What is the solution to the equation below? Round youranswer to two decimal places.

What Is The Solution To The Equation Below? Round Youranswer To Two Decimal Places.

Answers

Answer 1

Solution:

Given the equation below;

\(e^{0.3x}=0.3\)

Evaluating the expression,

\(\begin{gathered} \ln e^{0.3x}=\ln0.3 \\ 0.3x=\ln \left(0.3\right) \\ x=\frac{\ln(0.3)}{0.3} \\ x=-4.01\text{ \lparen two decimal places\rparen} \end{gathered}\)

Hence, the answer is option B


Related Questions

Have an amazing day :)
Will give brainlst! Pls help

Have an amazing day :) Will give brainlst! Pls help

Answers

Answer:

As the study time increases the test score increases

Step-by-step explanation:

Nonlinear because the points aren't going in a straight line, they points fluctuate over time

Simplify (w3)4•(w5)2

Answers

Answer:

\(w^{22}\)

Step-by-step explanation:

\((w^3)^4\cdot(w^5)^2=w^{3*4}\cdot w^{5*2}=w^{12}\cdot w^{10}=w^{12+10}=w^{22}\)

Please help me out!!!

Please help me out!!!

Answers

Answer:

Shifts 4 units down ---> \(g(x)=2x-10\)

Stretches f(x) by a factor of 4 away from x-axis--->\(g(x)=8x-6\)

Shifts f(x) 4 units right---> \(g(x)=2x-14\)

Compress f(x) by a factor of 1/4 toward the y-axis ---> \(g(x)=1/2x-3/2\)

Step-by-step explanation:

We are given \(f(x)=2x-6\)

We need to match the transformations.

1) shifts f(x) 4 units down.

When function f(x) shifts k units down the new function becomes f(x)-k

In our case

\(g(x)=2x-6-4\\g(x)=2x-10\)

So, Shifts 4 units down ---> \(g(x)=2x-10\)

2) Stretches f(x) by a factor of 4 away from x-axis

When function f(x) is stretched by a factor of b away from x-axis the new function becomes f(bx)

\(g(x)=2(4x)-6\\g(x)=8x-6\)

So, Stretches f(x) by a factor of 4 away from x-axis--->\(g(x)=8x-6\)

3) Shifts f(x) 4 units right

When function f(x) shifts h units right the new function becomes f(x-h)

\(g(x)=2(x-4)-6\\g(x)=2x-8-6\\g(x)=2x-14\)

So,  Shifts f(x) 4 units right---> \(g(x)=2x-14\)

4) Compress f(x) by a factor of 1/4 toward the y-axis

When function f(x) is compressed by h factor of a toward the y-axis the new function becomes h.f(x)

\(g(x)=1/4(2x-6)\\g(x)=1/2x-3/2\)

Compress f(x) by a factor of 1/4 toward the y-axis ---> \(g(x)=1/2x-3/2\)

(Option Not given)

(If we compress f(x) by a factor of 4 towards y-axis we get g(x)=8x-24)

Write the number in standard form. 900,00 + 80,000 + 500 + 7 HELP ME PLSS ILL GIVE U 100 DOLLARS

Answers

Answer:980,507

Step-by-step explanation:

Answer:

980,507

Step-by-step explanation:

hope this helps :)

A company uses six filling machines of the same make and model to place detergent into cartons that show a label of 32 ounces. The production manager has complained that the six machines do not place the same amount of fill into the cartons. A consultant requested that 20 filled cartons be selected randomly from each of the six machines and the content of each carton carefully weighed. The response is the deviation from 32 ounces.
(a) Is this study experimental, observations, or mixed?
(b) Identify all factors, factor levels, and factor-level combinations. For each factor indicate if it is experi- mental or observational.
(c) What type of design is being implemented here?
(d) We import the data and display the structure of the dataframe. We also coerse the variable Machine to a factor, and display the factor levels.

Answers

(a) This study is observational because the consultant is not manipulating any variables or imposing treatments on the machines.

(b) The factors are:

Machine (experimental factor): There are six machines, labeled A through F.

Carton (observational factor): There are 20 cartons selected randomly from each machine.

Deviation from 32 ounces (response variable): This is the weight difference between the actual fill amount and the target fill amount of 32 ounces.

The factor levels are:

Machine: A, B, C, D, E, F

Carton: 1, 2, 3, ..., 20

The factor-level combinations are all possible pairs of machine and carton, such as A-1, A-2, ..., F-20.

(c) This is a nested design because the 20 cartons selected from each machine are not interchangeable between machines.

(d) Here's an example code snippet in R to import the data and display the structure of the dataframe:

data <- read.csv("filling_machine_data.csv")

data$Machine <- factor(data$Machine)

levels(data$Machine)

Assuming the data is stored in a CSV file called "filling_machine_data.csv", the code reads in the data, coerces the Machine variable to a factor, and displays the factor levels of Machine

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help help help help help help help help help help help help help help help help help help ​

help help help help help help help help help help help help help help help help help help

Answers

Answer:

The answer to number one is 3 1/2, the answer to number two is 3 1/3, the answer to number three is 1 1/4, the answer to number four is 1 3/5, the answer to number five is 3 1/5, the answer to number six is 19/4, the answer to number seven is 27/5, the answer to number eight is 35/3, the answer to number nine is 24/7, and the answer to number ten is 13/6.

Step-by-step explanation:

To change an improper fraction into a mixed number, you hate to divide the numerator by the denominator. For example, if the improper fraction was 10/5, you would get 2 because 5 goes into 10 two times. If the improper fraction was 8/5, you would do the same thing and get 1 3/5 because 5 goes into 8 once, and since 8 minus 5 is 3, you get 3 over 5.

To change a mixed number into an improper fraction, you have to multiply the denominator my the whole number, and then take that number and add it by the numerator. For example, if the mixed number was 8 2/3, the improper fraction would be 26/3 because 3 times 8 is 24, and 24 plus 2 is 26.

I hope this helps you have a wonderful day :D

Answer:

for some reason the picture glitched for me

Step-by-step explanation:

:|


Find a if XZ = 125,
XY = 3a and YZ = 2a.

Answers

Y is 275.Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation.

How can I locate expressions that are equivalent?

Add any like terms together, combining x-terms with x-terms and constants with constants, on either side of the equation. The x-term is typically put before constants when arranging the terms in the same sequence. The two phrases are equal if each of the terms in both of them is the same.

Explanation:

x 2 + xy+xz=135; y 2 + yz+ xy=351; z 2 + xz+ yz=243; (iii)

When I (ii), and (iii) are added together, we obtain x 2 + y 2 + z 2 + 2(xy+yz+xz) = 729, which converts to (x+y+z) 2 = 27 2.

x+y+z=27

........

(iv)

According to equation I x 2 + x y + x z = 135 => x(x+y+z) = 135 => x27=135 => x=5

In equation (ii), we have y 2 + y z + x y = 351, which leads to y (x+y+z) = 351.

y×27=351 \s=>

y=13

Once more, we obtain the following from equation (iii): z 2 + x z + y z = 243; z (x + y + z) = 243; z 27 = 243.

z=9 \sx \s2 \s +y \s2 \s +z \s2 \s =5

2 \s +13 \s2 \s +9 \s2 \s =275.

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2/8 and 1/2 write < or >

Answers

Answer:

0.5 > 0.25

Step-by-step explanation:

2/8 = 1/4 = 0.25

1/2 = 0.5

Answer:

<

Step-by-step explanation:

1/2 equals more than 2/8.

Because if u simplify 2/8 it would equal 1/4 which is less than 1/2.

The graph of � = ∣ � ∣ y=∣x∣y, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right by 4 44 units. What is the equation of the new graph? Choose 1 answer: Choose 1 answer: (Choice A) � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 A � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 (Choice B) � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 B � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 (Choice C) � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 C � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 (Choice D) � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4y, equals, vertical bar, x, minus, 9, vertical bar, plus, 4 D � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4

Answers

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

What is a translation?

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The graph of = y=xy, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right

Can ya help me with this one?

Can ya help me with this one?

Answers

11 by 35

how?

well, i have no idea just found it on internet

Answer:

11/35 hr

Step-by-step explanation:

Find the difference:

3/5 - 2/7 =                          LCD is 5*721/35 - 10/35 =                   Bring the fractions to same denominator11/35                                   Simplify

A shipping company rounds up to the nearest ton to figure out shipping charges. If you want to ship 14, 700 statuettes, each weighing 15 ounces, how many tons will you be billed for?

Answers

Answer:

6.890625 Tons

Step-by-step explanation:

To get total in ounces: [(14,700 x 15) = 220,500 OZ].

To convert ounces to tons: [(220,500/32,000) = 6.890625 Tons]

Multiply both equations by a constant

Multiply both equations by a constant

Answers

Answer:

(- \(\frac{1}{3}\), \(\frac{3}{4}\) )

Step-by-step explanation:

9x + 8y = 3 → (1)

6x - 12y = - 11 → (2)

Multiplying (1) by 12 and (2) by 8 and adding will eliminate the y- term

108x + 96y = 36 → (3)

48x - 96y = - 88 → (4)

Add (3) and (4) term by term to eliminate y

156x = - 52 ( divide both sides by 156 )

x = \(\frac{-52}{156}\) = - \(\frac{1}{3}\)

Substitute this value into either of the 2 equations and solve for y

Substituting into (1)

9(- \(\frac{1}{3}\) ) + 8y = 3

- 3 + 8y = 3 ( add 3 to both sides )

8y = 6 ( divide both sides by 8 )

y = \(\frac{6}{8}\) = \(\frac{3}{4}\)

solution is (- \(\frac{1}{3}\), \(\frac{3}{4}\) )

what is -a^-2 if a+-5?

Answers

Answer: what method? GCF or LCM

Step-by-step explanation:

1
A farmer wants to grow cabbage and wheat in his field. He divides the field into two sections as shown below.
200 yd
In how much area of the field will the farmer grow whear?
OA 41,000 square yards
OB. 20,000 square yards
OC. 42,000 square yards
OD. 21,000 square yards
Reset
210 yd
Submit

Answers

21,000 yd² of the field will the farmer grow wheat.

We have,

Length of yard = 210 yd

width of yard = 200 yd

As per the figure the yard is cut in diagonal form in which half portion have wheat and half potion have Cabbage.

So, the resulting shape of field in which what will grow is right angles triangle

= 1/2 x base x height

= 1/2 x 200 x 210

= 100 x 210

= 21,000 yd²

Thus, 21,000 yd² of the field will the farmer grow wheat.

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6-68. Victor wants to play "Guess My Number." Use the clues below to figure out his number. Each
part is a new game. Homework Help
a. "When you double my number and subtract 9, you get my original number. What is my number?"
Work:
Answer:
b. "When you double my number and add 5, you get 17. What is my number?"
Work:
Answer:
+

6-68. Victor wants to play "Guess My Number." Use the clues below to figure out his number. Eachpart

Answers

a) The value of number is, 9.

b) The value of number is, 6.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

a) When you double my number and subtract 9, you get my original number.

b) When you double my number and add 5, you get 17.

For a;

Let a number = x

So, We can formulate;

When you double my number and subtract 9, you get my original number.

⇒ 2x - 9 = x

Solve for x;

⇒ 2x - 9 = x

⇒ 2x - x = 9

⇒ x = 9

For b;

When you double my number and add 5, you get 17.

⇒ 2x + 5 = 17

Solve for x;

⇒ 2x + 5 = 17

⇒ 2x = 17 - 5

⇒ 2x = 12

⇒ x = 6

Thus, We get;

a) The value of number is, 9.

b) The value of number is, 6.

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What are the characteristics of a density curve? Select all that apply.
A. The total area under the curve is always 1.
B. The area between any two points is always 0.5.
C. The curve always falls on or above the horizontal axis.
D. The percentage of values between any two points is the area of the figure
formed by the curve and the x-axis.

Answers

Answer:

b

Step-by-step explanation:

From the characteristics of a density curve, option (A), (C), (D) are the correct answers.

What is a density curve?

A density curve is a graph that shows probability. It is an idealized representation of a distribution in which the area under the curve is defined to be 1.The area under the curve is equal to 100 percent of all probabilities.

For the given situation,

Properties of density curves

• A density curve is always on or above the horizontal axis.

• The area underneath a density curve is exactly 1.

• The area under a density curve and above any range of values is the

relative frequency of all observations that fall in that range.

Hence we can conclude that from the characteristics of a density curve, option (A), (C), (D) are the correct answers.

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Can anyone help me find the correct angle for ZWP?

Can anyone help me find the correct angle for ZWP?

Answers

Answer:

56 degrees

Step-by-step explanation:

Here, I think you just accidentally put the value for the angle ZWX, which would be ZWP+PWX(56+56).

You actually already wrote it on the paper, so nothing wrong with your math here, just a thinking error :)

Suppose that, for budget planning purposes, the city in Exercise 24 needs a better estimate of the mean daily income from parking fees.
a) Someone suggests that the city use its data to create a confidence interval instead of the interval first created. How would this interval be better for the city? (You need not actually create the new interval.)
b) How would the interval be worse for the planners?
c) How could they achieve an interval estimate that would better serve their planning needs?
d) How many days' worth of data should they collect to have confidence of estimating the true mean to within

Answers

a) As per the given budget, the amount of interval that would be better for the city is 95% confidence interval.

b) The interval that be worse for the planners is depends on sample size

c) They achieve an interval estimate that would better serve their planning needs is depends on margin of error

d) The number of days worth of data should they collect to have confidence of estimating the true mean to 30 days

To obtain a better estimate, the city can create a confidence interval, which is a range of values that is likely to contain the true population mean with a certain degree of confidence.

However, there are also some disadvantages to using a confidence interval. The interval estimate may be wider than a point estimate, which means that the budget planners may have to allocate a larger budget to account for the uncertainty in the estimate.

To achieve a better interval estimate, the city could increase the sample size or reduce the variability of the data. Increasing the sample size reduces the margin of error and increases the precision of the estimate.

Finally, to determine how many days' worth of data the city should collect to estimate the true mean with a certain degree of confidence, the city would need to consider the desired level of precision, the variability of the data, and the desired level of confidence.

Typically, a larger sample size will provide a more accurate estimate, but this also depends on the variability of the data. In general, a sample size of at least 30 is recommended for a reasonably accurate estimate.

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The units of an item available for sale during the year were as follows: Jan. 1 Inventory 50 units at $124 Mar. 10 Purchase 60 units at $132 Aug. 30 Purchase 20 units at $138 Dec. 12 Purchase 70 units at $142 There are 80 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the ending inventory cost and the cost of goods sold by three methods. Round interim calculations to one decimal and final answers to the nearest whole dollar. blank Cost of Ending Inventory and Cost of Goods Sold Inventory Method Ending Inventory Cost of Goods Sold First-in, first-out (FIFO) $fill in the blank 1 $fill in the blank 2 Last-in, first-out (LIFO) fill in the blank 3 fill in the blank 4 Weighted average cost fill in the blank 5 fill in the blank 6

Answers

Ending Inventory Cost and Cost of Goods Sold using different inventory methods:

FIFO Method:

Ending Inventory Cost: $11,920

Cost of Goods Sold: $15,068

LIFO Method:

Ending Inventory Cost: $11,996

Cost of Goods Sold: $15,123

Weighted Average Cost Method:

Ending Inventory Cost: $11,974

Cost of Goods Sold: $15,087

Using the FIFO (First-In, First-Out) method, the cost of the ending inventory is determined by assuming that the oldest units (those acquired first) are sold last. In this case, the cost of the ending inventory is calculated by taking the cost of the most recent purchases (70 units at $142 per unit) plus the cost of the remaining 10 units from the March 10 purchase.

This totals to $11,920. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory at $124 per unit, 60 units from the March 10 purchase at $132 per unit, and 20 units from the August 30 purchase at $138 per unit), which totals to $15,068.

Using the LIFO (Last-In, First-Out) method, the cost of the ending inventory is determined by assuming that the most recent units (those acquired last) are sold first. In this case, the cost of the ending inventory is calculated by taking the cost of the remaining 10 units from the December 12 purchase, which amounts to $1,420, plus the cost of the 70 units from the August 30 purchase, which amounts to $10,576.

This totals to $11,996. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,123.

Using the Weighted Average Cost method, the cost of the ending inventory is determined by calculating the weighted average cost per unit based on all the purchases. In this case, the total cost of all the purchases is $46,360, and the total number of units is 200.

Therefore, the weighted average cost per unit is $231.80. Multiplying this by the 80 units in the physical inventory at December 31 gives a total cost of $11,974 for the ending inventory. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,087.

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Each of the following people bought a watch that costs 300. Which of the following people will pay the most for their purchase

Answers

The individual that will be paying the most for their purchase is: B.edgar paid with a credit card and paid the minimum payment each month

Which individual will pay the most?

The individual that will pay the most according to the data provided is Edgar. Edgar's payment is spread out to the longest length of time. So, he will have to pay the added dues for extending his payment.

Usually, the person who pays cash pays the least amount while the person who pays in installments is charged for additional time spent in making the payment.

Complete Question:

Each of the following people bought a watch that costs $300. Which of the following people will pay the most for their purchase A.Sarah paid cash B.edgar paid with a credit card and paid the minimum payment each month C.susan paid with a credit card and paid the minimum payment plus 30 each month D. Sean paid with a credit card and paid the full balance the first of the month

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Which is the radian measure for 30° and its associated coordinate point on the unit circle?
7 pie/6
Pie over 6

Answers

Answer:

57

Step-by-step explanation:

this is the boybfiend

Courtney ate thirty-six hundredths of a pound of strawberries. How is this number written in expanded notation?

Courtney ate thirty-six hundredths of a pound of strawberries. How is this number written in expanded

Answers

We have the following:

The first thing we have to do is express the value of thirty-six hundredths as a number, like this

\(0.36\)

Now we calculate the extended form

\(\begin{gathered} 0.36=0.30+0.06 \\ 0.30=3\cdot0.1 \\ 0.06=6\cdot0.01 \\ 0.36=(3\cdot0.1)+(6\cdot0.01) \end{gathered}\)

Therefore, the correct answer is the third option

A bag contains 6 red marbles, 4 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that all three marbles drawn will be red?

Answers

Answer:

20 marbles total...7 are green

Step-by-step explanation:

probability on first draw is 7/20...and since the marble was not replaced, the probability on the second draw is 6/19. And since they cant happen at the same time, we multiply

7/20 * 6/19 = 42/380 which reduces to 21/190

where is point b on the number line?​

Answers

Answer:

i dont know but can you pick me brainiest

Step-by-step explanation:

What is the distributive property?

What is the distributive property?

Answers

Answer:

The first option: A.) For any numbers a, b, and c, a(b + c) = ab + ac.

Step-by-step explanation:

So anytime that you have a number or letter in front of a set of parenthesis that has numbers within (such as the example problem of: a(b + c)), you need to take the number outside of the parenthesis (a) in this situation) and multiply it to all of the numbers inside the parenthesis, like this:

a(b + c).

Multiply a into b, then multiply a into c, so that the equation looks like this:

ab + ac.

I hope that this helps.

simplify:(⅓x²-8y) and (⅓x²+8y). Also find its value when x=1 and y=3

Answers

Answer:

the answer is is c I promise

Step-by-step explanation:

I just took the test

Answer:

-23.66666667

(⅓x²-8y)

Step-by-step explanation:

(⅓x²-8y) is the simplest form :)

ANSWER AS QUICK AS POSSIBLE WILL GET BRAINIEST!!!!!

:Which equation can be used to calculate the area of shaded triangles in the figure below:
A, 2 (12 x 4) = 96 feet.
B, 1/2 (12 x 4) = 24 square feet.
C, 2(12+4)=32 square feet
D, 1/2(4+12)= 8 square feet

ANSWER AS QUICK AS POSSIBLE WILL GET BRAINIEST!!!!!:Which equation can be used to calculate the area

Answers

Answer: da vinkiy

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

4 x 12

then divide by 2

which can also be known as mult 1/2

For what values of theta do maximum r-values occur on the graph the polar equation r = 2 cos4 theta? Note that the maximum r-value occurs at a point that is the maximum distance from the pole

Answers

Answer:r=2 cos^4(theta)

Step-by-step explanation:To find the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta), we need to find where the derivative of r with respect to theta is equal to zero, since the maximum r-values occur at these points.

First, we can simplify the equation by using the identity cos(2theta) = 2cos^2(theta) - 1 and substituting cos^2(theta) = (1 + cos(2theta))/2. This gives:

r = 2 cos^4(theta) = 2(1/2 + 1/2 cos(2theta))^2 = 1 + cos(2theta) + cos^2(2theta)/2.

Next, we can take the derivative of r with respect to theta, using the chain rule:

dr/dtheta = -sin(2theta) - 2cos(2theta)sin(2theta).

Setting this equal to zero and factoring out sin(2theta), we get:

sin(2theta)(-1 - 2cos(2theta)) = 0.

This equation is satisfied when sin(2theta) = 0 or cos(2theta) = -1/2.

When sin(2theta) = 0, we have 2theta = k*pi for some integer k. Therefore, theta = k*pi/2.

When cos(2theta) = -1/2, we have 2theta = 2*pi/3 + 2*k*pi or 2theta = 4*pi/3 + 2*k*pi for some integer k. Therefore, theta = pi/3 + k*pi or theta = 2*pi/3 + k*pi.

These are the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta).

Is 2/1/2 greater then 2/3/5

Is 2/1/2 greater then 2/3/5

Answers

Answer: yes you are correct 2 /1/2 is greater

Step-by-step explanation:

Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x)= 1= ² + 4
X-4

Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.f(x)= 1= + 4X-4

Answers

To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:

\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)

To simplify this expression, we can expand the square:

\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)

Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)

Next, let's find g(f(x)). We substitute f(x) into the function g(x):

\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)

Hence, g(f(x)) simplifies to 1/x^2.

In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.

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