Answer:
D
Step-by-step explanation:
y=a(1-r)^n
a is the initial cost of the vehicle
r is the percentage decrease in decimal
n is the number of years.
so y as the final cost is computed as:
8500(1-0.047)^6
we get $6367.61
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.
3x to the power of two minus x
Factor by gcf
Answer:
After factorizing the given expression we get the value as [tex]x(3x-1)[/tex].
Step-by-step explanation:
Given:
[tex]3x^2-x[/tex]
We need to factorize the given expression using GCF.
Solution:
[tex]3x^2-x[/tex]
Now GCF means Greatest common factor.
From the given 2 numbers we need to find the greatest common factor.
[tex]3\times x\times x- 1 \times x[/tex]
In the given expression GCF is 'x'.
Hence we can say that;
[tex]x(3x-1)[/tex]
Hence After factorizing the given expression we get the value as [tex]x(3x-1)[/tex].
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.
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 methodam 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
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
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.
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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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
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
Alton says that he can draw two triangles that are NOT congruent with two pairs of congruent corresponding angles and a congruent included side because he can extend the rays to meet somewhere other than point Q. Is he correct?
Answer:
No because if the Rays meet at a point other than Q the angles will change
Step-by-step explanation:
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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Can Anyone answer this equation??
It's pretty hard. And I don't get it whatsoever.
=======================================
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
In triangle ABC, A=25, c=55 and AB=60. What are the approximate measures of the remaining side lengths of the triangle?
Answer:
[tex]a\approx 31[/tex]
[tex]b\approx 72[/tex]
Step-by-step explanation:
Please find the attachment.
We have been given that in triangle ABC, A=25, C=55 and AB=60. We are asked to find the approximate measures of the remaining side lengths of the triangle.
We will use Law of Sines to solve for side lengths of given triangle.
[tex]\frac{\text{sin}(A)}{a}=\frac{\text{sin}(B)}{b}=\frac{\text{sin}(C)}{c}[/tex], where a, b and c are opposite sides corresponding to angles A, b and C respectively.
Upon substituting our given values, we will get:
[tex]\frac{\text{sin}(25)}{a}=\frac{\text{sin}(55)}{60}[/tex]
[tex]a=\frac{60\text{sin}(25)}{\text{sin}(55)}[/tex]
[tex]a=\frac{60*0.422618261741}{0.819152044289}[/tex]
[tex]a=\frac{25.35709570446}{0.819152044289}[/tex]
[tex]a=30.9552980807967304[/tex]
[tex]a\approx 31[/tex]
Therefore, the measure of side 'a' is approximately 31 units.
We can find measure of angle B using angle sum property as:
[tex]m\angle A+m\angle B+m\angle C=180[/tex]
[tex]25+m\angle B+55=180[/tex]
[tex]m\angle B+80=180[/tex]
[tex]m\angle B=100[/tex]
[tex]\frac{\text{sin}(100)}{b}=\frac{\text{sin}(55)}{60}[/tex]
[tex]b=\frac{60\text{sin}(100)}{\text{sin}(55)}[/tex]
[tex]b=\frac{60*0.984807753012}{0.819152044289}[/tex]
[tex]b=\frac{59.08846518072}{0.819152044289}[/tex]
[tex]b=72.1336967815383509[/tex]
[tex]b\approx 72[/tex]
Therefore, the measure of side 'b' is approximately 72 units.
A shop owner bought some shovels for $5,500. The shovels were sold for $7,300, with a profit of $50 per a shovel. How many shovels were involved?
A. 18.
B. 36.
C. 55.
D. 73.
E. 90.
F. None of these.
Answer:
B.
Step-by-step explanation:
Find the total profit.
P=7300-5500
P=1800
Since each shovel makes up 50 of the profit.
50N=1800
N=1800%2F50
N=36
36 shovels were sold.
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]
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:
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]
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.
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.
(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
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.
Right △ABC has its right angle at C, BC=4 , and AC=8 .
What is the value of the trigonometric ratio?
Drag a value to each box to match the trigonometric ratio.
Answer:
Therefore,
[tex]cos A=\dfrac{2\sqrt{5}}{5}[/tex]
[tex]\cot B =\dfrac{1}{2}[/tex]
[tex]\csc B = \dfrac{\sqrt{5}}{2}[/tex]
Step-by-step explanation:
Given:
Right △ABC has its right angle at C,
BC=4 , and AC=8 .
To Find:
Cos A = ?
Cot B = ?
Csc B = ?
Solution:
Right △ABC has its right angle at C, Then by Pythagoras theorem we have
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
Substituting the values we get
[tex](AB)^{2}=4^{2}+8^{2}=80\\AB=\sqrt{80}\\AB=4\sqrt{5}[/tex]
Now by Cosine identity
[tex]\cos A = \dfrac{\textrm{side adjacent to angle A}}{Hypotenuse}\\[/tex]
Substituting the values we get
[tex]\cos A = \dfrac{AC}{AB}=\dfrac{8}{4\sqrt{5}}=\dfrac{2}{\sqrt{5}}\\\\Ratinalizing\\\cos A=\dfrac{2\sqrt{5}}{5}[/tex]
[tex]cos A=\dfrac{2\sqrt{5}}{5}[/tex]
Now by Cot identity
[tex]\cot B = \dfrac{\textrm{side adjacent to angle B}}{\textrm{side opposite to angle B}}[/tex]
Substituting the values we get
[tex]\cot B = \dfrac{BC}{AC}=\dfrac{4}{8}=\dfrac{1}{2}[/tex]
Now by Cosec identity
[tex]\csc B = \dfrac{Hypotenuse}{\textrm{side opposite to angle B}}\\[/tex]
Substituting the values we get
[tex]\csc B = \dfrac{AB}{AC}=\dfrac{4\sqrt{5}}{8}=\dfrac{\sqrt{5}}{2}[/tex]
Therefore,
[tex]cos A=\dfrac{2\sqrt{5}}{5}[/tex]
[tex]\cot B =\dfrac{1}{2}[/tex]
[tex]\csc B = \dfrac{\sqrt{5}}{2}[/tex]
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
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.
Given the following functions find the following:
a. Domain
b. The Vertical Asymptote(s)
c. The Horizontal Asymptote
[tex]f(x) = \frac{4x}{2x^{2} +1}[/tex]
The asymptotes are found using the rational function ax^n/ bx^m where n is the degree of the numerator and m is the degree of the denominator.
In the given equation the numerator isn’t raised to any power so n is considered equal to 1. The Demi actor has x raised to the 2nd power so m equals 2.
If n < m then the c axis, y= 0 is the horizontal asymptote.
Also because n is less than m there are no vertical asymptote.
The domain is any real number so the domain would be (-infinity, infinity)
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 :
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 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