Answers
7) As x goes to 1, we have that the function itself is getting closer and closer to the value 4. It is important for this calculation to notice that we do not care about f(4) but rather the value of the function as x is around 4. This function could have been discontinuous at 4 (have a hole there or not be defined) but we would still have that [tex] \lim_{x \to 1} f(x)=4 [/tex] .
8) The value of the investment after 1 year will be equal to 400*(1.051); after 2 years the value will be equal to (400*1.051)*1.051 (the quantity after one year times (1+interest)) and after n years: [tex]400*1.051^n[/tex]. Substituting n=5 we get: 512.95$.
Now for the other part: [tex]400*1.051^n=1000[/tex] (We need to solve for n)
[tex]1.051^n=2.5[/tex] Taking logs each side:
[tex]n*log1.051=log2.5[/tex]
This yields n=18.42 years.
9) Let us take the cost: it has a fixed component of 350$ and a variable component of 20c=0.2$ per serving. Hence C(x)=350+0.2*x
The revenue function has only a variable component, 70 cents per serving. Similarly, R=0.7*x where x is the number of servings.
One has that P(x)=R(x)-C(x)=0.7*x-(350+0.2*x)=0.5x-350
Finally, if the Society breaks even, we have that P(x)=0. Solving that equation, we have: 0=0.5x-350 hence 0.5x=350 hence x=700; thus, 700 servings are needed in order for the society to break even.
10) Let us assume that q=a*p+b (general linear relationship). We have that a and b satisfy:
5000=a*60+b and 3500=a*75+b. We need to solve that system of equations to get the coefficient of our function. Subtracting both equations, we get that 1500=-15*a hence a=-100. Substituting back in the first equation, 5000=-100*60+b, yielding that b=11000. Hence the linear model that we were seeking is q=-100*p+11000.
11) If there is no surplus or shortage, we have that the price is chosen so that supply and demand are equal. Hence -3p+400=7p-500. 10p=900, hence p=90$. The required price is at 90$.
Related Questions
Which multiplication expression that does not belong based on scaling. Explain.
Choose an expression
6 x 2 1/2
6 x 3 3/5
1/2 x 6
2 2/5 x 6
Answers
how many miles will you go if you ride your bike for t hours at 9 miles per hour?
Answers
r = rate = 9 miles / hour
t = t hours
d = ???
d = 9 * t <<<<==== answer.
A polynomial that is written as a product has been ______.
Answers
The polynomial has been factored completely.
Hope this helps!
A polynomial that is written as a product has been "factored completely."
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
In the expression Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Since we know that factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
A polynomial which can be written as a product has been "factored completely."
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they knew that they could 3 miles in 20 minutes. how far can they ride in 45 minutes?
Answers
To find out how far the student can ride in 45 minutes, we calculate the speed of 0.15 miles per minute from the given 3 miles in 20 minutes, then multiply this speed by 45 minutes, resulting in a distance of 6.75 miles.
Explanation:The student has stated that they can travel 3 miles in 20 minutes. To find out how far they can ride in 45 minutes, we need to calculate their riding speed and then apply it to the longer time period.
Step 1: Calculate the riding speed
The speed can be calculated by dividing the distance (3 miles) by the time (20 minutes), which gives us a speed of 0.15 miles per minute.
Step 2: Use the speed to determine the distance in 45 minutes
Now that we know the speed, we can multiply it by the new time period (45 minutes) to find the distance they can ride. That calculation is 0.15 miles/minute × 45 minutes = 6.75 miles.
When we check whether the answer is reasonable, we can notice that 45 minutes is a little more than twice 20 minutes, and since they can ride 3 miles in 20 minutes, it makes sense that they could ride more than twice that distance in 45 minutes, so our answer of 6.75 miles seems reasonable.
They can ride 6.75 miles in 45 minutes.
Explanation:To find how far they can ride in 45 minutes, we can use the concept of average speed.
Given that they can ride 3 miles in 20 minutes, we can calculate their average speed as:
Average Speed = Distance / Time
Average Speed = 3 miles / 20 minutes
Average Speed = 0.15 miles per minute
Now, we can find how far they can ride in 45 minutes:
Distance = Average Speed x Time
Distance = 0.15 miles per minute x 45 minutes
Distance = 6.75 miles
Therefore, they can ride 6.75 miles in 45 minutes.
Ms. Maple is a teacher whose salary is $22,570 for this school year, which has 185 days. In Ms. Maple’s school district, substitute teachers are paid $80 per day. If Ms. Maple takes a day off without pay and a substitute teacher is paid to teach her classes, how much less does the school district pay in salary by paying a substitute teacher instead of paying Ms. Maple for that day?
Answers
Final answer:
The school district pays $42 less by hiring a substitute teacher for a day instead of paying Ms. Maple, calculating by comparing Ms. Maple's daily salary to a substitute teacher's daily rate.
Explanation:
To calculate how much less the school district pays by hiring a substitute teacher instead of paying Ms. Maple for a day, we first need to determine Ms. Maple’s daily salary. This is done by dividing her annual salary by the number of working days in the school year.
Ms. Maple’s daily salary = $22,570 / 185 days = $122 per day.Substitute teacher’s daily salary = $80 per day.The difference between what the school district pays Ms. Maple and what it pays a substitute teacher for one day = Ms. Maple’s daily salary - Substitute teacher’s daily salary = $122 - $80 = $42.Therefore, the school district pays $42 less by hiring a substitute teacher for a day instead of paying Ms. Maple.
Full-time ph.d. students receive an average of $12,837 per year with a standard deviation of $3000. find the probability that the average salary of a group of 16 randomly selected ph.d. students is more than $13,000.
Answers
Use the diagram of the right triangle above and round your answer to the nearest hundredth. If m
Answer choices:
A) 17.32 m
B) 6.83 m
C) 14 m
D) 9.99 m
Answers
Answer:
b. 6.93 m.
Step-by-step explanation:
We have been given triangle ABC and we are asked to find the measure of a.
We will use law of sines to solve our given problem.
[tex]\frac{a}{\text{Sin}(A)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are opposite sides of angle A, B and C respectively.
First of all, we will find the measure of angle B using angle sum property.
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]30^{\circ}+\angle B+90^{\circ}=180^{\circ}[/tex]
[tex]\angle B+120^{\circ}=180^{\circ}[/tex]
[tex]\angle B=180^{\circ}-120^{\circ}[/tex]
[tex]\angle B=60^{\circ}[/tex]
Upon substituting our given values in law of sines we will get,
[tex]\frac{a}{\text{Sin}(30^{\circ})}=\frac{12}{\text{Sin}(60^{\circ})}[/tex]
[tex]\frac{a}{0.5}=\frac{12}{\frac{\sqrt{3}}{2}}[/tex]
[tex]\frac{a}{0.5}=\frac{2*12}{\sqrt{3}}[/tex]
[tex]\frac{a}{0.5}*0.5=\frac{24}{\sqrt{3}}*0.5[/tex]
[tex]a=\frac{12}{\sqrt{3}}[/tex]
[tex]a=6.9282032302755\approx 6.93[/tex]
Therefore, the value of a is 6.93 meters and option 'b' is the correct choice.
How can you tell if the rule you have written for a set of points is correct?
Answers
In order to do that, you take both of the x values and plug them back in to see if you got the desired y value. If you do, it's correct.
For example:
If you had the equation:
y = 2x + 5
and had the points (5,15) and (3,1)
We would check the first coordinates by plugging in the x value:
y = 2(5) + 5
y = 15
Since 15 is our y value, we're correct.
For our next, we can do the same thing, and plug in the x value:
y = 2(3) + 5
y = 6 + 5
y = 11
Since we don't have our desired value, we know we're wrong.
Hope this helps!
What is f(2) if the linearization of f(x) at a = 2 is l(x) = 12x + 4?
Answers
.. l(x) ≈ f(a) +f'(a)*(x -a)
Then
.. l(a) = f(a)
f(2) = l(2) = 12*2 +4
f(2) = 28
How to find the area under the standard normal curve between z 1.5 and z 2.5?
Answers
However, tables/software have been developed to give the areas under the normal curve to the left of particular values of z. The function is the probability of Z<z, or P(Z<z).
The area between two values z1 and z2 (where z2>z1) is therefore
P(Z<z2)-P(Z<z1).
For example, to find the area between z1=1.5, z2=2.5
is
P(Z<2.5)-P(Z<1.5)
=0.99379-0.93319
=0.06060
(above values obtained by software, such as R)
For example, the value P(Z<2.5) can be calculated using
P(Z<2.5)=erf(2.5/sqrt(2))/2+1/2
where erf(x) is a mathematical function that does not have an explicit formula (calculated by summation of series, or tabulated).
We have that for the Question, it can be said that the area under the standard normal curve between z 1.5 and z 2.5 is
P(1.5 &2.5) =0.06
From the question we are told
How to find the area under the standard normal curve between z 1.5 and z 2.5?
Generally the equation for the probability is mathematically given as
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
Where
P(Z < 2.5) = 0.99
P(Z < 1.5) = 0.93
From Z Table
Therefore
P(1.5 &2.5) = P(Z < 2.5) - P(Z < 1.5)
P(1.5 &2.5) =0.06
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Abby Mia wants to know how much must be deposited in her local bank today so that she will receive yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually. (Use the tables found in the textbook.)
Answers
[tex]P=\frac{A*((1+i)^n-1)}{i*(1+i)^n}[/tex]
where
P=amount to be deposited today, to be found
A=amount withdrawn each year=18000
i=Annual interest=9%
n=number of years = 20
Substituting values,
[tex]P=\frac{A*((1+i)^n-1)}{i*(1+i)^n}[/tex]
[tex]=\frac{18000*((1+0.09)^{20}-1)}{0.09*(1+0.09)^{20}}[/tex]
=164313.82 to the nearest cent
seth made 4 quarts of fruit punch for a birthday party. How many cups of fruit punch did he make
Answers
4 liquid quarts would equal 16 cups if you do the conversion.
Happy to help!
~Brooke❤️
So if there are 4 quarts and 4 cups in each quart, you have to multiply 4*4.
4*4=16
Seth made 16 cups of fruit punch.
Find the slope of the line that passes through (-95, 31) and (-94, 6).
Answers
Answer:
The slope of the line that passes through (-95, 31) and (-94, 6) is -25.
Step-by-step explanation:
The equation of a line has the following format:
[tex]y = ax + b[/tex]
In which a is the slope.
Passes through the point (-95, 31).
When [tex]x = -95, y = 31[/tex]
[tex]y = ax + b[/tex]
[tex]31 = -95a + b[/tex]
Passes through the point (-94, 6).
When [tex]x = -94, y = 6[/tex]
[tex]y = ax + b[/tex]
[tex]6 = -94a + b[/tex]
We have to solve the following system:
[tex]31 = -95a + b[/tex]
[tex]6 = -94a + b[/tex]
We want to find a.
From the first equation
[tex]b = 31 + 95a[/tex]
Replacing in the second equation:
[tex]6 = -94a + 31 + 95a[/tex]
[tex]a = -25[/tex]
The slope of the line that passes through (-95, 31) and (-94, 6) is -25.
Tickets for the movies are $7 for adults and $4 for children. Fourteen people paid a total of $68 for tickets. How many were adults and how many were children?
Answers
7a+4c=68
sincr it was 14 ppl,
let a+c=14
so, system of equations.
multiply a+c= 14 all by 4 to get
4a+4c=56 subtract this from the other
7a+4c=68
-3a=-12
a=4
plug in to either. for a
4+c=14
c=10
plug into other equation to check.
7(4)+4(10)=68
28+40=68
For any value of n, list the numbers ln, rn, mn, tn and i in increasing order. (enter your answers as a comma-separated list. enter your answer using the variables rather than numerical values.)
Answers
The correct order is [tex]l_n,\ m_n,\ t_n,\ r_n,\ i[/tex].
To list the values ln, rn, mn, tn and i in increasing order for any value of n, we need to understand the relationship between these variables.
The variables ln, rn, mn, and tn likely represent different measures, such as left endpoint, right endpoint, midpoint, and trapezoid point in numerical methods, while i often represents the imaginary unit iota in mathematics.
Commonly, if we assume these have increasing values when ordered, they would be listed as:
[tex]l_n[/tex][tex]m_n[/tex][tex]t_n[/tex][tex]r_n[/tex]iTherefore, the values in increasing order are:
[tex]l_n,\ m_n,\ t_n,\ r_n,\ i[/tex]
Using the zero product property to find the solutions to the equation x^2-9=16
Answers
Answer:
x=-5, 5
Step-by-step explanation:
To find the solutions, use inverse operations to rearrange the equation to be equal to 0.
[tex]x^2-9-16=16-16\\x^2-25=0[/tex]
Factor the equation and then set each equal to 0 to solve for x.
[tex]x^2-25=0\\(x+5)(x-5)=0[/tex]
x+5=0
x=-5
x-5=0
x=5
What is the volume of a right circular cylinder with a radius of 3in and a height of 10in
Answers
Answer:
282.6 inches cubed
Step-by-step explanation:
The volume of the cylinder with radius 3 in and height 10 in is
[tex]V=\pi (3^2)(10)= \pi (9)(10)= 90\pi = 90(3.14) = 282.6 in^3[/tex]
Answer:
90 in3
Step-by-step explanation:
A company sells brass and steel machine parts.One shipment contains 3 brass and 10 steel parts and costs $48. A second shipment contains 7 brass and 4 steel parts and costs $54. Find the cost of each type of machine part.
Answers
x--------------> brass cost
y--------------> steel cost
we know that
3x+10y=48
7x+4y=54 -------------------> multiply by -3/7----------> -3x-(12/7)y=-162/7
3x+10y=48
-3x-(12/7)y=-162/7
---------------------------
0x+8.29y=24.86-------------> y=3
3x+10y=48------> 3x+10*3=48----------> x=(48-30)/3=6
the answer is
brass machine parts cost $6
steel machine parts cost $ 3
A fourth as much as the product of two thirds and 0.8
Answers
The product of is the answer to a multiplication problem, so it would be 2/3 x 0.8. One fourth of this means that we are finding that part of the answer. To show this we would multiply 1/4 by that answer. Please see the attached picture for the written out problem and the work. The answer is 2/15.
A fourth as much as the product of two thirds and 0.8 is ²/₁₅
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
First, we will translate this word problem into a mathematical equation.
The product of two thirds and 0.8
[tex]\frac{2}{3} \times 0.8[/tex]
A fourth as much as the product of two thirds and 0.8
[tex]\frac{1}{4} (\frac{2}{3} \times 0.8)[/tex]
[tex]= \frac{1}{4} (\frac{2}{3} \times \frac{4}{5})[/tex]
[tex]= \frac{1}{4} (\frac{2 \times 4}{3 \times 5})[/tex]
[tex]= \frac{1}{4} (\frac{8}{15})[/tex]
[tex]= \frac{1}{4} \times \frac{8}{15}[/tex]
[tex]= \frac{1 \times 8}{4 \times 15}[/tex]
[tex]= \frac{8}{60}[/tex]
[tex]= \frac{8 \div 4}{60 \div 4}[/tex]
[tex]= \boxed {\frac{2}{15}}[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
NEED HELP ASAP What is the simplified form of the following expression? 4 sqrt 3/2x Assume x>0
Answers
Answer:
[tex]\frac{4\sqrt{6x}}{2x}[/tex]
Explanation:
The problem we are given is
[tex]4\sqrt{\frac{3}{2x}}[/tex]
We can write the square root of a fraction as a fraction with a separate radical for the numerator and denominator; this gives us
[tex]4\times \frac{\sqrt{3}}{\sqrt{2x}}[/tex]
We can write the whole number 4 as the fraction 4/1; this gives us
[tex]\frac{4}{1}\times \frac{\sqrt{3}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}}{\sqrt{2x}}[/tex]
We now need to "rationalize the denominator." This means we need to cancel the square root in the denominator. In order to do this, we multiply both numerator and denominator by √(2x); this is because squaring a square root will cancel it:
[tex]\frac{4\sqrt{3}}{\sqrt{2x}}\times \frac{\sqrt{2x}}{\sqrt{2x}}\\\\=\frac{4\sqrt{3}\times \sqrt{2x}}{2x}[/tex]
When multiplying radicals, we can extend the radical over both factors:
[tex]\frac{4\sqrt{3} \times \sqrt{2x}}{2x}\\\\=\frac{4\sqrt{3\times 2x}}{2x}\\\\=\frac{4\sqrt{6x}}{2x}[/tex]
Answer:
The correct answer is ^4sqrt24x^3/2x or B on edge.
Step-by-step explanation:
Mike drew a quadrilateral with four right angles. What shape could be drawn?
Answers
A rectangle, or a square.
All of their angles are 90° angles, which are right angles.
Hope this helped!
A university is trying to determine what price to charge for tickets to football games. At a price of $18 per ticket, attendance averages 40,000 people per game. Every decrease of $3 adds 10,000 people to the average number. Every person at the game spends an average of $4.50 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?
Answers
Final answer:
To maximize revenue from football game ticket sales and concessions, we create a revenue function based on ticket price adjustments and evaluate changes in quantity demanded. The optimal price and attendance are found by analyzing the combined revenue function, deriving it with respect to the number of price decreases, and finding the maximum value of this function.
Explanation:
To determine the ticket price that should be charged by the university to maximize revenue from football game attendance, we need to analyze the effect of price changes on the quantity demanded. We can create a revenue function based on the given figures and the assumptions that a decrease of $3 in ticket price increases attendance by 10,000 people, and each person spends an average of $4.50 on concessions.
Let x represent the number of $3 decreases in price from the original $18. The ticket price can then be expressed as P = 18 - 3x, and attendance as A = 40000 + 10000x. The revenue from ticket sales is R1 = P × A, which gives us R1 = (18 - 3x) × (40000 + 10000x). The concession revenue per person is $4.50, so total concession revenue is R2 = 4.50 × A, which gives us R2 = 4.50 × (40000 + 10000x).
To maximize total revenue R = R1 + R2, we need to find the maximum of the function R = (18 - 3x) × (40000 + 10000x) + 4.50 × (40000 + 10000x). To find this, we can use calculus to take the derivative of R with respect to x and find the value of x that makes this derivative zero. This will be the critical point which we can then test to confirm it provides a maximum.
6. Alice and Alma have to fill a workbook. Alice has already completed 3 pages and can do 7 pages per hour. Alma has completed 11 pages, but can only work at a rate of 3 pages per hour. Eventually Alice will catch up and the two will be working on the same page. How long will that take? How many pages will each of them have finished?
Answers
Since Alice can do 7 pages per hour, we can represent this part of the equation as 7p. She has already completed 3 pages, so we just add the 3 to the 7p:
7p + 3
Since Alma can do 3 pages per hour, we can represent this part of the equation as 3p. She has already completed 11 pages, so we just add 11 to the 3p:
3p + 11
To determine when both girls will have written the same amount of pages, we set the two equations equal to each other:
7p + 3 = 3p + 11
Then, we solve for p. First, the variables must be on the same side of the equation. We can do this by subtracting 3p from both sides of the equation:
4p + 3 = 11
Next, we must get p by itself. We work towards this by subtracting 3 from both sides of the equation:
4p = 8
Last, we divide both sides by 4. So p = 2.
This means that it will take 2 hours for Alice and Alma to have read the same amount of pages. If we want to know how many pages they will have read, we simply plug the 2 back into each equation:
7p + 3
= 7 ( 2 ) + 3
= 14 + 3
= 17
3p + 11
= 3 ( 2 ) + 11
= 6 +11
= 17
After 2 hours, Alice and Alma will have read the same amount of pages: 17 pages.
Donte simplified the expression below. mc024-1.jpg What mistake did Donte make? He did not apply the distributive property correctly for 4(1 + 3i). He did not distribute the subtraction sign correctly for 8 – 5i. He added the real number and coefficient of i in 4(1 + 3i). He added the two complex numbers instead of subtracted.
Answers
4(1 + 3i) – (8 – 5i) = –4 + 8i
And the set of options are:
What mistake did Donte make?
A.He did not apply the distributive property correctly for 4(1 + 3i).
B.He did not distribute the subtraction sign correctly for 8 – 5i.
C.He added the real number and coefficient of i in 4(1 + 3i).
D.He added the two complex numbers instead of subtracted.
Answer: option A: he did not apply the distributive property correctly for 4(1 + 3i)
Explanation:
The correct application leads to: 4*1 + 4*3i = 4 + 12i
If you, incorrectly, make 4*1 + 3i, then you get 4 + 3i, and when you subtract (8 - 5i) you get:
4 + 3i - (8 - 5i) = 4 + 3i - 8 + 5i = - 4 + 8i which is what Donte obtained..
Therefore, he applied the distrituvie property incorrectly for 4(1 + 3i)
^4sqrt6/^5sqrt6 I don't have square root signs
Answers
[tex] = \dfrac{ 6^{\frac{1}{4}} }{ 6^{\frac{1}{5}} } [/tex]
[tex] = 6^{\frac{1}{4} - \frac{1}{5}} [/tex]
[tex] = 6^{\frac{5}{20} - \frac{4}{20}} [/tex]
[tex] = 6^{\frac{1}{20}} [/tex]
[tex] = \sqrt[20]{6} [/tex]
Answer:
6^1/20
Step-by-step explanation:
you multiply the two exponents
in fifteen minutes greg sailboat went 3/6 miles, gina sailboat went 6/6 miles, and stuart sailboat went 4/6 miles. whose sailboat went the longest distance in fifteen minutes?
Answers
Find the quadratic function whose zeros are 2 and -2 and has maximum value
Answers
y = - a * (x - 2)(x + 2)
y = - a * (x^2 - 4)
a > 0 meaning that a must have a value greater than 0.
• Given the function, f(x) = x3 – 5x2 + 9x – 45, determine the number of roots and identify them.
Answers
Final answer:
The given function f(x) = x3 – 5x2 + 9x – 45 has rational roots ±1, ±3, ±5, and ±9.
Explanation:
To determine the number of roots and identify them for the function f(x) = x3 – 5x2 + 9x – 45, we can use the Rational Root Theorem and synthetic division. The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation, then p must divide the constant term (in this case, 45) and q must divide the leading coefficient (in this case, 1). By trying all possible combinations of p and q, we can find the rational roots of the equation. In this case, the rational roots are ±1, ±3, ±5, and ±9.
The number of real roots is 1, and it is ( x = 5 ).
To determine the number of roots and identify them for the function[tex]\( f(x) = x^3 - 5x^2 + 9x - 45 \)[/tex], we can use various methods such as the Rational Root Theorem, Descartes' Rule of Signs, or graphing techniques. In this case, since the degree of the polynomial is 3, we know that there will be 3 roots in total.
We'll start by checking for rational roots using the Rational Root Theorem. According to this theorem, if a rational root [tex]\( \frac{p}{q} \)[/tex] exists for the polynomial [tex]\( f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 \), then \( p \)[/tex] is a factor of the constant term [tex]\( a_0 \) and \( q \)[/tex] is a factor of the leading coefficient [tex]\( a_n \)[/tex].
The constant term of [tex]\( f(x) \) is \( -45 \)[/tex]and the leading coefficient is ( 1 ). The factors of ( -45 ) are [tex]\( \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 \)[/tex]. The factors of \( 1 \) are \( \pm 1 \)[tex]\( 1 \) are \( \pm 1 \)[/tex].
By trying all possible combinations of these factors, we can find the rational roots of the polynomial. We'll then use synthetic division or polynomial long division to check if these roots are actually roots of the polynomial.
Let's proceed with the calculations:
1. Possible rational roots:
[tex]\( \pm 1, \pm 3, \pm 5, \pm 9, \pm 15, \pm 45 \)[/tex]
2. Testing these roots using synthetic division or polynomial long division:
Testing [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = (1)^3 - 5(1)^2 + 9(1) - 45 = 1 - 5 + 9 - 45 = -40 \][/tex]
Testing [tex]\( x = -1 \)[/tex]:
[tex]\[ f(-1) = (-1)^3 - 5(-1)^2 + 9(-1) - 45 = -1 - 5 - 9 - 45 = -60 \][/tex]
Testing [tex]\( x = 3 \)[/tex]:
[tex]\[ f(3) = (3)^3 - 5(3)^2 + 9(3) - 45 = 27 - 45 + 27 - 45 = -36 \][/tex]
Testing [tex]\( x = -3 \)[/tex]:
[tex]\[ f(-3) = (-3)^3 - 5(-3)^2 + 9(-3) - 45 = -27 - 45 - 27 - 45 = -144 \][/tex]
Testing ( x = 5 ):
[tex]\[ f(5) = (5)^3 - 5(5)^2 + 9(5) - 45 = 125 - 125 + 45 - 45 = 0 \][/tex]
[tex]\[ \Rightarrow \text{Root: } x = 5 \][/tex]
Testing ( x = -5 ):
[tex]\[ f(-5) = (-5)^3 - 5(-5)^2 + 9(-5) - 45 = -125 - 125 - 45 - 45 = -340 \][/tex]
Testing ( x = 9 ):
[tex]\[ f(9) = (9)^3 - 5(9)^2 + 9(9) - 45 = 729 - 405 + 81 - 45 = 360 \][/tex]
Testing ( x = -9 ):
[tex]\[ f(-9) = (-9)^3 - 5(-9)^2 + 9(-9) - 45 = -729 - 405 - 81 - 45 = -1260 \][/tex]
Testing ( x = 15 ):
[tex]\[ f(15) = (15)^3 - 5(15)^2 + 9(15) - 45 = 3375 - 1125 + 135 - 45 = 2340 \][/tex]
Testing ( x = -15 ):
[tex]\[ f(-15) = (-15)^3 - 5(-15)^2 + 9(-15) - 45 = -3375 - 1125 - 135 - 45 = -4680 \][/tex]
Testing ( x = 45 ):
[tex]\[ f(45) = (45)^3 - 5(45)^2 + 9(45) - 45 = 91125 - 10125 + 405 - 45 = 81060 \][/tex]
Testing ( x = -45 ):
[tex]\[ f(-45) = (-45)^3 - 5(-45)^2 + 9(-45) - 45 = -91125 - 10125 - 405 - 45 = -102705 \][/tex]
From these tests, we see that ( x = 5 ) is a root of the polynomial. The other roots are irrational or complex.
So, the number of real roots is 1, and it is ( x = 5 ).
8 oz of apple juice contains 0.9 milligrams of iron if the RDA for iron is 15 mg what percent of RDA of iron is provided by the apple juice
Answers
The 8 oz serving of apple juice provides 6% of the RDA of iron.
Alina has a spinner that has 5 equal sections: red, blue, green, purple, and orange. She spins the spinner 200 times. About how many times should Alina expect the spinner to land on either purple or orange?
Answers
Answer:
HI!
Your spinner has 5 colors, and if you spin it, the probability of landing in each color will be the same ( because the spiner has 5 equal sections).
So for every spin, the probability on landing on each color will be 20%.
If i spin it 200 times, then the 20% of 200 is 0.2*200 = 40.
It means that if you spin it 200 times, then each colour shows 40 times theoretically. The question is: how many times should Alina expect the spinner to land on either purple or orange?
you have 40 for purple and 40 for orange, then the total times that the spinner lands on either purple or orange is 80.