Which one of the following is a correct equation?

Answer:

Step-by-step explanation:

Given  g (x) = \(\frac{x+1}{x-2}\) and \(h(x) = 4-x\), we are to find \((goh)(-3)\)

First we need to get \((goh)(x)\)

\((goh)(x) = g(h(x))\\g(h(x))= g(4-x)\\g(4-x) = \frac{(4-x)+1}{(4-x)-2}\\ g(4-x) = \frac{5-x}{2-x}\\substitute \ x = -3 \ into \ resulting \ function\\ g(4-x) = \frac{5-x}{2-x}\\(goh)(-3) = \frac{5-(-3)}{2-(-3)}\\\\(goh)(-3) = \frac{8}{5}\\\)

Hence \((goh)(x)\ is \ Eight-fifths\)

Also given f(x) = x and g(x) = 1/x, we are to find \((fog)(x)\)

\((fog)(x) = f(g(x))\\f(g(x)) = f(\frac{1}{x} )\\ since \ f(x) = x^2, we\ will \ repalce\ x \ with \ \frac{1}{x} \ to \ have;\\ f(\frac{1}{x} ) =( \frac{1}{x})^2\\\\\)

\(f(\frac{1}{x} ) = \frac{1}{x^2}\)

For the pair of function f(x) = 2/x and g(x) = 2/x

f(g(x)) = f(2/x)

f(2/x) = 2/(2/x)

f(2/x) = 2*x/2

f(2/x) = x

Hence f(g(x)) = x

For the pair of function f(x) = x-2/3 and g(x) = 2-3x

f(g(x)) = f(2-3x)

f(2-3x) = (2-3x-2)/3

f(2-3x) = -3x/3

f(2-3x) = -x

f(g(x)) = -x for the pair of function

For the pair of function f(x) = x/2 - 2 and g(x) = x/2 + 2

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

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

f((x+4)/2) =  [(x+4)/2]/2 - 2

f((x+4)/2) =  (x+4)/4 - 2

find the LCM

f((x+4)/2) =  [(x+4)-8]/4

f((x+4)/2) =  (x-4)/4

Hence f(g(x)) for the pair of function is (x-4)/4

Answer:

The range of g(x) is y > 0

The ranges of f(x) and h(x) are different from the range of g(x)

Answer:

Step-by-step explanation:

-2/3 * (-1/4) =

2/3 * 1/4 =

2/12 =

1/6

Answer:

1. City A
2. Exponential Growth
3. Linear

Step-by-step explanation:

The equation for exponential growth is f(x)=a(1+r/100)^x, where a is the initial growth/starting population, r is the growth rate, and x is the time intervals.

City A
f(x)=200(1+1.05/100)^x
Simplify:
f(x)=200(1.105)^x

City B
An increase in 20 people each year is NOT exponential but linear:
f(x)=20x+200

Now we plug in x for 1 to stand for 1 year and see which city has a greater number:
City A:
f(1)=200(1.105)^1
f(1)=200 x 1.105
f(1)=221

City B:
f(1)=20(1)+200

f(1)=20+200

f(1)=220

City A will have more people.

City A is an exponential function because there's a percent increase every year, and there will be more people every year because there are more people. This is kind of how compound interest also works

City B is a linear equation because a set number of people are added every year and doesn't change based on the amount of people already in it.

1. City B will have more population after 1 year.

In this case, we have been given of both the cities A and B with each year's growth factor and we have been told to find out, which city will have more population after 1 year. So to find out the comparison, first we need to find out the individual popoulation of both the cities after 1 year of interval.

So, population of City A after 1 year will be 200 * 1.05 = 210

Similarly,  population of City B after 1 year will be 200 + 20 = 220

It is clear that City B has more population as compared to City A.

Therefore, after 1 year City B has more population.

2. equation for City A is Exponential Growth Equation.

Exponential growth is the growth which takes place when a particular quantity increases at a constant rate over a fixed time period. It is given in the form of \(P = P_{0} * (1 + r)^t\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

3. equation for City B is Linear Equation.

Linear equation is a representation of a straight line when graphed on paper. It has constant coefficients and variables raised to power 1. It is given in the form of \(P = P_{0} + rt\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

To study more about Exponential Growth Equation:

https://brainly.com/question/30690645

The number of seashells jacob has before the collections were combined is 134.

As evident from the task content; the number of seashells Jacob had before the collections were combined is to be determined.

Number of seashells Maria has = 39

Number of seashells Jacob has = x

Total number of seashells when combined = 173

Total number of seashells when combined = Number of seashells Jacob has + Number of seashells Maria has

173 = x + 39

subtract 39 from both sides

173 - 39 = x

134 = x

In conclusion, Jacob has 134 seashells before the collections were combined.

Read more on word problems:

https://brainly.com/question/21405634

#SPJ1

Answer:

25 hours per week

Step-by-step explanation:

Step one:

given data

Suri makes $15 per hour and gets a weekly bonus of $25

Juan makes $14 per hour and gets a weekly bonus of $50.

Let the number of hours worked be x

and let the total earned be y

For Surl

The expression for the total is

y= 25+15x-----------1

For Juan

The expression for the total is

y= 50+14x-----------2

Step two:

Equate the two expressions we have

25+15x=50+14x

collect like terms we have

25-50= 14x-15x

-25= -x

x= 25

Yes its is possible that they earned the same amount if they work for 25 hours

The error occurred when she incorrectly multiplied the 3 by 75.

Joanie made a mistake in her reasoning by incorrectly multiplying both sides of the equation. Let's go through the steps to see where the error occurred.

The original proportion is:

50/3 = 75/x

To solve for x, one common approach is to cross multiply. This involves multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa. In this case, it would look like:

(50)(x) = (3)(75)

This step correctly cross-multiplies the fractions, resulting in:

50x = 225

Now, let's examine the steps Joanie took:

She multiplied both sides of the equation by x:

50x/3 = 75

Next, she multiplied both sides of the equation by 3:

her results is

50x = 75

This step is incorrect because she didn't multiply both terms in the fraction by 3; she only multiplied the left side term. The correct equation should be:

50x = 225

The error occurred when she incorrectly multiplied the 3 by 75. If she had multiplied correctly, she would have obtained:

50x = 225

By cross multiplying correctly, we obtain the correct equation and solution.

Learn more about Cross multiplication here

https://brainly.com/question/27812904

#SPJ4

Answer: its A

Step-by-step explanation:

Trust me I learned the hard way

The length of AC after dilation will be 20. Then the measure of the angle ∠A' will be 37°.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

here, we have,

We have given that,

Triangle ABC is dilated by a factor of 4 to produce AA'B'C'.

The triangle ΔABC is dilated by a factor of 4 to produce the triangle ΔA'B'C'.

Then the length of AC after dilation. We have

A'C' = scale factor x AC

A'C' = 4 x 5

A'C' = 20

Then the measure of the angle ∠A' will be

There is no effect of dilation on the angle.

∠A = ∠A' = 37°

Thus, the correct option is A.

More about the dilation link is given below.

brainly.com/question/2856466

#SPJ5

Answer:

1000 grams of fish= 1500 calories

1334 grams of fish= 2001 calories

1 gram of fish= 1.5 calories

The expression x + 80 represents the number of coins Arthur has now, since he x pennies and an additional 6 dimes and 4 nickels.

We shall convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

A penny = 1 cent, so

x pennies = x cents

A dime = 10 cents so;

6 dimes = 6 × 10cents

6 dimes = 60 cents

A nickel = 5 cents so;

4 nickels = 4 × 5 cents

4 nickels = 20 cents

Arthur's coins in total = (x + 60 + 40) cents

Arthur's coins in total = (x + 80) cents.

Therefore, the expression expression x + 80 represents the number of coins Arthur will have in total, wether in pennies, dimes or nickels.

Learn more about pennies, nickels and dimes here: https://brainly.com/question/5193496

#SPJ1

the hypotenuse of the right triangle is 65, and one of the legs measures 60. We need to find the length of the third side.

To find the length of the third side, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. Therefore:a² + b² = c²where a and b are the lengths of the legs, and c is the length of the hypotenuse.

In this case, we can plug in the values that we know:60² + b² = 65²Simplifying, we get:3600 + b² = 4225Subtracting 3600 from both sides, we get:b² = 625Taking the square root of both sides, we get: b = 25Therefore, the length of the third side is 25 units long.

To know more about hypotenuse

https://brainly.com/question/16893462

#SPJ11

The total area of the given shape is 71cm².

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina. A shape's area can be calculated by contrasting it with squares of a known dimension. The square meter (abbreviated as m²), which is the area of a square whose sides are one metre long, is the common measure of area in the International System of Units (SI). Three such squares would be the same size as a shape with a three square metre surface.

The following figure can be divided into a rectangle 7cm x 8cm and a triangle of height and base 6 cm and 5 cm respectively.

Area of rectangle= 7*8= 56 cm²

Area of triangle= 1/2* base*height= 1/2*6*5 = 15 cm²

Total area of shape = 56+15= 71 cm²

To know more about area , visit

https://brainly.com/question/27683633

#SPJ1

Answer:

.05

Step-by-step explanation:

to get a percent, you multiply by 100. so take 5 and divide by 100 to get decimal

The standard deviation is relatively small when the data are all concentrated close to the mean, exhibiting little variation or spread.

The standard deviation could be a degree of the changeability or spread of a set of information. It is calculated by finding the square root of the normal of the squared contrasts between each information point and the cruel(mean).

In other words, it tells us how much the information values are scattered around the mean.

When the information is all concentrated near the cruel(mean), it implies that the contrasts between each information point and the cruel are moderately little.

This comes about in a little while of squared contrasts, which in turn leads to a little standard deviation. On the other hand, when the information is more spread out, it implies that the contrasts between each information point and the cruel are bigger.

This comes about in a bigger entirety of squared contrasts, which in turn leads to a bigger standard deviation.

For case, let's consider two sets of information:

Set A and Set B.

Set A:

2, 3, 4, 5, 6

Set B:

1, 3, 5, 7, 9

Both sets have the same cruel(mean) (4.0), but Set A encompasses a littler standard deviation (1.4) than Set B (2.8).

This is because the information values in Set A are all moderately near to the cruel(mean), while the information values in Set B are more spread out.

Subsequently, we will say that the standard deviation is generally small when the information is all concentrated near the mean, showing a small variety or spread.

To know more about standard deviation refer to this :

https://brainly.com/question/24298037

#SPJ4

The value of the additional data point is 36

To find the value of the additional data point, we can use the concept of the sample mean.

Given the data set: 23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19.

The sample mean of this data set is 26.5.

To find the value of the additional data point, we can use the formula for the sample mean:

(sample mean) = (sum of all data points) / (number of data points)

In this case, we have 11 data points in the original data set. Let's denote the value of the additional data point as x.

Therefore, we can set up the equation:

26.5 = (23 + 28 + 20 + 33 + 42 + 12 + 19 + 50 + 36 + 25 + 19 + x) / 12

Multiplying both sides of the equation by 12 to eliminate the fraction, we have:

318 = 282 + x

Subtracting 282 from both sides of the equation, we find:

x = 318 - 282

x = 36

Know more about sample mean here;

https://brainly.com/question/33323852

#SPJ11

.

Answer: Take your pick, Emily.

Step-by-step explanation:

1) Assuming Emily wants both Chocolate Chip(CC) and Sugar Cookies(SC) in each basket, she could make 20 baskets having 1 CC and 2 SC in each basket. That would leave 8 SC (48-40) without any matching CC.

2) If Emily doesn't care about the makeup of each basket (e.g., some baskets may have any combination of cookies), she has a total of (20 + 48) or 68 cookies. She has the following choices:

1 cookie each: 68 baskets

2 cookies each: 34 baskets

3 cookies each: 22 baskets with 2 cookies left over

And so forth.

Unless Emily was given some other condition (e.g., a minimum of 5 cookies/basket), there are many possible answers.

21 miles per hour is the speed of boat still in water and 9 miles per hour is the speed of current.

Downstream - A boat is said to be moving downstream if it is moving in the same direction as the stream.

Upstream - A boat is said to be moving upstream if it is moving downstream of the stream. The term "upstream speed" in this context refers to the boat's net speed.

13) Given that, a boat traveled 280 miles downstream and back.

Time taken by boat in downstream is 7 hours and in upstream is 14 hours.

Let the speed of a boat be x miles per hour and the speed of a current be y miles per hour.

So, the total speed in downstream is x+y miles per hour and the total speed in upstream is x-y miles per hour.

We know that, Distance = Speed × Time

Now, 280=(x+y)×7

⇒ x+y=40 ------(I)

Here, 280=(x-y)×14

⇒ x-y=20 ------(II)

Add equation (I) and (II), we get

x+y+x-y=40+20

⇒ 2x=60

⇒ x=30 miles per hour

So, x+y=40

⇒ y=10 miles per hour

14) Given that, a boat traveled 252 miles downstream and back.

Time taken by boat in downstream is 12 hours and in upstream is 84 hours.

Let the speed of a boat be p miles per hour and the speed of a current be q miles per hour.

So, the total speed in downstream is p+q miles per hour and the total speed in upstream is p-q miles per hour.

We know that, Distance = Speed × Time

Now, 252=(p+q)×12

⇒ x+y=21 ------(I)

Here, 252=(p-q)×84

⇒ p-q=3 ------(II)

Add equation (I) and (II), we get

p+q+p-q=21+3

⇒ 2p=24

⇒ p=12 miles per hour

So, p+q=21

⇒ q=9 miles per hour

Therefore, the speed of boat still in water is 21 miles per hour and the speed of current is 9 miles per hour.

Learn more about the downstream speed and upstream speed here:

https://brainly.com/question/17300107.

#SPJ1

Answer:

The equation 2 x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions.

Answer:

9-3x+1/3-2+10+3/2

17-3x+11/6

113/6-3x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let ‘x’ be the number

So; the difference of a number and three implies; 3 - x

Therefore, the expression is;

2 (3 - x) or (3 - x) * 2

Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

To know more about polynomials,

brainly.com/question/11536910

#SPJ1

To calculate the sample size required to detect a true mean speed of 94 meters per second with a power of at least 0.85, we need to know the significance level and the standard deviation of the population.

Assuming a 5% significance level (alpha = 0.05) and a standard deviation of 10 meters per second, we can use the following formula:

n = (Z_beta + Z_alpha/2)^2 * σ^2 / d^2

where:

Z_beta is the Z-score for the desired power (0.85) from the standard normal distribution, which is approximately 1.04.

Z_alpha/2 is the Z-score for the desired significance level (0.05/2 = 0.025) from the standard normal distribution, which is approximately 1.96.

σ is the standard deviation of the population, which is 10 meters per second.

d is the difference between the true mean speed and the hypothesized mean speed, which is 100 - 94 = 6 meters per second.

Substituting these values into the formula, we get:

n = (1.04 + 1.96)^2 * 10^2 / 6^2

≈ 49.56

Therefore, a sample size of at least 50 would be required to detect a true mean speed as low as 94 meters per second with a power of at least 0.85, assuming a 5% significance level and a standard deviation of 10 meters per second.

To learn more about standard deviation : brainly.com/question/29115611

#SPJ11

The student's final moment of inertia is 18.18 kgm².

The moment of inertia of an objecr is the property of an object which shows its ability to rotate.

Since a student is standing with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kgm². To find the r final moment of inertia, we use the law of conservation of angular momentum.

The law of conservation of angular momentum states that for any rotation, angular momnetum is constant.

So, Iω = constant where

So, Iω = I'ω' where

Making I' subject of the formula, we have that

I' = Iω/ω'

So, substituting the values of the variables into the equation, we have that

I' = Iω/ω'

I' = 25 kgm² × 1.6 rev/s ÷ 2.2 rev/s

= 40 kgm²rev/s ÷ 2.2 rev/s

= 18.18 kgm²

So, the final moment of inertia is 18.18 kgm².

Learn more about moment of inertia here:

https://brainly.com/question/29471030

#SPJ1

To estimate the probability that a randomly selected person would pass the driving test on the first attempt, we can divide the number of people who passed on the first attempt (6500) by the total number of people who took the test (10,000).

Probability = Number of favorable outcomes / Total number of possible outcomes.In this case, the favorable outcome is passing the test on the first attempt, and the possible outcomes are all the people who took the test.

Probability = 6500 / 10000= 0.65

Therefore, the estimated probability that a randomly selected person would pass the driving test on the first attempt is 0.65 or 65%. This means that there is a 65% chance that a randomly selected person from the group of 10,000 would pass the driving test on their first try.

For more such questions on probability

https://brainly.com/question/24756209

#SPJ11

The probabilities are given as follows:

a) Square: 1/6.

b) Not the triangle: 43/48.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total area of the figure is given as follows:

12 x 8 = 96 units². (rectangle).

The area of the square is given as follows:

4² = 16 units² (square of the side lengths).

Hence the probability of the square is given as follows:

p = 16/96

p = 1/6.

The area of the triangle is given as follows:

A = 0.5 x 4 x 5 = 10 units². (half the multiplication of the side lengths).

Hence the complement of the area of the triangle is of:

96 - 10 = 86 units².

And the probability of the complement is of:

86/96 = 43/48.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

The trigonometric values for a right triangle can be obtained through the measurements of the different sides,

this can be found in a triangle like this,

then, identify the measurements in the given triangle

then,

Answer:

$64.60

Step-by-step explanation: I believe this is right if not sorry. The first step is to multiply $85 by .24 and that is $20.40. Then take $20.40 from $85 (85-20.40) which is $64.60

The given series is divergent.

We can use the limit comparison test to determine the convergence or divergence of the given series:

First, note that for all n ≥ 1, we have: \(\frac{(n^9 + 1) }{ (n^10 + 1)}\) ≤ \(\frac{n^9 }{n^10} = \frac{1}{n}\)

Therefore, we can compare the given series to the harmonic series ∑ 1/n, which is a well-known divergent series. Specifically, we can apply the limit comparison test with the general term \(a_n = \frac{(n^9 + 1)}{(n^{10} + 1)}\) and the corresponding term \(b_n = \frac{1}{n}\):

lim (n → ∞) \(\frac{a_n }{ b_n}\) = lim (n → ∞) \(\frac{\frac{(n^9 + 1)}{(n^10 + 1)} }{\frac{1}{n} }\)

= lim (n → ∞) \(\frac{ n^{10} }{ (n^9 + 1)}\)

= lim (n → ∞) \(\frac{n}{1+\frac{1}{n^{9} } }\)

= ∞

Since the limit is positive and finite, the series ∑ \(\frac{(n^9 + 1) }{ (n^10 + 1) }\) behaves in the same way as the harmonic series, which is divergent. Therefore, the given series is also divergent.

To know more about "Harmonic series" refer here:

https://brainly.com/question/31582846#

#SPJ11

Answer:

Look at the picture attached.

Step-by-step explanation:

Your x-intercept is 6 and your y-intercept is 4, that is where your 2 points will go. According to the slope, you should go up 2 and over 3, if you don't want to find the x-intercept. Then you would just plot the y-intercept which is 4, and then go up 2, over three and plot the next.

Hope this helps! :)

Answer:

Answer is in the picture, hope i got it right :)

Answer:

5 buses

Step-by-step explanation:

Total number of 6th graders going for the field trip = 184

Step 1

Divide the total number of students by 4

184/4 = 46

We have 46 groups of six graders.

Step 2

There needs to be one chaperone for every four students.

We have 46 groups of six graders

This means there is need for 1 chaperone per group

Hence, we have 46 chaperones

Step 3

Find total number of people going for the field trip

184 students + 46 chaperones

= 230 people

Step 4

If a bus can hold 50 people, how many buses will they need for the trip?

50 people = 1 bus

230 people = ??y

50 × y = 230

y = 230/50

y = 4.6 buses

Hence, 4.6 buses would be needed but since we can't have 0.6(part) of a bus figuratively, as buses come in whole numbers, we approximate to the nearest whole number

= 4.6 ≈ 5

Therefore, they would be needing 5 buses for the trip.

5 buses

Step-by-step explanation:

i got 10 out of 10