Answer:
proper fraction
Step-by-step explanation:
This is a proper fraction, which has a numerator smaller than the denominator
a mixed number has a whole number in front such as 1 3/5
An improper fraction has a numeration greater than a denominator such as 7/6
Find the area of a triangle with the given description. (Round your answer to one decimal place.)
a triangle with sides of length 14 and 28 and included angle 20°
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Answer:
67.0 square units
Step-by-step explanation:
The formula for the area is ...
Area = 1/2ab·sin(C)
Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units
The area of the triangle is about 67.0 square units.
use induction method to prove that 1.2^2+2.3^2+3.4^2+...+r(r+1)^2= n(n+1)(3n^2+11n+10)/12
Base case (n = 1):
• left side = 1×2² = 4
• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4
Induction hypothesis: Assume equality holds for n = k, so that
1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12
Induction step (n = k + 1):
1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²
= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²
= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)
= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))
= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)
= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)
On the right side, we want to end up with
(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12
which suggests that k + 2 should be factor of the cubic. Indeed, we have
3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)
and we can rewrite the remaining quadratic as
3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10
so we would arrive at the desired conclusion.
To see how the above rewriting is possible, we want to find coefficients a, b, and c such that
3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c
Expand the right side and collect like powers of k :
3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c
==> a = 3 and 2a + b = 17 and a + b + c = 24
==> a = 3, b = 11, c = 10
Charity is planting trees along her driveway, and she has 6 pine trees and 6 willows to plant in one row. What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other
Answer:
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the elements are arranged, so we have to use the arrangements formula.
Arrangements formula:
The number of possible arrangements of n elements is:
[tex]A_{n} = n![/tex]
Desired outcomes:
Pine trees(6!) then the willows(6!) or
Willows(6!) then the pine trees(6!). So
[tex]D = 2*6!*6! = 1036800 [/tex]
Total outcomes:
12 trees, so:
[tex]T = 12! = 479001600 [/tex]
What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other?
[tex]p = \frac{D}{T} = \frac{1036800 }{479001600 } = 0.0022[/tex]
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
Write the piecewise defined function for the total cost of parking in the garage. That is, state the function C(x), where x is the number of hours a car is parked in the garage.
Answer:
[tex]C(x) = \left[\begin{array}{ccc}4x &0 \le x \le 2& \\4 +2x &2 < x \le 6& \\16 &6<x\le 8& \end{array}\right[/tex]
Step-by-step explanation:
Given
See attachment for question
Required
The piece-wise function
From the attachment, we have:
(1) $4/hr for first 2 hours
This is represented as:
[tex]C(x) = 4x[/tex]
The domain is: [tex]0 \le x \le 2[/tex]
(2) $2/hr for next 4 hours
Here, we have:
[tex]Rate = 2[/tex]
The total cost in the first 2 hours is:
[tex]C(x) = 4x[/tex]
[tex]C(2) = 4*2 = 8[/tex]
So, this function is represented as:
[tex]C(x) = C(2) + Rate * (Time - 2)[/tex] ----- 2 represents the first 2 hours
So, we have:
[tex]C(x) = C(2) + Rate * (Time - 2)[/tex]
[tex]C(x) =8 + 2(x - 2)[/tex]
Open brackets
[tex]C(x) =8 + 2x - 4[/tex]
Collect like terms
[tex]C(x) =8 - 4+ 2x[/tex]
[tex]C(x) =4+ 2x[/tex]
The domain is:
[tex]2 < x \le 2 + 4[/tex]
[tex]2 <x \le 6[/tex]
(3) 0 charges for the last 2 hours
The maximum charge from (2) is:
[tex]C(x) =4+ 2x[/tex]
[tex]C(6) = 4 + 2*6[/tex]
[tex]C(6) = 4 + 12[/tex]
[tex]C(6) = 16[/tex]
Since there will be no additional charges, then:
[tex]C(x) = 16[/tex]
And the domain is:
[tex]6 < x \le 8[/tex] --- 8 represents the limit
So, we have:
[tex]C(x) = \left[\begin{array}{ccc}4x &0 \le x \le 2& \\4 +2x &2 < x \le 6& \\16 &6<x\le 8& \end{array}\right[/tex]
Select the statement that best justifies the conclusion based on the given information.
If a(b + c) = d, then ab + ac = d.
associative
commutative
distributive
closure
Answer:
distributive
Step-by-step explanation:
a(b + c)=ab + ac
it's distributive one
A chemical company makes two brands of antifreeze. The first brand is
55%
pure antifreeze, and the second brand is
80%
pure antifreeze. In order to obtain
130
gallons of a mixture that contains
70%
pure antifreeze, how many gallons of each brand of antifreeze must be used?
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Answer:
52 gallons of 55%78 gallons of 80%Step-by-step explanation:
Let x represent the quantity of 80% solution. Then the quantity of 55% solution is (130-x) and the total amount of antifreeze in the mix is ...
0.55(130 -x) +0.80(x) = 0.70(130)
0.25x +71.5 = 91 . . . simplify
0.25x = 19.5 . . . . . . subtract 71.5
x = 78 . . . . . . . . . . . divide by 0.25; amount of 80%
130-78 = 52 . . . . amount of 55%
52 gallons of the 55% brand, and 78 gallons of the 80% brand must be used.
Work out the surface area of this solid quarter cylinder. give your answer in terms of pi. r:8cm h:15cm
Answer:
248 pi cm^2
Step-by-step explanation:
The surface area of a cylinder is given by
SA = 2 pi r^2 + pi rh where r is the radius and h is the height
= 2 pi( 8)^2 + pi (8)(15)
128 pi +120pi
248pi
Part b c and d please help
Answer:
b) Y =5.73X +4.36
C) =5.73225*(21)X +4.359
124.73625
D) 163.728 = 5.73X +4.36
X = (163.728 - 4.36)/5.73
X = 27.81291449
Year would be 2027
Step-by-step explanation:
x1 y1 x2 y2
4 27.288 16 96.075
(Y2-Y1) (96.075)-(27.288)= 68.787 ΔY 68.787
(X2-X1) (16)-(4)= 12 ΔX 12
slope= 5 41/56
B= 4 14/39
Y =5.73X +4.36
Inverse Function Question
Determine the expression of f^-1(x) for f(x)=e^x
First, find the inverse of f,
[tex]y=e^x[/tex]
[tex]x=e^y[/tex]
Now take the natural logarithm on both sides,
[tex]\ln x=\ln e^y\implies f^{-1}(x)=\boxed{\ln(x)}[/tex]
Second, find the inverse of g,
[tex]y=5x\implies g^{-1}(x)=\boxed{\frac{x}{5}}[/tex]
Now take their composition,
[tex](g\circ f)(x)=g(f(x))=\frac{\ln(x)}{5}[/tex]
Let [tex]y=\frac{\ln(x)}{5}[/tex], now again find the inverse,
[tex]x=\frac{\ln(y)}{5}[/tex]
[tex]5x=\ln y[/tex]
exponentiate both sides to base e,
[tex]e^{5x}=e^{\ln y}\implies (g\circ f)^{-1}(x)=\boxed{e^{5x}}[/tex]
Hope this helps :)
Simplify i12
A.-1
B.-i
C.i
D.1
Answer:
D 1
Step-by-step explanation:
i^12
We know i^4 = 1
Rewriting
i^4^3
1^3
1
Answer:
part 1- D. 1
part 2- Square root of -144 =12i
Step-by-step explanation:
Got them correct
Round the number to the given place value. 47,709,982; millions
Answer:
48,000,000
Step-by-step explanation:
47,709,982
Look at the millions place and then see if the number after that is a greater number than 4. If it isn't, round down but if it is, round up
Air-USA has a policy of booking as many as 22 people on an airplane that can only seat 20 people. (Past studies have revealed that only 82% of the booked passengers actually show up for the flight.) a) Find the probability that if Air-USA books 22 people, not enough seats will be available. Round your answer to 4 decimal places. P ( X > 20 )
Answer:
The answer is "0.07404893".
Step-by-step explanation:
Applying the binomial distribution:
[tex]n = 22\\\\p= 82\%=0.82\\\\q = 1-0.82 = 0.18\\\\[/tex]
Calculating the probability for not enough seats:
[tex]=P(X>20)\\\\= P(21) + P(22)\\\\[/tex]
[tex]= \binom{22}{21} (0.82)^{21}(0.18)^1+ \binom{22}{22} (0.82)^{22}(0.18)[/tex]
[tex]=0 .06134598+ 0.01270295\\\\=0.07404893[/tex]
Question 19 of 28
Which of the following equations can be used to find the length of BC in the
triangle below?
B
10
А
30
с
A. BC = 30 + 10
B. (BC)2 = 102 + 302
C. BC = 30 - 10
D. (BC)2 = 302 - 102
Answer:
BC^2=10^2+30^2
Step-by-step explanation:
P=10B=30Using pythagorean theorem
[tex]\\ \sf\longmapsto BC^2=10^2+30^2[/tex]
[tex]\\ \sf\longmapsto BC^2=100+300[/tex]
[tex]\\ \sf\longmapsto BC^2=400[/tex]
[tex]\\ \sf\longmapsto BC=\sqrt{400}[/tex]
[tex]\\ \sf\longmapsto BC=20[/tex]
11
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
O A. In 2 – In x
OB. 1 + In 2 - In x
Oc. In 2 + In x
OD. In 1 + In 2 - In
Reset
Next
Answer:
B. 1 + ln 2 - ln x
General Formulas and Concepts:
Algebra II
Natural logarithms ln and Euler's number eLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex] Logarithmic Property [Dividing]: [tex]\displaystyle log(\frac{a}{b}) = log(a) - log(b)[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle ln(\frac{2e}{x})[/tex]
Step 2: Simplify
Expand [Logarithmic Property - Dividing]: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2e) - ln(x)[/tex]Expand [Logarithmic Property - Multiplying]: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + ln(e) - ln(x)[/tex]Simplify: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + 1 - ln(x)[/tex]Rewrite: [tex]\displaystyle ln(\frac{2e}{x}) = 1 + ln(2) - ln(x)[/tex]The second term in a geometric sequence is 50. The forth term in the same sequence is 112.5. what is the common ratio in this sequence?
Answer:
1.5
Step-by-step explanation:
Let the first term be a and the common ratio be r
ATQ, ar=50 and ar^3=112.5, divide these two. r^2=2.25, r=1.5
Help me with this question please...
Each of the following statements is true or false. Which statements are true?
A. A triangle where at least two angles are acute is called an acute triangle.
B. Some polygons are neither convex nor concave.
C. The sum of the interior angles of a concave pentagon is $540^{\circ}.$
D. The interior angles of a regular $1000$-gon are greater than the interior angles of a regular $100$-gon.
E. The exterior angles of a regular $1000$-gon are greater than the exterior angles of a regular $100$-gon.
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Answer:
A. False
B. False
C. True
D. True
E. False
Step-by-step explanation:
A. False -- any triangle has at least two acute angles, whether it is acute, right, or obtuse.
B. False -- by definition, any polygon that is not convex is concave.
C. True -- the angle sum is the same regardless of whether the pentagon is convex or concave. (Provided it is a "simple" polygon, with no crossing sides.)
D. True -- the measure of the interior angle of a regular polygon increases as the number of sides increases. (see E)
E. False -- the exterior angles of a regular polygon are 360° divided by the number of sides. As the number of sides increases, the measure of each exterior angle decreases. (Interior angles are the supplement of exterior angles, so they increase as the number of sides increases.)
A box contains two blue cards numbered 1 and 2, and three green numbered 1 through 3. A blue card ins picked, followed by a green card. Select sample space for such experiment
a) {1, 1), (1, 2, (1, 3)(2, 1), (2, 2), (2, 3)}
b) {(1, 1)(1, 2), (2, 1), (2, 2), (3, 1), (3, 2)}
c) {5}
d) {6}
Answer:
The answer is a.
Solve the system of equations.
6x−y=−14
2x−3y=6
whats the answer please C:
Answer:
Step-by-step explanation:
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and a third side is 22 more than the length of the shortest side. Find the dimensions if the perimeter is 182 feet.
Answer:40, 80 and 62
Step-by-step explanation:
182-22= 160
160/4 = 40 so,
Shortest side is 40
Longest is 80
Third side is 62
What is the answer for 75% of test takers whovscored below average withou an unknown mean and standard deviation
Answer:
sir she hey Jen Jen Jenn receive surge
Answer:
Hello,
Step-by-step explanation:
z=0.7734
p(z<?)=0.75 ==> ?=0.7734
18. The function f(x) = 4x - 8 is reflected across the y-axis, resulting in a new
function, g(x). Write the equation of g(x).
Please explain the steps!! ❤️
The equation of the reflected function across the y-axis is g(x) = -4x - 8.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function f(x) = 4x - 8 is reflected across the y-axis.
The function g(x) will be given by putting the negative x in place of x. Then the reflected function is obtained.
g(x) = -4x - 8
Then the equation of the reflected function across the y-axis is g(x) = -4x - 8.
The graph of the reflected graph is given below.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ2
Find y' for the following.
Answer:
[tex]\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 5x^2 - 2x^2y^2 + 4y^3 - 7 = 0[/tex]
Step 2: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[5x^2 - 2x^2y^2 + 4y^3 - 7] = \frac{dy}{dx}[0][/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{dy}{dx}[5x^2] - \frac{dy}{dx}[2x^2y^2] + \frac{dy}{dx}[4y^3] - \frac{dy}{dx}[7] = \frac{dy}{dx}[0][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle 5\frac{dy}{dx}[x^2] - 2\frac{dy}{dx}[x^2y^2] + 4\frac{dy}{dx}[y^3] - \frac{dy}{dx}[7] = \frac{dy}{dx}[0][/tex]Basic Power Rule [Product Rule, Chain Rule]: [tex]\displaystyle 10x - 2 \Big( \frac{d}{dx}[x^2]y^2 + x^2\frac{d}{dx}[y^2] \Big) + 12y^2y' - 0 = 0[/tex]Basic Power Rule [Chain Rule]: [tex]\displaystyle 10x - 2 \Big( 2xy^2 + x^22yy' \Big) + 12y^2y' - 0 = 0[/tex]Simplify: [tex]\displaystyle 10x - 4xy^2 - 4x^2yy' + 12y^2y' = 0[/tex]Isolate y' terms: [tex]\displaystyle -4x^2yy' + 12y^2y' = 4xy^2 - 10x[/tex]Factor: [tex]\displaystyle y'(-4x^2y + 12y^2) = 4xy^2 - 10x[/tex]Isolate y': [tex]\displaystyle y' = \frac{4xy^2 - 10x}{-4x^2y + 12y^2}[/tex]Simplify: [tex]\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
What is the common ratio for this geometric sequence?
27, 9, 3, 1, ...
Answer:
27:9 3:1.................
Hellp PLZZzzzzzzzxxxmxxxxxxxxxx
Answer:
12. We use Rational numbers when the number is in P/q form
we don't use integers because they are not in p/q form
13. Aron is wrong . he is not correct
an opposite of rational number can out be negative it should be irrational number
opposite of integers are negative that's why
*so opposite of rational numbers will ne irrational numbers not negative
14. Greatest to least
-3.02 , -4 , -4.09 , -4.32, -4,35 , -5.11
plzzzzz helllllllppppppp worth 25 points
Answer:
Step-by-step explanation:
Let's fill that in with what the variables are "worth":
(3)(-3)+2(-2) and simplify to
-9 + (-4) which, when you add those 2 negatives, gives you
-13, choice B.
Answer:
[tex]x = 3 \\ y = - 3 \\ z = - 2 \\ xy + 2z = 3 \times - 3 + 2 \times - 2 \\ = - 9 - 4 \\ = - 13 \\ thank \: you[/tex]
The length of a rectangle is 10 yd less than three times the width, and the area of the rectangle is 77 yd^2. Find the dimensions of the rectangle.
Answer:
W=7 and L=11
Step-by-step explanation:
We have two unknowns so we must create two equations.
First the problem states that length of a rectangle is 10 yd less than three times the width so: L= 3w-10
Next we are given the area so: L X W = 77
Then solve for the variable algebraically. It is just a system of equations.
3W^2 - 10W - 77 = 0
(3W + 11)(W - 7) = 0
W = -11/3 and/or W=7
Discard the negative solution as the width of the rectangle cannot be less then 0.
So W=7
Plug that into the first equation.
3(7)-10= 11 so L=11
PLEASE HELPPPPPPPPPP
Answer: SORRY NEED AN ACCOUNT ON - 10
Step-by-step explanation:
To resolve the proposed issue, an explanation is needed in which the subject is addressed
can anybody help with this ?
Answer:(
fx).(gx)=D. -40x^3+25x^2+45
Step-by-step explanation:
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! Given this frequency chart of 1490 passengers from the Titanic who died, choose the class(es) whose relative frequency would comprise just under, 1/2 of a pie chart
Answer:
b and eStep-by-step explanation:
Second and Third which gives in total:
0.112 + 0.354 = 0.466This is under 1/2 and greater than Crew.
14. A quadratic equation is graphed above.
Which of the following equations could be
paired with the graphed equation to create
a system of equations whose solution set is
comprised of the points (2,-2) and (-3, 3)?
A. y = x + 6
B. y = x - 6
C. y = X
D. y = -x
Answer:
D.
Step-by-step explanation:
2=-2，3=-3
2²=-2²，3²=3²
