Evalúe the limit. Show steps

After evaluating the limit we have came to find that the limit of       [tex]\lim_{x\rightarrow 1 }\frac{x-2}{x^2-10x + 25}[/tex] as x approaches 1 is −0.0625

In mathematics, a limit is the value that a function, sequence, or index approaches as an input or as an index approaches a specific value. Limits are crucial to calculus and mathematical analysis and are necessary for the definitions of continuity, derivatives, and integrals.

The idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network, in addition to sharing a connection with the category theory concepts of limit and direct limit.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit

⇒ [tex]\lim_{x\rightarrow 1 }\frac{x-2}{x^2-10x + 25}[/tex]

Evalúe 2 as x

⇒ [tex]\frac{1-2}{1^2-10(1) + 25}[/tex]

⇒ [tex]\frac{-1}{-9 + 25}[/tex]

⇒ [tex]\frac{-1}{16}[/tex]

⇒−0.0625

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Bill's projected monthly payment under the Monthly Payments for Long-Term Loans using the Rule of Thumb is $870.00.

Bill's exact monthly payment using the Monthly Payments calculation is $933.36.

The real monthly payment is approximately $63.36 more than the predicted cost.

Simple procedures may be used to calculate the Monthly Payments for Long-Term Loans Rule of Thumb.

To begin, divide the annual percentage rate (APR) by 12 to obtain the monthly percentage rate (MPR).

Second, calculate the MPR on the principal amount. The product is the estimated monthly payment, which is similar to the real monthly payment and was computed using a financial calculator below.

Estimated Monthly Payment:

Home Mortgage = $116,000

Term of loan = 30 years

APR = 9%

Monthly interest rate = 0.0075 (0.09/12)

Estimated monthly payment based on the Monthly Payments for Long-Term Loans Rule of Thumb

($116,000 x 0.0075) = $870

Actual Monthly Payment Formula:

N (# of periods) = 360 months (30 x 12)

I/Y (Interest per year) = 9%

PV (Present Value) = $116,000

FV (Future Value) = $0

The outcome is given as:

PMT = $-933.36

Sum of all periodic payments = $-336,010.40

Total Interest = $220,010.40

Actual monthly payment =  $933.36

Estimated monthly payment 870.00

Difference = $63.36


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Answer:

  c.  3

Step-by-step explanation:

You want to know the limit of the composite function f(f(x)) as x approaches zero.

The function f(x) can be evaluated at x=0. The graph shows the value to be ...

  f(0) = 2

The function f(x) can also be evaluated at x=2. The graph shows the value to be ...

  f(2) ≈ 3

The nearest value to f(f(0)) is 3.

__

Additional comment

For a continuous function, the limit at a point is simply the value at that point. F(x) is continuous in the neighborhoods of the points of interest, so we simply need to find the function value.

The annual rate of change of the boat's value is $5334.

Given,

Chris bought a new boat in 2008.

The value of boat in 2008 (Initial value) = $35000

The value of boat in 2011 = $19000

Chris knows that the value of the boat depreciated linearly.

We have to find the annual rate of change of the boat's value, x.

Number of years, n = 2008 to 2011 = 3 years

Here, x be a constant.

So,

Value in 2011 = Initial value - nx

19000 = 35000 - 3x

3x = 35000 - 19000

3x = 16000

x = 16000/3

x = 5333.33

x = 5334

That is,

The annual rate of change of the boat's value is $5334.

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Lenght of a rectangle: L

Widht of the rectangle: W

Perimeter of the rectangle: P

length of a rectangle is four times it's width: L = 4W

Perimeter is at most 106: P <= 106

Perimeter is 2L + 2W: P = 2L + 2W

P <= 106

if we use the value of P = 2L + 2W, we can write:

2L + 2W <= 106

Since L = 4W, then we can write this equation:

2L + 2W <= 106

2(4W) + 2W <= 106

8W + 2W <= 106

10W <= 106

W <= 106/10 = 10.6

W <= 10.6

Therefore, the greatest possible value for the width is 10.6

Answer:

10.6

Answer: 4/3 or 1.33

Step-by-step explanation:

Answer: 0.007

Step-by-step explanation: 70 x 10^-4= 0.0001

70 x 0.0001

7 x 0.001

0.007

Hope this helps!

The standard notation of 7 x [tex]10^{-4}[/tex] is 0.0007.

The given expression is;

7 x [tex]10^{-4}[/tex]

To write 7 x [tex]10^{-4}[/tex] in standard notation,

When multiplying an integer by a power of ten, the decimal point is moved to the right or left by the number of zeroes in the exponent.

So, for7 x [tex]10^{-4}[/tex],

Move the decimal point 4 places to the left.

Starting with 7, Move the decimal point 1 place to the left to get 0.7.

Move it another 3 places to the left to get 0.0007.

Therefore,

7 x [tex]10^{-4}[/tex] in standard notation is 0.0007.

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Using the  sinking fund formula, the monthly payment needed to accumulate 270,000 with 5% interest or combine did monthly for 28 years, the monthly invested payment is 369.65.

A sinking fund, also referred to as a sinking fund, is defined by its name. Fundamentally speaking, it is built to sink. Although there are some similarities between a sinking fund and a reserve fund, their purposes differ significantly. Unlike reserve funds, which typically serve no particular purpose, sinking funds have a designated purpose.

Simply put, a reserve fund is a company's method of saving its surplus funds. There are numerous uses for reserve funds. They can be applied to a variety of costs, including those related to emergency situations, asset purchases, business expansions, and capital expenditures.

Sinking fund (A) = P × [tex]\frac{(1+r/n)^{tn}-1}{r/n}[/tex]

Where

A – Money accumulated

P – Periodic contribution,

r – Interest rate

t – Number of years

n – Number of payments per year

So, periodic contribution P = A / (((1 + r / n) ^ (t * n) – 1) / (r / n))

Here given that,

A – 270,000

r – 5%

t – 28 years

n – 12

P – To find

Substituting the values we get

P = [tex]270000/(((1+0.05/12)^{\left(28\times 12\right)}-1)/(0.05/12))[/tex]

P = 369.649667

P = 369.65

Therefore, the monthly payment needed to accumulate 270,000 with 5% interest or combine did monthly for 28 years, the monthly invested payment is 369.65.

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Marie should buy the bag with green apples as it has more weight hence it will have more apples eventually making her pie tastier

Comparison: When we compare, we look for similarities among the characteristics of other items or objects. Mathematicians use the concept of comparing and ranking numbers to identify the smaller and larger numbers and to determine whether they should be arranged in ascending or descending order.

Weight of bag with green apples = 4.75 pounds

Weight of bag with red apples = 4.54 pounds

Since the bag with green apples weighs heavier and contains more apples overall, Marie should purchase it because it will make her pie taste better.

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Step 1

Given;

Required; To find the dot product

Step 2

Find the dot product

The answer thus is;

Create an In-Out table with your findings. Make a table with the number of bagels she has when she gets home as the In and the number she had to start with as the Out.

Try several numbers for the number she has when she arrives home to explore this expansion, such as 3, 4, 5, or even 0. You should presume that, other from this number, everything in the problem is the same as it was in the original problem.

Create an In-Out table with your findings. Make a table with the number of bagels she has when she gets home as the In and the number she had to start with as the Out. Once you've added numerous entries to the table, search for a connection between the Out and the In before attempting to identify a rule that can explain this connection.

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Answer:

Let width of rectangle be x cm.

Width = x cm

Length = 4x cm

Area of rectangle = length x width

4x × x = 144

4x² = 144

x² = 144 ÷ 4 = 36

x = √36 = 6

Width = 6 cm

Length = 6 × 4 = 24cm

Perimeter = 6 + 24 + 6 + 24 = 60 cm

there is no proportional relationship between the two qualities

For two quantities to be proportional, it must follow the formula:

y = kx

where k = proiportionality constant

k = y/x

if y = 950, x = 1

inserting in the equation:

950= 1k

k = 950

The equation becomes: y = 950 × x

We check for other values. if k is the same, it is proportional

when y = 2852, x = 3

2852 = k × 3

k = 2852/3 = 950.67

when y = 5.1, x = 4845

4845 = k × 5.1

k = 4845/5.1 = 950

From the above, the value of k which is different is for the 2nd value.

Since they are not all the same, we say there is no proportional relationship between the two qualities

We are asked to solve for a number such that:

Twice that number plus 4 equals 6

Which can be written in math terms as:

2 x + 4 = 6

Now we proceed to isolate the unknown in steps.

First we subtract 4 from both sides:

2 x + 4 - 4 = 6 + 4

we combine like terms:

2 x = 10

Now we divide both sides by 2 so as to cancel the factor 2 that accompanies "x":

2 x / 2 = 10/ 2

perform the indicated operations:

x = 5

Answer:

to solve for x, you gotta make the two equations equal to each other then you can move the numbers to get the value of x

20x+10=30x-10

20x-30x=-10-10

-10x=-20

x=2

Answer:

x=2

Step-by-step explanation:

if m/A and m/B are equal, to find x, your equation would be 20x+10=30x-10. doing two step equations, you would substract 20x from both sides, making your equation look like 10=10x-10. then you would add 10 from both sides making your equation 20=10x. then you would divide 10x from both sides making x=2.

Answer:

no solution that's my answer

The valid solution to the problem is: The smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8 is 34/85.The smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8 is 34/85.

Let's solve the problem step by step to determine the smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8. We'll express the answer as a reduced fraction.

We have 4 boxes arranged in a square as described:

 A  B

 C  D

The fraction can be represented as AB/CD.

To make the fraction as small as possible, we need to arrange the digits in a specific way. We want to minimize the numerator (AB) and maximize the denominator (CD).

For the numerator (AB), we want the smallest two-digit number. The smallest two-digit number that can be formed using the digits 3, 4, 5, and 8 is 34.

For the denominator (CD), we want the largest two-digit number. The largest two-digit number that can be formed using the digits 3, 4, 5, and 8 is 85.

Therefore, the smallest fraction that can be formed is 34/85.

To ensure that this fraction cannot be further reduced, we need to check if 34 and 85 share any common factors greater than 1. If they do not share any common factors other than 1, then the fraction is in its reduced form.

Checking for common factors:

Factors of 34: 1, 2, 17, 34

Factors of 85: 1, 5, 17, 85

The only common factor is 1, which means the fraction 34/85 is already in its reduced form.

Thus, the valid solution to the problem is:

The smallest value of all the common fractions that can be formed using the digits 3, 4, 5, and 8 is 34/85.

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The matrix equation is given to be:

where A is the coefficient matrix of the system.

To get the value of X, we need to multiply both sides of the equation by the inverse of A, since:

Therefore, we have:

he TLAST OPTION is correct.

The number of chips and drinks are 46 chips and 56 drinks respectively.

Let the number of drinks be d.

Let the number of chips be c.

From the information, he works at a football concession stand selling drinks for $2 and bags of chips for $3 and he makes a total of $246 and sells a total of 100 drinks and bags of chips.

This will be:

c + d = 100 ........ i

2d + 3c = 246 ........ ii

From equation i, c = 100 - d

Substitute this into equation ii

2d + 3c = 246

2d + 3(100 - d) = 246

2d + 300 - 3d = 246

Collect like terms

2d - 3d = 246 - 300

-d = -54

d = 54

Number of drinks = 54

Since c + d = 100

c + 54 = 100

c = 100 - 54 = 46

Chips = 46

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Complete question

Russell works at a football concession stand selling drinks for $2 and bags of chips for $3. At one football game, Russell makes a total of $246 and sells a total of 100 drinks and bags of chips. Calculate the number of drinks and chips sold.

The probability that a ball is not red is 3/5 and the probability that the ball is red or white is 2/3 .

Mathematical descriptions of the likelihood that an event will happen or that a proposition is true are dealt with in the discipline of mathematics known as probability.

In the given question there are  6 red balls, 4 white balls, and 5 blue

balls.

Total number of balls = 6+4+5 = 15 balls (sample space)

Red balls = 6

Not red balls = 15 - 6 = 9

Probability that the ball is red = 9/15 = 3 /5

Red and white balls = 6 + 4 =10

Probability that the ball is red or white = 10 / 15 = 2 / 3

Hence the probability that a ball is red or white is 2 / 3.

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Disclaimer : The complete question is :

A ball is drawn at random from a box containing 6 red balls, 4 white balls, and 5 blue balls. Determine the probability that it is

(a) not red

(b) red or white

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The equation of the line passing from found as y = 5.

The formula for finding the slope is;

m = Δy/Δx

Where, m is the slope

The given equation of line is;

x = 3 comparing it with standard form of equation;

y = mx + c

As, the equation is a straight line passing parallel to x axis, the slop of line x = 3 is ∞.

Thus, m₁ =  ∞.

Now, let the slops of the line passing from (-2, 5) is m₂,

The, as both line are perpendicular.

Thus,

m₁ x m₂ = -1

m₂ = -1/∞

m₂ = 0

The equation of line is found by

y - y₁ = m₂(x - x₁)

Put the values;

y - 5 = 0(x + 2)

y = 5

Therefore,the equation of the line passing from found as y = 5.

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Answer:

1.) 12 yards (the one you selected is correct)

2.) 1.1 with the bar over the decimal (the one you selected is correct)

Step-by-step explanation:

1.) It looks like Aaron dropped back 5 yards from the line of scrimmage and threw to the 7 yard line for a total of 12 yards.

2.) If you enter 10 divided by 9 into your calculator you will get back 1.11111111111111 that keeps repeating for how ever many digits your calculator can show.  We write this as 1.1 with the bar over the decimal.

The exponent is 81[tex]m^{} 4[/tex] [tex]n^{20}[/tex]

An exponent is a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.

Here we have to determine the sign for exponential or radical expression

(-3m[tex]n^{5}[/tex])^4

Simplify using the exponent rule with the same exponent [tex](ab)^{n}[/tex] = [tex]a^{n}[/tex] . [tex]b^{n}[/tex]

Similarly

(-3m[tex]n^{5}[/tex])^4

= [tex](-3)^{4}[/tex] . [tex]m^{4}[/tex]. [tex](n^{5} )^{4}[/tex]

Now using the exponent  power rule [tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex]. We get

= 81 . [tex]m^{4}[/tex].[tex]n^{20}[/tex]

Therefore the exponent as a product of power is 81[tex]m^{4} n^{20}[/tex].

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Answer:

  (a) ∠e +∠d = 180°  is false

Step-by-step explanation:

You want to know which angle expression is not true.

We can figure the measures of all of the unknown angles, then check the given expressions.

Angles 'a' and 130° are corresponding angles, so congruent:

  a = 130°

Angles 'a' and 'e' are vertical angles, so congruent:

  e = a = 130°

Angle 'd' and 62° are vertical angles, so congruent:

  d = 62°

Angles 'b' and 'd' are corresponding angles, so congruent:

  b = d = 62°

Angles 'f' and 62° are corresponding angles, so congruent:

  f = 62°

Angles 'c' and 130° are a linear pair, so supplementary:

  c + 130° = 180°

  c = 50° . . . . . . subtract 130°

(a) ∠e +∠d = 180°   ⇒   130° +62° = 180° . . . . false

(b) ∠d +∠b = 124°   ⇒   62° +62° = 124° . . . . true

(c) ∠a +∠c = 180°   ⇒   130° +50° = 180° . . . . true

(d) ∠ 180° -∠f = 118°   ⇒   180° -62° = 118° . . . . true

The rate is given by

and since the one-time charge is $0.25, the expression is

where n denotes the number of days. Then, the answer is the second option

Step-by-step explanation:

collect like terms

[tex]5x - x - 6y + 3y \\ 4x - 3y [/tex]

For every 4 liters of synthetic oil, there are 7 liters of natural oil. 671 liters of Petrolyn oil. 244 liters of synthetic oil is needed and 427 liters of natural oil is needed.

Given that,

Petrolyn motor oil is a blend of synthetic and natural oil. For every 4 liters of synthetic oil, there are 7 liters of natural oil. 671 liters of Petrolyn oil are needed to produce it.

We have to find how much synthetic oil, in liters, is required.

According to the given values;

The ratio of natural to synthetic oil

= 7:4

If 671 liters have to be made then,

By adding 7+4=11

So, 7/11 of 671 liters will be = 427 liters of natural oil

and, 4/11 of 671  liters will be = 244 liters of synthetic oil

Therefore,244 liters of synthetic oil is needed and 427 liters of natural oil is needed.

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do the sum

the number is 40 because 40 is 8 more than 32

Given:

The company claims that its heaters last more than 5 years.

Find: null alternative hypotheses.

Sol: