Just Add All The Numbers Up
If the PPF is a downward-sloping straight line, then the law of increasing opportunity cost does not hold. Instead, the opportunity cost of producing an additional unit of good 1 or good 2 remains constant as more of either is produced (i.e., there are constant opportunity costs in production).
A straight line PPF indicates constant opportunity costs in production is TRUE.
The Production-Possibility Frontier (PPF) is a graphical representation of the maximum amount of two goods that can be produced given a certain number of resources.
If the PPF is a straight line, then the opportunity cost of producing an additional unit of one good is the same regardless of how much of that good is already being produced. This means that the resources used to produce the two goods are perfectly substitutable and there are no increasing opportunity costs.
However, if the PPF is a curved line, then the opportunity cost of producing an additional unit of one good increase as more of that good is produced. This is because the resources used to produce the two goods are not perfectly substitutable and there are increasing opportunity costs.
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What is the value of the expression below ? 2[32-(4-1)]
There is a 3 in between the ) 3 ] but it looks like square / cubes something
The value of the expression \(2[32-(4-1)]\) is \(58\) by simplifying.
SimplificationSimplification is the process of replacing a mathematical expression with an equivalent one, that is simpler and usually shorter.
How to simplify an algebraic expression?Apply the BODMAS rule to simplify the algebraic expression.
Given that the expression is \(2[32-(4-1)]\)
First, simplify the bracket \((4-1)\)
Then, \(2[32-(4-1)]=2[32-3]\)
Simplify the bracket \([32-3]\)
Then, \(2[32-3]=2\) × \(29\)
Multiply the numbers \(2\) and \(29\)
\(2\) × \(29=58\)
Hence, the expression \(2[32-(4-1)]\) is simplified to \(58\).
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To make a specific hair dye, a hair stylist uses a ratio of 1 1/8 oz of red tone, 3/4 oz of gray
tone, and 5/8 oz of brown tone. If the stylist needs to make 20 oz of dye, how much of
each dye color is needed
Answer:
We can call the amounts of red, gray, and brown dye 1 1/8x, 3/4x and 5/8 x respectively and we can write the equation:
1 1/8x + 3/4x + 5/8x = 20
2 1/2x = 20
x = 8 which means that the stylist needs 1 1/8 * 8 = 9 oz red, 3/4 * 8 = 6 oz gray and 5/8 * 8 = 5 oz brown.
Given the following data for simple curve station Pl=110+80.25, Delta =4∘00′00′′,D=3∘00′00′′. find R,T,PC,PT, and LC by arc definition.
The PC and PT are found by using the equations, PC = Pl - TPT = Pl + LC Where Pl is the station of the point of curvature and LC is the length of the curve.
The given data for simple curve station Pl = 110 + 80.25, Delta = 4∘00′00′′, D = 3∘00′00′′ is used to find R, T, PC, PT, and LC by arc definition. Radius R is given by the formula, R = (Delta/2π) x (D + 100 ft/2)Where Delta is the central angle and D is the degree of curve in a chord of 100 feet.
Putting the given values of Delta and D into the formula, we have; R = (4/360 x 2π) x (3 + 100/2)R = 25.67 ft The tangent distance T is given by the formula, T = R x tan (Delta/2)Where Delta is the central angle. Putting the given value of Delta into the formula, we have;
T\(= 25.67 x tan (4/2)T = 9.72 ft\)The external distance X is given by the formula, X = R x sec (Delta/2) - R Where Delta is the central angle.
Putting the calculated value of R into the formula, we have; D = \(5729.58/25.67D = 223.10 ft\)
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Multiple Choice!!!!!!What congruence theorem can you use to show that the two skateboard ramps have the same height?
Answer:HL
Step-by-step explanation:
What is the distance between (4, 7)(4,7)left parenthesis, 4, comma, 7, right parenthesis and (2, 2)(2,2)left parenthesis, 2, comma, 2, right parenthesis? Choose 1 answer: Choose 1 answer: (Choice A) A \sqrt{10} 10 square root of, 10, end square root (Choice B) B \sqrt{29} 29 square root of, 29, end square root (Choice C) C 888 (Choice D) D 99
Answer:
Choice B) B \sqrt{29} 29 square root of, 29, end square root = √29
Step-by-step explanation:
When given coordinates, the distance between those points(coordinates) is calculated as:
Distance = √(x2 - x1)² +(y2 - y1)²
Given(x1, y1), (x2, y2)
Fromm the question, we are given points(4,7) and (2,2)
Distance = √(x2 - x1)² +(y2 - y1)²
= √(2 - 4)² + (2 - 7)²
= √-2² + -5²
= √4 + 25
= √29
Therefore, Choice B is the answer = √29
What's a central angle
Answer:
What's a central angle?
the central angle is 90 °
Determine whether Δ P Q R≅ Δ X Y Z . (Lesson 4-4)
P(3,-5), Q(11,0), R(1,6), X(5,1), Y(13,6), Z(3,12)
ΔPQR ≅ ΔXYZ based on the given information. There are other criteria for triangle congruence, such as angle-angle-side (AAS), but in this case, we have established congruence using the SSS criterion.
The question is asking whether triangle PQR (with vertices P(3,-5), Q(11,0), R(1,6)) is congruent to triangle XYZ (with vertices X(5,1), Y(13,6), Z(3,12)).
To determine if the triangles are congruent, we need to compare their corresponding sides and angles. There are a few criteria for triangle congruence, such as side-side-side (SSS), side-angle-side (SAS), and angle-side-angle (ASA).
Let's compare the corresponding sides of the two triangles:
Side PQ and side XY:
Using the distance formula, we can calculate the lengths of PQ and XY:
PQ = √[(11-3)² + (0-(-5))²] = √[64 + 25] = √89
XY = √[(13-5)² + (6-1)²] = √[64 + 25] = √89
Side QR and side YZ:
QR = √[(1-11)² + (6-0)²] = √[100 + 36] = √136
YZ = √[(3-13)² + (12-6)²] = √[100 + 36] = √136
Side PR and side XZ:
PR = √[(1-3)² + (6-(-5))²] = √[4 + 121] = √125 = 5√5
XZ = √[(5-3)² + (1-12)²] = √[4 + 121] = √125 = 5√5
By comparing the lengths of the corresponding sides, we can see that PQ = XY, QR = YZ, and PR = XZ.
Since all three pairs of corresponding sides are congruent (SSS), we can conclude that triangle PQR is congruent to triangle XYZ.
Therefore, we can state that ΔPQR ≅ ΔXYZ based on the given information.
It's important to note that there are other criteria for triangle congruence, such as angle-angle-side (AAS), but in this case, we have established congruence using the SSS criterion.
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If a = 9, then 5a is _______
The required simplified solution of the given expression is 45.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given an expression, 5a,
we have given that a = 9,
Now, put a = 9 in the given expression,
= 5 (9)
= 45
Thus, the required simplified solution of the given expression is 45.
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the watch bee would like to buy costs $10 less then 2 times the amount she has saved the watch costs $50. how much money does bee have saved?
Answer:
20$
Step-by-step explanation:
50 - (2x - 10) = x
50 + 10 = x + 2x
60 = 3x
60/3 = x
20 = x
1.2cm radius
4cm height
Pls help me find the surface area and volume
Answer:
if its a circle
Volume - 7.20 cm
Surface area 18.1 cm
Step-by-step explanation:
Volume of a sphere = 4/3 πr^3
4/3 (3.14) 1.2^3
4/3 (3.14) 1.728
4/3 of 5.42592=
7.23456 or 7.20
Surface area of sphere = 4πr²
4(3.14) 1.2^2
4(3.14) 1.44
4 (4.5216) =
18.0864 or 18.1
I need help plz!!!!!!!!
Answer: 75
Step-by-step explanation:
I'm quite sure about the answer
find the circumference of the circle below
Hello !
Answer:
\(\boxed{\sf C\approx62.8 ft}\)
Step-by-step explanation:
To find the circumference of a circle with its radius, we will apply the following formula:
\(\sf C=2\pi r\)
Where r is the radius of the circle.
Given :
diameter = 20 ftWe know that the diameter is equal to two times the radius, so \(r=10\) ft.
Let's substitute our value into the formula :
\(\sf C=2\times \pi\times 10\\\boxed{\sf C\approx62.8 ft}\)
Have a nice day !
Answer:
62.8 ftStep-by-step explanation:
GivenDiameter = 20Radius= ? Circumference = ?To find outCircumferenceBy UsingCircumference of circle = 2πrSolutionWe know that
Radius = d/2So,
→ R = 20/2
→ R = 10
Now,
We know that,
Circumference of circle = 2πr
→ 2 × 22/7 × 10
→ 440/7
→ 62.8 ft
Hence ,
Option d is correct answerPlease help me I've been stumped on this problem
The measure of ∠CFE is 40°
How do we find ∠CEF?To solve for triangle ∠CEF, we know that
Parallel to DE is BC
Arc length BD = 58°
Arc length DE = 142°
We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.
The arcs BD and DE are split in half by the line ZT.
Which is:
Arc SC = 1/(1/2(arc BC) = 1/(58)
Arc SC = 29°
142 = 1/2(arc DE) + arc TE
Arc TE = 71°
Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE
29° + Arc CE + 71° = 180°
Arc CE + 100° = 180°
Arc CE = 180-100
Arc CE = 80°
Angle inscribed equals half of angle intercepted
CFE = 1/2 of Arc CE
<CFE = 1/2(80)
< CFE = 40°
The above answer is based on the full question below;
In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer
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SH With a Graph
Which graph represents the function f(x) = 3 (2)"?
y
10
TY
10
8
6
8
6
10
8
6
4
y
10
8
6
4
4
2
x
23
0
O
5 Intro
The graph that represents \(f(x) = 3(2)^x\) is graph (d)
The function is given as:
\(f(x) = \frac 32(2)^x\)
The given function is an exponential function.
An exponential function is represented as:
\(f(x) = ab^x\)
Where a and b represent the initial value and the rate, respectively.
So, by comparison:
\(a = \frac32\)
\(b =2\)
This means that, the graph of \(f(x) = \frac 32(2)^x\) has an initial value of 3/2, and rate of 2
Hence, the graph that represents \(f(x) = 3(2)^x\) is (d)
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Please help me! I will mark Brainliest if you answer all of these portfolio questions!
+75 POINTS!
Fr0ggyLikeSMELLY avatar
I WILL MARK BRAINLIEST! PLEASE HELP ME! THIS COUNTS 50% OF MY GRADE!
Answer:
a
Step-by-step explanation:
HURRY PLEASE I’ll mark you as brainliest
What is the line's y-intercept?
Answer:
1
Step-by-step explanation:
A is reflected over the x-axis to create A'. Then, points A, A', B and a fourth point become the vertices of a rectangle. What are the coordinates of the fourth point?
(3, -5)
(-6, -5)
(6, 5)
(-3, -5)
The fourth point has coordinates (-17, 0).
The x-coordinate of A remains constant but the sign of the y-coordinate changes if A is mirrored over the x-axis to form A'. Hence, if Has a coordinates (a, b), A' must also have coordinates (a, -b).
Given that A and A' are the corners of a rectangle that are opposite one another, the other two corners of the rectangle must be on a horizontal line that passes through A and A"s midpoint (a, 0). Since (a, 0) and the fourth point (let's call it C) are separated by 2|b|, the distance between A and A' is also 2|b|. This indicates that depending on which side of the line AA' C is on, it has coordinates of (a + 2|b|, 0) or (a - 2|b|, 0).
In this instance, the coordinates of A are (3, 5) and those of A' are (3, -5). The intersection of A and A' is (3, 0). A and A' are separated by 2|5|, which equals 10.
The fourth point, C, thus, has coordinates of either (3 + 2(10), 0) = (23, 0) or (3 - 2(10), 0) = (-17, 0).
The right response is (3 - 2(10), 0), which can be deduced from the graph since the rectangle is symmetric about the y-axis (-17, 0).
The fourth point therefore has coordinates (-17, 0).
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Find all values of x for which the series converges. (Enter your answer using interval notation ) (9x)n n = 1 For these values of X, write the sum of the series as a function of X. f(x)'
So, the sum of the series as a function of x is: f(x) = 9x / (1 - 9x).
To determine the values of x for which the series converges, we need to find the values of x that satisfy the convergence criteria for the given series.
The series \((9x)^n, n = 1\), will converge if the absolute value of (9x) is less than 1.
|9x| < 1
To find the values of x that satisfy this inequality, we can solve it as follows:
-1 < 9x < 1
Divide all terms by 9 (since 9 is positive):
-1/9 < x < 1/9
Therefore, the series converges for x values in the interval (-1/9, 1/9).
The sum of the series as a function of x, denoted as f(x), can be found using the formula for the sum of a geometric series:
f(x) = a / (1 - r)
where a is the first term and r is the common ratio. In this case, the first term is \((9x)^1 = 9x\), and the common ratio is \((9x)^n / (9x) = (9x)^{(n-1)\).
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 helllpppppp asapppp!!!!!determine whether the result after the operation will be rational or irrational. Fill in rational or irrational and each blank.
Answer:
the answer is 245.67 and 56.9
Step-by-step explanation:
hi
The only information you have about a certain function f[x] is:
-1 ≤ f[x] ≤ 1
for all the x's between -[infinity] and [infinity].
Is it possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity]?
Why?
Yes, it is possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity].
Explanation:
We can approximate f(x) as a Fourier series, as follows:
\($$f(x) = \sum_{n=0}^{\infty}a_n\cos\left(\frac{n\pi x}{L}\right)+\sum_{n=1}^{\infty}b_n\sin\left(\frac{n\pi x}{L}\right)$$\)
If f(x) is an odd function, the cosine terms are gone, and if f(x) is an even function, the sine terms are gone.
We can create an approximation for f(x) using only the first n terms of the Fourier series, as follows:
\($$f_n(x) = a_0 + \sum_{n=1}^{n}\left[a_n\cos\left(\frac{n\pi x}{L}\right)+b_n\sin\left(\frac{n\pi x}{L}\right)\right]$$\)
For any continuous function f(x), the Fourier series converges uniformly to f(x) on any finite interval, as given by the Weierstrass approximation theorem.
However, if f(x) is discontinuous, the Fourier series approximation does not converge uniformly.
Instead, it converges in the mean sense or the L2 sense. The L2 norm is defined as follows:
\($$\|f\|^2 = \int_{-L}^{L} |f(x)|^2 dx$$\)
Hence, it is possible for a plot of a partial expansion of f(x) to share ink with the plot of f(x) all the way from -[infinity] to + [infinity].
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what is the value of the following expression tan (-5pi/6)
The value of the expression tan(-5π/6) can be determined using trigonometric properties and identities.
First, let's consider the unit circle. The angle -5π/6 is measured in the clockwise direction from the positive x-axis. In this position, the reference angle is π/6, which is the positive angle formed with the x-axis.
The tangent function (tan) is defined as the ratio of the sine (sin) of an angle to the cosine (cos) of the angle. Using the reference angle π/6, we can determine the value of tan(π/6) as the ratio of sin(π/6) to cos(π/6). sin(π/6) equals 1/2, and cos(π/6) equals √3/2. Therefore, tan(π/6) is (1/2) divided by (√3/2), which simplifies to 1/√3 or √3/3. Since tan is an odd function, tan(-5π/6) is equal to the negative of tan(5π/6). Therefore, tan(-5π/6) has the same value as -√3/3.
In conclusion, the value of tan(-5π/6) is -√3/3, which means that the tangent of the angle -5π/6 is negative and equal to the ratio of -√3 to 3.
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Type the correct answer in the box. Use numerals instead of words.
For this item, if the answer is not a whole number, enter it as a fraction in simplest form using / as the fraction bar.
Isolde is stacking books. The stack of books forms a rectangular prism.
Each book is the same size. Isolde knows the area of the base of one book is 22 1/2 square inches and each book is 3/4 inch thick.
The volume of a stack of 9 books is cubic inches.
The volume of a stack of 9 books is 1368.75 cubic inches.
Volume of a book stackTo find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.
Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.
Therefore, the volume of the stack of 9 books is:
Volume = Area of base x heightVolume = (202 1/2 square inches) x (6 3/4 inches)Volume = 1368.75 cubic inchesMore on volume of stacked books can be found here: https://brainly.com/question/1058070
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Several friends (Calvin, Dean, Kelli, and Lee) went to Cal's Late Night Diner for a bite to eat. Match each person to their drink (Iced tea, Lemonade, Root Beer, and Water) and determine how much each paid ($4.99, $5.99, $6.99, and $7.99) for their meal.
Clues:
1. The Diner who paid $4.99 was either Calvin or the one who got the Root Beer.
2. Kelli paid $6.99
3. The one who got the water paid 1 dollar less than Dean.
4. Calvin paid more than Lee.
5. The one who got the Root beer paid 1 dollar less than the one who got the Iced Tea.
Based on the given clues, we can determine the person, drink, and price paid for each individual:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
How to determine how much each friends paidFrom clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.
From clue 2, Kelli paid $6.99.
From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.
From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.
Therefore, the final assignments are:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
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whats the perimiter of the following rectangle? The side says x - 2 and the bottom says 2x + 1
Answer:
6x-2
Step-by-step explanation:
The perimeter of a rectangle is found by
P = 2(l+w)
=2( x-2 + 2x+1)
Combine like terms
P = 2(3x-1)
Distribute
P = 6x-2
page 1 of 2
In Target One Fractions, players choose three numbers to create a whole number and
a fraction that have a product close to 1. Their score is the difference between their
product and 1, and the lowest score wins the round.
1 Erica is playing Target One Fractions. She has these cards: 1, 2, 3, 4, 6.
a Which three cards should she choose to make a whole number and a fraction
that have a product close to 1?
62/3
b Write an expression for the problem Erica will solve.
2/3×4=4
c Solve the problem.
6=2₁b = 6₁ c=30r a=3,5=60-a
d What is Erica's score for this round?
Answer: a) Erica should choose 2, 3, and 6 to make a whole number and a fraction that have a product close to 1.
2 x 3 x 6 = 36, which is close to 1 when expressed as a fraction: 1/36.
b) (2/a) x (3/b) x (6/c) = 1
c) Multiplying both sides by a, b, and c, we get:
6bc = 2ac
3ac = ab
6ab = bc
Multiplying the three equations together, we get:
(6abc)^2 = (2ac) x (3ab) x (6bc)
216a^2 b^2 c^2 = 36a^2 b^2 c^2
a^2 b^2 c^2 = 1/6
Taking the square root of both sides, we get:
abc = 1/sqrt(6)
So, Erica's whole number is 2 x 3 x 6 = 36, and her fraction is 1/sqrt(6). The product of these is:
36 x 1/sqrt(6) = 6sqrt(6)
Her score is the absolute difference between 6sqrt(6) and 1:
|6sqrt(6) - 1| = 13.97 (rounded to two decimal places).
d) Erica's score for this round is 13.97.
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST!!!!
Answer: 36 degrees
Step-by-step explanation: 180 degrees - 144 degrees = 36 degrees
Answer:
A = 54 d and x = 45 B = 45 so a = 54 and x= 45 and b= 45 and x = 45
Under her cell phone plan, Ava pays a flat cost of $58 per month and $4 per gigabyte.
She wants to keep her bill at $62.40 per month. How many gigabytes of data can she
use while staying within her budget?
Which shows the scale factor used to dilate triangle XYZ to form triangle X'Y'Z'?
A( 1/2 x, 1/2 y)
B (1/3 x, 1/3 y)
Answer:
B
Step-by-step explanation:
A is wrong lol, trust me.
find the volume of the sphere d=18
Answer:
3053.62806
Step-by-step explanation:
d=18 so r=9
(check attachement)