The function operation (f/g)(x) in the functions f(x) = 10x-15 and g(x) =2x-3 is 5.
What is the function operation (f/g)(x) in the given function?A function is simply a relationship that maps one input to one output.
Given that;
f( x ) = 10x - 15g( x ) = 2x - 3( f / g )( x ) = ?First, we replace the function designators in f/g with the actual functions.
(f / g )(x) = f(x) / g(x)
(f / g )(x) = ( 10x - 15 ) / ( 2x - 3 )
Now, factor out 5 from 10x and -15
(f / g )(x) = 5( 2x - 3 ) / ( 2x - 3 )
Cancel the common factor of 2x - 3
(f / g )(x) = 5( 1 ) / ( 1 )
(f / g )(x) = 5 / 1
(f / g )(x) = 5
Therefore, the function operation (f/g)(x) equals 5.
Learn more about functions here: brainly.com/question/2541698
#SPJ1
solve the equation s - 12 equals 20
ASAP pls
Answer:
s = 32
Step-by-step explanation:
s - 12 = 20
s (- 12 + 12) = 20 + 12
s = 32
Step-by-step explanation:
s-12=20
s=20+12
s=32
Hope it helps.
What is 234.506 rounded to the nearest hundredth
Answer:
Rounded to the nearest hundredth, 234.506 becomes 234.51.
uppose you are performing a hypothesis test with H subscript 0 superscript blank space colon space mu equals 10 and H subscript A colon mu greater than 10, using a sample size of 50 observations. You sample data has a mean of 10.7, with a standard deviation of 3.1. Compute the test statistic for this hypothesis test
Answer: The test statistic for this hypothesis test =1.597
Step-by-step explanation:
When population standard deviation is unknown, we use t-test statistic:
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]\overline{x}[/tex] = sample mean, [tex]\mu[/tex] = population mean , s= sample standard deviation, n = sample size.
As per given,
[tex]t=\dfrac{10.7-10}{\dfrac{3.1}{\sqrt{50}}}\\\\=1.59669273171\approx1.597[/tex]
Hence, the test statistic for this hypothesis test =1.597
Please help me solve this math problem and explain it. Will give BRANIEST!
(X^2+2xy+y^2)^2
Answer:
I'm sorry hindi ko po alam eh
There was a seller of horses, who sold all his horses to three people. To the first man he sold half of all his horses and a half of a horse. To the second man he sold half of what he had left and a half of a horse. To the third man he again sold half of what was left and a half of a horse. How many horses did he have at first? (No horses were harmed!)
Answer:
7
Step-by-step explanation:
3RD MAN: 1
2ND MAN: 2
1ST MAN: 4
3rd Man = 1/2+1/2 = 1
2nd Man = 1+1 = 2
1st Man = 2*2 = 4
Polly had 5 times as many red balloons as many red balloons as blue ones. She had 18 all together. How many of her balloons were blue ones?
Answer: 3 were blue
Step-by-step explanation:
Blue + Red = 18....so.....
B + 5B = 18
6B = 18
B =18 / 6 = 3 blue
What is the name of the following net?
Answer:
[tex]\large\colorbox{gold}{sǫᴜᴀʀᴇ ᴘʏʀᴀᴍɪᴅ}[/tex]
Two cards are drawn without replacement from an ordinary deck, find the probability that the second is not a black card, given that the first is a black card. What is the conditional probability?
(a) [tex]\frac{26}{51}[/tex]
(b) [tex]\frac{26}{51}[/tex]
Step-by-step explanation:(i) Probability is the likelihood of whether or not an event will occur. It is given by the ratio of the number of favourable outcomes to the number of expected outcomes. i.e
P = number of favourable outcomes / total number of possible outcomes
For drawing a first card which is black,
number of favourable outcomes = 26 (since there are a total of 26 black cards in a deck of card)
total number of possible outcomes = 52 (since the total number of cards in a deck of card is 52)
∴ Probability of drawing the first black card = 26 / 52 = 1 / 13
Since the second card is not a black card, it is a red card.
number of favourable outcomes = 26 (since there are a total of 26 red cards in a deck of card)
total number of possible outcomes = 51 (since a black card has been previously picked from the deck)
∴ Probability of drawing a second black card = 26 / 51
The probability that the second is not a black card is 26 / 51
(ii) The conditional probability of a given event B is the probability that the event will occur knowing that a previous event A has already occurred,
It is given by;
P(B|A) = P(A and B) ÷ P(A)
In this case;
event B is drawing a second card which is not black
event A is drawing a first card which is black
This implies that;
P(A and B) = [tex]\frac{1}{13}[/tex] x [tex]\frac{26}{51}[/tex]
P(A) = [tex]\frac{1}{13}[/tex]
Substitute these values in the equation for conditional probability as follows;
P(B|A) = [tex]\frac{1}{13}[/tex] x [tex]\frac{26}{51}[/tex] ÷ [tex]\frac{1}{13}[/tex]
P(B|A) = [tex]\frac{1}{13}[/tex] x [tex]\frac{26}{51}[/tex] x [tex]\frac{13}{1}[/tex]
P(B|A) = [tex]\frac{26}{51}[/tex]
Therefore the conditional probability is [tex]\frac{26}{51}[/tex]
An airplane flying into a headwind travels the -mile flying distance between Indianapolis, Indiana, and Phoenix, Arizona, in hours. On the return flight, the airplane travels this distance in hours and minutes. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.
Answer:
the airspeed of the plane = 660 miles/hr
the speed of the wind = 60 miles/hr
Step-by-step explanation:
The values are missing in the given information in the question.
To able to solve this question, we will make some assumptions.
Let's assume that:
The airplane heading into the wind travels 1800 miles in 3 hours.
While returning via the same distance, it travels 2 hours 30 minutes.
We are to determine the plane's airspeed as well as the wind speed.
First, let us say that the speed of the plane is p and the wind speed is q
during the time the plane is traveling for 1800 miles in 3 hrs.
Then, we can say
3p -3q = 1800 ----- (1)
However, in 2hours 30 minutes, we have 2.5 hours
So, when the plane is returning, we have the following equation:
2.5p + 2.5q = 1800 ---- (2)
So, to find p and q, we can use the elimination method.
Simply by multiplying equation (1) with 5 and equation (2) with 6
(5)3p - (5)3q = (5) 1800
(6)2.5p + (6)2.5q = (6) 1800
15p - 15q = 9000
+
15p + 15q = 10800
30p - 0 = 19800
30p = 19800
p = 19800/30
p = 660
Since p = 660, then from equation (1) we can obtain the value of q:
So; Using equation (1):
3p -3q = 1800
3(660) - 3q = 1800
1980 - 3q = 1800
-3q = 1800 - 1980
-3q = -180
q = 180/3
q = 60
Therefore, the airspeed of the plane = 660 miles/hr
the speed of the wind = 60 miles/hr
what is the answer to this question. i made it 20 pts
Answer:
the second choice
3. Given the bar chart below,
(a) draw a frequency table from the graph.
(b) calculate the mean mark.
(c) what is the modal mark?
(d) find the median mark.
(e) if a student is selected at random, what is the probability that he/she scored
not less than 3 marks?
7
Frequent
п
0
-
0
3
5
N
6
6
Marks
Answer: shehshywhwyw
Step-by-step explanation:
Each (hypothetical) data set below represents some readings on span gas. Assume the Gauss model, with errors following the normal curve. However, bias may be present. In each case, make a t-test to see whether the instrument is properly calibrated or not. In one case, this is impossible. Which one, and why?
a. 71, 68, 79
b. 71, 68, 79, 84, 78, 85, 69
c. 71
d. 71, 84
Answer:
71 ( C ).
Step-by-step explanation:
The impossible case is the third case i.e.71
because there is only one reading on the span gas hence it is impossible to carry out a t-test on just one valid reading in an experiment.
Part B: Plot point C(2,7). If M is the midpoint of CD, what are the coordinates of D?
Answer:
[tex]D = (-4,-9)[/tex]
Step-by-step explanation:
Given
[tex]C =(2,7)[/tex]
[tex]M=(-1,-1)[/tex]
Required
The coordinates of D
Represent D with:
[tex]D = (x_2,y_2)[/tex]
Using midpoint formula, we have:
[tex]M(x,y) = \frac{1}{2}(x_1 + x_2, y_1 + y_2)[/tex]
So, we have:
[tex](-1,-1) = \frac{1}{2}(2 + x_2, 7 + y_2)[/tex]
Multiply both sides by 2
[tex](-2,-2) = (2 + x_2, 7 + y_2)[/tex]
Compare both sides
[tex]2 + x_2 = -2[/tex]
[tex]7 + y_2 =-2[/tex]
In [tex]2 + x_2 = -2[/tex], we have:
[tex]x_2 =-2-2[/tex]
[tex]x_2 =-4[/tex]
In [tex]7 + y_2 =-2[/tex], we have:
[tex]y_2 = -2 - 7[/tex]
[tex]y_2 = -9[/tex]
So, the coordinates of D is:
[tex]D = (x_2,y_2)[/tex]
[tex]D = (-4,-9)[/tex]
If the following picture below was rotated about the y-axis, what 3-D shape would it make? ( HELP PLEASEE )
Rotating the figure about the y-axis results in the creation of a cylindrical figure of radius 2 units and 6 units tall.
A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?
Answer:
The probability that the month starts with the letter J or the letter M is 41.66%.
Step-by-step explanation:
Given that a month of the year is chosen at random, to determine what is the probability that the month starts with the letter J or the letter M, the following calculation must be performed:
January - March - May - June - July = 5 months
(5/12) x 100 = X
0.4166 x 100 = X
41.66 = X
Therefore, the probability that the month starts with the letter J or the letter M is 41.66%.
Answer:
5/12
Step-by-step explanation:
Months that start with the letter M are March and May
Months that start with J are January, June, July
So, in total the months that start with J and M are 5 in number.
Total number of months = 12
Therefore the probability = 5/12 or 0.416 (bar on 6)
Hope u understood
Please mark as brainliest
Thank You
PLEASE HELP ME !!! Can anyone help me find the function for this trig graph ?? i need a specific answer for the function , 50 pts and i will mark brainliest !!
Answer:
y = 5 sin (2x) + 4
Step-by-step explanation:
this is sines function,
the amplitude is [9 - (-1)]/2 = 10/2 = 5
the period is 2πx/π = 2x
the x-axis of actual function is at y = 4
so, the function is :
y = 5 sin (2x) + 4
x^2log2x+secx differential equation plz solve the question and give ans
Answer:
only 5 points
Step-by-step explanation:
Why does 5(x+20) equal 15x? I'm so confused.
Answer:
Nobody knows its a mistery :'D
Answer:
Because lma/os
Step-by-step explanation:
5 ( x + 20 )
-----------------
1. Simplifly
2. Distribute
3. 5 ( x + 20 )
5 x + 100
Please HELPP with this question
9514 1404 393
Answer:
551.07 yd²
Step-by-step explanation:
For radius r and height h, the total surface area of the cylinder is given by ...
SA = 2πr(r +h)
Here, the radius is 4.5 yards (half the diameter) and the height is 15 yards. That makes the surface area ...
SA = 2(3.14)(4.5 yd)(4.5 +15 yd) = 551.07 yd²
-2x +9y=8
x=y+3
Step by step
Jerome purchased a 4-year old car for $12,000. He was told this make a model depreciates exponentially at a rate of 5.7% each year. What was the original price to the nearest hundred dollars?
Group of answer choices
$19,300
$15,200
$12,500
$17,500
Is this correct. Please let me know thank you
Answer:
Yes it is correct, the amount of flour is 1.5 times larger than eggs needed
Step-by-step explanation:
Find 35% of a number is 70 find the number
Answer:
200.
Step-by-step explanation:
35% = 0.35 so
0.35x = 70
x = 70 / 0.35
= 200.
Answer:
200
Step-by-step explanation:
Let the number = x
35% of x = 70
35/100 * x = 70 Multiply by 100
35x = 70 * 100
35x = 7000 Divide by 35
x = 7000/35
x = 200
Which of the following formulas does not represent finding The height of a rectangular prism with a volume of 200 in.³, a length of 4 inches, and a with of 5 inches?
Write the Plural! Spanish, help!!
At a factory, light bulbs are packed in boxes that are then placed in a shipping container.
• Each box is in the shape of a cube.
• Each box has an edge length of foot.
• A shipping container has dimensions of feet by 1 foot by 2 feet.
What is the total number of boxes of light bulbs that the shipping container can hold when completely full?
Answer: 144
Step-by-step explanation: You need to find the volume of the shipping container and divide it by the volume of a box.
2 2/3 x 1 x 2 = 16/3
1/3 x 1/3 x 1/3 = 1/27
16/3 divided by 1/27 is 144.
Find the volume of the pyramid. Round to the nearest tenth if necessary.
13 +22
if r = -3 and s = 4
35 is the answer
have a wonderful day
En 9 días, un grupo de trabajadores puede sembrar 72 hectáreas.
¿Cuál es su tasa en hectáreas por día?
Answer:
8 hectáreas por día
Step-by-step explanation:
72 hectares en 9 días por eso divides 72 por 9 para encontrar la repusta es 8
¡Espero que esta te ayudar! :)
(y sí, hablo un poco de español porque he aprendido desde el primer grado)
The kinetics of some phase transformations obey the Avrami relationship. Using the fraction transformed-time data given below, determine the total time required for the transformation to go to 92% completion. Fraction transformed Time (s) 0.2 12.6 0.7 25.7 Enter your answer in accordance to the question statement s
Solution :
Avrami relationship
[tex]$1-y=exp(-kt^n)$[/tex]
[tex]$\ln(1-y)=-kt^n$[/tex]
[tex]$-\ln(1-y)=kt^n$[/tex]
[tex]$\ln\left[\ln\left(\frac{1}{1-y}\right)\right]=\ln k + n \ln t$[/tex]
The fraction transformed is 0.2 at 12.6 s,
[tex]$\ln\left[\ln\left(\frac{1}{1-0.2}\right)\right]=\ln k + n \ln (12.6)$[/tex]
[tex]$-1.5 = \ln k + 2.533 n$[/tex] .........(i)
The fraction transformed is 0.7 at 25.7 s,
[tex]$\ln\left[\ln\left(\frac{1}{1-0.7}\right)\right]=\ln k + n \ln (25.7)$[/tex]
[tex]$0.5 = \ln k + 3.24 n$[/tex] ..............(ii)
Subtract (ii) from (i),
-2 = -0.71 n
n = 2.81
Therefore, from (i),
[tex]$-1.5 = \ln k + 2.533 (2.81)$[/tex]
k = 0.000181
Now if the fraction transformed is 0.92, then
[tex]$kt^n=-\ln (1-y)$[/tex]
[tex]$t=\left[\frac{-\ln (1-y)}{k}\right]^{\frac{1}{n}}$[/tex]
[tex]$t=\left[\frac{-\ln (1-0.92)}{0.000181}\right]^{\frac{1}{2.81}}$[/tex]
t = 29.8528 s