The converted money in Canadian dollars is $111.6.
Given that, Irlene has just returned from a business trip in Britain with £200 of uncashed traveler's cheques.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the converted Canadian dollars be x.
x = 200 × 0.5544 + 0.65% of 200 × 0.5544
= 110.88 + 0.0065 × 110.88
= 111.60072
≈ 111.6
Therefore, the converted money in Canadian dollars is $111.6.
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Identify the domain, vertical asymptotes and horizontal asymptotes of the following rational function: f(x)= \frac{3x-4}{x^3-16x} Domain is all real numbers except x\neq Answer , Answer and AnswerVertical asymptote at x= Answer , Answer and AnswerHorizontal asymptote at y= Answer
Answer
Domain is all real numbers except x ≠ 0, -4, and 4
Vertical asymptote at x = 0, -4, and 4
Explanation
Given function:
[tex]f(x)=\frac{3x-4}{x^3-16x}[/tex]Note: The domain of a function is a set of input or argument values for which the function is real and defined.
For the function to be real; the denominator must not be equal zero, i.e.
[tex]\begin{gathered} x^3-16x\ne0 \\ x(x^2-16)\ne0 \\ x(x-4)(x+4)\ne0 \\ x\ne0,x-4\ne0,\text{ and }x+4\ne0 \\ \therefore x\ne0,x\ne4,\text{ and }x\ne-4 \end{gathered}[/tex]Hence, the domain is all real numbers except x ≠ 0, -4, and 4.
Note: A vertical asymptote with a rational function occurs when there is division by zero.
Hence, the vertical asymptote at x = 0, -4, and 4
A printer takes 5 seconds to print 3 pages. How many pages can it print in 125 seconds? Enter the answer in the box.
Answer: 75
Step-by-step explanation:
So first, we need to divide 125 by 5
125÷5=25
Next we need to multiply 3 by 25.
25×3=75
The printer can print 75 pages in 125 seconds.
During a food drive, a local middle school collected 3,195…
Answer:
100 cans
Explanation:
• The total number of canned food items collected = 3,195
,• The number of classrooms that participated = 28
To estimate the number of items each classroom donated, divide 3195 by 28.
[tex]\frac{3195}{28}\approx\frac{3000}{30}=100[/tex]Note: Round to a whole number since the number of cans cannot be a decimal.
Each class donated about 100 cans.
Enzo counted the number of sunny days each of his favorite towns had in the year 2013 and graphed theresults.Light LandBright VillagePlaceShiny TownSun City -050100150200250300Number of Sunny Days
From the graph, we can see that the town that had most sunny days was Shiny Twon.
So, between this town and Sun City, we have Bright Viallge, that had a number of sunny days between Sun City and Shiny Town.
So the answer is Bright Village.
I am an even number.
I have three digits and they are all the same.
If you multiply me by 4, all of the digits in the product are 8.
What number am l?
Answer:
Step-by-step explanation:
The number is 2.
222x4=888
Hence, the number am I is [tex]888[/tex].
What is the even number?
A number that is divisible by [tex]2[/tex] and generates a remainder of [tex]0[/tex] is called an even number.
Here given that,
I am an even number. I have three digits and they are all the same.
If you multiply me by [tex]4[/tex], all of the digits in the product are [tex]8[/tex].
The number is [tex]2[/tex] sp ot would be
[tex]222[/tex]x[tex]4=888[/tex]
Hence, the number am I is [tex]888[/tex].
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the variables x and y vary inversely. use x=-2 and y=3 to write and equation relating x and y. then find y when x=-1
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define the variation that occurs in the Question.
Inverse Variation: Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.
STEP 2: Interpret the statements in the question tab
[tex]\begin{gathered} x\text{ varies inversely as y} \\ x\propto\frac{1}{y} \end{gathered}[/tex]STEP 3: Get the constant of variation
[tex]\begin{gathered} x\propto\frac{1}{y} \\ \text{Introducing the constant, we have;} \\ x=k\times\frac{1}{y},x=\frac{k}{y} \\ By\text{ cross multiplication,} \\ x=ky \\ \text{Divide both sides by y} \\ \frac{x}{y}=k \end{gathered}[/tex]STEP 4: Use the given values to get the equation relating x and y
[tex]\begin{gathered} \frac{x}{y}=k,x=-2,y=3 \\ By\text{ substitution,} \\ \frac{-2}{3}=k \\ k=\frac{-2}{3} \\ \\ \text{The equation relating x and y will be:} \\ x=-\frac{2}{3}y \\ x=\frac{-2y}{3} \end{gathered}[/tex]Hence, the equation relating x and y is:
[tex]x=\frac{-2y}{3}[/tex]STEP 5: Find y when x=-1
[tex]\begin{gathered} x=ky \\ \text{Divide both sides by k to get the value of y} \\ y=\frac{x}{k} \\ x=-1,k=-\frac{2}{3} \\ By\text{ substitution,} \\ y=\frac{-1}{\frac{-2}{3}} \\ y=-1\div-\frac{2}{3} \\ y=-1\times\frac{-3}{2}=\frac{-1\times-3}{2} \\ y=\frac{3}{2} \end{gathered}[/tex]Hence, the value of y when x=-1 is 3/2
Tristan tried his luck with the lottery. He can win $85 if he can correctly choose the 3 numbers drawn. If order matters and there are 13 numbers in the drawing, how many different ways could the winning numbers be drawn?
The ways to select the winning numbers is 286
How to determine the ways the winning numbers could be drawn?From the question, we have
Total numbers, n = 13Numbers to select, r = 3The winning numbers could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 13 and r = 3
Substitute the known values in the above equation
Total = ¹³C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 13!/10!3!
Evaluate
Total = 286
Hence, the number of ways is 286
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What is 13.496 rounded to the nearest tenth?A.13B.13.4C.13.5D.14
1) When we need to round up or down to the nearest tenth, it's necessary to consider the hundredth's place.
2) Note this number:
We can see that 13.496 is greater than 13.45 so it is closer to 14 than 13, then we can round it off to the nearest greater number than 4.
3) Thus, we can round it off to:
[tex]13.5[/tex]Solve for the triangle where there is a question mark!
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Label the right-angled triangle
STEP 2: Write the trigonometry ratios
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}[/tex]STEP 3: Write the given values to decide which ratio to use
Let the part with the question be represented by m
[tex]\begin{gathered} \text{adjacent}=7,\text{hypotenuse}=12,m=\text{?} \\ U\sin g\text{ the cos ratio from step 2;} \\ \cos m=\frac{7}{12} \\ m=\cos ^{-1}(\frac{7}{12})=\cos ^{-1}0.5833333333 \\ m=54.31466529 \\ m\approx54.31 \end{gathered}[/tex]Therefore, the value of mising angle labelled m is approximately 54.31 degrees
The amount of freight transported by rail in the u.s was about 580 billion ton-miles in 1960 and has been increasing at a rate of 2.32% per year since then.a. write a function representing the amount of freight, in billions of ton-miles, transported annually. ( 1960 = year 0 )b. graph the functionc. in what year would you predict that the number of ton-miles would have exceeded or would exceed 1 trillion (1,000 billion)?
The amount of freight transported by rail was 580 billion ton-miles in 1960.
The amount increased at a rate of 2.32% per year.
a. The growth in freight transport with respect to the passing years can be expressed as exponential growth. The general form of this equation is
[tex]y=a(1+r)^x[/tex]Where
y represents the final number after "x" periods of time
a represents the initial number at x=0
r represents the growth rate, expressed as a decimal value
x represents the number of time intervals that have passed
For this example, the initial amount is a=580 billion
The growth rate is r=2.32/100=0.0232
You can determine the equation as follows:
[tex]y=580(1+0.0232)^x[/tex]b. This function is of exponential increase, its domain is all real numbers and its range is all positive real numbers, you can symbolize it as y > 0, it's increasing, and it has a horizontal asymptote as x approaches -∞
To graph it, you have to determine at least two points of the graph, I will determine 3
For x=-100
[tex]\begin{gathered} y=580(1+0.0232)^{-100} \\ y=58.53 \end{gathered}[/tex]For x=0
[tex]\begin{gathered} y=580(1+0.0232)^0 \\ y=580 \end{gathered}[/tex]For x=10
[tex]\begin{gathered} y=580(1+0.0232)^{10} \\ y=729.51 \end{gathered}[/tex]The points are
(-100,58.53)
(0,580)
(10,729.51)
Plot the points and then draw an increasing line from -∞ to +∞
c. To determine the time when the freight transported will exceed 1000 billion tom-miles, you can use the graph, just determine the value of x, for which y=1000
This value is approximate x=23.57
This means that counting from 1960 will take 23 and a half years to reach over a trillion ton-miles transported.
Add the number of years to the initial year to determine the date:
[tex]1960+23=1983[/tex]By 1983 the number of ton-miles transported will exceed the trillion.
If f(2)= Vwhat is the rule of the inverse?
To find the inverse do these steps
1- Put f(x) = y
2- Switch x and y
3- solve to find the new y
Let us do that
[tex]y=\sqrt[]{\frac{x+4}{3}}[/tex]Switch x and y
[tex]x=\sqrt[]{\frac{y+4}{3}}[/tex]Now square the two sides to cancel the root
[tex]x^2=\frac{y+4}{3}[/tex]Multiply both sides by 3 to cancel the denominator
[tex]3x^2=y+4[/tex]Subtract 4 from both sides
[tex]3x^2-4=y[/tex]The rule is the answer D
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
The binomials x - 4, x + 1 and 2 · x - 3 are factors of the polynomials.
How to derive the equations of the factors of a polynomial
Herein we know the x-values of a polynomial such that the expression is equal to zero. Mathematically speaking, these x-values are known as roots and the mathematical expressions that contain them are known as factors, which are represented by binomials of the form:
a · r - b = 0
Where a, b are real coefficients.
If we know that x₁ = 4, x₂ = - 1, x₃ = 3 / 2, then the factors of the polynomials are listed below:
x₁ = 4:
x - 4 = 0
x₂ = - 1:
x + 1 = 0
x₃ = 3 / 2
2 · x - 3 = 0
x - 4, x + 1 and 2 · x - 3 are factors of the polynomials.
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According to a 2017 Wired magazine article, 40% of emails that are received are tracked using software that can tell the email sender when, where, and on what type of device the email was opened (Wired magazine website). Suppose we randomly select 70 received emails.
(a)
What is the expected number of these emails that are tracked?
(b)
What are the variance and standard deviation for the number of these emails that are tracked? (Round your answers to three decimal places.)
Var(x)
=
=
Using the binomial distribution, the measures are given as follows:
a) Expected value: 28.
b) Variance of 16.8 and standard deviation of 4.099.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.Hence, in the context of this problem, the values of these parameters are given as follows:
p = 0.4, n = 70.
The expected value of the distribution is calculated as follows:
E(X) = np.
Hence:
E(X) = 70 x 0.4 = 28.
The variance of the distribution is calculated as follows:
V(X) = np(1 - p) = 70 x 0.4 x 0.6 = 16.8.
The standard deviation of the distribution is calculated as follows:
sqrt(V(X)) = sqrt(16.8) = 4.099.
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11) -3(1 + 6r) = 14 - r 12) 660+6)-5=1+6v 13) -4k + 2(5k - 6) = -3k - 39 14) -16 + 5n=-71-
-3(1+6r) = 14 -r
-3-18r = 14 - r
-3-14 = -r +18r
-17 = 17r
17r/17 = -17/17
r = -1
I really need help solving this problem from my trigonometry prepbook
The terminal ray of 145° lies in II Quadrant.
The terminal ray of -83° lies in IV Quadrant.
The terminal ray of -636 lies in I Quadrant.
The terminal ray of 442 lies in I Quadrant.
Anna's room is a rectangle. Its length is 15 feet and its width is 4 yards. What is the perimeter of the room?
Answer:
38
Step-by-step explanation:
Perimeter is basically each side added together. 15 + 15 + 4 + 4 is 38. Therefore, it's 38.
You borrow $12,000 from your bank to help pay for some emergency home repairs.
.
This loan is paid back by making quarterly payments of $1100 for a total of 3 years.
.
What is total amount of interest paid on this loan?
The amount of interest paid is $21000
What is interest?
In finance and economics, interest is the payment of an amount over repayment of the principle sum (that is, the amount borrowed) by a borrower or deposit-taking financial institution to a lender or depositor at a certain rate by a borrower or deposit-taking financial institution. It differs from a charge that the borrower may pay to the lender or a third party. Interest is also distinct from a dividend, which is given by a firm to its shareholders (owners) from its profit or reserve, but not at a fixed rate, but rather on a pro rata basis as a portion of the reward achieved by risk-taking entrepreneurs when revenue exceeds total expenditures.
Total amount paid = $11000x3 = $33000
Interest paid = $(33000-12000) = $21000
Hence, the amount of interest paid is $21000
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Solve for x in the parallelogram below.
Answer:
3
Step-by-step explanation:
In parallelogram, opposite sides are equal.
Here,
5x + 2 and 17 are opposite sides.
5x + 2 = 17
5x = 17 - 2
5x = 15
x = 15 / 5
x = 3
Three different transformation are performed on the shaded triangle. Each transformation results in on of three images. Match each image to the transformation applied on the shaded triangle
We are given a triangle and three possible transformations performed on it. The first transformation shows that the triangle has no change in orientation, therefore, this transformation is a translation only.
For image 2 we notice that the orientation of the triangle changes. If we draw a horizontal line in the middle of the shaded triangle and image 2 we notice that these two images are related by a reflection, also after this reflection the image was translated therefore, for image two we have reflection across a horizontal line followed by a translation.
For image 3 we can draw a vertical line in the middle of the shaded triangle and image 3 and we do a reflection across this vertical line since there is a change in the orientation of the figure.
Kareem wants to attend a college that will cost $13.800 for the first year. His uncle gave him a special gift of 3000 to use toward the cost. Kareem plans to attend the college in 3 years. How much must Kareem save each month to have enough for the year cost?
Kareem needs to save $13,800 in total
He already got $3000 from his uncle.
Thus, he needs $13,800 - $3000 = $10,800 more
He will need to save up $10,800 in 3 years, that is 3 x 12 = 36 months
To find the amount he must save each month, we will divide $10,800 by 36:
[tex]\frac{10,800}{36}=\$300[/tex]Answer$300Frankenstein was in charge of bringing punch to the Halloween party. He brought 36 liters of his famous eyeball punch. How many gallons was this?
Answer: 9.5112
Step-by-step explanation:
There are 0.2642 gallons in a liter. So, in 36 liters, there are [tex]36(0.2642)=9.5112 \text{ gal }[/tex]
In the similaritytransformation of AABCto ADFE, AABC was dilated bya scale factor of 1/2, reflected4 across the x-axis, and movedthrough the translation [? ].
We have to identify the translation.
We can see that the green triangle represents the transformation of triangle ABC after a dilation with a scale factor of 1/2 and a reflection across the x-axis.
We can then find the translation in each axis from the image as:
Triangle is DEF is translated 3 units to the left (and none in the vertical axis).
We can express this translation as this rule:
[tex](x+3,y+0)[/tex]Answer: (x+3, y+0)
log 2x = 3 what is x
The value of x is 10.04 using log properties.
What is the log in math?The power to which a number must be increased in order to obtain another number is known as a logarithm. The exponential function is thought of as the inverse of the logarithmic function because of their close relationship. The logarithmic function logₐN = x is created from the exponential function [tex]a^{x}[/tex] = N. For instance, since ten raised to the power of two equals 100, the base ten logarithms of 100 is 2: log 100 = 2.
logₐ xy = logₐ x + logₐ y (product property)
logₐ x/y = logₐ x - logₐ y (quotient property)
logₐ [tex]x^{y}[/tex] = ylogₐ x (power property)
log2x = 3
2x = e³
x = e³/2
= 10.04
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NO LINKS!! Show all work where necessary to get full credit
16. Circle F
You name a circle using the center.17. BF
A radius connects the center to a point on the circumference of the circle.18. CD
A chord is a segment connecting two points on the circumference of the circle.19. BE
A diameter is a segment that passes through the center while also connecting two points on the circumference of the circle.20. FA
See 17 and 19.Answer:
16. F
17. FA
18. CD
19. BE
20. FA
Step-by-step explanation:
Question 16
A circle is named by its center.
The center of the given circle is F, therefore the name of the given circle is F.
Question 17
The radius of a circle is a straight line segment from the center to the circumference.
Therefore, the radii of the given circle are:
FA, FB and FE.Question 18
A chord is a straight line segment joining two points on the circumference of the circle.
Therefore, the chords of the given circle are:
BE and CD.Question 19
The diameter of a circle is the width of the circle at its widest part. It is a straight line segment that passes through the center of the circle and whose endpoints lie on the circumference.
Therefore, the diameter of the given circle is:
BE.Question 20
As the diameter is BE, it contains the radii FB and FE.
Therefore, the radius that is not contained in the diameter is:
FA.use a sum or difference identity to find the exact value of :
Using the rule
[tex]\sin (x+y)=\sin x\cos y+\cos x\sin y[/tex][tex]\begin{gathered} \sin (225+60)=\sin 225\cos 60+\cos 225\sin 60 \\ \end{gathered}[/tex]Sine is negative in the third quadrant therefore,
[tex]\begin{gathered} -(\sin 45)\cos 60+\cos 225\sin 60 \\ \sin \text{ 45=}\frac{\sqrt[]{2}}{2}\text{ then the negative sign} \\ -\frac{\sqrt[]{2}}{2} \\ -\frac{\sqrt[]{2}}{2}\cos 60+\cos 225\sin 60 \\ \cos \text{ 60=}\frac{1}{2} \\ -\frac{\sqrt[]{2}}{2}(\frac{1}{2})+\cos 225\sin 60 \end{gathered}[/tex]Let us find the other side
[tex]\begin{gathered} \cos \text{ 45=}\frac{\sqrt[]{2}}{2} \\ cos\text{ is negative in the third quadrant } \\ -\frac{\sqrt[]{2}}{2} \\ \sin \text{ 60=}\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Bring everything together
[tex]\begin{gathered} -\frac{\sqrt[]{2}}{2}(\frac{1}{2})-\frac{\sqrt[]{2}}{2}(\frac{\sqrt[]{3}}{2}) \\ -\frac{\sqrt[]{2}}{4}-\frac{\sqrt[]{6}}{4}=\frac{-\sqrt[]{2}-\sqrt[]{6}}{4}=-0.965925826\ldots... \end{gathered}[/tex]In an experiment, the probability that event B occurs is , and the probability that event A occurs given that event B occurs is 3 7) What is the probability that events A and B both occur? Simplify any fractions.
We have to use the conditional probability formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Where P(A|B) is the probability that A occurs given that B occurs, P(B) is the probability that B occurs, and P(A∩B) is the probability that both events A and B occur.
In this case, since we are asked for the probability that events A and B both occur, we need to solve the equation for P(A∩B):
[tex]P(A\cap B)=P(A|B)\cdot P(B)[/tex]And the information we have about the problem is:
[tex]\begin{gathered} P(A|B)=\frac{3}{7} \\ P(B)=\frac{2}{9} \end{gathered}[/tex]We substitute this into the formula for P(A∩B):
[tex]P\mleft(A\cap B\mright)=\frac{3}{7}\cdot\frac{2}{9}[/tex]Solving the multiplication of fractions:
[tex]\begin{gathered} P\mleft(A\cap B\mright)=\frac{3\cdot2}{7\cdot9} \\ P\mleft(A\cap B\mright)=\frac{6}{63} \end{gathered}[/tex]And finally, we simplify the fraction by dividing both numbers in the fraction by 3:
[tex]P\mleft(A\cap B\mright)=\frac{2}{21}[/tex]Answer: 2/21
Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
We will have the following:
[tex]\sin (2\theta)=-\frac{1}{2}\Rightarrow2\theta=2\pi n_1+\frac{7\pi}{6}[/tex][tex]\Rightarrow\theta=\pi n_1+\frac{7\pi}{12}[/tex]Now, we will solve for the following:
[tex]\Rightarrow\pi n_1+\frac{7\pi}{12}\le2\pi\Rightarrow\pi n_1\le\frac{17\pi}{12}[/tex][tex]\Rightarrow n_1\le\frac{17}{12}[/tex]This value in degrees is:
[tex]\frac{17}{12}\text{radians}=81.169\text{degrees}[/tex]So, the solution is located in the interval:
[tex]\lbrack0,81\rbrack[/tex]What is the factorization of496^4-9
The given expression is
[tex]496^4-9[/tex]To factorize this, we find the square root of each term.
[tex]\begin{gathered} \sqrt[]{496^4}=496^2 \\ \sqrt[]{9}=3 \end{gathered}[/tex]Then, we use the difference of perfect square which states
[tex]a^2-b^2=(a+b)(a-b)[/tex]So, we have
[tex]496^4-9=(496^2+3)(496^2-3)[/tex]110,169 is larger than 110,72
110,169 is larger than 110,72
This is false as the first decimal of 110.169 is 1 and the first decimal of 100,72 is 7.
110,169 is larger than 110,72
This is false as the first decimal of 110.169 is 1 and the first decimal of 100,72 is 7.
What is this sign of 30ﾟ angle and the sign of the 60ﾟ angle
We are asked to find out the values of sine 60° and sine 30°
Recall from the trigonometric ratios,
[tex]\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]From the given triangle,
With respect to angle 60°, the opposite side is 25√3 ft and the hypotenuse is 50 ft.
Let us substitute these values into the above sine ratio
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin 60\degree=\frac{25\sqrt[]{3}}{50} \\ \sin 60\degree=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]So, the value of sine 60° is √3/2
From the given triangle,
With respect to angle 30°, the opposite side is 25 ft and the hypotenuse is 50 ft.
Let us substitute these values into the above sine ratio
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin 30\degree=\frac{25}{50} \\ \sin 30\degree=\frac{1}{2} \end{gathered}[/tex]So, the value of sine 30° is 1/2
Therefore, the sine of 60ﾟ angle is √3/2 and the sine of 30ﾟ angle is 1/2
