Question 3 4.5 pts At the honor roll party, students had the choice of cheese or pepperoni pizza and coke or sprite. Of the 125 students that made the honor roll 64% had cheese pizza. There were 48 students that had cheese pizza and a coke. 5 more students chose to have a Coke rather than Sprite. Complete the table below.
Answers
The table would look like this;
We are told that Of the 125 students that made the honor roll 64% had cheese pizza.
64% of 125 is 80 students, therefore, 80 students in total had cheese pizza.
Let's fill that in.
We now know that those who had pepperoni pizza are 125 - 80 = 45 in number.
There were 48 students that had cheese pizza and a coke, let's fill that in too, we have.
This means that the number of students that had a cheese and sprite is 80 - 48 = 32 students.
We are also told that 5 more students chose to have a coke than a sprite.
Let the total number that chose coke be x.
Then the total who chose sprite would be x - 5.
But these total must add up to 125.
So;
[tex]\begin{gathered} x+x-5=125 \\ 2x-5=125 \\ 2x=130 \\ x=\frac{130}{2}=65 \\ x-5\text{ = 60} \end{gathered}[/tex]Therefore, 65 students took coke in total and 60 took sprite, let's fill that in too.
We can now fill in the pepperoni column.
For pepperoni and coke, we subtract 48 from 65 to obtain 17
For pepperoni and sprite, we subtract 32 from 60 to obtain 28
ii. The joint relative frequency of the students who had a sprite and pepperoni pizza.
From the table, the joint relative frequency of those who had a sprite and a pepperoni pizza is
[tex]\begin{gathered} \frac{28}{45} \\ \end{gathered}[/tex]i.e 28/45 or 0.6 of those who had pepperoni pizza, took sprite.
Related Questions
10 Zara writes a sequence of five numbers. The first number is 2. The last number is 18. Her rule is to add the same amount each time. Write the missing numbers. 2,____ ,_____,______, 18
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If the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that, the first number is 2 and the last number is 18,
a = 2
L=18
n=5
a₅=5
a₅=a+(5-1)d
18=2+4d
4d = 18-2
4d = 16
d= 16 / 4
d=4
The terms of the sequence are,
a₁=2
a₂=2+4=6
a₃=6+4=10
a₄=10+4=14
a₅=14+4=18
Thus, if the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
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Benny is flying a kite directly over his friend Frank, who is 125 meters away.When he holds the kite string down to the ground, the string makes a 39° anglewith the level ground. How high is Benny's kite?Draw a sketch depicting the situation above.b.)Use trigonometry to determine the height of Benny's kite.
Answers
Solution
Let us draw a diagram to illustrate the information
Using SOHCAHTOA
[tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ \\ tan39=\frac{h}{125} \\ cross\text{ multiply} \\ h=125\times tan39 \\ \\ h=101.2230041 \\ \\ h=101.22m\text{ \lparen to two decimal places\rparen} \end{gathered}[/tex]Please help ASAP thank you
Answers
Answer:
Shade 6 strips out of the 9.
Step-by-step explanation:
Let us find 2/3 of 9
We can write 2/3 of 9 as 2/3 × 9
To multiply fractions through the following steps:
Now, 2/3 × 9 = (2 × 9) / 3 = 18/3 = 6
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?
Answers
c = price of a slice of Cheese pizza
m= price of a slice of mushroom pizza
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50
3c + 4 m = 12.50
Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50.
3c + 2m = 8.50
We have the system of equations:
3c + 4 m = 12.50 (a)
3c + 2m = 8.50 (b)
Subtract (b) to (a) to eliminate c
3c + 4m = 12.50
-
3c + 2m = 8.50
_____________
2m = 4
Solve for m:
m = 4/2
m=2
The cost of one slice of mushroom pizza is $2
What is a feature of function g if g(x) = log (x-4) -8
Answers
The domain and range of the logarithmic function are
[tex]\begin{gathered} \text{domain}(\log x)=(0,\infty) \\ \text{range}(\log x)=(-\infty,\infty) \end{gathered}[/tex]Therefore, if
[tex]g(x)=\log (x-4)-8[/tex]We require that
[tex]\begin{gathered} x-4>0 \\ \Rightarrow x>4 \end{gathered}[/tex]Notice that the -8 term does not affect the range of function g(x); thus,
[tex]\begin{gathered} \text{domain}(g(x))=(4,\infty) \\ \text{range}(g(x))=(-\infty,\infty) \end{gathered}[/tex]Set g(x)=-8; then,
[tex]\begin{gathered} \Rightarrow\log (x-4)-8=-8 \\ \Rightarrow\log (x-4)=0 \\ \Rightarrow x=5 \end{gathered}[/tex]Therefore, y=-8 is not an asymptote of g(x), and, as shown above, the domain and range of g(x) are x>4, y->all real numbers.
Calculate the limit when x->4 as shown below,
[tex]\lim _{x\to4}g(x)=(\lim _{x\to4}\log (x-4))-8=(-\infty)-8=-\infty[/tex]Therefore, there is a vertical asymptote at x=4
Answer:
Hope this helps ;)
Step-by-step explanation:
If $5000 is invested at 9% annual simple interest, how long does it take to be worth $9050?
Answers
It takes 9 years to make $9050 from $5000 investment.
Given that, Principal = $5000, rate of interest = 9% and Amount = $9050.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Here, S.I. = Amount - Principal
= 9050-5000 = $4050
Now, 4050=(5000×9×T)/100
⇒ 4050/450 = T
⇒ T = 9 years
Therefore, it takes 9 years to make $9050 from $5000 investment.
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Hi, can you help me answer this question please, thank you!
Answers
1. Test statistic:
To find the test statistic, we use the formula:
[tex]\begin{gathered} Z=\frac{\bar{X_d}-\mu_d}{\frac{s_d}{\sqrt[]{n}}} \\ \text{where,} \\ \bar{X}_d=sample\text{ difference} \\ \mu_d=\text{population difference} \\ s_d=\text{standard deviation of the differences } \\ n=\text{ number of people in the survey.} \\ \\ \text{ We use Z statistic because the number of people are more than 30} \end{gathered}[/tex]Solving for Z, we have:
[tex]\begin{gathered} \bar{X}-\mu_d=3.1\text{ (Average difference given in the question)} \\ \\ \therefore Z=\frac{3.1}{\frac{13.8}{\sqrt[]{40}}}=1.4207\approx1.421\text{ (To 3 decimal places} \end{gathered}[/tex]Thus, the test statistic is 1.421
2. P-value:
To find the p-value, we check the Z-distribution table.
The value for the p-value is
[tex]2\times0.077658=0.15532\approx0.1553\text{ (To 4 decimal places)}[/tex](We multiply by 2 because it is a two-tailed test.
3. Comparison:
The alpha level is 0.001.
Thus, the p-value is greater than the alpha level
Write a pair of complex numbers whose sum is -4 and whose product is 53
Answers
The pair of complex numbers whose sum is -4 and whose product is 53 is illustrated as -b² - 4b - 53 = 0.
How to calculate the he value?Let the numbers be represented as a and b.
Therefore a + b = -4 .....i
a × b = 53 ........... ii
From equation I, a = -4 - b
Put this into equation ii
ab = 53
(-4 - b)b = 53
-b² - 4b = 53
Equate to 0
-b² - 4b - 53 = 0
The value can be found using the Almighty formula
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A homeowner estimates that it will take 9 days to roof his house. A professional roofer estimates that he could roof the house in 5 days. How long ( in days ) will it take if the homeowner helps the roofer?
Answers
Solution:
If x denote the days, the rate unit being Jobs per day is:
[tex]\frac{1}{x}=\frac{1}{9}+\frac{1}{5}[/tex]this is equivalent to
[tex]\frac{1}{x}=\frac{5+9}{45}=\frac{14}{45}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{45}{14}=3.2\text{ days}[/tex]that is just a little more than 3 days.
Brayden was given a box of assorted chocolates for his birthday. Each night, Brayden
treats himself to some chocolates. The number of chocolates remaining in the box t
days after Brayden's birthday can be modeled by the equation C = -3t+ 12. What
is the slope of the equation and what is its interpretation in the context of the
problem?
Answers
Answer:
Step-by-step explanation:
The slope of the function is -3 which reveals the number of chocolates Brayden eats each night.
Please see the picture below,PART BUse the real zeros to factor f
Answers
Explanation:
The polynomial is given below as
[tex]f(x)=x^4+2x^3-7x^2-8x+12[/tex]Given in the question above the real zeros are gotten below as
[tex]x=-3,-2,1,2[/tex]Concept:
To figure out the factor form of the polynoimial, we will equate each zero to x below as
[tex]\begin{gathered} x=c \\ (x-c) \end{gathered}[/tex]Therefore,
The factored form of the polynomial will be
[tex]\begin{gathered} f(x)=x^{4}+2x^{3}-7x^{2}-8x+12 \\ x=-3,x=-2,x=1,x=2 \\ f(x)=(x+3)(x+2)(x-1)(x-2) \end{gathered}[/tex]Hence,
Using the real zeros of f(x) , the factored form of the polynomial is
[tex]\Rightarrow f(x)=(x+3)(x+2)(x-1)(x-2)[/tex]Question 11:What is the maximum height of the driver off the diving board
Answers
To find the maximun height (y) given a quadratic equation as above you find the coordinates of the vertex (maximum or minimun point of a parabola)
1. Use the next formula to find the x- coordinate of the vertex
[tex]\begin{gathered} y=ax^2+bx+c \\ \\ x=-\frac{b}{2a} \end{gathered}[/tex][tex]\begin{gathered} x=-\frac{\frac{24}{9}}{2(-\frac{4}{9})} \\ \\ x=-\frac{\frac{24}{9}}{-\frac{8}{9}}=\frac{-24}{-8}=3 \end{gathered}[/tex]2. Use the value of x above to find y-coordinate in the vertex:
[tex]\begin{gathered} y=-\frac{4}{9}(3)^2+\frac{24}{9}(3)+12 \\ \\ y=-\frac{4}{9}(9)+\frac{72}{9}+12 \\ \\ y=-4+8+12 \\ \\ y=16 \end{gathered}[/tex]Then, the maximum height of the diver is 16 feetFind the set An B.
U = {1, 2, 3, 4, 5, 6, 7, 8)
A = {1, 2, 3, 4)
B = {1, 2, 6}
Answers
Step-by-step explanation:
I assume A n B means the intersection of the sets A and B.
that means all the elements that are in A and in B.
that is the set {1, 2}
state income tax? Jim Koslo earns $156,200 annually as a plant manager. He is married and supports 3 children. The state tax rate in his state is 3.55% of taxable income. What amount is withheld yearly for state income tax?
Answers
Answer:
44,000
Let me know if its wrong
2 ABC Company has a large piece of equipmentthat cost $85,600 when it was first purchased 6years ago. The current value of the equipment is$30,400. What is the average depreciation of theequipment per year?F. $ 5,800G. $ 9,200H. $15,200J. $27,600K. $42,800
Answers
The intial cost of the equipment is C, which is given as 85,600.
The present value is PV, which is given as 30,400.
This simply means the total depreciation over the last 6 years can be derived as;
Depreciation = C - PV
Depreciation = 85600 - 30400
Depreciation = 55200
However, the method of depreciation is not given/specified, and hence the question requires that you calculate the average depreciation per year. That is, the total depreciation would be evenly spread over the 6 year period (which assumes that the depreciation per year is the same figure)
Average depreciation = Total depreciation/6
Average Depreciation = 55200/6
Average Depreciation = 9200
The correct option is option G: $ 9,200
Consider the following equation of a parabola.(y- 7)? = -4(x - 3)Step 1 of 3: Find the focus of the parabola.
Answers
Answer
Focus = (2, 7)
Explanation
Given:
The following is the equation of a parabola
[tex](y-7)^2=-4x(x-3)[/tex]What to find:
To find the focus of the parabola.
Step-by-step solution:
The general equation of a parabola can be given as,
[tex](y-k)^2=4p(x-h)[/tex]Comparing the general equation of a parabola with the given equation of a parabola, we have
4p = -4
∴ p = -4/4 = -1
Also,
h = 3
k = 7
Since h ± c = F
We have,
3 - 1 = 2
Therefore, the focus will be (h ± c, k) = (2, 7)
Solve the inequality and graph the solution on the line provided.
< > M >
Inequality Notation:
Number Line:
or
-12 -10 -8 -6
-4 -2
0 2 4
Click and drag to plot line.
2x64 -48
6
8
10 12
Answers
Answer:
x ≥ 8Step-by-step explanation:
GivenInequality 2x - 64 ≥ - 48Solution2x - 64 ≥ - 482x ≥ 64 - 482x ≥ 16x ≥ 8To graph the solution, plot the point x = 8, make it closed dot, shade the line to the right from this point.
Kaitlin's family is planning a trip from WashingtonD.C., to New York City New York City is 227 miles from Washington, D.C.and the family can drive an average of 55mi / h . About how long will the trip take?
Answers
Kaitlin's family's trip from Washington D.C., to New York City of 227 miles at average rate of 55 miles per hour is 4 hours 8 minutes
How to determine the how long the trip will takeinformation gotten from the question include
Washington D.C., to New York City is 227 miles
Kaitlin's family can drive an average of 55mi / h
Average speed is a function of ratio distance covered with time. this is represented mathematically as
average speed = distance covered / time
55 miles / h = 227 miles / time
time = 227 / 55
time = 4.127 hours
The trip take 4.127 hours
0.127 * 60 = 7.62 ≅ 8 minutes
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solve the equation x 1.)132.)13/33.) 104.) none of these choices
Answers
Answer:
2. 13/3
Step-by-step explanation:
x will be equal to 13/3.
Given,
5^(2x - 1) = 5^(5x - 14)
We can see that base is the same for both the exponents on each side of the equation.
Now, on using the Logarithm on both sides with base 5, we can see that the base on both sides of the equation cancels out with the log (base 5) function.
And new equation becomes:
(2x - 1) = (5x - 14)
This derives us to another conclusion that if the base of an exponent is equal then,
the powers must be equal too.
(2x - 1) = (5x - 14)
=> 5x - 2x = -1 + 14
=> 3x = 13
which gives us,
=> x = 13/3.
Therefore x = 13/3.
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An amusement park's owners are considering extending the weeks of the year that it is opened. The owners would like to survey 100 randomly selected families to see whether an extended season would be of interest to those that may visit the amusement park.What is the best way to randomly choose these 100 families? Have the owners of the amusement park ask the first 100 people they see.Choose a neighborhood near the amusement park and ask 100 families in this neighborhood.Ask the first 100 families that enter the amusement park on a busy weekend day.Allow a random number generator to come up with 100 families within a 50 radius of the amusement park.
Answers
Solution
Option 1:
- The owners asking the first 100 people they see would mean that they would see only those around them. This could be anyone at all from workers in the amusement park to people outside the park; these would not be random, and would not necessarily be a family but the survey is talking about randomly choosing 100 families. Because of these reasons, this is not the best way to randomly choose 100 families.
Option 2:
- Choosing a neighborhood near the amusement park would mean that they go to a neighborhood with families that might visit the amusement park and there would be many families to randomly choose from.
- This option seems like a good choice to randomly choose these 100 families that might visit the amusement park.
Option 3:
- Asking the first 100 families that enter the amusement park on a busy weekend would definitely bias the survey since families that you find in the amusement park are families that definitely want to be there and if they are there on a busy weekend, they certainly would not mind extending the season
A boy goes to school by first taking a bus for 1 3/4 km and then by walking 1/3 km. Find the distance of his house from the school.
Answers
The boy goes to school by bus for 1 3/4km, then he walks 1/3 km.
To determine the total distance he traveled you have to add both distances:
[tex]1\frac{3}{4}+\frac{1}{3}[/tex]To solve this sum, add the fractions first and then add the result to the whole number:
- Add both fractions:
[tex]\frac{3}{4}+\frac{1}{3}[/tex]To add both fractions you have to express them using the same denominator first. A common multiple between the denominators "4" and "3" is "12". Multiply the first fraction by 3 and the second by 4 to express them as their equivalent fractions with denominator 12. Then proceed to add them:
[tex]\frac{3\cdot3}{4\cdot3}+\frac{1\cdot4}{3\cdot4}=\frac{9}{12}+\frac{4}{12}=\frac{9+4}{12}=\frac{13}{12}[/tex]The result is 13/12, as you can see the numerator is greater than the denominator, which indicates that this is an improper fraction, i.e. its value is greater than 1. You can write this fraction as a mixed number as follows:
- Solve the division:
[tex]13\div12=1.08\bar{3}[/tex]The mixed number will have the whole number "1".
- To express the decimal value as a fraction, multiply it by 12
[tex]0.08\bar{3}\cdot12=1[/tex]The result is the numerator of the fraction, and the denominator will be 12, so:
[tex]0.08\bar{3}=\frac{1}{12}[/tex]And the resulting mixed number is:
[tex]\frac{13}{12}=1\frac{1}{12}[/tex]Finally, add the remaining whole number from the first sum to determine the distance between his house and the school:
[tex]1+1\frac{1}{12}=2\frac{1}{12}[/tex]The distance he traveled from home to school is 2 1/12 km.
All the formation your name is on the picture picture provided
Answers
The range of the data is the difference between the maximum data value and the minimum.
In a box plot, the maximum and the minimum are indicated by the dots at the end of the horizontal line.
Here,
Maximum = 10
Minimum = 4.5
Thus, the range of the data is:
[tex]Range=10-4.5=5.5[/tex]During a tropical storm, the temperature decreased from 84° to 63º. Find the percent decrease in temperature during the storm. (a) 33% (b) 25% (c) 40% (d) 75%
Answers
To find the percentage of decrease, first, we divide.
[tex]\frac{63}{84}=0.75[/tex]This means 63° represents 75% of 84°. In other words, the temperature decreased by 25%.
Hence, the answer is B.Consider the function f(x)= square root 5x-10 for the domain [2, +infinity). find f^-1(x), where f^-1 is the inverse of f. also state the domain of f^-1 in interval notation.edit: PLEASE DOUBLE CHECK ANSWERS.
Answers
let f(x) = y
To find the inverse of f(x), we would interchange x and y:
[tex]\begin{gathered} y\text{ = }\sqrt[]{5x\text{ - 10}} \\ \text{Interchanging:} \\ x\text{ = }\sqrt[]{5y\text{ - 10}} \end{gathered}[/tex]Then we would make the subject of formula:
[tex]\begin{gathered} \text{square both sides:} \\ x^2\text{ = (}\sqrt[]{5y-10)^2} \\ x^2\text{ = 5y - 10} \end{gathered}[/tex][tex]\begin{gathered} \text{Add 5 to both sides:} \\ x^2+10\text{ = 5y} \\ y\text{ = }\frac{x^2+10}{5} \\ \text{The result above is }f^{\mleft\{-1\mright\}}\mleft(x\mright) \end{gathered}[/tex][tex]\begin{gathered} f^{\mleft\{-1\mright\}}\mleft(x\mright)\text{ = }\frac{x^2+10}{5} \\ The\text{ domain of the inverse is all real numbers} \\ \text{That is from negative infinity to positive infinity} \end{gathered}[/tex]In interval notation:
[tex]\begin{gathered} \text{Domain = (-}\infty,\text{ }\infty) \\ f^{\{-1\}}(x)\text{ = }\frac{x^2+10}{5}\text{for domain (-}\infty,\text{ }\infty) \end{gathered}[/tex]Solve the equation by identifying the quadratic form. Use a substitute variable(t) and find all real solutions by factoring. Type your answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. When typing exponents do not use spaces and use the carrot key ^ (press shift and 6). For example, x cubed can be typed as x^3.x^{10}-2x^5+1=0Step 1. Identify the quadratic formLet t= Answer. We now have:t^2-2t+1=0Step 2. FactorFactor this and solve for t to get t=Answer Step 3. Solve for xWe have solved for t now we need to use this value for t to help us solve for x. Revisit step 1 to remind you of the relationship between t and x. Type your real solutions (no extraneous) from smallest to largest.x= Answer
Answers
Given:
[tex]x^{10}-2x^5+1=0[/tex]Step 1: To identify the quadratic form of the given equation.
[tex]\begin{gathered} x^{10}-2x^5+1=0 \\ (x^5)^2-2x^5+1=0 \\ \text{Put x}^5=t,\text{ it gives} \\ t^2-2t+1=0 \end{gathered}[/tex]So, t = x²
Step 2: Factor the quadratic equation in step 1.
[tex]\begin{gathered} t^2-2t+1=0 \\ t^2-t-t+1=0 \\ t(t-1)-t(t-1)=0 \\ (t-1)(t-1)=0 \end{gathered}[/tex]Thus, the factors of the equation is
[tex](t-1)(t-1)=0[/tex]Step3: solve for x.
[tex]\begin{gathered} (t-1)(t-1)=0 \\ (x^5-1)(x^5-1)=0 \\ \Rightarrow x^5-1=0,x^5-1=0 \\ \Rightarrow x=1 \end{gathered}[/tex]Answer: x = 1
Find each unit price and decide which is the better buy. Assume that we are comparing different sizes of the same brand.Frozen orange juice:$1.57 for 14 ounces$0.57 for 4 ounces----------------------------Find the unit price of a frozen orange juice which costs $1.57 for 14 ounces.$ (blank) per ounce(Type a whole number or a decimal. Round to three decimal places as needed.)Find the unit price of a frozen orange juice which costs $0.57 for 4 ounces.$ (blank) per ounce(Type a whole number or a decimal. Round to three decimal places as needed.)Which is the better buy?A. $1.57 for 14 ouncesB. $0.57 for 4 ounces
Answers
The different sizes of the given brands are
Frozen orange juice:
$1.57 for 14 ounces
$0.57 for 4 ounces
The unit price of a frozen orange juice which costs $1.57 for 14 ounces is
1.57/14 = 0.112
The unit price of a frozen orange juice which costs $0.57 for 4 ounces is
0.57/4 = 0.1425
The better buy is the size that has the lowest cost per ounce. Looking at our calculations, the lowest cost per ounce is $0.112
Therefore, the frozen orange juice which costs $1.57 for 14 ounces is the better buy.
Solve the problem15) 21 and 22 are supplementary angles. What are the measures to the nearest hundredth) of the two angles?5x - 92I
Answers
∠1 is 31.5°
∠2 is 148.5°.
Given:
∠1 = x
∠2 = 5x-9
The measure of ∠1 and ∠2 are supplementary angles.
First, the value of x can be calculated as,
[tex]\begin{gathered} \angle1+\angle2=180\degree \\ 5x-9+x=180\degree \\ 6x-9=180\degree \\ 6x=180+9 \\ 6x=189 \\ x=\frac{189}{6} \\ x=31.5 \\ x=\angle1 \end{gathered}[/tex]Substitute the value of x in ∠2.
[tex]\begin{gathered} \angle2=5x-9 \\ =5(31.5)-9 \\ =157.5-9 \\ =148.5 \end{gathered}[/tex]Hence, the measure of ∠1 is 31.5° and the measure of ∠2 is 148.5°.
Solve the following inequality: 6p - 15 < 33
Answers
WE are to solve an inequality, so we proceed to isolate the variable "p" on one side of the inequality symbol:
6 p - 15 < 33
we add 15 to both sides:
6 p < 33 + 15
6 p < 48
now divide both sides by 6 (notice that since 6 is a positive number, the division doesn't change the direction of the inequality)
p < 48/6
p < 8
So we need to highlight on the number line, the line that starts at "8" and goes all the way to the left (to minus infinity), and make sure that at the point "8" you draw an "empty" circle to indicate that the number 8 itself is NOT included in your set of solutions.
Which table shows a proportional relationship between miles traveled and gas used?
Miles Traveled Gas Used
27.3 mi 1.5 gal
49.16 mi 3.8 gal
Miles Traveled Gas Used
120 mi 6.2 gal
180 mi 12.2 gal
Miles Traveled Gas Used
135 mi 7.4 gal
135.5 mi 7.9 gal
Miles Traveled Gas Used
270 mi 15 gal
135 mi 7.5 gal
Answers
Answer:
D
Step-by-step explanation:
270mi 15gal
135mi 7.5gal
135/270=0.5
7.5/15=0.5
or
135/7.5=18
270/15=18
Convert the following rectangular equation to polar form.Assume a>0 3x^2+3y^2-4x+2y=0
Answers
The given equation is,
[tex]3x^2+3y^2-4x+2y=0[/tex]The polar form of the equation can be determined by using the substitution
[tex]\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}[/tex]using the substitution,
[tex]\begin{gathered} 3(x^2+y^2)-4x+2y=0 \\ 3(r^2\cos ^2\theta+r^2\sin ^2\theta)-4r\cos \theta+2r\sin \theta=0 \\ 3r^2-4rcos\theta+2r\sin \theta=0 \\ r(3r-4\cos \theta+2\sin \theta)=0 \\ r=0\text{ and }(3r-4\cos \theta+2\sin \theta)=0 \\ (3r-4\cos \theta+2\sin \theta)=0 \end{gathered}[/tex]Thus, the above equation gives the required polar form of the circle.
