14 bags of candy for 36.26

The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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Answer: b

Step-by-step explanation:

Answer:

So, the probability of selecting a number from 1 to 100 that is divisible by 5 or 7 is 0.32.

Hope this helped!

The probability that the actual weight is within 0.2 g of the prescribed weight is 0.6827 (rounded to four decimal places)

To answer these questions, we need to use the concept of normal distribution. Let's assume that the weights of the pills follow a normal distribution with mean μ = 2 g and standard deviation σ = 0.1 g.

(d) To find the probability that the actual weight is within 0.2 g of the prescribed weight, we need to find the area under the normal curve between the values of 1.8 g and 2.2 g (i.e., within 0.2 g of the mean). We can use a standard normal distribution table or a calculator to find this probability.

Using a calculator, we can use the normalcdf function with the following inputs: normalcdf(1.8, 2.2, 2, 0.1). This gives us a probability of 0.6827. Therefore, the probability that the actual weight is within 0.2 g of the prescribed weight is 0.6827 (rounded to four decimal places).

(e) To find the probability that the actual weight differs from the prescribed weight by more than 0.3 g, we need to find the area under the normal curve outside the values of 1.7 g and 2.3 g (i.e., more than 0.3 g away from the mean). We can use a standard normal distribution table or a calculator to find this probability.

Using a calculator, we can find the probability of being below 1.7 g and above 2.3 g separately and then add them together. For example, we can use the normalcdf function with the following inputs: normalcdf(-1000, 1.7, 2, 0.1) + normalcdf(2.3, 1000, 2, 0.1). This gives us a probability of 0.0228. Therefore, the probability that the actual weight differs from the prescribed weight by more than 0.3 g is 0.0228 (rounded to four decimal places).

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Solution

- The formula for the exponential function is:

- Thus, the function required is

The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

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Answer:

48 gallons

Step-by-step explanation:

\( \frac{3}{4} = \frac{6}{8} \\ \frac{6}{8} - \frac{1}{8} = \frac{5}{8} \\ 5 \div 30 = 6 \\ 6 \times 8 = 48\)

The equation which shows the commutative property of addition is (A) 4+3=3+4.

So,

The commutative property for addition states that, a + b = b + a .

Where a, b is any number.

The above condition is satisfied by the equation

Therefore, the equation which shows the commutative property of addition is (A) 4+3=3+4.

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The correct question is given below:

Which equation shows the commutative property of addition?

A. 4+3=3+4

B. 1(3)=3

C. (2+7)+12=2+(7+12)

D. 4+0=4

tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

The tangent of 36° can be expressed in terms of its cofunction, which is the cotangent. The cotangent of an angle is equal to the reciprocal of the tangent of that angle. Therefore, we can rewrite tan 36° as cot (90° - 36°).

Now, cot (90° - 36°) can be simplified further. The angle 90° - 36° is equal to 54°. So, we have cot 54°.

The cotangent of 54° can be determined using the unit circle or trigonometric identities. In this case, the exact answer for cot 54° is (√3 + 1) / (√3 - 1).

Hence, tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

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The derivate of a function f(x) is determinated as:

For the function

First we have to determine de f ( x + h ) as follow:

Then we calculate and simplify the coeficient in the first formula

------------------------------------------------------------------------------------The equation of the tangent:

First you need to know that the derivate of a function is equal to the slope (m) of the tangent of this function

And the equation to thist tangent in a specific point will be find using the next formula:

We have to calculate the slope in the point x =4 using the derivate:

In the point x=4

Calculate the value of f(x0) substituting in the function the given point x:

Knowing that we put the value of m and f(x0) in the equation of the tangent:

---------------------------------------------------------------------------

The normal line

The slope of the normal line is the opposite of the slope of theu tangent in an espesific point:

So in this situation is:

The equation of the normal line is given by the next formula:

Replacing the data we obtain:

x + 210  = 1.15x        where x is the amount in their accounts in March....subtract x from both sides 210 = .15x   divide both sides by .15 x = $ 1400 Hope you get an A+ :))

Answer:

B. 9

Step-by-step explanation:

m∠U = 2x°

m∠V = 4m∠U

        = 4(2x°)

        = 8x°

Complementary angles add up to 90°.

∠U + ∠V = 90°

2x° + 8x° = 90°

10x° = 90°

x = 90° ÷ 10°

  = 9

Answer:

(a) An  = 2n +8

(b) F(n) = 10 + (n-1)2

(c) 38ft tall

Step-by-step explanation:

The tree is currently 10 feet long and grown 2 feet per year.

The arithmetic sequence is

10 , 12, 14 , 16 , 18 ..............

a( initial value) = 10 , d (common difference) = 2

Explicit forms

(a) An = a +(n-1)d

     An = 10 + (n-1)2

            = 10 + 2n -2

           An  = 2n +8

(b) F(n) = 10 + (n-1)2

(c) Height of the tree after 15 years

       F(15) = 10 + (15-1)2

                 = 10 + 28

                  = 38ft

So the tree will be 38ft tall after 15 years.

The power series solution to x²y'' - x(1 + x)y' + y = 0 at x = 0 with the general formula for the coefficients.

The differential equation is x²y'' - x(1 + x)y' + y = 0.

To find the power series solution for this differential equation at x = 0, we assume a power series solution of the form y = ∑anxⁿ.

We substitute this power series in the differential equation and we get:

(x²y'' - x(1 + x)y' + y) = 0  

x²(∑anⁿ(n - 1)xⁿ⁻²) - x(1 + x)(∑anⁿxⁿ⁻¹) + (∑anxⁿ) = 0.

We use the product rule of differentiation to get:

(x²∑anⁿ(n - 1)xⁿ⁻²) - (x²∑anⁿ(n - 1)xⁿ⁻² + x∑anⁿxⁿ⁻¹) + (∑anxⁿ) = 0.

This can be simplified as:

(∑anⁿ(n - 1)xⁿ) - (∑anⁿ(n + 1)xⁿ) + (∑anxⁿ) = 0.(∑anⁿ(n - 1)xⁿ) - (∑anⁿ(n + 1)xⁿ) + (∑anxⁿ) = 0.

This equation holds true for all x. For simplicity, we can set the coefficients of xⁿ to zero.

Then, we have the following relations for the coefficients:For n = 0, an + a1 = 0.

For n > 1, an = (n + 1)aₙ₋₁ / (n - 1) - aₙ₋₂.The general formula for the coefficients is given by:an = (n + 1)aₙ₋₁ / (n - 1) - aₙ₋₂.

We can use the initial conditions to determine the values of a0 and a1.

We can also use the recurrence relation to calculate the other coefficients.

Thus, we can obtain the power series solution to x²y'' - x(1 + x)y' + y = 0 at x = 0 with the general formula for the coefficients.

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Answer:

There's no context for a conclusion.

Step-by-step explanation:

Comment when you've edited the question.

Answer:

the answer is 14

Step-by-step

multiply 2x7

Answer:

3.84

Step-by-step explanation:

 ((24) + 5(12) + 10(10) + 25(8)) ÷ 100 = (24 + 60 + 100 + 200) ÷ 100 Multiply.

                                                        = (384) ÷ 100                                 Add.

                                                        = 3.84                                         Divide.

Step-by-step explanation:

a) There are 4 Queens in a deck, so the probability the first card is a Queen is 4/52 = 1/13.

There are 4 10s in a deck, so the probability the second card is a 10 is 4/52 = 1/13.

The probability of both events is 1/13 × 1/13 = 1/169.

b) There is 1 Queen of Hearts in a deck, so the probability the first card is a Queen of Hearts is 1/52.

There are 4 8s in a deck, so the probability the second card is a 8 is 4/52 = 1/13.

The probability of both events is 1/52 × 1/13 = 1/676.

c) There are 4 Jacks in a deck, so the probability the first card is a Jack is 4/52 = 1/13.

There are 4 Jacks in a deck, so the probability the second card is a Jack is 4/52 = 1/13.

The probability of both events is 1/13 × 1/13 = 1/169.

d) There is 1 5 of Spades in a deck, so the probability the first card is a 5 of Spades is 1/52.

There is 1 Ace of Hearts in a deck, so the probability the first card is a Ace of Hearts is 1/52.

The probability of both events is 1/52 × 1/52 = 1/2704.

The correct answer is:

\(b. \sum f^n(2)/n! (x-2)^n = -3 +16(x-2) + 20(x-2)^2 + \sum 8(x-2)^3^/^n! + \sum (x-2)^4^/^n!\)

The Maclaurin series is:

\(f(x) = \sum (-1)^n (2x)^(^4^n^+^1^)/(3^(^2^n^)^(^2^n^)!) = \sum (-1)^n (2^(^4^n^+^1^)/3^(^2^n^)^(^2^n^)!) x^(^4^n^+^1^)\)

The indefinite integral of (cos(x) - 1/x) can be expressed as an infinite series.

The correct answer for the Taylor series of f(x) = x^4 - 4x^2 + 3 centered at a = 2 is:

\(b. \sum f^n(2)/n! (x-2)^n = -3 +16(x-2) + 20(x-2)^2 + \sum 8(x-2)^3^/^n! + \sum (x-2)^4^/^n!\)

The associated radius of convergence for this series is infinity, since the power series expansion of f(x) exists for all real numbers x.

To obtain the Maclaurin series for \(f(x) = 2x cos(1/3x^2)\), we can first find the Maclaurin series for \(cos(x^2^/^3^)\) and then multiply by 2x:

\(cos(x^2/3) = \sum (-1)^n (x^2/3)^(2n)/(2n)! = \sum (-1)^n x^(^4^n^)/(3^(^2^n^)^(^2^n^)!)\)

Therefore, the Maclaurin series for \(f(x) = 2x cos(1/3x^2)\) is:

\(f(x) = \sum (-1)^n (2x)^(^4^n^+^1^)/(3^(^2^n^)^(^2^n^)!) = \sum (-1)^n (2^(^4^n^+^1^)/3^(^2^n^)^(^2^n^)!) x^(^4^n^+^1^)\)

To evaluate the indefinite integral ∫(cos(x) - 1/x) dx as an infinite series, we can use the Maclaurin series for cos(x) and the power series expansion of \(ln(x) = \sum(-1)^(^n^+^1^) (x-1)^n/n\), which converges for 0 < x ≤ 2. Thus, we have:

\(\int(cos(x) - 1/x) dx = \intcos(x) dx - \int(1/x) dx = \sum(-1)^n x^(^2^n^+^1^)/(2n+1)! - ln|x| + C\)

where C is the constant of integration. We can simplify this expression as follows:

\(\int (cos(x) - 1/x) dx = \sum (-1)^n x^(^2^n^+^1^)/(2n+1)! - ln|x| + C\)

\(= -ln|x| + \sum(-1)^n x^(^2^n^+^1^)/(2n+1)!\)

\(= -ln|x| + \sum(-1)^n (x-1)^(^2^n^+^1^)/(2n+1)x^(^2^n^+^1^)\)

Thus, the indefinite integral of (cos(x) - 1/x) can be expressed as an infinite series.

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Answer:

I know that 2 is 18

Variation can be direct, inverse or jointly

Jordan's first error is that he incorrectly calculated the value of proportionality constant

From the question, we understand that f varies directly as the square root of g.

This variation is represented as:

\(\mathbf{ f\ \alpha\ \frac{1}{\sqrt{g}}}\)

Express as a equation

\(\mathbf{ f\ \ =\ k\frac{1}{\sqrt{g}}}\)

When f = 4, k = 4.

So, we have:

\(\mathbf{ 4\ \ =\ k\frac{1}{\sqrt{4}}}\)

\(\mathbf{ 4\ \ =\ \frac{k}{2}}\)

Multiply both sides by 2

\(\mathbf{ k = 8}\)

When g = 100, we have:

\(\mathbf{ f\ \ =\ k\frac{1}{\sqrt{g}}}\)

\(\mathbf{ f\ \ =\ 8 \times \frac{1}{\sqrt{100}}}\)

\(\mathbf{ f\ \ =\ 8 \times \frac{1}{10}}\)

\(\mathbf{ f\ \ = 0.8}\)

This means that, Jordan incorrectly calculated the value of proportionality constant

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a) To make the table for the proportional relationship, given that he delivers 14 newspapers in 20 minutes, the first step is to determine the unit rate (or constant of proportionality), that is, the number of papers he delivers in one minute.

Let x be the time in minutes and y be the number of newspapers delivered, their relationship can be expressed as:

Where k is the constant of proportionality, you can calculate it as:

For x=20 and y=14

The unit rate is 0.7 newspapers per minute.

(a) is a prime ideal of R, and since v is contained in (a), we have either v = (a) or v = R. Therefore, The only ideals of R containing u are u and R itself.

To prove that if v is an ideal of r and r ⊃ v ⊃ u, then either v = r or v = u, we need to use the fact that the only ideals of r are the trivial ones (0 and r) and the maximal ones (prime ideals). Since u is not a prime ideal (since it contains multiples of 17), the only possibilities for v are u and r. To see this, suppose that v is a proper ideal of r containing u. Then there exists some non-zero element a in v that is not in u. Since a is not a multiple of 17, it must have a prime factor p that is not 17 (otherwise, it would be a multiple of 17). But then (a) is a prime ideal of r (since r is a UFD), and since v is contained in (a), we have either v = (a) or v = r. Therefore, we have shown that if v is an ideal of r and r ⊃ v ⊃ u, then either v = r or v = u. We can generalize this result to any ring R and any proper ideal u of R by using the same argument. If v is a proper ideal of R containing u, then there exists some non-zero element a in v that is not in u. But then (a) is a prime ideal of R, and since v is contained in (a), we have either v = (a) or v = R. Therefore, the only ideals of R containing u are u and R itself.

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The second bank is better since they've a higher interest rate.

Tommy earned $76.00 in interest after 5 years on a principal of $400. The interest rate will be calculated thus:

Rate = 100I / PT

where I = interest

p = principal

t = time

Rate = 100I / PT

Rate = (100 × 76) / 400 × 5

Rate = 7600 / 2000

Rate = 3.8%

Jane earned $82.00 in interest after 2 years on a

principal of $1,000. The interest rate will be calculated thus:

Rate = 100I / PT

where I = interest

p = principal

t = time

Rate = 100I / PT

Rate = (100 × 82) / 1000 × 2

Rate = 8200 / 2000

Rate = 4.1%

The second bank is better.

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Answer:

Step-by-step explanation:

According to the question a.)  the probability that a customer will take less than two minutes is 0.424 or 42.4%. b.) the probability that a customer will take more than four minutes is 0.097 or 9.7%.

Let's calculate the probabilities using the given information.

a. Probability that a customer will take less than 2 minutes:

The average customer service time is 3.9 minutes, which corresponds to λ (lambda) in the exponential distribution. Plugging in the values, we have:

\(P(X < 2) = 1 - e^\(-3.9 * 2\)

Calculating this expression, we find:

P(X < 2) ≈ 0.424

Therefore, the probability that a customer will take less than two minutes is approximately 0.424 or 42.4%.

b. Probability that a customer will take more than 4 minutes:

Using the same average customer service time of 3.9 minutes, we can calculate:

\(P(X > 4) = e^\(-3.9 * 4\)

Calculating this expression, we find:

P(X > 4) ≈ 0.097

Therefore, the probability that a customer will take more than four minutes is approximately 0.097 or 9.7%.

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Answer:

1 . Chicken curries - £6.20 X 2 =  £12.40  15% of  £ 12.40 is £1.86 off = £10.54  +

2 .Onion Soups - £4.00 x 2 = £8.00    15% OF £8.00 is £ 1.20 off =       £6.80

3. One Naan bread = £.2.80    15% of £ 2.80 is £ 0.42 p  off  =              £2.38

4. One mint parfait = £ 3.80     15% of £ 3.80 is £ 0.57 p off  =               £ 3.23

5 .One ice cream delight = £2.60  15% of £ 2.60 is £0.39 p off             £ 2.21

                                                                                                           =      £ 25.16

Step-by-step explanation:

1. to find out 15% from £12.40 you can divide 12.40 / 100 = 0.124 and then times 0.124 by the percentage = 0.124 x 15 = £ 1.86

2 . to find out 15% from £8.00 you divide again £8.00 / 100 =0.08 and then times 0.08 by the percentage 15 %= 0.08 x 15 = £1.20 off

3.  £ 2.80 / 100 =0.028 x 15% =  £0.42 p off

4.    £ 3.80 /100 = 0.038 x 15% = £ 0.57 p off

5.     £ 2.60 /100 = 0.026 x 15% = £ 0.39 p off

Hope that helped !

Answer:

$1.50 per pound

Step-by-step explanation:

You divide 6 by 4 to get 1.5

Answer:

The record time that was achieved in 1970 was 5.78 seconds.

Step-by-step explanation:

It is given that the first one-mile speed record was made by Henry Ford in 1904 when he drove the mile in 39.40 seconds.

It is further stated that this time was 33.62 s slower than the record achieved in 1970.

Now, let us consider the first statement;

Henry Ford covered one mile in time (1904) = 39.40 sec

Now, let us consider the second statement given;

Time taken by Henry Ford (1940) was slower than the time someone else achieved in one miles by = 33.62 sec

So, to calculate the time taken in 1970;

=> 39.40 - 33.62 sec

=> 5.78 sec

Therefore, the record time that was achieved in 1970 was 5.78 seconds.

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Answer:

i don't know but o o o o right e o right e auto park

Answer:

4234324tgfgdfgdgd

Step-by-step explanation: