Please explain why 31% is the answer

The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Answer:

85

Step-by-step explanation:

Answer:

11 can't be divided with negative number

so it's answer will be zero

hope it is helpful to you ☺️☺️☺️☺️☺️

Answer:

E

Step-by-step explanation:

using the Sine rule in Δ ABC

\(\frac{a}{sinA}\) = \(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

where a is the side opposite ∠ A , b opposite ∠ B , c opposite ∠ C

we require to calculate ∠ C

∠ C = 180° - (64 + 85)° = 180° - 149° = 31°

then to find a , using

\(\frac{a}{sinA}\) = \(\frac{c}{sinC}\)

\(\frac{a}{sin64}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

a × sin31° = 9.3 × sin64° ( divide both sides by sin31° )

a = \(\frac{9.3sin64}{sin31}\) ≈ 16.23 ( to 2 decimal places )

then to find b , using

\(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

\(\frac{b}{sin85}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

b × sin31° = 9.3 × sin85° ( divide both sides by sin31° )

b = \(\frac{9.3sin85}{sin31}\) ≈ 17.99 ( to 2 decimal places )

The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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The following statements is incorrect about the data set that includes 1,2,3,4,5,6,7  the data set has a second quartile of 6.

What is data set?

A dataset is a collection of data points or observations that are organized or presented in a structured or unstructured way. In other words, it is a set of information that has been collected, usually for a specific purpose or research question, and is represented in a form that can be analyzed and used to draw conclusions or make decisions.

A dataset can take many different forms, such as a table, a spreadsheet, a database, or a text file. It can contain various types of data, such as numerical, categorical, or textual data, depending on the nature of the problem being studied. Examples of datasets include demographic data, sales data, weather data, medical records, and social media data.

Statement D is incorrect.

The data set that includes 1,2,3,4,5,6,7:

A. The data set has no mode. (There is no value that occurs more frequently than others, so there is no mode.)

B. The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1). The quartiles of the data set are:

Q1 = 2

Q2 (median) = 4

Q3 = 6

So, the interquartile range is Q3 - Q1 = 6 - 2 = 4.

C. The data set has the same mean and median. (The median is 4, which is also the mean of the data set.)

D. The second quartile is the same as the median, which is 4, not 6.

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In order to compare the lengths we will convert them into decimals:

Bug. Length in inches

Lady bug= 3/8 = 0.375

Ant= 1/4 = 0.25

Firefly= 7/8 = 0.875

honeybee= 0.8

Deer tick= 0.2

Now we know that the order, from shortest to longest, is:

0.2, 1/4, 3/8, 0.8, 7/8

Answer:

radius

Step-by-step explanation:

If 1% of a number equals 5, find 2% of that number is 2

Algebraic expressions are described as expressions composed of variables, constants, factors, coefficients and terms.

Arithmetic operations also make up these expressions, they are;

Also, fractions are described as part of a whole element, number or variable

From the information given, we have that;

1% of a number is 5

Let the number be x

1/2x = 5

Make 'x' the subject

x = 10

Substitute the value

2/10 of x

2/10 × 10

2

Thus, the value is 2

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Answer:   -2

:)

Step-by-step explanation:

Answer:

√7 is less than 14/5

Step-by-step explanation:

√7 equals about 2.6

14/5 equals 2.8

In statistics, a residual is defined as the difference between the predicted value of an outcome variable and the observed value of that variable. Residuals are used to evaluate how well a regression model fits the data.In order to calculate the residuals for a scatterplot, follow these steps:

Step 1: Plot the data on a scatterplot.

Step 2: Perform a regression analysis on the data to find the equation of the regression line. This equation should take the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Step 3: Using the equation of the regression line, calculate the predicted value of y for each data point in the scatterplot.

Step 4: Subtract each predicted value of y from the actual value of y for each data point in the scatterplot. This difference is the residual for that data point.

Step 5: Plot the residuals on a new scatterplot. The x-axis of this scatterplot should be the independent variable, and the y-axis should be the residual values.

Step6: This scatterplot is called a residual plot.Residuals are useful for identifying patterns in data that the regression model fails to capture. If the residuals are randomly scattered around the horizontal axis, then the regression model is a good fit for the data. If there are clear patterns in the residual plot, then the regression model may not be a good fit for the data and further analysis is required.

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Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

40 degrees Celsius (40°C)

hopefully this helped :3

Answer:

c. (√3 + √5) - i

Step-by-step explanation:

(√3+i) + (√5-2i) =  √3+i + √5-2i = (√3 + √5) + (i - 2i) = (√3 + √5) - i

Answer: 84

Step-by-step explanation:

Question requires finding the 16th term in this sequence:

= -6 + ( n - 1 )(6)

= -6 + ( 16 - 1) (6)

= -6 + (15 * 6)

= 84

3.4

Step-by-step explanation:

The pH or acidity of a solution is given by the equation

\(pH = -\log{[H]}\)

where [H] is the concentration of \(H^+\) ions. If the \(H^+\) concentration is 0.0004 (=\(4×10^{-4}),\) then its pH level is

\(pH = -\log{(4×10^{-4})} = 3.4\)

Answer:

Step-by-step explanation:

A graph shows real zeros at ±2.203 and -1. The value of f(x) changes sign at each of these.

The positive leading coefficient indicates the graph trends generally upward, so the function will be positive in intervals with an even number of zeros to the right.

There are an even number of zeros to the right of x = 2.203 and the interval (-2.203, -1).

  f(x) is positive in the intervals (-2.203, -1) or (2.203, ∞).

The function will be negative where it is not positive (except at the zeros)

  f(x) is negative in the intervals (-∞, -2.203) or (-1, 2.203).

_____

Additional comment

The graph shows the only rational real root of the function is x=-1. Using synthetic division to reduce the polynomial, we find ...

  f(x) = (x +1)(x^4 -3x^2 -9)

The remaining factor is a quadratic in x^2, which has roots ...

  x = ±√(1.5 ±√11.25)

The real roots are approximately ±2.20320266118. The value 2.203 used above is a stand-in for the exact value √(1.5 +√11.25)).

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

41

Step-by-step explanation:

= B', c'= 41 units so B, C also equals 41 units.  

In conclusion, BC=41BC=41B, C, equals, 41 units.

Answer:

Step-by-step explanation:

The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

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Answer: Zero

Step-by-step explanation: The temperature is constant because the problem says nothing about it changing so, this line is not moving. Also I just took the test:)

Answer:

Well obviously, it’s zero

Step-by-step explanation:

If your freezer went up in temperature or down in temperature overtime, that would be an issue.

and we can also exclude undefined because it’s obviously would be defined because the question tells us all about the slope.

Answer:

A. the angular speed is 3771.4 rad/min

b. 5921 rpms

Step-by-step explanation: I just got this same question right on a test.

Answer: To calculate the amount of canvas needed for one tent, we need to calculate the total surface area of the tent. The tent consists of two parts: the cylindrical lower part and the conical upper part.

The surface area of the cylindrical part can be calculated as follows:

The base area of the cylinder = π × r² = π × 2.8² ≈ 24.61 m²

The lateral area of the cylinder = 2 × π × r × h = 2 × π × 2.8 × 3.5 ≈ 54.99 m²

So, the total surface area of the cylindrical part is the sum of the base area and lateral area, which is:

Total surface area of cylindrical part = 24.61 + 54.99 ≈ 79.60 m²

The surface area of the conical part can be calculated as follows:

The slant height of the cone = √(r² + h²) = √(2.8² + 2.1²) ≈ 3.44 m

The lateral area of the cone = π × r × slant height = π × 2.8 × 3.44 ≈ 24.12 m²

So, the total surface area of the conical part is the sum of the base area and lateral area, which is:

Total surface area of conical part = 24.61 + 24.12 ≈ 48.73 m²

Therefore, the total surface area of one tent is:

Total surface area of one tent = 79.60 + 48.73 ≈ 128.33 m²

To make 1500 tents, the total amount of canvas required is:

Total amount of canvas required = 1500 × 128.33 ≈ 192,495 m²

The cost of the canvas is given as Rs 120 per m². Therefore, the total cost of the canvas required to make the tents is:

Total cost of canvas = 192,495 × 120 ≈ Rs 23,099,400

As 50 schools have decided to share the expenditure equally, the amount shared by each school will be:

Amount shared by each school = Total cost of canvas / 50

Amount shared by each school = 23,099,400 / 50

Amount shared by each school ≈ Rs 461,988

Therefore, each school will have to contribute approximately Rs 461,988 to set up the tents.

Step-by-step explanation:

The figure labelled JKLM is a kite and the length ML is equal to 11.

A kite is a quadrilateral that have two pairs of equal length of sides and these sides are adjacent to each other. It can be viewed as a pair of congruent triangles with a common base.

The line JM bisects the kite into two congruent triangles, and thus;

the lengths ML and MK are equal.

ML = 5x - 4 and MK = 2x + 5 so;

5x - 4 = 2x + 5 {collect like terms}

5x - 2x = 5 + 4

3x = 9

x = 9/3 {divide through by 3}

x = 3

we substitute 3 for x;

ML = 5(3) - 4

ML = 15 - 4

ML = 11

Therefore, the value of length ML for the kite is equal to 11.

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a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c) . A 90% confidence interval would be wider than the 95% interval

To verify the Central Limit Theorem (CLT) conditions, we need to check the following:

1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.

2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.

3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.

Therefore, the Central Limit Theorem conditions are met.

b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:

CI = p ± z * √(p(1-p)/n)

where:

- p is the sample proportion (82% or 0.82 in decimal form).

- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

- n is the sample size (800).

Calculating the confidence interval:

CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)

CI = 0.82 ± 1.96 * √(0.82*0.18/800)

CI = 0.82 ± 1.96 * √(0.1476/800)

CI = 0.82 ± 1.96 * √0.0001845

CI ≈ 0.82 ± 1.96 * 0.01358

CI ≈ 0.82 ± 0.0266

The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.

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Answer:

any number from 6 and above

Answer:

a rectangle is having 4 lines of symmetry but a trapezium is having 2 lines of symmetry

The quadrilateral with two lines of symmetry is a rhombus and not a rectangle. Therefore, the statement given by the Dave is not correct.

By the above discussion we conclude that the quadrilateral with two lines of symmetry is a rhombus and not a rectangle. Therefore, the statement given by the Dave is not correct.

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