15y ─13y ─2y + 3y = 9

The required particular solution isf(x) = -2ln(x) + 7x - 2. Hence, the solution is f(x) = -2ln(x) + 7x - 2.

Given differential equation is f''(x) = 4/x^2 .

To find the particular solution of the differential equation that satisfies the initial equations we have to solve the differential equation.

The given differential equation is of the form f''(x) = g(x)f''(x) + h(x)f(x)

By comparing the given equation with the standard form, we get,g(x) = 0 and h(x) = 4/x^2

So, the complementary function is, f(x) = c1x + c2/x

Since we have × > 0

So, we have to select c2 as zero because when we put x = 0 in the function, then it will become undefined and it is also a singular point of the differential equation.

Then the complementary function becomes f(x) = c1xSo, f'(x) = c1and f''(x) = 0

Therefore, the particular solution is f''(x) = 4/x^2

Now integrating both sides with respect to x, we get,f'(x) = -2/x + c1

By using the initial conditions,

f'(1) = 5and f(1) = 5, we get5 = -2 + c1 => c1 = 7

Therefore, f'(x) = -2/x + 7We have to find the particular solution, so again integrating the above equation we get,

f(x) = -2ln(x) + 7x + c2

By using the initial condition, f(1) = 5, we get5 = 7 + c2 => c2 = -2

Therefore, the required particular solution isf(x) = -2ln(x) + 7x - 2Hence, the solution is f(x) = -2ln(x) + 7x - 2.

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The appropriate response will be (A). The first equation of motion gives the link between "velocity and time."

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

An equation is a mathematical representation of two equal objects, one on each side of a "equals" sign. We can solve challenges in our daily lives with the aid of equations. Most of the time, we look for help with pre algebra to resolve problems in real life. Pre-algebra concepts contain the fundamentals of mathematics.

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With Alpha set to .05, increasing the sample size would not directly reduce the probability of a Type I error. The probability of a Type I error is determined by the significance level (Alpha) and remains constant regardless of the sample size.

However, increasing the sample size can indirectly affect the probability of a Type I error by increasing the statistical power of the test. With a larger sample size, it becomes easier to detect a statistically significant difference between groups, reducing the likelihood of falsely rejecting the null hypothesis (Type I error).

Increasing the sample size generally decreases the probability of a Type II error, which is failing to reject a false null hypothesis. With a larger sample size, the test becomes more sensitive and has a higher likelihood of detecting a true effect if one exists, reducing the likelihood of a Type II error. However, it's important to note that other factors such as the effect size, variability, and statistical power also play a role in determining the probability of a Type II error.

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If f(x)=2x²-5x-3 g(x)=2x²+5x+2 then (f/g)(x) = (x - 3) / (x + 2).

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find (f/g)(x), we need to divide f(x) by g(x) as follows:

f(x) = 2x² - 5x - 3

g(x) = 2x² + 5x + 2

f(x) / g(x) = (2x² - 5x - 3) / (2x² + 5x + 2)

To simplify this expression, we can factor the numerator and denominator:

f(x) / g(x) = [(2x + 1)(x - 3)] / [(2x + 1)(x + 2)]

Now, we can cancel out the common factor of (2x + 1) from both the numerator and denominator:

f(x) / g(x) = (x - 3) / (x + 2)

Therefore, (f/g)(x) = (x - 3) / (x + 2).

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To draw a rectangular array for 24 x 18 on graph paper, we create a grid with 24 rows and 18 columns.

The partial-products algorithm for multiplying 24 and 18 involves breaking down the multiplication into smaller, manageable steps. The array helps visualize these steps and demonstrates why the algorithm yields the correct answer. Using the array, we start by dividing the 24 x 18 rectangle into smaller squares that represent individual partial products. Each row in the array corresponds to a digit in the multiplier (24), and each column corresponds to a digit in the multiplicand (18). We fill in the array by multiplying the corresponding digits in the multiplier and multiplicand.

For example, the first partial product is obtained by multiplying the rightmost digit of the multiplier (4) by each digit in the multiplicand (8, 1). We place the result, 32, in the corresponding square in the array. Similarly, we calculate the other partial products and place them in the corresponding squares. To find the final product, we sum up all the partial products in the array. In this case, we add up the values in all the squares to get 432, which is the correct answer to 24 x 18.

The array demonstrates why the partial-products algorithm works. By breaking down the multiplication into smaller steps and organizing them in the array, we ensure that each digit in the multiplier is multiplied by each digit in the multiplicand. The array visually represents the distributive property of multiplication, where each digit in one number is multiplied by each digit in the other number. Adding up the partial products gives the total product, ensuring the correct result. The array provides a visual proof of why the partial-products algorithm yields the correct answer to the multiplication problem.

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Step-by-step explanation:

= ( 3x + 5 ) ( 4x² + 8x + 40 )

= 3x ( 4x² + 8x + 40 ) + 5 ( 4x² + 8x + 40 )

= 12x³ + 24x²+ 120x + 20x² + 40x + 200

= 12x³ + 24x² + 20x² + 120x + 40x + 200

= 12x³ + 44x² + 160x + 200

Answer:

12x^3 +44x^2 +160x +200

Step-by-step explanation:

Distribute:

(3x+5)(4x^2 +8x+40)

3x(4x^2 +8x+40) +5(4x^2 +8x+40)

Then it would be:

(12x^3 +24x^2 +120x) + (20x^2 + 40x +200)

therefore the soloution is:

12x^3 +44x^2 +160x +200

Answer:

17/6

So this is the answer. If you want to convert to decimal... The answer will be 2.83..hope it is right

Answer: 5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

The slopes of both equations are identical (both being 2/3), therefore the only possible answers would be "infinitely many solutions" and "no solution". Because of the fact that the y-intercepts of the equations are different (-10 and 10) they two lines will never cross, meaning there is no solution.

Answer:

no solution

Step-by-step explanation:

\(\frac{2}{3} x - 10 = \frac{4}{6} x + 10\)

Reduce the fraction:

\(\frac{2}{3} x - 10 = \frac{2}{3} x + 10\)

Rearrange variables to the left side of the equation:

\(\frac{2}{3} x - \frac{2}{3} x = 10 + 10\)

Apply the inverse property of addition

0 = 10 + 10

0 = 20

Based on the given conditions, the system of equations has no solution.

hope this helps!! p.s. i really need brainliest :)

Answer

The function rule that models the total cost of a purchase is

f(x) = 1.19x dollars

15 bottles will cost $17.85

Explanation

Each bottle costs $1.19.

If one buys x bottles, the total cost of purchase will be

f(x) = 1.19 × x = 1.19x dollars.

Hence, the function rule that models the total cost of a purchase is

f(x) = 1.19x dollars

So, to evaluate the function for 15 bottles.

When x = 15

f(15) = 1.19 × 15 = $17.85

Hope this Helps!!!

The surface area of the rectangular prism represented by the given net is 176 square units.

To calculate the surface area of the rectangular prism represented by the net,

we have to identify the dimensions of the rectangular prism from the given net.

The figure of the given net is shown below:

Net for a rectangular prism:

We can see that the net consists of three rectangles, two of which are congruent, and one of them is different in size. The dimensions of the three rectangles are as follows:

Length of rectangle = 6 units

Width of rectangle = 4 units

Length of rectangle (congruent to first rectangle) = 6 units.

Width of rectangle (congruent to first rectangle) = 4 units.

Length of the third rectangle = 8 units

Width of the third rectangle = 4 units

We can observe from the net that the length of the rectangular prism is represented by the third rectangle, which is 8 units.

The width of the rectangular prism is represented by the length of the other two congruent rectangles, which is 6 units. The height of the rectangular prism is represented by the width of the two congruent rectangles, which is 4 units.

Now, we can calculate the surface area of the rectangular prism as follows:

Surface Area = 2(lb + bh + lh)

where l = length,

b = width, h = height

Substituting the values of l, b, and h, we get,

Surface Area = 2(6 × 4 + 4 × 4 + 8 × 6) = 2(24 + 16 + 48) = 2(88) = 176

Thus, the surface area of the rectangular prism represented by the given net is 176 square units.

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The range of possible distances from the beach to the theater is 2 km to 16 km, calculated by subtracting the distance between the theater and the house (7 km) from the distance between the beach and the house (9 km), and adding it back.

To calculate the range of possible distances from the beach to the theater, we can use the information provided

Start with the distance between the beach and the house: 9 km.

Subtract the distance between the theater and the house: 7 km.

9 km - 7 km = 2 km.

This gives us the minimum possible distance from the beach to the theater: 2 km.

Add the distance between the theater and the house: 7 km.

9 km + 7 km = 16 km.

This gives us the maximum possible distance from the beach to the theater: 16 km.

Therefore, the range of possible distances is from 2 km to 16 km.

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--The given question is incomplete, the complete question is given below " Describe the range of possible distances from the beach to the theater "--

Answer:

1,008 pairs of earrings

Step-by-step explanation:

14 multiplied by 72 equals 1,008

Answer: D.

Step-by-step explanation:

The formula for a z-score in statistics is:
(x-value - mean) / standard deviation

We are given all three values, so we can simply plug them in:

z = (62 - 79)/4

z = -17/4

z = -4.25

Answer: Down

Step-by-step explanation:

down nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Using the laws of exponents, we can rewrite the expression as:

b^4 * b^(-1/4) = b^(4 - 1/4) Simplifying the exponent, we get:

b^(15/4). Therefore, the expression in the form bn is b^(15/4).

To rewrite the expression b^4 * b^(-1/4) in the form bn, we need to apply the laws of exponents. The law of exponents states that when multiplying two powers with the same base, we can add the exponents. In this case, we have b^4 multiplied by b^(-1/4), which means that we have the same base b. Using the law of exponents, we add the exponents 4 and -1/4 to get 4 - 1/4 = 15/4. Thus, we have simplified the expression b^4 * b^(-1/4) to b^(15/4). This is in the form of bn, where b is the base and n is the exponent. Therefore, the expression b^4 * b^(-1/4) is equivalent to b^(15/4).

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The number of new biking outfits that Zendaya can buy will be 5 outfits

Let the number of new biking outfits that can be purchased be x

Amount to spend = $700

Based on the information given, the equation to use will be:

242.33 + (3 × 7.17) + 33.68 + (77.40 × x) = 700

242.33 + 21.51 + 33.68 + 77.40x = 700

Collect like terms

77.40x = 700 - 242.33 - 21.51 - 33.68

77.40x = 402.48

x = 402.48/77.40

x = 5.2

The number of new biking outfits that Zendaya can buy is 5 outfits

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The local maximum and minimum values of the function f(x) = -x - x^49, obtained using the Second Derivative Test, are as follows:

Local maximum: None

Local minimum: (0, 0)

To determine the local maximum and minimum values of the given function, we need to find its critical points and apply the Second Derivative Test.

Find the first derivative of f(x):

f'(x) = -1 - 49x^48

Find the critical points by setting f'(x) = 0:

-1 - 49x^48 = 0

49x^48 = -1

x^48 = -1/49

Since x^48 cannot be negative, there are no real solutions for x. Therefore, there are no critical points.

Find the second derivative of f(x):

f''(x) = -2352x^47

Evaluate f''(x) at x = 0:

f''(0) = -2352(0)^47

f''(0) = 0

According to the Second Derivative Test, if f''(c) > 0, then f(c) has a local minimum at x = c. Conversely, if f''(c) < 0, then f(c) has a local maximum at x = c. In our case, since f''(0) = 0, the Second Derivative Test is inconclusive.

Therefore, the only point we have is (0, 0), which is a local minimum for the function f(x) = -x - x^49. There are no local maximum values for this function.

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Answer:

26cm^2

Step-by-step explanation:

To calculate area of a triangle we multiply height with base and that divided by two

13 × 4 ÷ 2 = 26cm^2

Answer:

the correct answer of x is 16

Answer:

3rd is the answer!! Hope this helps

a. The null and alternative hypotheses can be set up as follows:

Null Hypothesis (H0): There is no relationship between assertiveness and leadership ability.

Alternative Hypothesis (Ha): Leadership ability increases at a decreasing rate with assertiveness.

b. To conduct the test, we need to examine the p-value associated with the coefficient estimate for the quadratic term (x2) in the quadratic regression model. The reported results show that the p-value for x2 is less than 0.01 (< 0.01), which is below the significance level of 0.05.

c. Since the p-value is less than the significance level (p-value < 0.05), we can reject the null hypothesis. This indicates that there is evidence to support the alternative hypothesis that leadership ability increases at a decreasing rate with assertiveness. In other words, the researchers' theory is supported by the data, suggesting that as assertiveness increases, leadership ability also increases but at a decreasing rate.

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No, it is not it true that for any integer n ≤ 2, φ(n) has a primitive root

In modular arithmetic, a number g is called a primitive root modulo n if every number  coprime to n is congruent to a power of  modulo . Mathematically, g is a primitive root modulo n if and only if for any integer  a such that gcd(a, n)=1 , there exists an integer k such that:

.\(g^{k}\)≡ a (mod n)

Now,

Existence of Primitive root modulo n exists if and only if:

So,

if n be a positive integer. A primitive root mod n is an integer g such that every integer relatively prime to n is congruent to a power of g mod n.

For example,

As ϕ(11)=10, the order of 2(mod11) must divide 10.  

So we check 22≡4(mod11) and 25≡10(mod11).

Since neither of these are 1, and

we know 2ϕ(11)=210≡1(mod11) by Euler's Theorem,

ord112=ϕ(11), making 2 a primitive root modulo 11.

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(a) the mean value of To is 28 degrees and the standard deviation is 1.96 degrees. (b) The probability of P(26T < 30) is 0.6922. (c) The probability of P(T < 32) is 0.9798.

(a) The mean value of To can be found by multiplying the mean temperature of each town (2 degrees) by the number of towns (14), resulting in a mean value of 28 degrees.

The standard deviation of To can be found by multiplying the standard deviation of the temperature in each town (0.4 degrees) by the square root of the number of towns (14), resulting in a standard deviation of 1.96 degrees.

(b) To find the probability P(26T < 30), we need to standardize the values and use the standard normal distribution. First, we calculate the z-score for both values:

z1 = (26 - 28) / 1.96 = -1.02

z2 = (30 - 28) / 1.96 = 1.02

Next, we look up the corresponding probabilities in the standard normal distribution table.

P(26T < 30) can be calculated as the difference between the cumulative probabilities of z2 and z1:

P(26T < 30) = P(z < 1.02) - P(z < -1.02)

Using the standard normal distribution table, we find P(z < 1.02) = 0.8461 and P(z < -1.02) = 0.1539.

Therefore, P(26T < 30) = 0.8461 - 0.1539 = 0.6922.

(c) To find the probability P(T < 32), we need to calculate the z-score for this value:

z = (32 - 28) / 1.96 = 2.04

Next, we look up the corresponding probability in the standard normal distribution table: P(z < 2.04) = 0.9798.

Therefore, P(T < 32) = 0.9798.

In summary, (a) the mean value of To is 28 degrees and the standard deviation is 1.96 degrees. (b) The probability of P(26T < 30) is 0.6922. (c) The probability of P(T < 32) is 0.9798.

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Answer:

7 * 4 / 2 = 28/2 = 14

Step-by-step explanation:

You are timed. I will just give you the formula where its multiplying the Diagonals and dividing by 2.

x= -4 w= 1 z= -3 y= 5

This is the answer!