Compounded continuously the balance grows at a continuous rate of 1.7%.
What is compound interest ?
Compound interest is when you earn interest on both the money you've saved and the interest you earn. So let's say you invest $1,000 (your principal) and it earns 5 percent (interest rate or earnings) once a year (the compounding frequency).The model used for continuous compounding is
f(t) = Pe^(rt)
where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have
f(t) = 1000·e^(0.017t)
Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.
Therefore, the balance grows at a continuous rate of 1.7%.
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Anna wanted to buy a camera. The first discount store sold her favorite camera for $95. The second store sold the same camera for $115, but it was on sale for 20% off. The third store carried the camera for $105 but offered it at 10% off with a coupon. which store had the better buy?
Answer: third store
Step-by-step explanation:
1
First store: 95
Second store: 0.8*115=92
Third store: 0.9*105=94.5
A clock is showing the correct time at 8 am. if it gains four minutes in every hour what time will it be showing five and a half hours later ?
Answer:
1:52 PM
Step-by-step explanation:
It gains 4 min every hour so it gains 4 * 5.5 = 22 minutes
8 oclock + 5.5 hrs + 22 minutes =
1:52
A coffee shop sells coffee, tea and pastries. The owner analysed her profits from the shop this week and found that
two-fifths of the profit was from the sale of collee and one third of the profit was from the sale of pastries. The rest of
the profit was from the sale of tea.
What fraction of the colfee shop's profit was from the sale of tea?
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y,z)=x2 y2 z2; 3x 4y−3z=34
The extremum of f(x,y) is subject to the given constraint, There is a global minimum (x,y,z.) (4,2,-8).
An instance of a constraint is the fact that there are only so many hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. one which restricts, limits, or regulates; a test.
A constraint is something that limits or controls what you may do. Their decision to abandon the ride turned into made due to economic constraints. Water shortages in the location could be the main constraint on development. Synonyms: limit, drawback, scale back, rein more Synonyms of constraint.
predicament or restriction. repression of herbal emotions and impulses: to exercise constraint. unnatural restraint in manner, communique, and many others.; embarrassment. Something that constrains.
By lagranier multi plur
of = hog
(2x, is, 22>= 25-47
8x=42
10x + 2 = 42
2
28
2x=4, 4= 2
=2
722 (4)
(4.9,2) = (4.2-8)
(4,2-8)= 84
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Simplify the following polynomial expression.
(5x4 - 9x3 + 7x - 1) + (-8x4 + 4x2 - 3x + 2) - (-4x3 + 5x - 1)(2x - 7)
Answer:
5x^4 -37x^3 -6x^2 +41x -6
Step-by-step explanation:
We simplify this expression by removing parentheses and combining like terms. Parentheses are removed using the distributive property.
Form the productThe product of the final pair of polynomials in parentheses is ...
(-4x^3 +5x -1)(2x -7) = (-4x^3 +5x -1)(2x) +(-4x^3 +5x -1)(-7)
= -8x^4 +10x^2 -2x +28x^3 -35x +7
= -8x^4 +28x^3 +10x^2 -37x +7
Combine with remaining sums= (5x^4 -9x^3 +7x -1) + (-8x^4 +4x^2 -3x +2) - (-8x^4 +28x^3 +10x^2 -37x +7)
= (5 -8 -(-8))x^4 +(-9 -28)x^3 +(4 -10)x^2 +(7 -3 -(-37))x +(-1 +2 -7)
= 5x^4 -37x^3 -6x^2 +41x -6
Total area=
What is the total area?
Help me asap! Please!! Thanks so much :)
The total surface area of this shaded region is 1000 units²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The total surface area of a polygon is the sum of the individual areas of each surface.
Total area of the figure = 2(20 * 10) + 2(10 * 10) + 2(20 * 10) = 1000 units²
The total surface area of this shaded region is 1000 units²
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Find the mean and standard deviation for the set of data. {16,22,8,5,20,18,14,17,24}
The mean of the set is : 16
The Slandered deviation of set : 5.8689389538863
What is mean?Moderation is the quality of falling at or close to a medium point, whether it is in terms of location, period of time, quantity, or rate. 2 is the arithmetic mean. 3 denotes a plural noun: a tool for achieving one's goals. Attempt to locate it using all available techniques.
The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.
What is Standard Deviation?An indicator of how much a group of numbers vary or are dispersed is the standard deviation. When the standard deviation is low, the values tend to fall within a narrow range of the set's mean, but when it is large, the values tend to deviate from that mean more.
Calculating average:Average x = 16
Count n = 9
Sum Sum =144
Average = Sum / Count
= 144 / 9
= 16
Standard Deviation, σ: 5.8689389538863
Count, N = 9
Sum, Σx: = 144
Mean, μ: = 16
Variance, σ²: = 34.444444444444
Calculating slandered devotion:
[tex]\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\mu\right)^{2}}[/tex]
[tex]\sigma^{2}=\frac{\sum\left(x_{i}-\mu\right)^{2}}{N}[/tex]
[tex]=\frac{(16-16)^{2}+\ldots+(24-16)^{2}}{9}[/tex]
= 310/9
= 34.444444444444
σ = √34.444444444444
σ = 5.8689389538863
The mean of the set is : 16
The Standard deviation of set : 5.8689389538863
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What is the solution to 3/2b + 5 < 17? Explain how.
(1) b < 8
(2) b > 8
(3) b < 18
(3) b > 18
Answer:
[tex] \blue{b < 8}[/tex]
Answer 1 is correct
Step-by-step explanation:
[tex] \frac{3}{2} b + 5 < 17[/tex]
Take 5 to the right side.
[tex] \frac{3}{2} b < 17 - 5 [/tex]
[tex]\frac{3b}{2} < 12 [/tex]
Multiply both sides by 2.
[tex]3b <12 \times 2[/tex]
[tex]3b < 24[/tex]
Divide both sides by 3.
[tex]b < 8[/tex]
The peak current passing through an inductor is 2. 0 aa. part a what is the peak current if the peak emf e0e0 is doubled?
Answer:
22
I remember this question in school
Calvin has a book with 120 pages. The page numbers are only printed on the odd numbered pages. What is the sum of these numbers on these odd numbered pages?
Answer:
now we know that
book is 120page
__6785
please help! find the distance of AG if A (4,4) and G (-1,-1)
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
By using distance formula :
[tex]\qquad \sf \dashrightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{(4 - ( - 1)) {}^{2} + (4 - ( - 1)) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{(4 + 1) {}^{2} + (4 + 1) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{2(5) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: 5 \sqrt{2 }\: \: units[/tex]
The distance between two points [tex]\rm{A(x_1,y_1)} [/tex] and [tex]\rm{B(x_2,y_2)}[/tex] is given by the formula,
[tex] \rm{AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
Proof:
[tex] \rm{Let \: X'OX \: and \: YOY' \: be \: the \: z-axis \: and \: y-axis \: respectively. Then, O \: is \: the \: origin.}[/tex]
[tex] \rm{Let \: A(x_1,y_1) \: and \: B(x_2,y_2) \: be \: the \: given \: points.}[/tex]
[tex] \rm{Draw \: AL \perp \: OX, BM \perp \: OX \: and \: AN \perp BM }[/tex]
Now,
[tex] \rm{OL=x_1,OM=x_2,AL=y_1 \: and \: BM=y_2}[/tex]
[tex]\rm\therefore{AN=LM=(OM-OL)=(x_2-x_1)}[/tex]
[tex] \: \: \: \: \rm{BN=(BM-NM)=(BM-AL)=(y_2-y_1)}[/tex]
[tex] \rm{In \: right \: angled \: \triangle ANB, by \: Pythagorean \: theorem,}[/tex]
We have,
[tex] \: \: \: \: \rm{AB^2=AN^2+BN^2}[/tex]
[tex] \rm{or,AB^2=(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex] \rm\therefore AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
The Given question,
Find the distance of AG if A (4,4) and G (-1,-1).
Solution,
The given points are A(4,4) and G(-1,-1).
Then,
[tex] \rm{(x_1=4,y_1=4) and (x_2=-1,y_2=-1)}[/tex]
We know that,
The distance formula,
[tex] \rm{AG= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{ {( - 1 - 4)}^{2} + {( - 1 - 4)}^{2} } [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{ {( - 5)}^{2} + {( - 5)}^{2} } [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{25 + 25} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{50} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)(25)} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)(5)(5)} [/tex]
[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)( {5}^{2}) } [/tex]
[tex] \rm \: \: \: \: \: \: \: \: = 5 \sqrt{2} \: units[/tex]
Answered by:
[tex]\frak{\red{moonlight123429}}[/tex]
Robert bought a combination of 15 colored and normal pencils. Each pencil wad $0.60 and each colored pencil was $0.45. In total he paid $8.70. How many colored pencil and pencil did he buy?
Show equation
Answer:
Robert bought 13 colored pencils and 2 pencils
Step-by-step explanation:
13 x 0.60 = 7.8
2 x 0.45 = 0.9
7.8 + 0.9 = 8.70
13 colored pencils are $7.80
2 pencils are $0.9
15 total is $8.70
drake has 7 song that he choose to sing in the shower each day of the week, one song per day. If he never sings the same song twice in week, how many different ways can he choose his song throughout the week?
Answer:
5040 ways
Step-by-step explanation:
7! = 5040
7 choices on day 1
6 choices on day 2
5 choices on day 3
4 choices on day 4
3
2
1 7 x 6 x 5 x 4 x 3 x 2 x1 = 5040
please help!! a probability question :/
Answer:
B. 10/13
Step-by-step explanation:
There are 52 cards in a deck. Divide that by 4 and get 13, thats how many diamonds there are. There are 36 number cards. Since 9 of the cards in diamonds are numbers, we dont count those ones. 13-9 is 4, so we add that to our total to get 40. 40/52 is the same as 10/13.
Answer: 10/13
Step-by-step explanation:
There are 52 cards in a deck. Every 13 cards, 9 will be number cards so there are 36 number cards. There are 13 diamond cards. There are 9 diamond cards that are number cards. So the probability of the following is (36+13-9)/52 = 40/52 = 10/13
Write an expression to represent: 3 minus the quotient of x and 4
Answer:3 - x/4
Step-by-step explanation: quotient of x and 4 = x/4. 3 minus x/4 = 3 - x/4.
The expression representing the sentence is [tex]$3 -\frac{x}{4}[/tex].
We have a sentence - "3 minus the quotient of x and 4".
We have to determine the expression that represents the sentence.
Express the statement - "The difference of x and y is equal to an irrational number" in the form of expression.The expression representing the above statement is -
x - y = π.
According to the question, we have -
3 minus the quotient of x and 4.
Using the Division Algorithm -
x = 4q + r
Substituting r = 0 by introducing decimals in the quotient, we get -
q = [tex]$\frac{x}{4}[/tex]
Therefore -
[tex]$3 -\frac{x}{4}[/tex]
Hence, the expression representing the sentence is [tex]$3 -\frac{x}{4}[/tex].
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Question 10 of 10
The function F(x) = log5 x is decreasing.
A. True
B. False
SUBMIT
Answer: False
Step-by-step explanation:
The base is more than 1, so the function is increasing.
The first and second steps to solve the equation StartFraction 3 x over 5 EndFraction + 5 = 20 are shown below. StartFraction 3 x over 5 EndFraction + 5 minus 5 = 20 minus 5 StartFraction 3 x over 5 EndFraction (Five-thirds) = 15 (five-thirds) Which property was applied in the second step?
The multiplication property of equality has been used in the second step when both sides of the equation have been multiplied by 5/3.
State the Multiplication Property of Equality:
The Multiplication Property of Equality states that multiplying both sides of the equation with the same number, expression, or variable, the equation remains unchanged, i.e. equality is maintained.
Use of Multiplication Property of Equality in the Second Step:
The given equation was,
3x/5 + 5 = 20
In the first step, subtraction property of equality is applied as follows,
3x/5 + 5 - 5 = 20 - 5
3x/5 = 15
Now, for isolating x on the left hand side, we must apply multiplication property of equality by multiplying both sides of the equation by 5/3.
We get,
3x/5 × 5/3 = 15 × 5/3
x = 25
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In the expression (ax+b)*(cx^2+dx+e), find two set of values of a,b,c,d and e so that the coefficient of x^3and x terms after expansion are 4and 10 respectively.
Answer:
2, 0, 2, 3, 5
1, 2, 4, 0, 5
Step-by-step explanation:
(ax + b)(cx² + dx + e)
acx³ + adx² + aex + bcx² + bdx + be
2(2)x³ + 2(3)x² + 2(5)x + 0 + 0 + 0
4x³ + 6x² + 10x
a = 2
b = 0
c = 2
d = 3
e = 5
1(4)x³ + 1(0)x² + 1(10)x + 2(4)x² + 0 + 10
4x³ + 8x² + 10x + 10
a = 1
b = 2
c = 4
d = 0
e = 5
what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created? Select three options.
positive slope
negative slope
constant slope
increasing function
decreasing function
Answer: negative slope
constant slope
decreasing function
B-C-E
Step-by-step explanation:negative slope
constant slope
decreasing function
Prove this please
Optional Math
Cos2A =
[tex] \frac{( \cot\alpha - \tan\alpha ) }{( \cot\alpha + \tan\alpha ) } [/tex]
Step-by-step explanation:
proof from r.h.s to l.h.s
(cot(a)-tan(a))(cot(a)+tan(a))
cot(a)=cos(a)/sin(a)
tan(a)=sin(a)/cos(a)
(cot(a)-tan(a))=cos(a)/sin(a) - sin(a)/cos(a)
=cos²(a)-sin²(a)/sin(a)cos(a)
from trigonometry identity cos²(a)-sin²(a)=cos2(a)
so we have cos2(a)/sin(a)cos(a)
(cot(a)+tan(a))=cos(a)/sin(a) +sin(a)/cos(a)
=cos²(a)+sin²(a)/cos(a)sin(a)
from trigonometry identity cos²(a)+sin²(a)=so we have 1/cos(a)sin(a)
(cot(a)-tan(a)) ÷(cot(a)+tan(a))
=cos2(a)/cos(a)sin(a) ÷ 1/cos(a)sin(a)
=cos2(a)/cos(a)sin(a) * cos(a)sin(a)
=cos2(a)
proved
x-13=x+1
Please help mee
A 75-gallon tank is filled with brine (water nearly saturated with salt; used as a preservative) holding 11 pounds of salt in solution. A salt solution containing 0.6 pounds of salt per gallon is added to the tank at the rate of 3gal/min. The contents of the tank are continuously and thoroughly mixed and drained out at thirteen quarts per minute. What is the amount of salt in the tank after an hour
Let [tex]A(t)[/tex] = amount of salt (in pounds) in the tank at time [tex]t[/tex] (in minutes). Then [tex]A(0) = 11[/tex].
Salt flows in at a rate
[tex]\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}[/tex]
and flows out at a rate
[tex]\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}[/tex]
where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.
Then the net rate of salt flow is given by the differential equation
[tex]\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}[/tex]
which I'll solve with the integrating factor method.
[tex]\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95[/tex]
[tex]-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}[/tex]
[tex]\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}[/tex]
Integrate both sides. By the fundamental theorem of calculus,
[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}} [/tex]
[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right) [/tex]
[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}[/tex]
[tex]\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}[/tex]
[tex]\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}[/tex]
After 1 hour = 60 minutes, the tank will contain
[tex]A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131[/tex]
pounds of salt.
Can someone help me with this question?
Answer:
25/81.
Step-by-step explanation:
(27/8)^-4/3
= 8^4/3 / 27^4/3
= (∛8)^4 / (∛27)^4
= 16 / 81
(64/125)^-2/3
= (125)^2/3 / (64)^2/3
= (∛125)^2 / (∛64)^2
= 5^2 / 4^2
= 25/16
So the answer is
16/81 * 25/16
= 25/81.
Answer:
25 / 81(25 by 81) is your answer.
WILL MARK U BRAINLIEST
Answer:
90
Step-by-step explanation:
First, we should find the area of the trapezoid, and then subtract the area of the removed triangle in order to find the shaded area.
Area of the trapezoid
1) Area of the rectangle in the middle.
Base Length: 10
Height Length: 10
Area: 10 x 10 = 100
2. Area of the triangles on the side
Base Length: (14 - 10)/2 = 2
Height Length: 10
Area: 2 x 10 x 1/2 = 10
There are two triangles: 10 x 2 = 20
Area of the trapazoid: 100 + 20 = 120
Area of the triangle that's been removed
Base Length: 10
Height Length: 10 - 4 = 6
Area: 10 x 6 x 1/2 = 30
Shaded area
Area of the trapezoid - Area of the triangle
120 - 30 = 90
Area of the shaded region is 90.
Which of the following statements does not describe a characteristic of the line of best fit for a scatter plot?
A statement which does not describe a characteristic of the line of best fit for a scatter plot is that: A. the line of best fit should be the average of all the data points.
What is a scatter plot?A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
What is a line of best fit?A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.
The characteristics of a line of best fit.The statements which describe a characteristic of the line of best fit for a scatter plot include the following:
The line should be as close to the points as possible.The number of points above the line should be equal to the number of points below the line.The distance between the points above the line and the line should be relatively equal to the distance between the points below the line and the line.Read more on scatterplot here: brainly.com/question/6592115
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A supplier sold a scanner machine for Rs 41,400 with 15% VAT after allowing 10% discount on it's marked price and gained 20%. By how much is the discount percent to be reduced to increase the profit by 4%?
3%
Answer:
Selling price with VAT {15%} = Rs 41400
S.P +15% of S.P =Rs 41400
S.P(1+15%)=Rs 41400
S.P=Rs 41400/1.15
Selling price without VAT =Rs 36000
Again
Discount = 10%
M.P =S.P+ Discount % of M.P
M.P-Discount% of M.P= S.P
M.P(1-Discount%)=Rs 36000
M.P(1-10%)=Rs 36000
M.P=Rs 36000/0.9
Marked Price = Rs 40,000
again
Discount =Discount % of M.P
=10% of 40000
=Rs 4,000
Again
Profit=20%
For 20% profit
Cost price = (S.P*100)/(100+profit%)
=(36000*100)/(100+20)
= Rs 30000
For 24% profit
selling price = (100+profit%)*C.P/100
=(100+24)*30000/100
=Rs 37200
Again
Discount = 40000–37200 = Rs2800
Discount % = discount/M.P*100%
=2,800/40,000* 100 = 7%
Finally
Discount percent to be reduced =10%–7%= 3%
Figure 2 was constructed using figure 1.
On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0). Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.
For the transformation to be defined as a rotation, which statements must be true? Select three options.
The options A, C, E are correct. On the basis of the theory of the rotation and transformation on the parallelogram.
According to the statement
we have given that the
Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0)
And we have to find that the which terms are corrected from the given options when Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.
So, For this purpose we know that the
A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.
And According to the given statement
when parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.
Then the conditions A, C, E are applicable because on rotation these things are applicable.
So, The options A, C, E are correct. On the basis of the theory of the rotation and transformation on the parallelogram.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
Figure 2 was constructed using figure 1.
On a coordinate plane, 2 parallelograms are shown.
Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0).
Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.
For the transformation to be defined as a rotation, which statements must be true? Select three options.
A. The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).
B. The transformation is rigid.
C. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.
D.Segment CP is parallel to segment CP'.
E. If figure 1 is rotated 180° about point C, it will be mapped onto itself.
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A study of the annual population of bees in a county park shows the population, B(t), can be represented by the function B(t)=182(1.065)t, where the t represents the number of years since the study started. Based on the function, what is the growth rate?
The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
From the function [tex]B(t) = 182(1.065)^t[/tex]:
b = 1.065
Growth rate = 1.065 - 1 = 0.065 = 6.5%
The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.
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The graph shows the amount of money that the journalism club raised for a scholarship fund over a 5-week period If x represents the number of weeks, which function is the BEST fit for the information in this graph?
The linear function of best fit for the information on the graph is:
f(x) = 200x + 100.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The function on the graph goes through points (3,700) and (4,900), that is, when x changes by 1, y changes by 200, which means that the slope is of 200 and the function is:
f(x) = 200x + b.
When x = 3, f(x) = 700, hence we use it to find b.
700 = 200(3) + b
b = 100.
Hence the function is:
f(x) = 200x + 100.
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Jude Enjoys Eating Potato Chips. He likes to place 3 chips together in a stack to make interesting flavours. If he only has one flavour of chip, for example, original, then he will only have one way to stack the chips: original, original, original, which can be written as O,O,O
The order in which the chips are stacked does not matter. For example, Jude has two different flavours: original and pizza. Stacking them as original, orginal, pizza (O,O, P) would be the same as stacking them as original, pizza, orignal (O,P,O.). In both stacks, he had two original-flavor chips and one pizza-flavor chip.
If Jude has four flavours, Original (O), pizza (P), and chicken (C) and BQQ (B), how many different stacks can he make
Using the combination formula, it is found that he can make 4 different stacks.
The order in which the balls are selected is not important, as stated in the problem. hence the combination formula is used to solve this question. If the order was important, then the permutation formula would be used.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, he has four flavors, and will choose three of them for the stacks, hence the number of different stacks is given as follows:
[tex]C_{4,3} = \frac{4!}{3!1!} = 4[/tex]
He can make 4 different stacks.
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