Given:
The expression is [tex]\sqrt{4-6a}[/tex].
To find:
The domain of the expression.
Solution:
We have,
[tex]\sqrt{4-6a}[/tex]
We know that, the square root is defined for only non-negative values. So,
[tex]4-6a\geq 0[/tex]
[tex]4\geq 6a[/tex]
Divide both sides by 6.
[tex]\dfrac{4}{6}\geq a[/tex]
[tex]\dfrac{2}{3}\geq a[/tex]
Thus, the value of variable less than [tex]\dfrac{2}{3}[/tex] make any sense.
Therefore, the domain of the given expression is [tex](-\infty,\dfrac{2}{3}][/tex].
The domain of a function is the set of input values the function can take
The domain of the expression is: [tex]\mathbf{(-\infty, \frac 23]}[/tex]
The expression is given as:
[tex]\mathbf{\sqrt{4 - 6a}}[/tex]
Set the radicand to 0
[tex]\mathbf{4 - 6a = 0}[/tex]
Add 6a to both sides
[tex]\mathbf{6a = 4}[/tex]
Divide both sides by 6
[tex]\mathbf{a = \frac 23}[/tex]
This means that, the value of a must not be greater than 2/3.
Hence, the domain of the expression is: [tex]\mathbf{(-\infty, \frac 23]}[/tex]
Read more about domain at:
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Please someone help me with this
(You have to add both answers)
The diameter of circle is 4cm. Determine the are of the circle.
Answer: Area of circle = 12.57cm² (I am assuming you mean area here)
Step-by-step explanation:
Area = πr²
radius = diameter ÷ 2
r = 4 ÷ 2
r = 2
π = 3.14159265359
shorten π to 3.14 for future reference. I just used the π button a a calculator for this answer though.
A = π × 2
A = 12.57
Ms. Garcia is an electrician and has a length of wire that is 32.7 meters long. She has another length of wire that is 15.33 meters long. How much longer is the one wire than the other? Solve this problem any way you choose.
Answer:
Ans =17.37
32.7 -15.33=17.37
Marcus hiked 4 3/2 miles. John hiked 3 1/3 miles. How much further did Marcus hike?
Answer:
2.16666666667
plz give me brainliest
What is the product of (–0.9)(–2.4)?
–3.3
–2.16
2.16
3.3
Answer:
-2.16
Step-by-step explanation: for all you edge people
John has 6 pancils, 3 blue pens, 5 black pens, and 2 red pens in a cup on his desk Without looking, John pulls a writing utensil out of the cup. Enter the probability that John pulls out a pencil.
Answer:
john has a 6 out of 10 chance of picking a pencil
Answer:
P=37.5%
Step-by-step explanation:
Frequentist Probability
The probability of an outcome is defined as the frequency of the number of times the outcome occurs relative to the number of times that it could have occurred.
The equation to calculate the probability is:
[tex]\displaystyle P=\frac{f}{n}[/tex]
Where f is the number of favorable cases and n is the total cases.
John has in a cup of his desk:
6 pencils
3 blue+5 black+2 red pens=10 pens
Picking one of the utensils from the cup can be done in 16 different ways. That is the total number of cases n=16
The outcome of taking a pencil can be done in 6 ways. That is the number of favorable cases. f=6.
The probability is:
[tex]\displaystyle P=\frac{6}{16}[/tex]
Simplifying:
[tex]\displaystyle P=\frac{3}{8}[/tex]
Or expressed as a percentage:
P=3/8*100%
P=37.5%
According to an airline, flights on a certain route are on time % of the time. Suppose flights are randomly selected and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Find and interpret the probability that exactly flights are on time. (c) Find and interpret the probability that fewer than flights are on time. (d) Find and interpret the probability that at least flights are on time. (e) Find and interpret the probability that between and flights, inclusive, are on time.
Answer:
(a) Explained below.
(b) 0.0294
(c) 0.0173
(d) 0.09827
(e) 0.0452
Step-by-step explanation:
The complete question is:
According to an airline, flights on a certain route are on time 80% of the time. Suppose 25 flights are randomly selected and the number of on-time flights is recorded.
(a) Explain why this is a binomial experiment.
(b) Find and interpret the probability that exactly 16 flights are on time.
(c) Find and interpret the probability that fewer than 16 flights are on time.
(d) Find and interpret the probability that at least 16 flights are on time.
(e) Find and interpret the probability that between 14 and 16 flights, inclusive, are on time.
Solution:
(a)
Let the random variable X be defined as the number of on-time flights.
A Binomial experiment has the following properties:
There are a fixed number of trials (n). Each trial are independent of the others. Each trial has only two outcomes: Success and Failure Each trial has the same probability of success (p).If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.
All of these properties can be confirmed for the random variable X.
Thus, this is a binomial experiment.
(b)
Compute the probability that exactly 16 flights are on time as follows:
[tex]P(X=16)={25\choose 16}(0.80)^{16}(0.20)^{25-16}[/tex]
[tex]=2042975\times 0.0281475\times 0.000000512\\=0.029442375072\\\approx 0.0294[/tex]
Thus, the probability that exactly 16 flights are on time is 0.0294.
(c)
Compute the probability that fewer than 16 flights are on time as follows:
[tex]P(X<16)=\sum\limits^{15}_{x=0}{{25\choose x}(0.80)^{x}(0.20)^{25-x}}[/tex]
[tex]=0.0000+0.0000+....+0.011777\\=0.0173[/tex]
Thus, the probability that fewer than 16 flights are on time is 0.0173.
(d)
Compute the probability that at least 16 flights are on time as follows:
[tex]P(X\geq 16)=1-P(X<16)[/tex]
[tex]=1-0.0173\\=0.9827[/tex]
(e)
Compute the probability that between 14 and 16 flights, inclusive, are on time as follows:
[tex]P(14\leq X\leq 16)=\sum\limits^{16}_{x=14}{{25\choose x}(0.80)^{x}(0.20)^{25-x}}[/tex]
[tex]=0.004+0.0118+0.0294\\=0.0452[/tex]
Thus, the probability that between 14 and 16 flights, inclusive, are on time is 0.0452.
*
1. What is the measure of angle A?
A long year-end status report for work is 162 pages long. You need to print 16 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.84 each
Answer:
23.04
Step-by-step explanation:
A car can travel 38 miles on each gallon of gasoline. At that rate, how many gallons of gasoline will it take to travel 190 miles?
Answer:
5
Step-by-step explanation:
Answer:
5 Gallons of gasoline
Step-by-step explanation:
This is true because 190÷38 is five. If you want to check the work 38×5 is 190.
I also got it right on edg. 2020
What percent of the employees earn more than $400 per week?
Answer: 26%
Step-by-step explanation:
Only 13 out of the 50 make more than 400$ a week. So it’s 13/50=26%
Answer:
26%
Step-by-step explanation:
find the total
19+18+8+5=50
find the ppl who earn >400
last 2 columns
8+5=13
find the percent
13/50=26/100
=26%
what's the answer? please help
Answer:
the slope is -7/3
Step-by-step explanation:
8-15/10-7
-7/3
how many days are in 2 years + 18 months?
please help!!!!
Answer:
1277
Step-by-step explanation:
Answer:
1278.04
Step-by-step explanation:
Why? In 1 year there are approximately 365.24 days, but in 1 month there are approx 30.42 days.
So 365.24 × 2 = 730.48
And 30.42 × 18 = 547.56 (+
-----------------------
1278.04
Divide.
4 1/5 divided by 2/3
Express your answer as a mixed number in simplest form.
Enter your answer in the box.
Answer:
63/10 or 6 3/10
Step-by-step explanation:
Cual es El opuesto de 0?
Answer: no hay opuesto de cero, cero es el último número de positivos y negativos
Turn 4.131313 into a mixed fraction
Answer:
1313
4 -------
10000
Step-by-step explanation:
just imagine if they were a fraction
stwyrthegfcvidfghhuw cgy5wd
A clothing company wants to ship more items per box. The length, width and height of the new boxes are all twice as long as those of the old
boxes
How does the volume of a new box compare to the volume of an old box?
O A The volume of the new box ls 2 times the volume of the old box.
OB The volume of the new box is 4 times the volume of the old box.
O c The volume of the new box is 6 times the volume of the old box
OD. The volume of the new box is 8 times the volume of the old box.
Answer:
I believe the answer is A
Step-by-step explanation:
I say it's A because the volume is double like it told us. Compared to the new box it's twice as long as the old boxes.
I hope this helps! ~~~~
The volume of the new box is 8 times the volume of the old box.
The correct answer is option (D).
Volume of rectangular box:The volume of a rectangular box with length L, width W and height H is,
V = L × W × H
Given: -
Let [tex]l,w,h[/tex] represents the length, width and height of the old rectangular boxes.
Let [tex]V_o[/tex] represents the volume of the old rectangular box.
⇒ [tex]V_o=l\times w \times h[/tex]
The length, width and height of the new boxes are all twice as long as those of the old boxes.
This means the length, width and height of the new boxes would be [tex]2l,2w,2h[/tex].
Let [tex]V_n[/tex] represents the volume of the new rectangular box.
So, the volume of the new rectangular box would be,
⇒ [tex]V_n=2l \times 2w \times 2h[/tex]
⇒ [tex]V_n = 8 \times l \times w \times h[/tex]
⇒ [tex]V_n=8 \times V_o[/tex]
This means, the volume of the new box is 8 times the volume of the old box.
Hence, option (D) is the correct answer.
Learn more about rectangular prism here:
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what is the slope of the table shown I NEED THIS QUICK
Answer:
5
Step-by-step explanation:
Slope is defined as rise over run, so it is (26-11)/(5-2) = 15/3 = 5
Answer:
slope is 5
Step-by-step explanation:
slope formula says m= y2-y1/x2-x1
m=26-11/5-2
m=15/3
m=5
The length of a rectangle is 11 feet more than the width. If the perimeter is 46 feet, then what is the length of the rectangle, in feet?
Answer:
Hi there!
Your answer is:
The length is 17
Step-by-step explanation:
L= 11+w
P=46
perimeter formula:
W+W+L+L = P
W+W+(11+w)+(11+w) = P
First solve for W
4W+22 = 46
-22
4w=24
/4
w=6
Now plug in W for the L formula
l=11+w
L= 11+ 6
L=17
The Enormous State University History Department offers three courses—Ancient, Medieval, and Modern History—and the chairperson is trying to decide how many sections of each to offer this semester. The department is allowed to offer 45 sections total, there are 4,700 students who would like to take a course, and there are 58 professors to teach them. Sections of Ancient History have 100 students each, sections of Medieval History hold 50 students each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of two professors, while Ancient and Medieval History need only one professor per section. How many sections of each course should the chair schedule in order to offer all the sections that they are allowed, accommodate all of the students, and give one teaching assignment to each professor?
Answer:
The number of sections in Ancient history is 10, number of students in Medieval history is 22 and the number of students in Modern history is 13.
Step-by-step explanation:
[tex]x[/tex] = Number of sections in Ancient history
[tex]y[/tex] = Number of sections in Medieval history
[tex]z[/tex] = Number of sections in Modern history
The number of sections that are allowed is 45 so
[tex]x+y+z=45[/tex]
The number of students in each section is 4700 where 100 of them take ancient history 50 of them take medieval history and 200 take modern history so
[tex]100x+50y+200z=4700[/tex]
The number of professors is 58 where Ancient and Medieval History need only 1 professor per section and Modern History sections are taught by a team of 2 professors, so
[tex]x+y+2z=58[/tex]
Solving the first and last equations by subtracting them we get
[tex]-z=-13\\\Rightarrow z=13[/tex]
Substituting this value in the second equation and first equation we get
[tex]100x+50y+2600=4700\\\Rightarrow 100x+50y=2100\\\Rightarrow 2x+y=42[/tex]
[tex]x+y+13=45\\\Rightarrow x+y=32[/tex]
Solving these equations by subtracting them we get
[tex]x=10[/tex]
[tex]x+y=32\\\Rightarrow y=32-10=22[/tex]
So, [tex]x=10, y=22, z=13[/tex]
Hence, the number of sections in Ancient history is 10, number of students in Medieval history is 22 and the number of students in Modern history is 13.
A box contains 180 wooden cubes. You open the top of the box and count 9 cubes across the front and 4 cubes along a side. How many layers of wooden cubes are in the box?
Answer:
5
Step-by-step explanation:
9 x 4 = 36
180/36 = 5
Hey
What’s 8=D mean? I see it all the time but can’t figure it out! Help! My peers laugh at me. Is it simple math?
Answer:
it's a dirty joke, like when you type things into a calculator and turn it upside down to make it look like a word. It's not an equation
Step-by-step explanation:
Answer:
its a depiction using symbols from a calculator about mens sexual organs its really dirty and you shouldn't use it especially if you are too inoccent to know what it is
Please help
A population’s instantaneous growth rate is the rate at which it grows for every instant in time. Function r gives the instantaneous growth rate of a fruit fly population x days after the start of an experiment.
Given:
The function is
[tex]r(x)=0.05(x^2+1)(x-6)[/tex]
where, function r gives the instantaneous growth rate of a fruit fly population x days after the start of an experiment.
To find:
Number of complex and real zeros.
Time intervals for which the population increased and population deceased.
Solution:
We have,
[tex]r(x)=0.05(x^2+1)(x-6)[/tex]
[tex]r(x)=0.05(x^3+x-6x^2-6)[/tex]
Here, degree of function x is 3. It means, the given function has 3 zeros.
From the given graph it is clear that, the graph of function r(x) intersect x-axis at once.
So, the given function r(x) has only one real root and other two real roots are complex.
Therefore, function r has 2 complex zeros and one real zero.
Before x=6, the graph of r(x) is below the x-axis and after that the graph of r(x) is above the x-axis.
Negative values of r(x) represents the decrease in population and positive value of r(x) represents the increase in population.
Therefore, based on instantaneous growth rate, the population decreased between 0 and 6 hours and the population increased after 6 hours.
Answer:
Function r has two complex zeros and one real zero. Based on the instantaneous growth rate, the population decreased between 0 and 6 hours and the population increased after 6 hours.
Step-by-step explanation: I got it right
Find the lcm of 2,3,7 and tell me how u got ur answer
if its CORRECT with ur reasoning ill give brainlest
Answer:
42
Step-by-step explanation:
I have 3 times as many nickels as quarters. How many quarters do I have if I have
a total of $2.40
Answer:
18 Nickels, 6 Quarters
Step-by-step explanation:
For this problem, let's build a system of equations to find the number of nickels and dimes you have. Let N represent the number of nickels and Q represent the number of quarters you have.
The first equation, you have 3 times as many nickels as quarters:
N = 3Q
The second equation, you have a total of $2.40. Given we know nickels are $0.05 and quarters are $0.25:
0.05N + 0.25Q = 2.40
Now, let's use the two equations to find the number nickels and quarters you have.
N = 3Q
0.05N + 0.25Q = 2.40
0.05(3Q) + 0.25Q = 2.40
0.15Q + 0.25Q = 2.40
0.4Q = 2.40
Q = 6
Now, let's plug the value back into the equation:
N = 3Q
N = 3(6)
N = 18
And we can verify these values with the second equation:
0.05N + 0.25Q = 2.40
0.05(18) + 0.25(6) ?= 2.40
0.90 + 1.50 ?= 2.40
2.40 == 2.40
Therefore, we have found and verified the amount of Nickels and Quarters you have.
Cheers.
round 75. 9913 to the nearest tenth, hundredth, thousandth
what is the square root of 49
Answer:
2
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Write the number in exponential form with the base of 7
[tex]\sqrt{7^{2} }[/tex]
Reduce the index of the radical and exponent with 2
7
Solution
7
What is the greatest common divisor of 6, 9, and 12? *
f(n)=3+4)2 find the 4 terms of the sequence
Answer:25 + 24 + 49 :)
Step-by-step explanation:
Hope this helped :)
Write the following repeating decimal using a bar over the repeated digit(s).
0.355555555...
Answer:
just write 0.35 and write a line like this "---" above the five since it's the number repeating.
Step-by-step explanation:
