What are the domain and range of the function f(x)= X-7+9?

Given that the function f is defined as below;f(x) = { e^(-2x) / (1-2) } if x < 0x if x ≥ 0 The question is to find the domain of f and f^-1.Domain: The set of all values that x can take is called the domain of the function.

From the function f, we can observe thatx can take values from negative infinity to zero (-∞, 0) and from 0 to positive infinity [0, ∞). Thus, the domain of the function f is given by Df = (-∞, 0) U [0, ∞).Now, we need to find f^-1. To do this, we must interchange the position of x and f(x), and solve for x. Let y = f(x)f(x) = { e^(-2x) / (1-2) } if x < 0x if x ≥ 0Now, let us consider y < 0For y < 0, we have y = e^(-2x) / -1 ⇒ e^(-2x) = -y.0

But the exponential function e^(-2x) is always positive, for all x. Therefore, there does not exist any value of x such that e^(-2x) = -y for y < 0, and hence f^-1 is not defined for y < 0.Now, let us consider y = 0For y = 0, we have y = e^(-2x) / (1-2) if x < 0x if x ≥ 0Simplifying, we get;{ e^(-2x) / -1 } = 0 if x < 0x = 0 if x ≥ 0Clearly, we can see that x = 0 is the only value for which y = 0. Therefore, f^-1(0) = 0.Now, let us consider y > 0For y > 0, we have y = e^(-2x) / (1-2) if x < 0x if x ≥ 0Simplifying, we get;e^(-2x) = -y / 1 if x < 0x = y if x ≥ 0Now, we must solve for x in the equation e^(-2x) = -y / 1The solution to the above equation is given by;x = - (1/2) ln(y), where y > 0Therefore, the inverse of the function f is given by:f^-1(y) = { 0, y = 0- (1/2) ln(y), y > 0 }

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Answer:

A

Step-by-step explanation:

I don't think you have the right equation down, so this more of an educated guess than an actual direct answer

Answer:

Step-by-step explanation:

a. The probability that the selected country won greater than 50 medals is 0.0348

b. The probability that the selected country did not win greater than 100 medals is 0.988

c. The probability that the selected country won 10 or less is 0.744.

d. The probability that the selected country won in between 11 and 50 is 0.22

Given that,

There are total 86 countries who won medals at the Olympics in some years.

From the given countries and medal we find

a. We have to find what is the probability that the selected country won more than 50 medals.

The country won greater than 50 medals = The countries won between 51 and 100 medals + The country won more than 100 medals

= 2+ 1 = 3

The probability is

= \(\frac{3}{86}\)

= 0.0348

Therefore, The probability that the selected country won greater than 50 medals is 0.0348

b. We have to find what is the probability that the selected country did not win more than 100 medals.

The country did not win more than 100 medals = Total countries - the countries won more than 100 medal

= 86 - 1 = 85

The probability is

= \(\frac{85}{86}\)

= 0.988

Therefore, The probability that the selected country did not win greater than 100 medals is 0.988.

c. We have to find what is the probability that the selected country won 10 or fewer medals.

The countries won 10 or fewer medals = 10 + 54 = 64

The probability is

= \(\frac{64}{86}\)

= 0.744

Therefore, The probability that the selected country won 10 or less is 0.744.

d. We have to find what is the probability that the selected country won between 11 and 50 medals.

The countries won between 11 and 50 medals = 4 + 5 + 10 = 19

The probability is

= \(\frac{19}{86}\)

= 0.22

Therefore, The probability that the selected country won between 11 and 50 medals is 0.22

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The print you specifically described is entitled "No se puede saber por qué" (translated as "One cannot know why") in Spanish.

Goya mocks the many superstitions and illogical ideas that were pervasive in Spanish culture at the time in this print. A crowd is gathered around a fortune teller who is looking into a crystal ball in the picture. The people are portrayed in a variety of excited and anxious states, indicating their readiness to accept the fortune teller's predictions in the face of a lack of proof or logic.

Even in modern times, the topic of irrational beliefs and superstitions persists, albeit it may take many forms depending on the culture or civilization. For instance, despite the fact that there is little scientific proof to back up their claims, some people continue to turn to astrology, psychics, or alternative medicine. Similar to this, false information and conspiracy theories are still proliferating quickly in the social media age, feeding irrational views and mistrust of authorities and organizations.

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We would need data on the population of individuals whose high-school GPA is 3.5 and their corresponding first-year college GPAs. We could then calculate the average first-year college GPA for this population.

It's important to note that the average first-year college GPA for individuals with a high-school GPA of 3.5 may not be representative of the overall population of college students. This is because there are likely many factors that influence college GPA beyond high-school GPA, such as course difficulty, study habits, and extracurricular activities.

Additionally, it's possible that the population of individuals with a high-school GPA of 3.5 is not a representative sample of the larger population of college students. For example, this group may be skewed towards students who attend high-achieving high schools or who have access to resources that support academic success.

Overall, the average first-year college GPA for individuals with a high-school GPA of 3.5 would need to be interpreted in the context of these limitations and with an understanding that it may not generalize to the larger population of college students.

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Developing strategies for remembering facts is essential for children before they engage in drill and practice activities to develop fluency. By establishing these strategies, children can effectively learn, retain, and recall information, ultimately enhancing their performance during practice sessions.

Yes, it is important for children to develop strategies for remembering facts before engaging in drills and practice to develop fluency. By doing so, children can enhance their ability to recall information more quickly and accurately, making it easier for them to perform well on tests and assignments. Strategies such as visualizing, chunking, and using mnemonic devices can help children remember information more effectively. Once these strategies are established, drill and practice can then be used to further reinforce their understanding and speed up their recall time. This approach can ultimately lead to improved academic performance and a stronger foundation for learning.

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Answer:

2 3/4-1 3/8=1.375

1. 1.375 cups needed (so 1 3/8 as a frac)

2. 4 days

Step-by-step explanation:

Therefore, approximately 18% of American men are estimated to be between 68.9 and 69.1 inches tall based on the given information.

The statement "p(69) = 0.18" means that the density function p(x) evaluated at x = 69 (height of 69 inches) is equal to 0.18.

In other words, it represents the probability density of American men having a height of exactly 69 inches.

To calculate the approximate percentage of American men between 68.9 and 69.1 inches tall, we need to consider the area under the density function between these two values.

Since the density function represents the probability density, integrating it over a range gives us the probability of falling within that range.

We can estimate this area by considering the values of the density function at 68.9 and 69.1 and taking their average:

p(68.9) + p(69.1) / 2

However, since we only have the value p(69) = 0.18, we can make an approximation assuming that the density is relatively constant around that point.

In this case, we can assume that p(x) is approximately 0.18 for the range between 68.9 and 69.1 inches.

Thus, the approximate percentage of American men between 68.9 and 69.1 inches tall would be:

0.18 * 100 = 18%

Therefore, approximately 18% of American men are estimated to be between 68.9 and 69.1 inches tall based on the given information.

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Answer:

I’m sorry i’m just trying to get more answers:( i hope u find yours though! xoxo

Step-by-step explanation:

The values of the interior angles, ( Angle A, Angle B and Angle C) of the triangles are 48°, 88° and 44° respectively.

Interior angle is the inner of the two angles formed where two sides of a polygon come together.

To find the measure of each interior angle of the triangle in the diagram, first, we need to find the value of x.

Recall that: The sum of the interior angles of a triangle is equal to 180°.

Using the formula,

From the triangle,

Substitute these values into equation 1

Solve for x

Therefore,

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Answer: C. x<-4

Step-by-step explanation:

-2x -8 > 3x + 12

     +8           +8

-2x> 3x +20

-3x   -3x

-5x > 20

/-5    /-5

x<-4  (the sign flips because you divide by a negative.)

a) The magnitude of the earthquake is approximately 3.0.

b) The intensity of the earthquake is approximately 1258.925.

(a) To find the magnitude of an earthquake based on the intensity, we can use the following equation:

Magnitude = log10(Intensity) + 1.5

Given that the intensity is 30.25, we can calculate the magnitude as follows:

Magnitude = log10(30.25) + 1.5 ≈ 1.48 + 1.5 ≈ 2.98

Rounding to one decimal place, the magnitude of the earthquake is approximately 3.0.

(b) To find the intensity of an earthquake based on the magnitude, we can use the following equation:

Intensity = 10^(Magnitude - 1.5)

Given that the magnitude is 4.6, we can calculate the intensity as follows:

Intensity = 10^(4.6 - 1.5) ≈ 10^3.1 ≈ 1258.925

Therefore, the intensity of the earthquake is approximately 1258.925.

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The length and width of the rectangle are (a) width = 7.5 m, length = 10.5 m

Let the width (W) = x

Length (L) = x+3

According to question,

Perimeter = 36m

Perimeter = 2(L + W)

           36 = 2(x+3+x)

      36 / 2 = 2x + 3

            18 = 2x + 3

       18 - 3 = 2x

            15 = 2x

              x = 15 / 2

              x = 7.5

Length = x+3

            = 7.5 + 3

            = 10.5

Hence, width = 7.5m and length = 10.5m

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The velocity, acceleration, and speed of the particle are
v(t) = 2ti + 2j + (7/t)k, a(t) = 2i - (7/t^2)k, s(t) = √((4t^4 + 4t^2 + 49) / t^2) respectivelty.

To find the velocity, acceleration, and speed of a particle with the given position function, we can differentiate the position function with respect to time. Let's go step by step:

1. Position function:
The given position function is r(t) = t^2i + 2tj + 7ln(t)k.

2. Velocity:
To find the velocity, we need to differentiate the position function with respect to time.
Velocity (v) is the derivative of position (r) with respect to time (t).

Taking the derivative of each component of the position function:
d/dt (t^2) = 2t
d/dt (2t) = 2
d/dt (7ln(t)) = 7/t

So, the velocity function (v) is:
v(t) = 2ti + 2j + (7/t)k

3. Acceleration:
To find the acceleration, we need to differentiate the velocity function with respect to time.
Acceleration (a) is the derivative of velocity (v) with respect to time (t).

Taking the derivative of each component of the velocity function:
d/dt (2t) = 2
d/dt (2) = 0
d/dt (7/t) = -7/t^2

So, the acceleration function (a) is:
a(t) = 2i + 0j - (7/t^2)k
or simply,
a(t) = 2i - (7/t^2)k

4. Speed:
The speed of a particle is the magnitude of its velocity vector.
The magnitude of a vector is found using the Pythagorean theorem.
For the velocity function v(t) = 2ti + 2j + (7/t)k, the magnitude of v(t) is:

|v(t)| = √((2t)^2 + (2)^2 + (7/t)^2)
      = √(4t^2 + 4 + 49/t^2)
      = √((4t^4 + 4t^2 + 49) / t^2)

Therefore, the speed function (s) is:
s(t) = √((4t^4 + 4t^2 + 49) / t^2)

This is the velocity, acceleration, and speed of the particle with the given position function.

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Answer:

B.

Step-by-step explanation:

5-2+2=5; -8+9+6=7;

3-1+5=7; 0-0+4=4.

finally, the result matrix is:

\(\left[\begin{array}{ccc}5 \ 7\\7 \ 4\end{array}\right]\)

The x-intercept and y-intercept of the equation 8x + 5y + 2 = 0 are (-0.25, 0) and (0, -0.4) respectively.

To find the x-intercept, we set y = 0 and solve for x. Plugging y = 0 into the equation 8x + 5y + 2 = 0, we get:

8x + 5(0) + 2 = 0

8x + 2 = 0

8x = -2

x = -2/8

x = -0.25

Therefore, the x-intercept is (-0.25, 0).

To find the y-intercept, we set x = 0 and solve for y. Plugging x = 0 into the equation, we have:

8(0) + 5y + 2 = 0

5y + 2 = 0

5y = -2

y = -2/5

y = -0.4

Thus, the y-intercept is (0, -0.4).

Therefore, the x-intercept and y-intercept of the equation 8x + 5y + 2 = 0 are (-0.25, 0) and (0, -0.4) respectively.

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Answer:

-1±√3,(1±4√2)/2, (2±3√2)/2,1±√3

Step-by-step explanation:

Simplify the roots, and simplify the fraction.

For example, for x=(-4±√48)/4, you can simplify √48 to be √16 * √3, which is just 4·√3 or 4√3. Now, the original fraction is (-4±4√3)/4, which can be simplified to -1±√3. Solve the other problems using the same method.

2. (1±4√2)/2

3.(2±3√2)/2

4. 1±√3

Answer:

∠DAB = 68

Step-by-step explanation:

∠DAB we need to find this

∠DAB = ∠C (vertically opposite angles are equal)

∠DAB = 68

By running this code, you will obtain the value of the mass m that satisfies the given conditions with an accuracy level of 0.1%.

To find the mass m that satisfies the given conditions, we can use the false position method (also known as the regula falsi method). This method involves finding a bracketing interval [a, b] where the function changes sign, and iteratively refining the interval to converge to the desired solution.

In this case, we want to find the mass m such that the velocity v is 35 m/s at 9 seconds. We'll set up the false position method to solve for m.

First, let's define the function f(m) as:

f(m) = gm - 35(1 - e^(-15m))

The false position method starts with an initial bracketing interval [a, b] where f(a) and f(b) have opposite signs. We can choose an initial interval by evaluating f(m) at some initial values.

Let's assume an initial interval [a, b] where f(a) is negative and f(b) is positive:

a = 0 (we can start with a mass of 0)

b = 10 (we can choose an arbitrary upper bound)

Next, we'll iterate the false position method until we reach the desired level of accuracy.

The false position iteration formula is:

m_new = a - (f(a) * (b - a)) / (f(b) - f(a))

We'll repeat this iteration until the absolute relative approximate error (ERel) is less than or equal to 0.1% (0.001).

Here's the Python code to implement the false position method:

```python

import math

def f(m):

   g = 9.8

   v = 35

   c = 15

   return g*m - v*(1 - math.exp(-c*m))

def false_position_method(a, b, max_error):

   m_new = a

   error = 1.0  # Set an initial error greater than the desired error

   while error > max_error:

       m_old = m_new

       f_a = f(a)

       f_b = f(b)

       m_new = a - (f_a * (b - a)) / (f_b - f_a)

       error = abs((m_new - m_old) / m_new) * 100  # Calculate the absolute relative approximate error

       if f(m_new) * f_a < 0:

           b = m_new

       else:

           a = m_new

   return m_new

# Set the initial bracketing interval [a, b] and the maximum error

a = 0

b = 10

max_error = 0.001

# Apply the false position method to find the mass m

m_solution = false_position_method(a, b, max_error)

print("The mass m that satisfies the given conditions is:", m_solution)

```

By running this code, you will obtain the value of the mass m that satisfies the given conditions with an accuracy level of 0.1%.

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Therefore, based on the given data, there is not enough evidence to suggest a statistically significant difference in ages between children assigned to the new drug and the placebo.

To determine if there is a statistically significant difference in ages between children assigned to the new drug and the placebo, we can perform a two-sample t-test.

Given:

Sample size of children assigned to the new drug (n1) = 125

Sample size of children assigned to the placebo (n2) = 125

Mean age of children assigned to the new drug (X1) = 12.4 years

Mean age of children assigned to the placebo (X2) = 13.0 years

Standard deviation of ages in the new drug group (s1) = 3.6 years

Standard deviation of ages in the placebo group (s2) = 4.0 years

Level of significance (α) = 0.05

The null hypothesis (H0) is that there is no difference in the mean ages between the two groups, and the alternative hypothesis (Ha) is that there is a difference.

We can calculate the test statistic using the formula:

t = (X1 - X2) / √((s1^2/n1) + (s2^2/n2))

Substituting the given values, we get:

t = (12.4 - 13.0) / √((3.6^2/125) + (4.0^2/125))

Calculating this, we find t ≈ -0.571.

The degrees of freedom (df) for the t-test is (n1 + n2 - 2) = (125 + 125 - 2) = 248.

Using the t-distribution table or a statistical calculator, at a significance level of 0.05 with df = 248, the critical t-value is approximately ±1.97 (two-tailed test).

Since the calculated t-value (-0.571) is not greater than the critical t-value (-1.97 or 1.97), we fail to reject the null hypothesis.

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Answer:

x = 15°

Step-by-step explanation:

angle S is 90° (right-angle) since RS is tangent to circle and S is a point on the circle.

angles in triangle add up to 180°.

so angle x must be 180 - 90 - 75 = 15°.

Answer:

it’s true.  :)

the answer is false

your welcome

Answer:

a) 12 + 0.5d               d=day

b) 0.195/0.5=0.39d

Step-by-step explanation:

Answer

(a) Find out the  a rule to describe the function.

To prove

Let us assume that the days be represted by d .

Let us assume that the height of plant be represted by y.

As given

A zucchini plant in Darnell’s garden was 12 centimeters tall when it was first planted.

it has grown approximately 0.5 centimeter per day.

Than the function becomes

y = 12 + 0.5 × d

y = 12 + 0.5d

(b) Find out after how many days will the zucchini plant be 0.195 meter tall .

To prove

Let us assume that the days be represted by d .

As given

A zucchini plant in Darnell’s garden was 12 centimeters tall when it was first planted.

it has grown approximately 0.5 centimeter per day.

As

1meter = 100cm

0.195 meter convert into centimeter.

= 19.5cm

Than the equation becomes

12 + 0.5d = 19.5

0.5d = -12 + 19.5

0.5d = 7.5

d = 15 days

Therefore 15 days will the zucchini plant be 0.195 meter tall .

Answer:

Step-by-step explanation:

11) 4(7x+3)=28x+12

12) 9(3y-5)=27y-45

The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

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The total amount paid by Jamal at the closing is  $410    .

In the question ,

it is given that ,

the total loan amount = $125000 ,

time for which the loan has been taken = 30 years

rate = 5.3% = 0.053 ,

percent of down payment made = 10% ,

that means loan amount = 125000 × 0.90 = 112500

Multiplying this loan amount by rate

= 112500 × 0.053

= 5962.50

to find the per day value , we divide it by 365 ,

= 5962.50/365

= $16.4 per day

it is given that the deal is closing on April 5th, and we know that  April has 30 days, so, there are 25 days still left.

So, the final amount paid is = 16.4 × 25 = $410

Therefore , The total amount paid by Jamal at the closing is  $410    .

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