A linear regression model for the revenue data for a company is R=25.9t + 204 where R is total annual revenue and t is time since 1/31/02 in years.
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The linear regression model is
[tex]R=25.9t+204[/tex]Where
R is the total annual revenue (dependant variable)
t is the time, in years, since 1/31/02 (independent variable)
To predict the annual revenue for the period ending 1/31/10, the first step is to determine the value of t. Considering that t=0 is the first recorded year (1/31/02), the value of t corresponding to period 1/31/10 is the number of years passed since, including 2002, which is 9 years.
So you have to calculate R for t=9. Replace the formula with t=9 and calculate the corresponding value of R
[tex]\begin{gathered} R=25.9\cdot9+204 \\ R=437.1 \end{gathered}[/tex]R≈437 billion dollars
Related Questions
a 14-member board used for admitted
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Using the Borda's method, when one person is ranked as 1st, he/she gets 3 points, if he/she is ranked 2nd, get 2 points, also, if he/she is ranked as 3rd get 1 point, and finally, 0 points if she/he is ranked as 4th
so, let's detemine how many points got each one
Cardona: Was selected 1st by 6 people, 2nd by 2 people, 3rd by 4 people and 4th by 2 people
[tex]C=3*6+2*2+1*4=26[/tex]So, that's a total of 26 points
Pitts-Jones: Was selected as: #1 by 4 people, #2 by 3 people, #3 by 6 people and 4th by 1 person
[tex]P=3*4+2*3+1*6=24[/tex]So, that's 24 points for Pitts-Jones,
De Plata: Was ranked #1 by 2 people, #2 by 8 people, #3 by 1 person and #4 by 3 people
[tex]D=3*2+2*8+1*1=23[/tex]That's 23 points for De Plata
Vincent: Was ranked as #1 by 2 people, #2 by 1 person, #3 by 3 people and #4 by 8 people
[tex]V=3*2+2*1+1*3=11[/tex]that's 11 points for Vincent,
Answer: From the above, we can conclude that the winner using Borda's method is Cardona
3, -10, 16, -36, 68, ___-3, 12, -33, 102, -303, ___Identify a pattern in each list of numbers. Then use this pattern to find the next number.
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As for the sequence 3,-10,16,-36,68,..., notice that
[tex]\begin{gathered} 3-13=-10 \\ -10+26=-10+2(13)=-10+2^1(13)=16 \\ 16-52=16-4(13)=16-2^2(13)=-36 \\ -36+104=-36+8(13)=-36+2^3(13)=68 \end{gathered}[/tex]Therefore, the next term is
[tex]68-2^4(13)=68-16(13)=-140[/tex]The answer is -140.
Regarding the second pattern, notice that
[tex]\begin{gathered} -3+15=12 \\ 12-45=12-3(15)=12-3^1(15)=-33 \\ -33+135=-33+9(15)=-33+3^2(15)=102 \\ 102-405=102-27(15)=102-3^3(15)=-303 \end{gathered}[/tex]Then, the next term of the sequence is
[tex]-303+3^4(15)=912[/tex]The answer is 912
Ary is writing thank you cards to everyone who came to her wedding. It takes her of an hour to write one thank you card. If it took her 8 hours to finish writing all of the cards, how many thank you cards did she write? 48 thank you cards 36 thank you cards 46 thank you cards 40 thank you cards
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The question doesn't specify which fraction of an hour it takes Ary to write a thank you card.
Let's imagine that it takes her 1/4 of an hour to write a thank you card.
In such case, in one hour she will be able to write 4 thank you cards.
and therefore in 8 hours, ishe will be able to write 32 thank you cards (8 times 4 cards).
If it takes her 1/6 of an hour to write a thank you card, then in hone hour she will write a total of 6 thank you cards, and therefore, in 8 hours she will be able to write 8 times 6 thank you cards: 8 x 6 = 48 thank you cards.
If it takes her 1/5 of an hour to write a thank you card, then in hone hour she will write a total of 5 thank you cards, and therefore, in 8 hours she will be able to write 8 times 5 thank you cards: 8 x 5 = 40 thank you cards.
You just use this type of criteria to solve the problem whatever the fraction of the hour it takes to write one card as they specify in the question.
I need help if u need a pic of the graph I’ll take a picture of it
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A.
Using the points (2,3) and (0,6) to find the slope (m), we have:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{6-3}{0-2}=\frac{3}{-2}[/tex]The slope is m= -3/2
B.
Using the points (-1, 7.5) and (1, 4.5) to find the slope (m), we have:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{4.5-7.5}{1-(-1)}=\frac{-3}{1+1}=\frac{-3}{2}[/tex]The slope is m= -3/2
C.
The slope is the same as we are finding the ratio of the vertical change to the horizontal change between two points. Since the function represents a linear equation the slope is going to be the same despite of the points you choose.
Hello I need help with this question as fast as possible please , I am on my last few questions and I have been studying all day for my final exam tomorrow. It is past my bed time and I am exhausted . Thank you so much for understanding:))
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Solution:
Given the inequality below
[tex]2\left(4+2x\right)\ge \:5x+5[/tex]Solving the inequality to find the value of x
[tex]\begin{gathered} 2\left(4+2x\right)\ge \:5x+5 \\ Expand\text{ the brackets} \\ 8+4x\ge \:5x+5 \\ Collect\text{ like terms} \\ 4x-5x\ge5-8 \\ -x\ge\:-3 \\ x\le \:3 \end{gathered}[/tex]Hence, the answer is
[tex]x\le \:3[/tex]#17 - A bin contains 90 batteries (all size C). There are 30 Eveready, 24 Duracell, 20 Sony,10 Panasonic, and 6 Rayovac batteries. What is the probability that the battery selected is aDuracell?0 27.6%0 26.7%24.6%0 29.2%
Answers
According to the basic definition of probability,
[tex]\text{Probability}=\frac{\text{ No. of favorable events}}{\text{ Total no. of events}}[/tex]Given that the bin contains total 90 batteries, out of which 24 are duracell.
So the probability that a randomly selected battery is Duracell, is calculated as,
[tex]\begin{gathered} P(\text{Duracell)}=\frac{\text{ No. of Duracell Batteries}}{\text{ Total no. of batteries}} \\ P(\text{Duracell)}=\frac{24}{90} \\ P(\text{Duracell)}\approx0.267 \\ P(\text{Duracell)}\approx26.7\text{ percent} \end{gathered}[/tex]Thus, the probability that a randomly selected battery is Duracell, is 26.7% approximately.
5 6 7 8. One times a number equals 4 1
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hello
to solve this problem, we need to find the property of equality
let the unknown number be represented by x
[tex]4=1\times x[/tex]to solve for x, divide both sides of the equation by 1
[tex]\begin{gathered} 4=1x \\ \frac{4}{1}=\frac{1x}{1} \\ x=4 \end{gathered}[/tex]the number here is 4
the property used to get the answer is division property of equality
Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?
Answers
We have to find how far is the bird from Amanda.
With the information given, we can draw:
We can start by finding the third angle.
The sum of the angles have to be equal to 180°, so we can find it as:
[tex]\begin{gathered} \alpha+55\degree+63\degree=180\degree \\ \alpha=180-55-63 \\ \alpha=62\degree \end{gathered}[/tex]Now, we can apply the Law of Sines to find the distance between Amanda (A) and the bird (B):
[tex]\frac{AB}{\sin J}=\frac{AJ}{\sin B}[/tex]where AJ is the distance between Amanda and Jamie and AB is the distance between the bird and Amanda.
We then can solve for AB as:
[tex]\begin{gathered} AB=AJ\cdot\frac{\sin J}{\sin B} \\ AB=25\cdot\frac{\sin63\degree}{\sin62\degree} \\ AB\approx25\cdot\frac{0.891}{0.883} \\ AB\approx25.23 \end{gathered}[/tex]Answer: 25.23 [Option A]
3. You draw one card from a standard deck.(a) What is the probability of selecting a king or a queen? (b) What is the probability of selecting a face card or a 10? (c) What is the probability of selecting a spade or a heart? (d) What is the probability of selecting a red card or a black card?
Answers
Given:
The objective is to find,
a) The probability of selecting a king or a queen.
b) The probability of selecting a face card or a 10.
Explanation:
The total number of cards in a deck is, N = 52 cards.
a)
Out of 52 cards, the number of king cards is,
[tex]n(k)=4[/tex]Similarly, out of 52 cards, the number of queen cards is,
[tex]n(q)=4[/tex]Then, the probability of drawing one out of 4 king cards or one out of 4 queen cards can be calculated as,
[tex]\begin{gathered} P(E)=P(k)+P(q) \\ =\frac{n(k)}{N}+\frac{n(q)}{N} \\ =\frac{4}{52}+\frac{4}{52} \\ =\frac{8}{52} \end{gathered}[/tex]Hence, the probsability of selecting a king or a queen is (8/52).
b)
Out of 52 cards, the number of face cards is 12.
[tex]n(f)=12[/tex]Similarly, out of 52 cards, the number of 10 is,
[tex]n(10)=4[/tex]Then, the probability of drawing one out of 12 face cards or one out of 4 ten cards can be calculated as,
[tex]\begin{gathered} P(E)=P(f)+P(10) \\ =\frac{12}{52}+\frac{4}{52} \\ =\frac{12+4}{52} \\ =\frac{16}{52} \end{gathered}[/tex]Hence, the probability of selecting a face card or a 10 is (16/52).
c)
Out of 52 cards, the number of spade cards is 13.
[tex]n(s)=13[/tex]Similarly, out of 52 cards, the number of heart cards is 13.
[tex]n(h)=13[/tex]Then, the probability of drawing one out of 13 spade cards or one out of 13 heart cards can be calculated as,
[tex]\begin{gathered} P(E)=P(s)+P(h) \\ =\frac{n(s)}{N}+\frac{n(h)}{N} \\ =\frac{13}{52}+\frac{13}{52} \\ =\frac{26}{52} \end{gathered}[/tex]Hence, the probability of selecting a spade or a heart is 26/52.
d)
Out of 52 cards, the number of red cards is,
[tex]n(r)=26[/tex]Out of 52 cards, the number of black cards is,
[tex]n(b)=26[/tex]Then, the probability of drawing one out of 26 red cards or one out of 26 black cards is,
[tex]\begin{gathered} P(E)=P(r)+P(b) \\ =\frac{n(r)}{N}+\frac{n(b)}{N} \\ =\frac{26}{52}+\frac{26}{52} \\ =\frac{52}{52} \\ =1 \end{gathered}[/tex]Hence, the probability of selecting a red card or a black card is 1.
PLEASE DO IT ASAP
What is the value of the expression?
0.3(1/4 - 1) + 0.35
-0.575
-0.125
0.125
1.4
1.925
Answers
The value of the expression 0.3(1/4 - 1) + 0.35 is 0.125
The expression is
0.3(1/4 - 1) + 0.35
The expression is defined as the sentence with a minimum of two variables and at least one math operation.
Here the expression is
0.3 (1/4 - 1) + 0.35
First do the arithmetic operation in the bracket
0.3(1/4 - 1) + 0.35 = 0.3 × -0.75 + 0.35
In next step do the multiplication
0.3 × -0.75 + 0.35 = -0.225 + 0.35
Do the addition of the numbers
-0.225 + 0.35 = 0.125
Hence, the value of the expression 0.3(1/4 - 1) + 0.35 is 0.125
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find the other binomial p squared -13 p +36 =(p-9)
Answers
To find the other factor of the polynomial
[tex]p^2-13p+36[/tex]We need to find two integers which multiplication gives 36 and addition is -13.
This integers would be -9 and -4, then we have
[tex]p^2-13p+36=p^2-9p-4p+36[/tex]now we factor the right term using common factors:
[tex]\begin{gathered} p^2-9p-4p+36=p(p-9)-4(p-9) \\ =(p-9)(p-4) \end{gathered}[/tex]Hence:
[tex]p^2-9p-4p=(p-9)(p-4)[/tex]Therefore, the other binomial we are looking for is (p-4).
Question 3 10 pts When solving an absolute value equation, such as |2x + 51 = 13, it is important to create two equations: 2x + 5= [ Select] and 2.1 + 5 = [Select ] [ Select] Resulting in z = vor [Select] Question 4 5 pts
Answers
1) Solving that absolute value equation:
|2x+5|=13 Applying the absolute value eq. property
2x +5 = 13 subtracting 5 from both sides
2x = 13-5
2x= 8 Dividing by 2
x =4
2x +5=-13 subtracting 5 from both sides
2x = -13-5
2x = -18 Dividing by 2
x= -9
Then x=4 or x =-9
2) The equations 2x +5 =13 and 2x +15= -13
Resulting in x=4 or x =-9
The students of a school were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard.Each penholder was to be radius of 3cm and height 10.5 cm. The school was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be brought for the competition. Assume: pi = 22/7
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Recall the surface area for the following figures.
[tex]\begin{gathered} \text{Cylinder}=2\pi rh+2\pi r^2 \\ \\ \text{The term }2\pi r^2\text{ includes a cover both the top and bottom of the cylinder} \\ \text{Since we will be using only the bottom modify the formula such that it only} \\ \text{includes the bottom part} \\ \\ \text{Pen Holder Surface Area}=2\pi rh+\pi r^2 \end{gathered}[/tex]Given that
height = h = 10.5 cm
radius = r = 3 cm
π = 22/7
Substitute the following given and we have the surface area for the pen holder
[tex]\begin{gathered} \text{Pen Holder Surface Area}=2\pi rh+\pi r^2 \\ \text{Pen Holder Surface Area}=2(\frac{22}{7})(3\operatorname{cm})(10.5\operatorname{cm})+(\frac{22}{7})(3\operatorname{cm})^2 \\ \text{Pen Holder Surface Area}=198\operatorname{cm}+(\frac{22}{7})(9\operatorname{cm}) \\ \text{Pen Holder Surface Area}=198\operatorname{cm}+\frac{198}{7}\operatorname{cm} \\ \text{Pen Holder Surface Area}=\frac{1584}{7}\operatorname{cm}^2 \end{gathered}[/tex]Now that we have the surface area, multiply it by 35 since there are 35 competitors in the competition
[tex]undefined[/tex]A student entering a doctoral program in educational psychology is required to select two courses from the list provided as part of his or her program (a)List all possible two-course selections (b)Comment on the likelihood that you EPR 625 and EPR 686 will be selected The course list EPR 613, EPR 664, EPR 625, EPR 685, EPR 686(a)select all the possible two-course selections belowA. 613, 686B. 625,686C. 613,613,664D. 664,685E. 625,685F. 625,672G. 613,625H. 685,686I. 664,625J 686,686K. 613,613L. 613,685M. 664, 686N. 613,664
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List of courses that the student entering a doctoral program in educational psychology can take:
EPR 613, EPR 664, EPR 625, EPR 685, EPR 686
Therefore, the possible two-course selections for the student are:
A. Both courses are on the list given: 613, 686
B. Both courses are on the list given: 625, 686
C. It's not possible. This option contains three courses.
D. Both courses are on the list given: 664, 685
E. Both courses are on the list given: 625, 685
F. It's not possible, Course 672 isn't available.
G. Both courses are on the list given: 613, 625
H. Both courses are on the list given: 685, 686
I. Both courses are on the list given: 664, 625
J. It's not possible. Just one course is given.
K. Same case than J. Just one course.
L. Both courses are on the list given: 613, 685
M. Both courses are on the list given: 664, 686
N. Both courses are on the list given: 613, 664
The total fixed costs of producing a product is $55,000 and the variable cost is $190 per item. If the company believes they can sell 2,500 items at $245 each, what is thebreak-even point?800 items900 items960 items 1,000 itemsNone of these choices are correct.
Answers
Let's call FC the fixed cost for production and VC the variable cost per item.
The company believes they can sell 2,500 items at $245 each.
Production costs:
For producing 2,500 items, the company has to spend (total cost, TC):
[tex]\begin{gathered} TC=FC+2,500\cdot VC \\ TC=55,000+2,500\cdot190 \\ TC=530,000 \end{gathered}[/tex]Sells:
Now, company sells eacho of the 2,500 items at $245, so, the company income (I) is:
[tex]I=245\cdot x[/tex]where x is the number of items sold.
Break-even point:
This point is reached when company can recover the money they spend (TC). So, we have the following eaquation to solve:
[tex]\begin{gathered} TC\text{ = I} \\ \to530,000=245\cdot x \\ \to x=\frac{530,000}{245}\text{ =2,163.3 (rounded) } \end{gathered}[/tex]Since company can not sell fractions of items, they have to sell 2,164 items to take back the money they invested.
So, "None of these choices are correct".
Function g can be thought of as a translated (shifted) version of f(x) = x?Y Y6+5+432f7 6 5 4 3 21 2 3 4 5 6 7-2--3+-6-7Write the equation for g(x).
Answers
Answer:
g(x) = (x + 5)²
Explanation:
g is the same function f shifted 5 units to the left.
Then, if we have a function h(x) =f(x+c), h(x) is f(x) shifted c units to the left.
So, to translate f 5 units to the left, we need to replace x by (x + 5), to get:
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=f(x+5) \\ g(x)=(x+5)^2 \end{gathered}[/tex]So, the equation for g(x) is:
g(x) = (x + 5)²
Let's find2. 1+5 3First write the addition with a common denominator.Then add.12— +51-4-13Х5
Answers
The given addition exercise is:
[tex]\frac{2}{5}+\frac{1}{3}[/tex]The LCM of the denominator (5 and 3) = 15
Multiply 2/5 by 3/3
[tex]\frac{2}{5}=\frac{2\times3}{5\times3}=\frac{6}{15}[/tex]Multiply 1/3 by 5/5
[tex]\frac{1}{3}=\frac{1\times5}{3\times5}=\frac{5}{15}[/tex]The addition becomes
[tex]\frac{6}{15}+\frac{5}{15}=\frac{11}{15}[/tex]Therefore, we can fill in the vacant boxes as shown below:
[tex]\frac{2}{5}+\frac{1}{3}=\frac{6}{15}+\frac{5}{15}=\frac{11}{15}[/tex]
A house casts a shadow that is 12 feet tall. A woman who is 5.5 feet tall casts a shadow that is 3 feet tall.
What is the height of the house?
A. 22 ft.
B. 55 ft.
C. 5.5 ft.
D.220 ft.
Answers
To find how many feet of shadow are cast from a one foot shadow, divide 5.5 by 3. This should give you about 1.83 ft of shadow per foot. Now, multiply the 12 foot shadow by 1.83 ft to get about 22 ft.
6. Point A is located at (7, -3) and point M is located at (-9,5). If M is themidpoint of segment AP, what are the coordinates of point P?"A) (-25, 13)B) (-1,1)C) (8,-4)OD) (25, -13)7 Name the ray that is opposite to ray CD."
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Answer:
The coordinates of P is;
[tex](-25,13)[/tex]Explanation:
Given that;
Point A is located at (7, -3) and point M is located at (-9,5).
And;
M is the midpoint of segment AP.
The coordinate of P will be represented by;
[tex]P=(x_2,y_2)[/tex]Using the formula for calculating midpoint;
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]Making x2 and y2 the subject of formula;
[tex]\begin{gathered} x_2=2x-x_1 \\ y_2=2y-y_1 \end{gathered}[/tex]So, substituting the given coordinates;
[tex]\begin{gathered} M=(x,y)=(-9,5) \\ A=(x_1,y_1)=(7,-3) \end{gathered}[/tex]So, we have;
[tex]\begin{gathered} x_2=2x-x_1 \\ x_2=2(-9)-7 \\ x_2=-25 \end{gathered}[/tex]And;
[tex]\begin{gathered} y_2=2y-y_1 \\ y_2=2(5)-(-3)=10+3 \\ y_2=13 \end{gathered}[/tex]Therefore, the coordinates of P is;
[tex](-25,13)[/tex]solve p(x+q)^4=r for x
Answers
Given the following equation:
[tex]p\mleft(x+q\mright)^4=r[/tex]You can solve for the variable "x" as following:
1. You need to apply the Division property of equality by dividing both sides of the equation by "p":
[tex]\begin{gathered} \frac{p\mleft(x+q\mright)^4}{p}=\frac{r}{p} \\ \\ \mleft(x+q\mright)^4=\frac{r}{p} \end{gathered}[/tex]2. Remember that:
[tex]\sqrt[n]{a^n}=a[/tex]Then:
[tex]\begin{gathered} \sqrt[4]{(x+q)^4}=\sqrt[4]{\frac{r}{p}} \\ \\ x+q=\sqrt[4]{\frac{r}{p}} \end{gathered}[/tex]3. Now you have to apply the Subtraction property of equality by subtracting "q" from both sides of the equation:
[tex]\begin{gathered} x+q-(q)=\sqrt[4]{\frac{r}{p}}-(q) \\ \\ x=\sqrt[4]{\frac{r}{p}}-q \end{gathered}[/tex]The answer is:
[tex]x=\sqrt[4]{\frac{r}{p}}-q[/tex]A model of a dinosaur skeleton was made using a scale of 1 in : 15 in in a museum. If the size of the dinosaur’s tail in the model is 8 in, then find the actual length of dinosaur’s tail.
Answers
The length of the real dinosaur's tail is 120 inches.
How to find the actual length of the tail?We know that the scale of the model is 1in : 15in, this means that each inch in the model represents 15 inches of the actual dinosaur.
So, if the tail of the model has a length of 8 inches, the length of the real tail will have 15 times that, so the length is given by the product:
8in*15 = 120in
Learn more about scale models.
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Solve. 4 + x/7 = 2Question 3 options:12-144210
Answers
1) Since we have a Rational Equation let's proceed with that, isolating the x on one side and then we can get rid of that fraction. This way:
[tex]\begin{gathered} 4+\frac{x}{7}=2 \\ 4-4+\frac{x}{7}=2-4 \\ \frac{x}{7}=-2 \end{gathered}[/tex]Notice that now, we're going to get rid of that fraction on the left side, multiplying it by 7 (both sides) :
[tex]\begin{gathered} 7\times\frac{x}{7}=-2\times7 \\ x=-14 \end{gathered}[/tex]Thus, the answer is -14
Sophia is in the business of manufacturing phones. She must pay a daily fixed cost of $200 to rent the building and equipment, and also pays a cost of $100 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
I need the equation
Answers
Answer:
C = 100p + 200
Step-by-step explanation:
Because C is the total cost per day, 200 is the y-intercept because it's paid daily. The 100 is the slope since "he pays a cost of $100 per phone produced
Select the sequence of transformations that will carry rectangle A onto rectangle A'. A) reflect over y-axis, rotate 90° clockwise, then reflect over x-axis B) rotate 180° clockwise, reflect over y-axis, then translate 3 units left C) rotate 180° clockwise, reflect over x-axis, then translate 2 units left D) rotate 90° clockwise, reflect over y axis, then translate 3 units left
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Let:
[tex]\begin{gathered} A=(3,4) \\ B=(4,2) \\ C=(1,-1) \end{gathered}[/tex]and:
[tex]\begin{gathered} A^{\prime}=(-3,1) \\ B^{\prime}=(-4,-1) \\ C^{\prime}=(-1,-4) \end{gathered}[/tex]After a reflection over the y-axis:
[tex]\begin{gathered} A\to(-x,y)\to A_1=(-3,4) \\ B\to(-x,y)\to B_1=(-4,2) \\ C\to(-x,y)\to C_1=(-1,-1) \end{gathered}[/tex]After a translation 3 units down:
[tex]\begin{gathered} A_1\to(x,y-3)\to A_2=(-3,1) \\ B_1\to(x,y-3)\to B_2=(-4,-1) \\ C_1\to(x,y-3)\to C_2=(-1,-4) \end{gathered}[/tex]Since:
[tex]\begin{gathered} A_2=A^{\prime} \\ B_2=B^{\prime} \\ C_2=C^{\prime} \end{gathered}[/tex]The answer is the option K.
How much would you need to deposit in an account now in order to have $20,000 in the account in 4 years? Assume the account earns 5% interest.I want answer and explanation.
Answers
The rule of the simple interest is
[tex]\begin{gathered} I=PRT \\ A=P+I \end{gathered}[/tex]I is the amount of interest
P is the initial amount
R is the interest rate in decimal
T is the time
We need to find the initial amount if the new amount is $20,000, the interest rate is 5% for 4 years, then
A = 20000
R = 5/100 = 0.05
T = 4
Substitute them in the rules above
[tex]\begin{gathered} I=P(0.05)(4) \\ I=0.2P \\ 20000=P+0.2P \\ 20000=1.2P \\ \frac{20000}{1.2}=\frac{1.2P}{1.2} \\ 16666.67=P \end{gathered}[/tex]You need to deposit $16,666.67
The rule of the compounded interest
[tex]A=P(1+r)^t[/tex]A is the new amount
P is the initial amount
r is the interest rate in decimal
t is the time
A = 20000
r = 0.05
t = 4
Substitute them in the rule above
[tex]\begin{gathered} 20000=P(1+0.05)^4 \\ 20000=P(1.05)^4 \\ \frac{20000}{(1.05)^4}=\frac{P(1.05)^4}{(1.05)^4} \\ 16454.05=P \end{gathered}[/tex]You need to deposit $16,454.05
How many roots does x^2-6x+9 have ? It may help to graph the equation.
Answers
The roots are those values that make a function or polynomial take a zero value. The roots are also the intersection points with the x-axis. In the case of a quadratic equation you can use the quadratic formula to find its roots:
[tex]\begin{gathered} ax^2+bx+c=y\Rightarrow\text{ Quadratic equation in standard form} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\Rightarrow\text{ Quadratic formula} \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} y=x^2-6x+9 \\ a=1 \\ b=-6 \\ c=9 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(1)(9)}}{2(1)} \\ x=\frac{6\pm\sqrt[]{36-36}}{2} \\ x=\frac{6\pm0}{2} \\ x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]As you can see, this function only has one root, at x = 3.
You can see this in the graph of the function:
a teacher bought 4 folders and 9 books for $33.75. on another day, she bought 3 folders and 12 books at the same prices for $34.50. how much did she pay for each folder and each book?
Answers
The teacher made two different purchases:
First purchase:
4 folders and 9 books for $33.75
Second purchase
3 folders and 12 books for $34.50
Let "f" represent the cost of each folder and "b" represent the cost of each book. You can express the total cost of each purchase as equations:
[tex]\begin{gathered} 1)4f+9b=33.75 \\ 2)3f+12b=34.50 \end{gathered}[/tex]Now we have established a system of equations, to solve it, the first step is to write one of the equations in terms of one of the variables.
For example, I will write the first equation in terms if "f"
[tex]\begin{gathered} 4f+9b=33.75 \\ 4f=33.75-9b \\ \frac{4f}{4}=\frac{33.75-9b}{4} \\ f=\frac{135}{16}-\frac{9}{4}b \end{gathered}[/tex]The second step is to replace the expression obtained for "f" in the second equation:
[tex]\begin{gathered} 3f+12b=34.50 \\ 3(\frac{135}{16}-\frac{9}{4}b)+12b=34.50 \end{gathered}[/tex]Distribute the multiplication on the parentheses term
[tex]\begin{gathered} 3\cdot\frac{135}{16}-3\cdot\frac{9}{4}b+12b=34.50 \\ \frac{405}{16}-\frac{27}{4}b+12b=34.50 \\ \frac{405}{16}+\frac{21}{4}b=34.50 \end{gathered}[/tex]Pass the number to the right side of the equal sign by applying the opposite operation to both sides of it
[tex]\begin{gathered} \frac{405}{16}-\frac{405}{16}+\frac{21}{4}b=34.50-\frac{405}{16} \\ \frac{21}{4}b=\frac{147}{16} \end{gathered}[/tex]Now divide b by 21/4 to cancel the multiplication and to keep the equality valid, you have to divide both sides of the expression, so divide 147/16 by 21/4 too, or multiply them by its reciprocal fraction, 4/21, is the same.
[tex]\begin{gathered} (\frac{21}{4}\cdot\frac{4}{21})b=(\frac{4}{21}\cdot\frac{147}{16}) \\ b=\frac{7}{4}\approx1.75 \end{gathered}[/tex]Each book costs $1.75
Now that we have determined how much does each book cost, we can determine the cost of each folder by replacing the value of "b" in the expression obtained for "f"
[tex]\begin{gathered} f=\frac{135}{16}-\frac{9}{4}b \\ f=\frac{135}{16}-\frac{9}{4}\cdot\frac{7}{4} \\ f=\frac{9}{2}\approx4.5 \end{gathered}[/tex]Each folder costs $4.50
Which function, A or B, has a greater rate of change? Be sure to include the values for the rates of change in your answer. Explain your answer.
Answers
The function B has a greater rate of change
Explanation:Function A is represented by the table:
Selecting the points (1, 5) and (2, 7)
The rate of change of function A:
[tex]\begin{gathered} m_A=\frac{7-5}{2-1} \\ \\ m_A=2 \end{gathered}[/tex]The rate of change of the function A = 2
Function B is represented by the graph:
(1, 1) and (2, 4)
[tex]\begin{gathered} m_B=\frac{4-1}{2-1} \\ \\ m_B=3 \end{gathered}[/tex]The rate of change of the function B = 3
The function B has a greater rate of change
12. Suppose you buy 20 gallons of gasoline in a city that collects excisetax of .16 per gallon. If you pay $1.25 per gallon, what percent of theprice is city excise tax?a.b.c.13.4%13.2%12.8%
Answers
We can calculate the percent of the price that is excise tax by dividing the amount of tax per gallon by the final price of the gallon.
If the tax is 0.16 per gallon and the final price is 1.25 per gallon, the percentage can be calculated as:
[tex]p=\frac{0.16}{1.25}\cdot100\text{ \%}=0.128\cdot100\text{ \%}=12.8\text{ \%}[/tex]The percentage that is city excise tax is 12.8% of the final price of the gasoline.
A certain orange colour requires mixing 5 parts of red paint with 7 parts of yellow paint.Roderick mixed 15 parts of red paint with 21 parts of yellow paint. Did he create the correct orange colour?
Answers
Answer:
Roderick has created the correct orange color.
Explanation:
The orange color required mixing 5 parts of red paint with 7 parts of yellow paint. The ratio is given below:
[tex]\operatorname{Re}d\colon\text{Yellow}=5\colon7[/tex]Roderick mixed 15 parts of red paint with 21 parts of yellow paint. This is expressed in ratio as:
[tex]\begin{gathered} \operatorname{Re}d\colon\text{Yellow}=15\colon21 \\ \text{Divide both sides by 3} \\ \frac{15}{3}\colon\frac{21}{3}=5\colon7 \end{gathered}[/tex]Since the two ratios reduces to the same value, they are equivalent, thus Roderick has created the correct orange color.