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Given, To evaluate the following limit To evaluate the given limit Let's first factorize the denominator\[x^{2}-16=(x+4)(x-4)\].

We can rewrite the given limit as follows Hence, the value of  Next, we need to evaluate the given limit\(\lim_{x \rightarrow 0}\left(x^{2} \sec ^{2} x+\frac{\tan x}{x}\right)\).

To evaluate the given limit\(\lim_{x \rightarrow  Thus, the value of Therefore, the values of the given limits are \(\frac{1}{4}\) and \(1\) respectively.

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Answer:

1. 6:2

2.for every 1 yellow paint, she needs 3 red paints

3.an orange

Step-by-step explanation:

1. It would be 6:2 because for every 2 parts yellow she needs 6 parts red

2. Since the ratio is first 6:2, just divide it by 2 since there is 2 yellow and it's asking how much red you need for 1 yellow

The three consecutive integers are 10, 11, and 12.

To find three consecutive integers, the sum of whose squares is 65 more than three times the square of the smallest, follow these steps:

1. Let the smallest integer be x. Then, the other two consecutive integers are x + 1 and x + 2.

2. The sum of their squares is x^2 + (x + 1)^2 + (x + 2)^2.

3. The given condition is that this sum is 65 more than three times the square of the smallest integer: x^2 + (x + 1)^2 + (x + 2)^2 = 3x^2 + 65.

4. Simplify the equation:
  x^2 + (x^2 + 2x + 1) + (x^2 + 4x + 4) = 3x^2 + 65

5. Combine like terms:
  3x^2 + 6x + 5 = 3x^2 + 65

6. Subtract 3x^2 from both sides to eliminate the x^2 terms:
  6x + 5 = 65

7. Subtract 5 from both sides:
  6x = 60

8. Divide by 6:
  x = 10

So, the three consecutive integers are 10, 11, and 12.

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The values of \(x\) are \(1+\sqrt{89}\) and \(1-\sqrt{89}\).

To find the values of x:

Given equation: \((x+7)(x-9)=25\)

Then: \(x(x-9)+7(x-9)=25\)

Using the distributive property: \(a.(b+c)=a.b+a.c\)

\(x^{2} -9x+7x-63=25\)

Combine like terms:

\(x^{2} -2x-63=25\)

Subtract 25 from both sides and obtain:

\(x^{2} -2x-88=0\)

Using completing square form:

Add and subtract \((\frac{2}{2} )^{2} =1\) we have:

\(x^{2} -2x-88+1-1=0\\(x-1)^{2} -89=0\)

Add 89 to both sides we have:

\((x-1)^{2} =89\)

Taking square roots on both sides, obtain:

\(x-1=\) ± \(\sqrt{89}\)

Add 1 to both sides we have:

\(x=1\)±\(\sqrt{89}\)

Therefore, the values of \(x\) are \(1+\sqrt{89}\) and \(1-\sqrt{89}\).

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The complete question is given below:

Use completing the square to solve (x + 7)(x – 9) = 25 for x.

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Since McKenzie fills the 2-quart pitcher 2 times, there are a total of 4 quarts.

2 quarts × 2 times filled = 4 quarts

Recall that

1 quart = 4 cups

Since each quart is 4 cups, having 4 quarts is equivalent to

4 quarts × 4 = 16 cups

Therefore, there are a total of 16 cups of juice that was made.

Answer:

4x -12

Step-by-step explanation:

8 - 4(-x + 5)

Distribute

8 -4(-x) -4(5)

8 +4x -20

4x -12

answer 4( - 3 + x)

answer

\(4( - 3 + x)\)

\(8 - 4( - x + 5)\)

answer

\( - 12 + 4x\)

The probability that the sampling error is less than 1 hour or more than 1 hour is 0.5854.

To calculate this probability, we start by transforming the sampling error \((\bar{x}-\mu)\) into z-scores using the formula \(Z = \frac{\bar{x}-\mu}{\sigma/\sqrt{n}}\), where \sigma is the standard deviation and n is the sample size.

In this case, the z-score for the sampling error less than -1 is   \(Z < \frac{-1}{1.833333}\) = -0.5455, and the z-score for the sampling error greater than 1 is \(Z > \frac{1}{1.833333}\) = 0.5455.

Using the standard normal distribution table or statistical software, we can find the corresponding probabilities associated with these z-scores.

\(P(Z < -0.5455) + [1 - P(Z < 0.5455)]\)= 0.5854

Therefore, the probability that the sampling error is less than 1 hour or more than 1 hour is 0.5854.

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Answer:

1) January is the one that looks like it has a bigger mean and median because mid way in the graph it goes up high for a long amount of time and February goes down and stays like that.

2) Because mid way in the graph it goes up high for a long amount of time and February goes down and stays like that.

3) I would be proud of sharing January because it is high and will show how effective airlines are.

Answer:

Step-by-step explanation:

3.4 times 2 is 6.8

pemdas for the second one. 2 times 6 is 12. 33+10-12, 31

102/22

4.3636

Answer:

1: 6.8

Work: 3.4 divided by 2 equals 6.8

2: 246

Work: 33 plus 10 minus 2 times 6 equals 246

3: 4

Work: 102 divided by 22 equals 4

Step-by-step explanation: I hope this helps! :)

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.

Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.

Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.

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Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

In plan A,

    Plans for saving = $500

  Amount of saving each week = $20

∴ Number of weeks needed to make goal = (500 ÷ 20) (by using division)

                                                                       = 25

In plan B,

    Plans for saving = $500

   Amount of saving each week = $30

∴ Number of weeks needed to make goal = (500 ÷ 30) (by using division)

                                                                       = 17

In plan C,

    Plans for saving = $500

   Amount of saving each week = $40

∴ Number of weeks needed to make goal = (500 ÷ 40) (by using division)

                                                                       = 13

In plan D,

    Plans for saving = $500

   Amount of saving each week = $50

∴ Number of weeks needed to make goal = (500 ÷ 50) (by using division)

                                                                       = 10

So, Todd use to save $500 in less than 16 weeks and have $20 extra in Plan C.

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By definition of the volume of cube, the side length of the cubic quart container is approximately equal to 9.818 centimeters.

A quart means a quarter of gallon and is equal to 946.353 cubic centimeters. The volume of the cube is equal to the cube of the side lengt, then:

x³ = 946.353

x = ∛946.353

x ≈ 9.818

By definition of the volume of cube, the side length of the cubic quart container is approximately equal to 9.818 centimeters.

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The rate of change of y with respect to x when t = 3 is = 3/25 and  the answer is not one of the options given.

An object moves in the xy-plane so that its position at any time tis given by the parametric equations x(t) = t° - 3t + 2 and y (t) = /t² + 16.

To find the rate of change of y with respect to x, we need to find dy/dx, which can be computed using the chain rule of differentiation:

(dy/dt) / (dx/dt) = dy/dx

We first compute dx/dt and dy/dt:

dx/dt = 1 - 3 = -2

dy/dt = 2t / (t² + 16)

When t = 3, we have:

dx/dt = -2

dy/dt = 2(3) / (3² + 16) = 6/25

Therefore, the rate of change of y with respect to x when t = 3 is:

(dy/dt) / (dx/dt) = (6/25) / (-2) = -3/25

So, the answer is not one of the options given.

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The conventional B/C ratio using the expected EUAC (Equivalent Uniform Annual Cost) can be computed as 1 / EUAC

To calculate the conventional B/C ratio using the expected EUAC, we need to determine the present value of costs and benefits over the project's life and then compare them.

Cost Data:

Year 1: $10,000

Year 2: $8,000

Year 3: $6,000

Benefit Data:

Year 1: $15,000

Year 2: $12,000

Year 3: $9,000

Life Probability Distribution:

Year 1: 0.2

Year 2: 0.5

Year 3: 0.3

To calculate the present value of costs and benefits, we multiply each cash flow by the respective probability and discount it to present value. Assuming a discount rate of r%, the present value (PV) can be calculated using the formula:

PV = Cash Flow / (1 + r)^n

where n is the year of the cash flow.

Calculating the present value of costs:

PV(Costs) = ($10,000 / (1 + r)^1) + ($8,000 / (1 + r)^2) + ($6,000 / (1 + r)^3)

Calculating the present value of benefits:

PV(Benefits) = ($15,000 / (1 + r)^1) + ($12,000 / (1 + r)^2) + ($9,000 / (1 + r)^3)

The expected EUAC can be calculated as the sum of PV(Costs) divided by the sum of PV(Benefits), considering the probabilities:

EUAC = (PV(Costs) * 0.2 + PV(Costs) * 0.5 + PV(Costs) * 0.3) / (PV(Benefits) * 0.2 + PV(Benefits) * 0.5 + PV(Benefits) * 0.3)

Finally, the conventional B/C ratio is obtained by taking the inverse of the EUAC:

B/C ratio = 1 / EUAC

The conventional B/C ratio using the expected EUAC for the given cost, benefit data, and life probability distribution can be computed using the provided calculations. This ratio allows for a comparison between the present value of costs and benefits over the project's life, considering the probability distribution.

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(a)To solve the system of equations, x^2 - y^2 = 16 and x^2 - y = 7, we can use substitution or elimination method to find the values of x and y.

(b) To graph the solution set of the system of inequalities, x^2 - y^2 > 7 and x^2 - y < 0, we need to plot the boundaries and shade the appropriate regions based on the given inequalities.

(a)Let's use the substitution method to solve the system of equations:

From the second equation, we can rewrite it as x^2 = y + 7.

Substituting this value of x^2 in the first equation, we get (y + 7) - y^2 = 16.

Rearranging the equation, we have -y^2 + y + 7 - 16 = 0.

Simplifying further, we get -y^2 + y - 9 = 0.

Now, we can solve this quadratic equation for y by factoring or using the quadratic formula.

After finding the values of y, we can substitute them back into the second equation to find the corresponding values of x.

(b)To graph the solution set, we first graph the boundaries of the inequalities. For x^2 - y^2 > 7, we draw the curve of the equation x^2 - y^2 = 7, which represents a hyperbola. For x^2 - y < 0, we graph the curve of the equation x^2 - y = 0, which represents a parabola opening upwards.

Next, we need to determine which regions satisfy the given inequalities. For x^2 - y^2 > 7, the shaded region lies outside the hyperbola. For x^2 - y < 0, the shaded region lies below the parabola.

By combining the shaded regions of both inequalities, we find the solution set of the system of inequalities. It includes the regions outside the hyperbola and below the parabola. We label the corners of the shaded region to indicate the solution set accurately.

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Answer:

perpendicular

Step-by-step explanation:

because of the opposite signs

Answer:

D. 60

Step-by-step explanation:

Height = constant / width

30 = c / 2

2* 30 = 60

c = 60

12 = c / 5

12 * 5 = 60

c = 60

10 = c / 6

10 * 6 = 60

c = 60

Step-by-step explanation:

please mark me as as pleaseWhen two lines intersect, the opposite (X) angles are equal. In the diagram above, the two green angles are equal and the two yellow angles are equal. These X angles are called vertically opposite angles because they are opposite each other at a vertex.

Answer:

See attached image

Step-by-step explanation:

Every step holds except for step 5

In mathematics, it deals with numbers of operations according to the statements.

Here,
Step 1 is the result of the distribution of -5 while opening the parenthesis, So, Step 1 holds the distributive property.

Step 2, states adding like terms across each side, so combining as terms hold,

Step 3, Addition over the equal sign. So it also holds

Step 4, subtraction of 12 over the equal sign. So subtraction of the terms also holds.

Step 5, does not hold because the number 12 gets divided by 8 it is not an associative property.

Thus, Every step holds except for step 5.

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The length of the credit card is either l = 8.5 or l = -5.5. Since length can't be negative, we know that: l = 8.5

First, we need to use the given information to set up an equation for the length and width of the credit card. We know that the width w is 3 centimeters shorter than the length l, so we can write:

w = l - 3

We also know that the area of the credit card is 46.75 square centimeters, which can be expressed as:

A = lw = 46.75

Now we can use these equations to solve for the length and width. Substituting the first equation into the second equation, we get:

(l - 3)l = 46.75

Expanding the left side, we get:

l^2 - 3l = 46.75

Rearranging and factoring, we get:

(l - 8.5)(l + 5.5) = 0

So the length of the credit card is either l = 8.5 or l = -5.5. Since length can't be negative, we know that:

l = 8.5

Using the first equation, we can then find the width:

w = l - 3 = 8.5 - 3 = 5.5

Now we can find the perimeter by adding up the four sides of the credit card:

P = 2l + 2w = 2(8.5) + 2(5.5) = 17 + 11 = 28

So the perimeter is 28 centimeters.

To solve this problem, we'll first use the given information to find the width (w) and length (l) of the credit card. Then, we'll calculate the perimeter using the formula: Perimeter = 2 * (length + width).

Given that the width (w) is 3 centimeters shorter than the length (l), we can express this as:

w = l - 3

We are also given the area of the credit card, which is 46.75 square centimeters. The area can be calculated as:

Area = length * width
46.75 = l * (l - 3)

Now, let's solve for l:

46.75 = l^2 - 3l
l^2 - 3l - 46.75 = 0

Solving this quadratic equation, we get:

l ≈ 7.25 cm

Now that we have the length, we can find the width:

w = l - 3
w = 7.25 - 3
w ≈ 4.25 cm

Finally, we can calculate the perimeter using the formula:

Perimeter = 2 * (length + width)
Perimeter = 2 * (7.25 + 4.25)
Perimeter ≈ 23 cm

So, the perimeter of the credit card is approximately 23 centimeters.

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The Bank 1's total amount of money to be received would be based on the loan amount, the monthly installment, and the duration of the loan.

To calculate the total amount of money expected to be received by Bank 1, we need to know the principal amount of the loan, the monthly installment, and the duration of the loan.

Since the question doesn't provide us with that information, we cannot accurately calculate the total amount of money expected to be received by Bank 1.

However, we do know that Bank 1 offered a loan repayable at a certain monthly installment for the same period of time as the car hire company at the same rate of 9% p.a.

Therefore, we can assume that Bank 1's total amount of money expected to be received would be based on the loan amount, the monthly installment, and the duration of the loan.

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Let's start by substituting the right-hand side of the equation into the left-hand side:

What does the math equation mean?

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

4y - 3 = 4(y + 1)

4y - 3 = 4y + 4

Now, we can isolate y by subtracting 4y from both sides:

0 = y + 4

-4 = y

So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.

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Answer:

2.4.

Step-by-step explanation:

the formula of the volume of a cylinder is ; πr²h.

so, we will have to substitute with the formula.

3.14 × 6 × 6 × h = 271.4

113.04h = 271.4

divide both sides by the number next to the unknown, which is 113.04.

you will get 2.4009200........

when u round off to the nearest tenths, you will get 2.4.

Answer: a

Step-by-step explanation:a

We can use the power series expansion of the exponential function e^(-x) to evaluate the sum of the series:

e^(-x) = ∑(n=0 to infinity) (-1)^n (x^n) / n!

Setting x = 3/2, we get:

e^(-3/2) = ∑(n=0 to infinity) (-1)^n (3/2)^n / n!

Multiplying both sides by (3/2)^2 and simplifying, we get:

(9/4) e^(-3/2) = ∑(n=0 to infinity) (-1)^n (3/2)^(n+2) / (n+2)!

Comparing this with the given series, we can see that they differ only by a factor of (-1) and a shift in the index of summation. Therefore, we can write:

∑(n=0 to infinity) (-1)^n (2n) (3/2)^(2n) / (2n)!

= (-1) ∑(n=0 to infinity) (-1)^n (3/2)^(n+2) / (n+2)!

= (-1) ((9/4) e^(-3/2))

= - (9/4) e^(-3/2)

Hence, the sum of the series is - (9/4) e^(-3/2).

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