denominator by 2 as follows;

Ratio = 4g/3.5g × 2/2

Ratio = 8g/7g

Ratio = 8/7

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Answer:

D. -1/3

The slopes of perpendicular lines are negative reciprocals of each other. In other words, the product of the slopes of perpendicular lines is -1. So the slope of a line perpendicular to a line with a slope of 3 will have a slope of -1/3. D is correct.

If you share 7 apples equally with 3 people, then there are 2 1/3 apples for each people when 7 divided by 3.

Given that,

7 apples are shared with 3 people.

Total number of apples = 7

Total number of people = 3

Number of apples each people get = 7/3 = 2 1/3

Here 2 means that 2 whole apples.

7 is not divisible by 3. So the number near to 7 which is divisible by 3 is 6.

6/3 = 2

Then the remaining 1 is divided in to 3 and 2 + 1/3 parts is given to each people.

Hence If you share 7 apples equally with 3 people, then there are 2 1/3 apples for each people.

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The associative property of 9 + (6 + 3) is 6+ (9 + 3) and it's simplified as 6+12 = 18.

The associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result.

For example, a+(b+c) is the same as b+(a+c). If a,b,c are real numbers.

This means that 9 + (6 + 3) can also be written as

6+ (9 + 3). The two expression must give thesame result.

6+ (9 + 3) = 6+ 12 = 18

Therefore the associative property of 9 + (6 + 3) is 6+ (9 + 3) and it's simplified as 6+12 = 18

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A two-dimensional graph, also known as a coordinate plane or Cartesian plane, is divided into four quadrants. The quadrants are numbered in a counterclockwise direction, starting from the top-right quadrant and going around to the other quadrants.

To name the quadrants on a graph:

Point C is in the fourth quadrant. We can verify this because it is located at a positive x-coordinate and a negative y-coordinate. (4,-4)

Answer: 10.46 m

Step-by-step explanation:

C=[tex]\pi d[/tex]

=[tex]\pi (3.33)[/tex]

=10.46 m

Answer:

Step-by-step explanation:

C = π × 3.33

C = 3.14 × 3.33

C = 10.45 m  (round 10.5 m)

Answer:

6

Step-by-step explanation:

2 x 3 = 6