HOW DO I SOLVE THIS 20POINTS

The (fg)(x) is the function 6ˣ, which is defined for all real numbers x, and that (f/g)(x) is the function (2ˣ)/(3x), which is defined for all real numbers except x = 0. We also evaluated (f/g)(4) and found that it is equal to 4/3.

To find (fg)(x), we need to first compute the product of f(x) and g(x), and then evaluate the resulting expression at x:

f(x) = 2ˣ

g(x) = 3x

(fg)(x) = f(x)g(x) = 2ˣ * 3x = 6ˣ

Therefore, (fg)(x) is the function 6ˣ, which is defined for all real numbers x.

To find (f/g)(x), we need to divide f(x) by g(x), and then evaluate the resulting expression at x:

(f/g)(x) = f(x)/g(x) = (2ˣ)/(3x)

The domain of (f/g)(x) is all real numbers except x = 0, since g(x) = 3x cannot be zero.

To evaluate (f/g)(4), we substitute x = 4 into the expression:

(f/g)(4) = (2⁴)/(3*4) = 16/12 = 4/3

Therefore, (f/g)(4) = 4/3.

To learn more about domain click on,

https://brainly.com/question/17303728

#SPJ1

The best estimate for the total number of games played in 4 years would be 80 games

To estimate the total number of games played in 4 years, we need to determine the average number of games played per season and then multiply it by 4.

Given that a team plays between 18 and 22 games per season, we can take the average of these two values:

Average number of games per season = (18 + 22) / 2 = 40 / 2 = 20

Total number of games played in 4 years = Average number of games per season * Number of seasons

Total number of games played in 4 years = 20 games/season * 4 seasons = 80 games

Know more about average number here;

https://brainly.com/question/16956746

#SPJ11

The statement is generally true.

In materials science, the close-packing of atoms in crystal structures can affect the mechanical properties of the material, such as its ductility and ability to undergo plastic deformation.

In general, structures with closely packed planes (i.e., structures with a higher atomic packing factor) are more likely to undergo plastic deformation because the closely packed planes allow for more slip planes for atoms to move along without disrupting the overall crystal structure.

This means that when a force is applied to the material, the planes can slide more easily past one another, leading to plastic deformation.

In contrast, structures that are not closely packed (i.e., structures with a lower atomic packing factor) have fewer slip planes and are less likely to undergo plastic deformation. Instead, they may experience brittle fracture or other types of failure when subjected to stress.

However, it is important to note that the relationship between atomic packing and plastic deformation is complex and depends on a variety of factors, including the type of crystal structure, the presence of defects or impurities in the material, and the conditions under which the material is being deformed.

Learn more about plastic deformation

brainly.com/question/30480072

#SPJ11

The equation of the function f(x) is f(x) = (x + 4)(x - 2)

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

A quadratic function is represented as

f(x) = a(x - roots)

Substitute the known values in the above equation, so, we have the following representation

f(x) = a(x + 4)(x - 2)

Using the other points, we have

a(1 + 4)(1 - 2) = -5

So, we have

a = 1

So, we have

f(x) = (x + 4)(x - 2)

Hence, the function is f(x) = (x + 4)(x - 2)

Read more about quadratic function at

https://brainly.com/question/25841119

#SPJ1

The interquartile range of the given data is 75.

The given data is 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 4, 5, 10, 16, 22, 26, 29, 28, 24, 18, 12, 6.

The order of given data is 4, 5, 6, 10, 12, 16, 18, 22, 24, 26, 28, 29, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100.

Median = (28+29)/2

= 28.5

Lowest number =4

Highest number =100

Mean = (4+5+6+10+ 12+ 16+ 18+ 22+ 24+ 26+ 28+29+ 78+ 80+ 82+ 84+ 86+ 88+ 90+ 92+ 94+ 96+ 98+ 100)/24

= 1268/24

= 52.8

Here, Q1 = (12+16)/2

= 14

Q3=(88+90)/2

= 89

IQR=Q3-Q1

= 89-14

= 75

Therefore, the interquartile range of the given data is 75.

Learn more about the interquartile range here:

https://brainly.com/question/4135956.

#SPJ1

Answer:

When James saw a pair of pants in the J Crew catalog for $25, he was ready to buy them. However, as he looked through the catalog more, he saw two other pairs of pants priced at $65 and $95. This made the $25 pair seem too cheap in comparison. James may now reconsider his choice and opt for a higher priced pair to ensure a better quality product. The presence of higher priced products can influence consumer spending and purchasing decisions.

Answer: 5/16

Step-by-step explanation:

If 1/8 of a fence is built in 2/5 of an hour, the question is how much of the fence will be completed in an hour.

To be able to solve this, we need to figure out what to multiply 2/5 of an hour by to make it become 1 hour so that we can do the same to 1/8.

To do this, we can divide 2/5 by 1. 1/(2/5) = 2.5. This means 2/5 x 2.5 = 1. If we have to multiply 2/5 x 2.5 to make 1 hour, then we have to multiply 1/8 x 2.5 to find the amount of fence done in one hour.

(1/8) x 2.5 = 0.3125. 0.3125% of the fence will be completed in 1 hour, or 5/16 of the fence.

The number of students for each favorite sport from the bar graph is:

Cricket = 75

Football = 35

Tennis = 50

Badminton = 30

Swimming = 65

We have,

From the bar graph,

We can find the number of students for each favorite sport.

Now,

Cricket = 75

Football = 35

Tennis = 50

Badminton = 30

Swimming = 65

Now,

The total number of students in the bar graph.

= 75 + 35 + 50 + 30 + 65

= 255

Thus,

The number of students for each favorite sport is:

Cricket = 75

Football = 35

Tennis = 50

Badminton = 30

Swimming = 65

Learn more about bar graphs here:

https://brainly.com/question/31158559

#SPJ1

When doing a single sample t-test using SPSS, the constant is called the Test Value.

Test Value is in a One Sample t-Test, the test variable's mean is compared against a "test value", which is a known or hypothesized value of the mean in the population. Test values may come from a literature review, a trusted research organization, legal requirements, or industry standards.

[tex](\bar{\text{x}}-\mu)\div\dfrac{\text{s}}{\sqrt{\text{n}}}[/tex]

In case statistics of two samples are to be compared, then a two-sample t-test is to be used, and its formula is expressed using respective sample means, sample standard deviations, and sample sizes. Mathematically, it is represented as, s2 = Standard Deviation of 2nd Sample.

Thus, When doing a single sample t-test using SPSS, the constant is called the Test Value.

Learn more about the Test Value with this given link.

https://brainly.com/question/15870238

No, it is not possible for a quadrilateral to have only 2 right angles. A quadrilateral is a polygon with four sides and four angles, and the sum of the interior angles of a quadrilateral is always 360 degrees.

If a quadrilateral has two right angles, that means the other two angles must add up to 180 degrees in order to make the total sum of the angles equal to 360 degrees. However, the only way for two angles to add up to 180 degrees is if they are both straight angles, which means they are equal to 180 degrees each. This would result in a total sum of 360 + 180 + 180 = 720 degrees, which is twice the sum of the interior angles of a quadrilateral. Therefore, it is not possible for a quadrilateral to have only 2 right angles. A quadrilateral can have at most one pair of opposite right angles, which would make it a rectangle.

Learn more about polygon here

https://brainly.com/question/29425329

#SPJ11

I ⊆ I' if and only if a' ≤ a and b ≤ b'. This relationship holds true for closed intervals I and I' in R. To show that I ⊆ I' if and only if a' ≤ a and b ≤ b', we will consider two cases:

1. If I ⊆ I', then for any x ∈ I, we have x ∈ I'. Since I and I' are closed intervals, we can write them as I = [a, b] and I' = [a', b']. We want to show that a' ≤ a and b ≤ b' in this case.

Since x ∈ I, we know that a ≤ x ≤ b. Now, since x also belongs to I', we have a' ≤ x ≤ b'. Since this is true for any x in I, we can conclude that a' ≤ a and b ≤ b'.

2. If a' ≤ a and b ≤ b', we want to show that I ⊆ I'. Let x be any element in I, so we have a ≤ x ≤ b. We are given that a' ≤ a and b ≤ b'. Since a' ≤ a and a ≤ x, we can infer that a' ≤ x. Similarly, since x ≤ b and b ≤ b', we can infer that x ≤ b'. Therefore, x ∈ I'.

Since x was an arbitrary element in I, we can conclude that I ⊆ I' when a' ≤ a and b ≤ b'.

In summary, I ⊆ I' if and only if a' ≤ a and b ≤ b'. This relationship holds true for closed intervals I and I' in R.

Learn more about intervals here:

brainly.com/question/30273384

#SPJ11

The approximate distance the wheel travels is 201 inches.

Each revolution means that the wheel travels a distance equal to its circumference, which is defined by:

C = 6.28*R

Where R is the radius.

Then 2 revolutions for a radius of 16 inches gives a distance of:

D = 2*6.28*16in = 200.96 in

That can be rounded to the next whole number to get 201 inches, then the correct option is B.

Learn more about circles at:

https://brainly.com/question/24375372

#SPJ1

The slope intercept form of the given equation is y=-2/5 x-5.

The given equation is 6x+15y=-75.

The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Here, 6x+15y=-75

3(2x+5y)=-75

2x+5y=-25

5y=-25-2x

y=-2/5 x-5

Therefore, the slope intercept form of the given equation is y=-2/5 x-5.

To learn more about the slope intercept form visit:

brainly.com/question/9682526.

#SPJ1

Answer: To find when both farmers charge the same amount for delivered produce, we need to set their equations equal to each other:

Amos: y = 22x

Calvin: y = 16x + 48

22x = 16x + 48

6x = 48

x = 8

So Amos and Calvin will charge the same amount when 8 boxes of potatoes are being delivered. To find the amount they will charge, we can substitute x = 8 into either equation:

Amos: y = 22(8) = 176

Calvin: y = 16(8) + 48 = 176

So they will both charge $176 for delivering 8 boxes of potatoes.

The value of the function f(x) at x = 1.477.

f(1.477) = 32.857

The value of the function g(x) at x = 20.

g(20) = 1.729

We have,

Two functions:

f(x) = b^x

g(x) = log_b(x)

Now,

From the table,

f(0.699) = b^0.699 = 5

Taking the logarithm of both sides with base b.

log_b(5) = 0.699

b = 5^(1/0.699)

b = 8.343

Now, we can find the value of f(1.477).

f(1.477) = b^1.477 = 8.343^1.477 = 32.857

Similarly, we can find the value of g(20).

g(20) = log_b(20) = log_8.343(20) = 1.729

Thus,

The value of the function f(x) at x = 1.477.

f(1.477) = 32.857

The value of the function g(x) at x = 20.

g(20) = 1.729

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

The value of x , y and z in the parallel line is 50 degrees.

When parallel lines are crossed by a transversal line, angle relationships are formed such as vertically opposite angles, alternate interior angles, alternate exterior angles, adjacent angles, corresponding angles etc.

Therefore, let's use the angle relationships to find the angle, x, y and z as follows:

Therefore,

x = 360 - 310(sum of angles in a point)

x = 50 degrees

Therefore,

x = y(alternate interior angles)

Alternate interior angles are congruent.

Hence,

y = 50 degrees

Therefore,

x = z(alternate interior angles)

z = 50 degrees.

learn more on angles here: https://brainly.com/question/17043791

#SPJ1

Answer:

25

Step-by-step explanation:

To find the radius of the circle that circumscribes the isosceles triangle, we can use the formula for the circumradius of a triangle:

R = (abc)/(4A)

the area of the an isoceles triangle = 1/2 base * height

height is the sqrt of [40²- (48/2)²]

so height = 32

so area = 768

sor R = 40*40*48/768 =25

The statement is true. A hypothesis test involves setting up a null hypothesis and an alternative hypothesis, and using statistical methods to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

When using a confidence interval to perform a hypothesis test, we calculate the interval based on the sample data and a specified level of confidence. If the null hypothesis value falls outside of this interval, we can reject the null hypothesis at the corresponding level of significance. In other words, if the null value is not within the confidence interval, we can conclude that it is unlikely to be the true value and therefore reject it in favor of the alternative hypothesis. It is important to note that the interpretation of a confidence interval depends on the level of confidence and the specific context of the study.

Learn more about hypothesis here:

brainly.com/question/29537948

#SPJ11

The probability of rolling a 1 with this loaded die is 1/9.

Let's first assign probabilities to the possible outcomes of rolling the die:

There are 3 even numbers (2, 4, and 6) and 3 odd numbers (1, 3, and 5) on a standard six-sided die.

Since rolling an even number is twice as likely as rolling an odd number, we can assign probabilities as follows:
P(2) = P(4) = P(6) = 2x
P(1) = P(3) = P(5) = x
Now, we need to remember that the total probability of all outcomes must add up to 1:
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = x + 2x + x + 2x + x + 2x = 9x
Since the total probability is 1, we can write the equation:
9x = 1.

Now, we can solve for x:
x = 1/9
Since we want the probability of rolling a 1, we just use the value of x:
P(1) = x = 1/9.

For similar question on probability.

https://brainly.com/question/28764815

#SPJ11

The value of the expression (a[1] + a[3]) is "BD". In this array declaration and initialization, the variable "a" is an array of type String that contains four elements: "A", "B", "C", and "D". The square brackets notation is used to access specific elements of the array.

In this case, a[1] refers to the second element of the array (remember that array indices start at 0), which is "B". Similarly, a[3] refers to the fourth element of the array, which is "D".

Therefore, the expression (a[1] + a[3]) concatenates the strings "B" and "D" to form the string "BD". This is the final value of the expression.

It's worth noting that the other options listed in the question ("AC", "ABC", and "CD") are not correct. "AC" is the result of concatenating the first and third elements of the array (a[0] + a[2]). "ABC" is the result of concatenating all four elements of the array (a[0] + a[1] + a[2] + a[3]). And "CD" is the result of concatenating the last two elements of the array (a[2] + a[3]).

To learn more about array : brainly.com/question/31605219

#SPJ11

The main difference between the denominator of the F-ratio (the error term) for a repeated-measures ANOVA and an independent-measures ANOVA lies in the way variability is accounted for within the groups.

In a repeated-measures ANOVA, the same participants are exposed to multiple conditions or measured at different time points. Therefore, this design accounts for individual differences, leading to a smaller error term in the denominator of the F-ratio.

The error term in repeated-measures ANOVA represents the variability due to individual differences and the residual error, but not the variability between participants. In contrast, an independent-measures ANOVA involves separate groups of participants for each condition, meaning that variability between participants is included in the error term.

As a result, the error term for the independent-measures ANOVA is larger than that of the repeated-measures ANOVA. This difference in the denominator of the F-ratio affects the sensitivity of the statistical test, with the repeated-measures ANOVA being more sensitive due to its smaller error term.

In summary, the denominator of the F-ratio (the error term) differs for a repeated-measures ANOVA compared to an independent-measures ANOVA in terms of the variability accounted for within groups. The repeated-measures ANOVA error term is smaller, as it controls for individual differences, while the independent-measures ANOVA error term is larger because it includes variability between participants.

Know more about  F-ratio   here:

https://brainly.com/question/31827066

#SPJ11

A negative goal is one from which behaviour is directed away, and is often referred to as an object or situation.

Certainly! In the field of psychology, goals can be categorized as either approach goals or avoidance goals. Approach goals are goals that individuals are motivated to achieve because they are attractive and desirable. In contrast, avoidance goals are goals that individuals are motivated to achieve because they are unattractive and undesirable. In other words, avoidance goals are goals that individuals try to avoid or move away from.

An avoidance object refers to an object or situation that is associated with an avoidance goal. For example, if an individual has a goal to avoid getting a bad grade in a class, the avoidance object would be the bad grade. The individual's behaviour would be directed away from the avoidance object (i.e., the bad grade) in order to achieve the avoidance goal (i.e., avoiding the bad grade).

In the original statement, the blank should be filled with "avoidance object", as an avoidance goal is often associated with an avoidance object.

Learn more about Avoidance conflicts

brainly.com/question/30396476

#SPJ11

The probability of randomly selecting the correct access code on the first try is 1/125 or approximately 0.008 or 0.8%.

The total number of possible access codes is the product of the number of choices for each digit.

In this case, there are 5 choices for each digit, so the total number of possible access codes is 5 * 5 * 5 = 125.

Since there is only one correct access code, the probability of randomly selecting it on the first try is simply 1 divided by the total number of possible access codes, which is 1/125.

So the probability of randomly selecting the correct access code on the first try is 1/125 or approximately 0.008 or 0.8%.

This means that if we were to make 125 attempts, we would expect to get the correct access code once, on average.

5 * 5 * 5 = 125

Since there is only one correct access code, the probability of randomly selecting it on the first try is:

1/125

For similar question on probability:

https://brainly.com/question/30034780

#SPJ11

An equation that can be used to find the length of the scarf in inches, y, with a number of rows is: A. y = 2/5(x).

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 4/10 = 6/15

Constant of proportionality, k = 2/5.

Therefore, the required linear equation is given by;

y = kx

y = 2/5(x)

Read more on proportional relationship here: brainly.com/question/28350476

#SPJ1

Possibilities that both Tyrone and Alisha are correct, depending on the specific expression they are trying to simplify.

In order to determine who is correct between Tyrone and Alisha, we must first look at the expression that they are trying to simplify.

Depending on the expression, different methods may be more appropriate. Without the expression provided, it is difficult to say definitively who is correct.
However,

If we assume that the expression is in the form of a fraction with variables raised to different powers, then both Tyrone and Alisha could potentially be correct.
Raising the numerator and denominator to the third power is a valid method of simplifying expressions that involve fractional exponents.

This is because raising a fraction to a power is equivalent to raising both the numerator and denominator to that power.

By doing this, we can eliminate the fractional exponents and potentially combine like terms.
On the other hand, applying the quotient of powers is another valid method of simplifying expressions with exponents.

This involves dividing the powers of the same base when they are being divided. For example, if we have ([tex]a^3[/tex])/([tex]a^2[/tex]), we can simplify this to a(3-2) = a.
It is important to remember that there may be multiple ways to simplify an expression and it is up to the individual to choose the method that they are most comfortable with.

For similar question on Possibilities:

https://brainly.com/question/30584221

#SPJ11

The mean value Taylor would use to compare with the other cars is approximately 11.2 seconds.

To find the mean value, we need to sum up the three recorded times and then divide by the number of trials (which is 3 in this case).

Sum of the recorded times:

11 seconds + 11.4 seconds + 11.2 seconds = 33.6 seconds

Mean value:

Mean = Sum of values / Number of values

Mean = 33.6 seconds / 3

Dividing:

Mean ≈ 11.2 seconds

Know more about mean value here:

https://brainly.com/question/14882017

#SPJ11

Their hourly wage in 9 more years is $23.60 per hour.

To find the hourly wage in 9 more years, we can use the formula for exponential growth:

A = [tex]P * (1 + r)^t[/tex]

Where:

To find the annual growth rate, we can use the formula:

r = [tex](A/P)^(^1^/^t^)[/tex] - 1

Substituting the given values, we get:

r = [tex](\$16.09 / \$6.90)^(^1^/^1^1^)[/tex] - 1

r = 0.0883 or 8.83%

Now we can use this growth rate to find the hourly wage in 9 more years:

A = $6.90 * [tex](1 + 0.0883)^9[/tex]

A = $23.60 (rounded to the nearest cent)

Therefore, the hourly wage of the automobile plant workers in 9 more years, if their wages continue to grow exponentially at the same rate, would be $23.60 per hour.

Learn more about hourly wage

brainly.com/question/1582269

#SPJ11