The value of the composite function g(f(x)) is 1 / 3 (81x² - 216x + 144) + 4
How to solve composite function?A composite function is a function that depends on another function. In a composite function, the output of one function becomes the input.
Therefore, let's solve the function as follows;
f(x) = 1 / 3 x² + 4
g(x) = 9x - 12
The value of g(f(x)) can be found as follows:
To find g(f(x)) we have to substitute the f(x) in g(x).
Therefore,
g(f(x)) = 1 / 3 (9x - 12)² + 4
(9x - 12)(9x - 12) = 81x² - 108x - 108x + 144
(9x - 12)(9x - 12) = 81x² - 216x + 144
Therefore,
g(f(x)) = 1 / 3 (81x² - 216x + 144) + 4
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riangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axiriangle QRS has vertices Q(8, −4), R(−1, 2), and S(3, 7). What are the coordinates of vertex Q after the triangle is reflected across the y-axi
Camera has Alyssa price of $768.95 before tax the sales tax rate is 8.25% final total find the total cost of the camera with sales tax included round your answer to the nearest cent as necessary
We know that the listed price of the camera is $768.95 and the tax rate is 8.25%.
To find the total cost we must use the next formula
[tex]\text{Total cost }=\text{listed price before tax+(listed price before tax }\cdot\text{rate tax)}[/tex]Now, we must replace the values in the formula using that 8.25% = 0.0825
[tex]\text{Total cost}=768.95+(768.95\cdot0.0825)[/tex]Simplifying,
[tex]\text{Total cost}=832.39[/tex]ANSWER:
$O32
Rami practices his saxophone for 5/6 hour on 4 days each week.
How many hours does Rami practice his saxophone each week?
[] 2/[] Hr
Answer:
you take 5/6 and multiply it by 4/1.
which gives you 20/6
then reduce it by dividing the top number by the bottom number
which gives you 3 with a remainder of 2
you then place the remainder over the
This tells you he practicedfor 3 2/6
Step-by-step explanation:
In the figure below, ZYZA and _YZX are right angles and _XYZ and ZAYZ arecongruent. Which of the following can be concluded about the distance frompoint A from point Z using Thales's method?O A. The distance between points A and Z is the same as the distancebetween points X and Z.B. The distance between points A and Z is the same as the distancebetween points A and Y.O C. The distance between points A and Z is the same as the distancebetween points Yand Z.D. The distance between points A and Z is the same as the distancebetween points X and Y.
Let's begin by identifying key information given to us:
[tex]\begin{gathered} \angle YZA=90^{\circ} \\ \angle YZX=90^{\circ} \\ \angle XYZ\cong\angle AYZ \end{gathered}[/tex]Thale's method shows that angles in a triangle opposite two sides of equal length are equal
[tex]undefined[/tex]As such, the answer is A (The distance between points A and Z is the same as the distance between X and Z)
Jackson bought a Ford Mustang for $40,000 and it depreciates in value 9% per year. Write an equation that
models the value of Jackson's car.
Answer:
[tex]v = 40000( {.91}^{x} )[/tex]
(2i) - (11+2i) complex numbers
Determine if the ordered pair provided is a solution to the linear system:3x+7y=1 and 2x+4y=0; (2,3) The system has no solution as the lines are parallel. The ordered pair (2, 3) is not a solution to the system. Yes, (2, 3) is a solution to the system. The system has no solution as the lines are perpendicular.
Answer:
The correct answer is:
The ordered pair (2, 3) is not a solution to the system.
Explanation:
The system given is:
[tex]\begin{cases}3x+7y={1} \\ 2x+4y={0}\end{cases}[/tex]If (2, 3) is a solution of the system, then replacing x = 2 and y = 3 on both equations should give a correct result and the same on both equatiions.
In the first equation;
[tex]\begin{gathered} 3\cdot2+7\cdot3=1 \\ 6+21=1 \\ 27=1 \end{gathered}[/tex]We can see that this result is not true, as 27 is not equal to 1.
In the second equation:
[tex]\begin{gathered} 2\cdot2+4\cdot3=0 \\ 4+12=0 \\ 16=0 \end{gathered}[/tex]Once again, a false result.
To see in the system has equations, let's solve for x in the second equation:
[tex]\begin{gathered} 2x+4y=0 \\ 2x=-4y \\ x=-2y \end{gathered}[/tex]Now, we can use substitution in the first equation:
[tex]3(-2y)+7y=1[/tex]And solve for y:
[tex]\begin{gathered} -6y+7y=1 \\ y=1 \end{gathered}[/tex]Now, we can find the value of x:
[tex]x=-2\cdot1=-2[/tex]The solution to the system is (-2, 1)
Thus, the correct option is "The ordered pair (2, 3) is not a solution to the system"
what is the final cost of the purchase at discount heaven?
First, let's sum the single costs of each item.
[tex]32+32+20=84[/tex]Because they are buying 1 jacket, 2 pairs of jeans, and 1 vest. So, the subtotal of these items is $84. (At Discount Heaven)
Then, we apply a 7% sales tax.
[tex]84+0.07\cdot84=84+5.88=89.88[/tex]As you can observe, the sales tax is $5.88 for all the items purchased, and the total cost they have to pay is $89.88.
I need help with my statistics homework " -compute the range ,sample variance,and sample standard deviation cost."
We need to find the range, sample variance, and sample standard deviation cost.
The range is already given: $247. It can be found by subtracting the least from the greatest value:
[tex]466-219=247[/tex]Now, in order to find the sample variance and the sample standard deviation, we first need to find the mean of the sample:
[tex]\text{ mean }=\text{ }\frac{415+466+400+219}{4}=\frac{1500}{4}=375[/tex]Now, we can find the sample variance s² using the formula:
[tex]s²=\frac{\sum_{i\mathop{=}1}^n(x_i-\text{ mean})²}{n-1}[/tex]where n is the number of values (n = 4) and the xi are the values of the sample.
We obtain:
[tex]\begin{gathered} s²=\frac{(415-375)²+(466-375)²+(400-375)²+(219-375)²}{4-1} \\ \\ s²=\frac{40²+91²+25²+(-156)²}{3} \\ \\ s²=\frac{1600+8281+625+24336}{3} \\ \\ s²=\frac{34842}{3} \\ \\ s²=11614 \end{gathered}[/tex]Now, the sample standard deviation s is the square root of the sample variance:
[tex]\begin{gathered} s=\sqrt{11614} \\ \\ s\cong107.8 \\ \\ s\cong108 \end{gathered}[/tex]Therefore, rounding to the nearest whole numbers, the answers are:
Answer
range: $247
s² = 11614 dollars²
s ≅ $108
The scale factor on a floor plan is 1 in8 ft. What is the actual distance represented by a 2.5 inches on the floor plan
Given:
Scale factor = 1 inch 8ft
Floor Plan measurement = 2.5 inches
Solution
We should re-write the scale factor in units of inches only.
Recall that:
[tex]1\text{ f}eet\text{ = 12 inches}[/tex]Then, the scale-factor in inch:
[tex]\begin{gathered} \text{Scale factor = 1 + 8 }\times\text{ 12} \\ =\text{ 1 + 96 } \\ =\text{ 97 inches} \end{gathered}[/tex]We can then find the actual distance by multiplying the represented distance (2.5 inches) by the scale factor.
So, we have:
[tex]\begin{gathered} \text{Actual distance = Represented distance }\times\text{ scale factor} \\ =2.5\text{ }\times\text{ 97} \\ =\text{ }242.5\text{ inches} \end{gathered}[/tex]Answer: Actual distance = 242.5 inches
What is the value of f(3) on the following graph?
Answer
f(3) = -2
Explanation
We are asked to find the value of f(3) from the graph.
This means we are looking for the value of f(x) or y on the graph, at a point where x = 3.
From the graph, we can see that at the point where x = 3, y = -2
Hence, f(3) = -2
Hope this Helps!!!
Solve the right triangle. Write your answers in simplified, rationalized form. DO NOT ROUND!
base = FG = root 30
perpendicular HG = x
angle = 45 degrees,
we know that
[tex]\text{tan}\theta=\frac{perpendicualr}{base}[/tex][tex]\tan 45=\frac{HG}{\sqrt[]{3}}[/tex][tex]\begin{gathered} 1=\frac{HG}{\sqrt[]{3}} \\ HG=\sqrt[]{3} \end{gathered}[/tex]so, the value of HG = root 3
The basic wage earned by a truck driver for a 40 - hour week is $560 How can I calculate the hourly rate for overtime, the driver is paid one and a half times the basic hourly?
First, find the hourly rate by dividing the total wage of $560 by the amount of time worked, which is 40 hours:
[tex]\frac{\text{\$}560}{40h}=\text{ \$}14\text{ per hour}[/tex]To find the hourly rate for overtime, multiply the basic hourly rate by 1.5:
[tex](\text{\$}14\text{ per hour})\times1.5=\text{ \$}21\text{ per hour}[/tex]Therefore, the hourly rate for overtime is $21.
Evaluate the expression whenb= 48 c= 7simplify as much as possible
Given:-
[tex]\frac{b}{3}+2c^2[/tex]To find the simplified value when b=48 and c=7.
So now we simplify the solution by substituting the values of b and c in the given equation and get the required solution.
So now we simplify. so we get,
[tex]\frac{b}{3}+2c^2=\frac{48}{3}+2\times7\times7=16+98=114[/tex]So the simplified solution is 114.
Which operation results in a binomial?+(3y6 + 4)(9y12 - 12y6 + 16)ResetNextntum. All rights reserved.
Answer:
Explanations:
According to the question, we need to determine which of the signs will fit in that will make the expression a binomial.
In simple terms, a binomial is a two-term algebraic expression that contains variable, coefficient, exponents, and constant.
We need to determine the required sign by using the trial and error method.
Using the positive sign (+) first, we will have:
[tex]\begin{gathered} =\mleft(3y^6+4\mright)+(9y^{12}-12y^6+16) \\ =3y^6+4+9y^{12}-12y^6+16 \\ =3y^6-12y^6+4+9y^{12}+16 \\ =-9y^6+9y^{12}+20 \end{gathered}[/tex]Using the product sign, this will be expressed as:
[tex]\begin{gathered} (3y^6+4)\cdot(9y^{12}-12y^6+16) \\ (3y^6+4)\cdot\lbrack(3y^6)^2-(3y^6)(4)^{}+4^2)\rbrack \end{gathered}[/tex]According to the sum of two cubes;
[tex]a^3+b^3=\mleft(a+b\mright)•(a^2-ab+b^2)[/tex]Comparing this with the expression above, we will see that a = 3y^6 and
b = 4. This means that the resulting expression above can be written as a sum of two cubes to have;
[tex]\begin{gathered} (3y^6+4)\cdot\lbrack(3y^6)^2-(3y^6)(4)^{}+4^2)\rbrack^{} \\ =(3y^6)^3-4(3y^6)^2+4(3y^6)^2+16(3y^6)+4(3y^6)^2-16(3y^6)+4^3 \\ \end{gathered}[/tex]Collect the like terms:
[tex]undefined[/tex]Why is it incorrect to write {∅} to denote a set with no elements?
Answer:
It's incorrect because {∅} is saying that the set contains empty sets, which is not the same as saying the set is empty (which can be denoted by { } or ∅
Step-by-step explanation: It's all in the answer.
help meeeeeeeeeeeeeeeee
For the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
As given in the question,
Given function :
f(x) = x³ +x +1
g(x) =-x
Composition of the given function is equal to :
(fog)(x) = f(g(x))
= f(-x)
= (-x)³ +(-x) +1
= -x³ -x +1
(g of)(x) = g(f(x))
=g(x³ +x+1)
= -(x³ +x+1)
Therefore, for the given function f(x) = x³ +x +1,g(x) =-x, composition of the given function is given by ( fog)(x) = -x³ -x +1 , ( g of)(x) = -(x³ +x +1).
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x = 3y for y how should we solve it
If x=3y is the equation then y = x/3.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given expression x equal to three y.
Here x and y are two variables.
The value of x is three times of y.
The value of y is x over three. If we know the value of x we can substitute in place of x and we can calculate it.
Divide both sides by 3.
y=x/3.
Hence the value of y is x/3.
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Multiply -5 1/2 × 7 5/6 =
You have to multiply:
[tex]-5\frac{1}{2}\cdot7\frac{5}{6}[/tex]First write the compound fractions as impropper fractions.
To do so, divide the whole number by one to express it as a fraction and add both fractions:
[tex]\begin{gathered} 5\frac{1}{2}=\frac{5}{1}+\frac{1}{2}\to\text{ common denominator 2} \\ \\ \frac{5\cdot2}{1\cdot2}+\frac{1}{2}=\frac{10}{2}+\frac{1}{2}=\frac{11}{2} \end{gathered}[/tex][tex]\begin{gathered} 7\frac{5}{6}=\frac{7}{1}+\frac{5}{6}\to\text{ common denominator 6} \\ \frac{7\cdot6}{1\cdot6}+\frac{5}{6}=\frac{42}{6}+\frac{5}{6}=\frac{47}{6} \end{gathered}[/tex]Rewrite the multiplication using the corresponding impropper fractions:
[tex]-\frac{11}{2}\cdot\frac{47}{6}[/tex]And solve the multiplication, numerator * numerator and denominator*denominator:
[tex]-\frac{11}{2}\cdot\frac{47}{6}=-(\frac{11\cdot47}{2\cdot6})=-\frac{517}{12}[/tex]if(f) (x)= x/2 - 2 and (g) (x) = 2x^2 + x - 3 find (f+g) (x)|| how do i add functions when the number is a fraction? ||
Solution
Given
[tex]\begin{gathered} f(x)=\frac{x}{2}-2 \\ \\ g(x)=2x^2+x-3 \\ \\ (f+g)(x)=f(x)+g(x)=\frac{x}{2}-2+2x^2+x-3=2x^2+\frac{3x}{2}-5 \end{gathered}[/tex]Given the zeros of the following polynomial 2 +2i, 3, - 4 select the corresponding factors AND the polynomia O (x + 2i) (2 - 2i) (2 - 3)(x+4) o f(c) = 24 - 23 822 - 42 - 48 0 (2 – 2i) (x + 2i) (2+3)(– 4) 24 – 13 + 82 40 - 48 0 (0 - 2) (+2)(x - 3)(x +4) 24 - 23 - 822 + 4x + 48 1 3 N
a)
d)
1) Since the zeros of that polynomial were given, then we can write it into the factored form. Note that there are 4 zeros, so we can write:
[tex]\begin{gathered} (x-x_1)(x-x_2)(x-x_3)(x-x_4)=0 \\ (x-(-2i))(x-2i)(x-3)(x-(-4))=0 \\ (x+2i))(x-2i)(x-3)(x+4))=0 \end{gathered}[/tex]2) To find out the corresponding polynomial then we can expand it by rewriting "i" as -1
[tex]\begin{gathered} (x+2i))(x-2i)(x-3)(x+4) \\ (x+2i)(x-2i)=x^2+4 \\ (x-3)(x+4)=x^2+4x-3x-12 \\ (x^2+4)(x^2+x-12) \\ x^4+x^3-8x^2+4x-48 \end{gathered}[/tex]3) Hence, the answers are
a)
d)
[tex]x^4+x^3-8x^2+4x-48[/tex]Which expressions are equivalent to (1/3x−4x−5/3x)−(−1/3x−3) ? Select all correct expressions. Responses −3+5x negaive 3 minus 5 x −2x+3−3x negative 2 x plus 3 minus 3 x −5x+3 negative 5 x plus 3 2x−3+3x 2 x minus 3 plus 3 x
The equivalent expression for the given expression (1/3x - 4x - 5/3x) - (- 1/3x - 3) is 3 - 7x / 3
Given,
The expression;
(1/3x - 4x - 5/3x) - (- 1/3x - 3)
We have to solve this and find the equivalent expression;
Here,
(1/3x - 4x - 5/3x) - (- 1/3x - 3)
= 1/3x - 4x - 5/3x + 1/3x + 3
= 3 - 4x - 5/3x
= 3 - (12x - 5x) / 3
= 3 - 7x / 3
That is,
The equivalent expression for the given expression (1/3x - 4x - 5/3x) - (- 1/3x - 3) is 3 - 7x / 3
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I need help on 3 it says find the value of x round each answer to the nearest tenth
In problem 3, we have a right triangle with:
• cathetus ,a = 7,,
,• cathetus ,b = x,,
,• and hypotenuse ,h = 9,.
Pigatoras Theorem states that:
[tex]h^2=a^2+b^2.[/tex]Where a and b are cathetus and h the hypotenuse.
Replacing the data of the problem in the equation above, we have:
[tex]9^2=7^2+x^2.[/tex]Solving for x the last equation, we get:
[tex]\begin{gathered} 81=49+x^2, \\ x^2=81-49, \\ x^2=32, \\ x=\sqrt[]{32}\cong5.7. \end{gathered}[/tex]Answer
The value of x to the nearest tenth is 5.7.
II
Finding simple interest without a calculator
Lella deposits $600 into an account that pays simple interest at a rate of 2% per year. How much interest will she be paid in the first 3 years?
The Solution:
Given:
Lella deposited $600 into an account that pays 2% simple interest per year.
Required:
To find the interest Lella will get in the first 3 years.
To find the interest, we shall use the formula below:
[tex]I=\frac{PRT}{100}[/tex]In this case,
[tex]\begin{gathered} P=\text{amount deposited=\$600} \\ T=\text{time in years =3 years} \\ R=\text{rate in percent=2\%} \\ I=\text{simple interest paid=?} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]I=\frac{600\times2\times3}{100}=6\times2\times3=\text{ \$36}[/tex]Thus, the interest she will be paid in 3 years is $36.00
Therefore, the correct answer is $36.00
At a point on the ground 35 ft from base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree. The height of the tree is ___. (ft^3, ft^2, or ft)(Simply your answer. Round to the nearest foot as needed)
At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree
see the attached figure to better understand the problem
Applying the Pythagorean Theorem
(3h+1)^2=h^2+35^2
9h^2+6h+1=h^2+1,225
solve for h
9h^2-h^2+6h+1-1,225=0
8h^2+6h-1,224=0
Solve the quadratic equation
Using a graphing tool
the solution is
h=12 ftPLS HELP ASAP I WILL GIVE BRAINLIEST
Answer: I think the answer is [tex]\frac{2/3}{1}\\[/tex] and [tex]\frac{3}{1}[/tex]
Step-by-step explanation: I hope this helps. Correct me if I am wrong.
AMNP ~ AQRP N x + 8 28 M 24 P 3x - 9 R Create a proportion and find the length of side PR*
Using thales theorem:
[tex]\begin{gathered} \frac{24}{28}=\frac{x+8}{3x-9} \\ 24(3x-9)=28(x+8) \\ 72x-216=28x+224 \\ 44x=440 \\ x=\frac{440}{44} \\ x=10 \\ PR=3(10)-9=21 \end{gathered}[/tex](Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) And determine the quadrants of A+B and A-B.
Given that:
[tex]\cos A=\frac{5}{13}[/tex]Where:
[tex]0And:[tex]\cos B=\frac{3}{5}[/tex]Where:
[tex]0You need to remember that, by definition:[tex]\theta=\cos ^{-1}(\frac{adjacent}{hypotenuse})[/tex]Therefore, applying this formula, you can find the measure of angles A and B:
[tex]A=\cos ^{-1}(\frac{5}{13})\approx67.38\text{\degree}[/tex][tex]B=\cos ^{-1}(\frac{3}{5})\approx53.13\text{\degree}[/tex](a) By definition:
[tex]\sin \mleft(A+B\mright)=sinAcosB+cosAsinB[/tex]Knowing that:
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]You can substitute the known values into the equation in order to find the opposite side for angle A:
[tex]\begin{gathered} \sin (67.38\text{\degree)}=\frac{opposite}{13} \\ \\ 13\cdot\sin (67.38\text{\degree)}=opposite \\ \\ opposite\approx12 \end{gathered}[/tex]Now you know that:
[tex]\sin A=\frac{12}{13}[/tex]Using the same reasoning for angle B, you get:
[tex]\begin{gathered} \sin (53.13\text{\degree)}=\frac{opposite}{5} \\ \\ 5\cdot\sin (53.13\text{\degree)}=opposite \\ \\ opposite\approx4 \end{gathered}[/tex]Now you know that:
[tex]\sin B=\frac{4}{5}[/tex]Substitute values into the Trigonometric Identity:
[tex]\begin{gathered} \sin (A+B)=sinAcosB+cosAsinB \\ \\ \sin (A+B)=(\frac{12}{13})(\frac{3}{5})+(\frac{5}{13})(\frac{4}{5}) \end{gathered}[/tex]Simplifying, you get:
[tex]\begin{gathered} \sin (A+B)=\frac{36}{65}+\frac{20}{65} \\ \\ \sin (A+B)=\frac{36+20}{65} \end{gathered}[/tex][tex]\sin (A+B)=\frac{56}{65}[/tex](b) By definition:
[tex]\sin \mleft(A-B\mright)=sinAcosB-cosAsinB[/tex]Knowing all the values, you get:
[tex]\begin{gathered} \sin (A-B)=(\frac{12}{13})(\frac{3}{5})-(\frac{5}{13})(\frac{4}{5}) \\ \\ \sin (A-B)=\frac{36-20}{65} \\ \\ \sin (A-B)=\frac{16}{65} \end{gathered}[/tex](c) By definition:
[tex]\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\cdot\tan B}[/tex]By definition:
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]Therefore, in this case:
- For angle A:
[tex]\tan A=\frac{12}{5}[/tex]- And for angle B:
[tex]\tan B=\frac{4}{3}[/tex]Therefore, you can substitute values into the formula and simplify:
[tex]\tan (A+B)=\frac{\frac{12}{5}+\frac{4}{3}}{1-(\frac{12}{5}\cdot\frac{4}{3})}[/tex][tex]\tan (A+B)=\frac{\frac{56}{15}}{1-\frac{48}{15}}[/tex][tex]\tan (A+B)=\frac{\frac{56}{15}}{-\frac{11}{5}}[/tex][tex]\tan (A+B)=-\frac{56}{33}[/tex](d) By definition:
[tex]\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\cdot\tan B}[/tex]Knowing all the values, you can substitute and simplify:
[tex]\tan (A-B)=\frac{\frac{12}{5}-\frac{4}{3}}{1+(\frac{12}{5}\cdot\frac{4}{3})}[/tex][tex]\tan (A-B)=\frac{\frac{16}{15}}{\frac{21}{5}}[/tex][tex]\tan (A-B)=\frac{16}{63}[/tex](e) Knowing that:
[tex]\sin (A+B)=\frac{56}{65}[/tex][tex]\tan (A+B)=-\frac{56}{33}[/tex]Remember the Quadrants:
By definition, in Quadrant II the Sine is positive and the Tangent is negative.
Since in this case, you found that the Sine is positive and the Tangent negative, you can determine that this angle is in the Quadrant II:
[tex]A+B[/tex]A country's population in 1994 was 182 million.In 2002 it was 186 million. Estimatethe population in 2004 using the exponentialgrowth formula. Round your answer to thenearest million.
we have the exponential formula
[tex]P=Ae^{(kt)}[/tex]so
we have
A=182 million ------> initial value (value of P when the value of t=0)
The year 1994 is when the value ot t=0
so
year 2002 -----> t=2002-1994=8 years
For t=8 years, P=186 million
substitute the value of A in the formula
[tex]P=182e^{(kt)}[/tex]Now
substitute the values of t=8 years, P=186 million
[tex]\begin{gathered} 186=182e^{(8k)} \\ e^{(8k)}=\frac{186}{182} \\ \text{apply ln both sides} \\ 8k=\ln (\frac{186}{182}) \\ k=0.0027 \end{gathered}[/tex]the formula is equal to
[tex]P=182e^{(0.0027t)}[/tex]Estimate the population in 2004
t=2004-1994=10 years
substitute the value of t in the formula
[tex]\begin{gathered} P=182e^{(0.0027\cdot10)} \\ P=187 \end{gathered}[/tex]therefore
the answer is 187 millionSpace shuttle astronauts each consume an average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish, and two different desserts. The astronauts can choose from 11 main dishes, 7 vegetable dishes, and 12 desserts. How many different meals are possible?
Okay, here we have this:
Considering the provided information, we are going to calculate how many different meals are possible, so we obtain the following:
There are 11 ways to choose a main dish, 7 ways to choose a vegetable, 12 ways to choose the first dessert, and 11 ways to choose the second dessert. Then:
We multiply to find the possible number of combinations:
[tex]\begin{gathered} 11\cdot7\cdot12\cdot11 \\ =10164 \end{gathered}[/tex]Finally we obtain that there are 10164 different meals possible.
