The integrand is odd.
[tex]f(x) = \dfrac{x^3 + 4x}{x^4 + 5} \implies f(-x) = \dfrac{(-x)^3 + 4(-x)}{(-x)^4 + 5} = \dfrac{-x^3-4}{x^4+5} = -f(x)[/tex]
The integral of an odd function over a symmetric interval is zero, so
[tex]\displaystyle \int_{-4}^4 \frac{x^3+3x}{x^4+5} \, dx = 0[/tex]
This is because
[tex]\displaystyle \int_{-a}^a f(x) \, dx = \int_{-a}^0 f(x) \, dx + \int_0^a f(x) \, dx \\\\ ~~~~ = -\int_0^{-a} f(x) \, dx + \int_0^a f(x) \, dx \\\\ ~~~~ = \int_0^{-a} f(-x) \, dx + \int_0^a f(x) \, dx \\\\ ~~~~ = -\int_0^a f(x) \, dx + \int_0^a f(x) \, dx = 0[/tex]
where we substitute [tex]x\mapsto-x[/tex] in the second-to-last equality.
number 5 ! help pls, will mark brainliest to whoever answers first
I NEED THE ANSWER FAST PLS HELP
Answer:
12 and 30
Step-by-step explanation:
6+6=12+6=24+6=30+6=36
Is 43/99 rational or irrational
Omar shops for a new television. He finds the same television at two different stores priced at $259.99. One store offers a mail-in rebate of $75. At a different store, the television is 30% off the regular price. At which store will Omar receive the better deal? Why?
Answer:
At the second store. Because 30% Of 259.99 is more than 75$.
Step-by-step explanation:
store 1.
259.99 - 75 = 184.90
stode 2.
259.99 * 30% = 78
259.99 - 78 = 181.99
A company ships gift baskets that contain apples and pears the distributions of weight for the apples the pears and baskets are each approximately normal with mean and standard deviation for each distribution as shown in the table below the way to the items are assumed independent let the random variable W represent the total weight for apple six pairs in one basket which of the following is closest standard deviation of W
Answer:
1.97
Step-by-step explanation:
Following are the solution to the given points:
Assume A, P, and B is the masses of apples, pears, and basket, respectively.
[tex]\to W = 4A + 6P + B[/tex]
Calculating the mean of W:
[tex]\to \bold{W = E(W) }[/tex]
[tex]\bold{= E(4A + 6P + B)} \\\\ \bold{= 4E(A) + 6E(P) + E(B)}\\\\\bold{= 4 \times 4.72 + 6 \times 5.41 + 13.52} \\\\ \bold{= 18.88 + 32.46 + 13.52} \\\\ \bold{= 64.86 }[/tex]
Calculating the variance of W:
[tex]\to \bold{W=Var(W)}\\\\[/tex]
[tex]\bold{= Var(4A + 6P + B)}\\\\ \bold{= 42 Var(A) + 62 Var(P) + Var(B)}\\\\\bold{= 16 \times 0.22 + 36 \times 0.182 + 1.882}\\\\ \bold{= 3.52 + 6.552 + 1.882}\\\\ \bold{= 5.3408}[/tex]
Calculating the standard deviation of W:
[tex]\to \bold{W= \sqrt{5.3408}= 2.311017}[/tex]
The linear combination of Normal random variables is known to follow the normal distribution.
[tex]\to \bold{W \sim N(64.86 , 2.311017)}[/tex]
Calculating the Probability of the Total Weight is more difficult.[tex]\to \bold{67 = P(W > 67)}[/tex]
[tex]\bold{= P[ Z > \frac{(67 - 64.86)}{ 2.311017}]}\\\\\bold{= P[Z > 0.93]}\\\\\bold{= 0.1762}[/tex] (Using Standard Normal distribution)
Therefore, the final answer is "64.86, 2.311017, and 0.1762".
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when you convert 10000 present dollars into future dollars of year 15 if the inflation rate is 77% per year, the result is equal to __________.
Answer:
$125,500
Step-by-step explanation:
From the question we are given the following
Present amount = 10000
Inflation rate = 77%
Time = 15years
Using the simple interest method n
Get the inflation amount after 15years
SI = Principal × Rate ×Time/100
SI = 10000×77×15/100
SI = 100×77×15
SI= $115500
The amount after 15years = Present amount + interest
Amount after 15years = 10000+115500
Amount after 15years = $125500
Hence the required result is equal to $125,500
A lifeguard can swim at a speed of 6 feet per second and run at a speed of 10 feet per second. The lifeguard is standing at the edge of a beach, looking at the ocean to the south. The lifeguard sees a drowning child in the ocean 100 feet east (down the shore) and 80 feet south (out at sea). How far should the lifeguard run before they start swimming?
The requried distance run and swam by the lifeguard is 100 - x. and √[x² + 80²] respectively.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The question seems to be incomplete, there must be a figure that illustrates the situation,
Since, as of the given data, he might run x distance less toward the east as of the 100 feet east, and than swim, the distance is given as,
= √[x² + 80²].
And the distance run = 100 - x.
Thus, the requried distance run and swam by the lifeguard is 100 - x. and √[x² + 80²] respectively.
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Joe borrowed $4,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 4 years?
Answer:
1,120 dollars interest will be paid by Joe in 4 years
Step-by-step explanation:
4,000 times 7 ( 0.07 ) is 280, and 280 times 4 is 1,120
What is the probability of getting number greater than 7 when 2 cards are drawn?
a) with replacement
b) without replacement
Please see the attached photos. Hope this helps :). A simpler approach is to think of the probability of the opposing happening, or not getting a number greater than 7 from either draw. I personally like this style of visualization though :)
The question is in the pic
Answer:
The answer is E.
Step-by-step explanation:
Divide it into rectangles
1) Target offers their employees group health
insurance and covers 70% of the cost. If the annual
premium for the insurance is $12,450.00 how much
is deducted from your monthly paycheck?
$311.25 is the amount deducted from the monthly paycheck, if, the annual premium for the insurance is $12,450.00 and target offers their employees group health insurance and covers 70% of the cost.
First, find the amount that the employee contributes to the cost. it can be calculated by multiplying the annual premium by the percentage they pay
$12450.00 x 70%
= $12450 x 70/100
= $8715
Now, subtract the employee's contribution from the total to find the amount that is being taken out of their pay check
12450 - 8715 = - 3735
To find the amount deducted monthly, divide the difference amount by 12
= $3735/12
= $311.25
The amount deducted from monthly paycheck is $311.25
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Convert 48 2/5 into a decimal
Answer:
48 and 2/5 converted into decimal form is 48.4
Answer:
[tex]48.4[/tex]
Step-by-step explanation:
[tex]48 \frac{2}{5} \\ \frac{242}{5} \frac{ \times 20}{ \times 20} = \frac{4840}{100} \\ = 48.4[/tex]
If the measure of angle 1= (6x+25) and the measure of angle 4= (10x-11) find the measure of angle 1
The measure of angle 1 is 79°
Given:
Value of angle 1 = (6x + 25)
Value of angle 4 = (10x - 11)
Find:
The measure of angle 1
Computation:
In the absence of complete question,
Assume;
Angle 1 = Angle 4
So,
6x + 25 = 10x - 11
10x - 6x = 25 + 11
4x = 36
x = 36 / 4
Value of x = 9
By putting value of x in angle 1
Value of angle 1 = (6x + 25)
Value of angle 1 = 6(9) + 25
Value of angle 1 = 54 + 25
Value of angle 1 = 79
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maria began the school year with $200 in her school lunch account .The amount of money in the account has decreased linearly after 3 months she had $155 in her account . after 5 months ,she had $125 in her account . witch function models the amount of money that maria had in her account at the end of n months .
Answer:
each mount she spins 15$
Step-by-step explanation:
answer 13/14 - 1/7 + 1/2 and 6/10 - 1/5 + 1/4
Answer:
mixed form: 1 131/140
decimal form: 1.93571
Answer:
first question is 18/14 simplify it's 9/7
Second question is 13/20
Step-by-step explanation:
Hope this helps
How do you determine the area under a curve in calculus using integrals or the limit definition of integrals?
Answer:
Please check the explanation.
Step-by-step explanation:
Let us consider
[tex]y = f(x)[/tex]
To find the area under the curve [tex]y = f(x)[/tex] between [tex]x = a[/tex] and [tex]x = b[/tex], all we need is to integrate [tex]y = f(x)[/tex] between the limits of [tex]a[/tex] and [tex]b[/tex].
For example, the area between the curve y = x² - 4 and the x-axis on an interval [2, -2] can be calculated as:
[tex]A=\int _a^b|f\left(x\right)|dx[/tex]
= [tex]\int _{-2}^2\left|x^2-4\right|dx[/tex]
[tex]\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx[/tex]
[tex]=\int _{-2}^2x^2dx-\int _{-2}^24dx[/tex]
solving
[tex]\int _{-2}^2x^2dx[/tex]
[tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1[/tex]
[tex]=\left[\frac{x^{2+1}}{2+1}\right]^2_{-2}[/tex]
[tex]=\left[\frac{x^3}{3}\right]^2_{-2}[/tex]
computing the boundaries
[tex]=\frac{16}{3}[/tex]
Thus,
[tex]\int _{-2}^2x^2dx=\frac{16}{3}[/tex]
similarly solving
[tex]\int _{-2}^24dx[/tex]
[tex]\mathrm{Integral\:of\:a\:constant}:\quad \int adx=ax[/tex]
[tex]=\left[4x\right]^2_{-2}[/tex]
computing the boundaries
[tex]=16[/tex]
Thus,
[tex]\int _{-2}^24dx=16[/tex]
Therefore, the expression becomes
[tex]A=\int _a^b|f\left(x\right)|dx=\int _{-2}^2x^2dx-\int _{-2}^24dx[/tex]
[tex]=\frac{16}{3}-16[/tex]
[tex]=-\frac{32}{3}[/tex]
[tex]=-10.67[/tex] square units
Thus, the area under a curve is -10.67 square units
The area is negative because it is below the x-axis. Please check the attached figure.
The high school swim team needs new equipment. They want to spend no more than $300. Swim caps, x ,cost $5 and kick boards, y ,cost $10.
What could NOT be a solution to this inequality? Let x represent swim caps and y represent kick boards.
A. (60,0)
B. (0,30)
C. (10,20)
D. (50,20)
Solve the system of linear equations.
5x + 10y=10
-x - 8y=4
The solution is ( , ).
Answer(4,-1)
Step-by-step explanation: Go on desmos graphing calculator next time. It will show you the answer.
Simplify 9 × d x e × 6
The simplification if the expression "9 × d x e × 6" involving whole number and variable is 54de
Simplification9 × d x e × 6
9 = whole numberd = variablee = variable6 = whole numberGiven the task content, this implies multiplying of all variables and whole numbers in the expression in order to arrive at a common result.
9 × d x e × 6
= 54de
It is very possible to simplify a mathematical statement whether or not the variables are letters, numbers, numbers and letters, like terms and unlike terms. So from the simplification above, 9 × d x e × 6 gives 54de.
Therefore, the simplification if the expression "9 × d x e × 6" involving whole number and variable is 54de
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A hot air balloon was at a height of 2180 feet It designated at a rate of 150 feet per minute for 6 minutes. Find it’s height
Mrs. Baxter deposits 2000 into an account that earns 5% simple interest how much is Mrs. baxters investment worth after 8 years
I believe your answer is 2954.9
Answer:
2800
Step-by-step explanation:
Interest earned = 2000 × [tex]\frac{5}{100}[/tex] × 8
= 800
Total earned = 2000 + 800
= 2800
Translate the sentence into an equation
two less than the product of 5 and a number equals 9
Use the variable y for the unknown number
Answer:
5y-2=9
Step-by-step explanation:
Hopefully this helps :)
a(b+8)= ab + ?
will crown you.
Answer:
ab + 8aStep-by-step explanation:
a(b+8)=
ab + 8a
Megavolt begins manufacturing evil light bulbs for his latest scheme. To ensure quality, he tests every 100th bulb manufactured, starting with the 42nd. What method is Megavolt use to select his sample?
Answer:
Megavolt used a Systematic sampling method.
Step-by-step explanation:
From the information given:
For every 100th evil light bulbs tested, he starts with the 42nd. This implies that;
The first bulb tested is the 142nd bulb, the second bulb tested is the 242nd...
The sequence is as follows:
142nd, 242nd, 342nd, 442nd, 542nd, 642nd .... etc
From the starting point of manufacturing the evil light bulb, the sequence is derived from sampling where each nth unit is known to be a sample, and this is only feasible in systematic sampling.
Which two statements are both true?
Answer:
(b) FG⊥HB and FG║DE
Step-by-step explanation:
You want to know two statements that correctly describe the diagram where HB crosses lines FG, DE, and AC.
PerpendicularLine HB is indicated as being perpendicular to lines FG and DE by the small square in the corner where the lines cross. It is true that ...
FG⊥HB
ParallelLines FG and DE are both perpendicular to line HB. LInes in a plane that are perpendicular to the same line are parallel to each other. It is true that ...
FG║DE
Calculate the slope of the line that passes through (-10, 3) and (2, -3
Answer:
slope = - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 10, 3 ) and (x₂, y₂ ) = (2, - 3 )
m = [tex]\frac{-3-3}{2-(-10)}[/tex] = [tex]\frac{-6}{2+10}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex]
What’s is the difference of 9.37 and 1.6
Answer:
7.77
Step-by-step explanation:
9.37 - 1.60 = Difference
Difference = 7.77
Example 2
What is the point of intersection
of the two equations?
TE
-4=2y-x
-3 + 2x = - y
Show
Graphically
Answer:
I need points sorry wish I could help
write it as a single logarithm
Answer:
0
Step-by-step explanation:
log b (3-3)
log b (0)
A ________ function specifies the relationship between the demand for a product LaTeX: x and the price of the product LaTeX: p.
Answer:
Price demand function
Step-by-step explanation:
The price demand function is the function in which there is a relationship between the demand and the price of the product
The Price demand function is
[tex]= Price \times demand[/tex]
[tex]= p \times x[/tex]
hence, the price demand function represents that there is a relationship that lies between the demand and the price