Step-by-step explanation:
[tex] = \tan(5\pi) [/tex]
[tex] = \tan(\pi + 4\pi) [/tex]
[tex] = \tan(\pi) [/tex]
[tex] = \tan(180 \degree) [/tex]
[tex] = 0[/tex]
The answer is A.
A patient takes 75mg of a medication every 12 hours; 60% of the medication in the blood is eliminated every 12 hours. (a) Let dn equal the amount of medication (in mg) in the bloodstream after n doses, where d1 = 75. Find a recurrence relation for dn.
The recurrence relation is dn = 0.4d(n-1) where d1 = 75
How to determine the recurrence relation?The given parameters are:
Initial, d1 = 75Rate of elimination, r = 60%Since, the medication is eliminated from the blood; then it means that the function is an exponential decay function.
This is represented as:
d(n) = d(n - 1) * (1 - r)
Substitute r = 60%
d(n) = d(n - 1) * (1 - 60%)
Evaluate the difference
d(n) = d(n - 1) * 0.4
Evaluate the product
dn = 0.4d(n-1)
Hence, the recurrence relation is dn = 0.4d(n-1) where d1 = 75
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Use a real number line to define la.
Choose the correct answer below.
OA. |a| = -a for any real number a.
B. The midpoint of the origin and a is la for any real number a.
OC. The distance from the origin to a is la for any real number a.
D. The distance from a to a is |a| for any real number a.
A number line is just that – a straight, horizontal line with numbers placed at even increments. The distance from the origin to a is |a| for any real number a. Thus, the correct option is C.
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
As we know that in the given function |a|, when any value is given to a, then the value that the function is written is equal to a.
Let a=-5, then the value that the function will return is 5. Which is the distance borigin and a, on the number line.
Hence, The distance from the origin to a is |a| for any real number a. Thus, the correct option is C.
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find the binomial expansion of (2+3x)^5 - (2 - 3x)^5
The binomial expansion of (2+3x)^5 - (2 - 3x)^5 is 480x + 2160x^3 + 486x^5
Concept: Binomial expansion is to expand and write the terms which are equal to the natural number exponent of the sum or difference of two terms.
For two terms x and y the binomial expansion to the power of n is (x + y)n = nC0 0 xn y0 + nC1 1 xn - 1 y1 + nC2 2 xn-2 y2 + nC3.
Binomial expansion of (2+3x)^5 =32+240x+720x^2+1080x^3+810x^4+243x^5
Binomial expansion of (2-3x)^5 = 32-240x+720x^2-1080x^3+810x^4-243x^5
Combining both the expansions,=32+240x+720x^2+1080x^3+810x^4+243x^5 - (32-240x+720x^2-1080x^3+810x^4-243x^5)
= 32+240x+720x^2+1080x^3+810x^4+243x^5 - 32+ 240x - 720x^2 +1080x^3 -810x^4 +243x^5
=480x + 2160x^3 + 486x^5
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What is 43.808 in written form
Answer:
fourty-three.(point) eight zero eight
Step-by-step explanation:
hope it helps...
y 2 +2y+1 Identify a= b= c= Factor m= Factor n= Factored Form :
Answer:
a = 1
b = 2
c = 1
Factored form: (y + 1)^2 or (y + 1)(y + 1)
Step-by-step explanation:
Simplify -2ab^3 (5a-4a^2 + 6ab^2 - 4b). ?
Answer:
10a^2b^3−8a^3b^3+12a^2b^5−8ab^4
Step-by-step explanation:
In parallelogram ABCD, diagonals AC and BD intersect at point E, AE = x^2 - 12, and CE = 4x What is AC?
The length of the AC is x^2 + 4x - 12.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given :
In Parallelogram ABCD, diagonals AC and BD intersect at point E.
such that
AE = x^2 - 12,
CE = 4x
We know that the diagonal of a parallelogram bisect each other.
x^2 - 12 = 4x
x^2 - 4x - 12= 0
(x-6)(x-2) = 0
Hence, the value of x = 6, 2.
AC = AE + CE = x^2 + 4x - 12.
The length of the AC is x^2 + 4x - 12.
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solve the system of equations for one of the variables x+4y=5 x-4y=5
Answer:
x=5 y=0
Step-by-step explanation:
cancel out the 4y's and then add the x's together. also add the 5s together. 2x = 10, x = 5, and plug it in, and 5 cancels out, leaving y by itself.
(3/7 * (- 5/8)) + (1/3 * 5/6) + |- 1/2 - 1/5|
Answer:
Exact Form:
1789/2520
Decimal Form:
0.70992063
f(x)=7; find f(-3) and f(0.1)
Answer:
f(-3) = 7
f(0.1) = 7
Step-by-step explanation:
The function f(x)=7 gives an output of 7 for all inputs. In other words, no matter what we plug in for x, f(x) will equal 7.
When graphed, f(x)=7 produces a horizontal line at y=7. From there, you can also see that any value of x gives an output of 7.
Use the zero x = 5, to help find the remaining zeros of x4 - 4x3 - 14x² + 36x + 45. Select one:
O a. x = 5, 3, and -3
O b. x = -1, 3, and -3
O c. None of these
O d. x = 1, 3, and -3
Answer:
huh
Step-by-step explanation:
If you have 100 apples and you take 30 how many do you have?
Answer:
70 (100-30)
Rambling (Unrelated):
Although if you take 30 apples from your own stockpile of 100 apples, you still have 100 apples
100 apples
(3x+7)(x+7)=0
What are the two possible values?
For the given equation, either 3x + 7 = 0 or x + 7 = 0
Now,
3x + 7 = 03x = -7 x = -7/3or
x + 7 = 0x = -7So, possible values of x is : -7 and -7/3
[tex](3x + 7)(x + 7) = 0 \\ \\ \\3x + 7 = 0 \\ \\ 3x = - 7 \\ \\ x = \frac{ - 7}{3} . \\ \\ \\ x + 7 = 0 \\ \\ x = - 7.[/tex]
Suppose you want to test the effectiveness of a certain drug for treating a disease that said you wanted to see if using the drug is better the standard treatment used to like 150 patients to give the drug and 150 patients to give the standard treatment name at least five factors you should control for in your samples to make the test more random
Five factors that should be controlled are the dose of the medicine, the time the patients take this medicine, their diet, the stage of this disease and medicine composition.
Why should some factors be controlled?This is done to avoid bias or imprecise results.
What factors should be controlled?Factors related to the medicine itself and factors that can affect the results should be controlled. This includes:
The dose given to the patients.The stage of the disease that should be similar for all patients.The medicine compositon and manufacturer.The number of day patients take the medicine.The patients' diet.Learn more about medicine in:https://brainly.com/question/21486381
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Express 5.5° as a fraction. .
Answer:
11/200
Step-by-step explanation:
Convert the percentage to a fraction by placing the expression over
100
Percentage means 'out of 100
5.5
100
Convert the decimal number to a fraction by shifting the decimal point in both the numerator and denominator. Since there is
1
number to the right of the decimal point, move the decimal point
1
place to the right.
55
1000
Cancel the common factor of
55
and
1000
11/200
[tex]4x {}^{2} + 20x + 25[/tex]
using appropriate identity factories the following
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's Solve ~
[tex]\qquad \sf \dashrightarrow \: 4 {x}^{2} + 20x + 25[/tex]
[tex]\qquad \sf \dashrightarrow \: 4 {x}^{2} + 10x + 10x + 25[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x(2x + 5) + 5(2x + 5)[/tex]
[tex]\qquad \sf \dashrightarrow \: (2x + 5) (2x + 5)[/tex]
[tex]\qquad \sf \dashrightarrow \: (2x + 5) {}^{2} [/tex]
or
[tex] \sf{\qquad \sf \dashrightarrow \: 4x² + 20x + 25 } [/tex]
[tex] \sf{\qquad \sf \dashrightarrow \: (2x)² + (2 \sdot 2x \sdot 5) + (5)²} [/tex]
[ it's similar to expression - a² + 2ab + b² that is equal to (a + b)² ]
so, let's use this identity here to factorise :
[tex] \sf{\qquad \sf \dashrightarrow \: (2x + 5)²} [/tex]
I hope it was helpful ~
A farmer has 250 ft of fencing and wants to enclose a rectangular area of 3750 ft². What dimensions should she use?
The length of the longer side of the fence is:
The length of the shorter side of the fence is:
Answer:
Longer side is 75 feet, shorter side is 50 feet.
Step-by-step explanation:
Let l be the length of the longer side and w be the length of the shorter side.
2l + 2w = 250, which simplifies to
l + w = 125. Solving for w, we have
w = 125 - l.
lw = l(125-l) = 3750
[tex] {l}^{2} - 125l - 3750 = 0[/tex]
[tex]( l - 50)(l - 75) = 0[/tex]
l = 75, w = 50
16 Let f(x) and g ) are function such that f () = x+5 and g(x) x+4, what is domain of f(x)+g(x)?
Answer: all real numbers
Step-by-step explanation:
I assume you meant to write:
Let f(x) and g(x) be functions such that f(x) = x+5 and g(x) = x+4. What is domain of f(x)+g(x)?[tex]f(x)+g(x)=(x+5)+(x+4)=2x+9[/tex]
Since this is a linear function, the domain is all real numbers.
how much 45 in hour how do
Answer:
45 minutes in an hour is also called three-quarters of a hour.
Step-by-step explanation:
If you are talking about money, then here is the answer.
Yearly (262 Work Days)=$94,320
Is $45 an hour good pay?
In short, yes! Forty-five dollars an hour is a great wage. It's above the median income in the United States and can provide you with a comfortable lifestyle. If you're looking to make more money, there are plenty of career choices that will have you on your way to making $45 an hour in no time.
Quadrilateral ABCD is inscribed in this circle. What is the measure of angle C?
Answer:
[tex]\boxed{\bf \angle \: C = 62^{o} }[/tex]
Step-by-step explanation:
The sum of the opposite angle of cyclic quadrilateral is 180°.
First, lets find x...
[tex]\bf \angle \: B + \angle \: D = {180}^{o} [/tex][tex]\bf (x + 20) + 3x = {180}^{o} [/tex][tex]\bf 4x + 20 = 180[/tex][tex]\bf 4x = 180 - 20[/tex][tex]\boxed{\bf x = {40}^{o}} [/tex]Now, let's find the measure of angle C....
[tex]\bf \angle \: a + \angle \: C = {180}^{o} [/tex][tex]\bf 2x + 38 + \angle \: C = {180}^{o} [/tex][tex]\bf 2(40) + 38 + \angle \: C = {180}^{o} [/tex][tex]\bf \angle \: C = 180 - 80 - 38[/tex][tex]\boxed{\bf \angle \: C = {62}^{o}}[/tex]________________________
Given the graph of the pre-image and image, identify the correct
coordinate transformation.
The preimage was shifted to the image by a translation 2 units right and 2 units up, so the answer is [tex](x,y) \longrightarrow (x+2, y+2)[/tex]
Ratio of men to women working for a company is 7to5 there are 75 women working for the company what is total number of employees
Answer:
There is a total of 180 employees.
Step-by-step explanation:
men : women
7 : 5
5 units = 75
1 unit = 15
12 units = 180
Solve x:
3x + 99x= 1224
10 pts
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3x + 99x = 1,224}\\\\\large\textbf{COMBINE the LIKE TERMS}\\\\\mathsf{(3x + 99x) = 1,224}\\\mathsf{3x + 99x = 1,224}\\\mathsf{\bold{102x} = 1,224}\\\\\large\textbf{DIVIDE 102 to BOTH SIDES}\\\\\mathsf{\dfrac{102x}{102} = \dfrac{1,224}{102}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\mathsf{x = \dfrac{1,224}{102}}\\\\\mathsf{x = 12}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 12}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]If f(x)=16x- 30 and g(x)= 14x-6, for which value of x does (f-g)(x)=0?
Answer:
x=12
Step-by-step explanation:
16x-30-(14x-6)=2x-24=0. add 24 on both sides to get 2x=24. divide by 2 on both sides to get x=12
In a statistics class with 36 students the professor wanted to know the probability that at least two students share the same birthday. The probability would be
The probability that at least two students share the same birthday is 83.22 %.
Probability of sharing the same birthdayLet P(A) = Probability that no two students share same birthdayLet P(A') = Probability at least two students share same birthday
There are 365 days in year and there 36 students in the class.
Total sample space, n = 365³⁶
36 students will be selected as [tex]365P_{36}[/tex]
[tex]P(A) = \frac{365P_{36}}{365^{36}} = 0.1678[/tex]
Probability at least two students share same birthdayP(A') = 1 - P(A)
P(A') = 1 - 0.1678
P(A') = 0.8322
P(A') = 83.22 %
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round 0.3391 to the nearest thousandth
Answer:
0.339
Step-by-step explanation:
Hope it helped!
Hii!
___________________________________________________________
Answer: 0.339
Explanation:
Rounding Rules
There are two rounding rules that will help us whenever we need to round a number! These are the rules.
If the number that you need to round is followed by a digit that is less than 5, you round down.If the number that you need to round is followed by a digit that is either greater than or equal to 5, you round up.---
Now that we know the rules, let's get down to solving our problem! ^^
The nearest thousandth is 3 decimal places.
_._ _ _ <==== Nearest thousandth
The third number after the decimal point is 9. After it is a digit that is less than 5. According to the rounding rules, we should round down.
[tex]\boldsymbol{0.3391=== > 0.339}[/tex]
--
Hope that this helped! Best wishes.
--
Solve x^2 - 10x = 30x
[tex]x^2-10x=30x\\x^2-40x=0\\x(x-40)=0\\x=0 \vee x=40[/tex]
find y please help meeee :)
Answer:
the interior angle of a triangle = 180- 89 ( forming linear pair)
= 91°
y = 91 + 23
Y = 114° ( sum of interior angle of a triangle ls equal to its outer angle)
Answer:
114
Step-by-step explanation:
Angle A + 89 = 180 (Sum ofAngles in a straight line)
Angle A = 180 - 89 = 91
Angle B + Angle A + 23 = 180 (Sum of angles in a triangle)
Angle B + 91 + 23 = 180
Angle B = 180 - 114 = 66
Angle B + y = 180 (Sum of angles in a straight line)
66 + y = 180
y = 180 - 66 = 114
Refer to the attached picture.
in a sale, the cost of a coat is reduced from 85 to 67.5
Answer:
I’m assuming you’re talking about what percentage was taken off, so in that case the answer would be approximately 20.6%
Step-by-step explanation:
67.5/85 X/100
cross multiply then divide by 100 to find for x and you get 79.4117
then, subtract this number from 100 and you will get 20.6%
How much extra snow would a child need to take a snowball with a diameter of 8 cm and increase its size to a snowball with a diameter of 12 cm?
The amount of the extra snow would a child need to take a snowball will be 636.71 cubic cm.
What is the volume of the sphere?Let d be the diameter of the sphere.
Then the volume of the sphere will be
V = 1/6 πd³ cubic units
Then the amount of the extra snow would a child need to take a snowball with a diameter of 8 cm and increase its size to a snowball with a diameter of 12 cm will be
Amount of snow = 1/6 π x 12³ - 1/6 π x 8³
Amount of snow = 288 π - 85.33π
Amount of snow = 636.71 cubic cm
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