Answer:
Step-by-step explanation:
Given functions are,
f(x) = x³ + 4x²
g(x) = 5x² - 1
(a). (f + g)(x) = f(x) + g(x)
= x³ + 4x² + 5x² - 1
= x³ + 9x² - 1
Since the composite function is defined for all values of x, domain of the function will be (-∞, ∞)
(b). (f - g)(x) = x³ + 4x² - (5x² - 1)
= x³ - x² + 1
Domain of the function : (-∞, ∞)
(c). (f.g)(x) = f(x) × g(x)
= (x³ + 4x²)(5x² - 1)
= 5x⁵+ 20x⁴ - x³ - 4x²
Domain of the function will be (-∞, ∞).
(d). [tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
= [tex]\frac{x^3+4x^2}{5x^2-1}[/tex]
Since this function is not defined at [5x² - 1 = 0] Or x = ±[tex]\frac{1}{\sqrt{5}}[/tex]
Therefore, Domain of the composite function will be,
(-∞, -[tex]\frac{1}{\sqrt{5}}[/tex]) ∪ [tex](-\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}})[/tex] ∪ ([tex]\frac{1}{\sqrt{5}}[/tex], ∞)
Is (1,9) a solution to this system of
equations?
y = x + 6
y = 2x + 7?
Answer:
No, the solution of the system is (-1,5)
Solve for y.
2y - x = 3/4 (-y +1 )
Answer:
kyskyskyskyskyskyskys
. Every month, there are 1000 independent TIE fighter flights, and each TIE fighter flight crashes with a probability of 0.0035. (a) What is the probability that at least 2 crashes occur in the next month
Answer:
[tex]\mathbf{P (X \geq 2) = 1 - P( X \leq 1) \sum \limits ^1_{x=0} ( ^{1000}_x) (0.0035)^x (0.9965)^{1000-x}}[/tex]
Step-by-step explanation:
From the information given:
The probability that at least 2 crashes occurs in the next month can be estimated by using Poisson distribution because the sample size is large and the probability of the event p = 0.0035 is rare.
∴
Let X be the random variable that follows a Poisson distribution
The probability that at least 2 crashes occurs in the next month is:
[tex]\mathbf{P (X \geq 2) = 1 - P( X \leq 1) \sum \limits ^1_{x=0} ( ^{1000}_x) (0.0035)^x (0.9965)^{1000-x}}[/tex]
Write the slope-intercept form of the equation of the line through the given point with the given slope. through: (3,1). slope= 4/3
Answer:
y = 4/3x - 3
Step-by-step explanation:
Use the slope intercept equation, y = mx + b, where m is the slope and b is the y intercept:
Plug in the point given and the slope to find b:
y = mx + b
1 = 4/3(3) + b
1 = 4 + b
-3 = b
Then, plug this and the slope into the equation:
y = 4/3x - 3 will be the equation
The Tigers had twice as many hits as the yanks.Let x= number of hits by yanks.Then ?= number of hits by tigers
Answer:
2x
Step-by-step explanation:
Since the tigers hit 2 times the number of x you would get that the tigers hit 2 times x or 2x balls
Answer:
2x.
hope it helps u...
plz mark as brainliest...
Complete the table shown below. f(x) = 2x2 - 8x + 6 1 0 2 y 3 4. 6 X= y = Z
Answer:
x = 6, y = -2, z = 0
Step-by-step explanation:
To find x, we have to plug 0 into f(x). Therefore, x = f(0) = 2 * 0² - 8 * 0 + 6 = 6. Similarly, to find y, we have to plug 2 into f(x) so y = f(2) = 2 * 2² - 8 * 2 + 6 = -2. Finally, z = f(3) = 2 * 3² - 8 * 3 + 6 = 0.
Answer:
6, -2, 0
Step-by-step explanation:
A boat sails on a bearing of 038°anf then 5km on a bearing of 067°.
a.how far is the boat from it's starting point
b.calculate the bearing of the boat from it's starting point
This question is not complete
Complete Question
A boat sails 4km on a bearing of 038 degree and then 5km on a bearing of 067 degree.(a)how far is the boat from its starting point.(b) calculate the bearing of the boat from its starting point
Answer:
a)8.717km
b) 54.146°
Step-by-step explanation:
(a)how far is the boat from its starting point.
We solve this question using resultant vectors
= (Rcos θ, Rsinθ + Rcos θ, Rsinθ)
Where
Rcos θ = x
Rsinθ = y
= (4cos38,4sin38) + (5cos67,5sin67)
= (3.152, 2.4626) + (1.9536, 4.6025)
= (5.1056, 7.065)
x = 5.1056
y = 7.065
Distance = √x² + y²
= √(5.1056²+ 7.065²)
= √75.98137636
= √8.7167296826
Approximately = 8.717 km
Therefore, the boat is 8.717km its starting point.
(b)calculate the bearing of the boat from its starting point.
The bearing of the boat is calculated using
tan θ = y/x
tan θ = 7.065/5.1056
θ = arc tan (7.065/5.1056)
= 54.145828196°
θ ≈ 54.146°
What is the standard form equation of the line shown below?
5
4
3
2 +
o
+ +
3 4
2
5
-5 -4 -3 -2 -1
-1
-2
-3
-4
-6
Margaret is going to paint a wall that 'is 8 feet high and 15 feet long. How many square feet will she be covering with paint?
Answer:
120 ft²
Step-by-step explanation:
the question is asking for the area of the wall, which we have been given.
8 ft high by 15 ft wide.
Area of a rectangle is length multiplied by breadth.
so, the area is 8 * 15 = 120 ft²
Samantha conjectures that for x < - 1 it is true that x ^ 5 - 2 > x her conjecture correct? Why or why not?
Answer:
Her conjecture is not correct
Step-by-step explanation:
Given
[tex]x^5 - 2 > x[/tex]
For [tex]x < -1[/tex]
Required
Determine if the conjecture is true
[tex]x < -1[/tex] implies that the values of x are:
-2, -3, -4, -5.....
Take any value of x and substitute in [tex]x^5 - 2 > x[/tex]
Let x = -3
[tex]x^5 - 2 > x[/tex] becomes
[tex]-3^5 - 2 > -3[/tex]
[tex]-243 - 2 > -3[/tex]
[tex]-245 > -3[/tex]
The above inequality is false;
Hence:
Her conjecture is not correct
Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
No singular point due to the exponent in the solution
The interval is [tex]-\infty <0 < \infty[/tex]
b
NONE
Step-by-step explanation:
From the question we are told that
[tex]\frac{dy}{dx} = 9y[/tex]
The generally solution is mathematically represented as
[tex]\frac{dy }{dx} = 9y[/tex]
=> [tex]\frac{dy}{y} = 9dx[/tex]
integrating both sides
[tex]\int\limits {\frac{ dy}{y} } \, = \int\limits {9} \, dx[/tex]
=> [tex]lny = 9x + c[/tex]
=> [tex]y = e^{9x +c }[/tex]
=> [tex]y = e^{9x} e^{c}[/tex]
Here [tex]e^c = C[/tex]
=> [tex]y = C e^{9x}[/tex]
From the above equation we see that the domain for x has no singular point the interval is
[tex]-\infty <0 < \infty[/tex]
Also there is no transient term in the general solution obtained because as [tex]x \to \infty[/tex] there no case where [tex]y \to 0[/tex]
Consider the following time series: t12345 6 11 9 14 15 a. Construct a time series plot. What type of pattern exists in the data
Answer:
Kindly check explanation and attached picture
Step-by-step explanation:
Given the time-series data:
Time (x) : 1 - - 2 - - 3 - - - 4 - - - 5
Data (yt) :6 - - 11 - - 9 - - 14 - - 15
The pattern which exists within the data is a linear pattern which could be inferred through the observable decrement and Incremental change in the y values at a steady or constant rate with time. The second attachment shows the linear trend line of the data.
Brainliests offered whoever answer my question.
1: find the value of 8 4s. It’s not 84 but it’s 8 and then at the top it’s 4.
2: a mug is 1/7 full. The mug contains 1/3 of a cup of water. Find the capacity of the mug. Write the answer a fraction or mixed number in simplest form.
Problem 1
If you meant to say [tex]8^4[/tex], then you would have four copies of 8 multiplied together
[tex]8^4 = 8*8*8*8 = 4096[/tex]
==============================================
Problem 2
1/7 full = 1/3 cup of water
7*(1/7 full) = 7*(1/3 cup of water) ... multiply both sides by 7
1 full = 7/3 cup of water
So a full mug has 7/3 cups of water. Let's convert this to a mixed number
7/3 = (6+1)/3
7/3 = 6/3 + 1/3
7/3 = 2 + (1/3)
7/3 = 2 & 1/3
The full capacity of the cup is 7/3 cups or 2 & 1/3 cups
7/3 is the improper fraction form
2 & 1/3 is the mixed number form
One way to think of it is to imagine there are 7 cookies and you want to distribute among 3 friends. We could say 7/3 = 2 remainder 1 meaning each person gets 2 full cookies and there's 1 left over. So that's how we'd get 2 & 1/3.
In a survey of 1,003 adults concerning complaints about restaurants, 732 complained about dirty or ill-equipped bathrooms and 381 complained about loud or distracting diners at other tables.
a. Construct a 95% confidence interval estimate for the population proportion of adults who complained about dirty or ill-equipped bathrooms )
b. Construct a 95% confidence interval estimate for the population proportion of adults who complained about loud or distracting diners at other tables.
c. How would the manager of a chain of restaurants use the results of (a) and (b)?
Answer:
a
[tex]0.716 < p < 0.744[/tex]
b
[tex]0.3498 < p < 0.4089[/tex]
c
With the result obtained from a and b the manager can be 95 % confidence that the proportion of the population that complained about dirty or ill-equipped bathrooms are within the interval obtained at a
and that
the proportion of the population that complained about loud or distracting diners at other tables are within the interval obtained at b
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 1003[/tex]
The number that complained about dirty or ill-equipped bathrooms is [tex]e = 732[/tex]
The number that complained about loud or distracting diners at other tables is [tex]q = 381[/tex]
Given that the the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100- 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Considering question a
The sample proportion is mathematically represented as
[tex]\r p = \frac{e}{n}[/tex]
=> [tex]\r p = \frac{732}{1003}[/tex]
=> [tex]\r p = 0.73[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]
[tex]E = 1.96* \sqrt{ \frac{ 0.73 (1- 0.73)}{1003} }[/tex]
[tex]E = 0.01402[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p +E[/tex]
[tex]0.73 - 0.01402 < p < 0.73 + 0.01402[/tex]
[tex]0.716 < p < 0.744[/tex]
Considering question b
The sample proportion is mathematically represented as
[tex]\r p = \frac{q}{n}[/tex]
=> [tex]\r p = \frac{381}{1003}[/tex]
=> [tex]\r p = 0.3799[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]
[tex]E = 1.96* \sqrt{ \frac{ 0.3799 (1- 0.3799)}{1003} }[/tex]
[tex]E = 0.0300[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p +E[/tex]
[tex]0.3798 - 0.0300 < p < 0.3798 + 0.0300[/tex]
[tex]0.3498 < p < 0.4089[/tex]
Merlyn had 22 magic tricks to perform. He had completed 4/5 of them when the fire alarm sounded. How many magic tricks had he performed?
Answer:
Merlyn realizo 17,6 trucos de magia
Step-by-step explanatio:
Hizo 17,6 trucos de magia porque 22 dividido 5 es igual a 4,4 entonces despues haces 22 menos 4,4 da 17,6
2. Metcalf School has two third-grade rooms (A and B) and two fourth-grade rooms
(C and D). Together, rooms C and D have 46 students. Room A has 6 more students
than room D. Room B has 2 fewer students than room C. Room D has 22 students.
How many students are there altogether in rooms A and B?
Answer: 50 students
Step-by-step explanation: Room D has 22 students, so room A has 28 (22+6). If room D has 22 students, then room C has 24 students (46-22). Room B has 22 students (26-2). In total, rooms A and B will have 50 students (28+22)
Is there a smallest decimal that is greater than the number 2? Explain your answer.
Answer:
Technically, yes. It's called epsilon, which is defined as an infinitely small number. So
2 + epsilon is the smallest number greater than 2. But for practical purposes no there isn't.
00
Step-by-step explanation:Not without limits. You can always move the .1 one place further from the interring. For example,
2.1>2.01
and
2.01>2.001
So, unless there are a limited number of decimal spaces, you can continually add an infinite amount of zeros behind the decimal point, followed by a one.
If you use two or three decimal spaces as a standard in your class, then the smallest decimal greater than 2 would be 2.01 or 2.001, respectively.
4.) In a cage are a total of 40 cats and dogs, each one being black or white . Eleven
of these animals are white, and 12 of the dogs are black. If there are 19 cats, how
many cats are white?
40-19＝21
21－12＝9
11-9＝2
2 white cats
Please help me with the question below
If the numbers are consecutive multiples of 6, and you want to call the smallest one ' n ', then the next one is (n+6) and the biggest one is (n+12).
Their sum is (3n + 18). That's choice-C .
If you run into the same problem again, you might like to call the middle number ' n '. Then the smallest one is (n-6) and the biggest one is (n+6),
and their sum is just 3n ! This is a lot easier to do in your head.
If you get this you are a critical thinker.
I enter the garden.
There are 34 people.
You kill 30.
How many people are in the garden.
Good luck!
If you get it correct your answer will be deleted and l will message you to continue the game.
Don't play if you are not going to continue party poopers!
I won against Lisa Swensrud
Answer:
5
Step-by-step explanation:
Because when you walk in there is now 35 people 35 - 30 = 5
There are 34 people in the garden.
In order to answer the question, you've to think critically, it should be noted that even if 30 people are killed, they are still in the garden.Also, the fact that you entered the garden still makes the total number 34. Therefore, in this situation, the total number of people in the garden is 34.Read related ink on:
https://brainly.com/question/17377020
Solve a combined inequality that is a conjunction of two linear equalities.
1.) solve for n. -1<9+n<17
2.) solve for x. -2<8x-12<_36
Answer:
-10 < n < 85/4 < x ≤ 6Step-by-step explanation:
1. Subtract 9:
-10 < n < 8
__
2. Add 12, then divide by 8:
10 < 8x ≤ 48
10/8 < x ≤ 6
5/4 < x ≤ 6 . . . . . with the fraction reduced
_____
The rules of equality allow us the do these operations, provided that we do them to all parts of the compound inequality. That is, when we say "subtract 9", we mean ...
-1 -9 < 9 +n -9 < 17 -9
This simplifies to the inequality we show above:
-10 < n < 8
Which is bigger 2.0 or 2
Answer:
both are the same
Step-by-step explanation:
2.0 = 2
hope this helps ^-^
Answer:
Both will be equal as 2.0 can also be written as 2
The average cost of a scientific calculator was $96.50 in 1970. The same type of calculator cost $21 in 2016. Assuming the exponential decay model applies, what will a similar calculator cost in the year 2019? Round your answer tbo the nearest cent.
Answer: the cost of a similar scientific calculate in 2019 will be $19.01
Step-by-step explanation:
Given that;
in 1970 cost of S.C = $96.50
in 2016 cost of same calculator = $21
In 2019 cost of a similar calculator = ?
Assuming the exponential decay model applies
dN/dt = -λN
we know that λ is the decay constant
⇒ N(t) = N₀e^-λt
N(t) is price at time t year, N₀ is initial price,
so t = 0 in 1970 thus N₀ = 96.50
also t = 46 in 2016 thus N₄₆ = 21
substituting into our initial expression
N(t) = N₀e^-λt
N(46) = N₀e^-λ×46
21 = 96.50e^-46λ ⇒ In 21/96.50 = -46λ
= -1.5250 = - 46λ
λ = -1.5250 / -46
λ = 0.03315
t = 0 in 1970 thus N₀ = 96.50
also t = 49 in 2019 thus N₄₉ = ?
so
using our initial expression again
N(49) = N₀ e^-49λ
= 96.5 × e^ (-49 × 0.03315 )
= 96.5 × 0.197014404
= 19.01189 ≈ 19.01
therefore the cost of a similar scientific calculate in 2019 will be $19.01
If y = 3. what is 6y?
Your question has been heard loud and clear.
If y = 3 , then 6y = 6(3) = 18
Thank you
How to find out if a number is transcendental?
Answer:
A transcendental number is a real number that is not the solution of any single-variable polynomial equation whose coefficients are all integers . All transcendental numbers are irrational numbers . But the converse is not true; there are some irrational numbers that are not transcendental.
Step-by-step explanation:
Total Price: The sales tax rate is 8%. If the sales tax on a 10-speed bicycle is $12, what is the purchase price? The purchase price is $ What is the total price? The total price is $ Get Help: Video eBook Points possible: 1
Answer:
Purchase Price = $150 and Total Price = $162
Step-by-step explanation:
Purchase price = Tax Amount / Tax Percentage (as decimal)
Purchase Price = $12 / .08
Purchase Price = $150
Total Price = Purchase Price + Tax
Total Price = 150 + 12 = $162
I hope this helps!
-The Business Man
why is 5.1 a rational number
Answer:
5.1 can be written as 51/10 (the quotient of the integers 51 and 10. So it is a rational number
Step-by-step explanation:
Recall that a rational number is a number that can be written as the quotient of two integer numbers.
In particular the number 5.1 can be written as 51/10 (the quotient of the integers 51 and 10. So it is a rational number.
You want to estimate the mean amount of time college students spend on the Internet each month. How many college students must you survey to be 95% confident that your sample mean
Answer:
752.95
Step-by-step explanation:
Data provided in the question
The standard deviation of population = 210
The Margin of error = 15
The confidence level is 75%, so the z value is 1.96
Now the required sample size is
[tex]= 1.96^2\times \frac{210^2}{15^2}[/tex]
= 752.95
Hence, the number of college students spends on the internet each month is 752.95
Simply we considered the above values so that the n could come
What is the equation of the line that passes through the points (- 2, 3) and (4, 1)
Answer:
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = ((- 2, 3) and (x₂, y₂ ) = (4, 1)
m = [tex]\frac{1-3}{4+2}[/tex] = [tex]\frac{-2}{6}[/tex] = - [tex]\frac{1}{3}[/tex] , thus
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 2, 3), then
3 = [tex]\frac{2}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{7}{3}[/tex] ← equation of line
A right angle intersects a line at point M
Answer:
where is the graph
Step-by-step explanation:
Answer:
Step-by-step explanation:
Here is the picture