The following table shows a company's annual income over a 6-year period. The equation y=60000(1.2)x describes the curve of best fit for the company's annual income (y). Let x represent the number of years since 2001.
Answers
Given that the annual income of a company over a 6-year period is described by the equation:
[tex]\begin{gathered} y=60000(1.2)^x \\ \text{where} \\ x\text{ is the number of years since 2001} \end{gathered}[/tex]The annual income at the end of each year since 2001 is as shown in the table below:
Required: To evaluate the company's approximate annual income in 2009.
Solution:
Given the annual income described as
[tex]y=60000(1.2)^x[/tex]The number of years between 2001 and 2009 is evaluated as
[tex]x\text{ = 2009 -2001 = 8 years}[/tex]thus, it's been 8 years since 2001.
The annual income in 2009 is thus evaluated by substituting 8 for the value of x in the annual income function.
This gives
[tex]\begin{gathered} y=60000(1.2)^x \\ x\text{ = 8} \\ \text{thus,} \\ y\text{ = 60000}\times(1.2)^8 \\ =\text{ 60000}\times4.29981696 \\ y=\text{ }257989.0176 \\ \Rightarrow y\approx258000 \end{gathered}[/tex]Hence, the company's approximate annual income in the year 2009 will be $ 258000.
The third option is the correct answer.
Related Questions
Find the equation of the line passing through the points (-11,-18) and (-22,-16). Write your answer in the
form y = mx + b.
Answer: y =
Write your answers as integers or as reduced fractions in the form A/B.
Answers
Answer:
y=−2/11x−20
Step-by-step explanation:
Vocabulary Are 23 and 24 adjacent angles? Explain. 1. 2. 3. 4 Reasoning Does every angle have a complement? Explain.
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We will have the following:
1. We have that 3 & 4 are not adjacent angles.
2. We have that 3 and 4 are adjacent angles.
3. We have that 3 and 4 are not adjacent angles.
4. Not every angle has a complement. A complement is when two angles add up to 90°, so any angle greater than 90° won't have a complement.
***Explainations***
1- 3 & 4 in order to be adjacent have to share the same vertex [They do] and have to be one right next to the other [They are not, there is another angle between them].
2. 3 & 4 are adjacent since they share the same vertex and are one next to the other.
3. 3 & 4 are not adjacent since they do not share a vertex.
Karen is planning to drive 870 miles on a road trip. If she wants to complete the trip in 6 days, how many miles will she need to drive each day??
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Answer:
145 miles
Step-by-step explanation:
870 ÷ 6 = 145
Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find AU (BNC).{
Answers
Solution:
Given that;
[tex]\begin{gathered} A=\left\{0,2,4,6\right\} \\ B=\left\{1,2,3,4,5\right\} \\ C=\left\{1,3,5,7\right\} \end{gathered}[/tex]For B∩C, i.e . common elements between bot sets
[tex]B\cap C=\lbrace1,3,5\rbrace[/tex]Then, A∪(B∪C), i.e. all the elements in A and B∩C
[tex]A∪\left(B∪C\right)=\lbrace0,1,2,3,4,5,6\rbrace[/tex]Hence, A∪(B∪C) is
[tex]\begin{equation*} \lbrace0,1,2,3,4,5,6\rbrace \end{equation*}[/tex]The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of k (in red).The function fis defined by f(x) = fx/.Write down the expression for k(x).
Answers
Solution
We have the original function defined as:
[tex]f(x)=-\sqrt[]{x}[/tex]And we want to obtain the new red line so then we need to check how many units down and right the function moves:
And we have 3 units to the right and 2 units down then the answer is:
[tex]h(x)=-\sqrt[]{x-3}-2[/tex]Then the final answer is:
h(x) = -sqrt(x-3) -2
How do we determine the number of hours each family used the sprinklers?
Answers
Given:
The output rate of Martinez family's sprinkler is 25L per hour and Green family's sprinkler is 35L per hour. The combined usage of sprinkler is 40 hours. The resulting water output is 1250L.
To find:
The number of hours each family used the sprinkler.
Solution:
Let Martinez family used sprinkler for x hours and Green family used sprinkler for y hours.
Since the combined usage of sprinklers is 40 hours. So,
[tex]x+y=40...\left(i\right)[/tex]The output rate of Martinez family's sprinkler is 25L per hour and Green family's sprinkler is 35L per hour. The resulting water output is 1250L. So,
[tex]\begin{gathered} 25x+35y=1250 \\ 5x+7y=250...\left(ii\right) \end{gathered}[/tex]Multiply (i) by 7 and subtract from (ii), to get:
[tex]\begin{gathered} 5x+7y-7\left(x+y\right)=250-7\left(40\right) \\ 5x+7y-7x-7y=250-280 \\ -2x=-30 \\ x=\frac{-30}{-2} \\ x=15 \end{gathered}[/tex]Now, we get x = 15, Put x = 15 in the equation (i):
[tex]\begin{gathered} 15+y=40 \\ y=40-15 \\ y=25 \end{gathered}[/tex]Thus, x = 15, y = 25.
Determine the required value of a missing probability to make the distribution a discrete probability distribution… p(4) =
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The table given showed the discrete probability distribution for random variables 3 to 6 and their corresponding probability except for the probability of 4
It should be noted that for a probability distribution, the cummulative probabibility (that is the sum of all the probability) must be equal to one.
This means that
[tex]P(3)+P(4)+P(5)+P(6)=1[/tex]From the given table, it can be seen that
[tex]\begin{gathered} P(3)=0.32 \\ P(4)=\text{?} \\ P(5)=0.17 \\ P(6)=0.26 \end{gathered}[/tex]Then, p(4) is calculated below
[tex]\begin{gathered} P(3)+P(4)+P(5)+P(6)=1 \\ 0.32+P(4)+0.17+0.26=1 \\ P(4)+0.32+0.17+0.26=1_{} \\ P(4)+0.75=1 \\ P(4)=1-0.75 \\ P(4)=0.25 \end{gathered}[/tex]Hence, P(4) is 0.25
Can anyone help me with this I’m stuck and this is pretty difficult.
Answers
Answer:
x=-1
Explanation:
Given the equation:
[tex]$$ 24=4(x-7)+8(1-6 x) $$[/tex]First, expand the brackets:
[tex]24=4x-28+8-48x[/tex]Next, collect like terms and simplify:
[tex]\begin{gathered} 24=4x-48x-28+8 \\ 24=-20-44x \\ \text{ Add 20 to both sides} \\ 24+20=-44x \\ 44=-44x \\ \text{ Divide both sides by -44} \\ \frac{44}{-44}=\frac{-44x}{-44} \\ x=-1 \end{gathered}[/tex]The solution to the equation is -1.
Mary used the quadratic formula to find the zeros of the equation below. Select the correct zeros of the equation:3x^2 - 9x + 2 = 0Answer choices include:x = fraction numerator 9 plus-or-minus square root of 57 over denominator 6 end fractionx equals fraction numerator negative 9 plus-or-minus square root of 57 over denominator 2 end fractionx equals fraction numerator 9 plus-or-minus square root of 105 over denominator 2 end fractionx equals fraction numerator negative 9 plus-or-minus square root of 105 over denominator 6 end fraction
Answers
We have the next quadratic function given:
[tex]3x^2-9x+2=0[/tex]Mary used the next quadratic formula:
[tex]x=\frac{-b^\pm\sqrt{b^2-4ac}}{2a}[/tex]Replace using the form ax²+bx+c
Where a= 3
b=-9
c=2
Then:
[tex]\begin{gathered} x=\frac{-\lparen-9)\pm\sqrt{\left(-9\right)^2-4\left(3\right)\left(2\right)}}{2\left(3\right)} \\ x=\frac{9\pm\sqrt[]{57}}{6}\frac{}{} \end{gathered}[/tex]Therefore, the correct answer is "x = fraction numerator 9 plus-or-minus square root of 57 over denominator 6 end fraction"
Which of the following is NOT an equation?1. 5(2x+1)=10x+52. 4x-13. 5+3=104. x/2+1=7
Answers
By definition, an equation is a statement that two mathematical expressions are equal.
Equations always contain the equal sign "="
Out of the 4 expressions listed, number 2. does not contain the equal sign, which means that this expression is not an equation.
All other expressions contain the equal sign, they can be considered equations.
What is the probability of drawing a jack from a standard deck of cards, replacing it,shuffling, then drawing an ace?
Answers
- We have 52 cards in a deck of cards.
- We have 4 cards of the same number (4 jack, 4 aces...).
Probability of drawing a jack = 4/52
Probability of drawing a jack followed by an ace =(4/52)*(4/52)=0.00592
Evaluate the expression shown below and write your answer as a fraction in
simplest form.
-3/8+(-9/10)
Answers
Answer:
-1 11/40
Step-by-step explanation:
-51/40 this is simplest form.
Step-by-step explanation:
Can you tell me if im right or wrong
Answers
I will begin typing in the answer tab. It will take me approximately _
Blackgrass black graph is the of y=f(x) chose the equation for the red graph
Answers
The Solution:
The correct answer is [option A]
Given:
Required:
To determine the equation of the red graph if the black graph function is y = f(x).
The correctb
Theoretical Probabilities. Use the theoretical method to determine the probability ofthe following outcomes and events. State any assumptions that you make. Drawing a red card (heart or diamond) from a standard deck of cards
Answers
Recall that the theoretical probability that an event occurring is given by the following quotient:
[tex]\frac{\text{favorable cases}}{total\text{ cases}}.[/tex]We know that there are 26 red cards in a standard deck, therefore:
[tex]P(\text{Drawing a red car)=}\frac{26}{52}=0.5.[/tex]Answer: 0.5.
What is the image point of (1,−3) after a translation right 2 units and up 2 units?
Answers
For this problem we have the following point given:
[tex]P=(1,-3)[/tex]And we want to determine the image point after a translation of 2 units to the right and upward. So then we just need to do the following:
[tex]I=(1+2,-3+2)[/tex]And after do the math we got:
[tex]I=(3,-1)[/tex]And the final answer for this case would be I=(3,-1)
The profit of a cell-phone manufacturer is found by the function y= -2x2 + 108x + 75 , where x is the cost of the cell phone. At what price should the manufacturer sell the phone tomaximize its profits? What will the maximum profit be?
Answers
Hello!
First, let's rewrite the function:
[tex]y=-2x^2+108x+75[/tex]Now, let's find each coefficient of it:
• a = -2
,• b = 108
,• c = 75
As we have a < 0, the concavity of the parabola will face downwards.
So, it will have a maximum point.
To find this maximum point, we must obtain the coordinates of the vertex, using the formulas below:
[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ Y_V=-\frac{\Delta}{4\cdot a} \end{gathered}[/tex]First, let's calculate the coordinate X by replacing the values of the coefficients:[tex]\begin{gathered} X_V=-\frac{b}{2\cdot a} \\ \\ X_V=-\frac{108}{2\cdot(-2)}=-\frac{108}{-4}=\frac{108}{4}=\frac{54}{2}=27 \end{gathered}[/tex]So, the coordinate x = 27.
Now, let's find the y coordinate:[tex]\begin{gathered} Y_V=-\frac{\Delta}{4\cdot a} \\ \\ Y_V=-\frac{b^2-4\cdot a\cdot c}{4\cdot a} \\ \\ Y_V=-\frac{108^2-4\cdot(-2)\cdot75}{4\cdot(-2)} \\ \\ Y_V=-\frac{11664+600}{-8}=\frac{12264}{8}=1533 \end{gathered}[/tex]The coordinate y = 1533.
Answer:
The maximum profit will be 1533 (value of y) when x = 27.
Cost of a CD: $14.50Markup: 30%
Answers
Given:
Cost of a CD = $14.50
Markup =30%
If markup 30% then:
[tex]\begin{gathered} =\frac{130}{100} \\ =1.3 \end{gathered}[/tex]So the cost is:
[tex]\begin{gathered} =1.3\times14.50 \\ =18.85 \end{gathered}[/tex]markup cost is 18.85
Please help asap will give Brainly!!!
Answers
The following completes the proof: D. The Alternate Interior Angles Theorem shows that the angles BAC and DCA are congruent.
The Alternate Interior Angles Theorem: What is it?
According to the alternate interior angles theorem, when a transversal cuts over two (2) parallel lines, the alternate interior angles that are created are congruent.
We can infer and logically derive from the Alternate Interior Angles Theorem that the sentence that correctly concludes the proof is that angle BAC and angle DCA are congruent.
Segment AB is parallel to segment DC, while segment BC is parallel to segment AD, according to the information provided. Create the diagonals A and C using a straight edge. By virtue of the Reflexive Property of Equality, it is congruent to itself.
to learn more about Alternate Interior Angles refer to:
https://brainly.com/question/1807741
#SPJ13
Michelle can wash dry and fold 5 loads of laundry in 3 1/2 hours. what is the average amount of time it takes Michelle to do one load of laundry
Answers
A set of 12 data points is given above. Which of thefollowing is true of these data?
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\lbrace14.9,21.1,21.2,8.4,14.5,5.9,7.6,10.0,4.8,3.2,28.7,29.5\rbrace[/tex]STEP 2: Find the mean ofthe data
[tex]\begin{gathered} The\:arithemtic\:mean\:\left(average\right)\:is\:the\:sum\:of\:the\:values\:in\:the\:set\:divided\:by\:the\:number\:of\:elements\:in\:that\:set. \\ \mathrm{If\:our\:data\:set\:contains\:the\:values\:}a_1,\:\ldots \:,\:a_n\mathrm{\:\left(n\:elements\right)\:then\:the\:average}=\frac{1}{n}\sum _{i=1}^na_i\: \\ Sum=169.8 \\ n=12 \\ mean=\frac{169.8}{12} \\ mean=14.15 \end{gathered}[/tex]STEP 3: Find the median
[tex]\begin{gathered} \mathrm{The\:median\:is\:the\:value\:separating\:the\:higher\:half\:of\:the\:data\:set,\:from\:the\:lower\:half.} \\ \:the\:number\:of\:terms\:is\:odd,\:then\:the\:median\:is\:the\:middle\:element\:of\:the\:sorted\:set \\ If\:the\:number\:of\:terms\:\:is\:even,\:then\:the\:median\:is\:the\:arithmetic\:mean\:of\:the\:two\:middle\:elements\:of\:the\:sorted\:set \\ \\ \mathrm{Arrange\:the\:terms\:in\:ascending\:order} \\ 3.2,\:4.8,\:5.9,\:7.6,\:8.4,\:10,\:14.5,\:14.9,\:21.1,\:21.2,\:28.7,\:29.5 \\ median=12.25 \end{gathered}[/tex]Hence, it can be seen here that the mean is larger than median.
STEP 4: Find the Interquartile range
[tex]\begin{gathered} The\:interquartile\:range\:is\:the\:difference\:of\:the\:first\:and\:third\:quartiles \\ First\text{ Quartile}=6.75 \\ Third\text{ quartile}=21.15 \\ IQR=14.4 \end{gathered}[/tex]STEP 5: Find the standard deviation
[tex]\begin{gathered} \mathrm{The\:standard\:deviation,\:}\sigma \left(X\right)\mathrm{,\:is\:the\:square\:root\:of\:the\:variance:\quad }\sigma \left(X\right)=\sqrt{\frac{\sum _{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1}} \\ Standard\text{ deviation}=9.11836 \end{gathered}[/tex]Hence, it can be seen from above that the interquartile range is larger than the standard deviation.
STEP 6: Find the range
[tex]\begin{gathered} \mathrm{The\:range\:of\:the\:data\:is\:the\:difference\:between\:the\:maximum\:and\:the\:minimum\:of\:the\:data\:set} \\ Minimum=3.2 \\ Maximum=29.5 \\ Range=26.3 \end{gathered}[/tex]STEP 7: Fnd the variance
[tex]\begin{gathered} \mathrm{The\:sample\:variance\:measures\:how\:much\:the\:data\:is\:spread\:out\:in\:the\:sample.} \\ \mathrm{For\:a\:data\:set\:}x_1,\:\ldots \:,\:x_n\mathrm{\:\left(n\:elements\right)\:with\:an\:average}\:\bar{x}\mathrm{,\:}Var\left(X\right)=\sum _{i=1}^n\frac{\left(x_i-\bar{x}\right)^2}{n-1} \\ Variance=83.14454 \end{gathered}[/tex]Hence, it can be seen that the range is not larger than the variance.
Therefore, the answer is I and II only.
what is the correct base and coefficient for the function:
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The general form of a logarithmic function is:
[tex]y=a\cdot\log _b(x)[/tex]Where a is the coefficient and b is the base. In the given picture, we can see that the coefficient is equal to 1, while the base is equal to 2.
Part I: Domain and Range-identify the domain and range of each graph. Problem / Work Answe 2+ 6+ 2+ 1. Week 15 Homework Packet pdf 2003
Answers
Domain is the set of input values,
In the graph x axis show the domain
Where the x values is lies at -2,-1,0,1,2
Sothe domain will be :
[tex]\text{Domain =-2}\leq x\leq2[/tex]Range is the set of output values,
In the graph the value of function at y axis is : 0,2,4,6,8-2,-4.....
So, the range will be :
[tex]\text{Range = -}\infty\leq y\leq\infty[/tex]xyx2xy1645256720 2258 484 1,2762873 7842,044 3294 1,0243,008 45141 2,025 6,345 ∑x=143 ∑y=411 ∑x2=4,573 ∑xy=13,393 Which regression equation correctly models the data?y = 2.87x + 0.12y = 2.87x + 11.85y = 3.39x – 14.75y = 3.39x – 9.24
Answers
We are asked to identify the correct regression equation.
The regression equation is given by
[tex]y=bx+a[/tex]Where the coefficients a and b are
[tex]a=\frac{\sum y\cdot\sum x^2-\sum x\cdot\sum xy}{n\cdot\sum x^2-(\sum x)^2}[/tex][tex]b=\frac{n\cdot\sum xy-\sum x\cdot\sum y}{n\cdot\sum x^2-(\sum x)^2}[/tex]Where n is the number of observations that is 5.
Let us substitute the following into the above formula.
∑x=143
∑y=411
∑x^2=4,573
∑xy=13,393
[tex]a=\frac{411\cdot4573-143\cdot13393}{5\cdot4573-(143)^2}=-14.75[/tex][tex]b=\frac{5\cdot13393-143\cdot411}{5\cdot4573-(143)^2}=3.39[/tex]So, the coefficients are
a = -14.75
b = 3.39
Therefore, the correct regression equation is
[tex]y=3.39x-14.75[/tex]determine how many vertices and how many edges the graph has
Answers
in the given figure,
there are 4 vertices
and there are 3 edges.
thus, the answer is,
vertiev
i have to find is they similar or not. help im lost
Answers
First we have to find the missing angle on each case.
In the first triangle we have
180°-(28°+80°)=72°
In the second triangle we have
180°-(28°+71°)=81°
Since the values of the angles are not the same for both triangles they are not similar.
Determine if the following statement uses inductive reasoning and explain in complete sentences. Find a counterexample, if possible.Statement: If the Charleston Chiefs score two touchdowns each quarter, then they must have won the game
Answers
Answer:
Explanation:
The given statement is
Statement: If the Charleston Chiefs score two touchdowns each quarter, then they must have won the game
It is an inductive statement
The counterexample would be
If the Charleston team won the game, they must have scored two touchdowns each quarter
The width of a 2-by-4 piece of wood is actually 34 inches. Find the total width of 28 2-by-4s laid side-by-side. Simplify youranswer.o 126 inchesO 98 inches0784 inches844 inches
Answers
The of one 2-by-4 piece of wood is 3.5 inches
To find the width of 28 pcs of wood, just multiply the number of wood to the actual width which is 3.5 inches
So we have :
[tex]28\times3.5=98[/tex]The answer is 98 inches
This is Calculus 1 Linear Optimization Problem! MUST SHOW ALL THE JUSTIFICATION!!!
Answers
Given:
Required:
We need to find the value of AB
Explanation:
Here ABC is the right anglr triangle
so
[tex]\begin{gathered} AB^2=BC^2+AC^2=36+36=72 \\ AB=6\sqrt{2} \end{gathered}[/tex]Final answer:
The minimum length of crease is
[tex]6\sqrt{2}[/tex]Express the repeating decimal 0.2 as a fraction
Answers
Answer:
The fraction form of the repeating decimal is;
[tex]\frac{2}{9}[/tex]Explanation:
We want to express the repeating decimal 0.2 (2 repeating) as a fraction.
let x represent the fraction;
[tex]\begin{gathered} x=0.2222\ldots \\ 10x=2.222\ldots \end{gathered}[/tex]Then subtract x from 10x;
[tex]\begin{gathered} 10x-x=2.222\ldots-0.222\ldots \\ 9x=2.0 \end{gathered}[/tex]Then we can divide both sides by the coefficient of x;
[tex]\begin{gathered} \frac{9x}{9}=\frac{2}{9} \\ x=\frac{2}{9} \end{gathered}[/tex]Therefore, the fraction form of the repeating decimal is;
[tex]\frac{2}{9}[/tex]