Answer:
[tex]2 \cos ^{2} (4x) - 1 = 0 \\ \cos ^{2} (4x) = \frac{1}{2} \\ \cos(4x) = \sqrt{ \frac{1}{2} } \\ 4x = { \cos }^{ - 1} ( \sqrt{ \frac{1}{2} } ) \\ x = \frac{ { \cos}^{ - 1} ( \sqrt{ \frac{1}{2} } )}{4} \\ x \isnt \: \frac{\pi}{2} [/tex]
The side length, s, of a cube is 4x2 + 3. If V = s3, what is the volume of the cube?
64x6 + 144x4 + 108x2 + 27
64x6 + 48x4 + 12x2 + 1
4x6 + 36x4 + 108x2 + 27
4x6 + 12x4 +12x2 + 1
Answer:
The answer is option 1.
Step-by-step explanation:
You have to substitute the expressions of s into the formula of volume :
s = 4x² + 3
V = s³
V = (4x² + 3)³
Then, you have to expand it :
V = (4x² + 3)³
V = (16x⁴ + 24x² + 9)(4x² + 3)
V = 16x⁴(4x²) + 16x⁴(3) + 24x²(4x²) +
24x²(3) + 9(4x²) + 9(3)
V = 64x⁶ + 48x⁴ + 96x⁴ + 72x² + 36x² + 27
V = 64x⁶ + 144x⁴ + 108x² + 27
The required volume of the cube is 64x⁶ + 144x⁴ + 108x² + 27. Answer: A.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property
The volume of the cube is given by V = s^3. Substituting s = 4x^2 + 3, we get:
V = (4x² + 3)³
= (4x²)³ + 3(4x²)²(3) + 3(4x²)(3²) + 3³
= 64x⁶ + 144x⁴ + 108x² + 27
Therefore, the volume of the cube is 64x⁶ + 144x⁴ + 108x² + 27. Answer: A.
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Create and expression that is equivalent to 3x+2x+x using the fewest terms
Answer:
6x
Step-by-step explanation:
add the terms to make one term
4. Sam has 6 rose bushes. He counted the flowers on each of them. There are 8, 2, 5,
4, 11 and 9. Find the Standard Deviation. Is 13 a "Usual” number of flowers?
Answer:
No
Step-by-step explanation:
SD=8+2+5+4+11+9÷6
13=10+9+20÷6
13=19+20÷6
13=39÷6
13=6.5-False=No
13 is not a usual number. A further solution of the given query is provided below.
Given:
Number of observations = 6
Series 8, 2, 5, 4, 11, 9
The Mean will be:
= [tex]\frac{Sum \ of \ observation}{Total \ number \ of \ observations}[/tex]
By substituting the values, we get
= [tex]\frac{8+2+5+4+11+9}{6}[/tex]
= [tex]\frac{32}{6}[/tex]
= [tex]6.5[/tex]
Now,
The Standard deviation will be:
= [tex]\sqrt{\frac{|x-\bar x|^2}{n} }[/tex]
= [tex]\sqrt{\frac{(1.5)^2+(4.5)^2+(1.5)^2+(2.5)^2+(4.5)^2+(2.5)^2}{6} }[/tex]
= [tex]3.0956[/tex]
13 is not within the range of standard deviation. Thus it is not a usual number.
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Pls help I’m failing math
Answer:
$27.14
Step-by-step explanation:
Price of 1 DVD: $9.10
Price of 4 DVDs: 4 * $9.10 = $36.40
Discount: 25%
Now we find 25% of $36.40.
25% of $36.40 =
= 0.25 * $36.40
= $9.10
The 25% discount amounts to $9.10. We now subtract $9.10 from $36.40 to find the discounted price.
$36.40 - $9.10 = $27.30
Now we need to apply the 6.75% tax to $27.30.
6.75% of $27.30 =
= 0.0675 * $27.30
= $1.84
The sales tax is $1.84.
Now we add the sales tax amount to the total discounted price.
$27.30 + $1.84 = $29.14
Answer: $27.14
The two triangles are similar.
What is the value of x?
Answer:
21
Step-by-step explanation:
Ratios are used.
10/30 = 12/36 = 7/x
1/3 = 7/x
x = 3*7 = 21
Help me please! I don’t understand! I’ll give you brainly!
Answer:
For number 2 it is = x(f + h)
For number 3 it is = x(g + h)
For number 4 it is = x(h + f)
For number 5 it is = x(f - g)
Hope this helps:)
3x + y = -3
y = x + 5
Substitution pls show solving
Answer:
( -2, 3 )
Step-by-step explanation:
3x + y = -3
y = x + 5
Since "y" has been given to us, all we need to do is substitute.
3x + x + 5 = -3
Combine like terms
4x + 5 = -3
Subtract 5 onto both sides
4x + 5 - 5 = -3 - 5
4x = -8
Divide by 4 into both sides to isolate the variable
4x/4 = -8/4
x = -2
Now that we have x ( -2 ), we can substitute that to get what y is.
y = x + 5
y = -2 + 5
y = 3
( x, y ) ---> ( -2, 3 )
Hope this helped!
Have a supercalifragilisticexpialidocious day!
[5x+10y+15z=60
[2x+4y+6z=60
[x+2y+3z=60
9514 1404 393
Answer:
no solution
Step-by-step explanation:
The equations are inconsistent. The set of equations reduces to ...
x + 2y + 3z = 12
x + 2y + 3z = 30
x + 2y + 3z = 60
No values of x, y, and z can satisfy all three equations. There is no solution.
How many four digit numbers can be formed using the digits 7, 6, 5 and 2 if no
repetitions are allowed?
Answer:
24
Step-by-step explanation:
4! = 4*3*2*1 = 24
24 numbers can be formed
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 71 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = Incorrect: Your answer is incorrect. (b) Find an expression for the number of cells after t hours. P(t) = Incorrect: Your answer is incorrect. (c) Find the number of cells after 8 hours. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) hr
Answer:
[tex]r=1.57[/tex], [tex]P(t)=71e^{3t\ln2}[/tex], [tex]P(8)=1191182336[/tex],[tex]P'(8)=2476994033[/tex] [tex]t=2.713\; hr[/tex]
Step-by-step explanation:
[tex](a)[/tex] Find the relative growth rate.
[tex]P=Ae^{rt}[/tex] where given [tex]A=71, P(t)=120\;\;and \;\; t=\frac{1}{3}[/tex]
Find the value of [tex]r[/tex]
[tex]\Rightarrow 120=71 e^{\frac{r}{3} }[/tex]
[tex]\Rightarrow \frac{120}{71} =e^{\frac{r}{3} }[/tex]
[tex]\Rightarrow 1.69=e^{\frac{r}{3} }[/tex]
[tex]\Rightarrow \ln1.69=\frac{r}{3}[/tex]
[tex]\Rightarrow 3\ln1.69=r \;\;\; or \;\;\; r=1.57[/tex]
[tex](b)[/tex] Find an expression for the number of cells after t hours.
[tex]P(t)=71e^{3t\ln2}[/tex]
[tex](c)[/tex] Find the number of cells after 8 hours.
[tex]P(8)=71e^{3\times 8\times \ln2}[/tex]
[tex]\Rightarrow P(8)=1191182336[/tex]
[tex](d)[/tex] Find the rate of growth after 8 hours.
[tex]P(t)=71e^{3\times t\times \ln2}[/tex]
Now differentiate w.r.t. [tex]t[/tex]
[tex]\Rightarrow P'(t)=71\times 3\ln2\times e^{3t\ln2}[/tex]
[tex]\Rightarrow P'(8)=3573547008\ln2[/tex]
[tex]=2476994033[/tex]
[tex](e)[/tex] When will the population reach 20,000 cells?
[tex]20,000=71e^{3t\ln2}[/tex]
[tex]\Rightarrow \ln\frac{20000}{71} =3t\ln2[/tex]
[tex]\Rightarrow \frac{ \ln\frac{20000}{71}}{3\ln2} =t[/tex]
S0, [tex]t=2.713 hr[/tex]
The price of a certain new car increases by the same amount each year the first year it was $17,200 and then the 12th year it was $30,400 in which year with a car cost $36,400?
Answer:
k47n4
Step-by-step explanation:
Answer: would it be the 12th year and a half
Step-by-step explanation: because since it increases then half of the year it would be $30,400
Simplify 8 - (14)
A- (-22)
B- (-6)
C- (6)
D- (22)
Answer:
B) -6 is the answer :) :) *-*
Find the equation of a line which passes through the point (3, –4) and has a slope of –3. Put your final answer in standard form
Answer: 3x+y=5
Step-by-step explanation:
Equation of a line that has slope(m) and passes through point (a,b) is given by :-
[tex](y-b)=m(x-a)[/tex]
Given: Point = (3,-4)
Slope =-3
Then, the equation of the required line:
[tex](y-(-4))=-3(x-3)\\\\\Rightarrow\ (y+4)=-3(x-3)\\\\\Rightarrow\ y+4=-3x+9\\\\\Rightarrow\ 3x+y=9-4\\\\\Rightarrow\ 3x+y=5\ \ \ \ [\text{Standard form: Ax+By=C}][/tex]
Hence, required equation: 3x+y=5
Isaac keeps track of the amount of money in his savings certificate each month. He has accumulated the following data:
(0,50); (1,55); (2,60.5); (4,66.55)
What is the common difference or ratio?
a. The common difference is 0.48
b. The common difference is 0.50
c. The common ratio is 0.98
d. The common ratio is 1.1
Answer:
d. The common ratio is 1.1
Step-by-step explanation:
To see if the data has a common ratio or common difference, we have to see if the division between them is equal(common ratio), or if the difference between them is equal(common difference).
In this case, since [tex]60.5 - 55 \neq 55 - 50[/tex], it has a common ratio.
To find it, we divide consecutive terms. For example:
[tex]\frac{55}{50} = 1.1[/tex]
So the correct answer is:
d. The common ratio is 1.1
How many cubic inches are in 19 cubic feet?
Answer:
32,832Step-by-step explanation:
What is the range of y = -5sin(x)?
E OF
all real numbers -5sys5
O all real numbers - sys
all real numbers -1Sys1
O all real numbers - sys
Answer:
[-5, 5] the Y value has a minimum of -5 and max of 5 so that is what your range is!
Step-by-step explanation:
[tex]\boxed{\boxed{\pink{\bf \leadsto The \ range \ of \ y \ is \ y \ \in \ [-5,5] .}}}[/tex]
Step-by-step explanation:A function is given to us and we need to find its range. So the given function is ,
[tex]\bf\implies y = -5\:sin(x) [/tex]
The lower bound of the range for sine is found by substituting the negative magnitude of the coefficient into the equation.
[tex]\bf \implies y = (-5) [/tex]
The upper bound of the range for sine is found by substituting the positive magnitude of the coefficient into the equation.
[tex]\bf \implies y = (5) [/tex]
Hence the range is ,
[tex]\boxed{\red{\bf -5 \leq y \leq 5 }}[/tex]
Interval Notation :-
[tex]\boxed{\red{\bf y \in [-5,5] }}[/tex]
Set builder Notation :-
[tex]\boxed{\red{\bf \{ y | -5 \leq y \leq 5 }}[/tex]
Graph of the function is attached .
Hence the range of y = -5 sin(x) is [-5,5].pls help!! thank you!!
Answer: 14 lbs
Step-by-step explanation:
shoot i hope this right
I BEG YOU PLEASE HELP ME ASAP PLEASE ♥♥♥♥ PLEASE
Why should anyone help you when you just post absurd answers for other people?
What's the Answer for (-8 ) – (- 8 ) =
Brainliest for first correct answer! Very very easy!
11.25 is ___ percent of 375
Answer:
11.25:375*100 =
(11.25*100):375 =
1125:375 = 3
Write an equation for the following table.
Answer:
Step-by-step explanation:
Lets pick to columns in the table
Lets so (6,228) and (7,266)
To find the slope you need to do y1-y2/x1-x2
7-6/266-228=1/38.
1/38 is the slope.
y=1/38x+b
to find B you have to plug any of the y with the corresponding x values back in and solve for b.
Lets choose 228.
228=1/38(6)+b
228=6/28+b
(28/6)(228)=b
b=1064
the equation will be y=1/38x+1064
Evaluate bd/a+c if a=−2 , b=3 , c=−12 , and d=−4
Answer:
6/7
Step-by-step explanation:
First you just have to plug the numbers in so you get 3*-4/-2+(-12) which simplifies to -12/-14 which can be simplified to 6/7
The value of expression bd/a+c will be 6/7.
What is substitution method?
To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The expression is ,
bd / a+c
And, The values are a=−2 , b=3 , c=−12 , and d=−4.
Now, Find the value of the expression we can substitute all the given values in the expression;
⇒ bd / a+c
⇒ 3 × (-4) / -2+(-12)
⇒ -12/-2-12
⇒ -12/-14
⇒ 12/14
⇒ 6/7
Thus, The value of expression bd/a+c will be 6/7.
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What is the product of 1/3 and 3/4
Answer:
1/4
aus74ebsi2neissnejws
Answer:
1/4 or . 25
Step-by-step explanation:
pls mark brainliest to help my rank :)
An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 500 million dollars. The additional cost of manufacturing each plane can be modeled by the function:
Answer:
The cost function is simply the initial cost plus the manufacturing cost.
C(x)=500+20x-5x^3/4+0.01x^2
The demand function was given to us.
p(x)=320-7,7x
The revenue function is simply x multiplied by the demand function.
R(x)=xp(x)=320x-7.7x^2
We find that when 20 planes are produced, that profit is currently maximized
We know that to maximize profit, marginal revenue must equal marginal cost.
C'(x)=20-15/4x^-1/4+0.02x
R'(x)=320-15.4x
x=19,57
We find that when 20 planes are produced, that profit is currently maximized.
Step-by-step explanation:
An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 500 million dollars. The additional cost of manufacturing each plane can be modeled by the function: , where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell planes.
(a) Find the cost, demand, and revenue functions.
(b) Find th eproduction level and the associated selling price of the aircraft that maximizes profit.
Jan is having the walls of her house painted. The cost
depends on the area of the walls.
Which is the dependent variable, and which is the independent variable?
A. The dependent variable is the cost, and the independent variable
is the area of the walls.
B. The dependent variable is the cost, and the independent variable is
the number of floors.
C. The dependent variable is the area of the walls, and the
independent variable is the cost.
D. The dependent variable is the number of floors, and the
independent variable is the cost.
Answer:
A
Step-by-step explanation:
Which region represents the solution to the system of inequalities?
Region A
Region B
Region C
RegionD
Answer:
A
Step-by-step explanation:
This is because the shaded regions are not required
Answer:
A
Step-by-step explanation:
its not shaded
1. 3(x + 12) =
2. 2(7 + 6x)
3. 9(5x−2)
Step-by-step explanation:
done....................I hope its right
Answer:
1. 3x + 36
2. 14 + 12x
3. 40x-18
Step-by-step explanation:
1. 3(x+12)
3x + 36
2. 2(7+6x)
14 + 12x
3. 9(5x-2)
40x-18
Ace Carlos
A set of 125 golf scores are normally distributed
with a mean of 76 and a standard deviation of
3. What is the probability that a score is no more than 79?
Answer:
84.1%
Step-by-step explanation:
Add up 0.1, 2.2, 13.6, 34.1, and 34.1 and you get that number. this is because that is the numbers in each column and you add those because they are below 79 mark.
You have a diner at a restaurant and the cost of your meal is $28.00. because of the mess you made, you want to leave a 20% tip. What is your total bill including tip?
Answer:
$33.60
Step-by-step explanation:
%20 of 28 is 5.6
add $5.60 to 28= 33.60
Answer:
$33.6
Step-by-step explanation:
28 x 0.20 = 5.6 ...tip
total cost = 28 + 5.6 = 33.6
Plzplzplzplzplzzpzlzpzp
Answer:
A 7/25
Step-by-step explanation:
1. Take inverse of theta
2. Substitute the inverse theta in the equation given in question