Part A is already answered

Part B asks: What is the length of the hypotenuse?

To find the value of f(-2) given the differential equation dy/dx = e^(x-1) * e^y with the initial condition f(1) = 0, we can use separation of variables and solve the differential equation.

Starting with the given differential equation:

dy/dx = e^(x-1) * e^y

Separating variables by multiplying both sides by dx and e^(-y):

e^(-y) dy = e^(x-1) dx

Now, we can integrate both sides of the equation:

∫ e^(-y) dy = ∫ e^(x-1) dx

Integrating the left side with respect to y and the right side with respect to x:

e^(-y) = e^(x-1) + C

Applying the initial condition f(1) = 0, where x = 1 and f(1) = 0:

e^(-0) = e^(1-1) + C

1 = 1 + C

C = -2

Substituting the value of C back into the equation:

e^(-y) = e^(x-1) - 2

Now, we can find the value of f(-2) by substituting x = -2 into the equation:

e^(-y) = e^(-2-1) - 2

e^(-y) = e^(-3) - 2

To find the value of f(-2), we need to solve for y:

e^(-y) = 2 - e^(-3)

y = -ln(2 - e^(-3))

Therefore, the value of f(-2) is f(-2) = -ln(2 - e^(-3)).

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The y-intercept for the given equation p = 285+45n is 285.

The Y-intercept is the point where the graph intersects the y-axis.

To find the y-intercept of a function y = f(x), substitute x=0 and solve for y.

According to the given question

we have an equation p = 285+45n

where,

p is the amount of profit

and, n is the number of necklaces

Let,  p = y and n = x

then the given equation becomes y=285+45x

substitute, x = 0 in equation y = 285+45x

⇒ y = 285

Hence, the y-intercept of the equation p=285+45n is 285.

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Answer:

This is a line that is parallel to Y-axis

Answer:

189cm^3

Step-by-step explanation:

First, we need to find the formula of "how to find the volume of any prism":

length * width *height

* = multiply

So that means we need to do:

7cm * 9cm * 3cm

= 189cm^3

^ = exponent

Hope this helped :)

Answer:

the two consecutive negative integers are -2 and -1.

Step-by-step explanation:

Represent these negative integers by m and n.

Then (because the integers are consecutive) n = m + 1, and m^2 = n + 5.

Substituting m + 1 for n in the second equation, we get:

m^2 = m + 1 + 5, or

m^2 - m - 6 = 0

This factors into (m - 3)(m + 2) = 0.  The only negative root is -2.  

Thus, the two consecutive negative integers are -2 and -1.

Check:  Is the  square of the first five more than the second?

Is (-2)^2 = -1 + 5?  YES

The integers aer -2 and -1.

Answer:

8 × 10⁻⁴

Step-by-step explanation:

Answer:

[tex]a_{n}[/tex] = n - 7

Step-by-step explanation:

There is a common difference between consecutive terms in the sequence

d = - 5 - (- 6) = - 4 - (- 5) = - 3 - (- 4) = 1

This indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 6 and d = 1 , then

[tex]a_{n}[/tex] = - 6 + 1 (n - 1) = - 6 + n - 1 = n - 7

Answer:

the answer is A:

sinA=h/c

sinC=h/a

Step-by-step explanation:

edge 2020

The pair of equations is sinA=h/a cosC=h/a

What is trigonometry?

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms.

When a altitude is drawn from the base of the triangle

we can write

sinA=height/ a where a, is the side length of AB

also,cos C=height/a where a, is the side length of AB

Therefore,The pair of equations is where a, is the side length of AB

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Answer:

17

Step-by-step explanation:

by Pythagoras

[tex]8 {}^{2} + 15 {}^{2} = {x}^{2} [/tex]

x=17

Answer:

1047.4 cm^3

Step-by-step explanation:

Answer:1047.4

Step-by-step explanation:

.

The null hypothesis for this test is that the probability that the home team wins is equal to or less than one half. The alternative hypothesis is that the probability that the home team wins is greater than one half.

1. Identify the null hypothesis (H0): The null hypothesis for this test is that the probability that the home team wins is equal to or less than one half (P ≤ 0.5).

2. Identify the alternative hypothesis (Ha): The alternative hypothesis is that the probability that the home team wins is greater than one half (P > 0.5).

3. Determine the significance level (α): The significance level, also known as the alpha level, is set at 0.01. This means that we are willing to accept a 1% chance of rejecting the null hypothesis when it is actually true.

4. Collect the sample data: In this case, we have a sample of 47 football games, where "at" of them were won by the home team (let's assume "at" to be a specific number).

5. Calculate the test statistic: To test the claim, we need to calculate the test statistic based on the sample data. Since we are comparing a proportion (probability), we can use the z-test. The test statistic formula is given by:

  z = (p - P) / √(P * (1 - P) / n)

  Where:

  p is the proportion of games won by the home team in the sample,

  P is the claimed probability that the home team wins (in this case, P = 0.5),

  n is the sample size.

6. Determine the critical value: Since we have a one-tailed test (alternative hypothesis is directional), we need to find the critical value corresponding to the significance level of 0.01 in the standard normal distribution (z-distribution). Using a z-table or a statistical software, the critical value for a 0.01 significance level is approximately 2.33.

7. Compute the test statistic: Plug in the values from the sample data into the test statistic formula calculated in Step 5 to obtain the z-value.

8. Compare the test statistic with the critical value: If the test statistic is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

9. Make a decision: If the test statistic is greater than the critical value, we reject the null hypothesis, indicating that there is sufficient evidence to support the claim that the probability that the home team wins is greater than one half. If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis, indicating that there is not enough evidence to support the claim.

10. Provide a conclusion: Based on the decision made in Step 9, state the conclusion in the context of the problem. For example, if we reject the null hypothesis, we can conclude that there is significant evidence to suggest that the home team has a greater than 50% chance of winning in these football games.

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The variance of the sampling distribution of means, on the other hand, is equal to the variance of all possible sample means of the same size taken from the population.

Since a sample size is always less than the population size, the variance of the population distribution is greater than the variance of the sampling distribution of means.

Therefore, option B is correct.
The probability of selecting one data value less than 190 IS (C)31%

When the variances of the population distribution and the sampling distribution of means are compared, the (B) population variance is larger than the sampling distribution variance.

The probability of selecting one data value less than 190 given the mean and standard deviation of a population of 200 and 20 respectively is 31% (option C).

Solution: Given,

mean (μ) = 200,

standard deviation (σ) = 20

We need to find the probability of selecting one data value less than 190.

P(x < 190) = ?

Z = (X - μ)/σ

Taking X = 190,

Z = (190 - 200)/20

= -0.5

From the standard normal table, the probability of

Z = -0.5 is 0.3085

Therefore,

P(x < 190) = P(Z < -0.5)

= 0.3085

= 31%

Hence, option C is correct.

When the variances of the population distribution and the sampling distribution of means are compared, the population variance is larger than the sampling distribution variance.

This can be explained as follows;

The population distribution is the distribution of an entire population, while the sampling distribution of the mean is the distribution of the means of all possible samples of a specific size drawn from that population.

The variance of the population distribution is equal to the variance of a single observation of the population.

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Answer:

The answer is A 56.25

Step-by-step explanation:

Since a square has 4 sides, divide 225 by 4 to get 56.25. To check your answer multiply 56.25 x 4 to get 225 in^2.

Hope this helps! Pls mark Brainliest!

Answer:

a.56.25

Step-by-step explanation:

Answer:

117 Degrees

Step-by-step explanation:

plz give brailiest, the 1 and 117 are the exact same angle

Answer:

Step-by-step explanation:

As triangles are similar

The ratio of the sides must be equal

so..

[tex]\frac{x}{8} =\frac{9}{5}[/tex]

[tex]x=\frac{9*8}{5}[/tex]

[tex]x=14.4[/tex]

hope it helps...

have a great day!!

Answer: i would say B because it makes the most sence

Step-by-step explanation:

Answer:

k = 8

Step-by-step explanation:

10*8 - 90 = -10

:/

The equation [tex](sin(x)cos(x))^2 = sin(2x)[/tex] is verified to be an identity.

Simplify LHS and RHS?

To verify whether the equation [tex](sin(x)cos(x))^2 = sin(2x)[/tex] is an identity, we can simplify both sides of the equation and see if they are equivalent.

Starting with the left side of the equation:

[tex](sin(x)cos(x))^2 = (sin(x))^2(cos(x))^2[/tex]

Now, we can use the trigonometric identity [tex]sin(2x) = 2sin(x)cos(x)[/tex] to rewrite the right side of the equation:

[tex]sin(2x) = 2sin(x)cos(x)[/tex]

Substituting this into the equation, we have:

[tex](sin(x))^2(cos(x))^2 = (2sin(x)cos(x))[/tex]

Next, we can simplify the left side of the equation:

[tex](sin(x))^2(cos(x))^2 = (sin(x))^2(cos(x))^2[/tex]

Since both sides of the equation are identical, we can conclude that the given equation is indeed an identity:

[tex](sin(x)cos(x))^2 = sin(2x)[/tex]

Hence, the equation [tex](sin(x)cos(x))^2 = sin(2x)[/tex] is verified to be an identity.

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Step-by-step explanation:

Reduce 5/35 to lowest terms

The simplest form of 535 is 17.

Answer:

1/7

Step-by-step explanation:

divide both sides by 5

To calculate the magnitude of the gravitational force A exerts on B and B exerts on A, we can use Newton's law of universal gravitation:

[tex]F = (G * m1 * m2) / r^2[/tex]

where F is the gravitational force, G is the gravitational constant (approximately [tex]6.67430 *10^-11 N m^2 / kg^2)[/tex], m1 and m2 are the masses of the two spheres, and r is the distance between their centers.

For the force A exerts on B:

[tex]F_AB = (G * m_A * m_B) / r^2[/tex]

Substituting the given values: m_A = 7.5 kg, m_B = 6.3 kg, and r = 0.59 m:

F_AB = (6.67430 × 10^-11 N m^2 / kg^2) * (7.5 kg) * (6.3 kg) / (0.59 m)^2

Calculating the above expression gives the magnitude of the gravitational force A exerts on B.

For the force B exerts on A, we use the same formula:

[tex]F_BA = (G * m_A * m_B) / r^2[/tex]

Substituting the given values: m_A = 7.5 kg, m_B = 6.3 kg, and r = 0.59 m:

[tex]F_BA = (6.67430 * 10^-11 N m^2 / kg^2) * (6.3 kg) * (7.5 kg) / (0.59 m)^2[/tex]

Calculating the above expression gives the magnitude of the gravitational force B exerts on A.

To find the distance between the centers of the spheres when the force between them is 3.50 times 10^-9 N, we rearrange the formula to solve for r:

r = √((G * m_A * m_B) / F)

Substituting the given values: m_A = 7.5 kg, m_B = 6.3 kg, and F = 3.50 × 10^-9 N:

r = √[tex]((6.67430 * 10^-11 N m^2 / kg^2) * (7.5 kg) * (6.3 kg) / (3.50 *10^-9 N))[/tex]

Calculating the above expression gives the distance between the centers of the spheres.

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Answer:

5%

Step-by-step explanation:

20=  100%

1 x100 = 100

100/20= 5

The coordinate vector of vector a = [2, 3, 4, 5] with respect to the basis B = [e22, e21, e12, e11] of M22 is [3, 4, 5, 2].

To find the coordinate vector, we need to express vector a as a linear combination of the basis vectors. The given basis B represents the standard basis for a 2x2 matrix.

Let's break down the process step by step:

Start with the basis vectors: e22, e21, e12, e11.

Express vector a as a linear combination of the basis vectors:

a = 2 * e22 + 3 * e21 + 4 * e12 + 5 * e11

The coefficients in front of each basis vector represent the coordinates of a with respect to the basis B.

Therefore, the coordinate vector of a with respect to B is [2, 3, 4, 5].

However, it's important to note that the given basis B is not the standard basis for a 2x2 matrix. The standard basis for a 2x2 matrix consists of the following vectors: e11 = [1, 0, 0, 0], e12 = [0, 1, 0, 0], e21 = [0, 0, 1, 0], e22 = [0, 0, 0, 1].

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Answer:

495

Step-by-step explanation:

Base area = 11*11 = 121

Lateral area = (11*4)*17/2 = 11*2*17 = 374

121+374=495

(a) The probability of the chosen hard drive to fail within one year is 0.005.

(b) The probability that the hard drive was manufactured by company C is 3.95%.

(a) The probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is:

Probability of choosing hard drive from company A and failure within one year + Probability of choosing hard drive from company B and failure within one year + Probability of choosing hard drive from company C and failure within one year

P(A and F) = P(A) x P(F|A) = 0.5 x 0.001 = 0.0005

P(B and F) = P(B) x P(F|B) = 0.3 x 0.002 = 0.0006

P(C and F) = P(C) x P(F|C) = 0.2 x 0.005 = 0.0010

The probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is:

0.0005 + 0.0006 + 0.0010 = 0.0021 (or 0.21%)

(b) Let F be the event that the hard drive fails within one year and C be the event that the hard drive is manufactured by company C.

We want to calculate P(C|F), the probability that the hard drive was manufactured by company C, given that it failed within one year;

P(C|F) = P(C and F) / P(F) = [P(C) x P(F|C)] / [P(A) x P(F|A) + P(B) x P(F|B) + P(C) x P(F|C)]

P(C|F) = (0.2 x 0.005) / (0.5 x 0.001 + 0.3 x 0.002 + 0.2 x 0.005)

P(C|F) = 0.083 / 0.0021 = 0.0395 (or 3.95%)

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The probability that the hard drive in my computer is manufactured by company C given that my computer experiences a hard drive failure within one year is approximately 0.74.

(a) Let the random variable X denote the number of hard drives in the computer manufacturer's hard drives that fail within one year. The probability distribution of X can be found as follows:

[tex]P(X = 0) = 0.5(1 - 0.001) + 0.3(1 - 0.002) + 0.2(1 - 0.005) = 0.9957[/tex]

[tex]P(X = 1) = 0.5(0.001) + 0.3(0.002) + 0.2(0.005) = 0.0016[/tex]

Thus, the probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is 0.0016.

(b) Let the event H denote that the computer I buy experiences a hard drive failure within one year. Let the event Ci denote that the hard drive in my computer is manufactured by company

i. Then, using Bayes' theorem, we have:

[tex]P(C3 | H) = P(H | C3)P(C3) / P(H)[/tex]

We can find the values of the three probabilities in the above formula as follows:

P(H | C1) = 0.001

P(H | C2) = 0.002

P(H | C3) = 0.005

P(C1) = 0.5

P(C2) = 0.3

P(C3) = 0.2

[tex]P(H) = P(H | C1)P(C1) + P(H | C2)P(C2) + P(H | C3)P(C3)≈ 0.00135[/tex]

Thus, P(C3 | H) = 0.005(0.2) / 0.00135 ≈ 0.74

Therefore, the probability that the hard drive in my computer is manufactured by company C given that my computer experiences a hard drive failure within one year is approximately 0.74.

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Answer:

Each month Bill reads 3 novels so you get

N = 3m

If you plug in 6 for m we get

N = 3(6) = 18

Bill needs to read 18 novels in 19 months

Step-by-step explanation:

Answer: 1/3

Step-by-step explanation:

2.5:7.5

3:9

just simplify

Answer:

44

Step-by-step explanation:

14x3.14 is 43.96 and that after being rounded to the nearest tenth becomes 44