Answer:
The fourth root is 3
If the 4th root is not a real therefore it must be a complex number (a+ib),and its conjugate will be also a root ,therefore there would be 5 roots instead of 4 roots.
Therefore the fourth root is real.
The roots are -1 with multiplicity 2 and 3 with multiplicity 2
Therefore it has four roots
Step-by-step explanation:
Given polynomial equation is [tex]X^4-4X^3-2X^2+12X+9=0[/tex]
And also given that 3,-1 and -1 are the roots of the given polynomial equation
To find the fourth root of the polynomial equation and to solve the fourth root is real :
By synthetic division
_3| 1 -4 -2 12 9
0 3 -3 -15 -9
___________________
_-1| 1 -1 -5 -3 0
0 -1 2 3
___________________
1 -2 -3 0
Therefore x-3 and x+1 is a factor
Therefore 3 and -1 are roots
Now we have the quadratic equation [tex]x^2-2x-3=0[/tex]
[tex](x+1)(x-3)=0[/tex]
Therefore x=-1,3 are the roots
Therefore the fourth root is 3
If the 4th root is not a real therefore it must be a complex number (a+ib),and its conjugate will be also a root ,therefore there would be 5 roots instead of 4 roots.
Therefore the fourth root is real.
The roots are -1 with multiplicity 2 and 3 with multiplicity 2
Therefore it has four roots.
Final answer:
The fourth root of the polynomial equation X⁴-4X³-2X²+12X+9=0 must be real because a polynomial of degree n has n roots, and since we already have real roots, the remaining root must also be real to have a pair. Upon analyzing, the fourth root is found to be 3.
Explanation:
The student has provided three roots of the fourth-degree polynomial equation X⁴-4X³-2X²+12X+9=0: 3, -1, and -1 (the latter being a repeated root). To determine why the fourth root must also be a real number, we can invoke the fundamental theorem of algebra, which states that a polynomial of degree n will have exactly n roots in the complex number system (including real and complex roots). Given that a polynomial with real coefficients will have complex roots that come in conjugate pairs, and since the known roots are all real, the unknown fourth root must also be real to satisfy the theorem.
Let's find the fourth root. The polynomial can be factored using the known roots:
(X-3) - Factor for root 3(X+1)² - Factor for the repeated root -1Therefore, we have the equation (X-3)(X+1)²(X-a)=0, where 'a' is the unknown root. The product of the roots taken one at a time equals the constant term (9) of the polynomial with an alternate sign. This gives us the equation: 3 × -1 × -1 × a = 9. Solving for 'a' yields a=3, which is the fourth root.
Roxanne is planning to enclose her right triangular shaped garden with a fence. How many
feet of fencing does she need to enclose her entire garden if the length of her garden
measures 19 feet and the hypotenuse of her garden measures 33 feet? Round your answer to
the nearest tenth of a foot.
**Remember... to find the perimeter of an object, you must ADD the lengths of all sides.
Answer:
The perimeter of Roxanne's right triangular garden is 79 feet.
Step-by-step explanation:
Given,
Length of 1 side = 19 feet
Hypotenuse = 33 feet
We have to find out the perimeter of the triangular garden.
Solution,
Since the garden is in shape of right triangle.
So we apply the Pythagoras theorem to find the third side.
"In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides".
So framing in equation form, we get;
[tex]33^2=19^2+(third\ side)^2\\\\1089=361+(third\ side)^2\\\\(third\ side)^2=1089-361\\\\(third\ side)^2=728[/tex]
Now taking square root on both side, we get;
[tex]\sqrt{(third\ side)^2} =\sqrt{728} \\\\third\ side=26.98\approx27\ ft[/tex]
Now we know that the perimeter is equal to sum of all the three side of a triangle.
Perimeter = [tex]19+27+33=79\ ft[/tex]
Hence The perimeter of Roxanne's right triangular garden is 79 feet.
Some number was divided by 6.After which the quotient is added to 11. Next the sum is multiplied by 6 which resulted in 60. Given this product find the initial number.
Answer:
-6
Step-by-step explanation:
am i correct on this equation??
-- need honest answers!!! --
Unfortunately you are incorrect. The answer is actually tan(y) = 20/21
The tangent of an angle is the ratio of the opposite and adjacent sides.
tan(angle) = opposite/adjacent
tan(K) = JL/LK
tan(y) = 20/21
----------------------
Side note: the tangent of angle x would be the reciprocal of this fraction since the opposite and adjacent sides swap when we move to angle J
tan(angle) = opposite/adjacent
tan(J) = LK/JL
tan(x) = 21/20
A, B, and C are collinear, and B is between A and C. The ratio of AB to AC is 4:5. If A is at (-3,7) and B is at (1,-5), what are the coordinates of point C?
Answer:
Step-by-step explanation:
AB:AC=4:5
AB:BC=4:5-4 OR 4:1
So B divides AC in the ratio 4:1
Mrs Klein made fruit buns. She sold 3/5 of it in morning and 1/4 in the afternoon. If she sold 200 more buns in the morning than afternoon, how many buns did she make?
Answer:
The total number of buns Mrs Klein made = 400
Step-by-step explanation:
Question
Mrs Klein made fruit buns. She sold 3/5 of it in morning and 1/4 of the remaining in the afternoon. If she sold 200 more buns in the morning than afternoon, how many buns did she make?
Given:
Mrs Klein sold [tex]\frac{3}{5}[/tex] of the buns in the morning.
Mrs Klein sold [tex]\frac{1}{4}[/tex] of the remaining buns in the evening.
She sold 200 more buns in the morning than afternoon.
To find the total number of buns she make.
Solution:
Let the total number of buns be = [tex]x[/tex]
Number of buns sold in the morning will be given as = [tex]\frac{3}{5}x[/tex]
Number of buns remaining = [tex]x-\frac{3}{5}x[/tex]
Number of buns sold in the evening will be given as = [tex]\frac{1}{4}(x-\frac{3}{5}x)[/tex]
Difference between the number of buns sold in morning and evening = 200
Thus, the equation to find [tex]x[/tex] can be given as:
[tex]\frac{3}{5}x-\frac{1}{4}(x-\frac{3}{5}x)=200[/tex]
Using distribution:
[tex]\frac{3}{5}x-\frac{1}{4}x+(\frac{1}{4}.\frac{3}{5}x)=200[/tex]
[tex]\frac{3}{5}x-\frac{1}{4}x+\frac{3}{20}x=200[/tex]
Multiplying each term with the least common multiple of the denominators to remove fractions.
The L.C.M. of 4, 5 and 20 = 20.
Multiplying each term with 20.
[tex]20\times \frac{3}{5}x-20\times\frac{1}{4}x+20\times\frac{3}{20}x=20\times 200[/tex]
[tex]12x-5x+3x=4000[/tex]
[tex]10x=400[/tex]
Dividing both sides by 10.
[tex]\frac{10x}{10}=\frac{4000}{10}[/tex]
∴ [tex]x=400[/tex]
Thus, total number of buns Mrs Klein made = 400
A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Upper H 0: p less than or equals 0.6 Upper H Subscript a: p greater than 0.6 What type of test is being conducted in this problem?
Answer: right-tailed
Step-by-step explanation:
By considering the given information , we have
Null hypothesis : [tex]H_0: p\leq0.6[/tex]
Alternative hypothesis : [tex]H_a: p>0.6[/tex]
The kind of test (whether left-tailed, right-tailed, or two-tailed.) is based on alternative hypothesis.
Since the given alternative hypothesis([tex]H_a[/tex]) is right-tailed , so out test is a right-tailed test.
Hence, the correct answer is "right-tailed".
I have 200 coins to put into 4 bags I put the coins into each bag so that each bag has 2 mote coins than the one before How many coins are on each bag
First bag has 47 coins and second bag has 49 coins and third bag has 51 coins and fourth bag has 53 coins
Solution:
Given that,
Total number of coins = 200
Number of bags = 4
I put the coins into each bag so that each bag has 2 more coins than the one before
Therefore,
Each bag has 2 more coins than the one before. Based on this we can say,
Let "x" be the number of coins put in first bag
Then, x + 2 is the number of coins put in second bag
Then, x + 4 is the number of coins put in third bag
Then, x + 6 is the number of coins put in fourth bag
We know that,
Total number of coins = 200
[tex]x + x + 2 + x + 4 + x + 6 = 200\\\\4x + 12 = 200\\\\4x = 200-12\\\\4x = 188\\\\x = 47[/tex]
Thus,
Coins put in first bag = x = 47
Coins put in second bag = x + 2 = 47 + 2 = 49
Coins put in third bag = x + 4 = 47 + 4 = 51
Coins put in fourth bag = x + 6 = 47 + 6 = 53
Thus number of coins in each bag are found
Final answer:
By setting up an algebraic equation to distribute 200 coins into 4 bags with each bag having 2 more coins than the previous one, we find the number of coins in each bag are 47, 49, 51, and 53, respectively.
Explanation:
The question involves distributing 200 coins into 4 bags so that each subsequent bag has 2 more coins than the previous one. To find out how many coins are in each bag, let's denote the number of coins in the first bag as x. Consequently, the second bag would have x + 2 coins, the third bag x + 4 coins, and the fourth bag x + 6 coins. The total number of coins across all bags would be x + (x + 2) + (x + 4) + (x + 6) = 200.
Simplifying the equation, we get 4x + 12 = 200, which simplifies further to 4x = 188. Dividing both sides by 4 yields x = 47. Therefore, the number of coins in each bag, starting from the first to the fourth, are 47, 49, 51, and 53, respectively.
If z=3−5i, find |z|.
Answer:
Step-by-step explanation:
The absolute value of z is the distance between the point graphed from the complex number and the origin on a complex plane. In a complex plane, the x axis is replaced by R, real numbers, and the y axis is replaced by i, the complex part of the complex number. Our real number is positive 3 and the complex number is -5, so we go to the right 3 and then down 5 and make a point. Connect that point to the origin and then connect the point to the x axis at 3 to construct a right triangle that has a base of 3 and a length of -5. To find the distance of the point to the origin is to find the length of the hypotenuse of that right triangle using Pythagorean's Theorem. Therefore:
[tex]|z|=\sqrt{(3)^2+(-5)^2}[/tex] and
[tex]|z|=\sqrt{9+25}[/tex] and
[tex]|z|=\sqrt{34}[/tex]
Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if a + d = b + c. Show that R is an equivalence relation.
Answer:
Therefore, we conclude that R is an equivalence relation.
Step-by-step explanation:
We know that a relation on a set is called an equivalence relation if it is reflexive, symmetric, and transitive.
R is refleksive because we have that a+b = a+b.
R is symmetric because we have that a+d =b+c equivalent with b+c =a+d.
R is transitive because we have that:
((a, b), (c, d)) ∈ R ; ((c, d), (e, f)) ∈ R
a+d =b+c ⇒ a-b=c-d
c+f =d+e ⇒ c-d =e-f
we get
a-b=e-f ⇒ a+f=b+e ⇒((a, b), (e, f)) ∈ R.
Therefore, we conclude that R is an equivalence relation.
The solution set of a linear system whose augmented matrix is [a b c d] is the same as the solution set of Ax = d, where A = [a b c]. Note: a, b, c, d are all column vectors.True/false
Answer:
True
Step-by-step explanation:
First statement
[a b c | d][x]
[a b c]x=d
ax+bx+cx=d
Second statement
Ax=d
Given that A = [a b c]
[a b c]x=d
ax+bx+cx=d
ax+bx+cx=d
Then, they are going to have the same solutions
The statement is false. The solution sets for the augmented matrix [a, b, c, d] and the matrix equation Ax = d (where A = [a, b, c]) are not the same unless 'd' is consistently a column vector with 'a', 'b', 'c'.
Explanation:The statement presented in the question is false. When we talk about a linear system, an augmented matrix generally pairs a coefficient matrix with an answer matrix. This would look like [A|d], where 'A' would be a matrix, and 'd' is the constants column vector.
Conversely, Ax = d is a matrix equation where 'A' is again the coefficient matrix, 'x' is the variable matrix, and 'd' is the constants column vector.
In your provided augmented matrix, [a b c d], unless 'd' is a consistent column vector with the other column vectors, it can't be virtually the same as the matrix system Ax = d where A = [a b c] because the augmented matrix [a b c d] would mean that A = [a b c] and d = [d].
Unless 'd' is mathematically consistent with the column vectors 'a', 'b', and 'c', the solution sets would not be the same.
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*50 POINTS -- FRESHMEN ~ ALGEBRA I *
Large boxes weigh 75 pounds, and small boxes weigh 40 pounds.
a. Write an inequality that represents the numbers of large, x, and small, y, boxes a 200-pound delivery person can take on the elevator.
b. Select the reason(s) why some solutions of the inequality might not be practical in real life.
>The number of boxes must be a whole number.
>The number of boxes must be a rational number.
>It is unlikely that one person will carry 20 large boxes.
>It is unlikely that one person will carry 45 small boxes.
For a, I got 75x + 40y ≤ 200 --- I got it wrong but I'm not sure why?
The maximum weight of boxes that can be placed into the elevator is:
[tex]\to 2000 - 200 = 1800 \ lbs[/tex]
(the load limit is the weight of a delivery person). Small crates weigh 40 pounds, whereas large boxes weigh 75 pounds.As a result, [tex]40X + 75Y = 1800[/tex].It should be noted that Y must be an even integer for the equivalence to hold, whereas X might be odd or even because 40X is always even.
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The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming the distribution of commuting times is known to be mound-shaped and symmetric, what percentage of these commuting times are between 50 and 110 minutes?
Answer:
81.85% of the workers spend between 50 and 110 commuting to work
Step-by-step explanation:
We can assume that the distribution is Normal (or approximately Normal) because we know that it is symmetric and mound-shaped.
We call X the time spend from one worker; X has distribution N(μ = 70, σ = 20). In order to make computations, we take W, the standarization of X, whose distribution is N(0,1)
[tex] W = \frac{X-μ}{σ} = \frac{X-70}{20} [/tex]
The values of the cummulative distribution function of the standard normal, which we denote [tex] \phi [/tex] , are tabulated. You can find those values in the attached file.
[tex]P(50 < X < 110) = P(\frac{50-70}{20} < \frac{X-70}{20} < \frac{110-70}{20}) = P(-1 < W < 2) = \\\phi(2) - \phi(-1)[/tex]
Using the symmetry of the Normal density function, we have that [tex] \phi(-1) = 1-\phi(1) [/tex] . Hece,
[tex]P(50 < X < 110) = \phi(2) - \phi(-1) = \phi(2) - (1-\phi(1)) = \phi(2) + \phi(1) - 1 = \\0.9772+0.8413-1 = 0.8185[/tex]
The probability for a worker to spend that time commuting is 0.8185. We conclude that 81.85% of the workers spend between 50 and 110 commuting to work.
Roger is having a picnic for 78guests. He plans to serve each guest at least one hot dog. If each package, p, contains eight hot dogs, which inequality could be used to determine the number of packages of hot dogs roger must buy?
Question is Incomplete; Complete question is given below;
Roger is having a picnic for 78 guests. He plans to serve each guest at least one hot dog. If each package, p, contains eight hot dogs, which inequality could be used to determine how many packages of hot dogs Roger will need to buy?
1) [tex]p \geq 78[/tex]
2) [tex]8p \geq 78[/tex]
3) [tex]8 +p \geq 78[/tex]
4) [tex]78 + p \geq 8[/tex]
Answer:
2) [tex]8p \geq 78[/tex]
Step-by-step explanation:
Given:
Number of guest in the picnic = 78 guest
Number of hot dog each guest will have = 1
Number of hot dogs in each package = 8 hot dogs.
We need to write the In equality used to determine the number of packages of hot dogs roger must buy
Solution:
Let the number of packages be 'p'.
First we will find the total number of hot dogs required.
so we can say that;
total number of hot dogs required is equal Number of guest in the picnic multiplied by Number of hot dog each guest will have.
framing in equation form we get;
total number of hot dogs required = [tex]78\times 1 =78[/tex]
Now we can say that;
Number of hot dogs in each package multiplied by number of packages should be greater than or equal to total number of hot dogs required.
framing in equation form we get;
[tex]8p\geq 78[/tex]
Hence The In equality used to determine the number of packages of hot dogs roger must buy is [tex]8p\geq 78[/tex].
A college faculty consists of 400 men and 250 women. The college administration wants to draw a sample of 65 faculty members to ask their opinion about a new parking fee. They draw a simple random sample of 40 men and another simple random sample of 25 women. What type of sample is this?
Answer:
The type of sample is Stratified sampling.
Step-by-step explanation:
Consider the provided information.
Types of sampling.
Random sampling is similar to placing the name of everyone in a hat and pulling out a few names.In Systematic sampling, we list of elements is counted off. Convenience sampling: data which is readily available is used. That is, the first people are running into by the surveyor.In Cluster sampling, we divide the population into groups, usually geographically. In Stratified sampling we divide population into groups called strata. but this time population might be separated into males and females.Here the population is divided into groups of males and females therefore it is stratified sampling.
Hence, the type of sample is Stratified sampling.
If there is no relationship (linear or otherwise) between two quantitative variables as observed on a scatterplot, the value of the correlation coefficient, r, is likely to be which of the following?1. Closer to 12. Closer to −13. Closer to 04. Either closer to −1 or 1
Answer:
Option 3) Closer to 0
Step-by-step explanation:
Correlation:
Correlation is a technique that help us to find or define a relationship between two variables. A positive correlation means that an increase in one quantity leads to an increase in another quantity A negative correlation means with increase in one quantity the other quantity decreases. Range of CorrelationValues between 0 and 0.3 tells about a weak positive linear relationship, values between 0.3 and 0.7 shows a moderate positive correlation and a correlation of 0.7 and 1.0 states a strong positive linear relationship.
Values between 0 and -0.3 tells about a weak negative linear relationship, values between -0.3 and -0.7 shows a moderate negative correlation and a correlation value of of -0.7 and -1.0 states a strong negative linear relationship.
A value of 0 tells that there is no correlation between the two variables.Thus, for the given situation, if there is no relationship between two quantitative variables then the value of the correlation coefficient, r, is close to 0
WILL GIVE BRAINLIEST PLS ANSWER
/Given: ABCD is a rhombus, m∠A = 70°
Find: (AREA OF CIRCLE) / (AREA OF RHOMBUS)
Answer:
Step-by-step explanation:
Check the attachment the solution of the work is given there
Answer: 0.74
Step-by-step explanation:
Let h = rhombus' height
Looking at the attachment, we see that the circle has an area of [tex]\pi *(\frac{h}{2}) ^{2}[/tex]
The rhombus has an area of [tex]\frac{h^2}{sin(70°)}[/tex]
because the base is [tex]\frac{b}{sin(90)} = \frac{h}{sin(70)}[/tex]
due to the law of sines
Thus, Area Circle / Area Rhombus is
[tex]\frac{(\pi(\frac{h}{2})^2)}{(\frac{h^2}{sin(70)}) } = 0.74[/tex]
(Score for Question 2: ___ of 6 points)
2. Solve each given equation and show your work. Tell whether it has one solution, an infinite number of
solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.
(c) 6x + 4x - 6 = 24 + 9x
(d) 25 - 4x = 15 - 3x + 10 - X
(e) 4x + 8 = 2x + 7 + 2x - 20
Answer:
Answer:
The answer to your question is below
Step-by-step explanation:
c) 6x + 4x - 6 = 24 + 9x
6x + 4x - 9x = 24 + 6
x = 30 This equation has one solution, it's an identity
d) 25 - 4x = 15 - 3x + 10 - x
-4x + 3x + x = 15 + 10 - 25
0 = 0 It has infinite number of solutions, it is an identity
e) 4x + 8 = 2x + 7 + 2x - 20
4x - 2x - 2x = 7 - 20 + 8
0 = -5 It has no solution it is a contradiction
Drag each expression to the box that describes the expression.
The drag force can be mathematically expressed as Fd = 0.5 × ρ × v^2 × A × Cd, where Fd is the drag force, ρ is the density of the fluid, v is the velocity of the object, A is the reference area, and Cd is the drag coefficient.
Explanation:The drag force can be mathematically expressed as:
Fd = 0.5 × ρ × v2 × A × Cd
Where:
Fd is the drag forceρ is the density of the fluidv is the velocity of the objectA is the reference areaCd is the drag coefficientLearn more about Drag force here:https://brainly.com/question/14748915
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Lilla read 1/5 of her book last week. This week she read 3 times as much as she read last week. a. Write an expression to show how much of her book Lilla has left to read. Then simplify the expression. _______________________________________________________ _______________________________________________________ b. There are 75 pages in Lilla's book. How many pages does she have left to read? Show your work. Solution:___________________________________________________
Answer: she has 30 pages left to read.
Step-by-step explanation:
Let x represent the total number of pages in the book which Lilla is reading.
Lilla read 1/5 of her book last week. This means that the number of pages that she read last week is
1/5 × x = x/5
This week she read 3 times as much as she read last week. This means that the number of pages that she read this week is
3 × x/5 = 3x/5
The number of pages that she has left to read would be
x - 3x/5
= (5x - 3x)/5 = 2x/5
b. There are 75 pages in Lilla's book. It means that the number of pages that she has left to read would be
(2 × 75)/5 = 150/5
= 30
Final answer:
Lilla read 4/5 of her book after two weeks and has 1/5, or 15 pages, left to read of her 75-page book.
Explanation:
Lilla read 1/5 of her book last week. This week she read 3 times as much as she read last week. To express how much of her book Lilla has left to read, let us denote the total amount of the book as 1 (or 100%).
a. The amount she read this week would be 3 times 1/5, which is 3/5. Thus, the total amount Lilla read over the two weeks is 1/5 + 3/5, which simplifies to 4/5 of the book. Therefore, the expression for the amount of the book Lilla has left to read is 1 - 4/5, which simplifies to 1/5 of the book.
b. Lilla's book has 75 pages. To find out how many pages she has left to read, we calculate 1/5 of 75. This is done by multiplying 75 by 1/5:
75 imes 1/5 = 75/5 = 15 pages
Therefore, Lilla has 15 pages left to read.
Define a function roll_hundred_pair() that produces a histogram of the results of 100 rolls of two 6-sided dice
Answer:
The code is attached. I used python to define the function and matplotlib library to plot the histogram.
Step-by-step explanation:
I defined a function called roll_hundred_pairI imported matplotlib.pyplot as plt and random I defined a list called diceI created an empty list to collect dice resultsI simulated 100 dice roll using a loop and random.sample finally I plot the histogram using plt.hist methodFind DC
HELP PLEASE!! :(
using sine cosine or tangent
DC=14
Explanation
consider triangle ADB
<BAD=54°
sin<BAD=opposite side/ hypotenuse
sin 54°=BD/BA
BD=BA sin 54°=20*0.8=16
consider triangle BDC
cos <BCD=adjacent side/hypotenuse
=DC/BC
cos 28°=DC/BC
DC=cos28° *BC
=0.88*16=14.08
A cardboard box manufacturing company is building boxes with length represented by x+ 1, width by 5- x, and height by x -1. The volume of the box is modeled by the function below V(x) 18 14 10 6 24 X 5 6 2 2 3 -2 -6 Over which interval is the volume of the box changing at the fastest average rate? [1,2] A. [1,3.5 B. C. [1,5] r0,3.51 D
Answer:
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
b. [1,3.5]
[tex] m =\frac{17-0}{3.5-1}=6.8[/tex]
c. [1,5]
[tex] m =\frac{0-0}{5-1}=0[/tex]
d. [0,3.5]
[tex] m =\frac{17-(-5)}{3.5-0}=6.29[/tex]
So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
Step-by-step explanation:
Assuming that we have the figure attached for the function. For this case we just need to quantify the slope given by:
[tex] m = \frac{\Delta y}{\Delta x}[/tex]
For each interval and the greatest slope would be the interval on which the volume of the box is changing at the fastest average rate
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
b. [1,3.5]
[tex] m =\frac{17-0}{3.5-1}=6.8[/tex]
c. [1,5]
[tex] m =\frac{0-0}{5-1}=0[/tex]
d. [0,3.5]
[tex] m =\frac{17-(-5)}{3.5-0}=6.29[/tex]
So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
The correct answer is A. [1,2].
To determine over which interval the volume of the box changes at the fastest average rate, we need to find the average rate of change of the volume function ( V(x) ) over the given intervals and compare them.
The volume ( V(x) ) of the box is given by:
[tex]\[ V(x) = (x + 1)(5 - x)(x - 1) \][/tex]
We first need to express ( V(x) ) in a simplified form. Let's expand the expression:
[tex]\[ V(x) = (x + 1)(5 - x)(x - 1) \]\[ V(x) = (x + 1)(x^2 - 6x + 5) \]\[ V(x) = x(x^2 - 6x + 5) + 1(x^2 - 6x + 5) \]\[ V(x) = x^3 - 6x^2 + 5x + x^2 - 6x + 5 \]\[ V(x) = x^3 - 5x^2 - x + 5 \][/tex]
Now, we calculate the average rate of change over each interval. The average rate of change of ( V(x) ) over an interval ([a, b]) is given by:
[tex]\[ \text{Average Rate of Change} = \frac{V(b) - V(a)}{b - a} \][/tex]
We need to compute this for each interval provided.
1. Interval [1, 2]:
[tex]\[ V(1) = (1 + 1)(5 - 1)(1 - 1) = 0 \]\[ V(2) = (2 + 1)(5 - 2)(2 - 1) = 3 \times 3 \times 1 = 9 \]\[ \text{Average Rate of Change} = \frac{V(2) - V(1)}{2 - 1} = \frac{9 - 0}{2 - 1} = 9 \][/tex]
2. Interval [1, 3.5]:
[tex]\[ V(1) = 0 \]\[ V(3.5) = (3.5 + 1)(5 - 3.5)(3.5 - 1) = 4.5 \times 1.5 \times 2.5 = 16.875 \]\[ \text{Average Rate of Change} = \frac{V(3.5) - V(1)}{3.5 - 1} = \frac{16.875 - 0}{3.5 - 1} = \frac{16.875}{2.5} = 6.75 \][/tex]
3. Interval [1, 5]:
[tex]\[ V(1) = 0 \]\[ V(5) = (5 + 1)(5 - 5)(5 - 1) = 6 \times 0 \times 4 = 0 \]\[ \text{Average Rate of Change} = \frac{V(5) - V(1)}{5 - 1} = \frac{0 - 0}{5 - 1} = 0 \][/tex]
4. Interval [0, 3.5]:
[tex]\[ V(0) = (0 + 1)(5 - 0)(0 - 1) = 1 \times 5 \times -1 = -5 \]\[ V(3.5) = 16.875 \]\[ \text{Average Rate of Change} = \frac{V(3.5) - V(0)}{3.5 - 0} = \frac{16.875 - (-5)}{3.5 - 0} = \frac{16.875 + 5}{3.5} = \frac{21.875}{3.5} \approx 6.25 \][/tex]
Comparing these average rates of change:
[tex]\([1, 2]\): 9\\ \([1, 3.5]\): 6.75\\ \([1, 5]\): 0\\ \([0, 3.5]\): 6.25[/tex]
The interval where the volume of the box is changing at the fastest average rate is [tex]\([1, 2]\)[/tex], with an average rate of change of 9.
Therefore, the correct answer is: A.[tex]\([1, 2]\)[/tex].
Complete question :
Can Anyone answer this equation??
It's pretty hard. And I don't get it whatsoever.
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The tangent of an angle is the ratio of the opposite over adjacent sides.
tan(angle) = opposite/adjacent
tan(theta) = 4/3
This means that
opposite = 4 and adjacent = 3
This only happens when angle P is the reference angle. In other words,
tan(P) = 4/3
A salesman packed 3 shirts and 5 ties. With one shirt, he could wear all 5 ties. With another shirt, he could wear 4 ties. With the third shirt, he could wear only 2 ties. How many different combinations did he have? a) 40 b) 22 c) 11 d) 10
Answer:
11 different combinations
Step-by-step explanation:
A salesman packed 3 shirts and 5 ties.
With one shirt, he could wear all 5 ties = 5 combinations
With another shirt, he could wear 4 ties = 4 combinations
With the third shirt, he could wear only 2 ties= 2 combinations
number of different combinations= [tex]5+4+2=11[/tex]
so answer is 11
A building was created from two stories. From a point 87 feet from the base of the building, the angle of elevation to the top of the first floor is 25° and the angle of elevation to the top of the second floor is 40°. To the nearest tenth of a foot, what is the height of the second floor?
- We´re gonna work with two separate triangles:
-The first one is the larger triangle (40º angle) and a vertical side that represents the ENTIRE height, b, of the tower.
Larger triangle with height b: tan 40°= [tex]\frac{b}{87}[/tex] ; .8390996312 = [tex]\frac{b}{87}[/tex]; b≈73.00166791
-The second one the smaller triangle (25º angle) and a vertical side, a, that represents the height of the first (bottom) section of the tower.
Smaller triangle with height a: tan 25°= [tex]\frac{a}{87}[/tex] ; ..4663076582 = [tex]\frac{a}{87}[/tex]; a≈40.56876626
-Then you need to solve for the vertical heights (b and a) in the two separate triangles.
-The needed height, x, of the second (top) section of the tower will be the difference between the ENTIRE height, b, and the height of the first (bottom) section, a. You will need to subtract.
In both triangles, the solution deals with "opposite" and "adjacent" making it a tangent problem.
Difference (b - a): 73.00166791 - 40.56876626 = 32.43290165 ≈ 32 feet
A local salesman receives a base salary of $925 monthly. He also receives a commission of 6% on all sales over $1700. How much would he have to sell in a month if he needed to have a monthly income of $2600?
Final answer:
To have a monthly income of $2600, the salesman needs to make total sales of $29,616.67, considering his base salary of $925 and a 6% commission for sales over $1700.
Explanation:
The question asks us to calculate how much a local salesman needs to sell to have a monthly income of $2600. The salesman receives a base salary of $925 and earns a commission of 6% for all sales over $1700.
To solve this, we need to figure out the total sales that would give the salesman an extra $1675 ($2600 total desired income minus the $925 base salary), knowing that he only gets a commission on the amount over $1700.
Let's denote the total amount in sales that the salesman needs to make as S.
The commission is only applied to the amount exceeding $1700, so the equation can be set up as follows:
0.06(S - $1700) = $1675. Solving this equation, we find that S - $1700 = $1675 / 0.06, which means S - $1700 = $27,916.67. Adding $1700 to both sides, we get S = $27916.67 + $1700, which equals $29,616.67.Therefore, the salesman would need to sell $29,616.67 worth of goods in a month to have a total monthly income of $2600.
The shape of France's production possibilities frontier (PPF) should reflect the fact that as France produces more cars and fewer trucks, the opportunity cost of producing each additional car?
Answer:
the opportunity cost of producing each additional car REMAINS CONSTANT
Marcelo had $49.13 in his bank account. He paid two fees of $32.50 each, and then he made two deposits of $74.25 each. What is the balance in dollars in Marcelo's account now?
Answer:
Current balance in Marcelo's account = $132.63
Step-by-step explanation:
Given:
Initial amount in Marcelo's bank account = $49.13
Amount paid in two fees = $32.50 each
Amount added by two deposits = $74.25 each
To find balance in dollars in Marcelo's account.
Solution:
Total amount paid in fees = [tex]2\times \$32.50=\$65[/tex]
Total amount deposited = [tex]2\times \$74.25=\$148.50[/tex]
The balance in Marcelo's account can be represented as:
⇒ Initial balance - Amount given in fees + Amount deposited
⇒ [tex]\$49.13-\$65+\$148.50[/tex]
⇒ [tex]\$132.63[/tex]
Thus, balance in Marcelo's account now = $132.63
Answer: 132.63
Step-by-step explanation:
I copied the other guy lol thanks for the points
In the context of the BCG (Boston Consulting Group) matrix, the _____ is a poor performer that has only a small share of a slow-growth market. a. cash cow b. question mark c. star d. dog
Answer:
d. dog
Step-by-step explanation:
The BCG matrix is a tool used to assess the performance of the products of an organization on the basis of market share and market growth.
Basically there are 4 classes of products namely; Star, cash cow, question mark and dog.
Dogs are product with low market share and low growth.
Question mark have high growth but low market share while cash cows are the products with high mark share but low growth.
Stars are products with high market share and high market growth.
Hence dog is a poor performer that has only a small share of a slow-growth market. Option d.
The average amount of a nutrient that is known to meet the needs of 50 percent of the individuals in a similar age and gender group is known as the?
Answer:
Estimated Average Requirement (EAR)
Step-by-step explanation:
The Estimated Average Requirement (EAR) is the average amount of daily intake value which is estimated to meet the needs of 50% of the healthy individuals.
The EAR is estimated on the basis of specific conditions of adequacy, and are derived from a careful study of the literature.
The major parameters which is selected for the criterion are reduction of disease risk.