If f(x) and its inverse function, are both plotted on the same coordinate plane, where is their point of intersection?

Answer:

0.15% of the students spent more than 557 on textbooks in a semester

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 473

Standard deviation = 28

According to the standard deviation rule, almost 0.15% of the students spent more than what amount of money on textbooks in a semester?

99.7% of the measures are within 3 standard deviations of the mean, so 100 - 99.7% = 0.3% are more than 3 standard deviations from the mean.

The normal distribution is symmetric, which means that 0.3%/2 = 0.15% spend less than 3 standard deviations below the mean, and 0.15% spend more than 3 standard deviations above the mean.

473 + 3*28 = 473 + 84 = 557

0.15% of the students spent more than 557 on textbooks in a semester

The value of x in the circle that shows diameter is calculated as:

x = -7

In a circle, the line segment that divides the circle into two halves is the diameter. Half of the circle is a semicircle which has a measure of 180 degrees.

Note: The measure of a central angle is also the same measure with that of the arc it intercepts.

Therefore, we have:

-8x + 9 + 50 + 65 = 180

-8x + 124 = 180

-8x = 180 - 124

-8x = 56

x = 56/-8

x = -7

Learn more about the diameter on:

https://brainly.com/question/30460318

#SPJ1

Answer:

Step-by-step explanation:

The total number of ratio units is 5+4 = 9, so each of them represents ...

  (54 g)/9 = 6 g

of fruit. Multiplying the ratio by this value shows you the amount of each kind of fruit:

  strawberry : blueberry = 5 : 4 = 5(6 g) : 4(6 g)

  strawberry : blueberry = 30 g : 24 g

There are 30 g of strawberry and 24 g of blueberry in the smoothie.

Answer:

D is 10

b/12

Step-by-step explanation:

Answer:

(3, -2) is the correct choice.

Answer:

y = -2/3 x - 13/3

Step-by-step explanation:

y = -2/3 x + 3/2

y = mx + b

m = -2/3

The slope of the given line is -2/3. Parallel lines have equal slopes, so our line also has slope -2/3.

m = -2/3

y = mx + b

y = -2/3 x + b

Substitute the given point for x and y and solve for b.

-7 = -2/3 (4) + b

-21/3 = -8/3 + b

b = -13/3

Answer: y = -2/3 x - 13/3

Answer:

The sum of the interior angle measures of a regular hexagon is 720°.

Step-by-step explanation:

To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:

Sum of interior angles = (n - 2) × 180°

In the case of a hexagon, n = 6. So, we can plug this value into the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:

Sum of interior angles of hexagon = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

Answer:

θ ≈ 40°

Step-by-step explanation:

Since, sinθ = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

cosθ = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

tanθ = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

In the picture attached,

Measures of adjacent side and opposite side of the triangle have been given. Therefore, tangent rule will be applied in the given triangle.

tanθ = \(\frac{19}{23}\)

θ = \(\text{tan}^{-1}(\frac{19}{23})\)

θ = 39.56

θ ≈ 40°

The probability that the teacher chooses a girl with glasses is 3/16, and the probability that the teacher chooses a boy with glasses is 1/4.

Let's calculate the probability that the teacher chooses a student with glasses.
a) A girl with glasses: There are 6 girls in the class, and 3 of them wear glasses. There are a total of 16 students (6 girls + 10 boys).
Probability = (Number of girls with glasses) / (Total number of students)
Probability = 3 girls with glasses / 16 total students
Probability = 3/16
b) A boy with glasses: There are 10 boys in the class, and 4 of them wear glasses.
Probability = (Number of boys with glasses) / (Total number of students)
Probability = 4 boys with glasses / 16 total students
Probability = 1/4
So, the probability that the teacher chooses a girl with glasses is 3/16, and the probability that the teacher chooses a boy with glasses is 1/4.

For more such questions on probability , Visit:

https://brainly.com/question/24756209

#SPJ11

Answer:

the answer is no

Answer:

\(\displaystyle y' = \frac{-2}{x \ln (10)[\log (x) - 2]^2}\)

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Addition/Subtraction]:                                                         \(\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\)

Derivative Rule [Basic Power Rule]:

Derivative Rule [Quotient Rule]:                                                                           \(\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}\)

Step-by-step explanation:

Step 1: Define

Identify.

\(\displaystyle y = \frac{\log (x)}{\log (x) - 2}\)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

112.5 ft not sure though

Answer:

112.5 ft

Step-by-step explanation:

15 is to 40 what x is to 300

15/40 = x/300 (cross multiplication)

(15 * 300) / 40 = 112.5 ft

The value of a is mathematically given as a=1.68989794. Both sides of the equation are unequal with -2 , Hence No, the student is not correct

An Equation is simply defined as an mathematical statement, where two mathematical expressions are made equal to one another.

Question Parameter(s):

. 3/a + 2 − 6a/a2 − 4 = 1 /a − 2

Firstly, for the student to be correct the value -2 as a value of a must render the equation equal to zero

Generally, the equation  is mathematically given as

3/a + 2 − 6a/a2 − 4 = 1 /a − 2

Subbing -2

3/(-2) + 2 − 6(-2)/(-2)2 − 4 = 1 /(2) − 2

-15.5-1.5

In conclusion, both sides are unequal

therefore, student, a is not correct

The correct value of a=1.68989794

Read more about Arithmetic

https://brainly.com/question/22568180

Answer:

No, the student did not check the solution to the derived equation in the original equation.

No, a possible solution is a = –2, but it does not check in the original equation because it makes two of the denominators equal to zero.

No, a = –2 is an extraneous solution, and there is no solution to the original rational equation.

Step-by-step explanation:

edge 2023

The next three fractions in the pattern are 4/20 = 5/25 = 6/30.

In mathematics, there are three primary types of fractions. These three categories are proper fractions, improper fractions, and mixed fractions. Fractions are expressions that have a prime and a denominator. We divide its types into these two categories.

Analysis

This is equivalent fraction multiply 1/5 with 4,5,6, up and down fraction.

1/5*4/4 = 4/20

1/5*5/5 = 5/25

1/5*6/6 = 6/30

So, the answer will be \(\frac{4}{20} =\frac{5}{25} = \frac{6}{30}\)

To know more about Fraction visit:

https://brainly.com/question/10354322

#SPJ1

The median of the distances is M = 6.5 kilometers

Given data ,

To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arranging the given set of numbers in ascending order: {4, 5, 8, 11}

Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:

(5 + 8) / 2 = 13 / 2 = 6.5

Hence , the median of the given set {4, 5, 8, 11} is 6.5

To learn more about median click :

https://brainly.com/question/28687994

#SPJ1

The probability of women will be 0.49.

Based on the information given, the probability women will be:

Number of women = 85 + 32 = 117

Number of men = 70 + 51 = 121

Total = 117 + 121 = 238

The probability of women will be:

= 117/238

= 0.49

The probability of women or summer will be:

= 0.49 × 155/238

= 0.32.

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer:

Step-by-step explanation:

The equation is poorly written and I cannot unfortunately solve it.

Answer:

378

Step-by-step explanation:

\(\frac{14}{x}\) = \(\frac{1}{27}\)  Cross multiply and solve for x

x = (14)(27)

x = 378

Helping in the name of Jesus.

1. Using the conversion rate of 1 kilometer = 0.621371 miles, Oskar determine the distance of his trip in miles.

2. Oskar's 165 kilometer trip is equivalent to 101.87995 miles.

3. The difference between kilometers and miles is that a kilometer is a metric unit of length and a mile is an imperial unit of length.

Paragraph 1: To convert kilometers to miles, Oskar will need to use the conversion rate of 1 kilometer = 0.621371 miles.

This conversion rate can be found on any formula sheet, and it will help Oskar determine the distance of his trip in miles.

Paragraph 2: To convert 165 kilometers into miles, Oskar will simply need to multiply 165 by 0.621371.

The result will give him the distance in miles.

For example, 165 * 0.621371 = 101.87995 miles. Therefore, Oskar's 165 kilometer trip is equivalent to 101.87995 miles.

Paragraph 3: Oskar might be traveling in a country where the maps are labeled in kilometers instead of miles. This is common in many countries, including most of Europe and many countries in Asia. The difference between kilometers and miles is that a kilometer is a metric unit of length and a mile is an imperial unit of length. A kilometer is equal to 0.621371 miles, while a mile is equal to 1.60934 kilometers. It's important to be aware of the units used in different countries to ensure accurate navigation.

Learn more about conversion rate on:

https://brainly.com/question/14514624

#SPJ1

Answer: C

Step-by-step explanation:

Answer:

2:45

Step-by-step explanation:

1 1/2 hour is 1 hour and 30 minutes.

If we add 30 minutes to 1:15, we get 1:45

if we add 1 hour to 1:45, we get 2:45, which is our answer.

Recall that

Var[aX + bY] = a ² Var[X] + 2ab Cov[X, Y] + b ² Var[Y]

Then

Var[3X - 7Y] = 9 Var[X] - 42 Cov[X, Y] + 49 Var[Y]

Now, standard deviation = square root of variance, so

Var[3X - 7Y] = 9×6² - 42×2 + 49×8² =  3376

The general result is easy to prove: by definition,

Var[X] = E[(X - E[X])²] = E[X ²] - E[X]²

Cov[X, Y] = E[(X - E[X]) (Y - E[Y])] = E[XY] - E[X] E[Y]

Then

Var[aX + bY] = E[((aX + bY) - E[aX + bY])²]

… = E[(aX + bY)²] - E[aX + bY]²

… = E[a ² X ² + 2abXY + b ² Y ²] - (a E[X] + b E[Y])²

… = E[a ² X ² + 2abXY + b ² Y ²] - (a ² E[X]² + 2 ab E[X] E[Y] + b ² E[Y]²)

… = a ² E[X ²] + 2ab E[XY] + b ² E[Y ²] - a ² E[X]² - 2 ab E[X] E[Y] - b ² E[Y]²

… = a ² (E[X ²] - E[X]²) + 2ab (E[XY] - E[X] E[Y]) + b ² (E[Y ²] - E[Y]²)

… = a ² Var[X] + 2ab Cov[X, Y] + b ² Var[Y]

Answer: i think that the only fraction that we can convert this into is 2111/1000

Answer:

\(\frac{2111}{1000}\)

Step by step:

2.111 = \(\frac{2.111}{1}\)

then, get rid of the decimal sign in 2.111 by multiplying it by 1000 since there are 3 numbers after the decimal point.

your new fraction is \(\frac{2111}{1000}\)

Answer:c

Step-by-step explanation:

c

Answer:b

Step-by-step explanation:

Answer: 6.08.

Explanation: 32% × 19 = 6.08.

The expected value of the random variable D is 6.. This gives us the following equation :E[D] = 0(1/6) + 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6)

The expected value of the random variable D, E[D], can be calculated using the following formula :E[D] = ΣD P(D) Where ΣD is the sum of all possible values of D and P(D) is the probability of each of those values. In this case, the possible values of D are 0, 1, 2, 3, 4, 5. The probability of each of these values is the same, since each has an equal chance of being rolled on the dice. To calculate the expected value, we must multiply each value of D with its probability, and then sum all of these products. This gives us the following equation:E[D] = 0(1/6) + 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) .E[D] = 36/6 = 6.Therefore, the expected value of the random variable D is 6.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

The correct statement regarding the inverse function of f(x) = 4x^4 is given as follows:

\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\); f^(-1)(x) is not a function.

The function in this problem is defined as follows:

f(x) = 4x^4.

To obtain the inverse of a function y = f(x), first the variables y and x are exchanged, as follows:

x = 4y^4.

Isolating the variable y, we have that:

y^4 = (x/4).

The inverse operation of the fourth power is the fourth root, hence:

\(y = \pm \sqrt[4]{\frac{x}{4}}\)

\(f^{-1}(x) = \pm \sqrt[4]{\frac{x}{4}}\)

\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\)

The plus/minus symbol means that for each input of x, the inverse function gives two outputs, meaning that there are multiple outputs mapped to each input, and thus the inverse is not a function.

This means that the second statement is correct.

More can be learned about inverse functions at https://brainly.com/question/3831584

#SPJ1

Answer:

  (d)  7/25 -(24/25)i

Step-by-step explanation:

You want the value of 4-3i divided by its conjugate.

The conjugate of a sum is the same sum with the sign changed.

  conjugate of 4-3i is 4+3i

  conjugate of 4+√2 is 4-√2

In algebra, a conjugate is often used when squaring one of the terms will make it "rational" or real (or both). That is because the product of a number and its conjugate is the difference of the squares of the parts of the sum.

  (a -b)(a +b) = a² -b²

You want the value of (4-3i) divided by its conjugate. Simplifying that expression will also make use of the conjugate.

  \(\dfrac{4-3i}{4+3i}=\dfrac{(4-3i)(4-3i)}{(4+3i)(4-3i)}=\dfrac{4^2+2(4)(-3i)+(3i)^2}{4^2-(3i)^2}=\dfrac{(16-9)-24i}{16+9}\\\\=\boxed{\dfrac{7}{25}-\dfrac{24}{25}i}\)

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1