in the number 714.438 how does the value of the digit 4 to the left of the decimal point compare to the value of the digit 4 to the right of the decimal point?



Sentence please

The combined amount in both accounts after 10 years is $16,869.58

To solve the problem, we need to use the following formulas:

Simple Interest = Principal x Rate x Time

Compound Interest = [tex]Principal * (1 + Rate/ n)^{n * Time}[/tex]

where:

Principal = the initial deposit

Rate = the interest rate (in decimal form)

Time = the number of years

n = the number of times interest is compounded per year

For Account 1:

Simple Interest = Principal x Rate x Time

= $6000 x 0.035 x 10

= $2100

The amount in Account 1 after 10 years will be the initial deposit plus the interest earned:

= $6000 + $2100

= $8100

For Account 2:

Since the interest is compounded annually, n = 1.

Compound Interest = [tex]Principal * (1 + Rate/ n)^{n * Time}[/tex]

= [tex]6000 *(1 + 0.035/1)^{1 * 10}\\= $6000 (1.035)^{10}\\= $8769.58[/tex]

After ten years, the amount in Account 2 will be $8769.58.

After ten years, the combined amount in both accounts will be:

$8100 minus $8769.58 equals $16869.58, resulting in a total of $16,869.58 in both accounts after ten years.

know more about simple interest visit:

https://brainly.com/question/25845758

#SPJ1

Positive divisors does n2 have are 5.

If an integer n has exactly three positive divisors, including 1 and n, it means that n is a perfect square of a prime number.

The reason for this is that a prime number has only two divisors: 1 and itself. Therefore, if n has exactly three positive divisors, n must be a perfect square of a prime number, since the only divisors of a perfect square are the divisors of its square root, and its square root must be a prime number.

Let's say that n is equal to p², where p is a prime number. The positive divisors of n are 1, p, and n (which is p²).

Now, to find the number of positive divisors of n², we can use the fact that any positive divisor of n² can be expressed in the form [tex]p^k[/tex], where 0 ≤ k ≤ 4 (since n² = p⁴).

Therefore, the positive divisors of n² are:

1, p, p², p³, and p⁴ (which is n²)

So, n² has 5 positive divisors: 1, p, p², p³, and n².

Hence, the answer is 5.

Learn more about positive divisors.

brainly.com/question/30207836

#SPJ11

The main topic is the split-half reliability test used in psychological research to assess the internal consistency of a scale.

In psychological research, reliability is a crucial aspect of measuring constructs or attributes. One commonly used method for assessing the reliability of a scale is the split-half reliability test.

In this test, the scale questions are divided into two parts equally, and the resulting scores of both parts are correlated against one another.

For example, if a scale had 20 items, the items could be randomly split into two groups of 10 items each.

Scores are then calculated for each group, and the scores are correlated with each other to determine the degree of consistency between the two halves.

The correlation coefficient obtained from this analysis provides an estimate of the internal consistency of the scale.

A high correlation coefficient indicates a high level of internal consistency, indicating that the two halves of the scale are measuring the same construct or attribute.

Conversely, a low correlation coefficient suggests that the two halves of the scale are not measuring the same construct or attribute, and the scale may need to be revised or abandoned.

Overall, the split-half reliability test provides a quick and efficient method for evaluating the reliability of a scale.

However, it is important to note that this method does have some limitations, such as the possibility of unequal difficulty or discrimination of the items in each half of the scale.

Therefore, researchers often use other methods, such as Cronbach's alpha, in conjunction with the split-half reliability test to provide a more comprehensive assessment of the reliability of a scale

Learn more about reliability test

brainly.com/question/27873337

#SPJ11

Therefore, the solution to the system of equations is (x, y) = (-3, 4).

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can be composed of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields such as physics, engineering, economics, and mathematics.

To solve the system of equations using elimination, we need to manipulate one or both equations so that one of the variables has the same coefficient with opposite signs. Here's how we can solve the system:

Multiply the first equation by -2 to get -4x - 10y = -28.

Add the second equation to the new equation to get -8y = -32.

Divide both sides by -8 to get y = 4.

Substitute y = 4 into either equation to solve for x.

Using the first equation:

[tex]2x + 5(4) = 14[/tex]

[tex]2x + 20 = 14[/tex]

[tex]2x = -6[/tex]

[tex]x = -3[/tex]

To learn more about equation, visit

https://brainly.com/question/10413253

#SPJ1

For a chi-square goodness-of-fit test with n observations sorted into k frequency bins, the degrees of freedom are equal to (k - 1).

The degrees of freedom for a chi-square goodness-of-fit test in this scenario would be (k-1) since there are k frequency bins and the total frequency is fixed (n). The chi-square test compares the observed frequencies with the expected frequencies in each bin, and the difference between these frequencies is used to calculate the test statistic. The degrees of freedom determine the critical value of the test statistic and are based on the number of independent pieces of information used to estimate the expected frequencies.
Hi! I'd be happy to help you with your question. In a chi-square goodness-of-fit test, the degrees of freedom can be calculated using the given terms: observations, frequency, and chi-square. Here's the step-by-step explanation:

1. You have a sample consisting of n observations.
2. These observations are sorted into k frequency bins.
3. The chi-square goodness-of-fit test is used to determine how well the observed frequencies match the expected frequencies.

To calculate the degrees of freedom for this test, use the following formula:
Degrees of freedom = (k - 1)
Where k is the number of frequency bins.

Learn more about chi-square goodness-of-fit test here:

https://brainly.com/question/30166929

#SPJ11

The degrees of freedom (df) for a chi-square goodness-of-fit test in this scenario is k-1.

The chi-square goodness-of-fit test is used to test whether a set of observed frequencies fits a theoretical distribution.

The observed frequencies are sorted into k bins.

The test statistic is calculated by comparing the observed frequencies to the expected frequencies under the theoretical distribution, and summing the squared differences divided by the expected frequencies.

The degrees of freedom for the chi-square goodness-of-fit test is calculated as (k-1), where k is the number of frequency bins.

This is because once we have chosen the observed frequencies for k-1 of the bins, the frequency for the last bin is completely determined by the total number of observations and the frequencies in the other k-1 bins.

So, we only have (k-1) degrees of freedom to choose the observed frequencies independently.

For similar questions on Degrees of Freedom

https://brainly.com/question/28527491

#SPJ11

Determine the recommended range of water consumption17.7 ≤ x ≤ 37.6

A.54 ≤ 1.41x + 29 ≤ 82; To stay within the range, the water usage should be between 17.7 and 37.6 HCF.

Scenario is that the water utility charges a fee of $29, plus an additional $1.41 per hundred cubic feet (HCF) of water, and the recommended monthly bill for a household is between $54 and $82.

Range of water usage in HCF (x) that fits this recommendation.
First, write the compound inequality to represent the scenario:
54 ≤ 1.41x + 29 ≤ 82
Now, to find the recommended range of water consumption, we need to isolate x in both inequalities.

Start with the left inequality:
54 ≤ 1.41x + 29
Subtract 29 from both sides:
25 ≤ 1.41x
Divide both sides by 1.41:
25 / 1.41 ≤ x
x ≥ 17.7 (rounded to one decimal place)
Next, consider the right inequality:
1.41x + 29 ≤ 82
Subtract 29 from both sides:
1.41x ≤ 53
Divide both sides by 1.41:
x ≤ 53 / 1.41
x ≤ 37.6 (rounded to one decimal place)
Combine both inequalities:

For similar questions on Range

https://brainly.com/question/24326172

#SPJ11

The volume of the basketball is 4.19x³

The volume of the box is 8x³

The volume of air is 3.81x³

We know that the basketball is a sphere of radius x, and the volume of a sphere of radius R is:

V = (4/3)*pi*R³

Where pi = 3.14

In this case the radius is x, so the volume is:

V = (4/3)*3.14*x³

V = 4.19x³

b) The cube has a side length of 2x, then the volume (the cube of that) is:

V = (2x)³

V = 8x³

c) The volume of air is the difference between the volume of the cube and the volume of the ball:

volume of air = 8x³ -  4.19x³ = 3.81x³

Laern more about volumes at:

https://brainly.com/question/1972490

#SPJ1

The total length of all 10 ribbons is 35 inches when they are placed end to end.

Inches are a unit of length in the imperial system of measurement, which is primarily used in the United States, the United Kingdom, and some other countries. One inch is equal to 1/12 of a foot or 2.54 centimeters.

The inch is commonly used to measure the length or distance of small objects, such as the size of a computer screen, the length of a pencil, or the height of a person. Inches are also used to measure the dimensions of larger objects, such as the width of a door or the size of a piece of furniture.

If John has 10 ribbons, each measuring 3 ½ inches long, we can find the total length of all the ribbons by multiplying the length of one ribbon by the number of ribbons:

Total length = 10 × 3 ½ inches

To multiply a whole number and a mixed number, we can first convert the mixed number to an improper fraction, then multiply:

Total length = 10 × (7/2) inches

Total length = 35 inches

Therefore, the 10 ribbons, placed end to end, would be 35 inches long.

To know more about the measurement visit:

https://brainly.com/question/4725561

#SPJ1

The two triangles are congruent based on the ASA Congruence Postulate.

The ASA Congruence Postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

The image shown above shows two triangles that has three pairs of congruent triangles and a pair of corresponding congruent sides.

Therefore, both triangles are congruent by the ASA Congruence Postulate.

Learn more about the ASA on:

https://brainly.com/question/2398724

#SPJ1

The histogram shows that the majority of velvetleaf plants produced between 0 and 500 seeds. The highest count was 2,000 seeds, and the lowest count was 0 seeds. On average, velvetleaf plants produce around 500 seeds.

If the researcher performed an ANOVA test and rejected the null hypothesis, it indicates that there is a significant difference between at least two group means.

To determine which specific groups differ significantly, post hoc tests are performed. If there are five levels of the independent variable, there are ten possible pairwise comparisons that can be made (5 choose 2).

Therefore, the researcher would make 10 post hoc comparisons. These tests would identify which specific groups differ significantly and would help the researcher draw more precise conclusions about the relationship between the independent variable and the dependent variable.

Learn more about the ANOVA test at

https://brainly.com/question/31192222

#SPJ4

Answer:

5x+20

Step-by-step explanation:

you are given that y=2x-5 so you can substitue that for the y value.

-3x-4(2x-5) is your new equation. You can further simply it and you will get:

-3x+8x+20

5x+20

The probability that Kylee wins at most 2 prizes in 3 attempts is 0.95625.

To answer this question, we can use the binomial distribution formula:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

where X is the number of times Kylee wins a prize, and P(X = k) is the probability of winning k prizes in 3 attempts.

Using the binomial distribution formula, we can calculate these probabilities using the following formula:

[tex]P(X = k) = (n choose k) × p^k × (1-p)^(n-k)[/tex]

where n is the number of trials (in this case, 3), p is the probability of winning a prize (0.45), and k is the number of

successes we want to calculate the probability for.

Now, let's plug in the values for k = 0, 1, and 2:

[tex]P(X = 0) = (3 choose 0) × 0.45^0 × (1-0.45)^3 = 0.342

P(X = 1) = (3 choose 1) × 0.45^1 × (1-0.45)^2 = 0.4095

P(X = 2) = (3 choose 2) × 0.45^2 × (1-0.45)^1 = 0.20475[/tex]

Now, we can add up these probabilities to find the probability that Kylee wins at most 2 prizes:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.342 + 0.4095 + 0.20475 = 0.95625

for such more question on probability

https://brainly.com/question/24756209

#SPJ11

the fraction that rounds to 5 is option B, 5 1/2.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

To round a fraction to 5, we need to find the fraction that is closest to 5. Therefore, we need to look at the fractional parts of each option and find which one is closest to 1/2.

A. 5 2/3 = 17/3, which is closer to 6 than to 5.

B. 5 1/2 = 11/2, which is exactly halfway between 5 and 6, so it rounds to 5.

C. 5 9/20 = 259/20, which is closer to 6 than to 5.

D. 4 9/20 = 209/50, which is closer to 4 than to 5.

Therefore, the fraction that rounds to 5 is option B, 5 1/2.

Learn more about Fraction, by the following link.

https://brainly.com/question/17220365

#SPJ9

The domain of the function 8 - [tex](x-3)^{2}[/tex] is R which is all the real numbers.

What is domain of a function?

The set or grouping of all potential values that may be used in the function is known as the domain.

We are given a function as 8 - [tex](x-3)^{2}[/tex].

Now, in order to find the domain, we need to find the values where the function is not defined for a value of x.

But, there is no such value for x where the function is not defined.

This means that all values of x give an output.

So, the domain is the set of all the real numbers.

Hence, the domain of the given function is R.

Learn more about domain of function from the given link:

https://brainly.com/question/1369616

#SPJ1

The integer that represents the change in temperature from morning to afternoon is 18.

To find the change in temperature from morning to afternoon, we need to calculate the difference between the afternoon temperature and the morning temperature.

The morning temperature was given as -8.7 F, which means the temperature was 8.7 degrees below the freezing point of water. The afternoon temperature was given as 9.3 F, which means the temperature was 9.3 degrees above the freezing point of water.

To find the change in temperature, we subtract the morning temperature from the afternoon temperature.

9.3 F - (-8.7 F) = 9.3 F + 8.7 F

Here, we add a negative number because we are subtracting a negative number. This gives us

= 18.0 F

So, the change in temperature from morning to afternoon is 18.0 F

Learn more about change in temperature here

brainly.com/question/23857480

#SPJ4

If there is no waste, Trevor will spend $204 on the tile.

What is area?

Area is a measure of the size of a two-dimensional surface or shape, typically measured in square units such as square inches, square centimeters, or square meters. It is the amount of space that is contained within a flat, closed figure or shape. The area of a shape is calculated by multiplying the length of the shape by its width or height, depending on the shape. For example, the area of a rectangle can be found by multiplying its length and width, while the area of a circle can be found by multiplying pi (3.14) by the square of its radius.

We can find the area of given figure by using formula of parallelogram and triangle.

area of parallelogram = base * height

area of triangle = 1/2 * base*height

so, area of give figure

= area of below parallelogram + area of right angled triangle + area of left triangular part

= base * height +  1/2 * base*height + 1/2 * base*height

= 12×5 + 1/2×9×4  + 1/2×12×4

= 60 + 18 + 24

= 102 ft²                

hence, the cost of covering will be : $2 × 102

                                                     = $204

To learn more about area visit the link:

https://brainly.com/question/25292087

#SPJ1

Complete question: Trevor is building a patio using the design below. The tile that he wants to use to cover the patio cost $2 per square feet .If there is no waste, Trevor will spend ---- on the tile

The two null hypothesis that are correct answer are two-sample t-test and one-sample t-test.

Among the group of answer choices provided, the tests that require calculating degrees of freedom are the two-sample t-test and the one-sample t-test. Both of these tests belong to the t-test family and involve using degrees of freedom to determine the critical t-value.

In summary:
- Null hypothesis: The assumption that there is no significant difference between the sample and population or between two samples.
- T-test: A statistical test used to determine if there is a significant difference between the means of two groups or between a sample and population mean.
- Degrees of freedom: A value used in statistical tests that represents the number of independent values in a data set, which can affect the outcome of the test.

So answer is: two-sample t-test and one-sample t-test.

Learn more about null hypothesis here:

https://brainly.com/question/28920252

#SPJ11

The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-

sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also

requires degrees of freedom, but it is not a test for a null hypothesis.

The correct answer is: all of the above.

All these tests require calculating degrees of freedom:

1. Two-sample t-test:

Degrees of freedom are calculated using the formula (n1 + n2) - 2, where n1 and n2 are the sample sizes of the two

groups being compared.
2. Chi-squared test:

Degrees of freedom are calculated using the formula (rows - 1) * (columns - 1), where rows and columns represent the

number of categories in the data.
3. One-sample t-test:

Degrees of freedom are calculated using the formula n - 1, where n is the sample size.

The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-

sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also

requires degrees of freedom, but it is not a test for a null hypothesis.

for such more question on null hypothesis

https://brainly.com/question/4436370

#SPJ11

From this graph , it takes 0.75 seconds to reach the highest position.

A graph is a visual representation of the relationship between two sets of data or variables, typically via lines or curves. A diagram or pictorial representation of facts or values that is arranged might be referred to as a graph in mathematics. The relationship between two or more items is frequently represented by the points on the graph

The graph indicates that the peak is at (0.75, 9)

The x-axis displays the time in seconds, while the y-axis displays the height in feet.

Consequently, it takes 0.75 seconds to reach the highest position.

To know more about graph visit:

brainly.com/question/17267403

#SPJ1

The value of x is 1.

What is a line segment?

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

Here, we have

Given:

The ratio of MM'/MM" is x/3.

We have to find the value of x.

MM' = 3 blocks

MM" = 9 blocks

MM'/MM" = 3/9 = 1/3 = x/3

x = 1

Hence, the value of x is 1.

To learn more about the line segment from the given link

https://brainly.com/question/17374569

#SPJ1

The inverse of (x-A)^c = B, where A = 2x + 1, is x = -(B^(1/c) + 1).

To find the inverse of the expression in (x - A)^c = B, where A = 2x + 1, we can use the following steps:

First, solve for x in terms of A

x = (A - 1) / 2

Substitute the expression for A into the original equation

(x - (2x + 1))^c = B

Simplify

(-x - 1)^c = B

Take the c-th root of both sides

-x - 1 = B^(1/c)

Solve for x

x = -(B^(1/c) + 1)

Therefore, the inverse of the expression in (x - A)^c = B, where A = 2x + 1, is given by

x = -(B^(1/c) + 1)

To know more about inverse of the expression:

https://brainly.com/question/12080785

#SPJ4

--The given question is incomplete, the complete question is given

" Inverse of this in (x-A)^c = (B)

—-

where A = 2X+1 "--

The value of x in the Intersecting chords is 15

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

Intersecting chords

The value of x is then calculated as

x = 1/2(30 - 2x + 30)

So, we have

2x = 30 - 2x + 30

Evaluate the like terms

4x = 60

Divide

x = 15

Hence, the value of x is 15

Read more about angles at

https://brainly.com/question/28293784

#SPJ1

The Buckley family would pay $51 either way if they rented the truck for 4 additional days.

To solve the question :

Total cost for Kendall's Moving :

= $27 + $6x,

where

x = Number of additional days rented.

Total cost for Newton Rent-a-Truck :

= $7 + $11x

To find the number of additional days we will put both the equations i.e., $27 + $6x and $7 + $11x, equal to each other.

= $27 + $6x = $7 + $11x

Subtracting $7 from both sides :

= $20 + $6x = $11x

Subtracting $6x from both sides :

= $20 = $5x

Dividing both sides by $5 :

= x = 4

Hence, the number of additional days is 4.

So,

Kendall's Moving and Newton Rent-a-Truck would be the same if the truck is rented for 4 additional days by the Buckley family :

Putting the values of x in the equations :

Total cost for Kendall's Moving :

= $27 + $6x,

= $27 + $6(4)

= $51

Total cost for Newton Rent-a-Truck

$7 + $11x

= $7 + $11(4)

= $51

Hence, the Buckley family would pay $51 either way if they rented the truck for 4 additional days.

To know more about, linear equations, visit :

https://brainly.com/question/29111179

The explanatory variable is whether or not a subject received tea before bedtime.

The theory behind this study is that drinking tea before bedtime may help with falling asleep faster.

Participants were randomly assigned to one group that received tea before bedtime and the other group that did not receive tea before bedtime.

The researcher then monitored the amount of time it took for each person to fall asleep.

The explanatory variable of this study is whether or not a subject received tea before bedtime, and the goal is to compare the amount of time it takes for each person to fall asleep depending on if they received tea before bedtime.

The results of this study will help determine if drinking tea before bedtime is an effective way to fall asleep faster.

The goal is to test whether or not this is true by comparing the amount of time it takes for each person to fall asleep depending on if they received tea before bedtime.

For similar question on explanatory variable:

https://brainly.com/question/11970099

#SPJ11

Therefore, if Tyrone saved $2500 per year, he would achieve his goal in approximately 2.7 years. This is about half the time it would take him if he saved $1250 per year.

A) Let x be the number of years Tyrone needs to save in order to reach his goal. Then, the algebraic expression that represents this scenario is:

[tex]3250 + 1250x = 10000[/tex]

B) To solve for x, we can isolate the variable x on one side of the equation. First, we can subtract 3250 from both sides:

[tex]1250x = 6750[/tex]

Then, we can divide both sides by 1250:

[tex]x = 5.4[/tex]

Therefore, it will take Tyrone approximately 5.4 years to achieve his goal.

C) If Tyrone saved $2500 per year instead of $1250, the algebraic expression that represents this scenario would be:

[tex]3250 + 2500x = 10000[/tex]

To solve for x, we can follow the same steps as in part B:

[tex]2500x = 6750[/tex]

[tex]x = 2.7[/tex]

Therefore, if Tyrone saved $2500 per year, he would achieve his goal in approximately 2.7 years. This is about half the time it would take him if he saved $1250 per year.

To know more about algebraic visit:

https://brainly.com/question/24875240

#SPJ1

Answer:

b

Step-by-step explanation:

in order to find the mean you have find the sum of the numbers and divide them by the amount of numbers.without 68 the sum is 310 divide it by 5 and tge answer is 62.however if you add 68 the sum is 378 divide it by 6 and the answer is 63.

therefore the answer increased by 1.

hope this helps :)

The Poisson distribution is applied to events where the probability of occurrence of a certain number of events in a fixed interval of time, space, or distance is small but not necessarily "very small". False.

The Poisson distribution is used to model events that occur randomly and independently over a continuous or discrete interval of time, space, or distance, such as the number of phone calls received at a call center in an hour, the number of cars passing through a toll booth in a given time period, or the number of emails received per day. The Poisson distribution is characterized by a discrete probability mass function that describes the probability of a certain number of events occurring in a given interval, and it is widely used in probability theory and statistics for modeling events with low to moderate occurrence rates.

Learn more about “  probability of occurrence  “ visit here;

https://brainly.com/question/28320298

#SPJ4

The poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is very small.

Given statement is False.

Because, The Poisson distribution is applied to events for which the probability of occurrence over a given span of time, space, or distance is not necessarily very small, but rather where the events occur randomly and independently at a constant average rate.

The Poisson distribution models the number of events that occur in a fixed time interval or within a certain area or volume of space, assuming that the events occur independently of each other and at a constant average rate. It is used in many fields, such as biology, physics, economics, and engineering, to model the occurrence of rare or common events.

The Poisson distribution has several important properties, including:

Its mean is equal to λ, and its variance is also equal to λ.

It is a discrete distribution, meaning that it models only whole numbers of events.

It is often used to model rare or unusual events, but can also be used for events that occur frequently, as long as they occur independently at a constant average rate.

For similar question on poisson distribution.

https://brainly.com/question/9123296

#SPJ11

We can use the formula for inverse variation, which states that the product of the time and the speed is constant:

time × speed = constant

Let's use t to represent the time needed to travel the distance at 54 miles per hour. We know that the time is 10 hours when the speed is 24 miles per hour. So we can set up the equation:

10 × 24 = t × 54

Simplifying, we get:

240 = 54t

Dividing both sides by 54, we get:

t = 240/54

Simplifying this fraction, we get:

t = 40/9

So it will take approximately 4.44 hours, or 4 hours and 26 minutes, to travel the same distance at 54 miles per hour.

The functions 7 are inverse functions while the functions 8 are not inverse functions

To verify that f and g are inverse functions, we need to show that:

Let's apply these conditions to the given functions:

f(x) = 5x + 2; g(x) = (x−2)/5

f(g(x)) = f((x−2)/5) = 5((x−2)/5) + 2 = x − 2 + 2 = x

g(f(x)) = g(5x + 2) = ((5x + 2) − 2)/5 = 5x/5 = x

Since f(g(x)) = x and g(f(x)) = x, we can conclude that f and g are inverse functions.

f(x) = ½x − 7; g(x) = 2x + 14

f(g(x)) = f(2x + 14) = ½(2x + 14) − 7 = x

g(f(x)) = g(½x − 7) = 2(½x − 7) + 14 = x − 7 + 14 = x + 7

Since f(g(x)) = x and g(f(x)) ≠ x, we can conclude that f and g are not inverse functions.

Read more about inverse functions at

https://brainly.com/question/3831584

#SPJ1