Using the given table, we can evaluate the expressions involving the functions f(x) and g(x). The results are as follows: (a) f(g(1)) = 3, (b) g(f(1)) = 5, (c) f(f(1)) = 4, (d) g(g(1)) = 3, (e) (g ∘ f)(3) = 4, and (f) (f ∘ g)(6) = 1.
To evaluate these expressions, we need to substitute the values from the table into the respective functions. Let's go through each expression step by step:
(a) f(g(1)): First, we find g(1) which equals 4. Then, we substitute this result into f(x), giving us f(4) = 3.
(b) g(f(1)): We start by evaluating f(1) which equals 1. Substituting this into g(x), we get g(1) = 4.
(c) f(f(1)): Here, we evaluate f(1) which is 1. Plugging this back into f(x), we have f(1) = 1, resulting in f(f(1)) = f(1) = 4.
(d) g(g(1)): We begin by calculating g(1) which is 4. Then, we substitute this value into g(x), giving us g(4) = 3.
(e) (g ∘ f)(3): We evaluate f(3) which equals 3. Substituting this into g(x), we get g(3) = 2. Therefore, (g ∘ f)(3) = g(f(3)) = g(3) = 4.
(f) (f ∘ g)(6): We first calculate g(6) which equals 3. Substituting this into f(x), we find f(3) = 3. Hence, (f ∘ g)(6) = f(g(6)) = f(3) = 1.
In summary, (a) f(g(1)) = 3, (b) g(f(1)) = 5, (c) f(f(1)) = 4, (d) g(g(1)) = 3, (e) (g ∘ f)(3) = 4, and (f) (f ∘ g)(6) = 1.
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A scientist mixes x liters of water into a container that had 10 liters of a mixture that is 12% salt and 88% water. The function f(x)=
Answer:
110 liters of water
Step-by-step explanation:
The computation of the number of liters of water added is shown below:
Let us assume the x be the liters of water
f(x) represents the salt percentage in the mixture
Given that
f(x) = 1.2 ÷ x + 10
f(x) = 1% = 1 ÷ 100 = 0.01
Now out the f(x) value in the above equation
0.01 = 1.2 ÷ x + 10
x + 10 = 1.2 ÷ 0.01
x + 10 = 120
x = 110 liters
If 12 blueberries weigh 7.2 grams, find the weight of 32 blueberries.
Answer:
The weight of 32 blueberries is 19.2
Step-by-step explanation:
We need to find what one blueberry weigh:
7.2 divided by 12 = 0.6
0.6 x 32 = 19.2
16,-8,4...;6th term
The 6th term of the sequence is______.
Answer:
- [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
1) 16
2) 16 ÷ ( - 2) = - 8
3) - 8 ÷ ( - 2) = 4
4) 4 ÷ ( - 2) = - 2
5) - 2 ÷ ( - 2) = 1
6) 1 ÷ ( - 2) = - [tex]\frac{1}{2}[/tex]
Two skateboarders are trying to build a ramp with an angle of 41°and a height of 3 ft. Which expression gives the length or
ramp?
Identify the factors of x^2 − 4x − 12. (4 points)
a(x + 4)(x − 3)
b(x − 4)(x + 3)
c(x − 2)(x + 6)
d(x + 2)(x − 6)
Answer:
(x-6)(x+2)
Step-by-step explanation:
The total cost c for p pounds of ham ig each pound costs $3.18
Answer:
Since 1 pound of copper costs 3.18, C = 3.18p
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2150. What was the rate charged per hour by each mechanic if the sum of the two rates was $145 per hour?
Answer:
Step-by-step explanation: 20x+15(160-x)=2625
20x+2400-15x=2625
5x=225
x=45
160-x=115
rate of first mechanic= $45/hr
rate of second mechanic=$115/hr
Which quotient is greater than 3?
Question 4 options:
42 ÷ 19
40 ÷ 18
38 ÷ 14
36 ÷ 11
Answer:
36/11
Step-by-step explanation:
Answer:
36/15
Step-by-step explanation:
The temperature in Minneapolis changed from -7 °F at 6 A.M. to 7°F at noon. How much did the temperature increase?
Answer:
14 degrees F
Step-by-step explanation:
Answer:
Step-by-step explanation:
from -7 degrees F to 0 are 7 degrees change
from 0 to 7 are also 7 degrees,
in total are 14 degrees in change
Surat As-Sajdah is Surah:
options:
a) Makeya
b) Madaniya
Answer:
a
Step-by-step explanation:
SURAH AS-SAJDHA IS MAKEYH SURAH
write a polynomial in standard form that represents the area of the shaded region.
Find the solution set of the inequality
8x - 8 ≤ -72
Answer:
x ≤ -8
Step-by-step explanation:
8x-8 ≤ -72
+8 +8
8x ≤ -64
divide by 8
8x/8 ≤ -64/8
x ≤ -8
A brace is needed at the corner of a table, as shown in the diagram.
9 in
6 in.
What is the approximate length of the brace? A. 130 inches
B. V45 inches
C. 117 inches. D.12 inches
E. 15 inches
Answer: it’s 30
Step-by-step explanation: I got it right on my exam
Place the circles in order from the circle with the largest area to the circle with the smallest area.
Answer:
explain how like uh 0Oo. done
Step-by-step explanation:
22 foot ladder is placed against a vertical wall of building with the bottom of the ladder standing on level ground 9 feet from the base of the building how high up the wall does the ladder reach
Answer:
20.1 feet
Step-by-step explanation:
We solve the above question using the Pythagoras Theorem
The Pythagoras Theorem =
Opposite² + Adjacent ² = Hypotenuse²
From the above question,
Opposite side = Height of the wall = x
Adjacent side = Distance from the base of the building = 9 feet
Hypotenuse = Length of the ladder = 22 feet
Hence:
x² + 9² = 22²
x² = 22² - 9²
x = √22² - 9²
x = √403
x = 20.0748599 feet
Approximately = 20.1 feet
Therefore, the height of the wall = 20.1 feet
PLSS HELPPP
FIRST PERSON TO ANSWER GETS BRAINLIEST!!!
Answer:
top angle: 38bottom left: 77bottom right: 65Step-by-step explanation:
How far is the portion of her route from A to D? Round to the nearest whole number. Explain. I NEED IT BY TONIGHT SO PLSS SOMEONE HELP ME!
9514 1404 393
Answer:
A to D is about 2087 ft
Step-by-step explanation:
For the portion of the path of interest, the sine and cosine relations apply.
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
__
AB is the adjacent side to the angle marked 33°, with hypotenuse 975 ft.
cos(33°) = AB/(975 ft)
AB = (975 ft)cos(33°) ≈ 817.70 ft
BC is the opposite side in the same triangle.
sin(33°) = BC/(975 ft)
BC = (975 ft)sin(33°) ≈ 531.02 ft
CD is the hypotenuse of the right triangle BCD. The side BC that we know is opposite the given angle, so the sine relation applies.
sin(46°) = BC/CD
CD = BC/sin(46°)
CD = (531.02 ft)/sin(46°) ≈ 738.21 ft
__
Now we know the segments of the path of interest:
A–D = AB +BC +CD
A–D = 817.70 ft + 531.02 ft + 738.21 ft = 2086.93 ft
A–D ≈ 2087 ft
_____
Additional comments
The attachment shows all of the segments computed working counterclockwise from A. The angles in triangle DEF are computed using the Law of Sines from sides DF and DE and angle DEF. Segments EG and GH are computed using the Law of Cosines.
When we get to points F, G, H, we find that there is some inconsistency with the locations that would be computed working clockwise using AB and angle BFA. This inconsistency shows up in an error in the 119° angle in the attached figure.
This means that segments on the back side of the route, along path EFGHA, will vary somewhat depending on how they're computed.
We assume that points B, C, F, G are collinear.
A and B together complete a work in 20days. They worked together for 5days and B leaves. How long will A takes to finish the remaining work if A alone can finish the work 36days.
Answer:
27 days
Step-by-step explanation:
A alone, rate per day = 1/36
A and B together, rate per day = 1 / 20
Total Workdone for 5 days :
1/ 20 * 5 = 5 / 20 = 1/4
Fraction of work left :
1 - 1/4 = 3/4
3 / 4 * 36 /1
= (3 * 36) / 4
= 108 / 4
= 27 days
On a map ,the distance between two towns is 2.6 cm .The scale of the map is 1 cm :50 km. What is the actual distance between the two towns ?
A-100km
B-70km
C-130km
D-150km
And how
Answer:
C-130km
Step-by-step explanation:
50 km = 5 000 000 cm
=> Actual distance between 2 towns = 2.6 x 5 000 000 = 13 000 000 cm = 130 km
=> C-130 km will be the correct ans.
Answer:
C - 130
Step-by-step explanation:
We have two towns that have a distance of 2.6cm, at the same time we know the scale of the map is 1cm : 50km and the question being asked is the actual distance between the two towns.
What we have to do to find the answer is multiply 2.6 by 50, since we know that one centimeter is equal to 50 kilometers on the scale, this is what we must do.
50 * 2.6
Therefore, the distance between the two towns is 130 kilometers.
Tyrone has 16 model airplanes on his shelf. He has 4 times as many model airplanes as model trains. How many model trains does Tyrone have?
Write multiplication and division equations to model and solve the problem. Use m for the unknown
Step-by-step explanation:
4m =16
divide both sides by 4
m = 4
he has 4 model trains
A right triangle is described as having an angle of measure six less than negative two times a number, another angle measure that is three less than negative one-fourth the number, and a right angle. What are the measures of the angles in degrees?
Violet creates two spinners for a game. Each spinner is spun once, and the sum is recorded. The table represents the sums of the spinners and the frequency of each sum. A 2-column table with 7 rows. The first column is labeled sum with entries 5, 7, 9, 11, 13, 15, 17. The second column is labeled frequency with entries 1, 2, 3, 4, 3, 2, 1. What statement is true about the mean of the sums of the two spinners? The mean is 12. The mean is 16. The mean is the same as the median. The mean is the same as the range.
Answer:
c
Step-by-step explanation:
edg 2021
no one bothers to read why anyways
The first column is labeled sum with entries 5, 7, 9, 11, 13, 15, 17.
The second column is labeled frequency with entries 1, 2, 3, 4, 3, 2, 1.
We have given,
Violet creates two spinners for a game.
Each spinner is spun once, and the sum is recorded.
The table represents the sums of the spinners and the frequency of each sum.
A 2-column table with 7 rows.
What is the sum ?
The sum is the forword counting of the numbers.
The first column is labeled sum with entries 5, 7, 9, 11, 13, 15, 17.
The second column is labeled frequency with entries 1, 2, 3, 4, 3, 2, 1.
The follow me to get 50 points.
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5. Which of the following ways would NOT be a correct way to name this angle?
A. СВА
B. CAB
C. ABC
E. B
Answer:
B
Step-by-step explanation:
I need help really fast!!!
Answer:
by using Pythagoras law
16²=(2x²)²+(2x²)²(since base angle of isosceles triangle is equal
16²=4x⁴+4x⁴
16²=16x⁴
16=x⁴
[tex]x = \sqrt[4]{16} [/tex]
x=2
Subtract.
(6x + 5) - (x+3)
O A. 5x + 2
B. 5x shig
C. 6x+8
0 D. 6x + 2
Help please !!!! thnk you!!!!
x = 2
The line of symmetry is the line at which the parabola is the same on each side. With the line x = 2 , each side of the parabola is the same.
I am not a professional, simply using prior knowledge!
Note- It would mean the world to me if you could mark me brainliest!
Please help me out thank you.
Answer:
A
Step-by-step explanation:
n>= -6 and n<= 3
hope this helps
Answer:
_____________
1. Noah had $ 5.25 and Lin had $ 8.95. How much did they have altogether?
2. Diego had $ 21.32 and gave $ 9.50 to Elena. How much did he have left?
3. Andre deposited $ 24.50 into his bank account each week for 5 weeks. What was the total amount Andre deposited?
4. Four friends did a job together that paid $ 85.20. How much should each get if they all get an equal amount?
1. 5.25 + 8.95 = 14.20
2. 21.32 - 9.50 = 11.82
3. 24.50 × 5 = 122.5
4. 85.20 ÷ 4 = 21.3
Hope this helped! Please comment if you have any questions regarding how I got my answers. Stay safe.
what is 1.4504 rounded to the neareast cent
Answer:
$1.45
When writing about money, you use the two places after the decimal. In the third place, the number is 0 which rounds down.
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The relative humidity is 100%, and the temperature is hot. In a few sentences, explain how the weather would change if the temperature drops and becomes cool.
Answer:
ohhh no typon hope it helps
Answer:
When the temperature drops the molecules form closer together causing the weather to feel cool. When the temperature drops the humidity drops as well causing there to be less chance of rain and why snow occurs instead of rain when humidity and temperature drops.
Step-by-step explanation:
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