On its website a tv station displays temperature data for each hour during the past 24 hours. The data are displayed as using two different functions on a line graph. One function shows the current temperature and the other function shows the historical average. Which quantities are represented by the y-values on the line graph
Answers
, Given the question, we are asked to find which of the quantities are represented by the y-values on the line graph .
Explanation
In the question, we are told that the tv station displays temperature data using two different functions on a line graph. One of the functions shows the current temperature and the other function shows the historical average.
A function, by definition, can only have one output value(y) for any input value. In this case the input values are the time the temperature which we result in the output value of the historical average and temperature.
Therefore,
Answer
Option D
Related Questions
Simplify the following expression 6 + (7² - 1) + 12 ÷ 3
Answers
You have to simplify the following expression
[tex]6+(7^2-1)+12\div3[/tex]To solve this calculation you have to keep in mind the order of operations, which is:
1st: Parentheses
2nd: Exponents
3rd: Division/Multiplication
4th: Addition/Subtraction
1) The first step is to solve the calculation within the parentheses
[tex](7^2-1)[/tex]To solve it you have to follows the order of operations first, which means you have to solve the exponent first and then the subtraction:
[tex]7^2-1=49-1=48[/tex]So the whole expression with the parentheses calculated is:
[tex]6+48+12\div3[/tex]2) The second step is to solve the division:
[tex]12\div3=4[/tex]Now the expression is
[tex]6+48+4[/tex]3) Third step is to add the three values:
[tex]6+48+4=58[/tex]Evaluate the expression for r = –31, s = 4, and t = –16.
Answers
Answer:
st - r = -33
Explanation:
We need to replace r by -31, s by 4 and t by -16, so the expression is equal to
st - r = 4(-16) - (-31)
st - r = - 64 + 31
st - r = -33
So, the answer is
st - r = -33
1.) You are buying flower bundles and have
$24 to spend. Rose bundles cost $4. Tulip bundles
cost $6. Write an equation to describe how many
types of each kind of bundle you can buy.
Answers
Answer:
[tex]4r+6t \leq 24[/tex]
Step-by-step explanation:
The cost of money spent on a rose bundle can be represented by 4r, where 4 is the cost of one rose bundle and r is the number of rose bundles purchased.
The cost of money spent on a tulip bundle can be represented by 6t, where 6 is the cost of one tulip bundle and t is the number of rose bundles purchased.
The amount spent on rose bundles added to the amount spent on tulip bundles must be equal to or less than $24, since that's all you have to spend. This can be represented using this equation:
[tex]4r + 6t \leq 24[/tex]
:)
In the diagram below, DE is parallel to yy. What is the value of x? 110° A. 90 0 B. 120 O C. 110 O D. 70
Answers
Angle shown x is corresponding angle to 110 degree angle shown (from property of transversal cutting a pair of parallel lines).
hence
x = 110
Write the equation of a line, in slope-intercept form, that has a slope of m= -2 and y-interceptof b = -8.Y=
Answers
Explanation
We are given the following:
[tex]\begin{gathered} slope(m)=-2 \\ y\text{ }intercept(b)=-8 \end{gathered}[/tex]We are required to determine the equation of the line in the slope-intercept form.
We know that the equation of a line in slope-intercept form is given as:
[tex]\begin{gathered} y=mx+b \\ where \\ m=slope \\ b=y\text{ }intercept \end{gathered}[/tex]Therefore, we have:
[tex]\begin{gathered} y=mx+b \\ where \\ m=-2\text{ }and\text{ }b=-8 \\ y=-2x+(-8) \\ y=-2x-8 \end{gathered}[/tex]Hence, the answer is:
[tex]y=-2x-8[/tex]A school is organising a fun runThe fun run involves a 4
1
2
mile run around the field, then a 3
2
5
mile run back to the school. Find the total distance of the fun run.Give your answer as a mixed number in its simplest form.
Answers
The total distance of the fun run is 7 9/10 miles and it can be written in the simplest fraction form.
Fraction:
The fraction is the part of the whole thing.
For example, a cake is divided into four equal pieces, then each piece is represented by ¼.
Given,
A school is organizing a fun run. The fun run involves a 4 1/2 mile run around the field, then a 3 2/5 mile run back to the school.
Now, we need to find the total distance of the fun run and we have to write it as simplest form.
First we have to convert the given fraction into simplest fraction then we get,
=> 4 1/2 = 9/2
=> 3 2/5 = 17/5
Now , we have to add these to fraction in order to get the total distance,
=> 9/2 + 17/5
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(9/2, 17/5) = 10
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
=> 45/10 + 34/10
=> 79/10
While we convert this into mixed number then we get,
=> 79/10 = 7 9/10
Therefore, the total distance is 7 9/10 miles.
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Question 3
If your rectangular yard is 8 feet wide and requires 160 pieces of sod that are cut into 1 foot squares. how
long is it?
Answers
The length of the rectangle yard is 2 feet.
What is a rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can also be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.So, the length f the rectangular yard:
Width is 8 feet.Requires 160 pieces of sod.Then 160ft² is the area of the rectangular yard.
Now, calculate the length as follows:
A = l × w160 = l × 80l = 160/80l = 2 feetTherefore, the length of the rectangle yard is 2 feet.
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A ball is thrown in the air. It's height, h (in meters).is given by h = -4.91 +306 + 6 where is thetime (in seconds). What is the height of the ballafter 3 seconds?
Answers
The given equation-
[tex]-4.9t^2+30t+6[/tex]After three seconds, we evaluate for t = 3.
[tex]-4.9(3)^2+30(3)+6=-4.9(9)+90+6=-44.1+96=51.9[/tex]Therefore, the height after 3 seconds is 51.9 meters.4 Use the sequence below to complete each task. -6, 1, 8, 15, ... a. Identify the common difference (a). b. Write an equation to represent the sequence. C. Find the 12th term (a) our Wilson (All Things Algebral. 2011 Enter your answer(s) here
Answers
we have
-6, 1, 8, 15, ...
so
a1=-6
a2=1
a3=8
a4=15
a2-a1=1-(-6)=7
a3-a2=8-1=7
a4-a3=15-8=7
so
the common difference is
d=7
Part 2
write an equation
we have that
The equation of a general aritmetic sequence is equal to
an=a1+(n-1)d
we have
d=7
a1=-6
substitute
an=-6+(n-1)7
an=-6+7n-7
an=7n-13
Part 3
Find 12th term
we have
n=12
a12=-7(12)-13
a12=71
Absolute risk is defined as the proportion or percentage of people in a group for whom an undesirable event occurs. In college classrooms, students typically can choose their own seats. Professors have noticed a difference in grades between students who choose to sit in the front and those who choose to sit in the back. For example, in one math class, 9 of the 20 students who sat in the back failed the class, but only 3 of the 20 students who sat in the front failed the class. What was the absolute risk of failing the class for students who sat in the back? For students who sat in the front? Give your answers as fractions, proportions, and percents.
Answers
Given in the scenario:
a.) 9 of the 20 students who sat in the back failed the class.
b.) 3 of the 20 students who sat in the front failed the class.
A.) The absolute risk of failing the class for students who sat in the back.
In the back, 9 of the 20 students who sat in the back failed the class.
The absolute risk in proportion = 9:20
The absolute risk in fraction = 9/20
The absolute risk in percentage = (9 ÷ 20) x 100 = 0.45 x 100 = 45%
B.) The absolute risk of failing the class for students who sat in the front.
In the front, 3 of the 20 students who sat in the front failed the class.
The absolute risk in proportion = 3:20
The absolute risk in fraction = 3/20
The absolute risk in percentage = (3 ÷ 20) x 100 = 0.15 x 100 = 15%
1. On Monday, Mike's account balance shows $-135, on Tuesday, Mikequickly deposited $200. What is his new balance on Tuesday? Write anequation for the situation and find the answer. *
Answers
Ok we need to write an equation for the situation and find the answer. So, let's do it:
Balance on tuesday=previus balance+deposit
Replacing we get:
Balance on tuesday=-135+200=$65
The new balance on tuesday is $65.
Classify the following triangle. Check all that apply.- A. AcuteB. ObtuseC. Right. D. Isosceles. E. EquilateralF. Scalene
Answers
The triangle above is
Acute since the other angles are less the 90°
Can not be obtuse since non of the angles is greater than 90°
Is a Right angle since one of the angles is 90°
Is isosceles since two of it side are equal
Is not equilateral because all its side and angle are not equal
Is not Scalene since two of its side are equal.
Hence the Triangle is Acute, Right and Isosceles
True or False-Choose "A" for true or "B" for false.40. The inverse property of addition states that a number added to its reciprocal equals one.41. The associative properties state that the way in which numbers are grouped does notaffect the answer.42. The identity property of addition states that zero added to any number equals thenumber.43. The distributive property is the shortened name for the distributive property ofmultiplication over addition.44. The commutative property of addition states that two numbers can be added in anyorder and the sum will be the same.45. is the multiplicative inverse of35346. One is the identity element for addition.
Answers
Given
Statements
Find
Correctness of statements
Explanation
40) False (sum of number and its opposite is 0)
41)True
42) True
43) True
44) True
45) True
46) False (One is Identity Element for multiplication)
Final Answer
40) False
41)True
42) True
43) True
44) True
45) True
46) False
Rewrite the following expression so it does not contain any radical term
Answers
Given:
The expression is given as,
[tex]\sqrt[]{36p^{10}m^6}[/tex]The objective is to rewrite the expression without any radical form.
Explanation:
The given expression can be written as,
[tex]\sqrt[]{36p^{10}m^6}=\sqrt[]{6^2p^{10}m^6}\text{ . . . . .(1)}[/tex]In general, the radical form of a square root can be written as,
[tex]\sqrt[]{x}=x^{\frac{1}{2}}[/tex]Then, the equation (1) can be written as
[tex]\sqrt[]{36p^{10}m^6}=(6^2p^{10}m^6)^{\frac{1}{2}}[/tex]On further solving the above expression,
[tex]\begin{gathered} \sqrt[]{36p^{10}m^6}=6^{2\times\frac{1}{2}}p^{10\times\frac{1}{2}}m^{6\times\frac{1}{2}} \\ =6p^5m^3 \end{gathered}[/tex]Hence, the simplified expression of the given term is,
[tex]6p^5m^3[/tex]In the past, Johnny got paid $111,180 annually. Since switching to a new career, he has been making 154.1% more. How much does Johnny make now?
Answers
The amount of money that Johnny makes now = $282,508.38
What is annual payment?Annual payment is the type of payment that is done every 12 month and by the end of the year.
The initial annual payment received by Johnny= $111,180
The new career pays the rate of 154.1% more that is;
( 154.2% of $111,180 ) + $111,180 Which is;
= (154.1/100 × 111,180) + $111,180
= (17,132,838/100) + $111,180
= $ 171,328.38 + $111,180
= $282,508.38.
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What is an equation of the points given? And is parallel to the line 4x-5y=5?
Answers
We know that two lines are parallel if they have the same slope. So we first find the slope of the given line. One way to do this is to rewrite the equation in its slope-intercept form, solving for y:
[tex]\begin{gathered} y=mx+b \\ \text{ Where} \\ m\text{ is the slope and} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 4x-5y=5 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=5-4x \\ -5y=5-4x \\ \text{ Divide by -5 from both sides} \\ \frac{-5y}{-5}=\frac{5-4x}{-5} \\ y=\frac{5}{-5}-\frac{4x}{-5} \\ y=-1+\frac{4x}{5} \\ y=\frac{4x}{5}-1 \\ y=\frac{4}{5}x-1 \end{gathered}[/tex]Now, we have the slope and a point through which the line passes:
[tex]\begin{gathered} m=\frac{4}{5} \\ (x_1,y_1)=(-5,2) \end{gathered}[/tex]Then, we can use the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=\frac{4}{5}(x-(-5)_{}) \\ y-2=\frac{4}{5}(x+5_{}) \end{gathered}[/tex]The above equation is the equation of the line in its point-slope form. However, we can also rewrite the equation of the line in its standard form by solving for the constant:
[tex]ax+by=c\Rightarrow\text{ Standard form}[/tex][tex]\begin{gathered} y-2=\frac{4}{5}(x+5_{}) \\ \text{ Multiply by 5 from both sides of the equation} \\ 5(y-2)=5\cdot\frac{4}{5}(x+5_{}) \\ 5(y-2)=4(x+5_{}) \\ \text{ Apply the distributive property} \\ 5\cdot y-5\cdot2=4\cdot x+4\cdot5 \\ 5y-10=4x+20 \\ \text{ Subtract 5y from both sides} \\ 5y-10-5y=4x+20-5y \\ -10=4x+20-5y \\ \text{Subtract 20 from both sides } \\ -10-20=4x+20-5y-20 \\ -30=4x-5y \end{gathered}[/tex]Therefore, an equation of the line that passes through the point (-5,2) and is parallel to the line 4x - 5y = 5 is
[tex]\boldsymbol{4x-5y=-30}[/tex]...........................
Answers
Solution
We have the following:
5!= 5*4*3*2= 20*3*2= 60*2= 120
A manager recorded the performance review scores for each employee and placed the results in the bar chart below. All employees received a rating on each of the Evaluation Categories. If Person 6 obtained the highest score possible, what score did Person 3 receive? Use the graph and tables below.EVALUATION CATEGORIESRATINGGeneral Quality of WorkDependabilityJob KnowledgeCommunication SkillsPersonalityManagement AbilityContribution to GroupProductivityAchievement of GoalsRating ScaleSCOREDESCRIPTION5Excellent4Very Good3Good2Fair1Poor253530
Answers
SOLUTION
Comparing the graphs and the options, it follows that each line on the graph represents 5 points. This means the person 6 obtained a score of 45, comparing this to the person 3, it means the person 3 obtained a score of 35.
So the answer is 35.
For the rating since person 6 has the highest possible score, which is 45, person 3 score becomes
[tex]\begin{gathered} \frac{35}{45}\times5 \\ =3.88888888 \\ which\text{ is approximately 4} \end{gathered}[/tex]so we can classify person 3 as very good
Whichatest initial value?Use the drop-down menus to show your answer.Function AX026y0515Function Choose...has the greatest initial value.Choose...Functionhas the greatest rate of change.410Function By = 3x - 165432-Function C1 2 3 4 5 6X
Answers
Given:
Function A:
Function- B
[tex]y=3x-1[/tex]Function C
Find-:
The function has the greatest initial value
The function has the greatest rate of change
Explanation-:
(A)
The function has the greatest initial value
Check the value at x=0
Value of y is:
For functi
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two ships leave a port at the same time. the first ship sails on a bearing of 55° at 12 knots (natural miles per hour) and the second on a bearing of 145° at 22 knots. how far apart are they after 1.5 hours (round to the nearest nautical mile)
Answers
Given that one of the ships travels at 12 nautical miles per hour, then after 1.5 hours, it will travel 12*1.5 = 18 miles
The other ship will travel 22*1.5 = 33 miles
The angle of 145° is measured with respect to the positive x-axis. Then, respect the negative x-axis, its measure is 180° - 145° = 35°
We have to use trigonometric functions to find x1, y1, x2, and y2, as follows:
sin(55°) = y1/18
sin(55°) *18 = y1
14.7 = y1
cos(55°) = x1/18
cos(55°)*18 = x1
10.3 = x1
sin(35°) = y2/33
sin(35°)*33 = y2
18.9 = y2
cos(35°) = x2/33
cos(35°)*33 = x
-27 = x2 (the minus sign comes from the graph)
The distance between two points (x1, y1) and (x2, y2) is computed as follows:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting with the values found,
[tex]\begin{gathered} d=\sqrt[]{(-27-10.3)^2+(18.9-14.7)^2} \\ d=\sqrt[]{(-37.3)^2+4.2^2} \\ d=\sqrt[]{1391.29+17.64} \\ d\approx38\text{ miles} \end{gathered}[/tex]In a recent survey of dog owners, it was found that 901, or 34%, of the owners take their dogs on vacation with them. Find the number of dog owners in the survey that do NOT take their dog on vacation with them rounded to the nearest whole number
Answers
we have that
34% represents 901 owners that take their dogs on vacation with them
so
the percentage of dog owners in the survey that do NOT take their dog on vacation is equal to
100%-34%=66%
Applying proportion
901/34=x/66
solve for x
x=(901/34)*66
x=1,749 ownersMr. Ocana drove 15 miles to go to work last week. Due to construction on the road, this week he drove 21 miles to go to work. What is the percent increase in the number of miles he drove to work this week? О 40% 50% ООО 60% O 70%
Answers
ANSWER:
40%
STEP-BY-STEP EXPLANATION:
In this case, what we must do is calculate the percentage that represents 21 miles, assuming that 100% is 15 miles, like this
[tex]21\cdot\frac{100}{15}=140\text{\%}[/tex]Now we subtract 100% from this value, like this:
[tex]140\text{\%}-100\text{\%}=40\text{\%}[/tex]152. ) Find all real x such that square root x + 1 = x - Square root x - 1.
Answers
Given the equation:
[tex]\sqrt[]{x}+1=x-\sqrt[]{x}-1[/tex]Solving for x:
[tex]\begin{gathered} \sqrt[]{x}+\sqrt[]{x}=x-1-1 \\ 2\sqrt[]{x}=x-2 \end{gathered}[/tex]Now, we take the square on both sides of the equation:
[tex]\begin{gathered} 4x=x^2-4x+4 \\ 0=x^2-8x+4 \end{gathered}[/tex]Now, using the general solution of quadratic equations:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From the problem, we identify:
[tex]\begin{gathered} a=1 \\ b=-8 \\ c=4 \end{gathered}[/tex]Then, the solutions are:
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4\cdot1\cdot4}}{2\cdot1}=\frac{8\pm\sqrt[]{64-16}}{2} \\ x=\frac{8\pm4\sqrt[]{3}}{2}=4\pm2\sqrt[]{3} \end{gathered}[/tex]But the original equation √(x), so x can not be negative if we want a real equation. Then, the only real solution of the equation is:
[tex]x=4+2\sqrt[]{3}[/tex]Using the Smith's BBQ Report, all of your hourly personnel are getting a promotion this week. As a result, your hourly wages for next week will be 8% more than the current week. What will be the approximate Total Payroll Variance from the current week to next week if all other factors remain the same?A 156B 9265C 842D 686
Answers
Given:
The current week hour wage is 8579
Total payroll =14081.
The hourly wage will be increased 8 %.
The 8% of 8579 is
[tex]=\frac{8}{100}\times8579=686.32[/tex]The hourly wage will be increased by 686 next week.
The total payroll also will be increased by 686.
So the total Payroll Variance from the current week to next week is 686.
Hence option D is correct.
Two buses leave a station at the same time and travel in opposite directions. One bus travels 16(km)/(h) slower than the other. If the two buses are 1040 kilometers apart after 4 hours, what is the rate of each busSolve using a system of linear equations
Answers
Let x be the velocity (rate of change ) of one of the buses. We know that the other one travels 16 km/h slower; this means that the second velocity is:
[tex]x-16[/tex]Now the combined velocity would be:
[tex]2x-16[/tex]We know that the distance is equal to time by velocity, then we have that:
[tex]4(2x-16)=1040[/tex]Solving for x we have:
[tex]\begin{gathered} 4(2x-16)=1040 \\ 2x-16=\frac{1040}{4} \\ 2x-16=260 \\ 2x=260+16 \\ 2x=276 \\ x=\frac{276}{2} \\ x=138 \end{gathered}[/tex]Therefore the rate of the faster bus is 138 km/h and the rate for the slower bus is 122 km/h.
Remember to write a let statement and answer the question. A collection of dimes abs quarters has a value of $1.35. List all possible combinations of dimes abs quarters.
Answers
Let d represents dimes and q represents quarter.
Note that a dime is 10 cent, which is same as one over ten, and a quarter is one over four
[tex]\begin{gathered} d=\frac{1}{10}=0.1 \\ q=\frac{1}{4}=0.25 \end{gathered}[/tex]Given that a collection of dimes abs quarters has a value of $1.35, then this can be represented as below:
[tex]0.1d+0.25q=1.35[/tex]Multiply through by 100 to get
[tex]\begin{gathered} 100\times0.1d+100\times0.25q=100\times1.35 \\ 10d+25q=135 \end{gathered}[/tex]To get the possible combinations of dimes and quarters, lets the try different values of that will satisfy the equation.
When q is 1,
[tex]\begin{gathered} 10d+25q=135 \\ q=1 \\ 10d+25(1)=135 \\ 10d+25=135 \\ 10d=135-25 \\ 10d=110 \\ d=\frac{110}{10}=11 \end{gathered}[/tex]Therefore, 11 dimes and 1 quarter abs is a possible combination
When q is 3
[tex]\begin{gathered} 10d+25(3)=135 \\ 10d+75=135 \\ 10d=135-75 \\ 10d=60 \\ d=\frac{60}{10} \\ d=6 \end{gathered}[/tex]Also, 6 dimes and 3 quarter abs is a possible combination
When q is 5
[tex]\begin{gathered} 10d+25(5)=135 \\ 10d+125=135 \\ 10d=135-125 \\ 10d=10 \\ d=\frac{10}{10} \\ d=1 \end{gathered}[/tex]Also, 1 dime and 5 quarter abs is a possible combination
When q is 7
[tex]\begin{gathered} 10d+25(7)=135 \\ 10d+175=135 \\ 10d=135-175 \\ 10d=-40 \\ d=\frac{-40}{10}=-4 \end{gathered}[/tex]Since negative answer was gotten for dimes, 7 quater wouldn't give any possible combination.
Hence, there are It can be found that there are there are three possible combinations, these are:
11 dimes and 1 quarter abs
6 dimes and 3 quarter abs
1 dime and 5 quarter abs
For how many integers n is 28÷n an interger
Answers
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integers: -1.43, 1 3/4, 3.14,.09, and 5,643. 1.
How do you determine an integer's number from a number?
Basic Interest Calculator
Simple interest is calculated by multiplying the principal by the time, interest rate, and time period. "Simple Interest = Principal x Interest Rate x Time" is the written formula. The simplest method for computing interest is using this equation.
The answer to the question "How many integers are there in n?" is n-1.
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[tex] \frac{x - 2}{x + 3} + \frac{10x}{x {}^{2 } - 9}[/tex]simplify the sum. state any restrictions on the variables.
Answers
We have
[tex]\frac{x-2}{x+3}+\frac{10x}{x{}^2-9}[/tex]first, we need to factorize the next term
[tex]x^2-9=(x+3)(x-3)[/tex]so we have
[tex]\frac{x-2}{x+3}+\frac{10x}{(x+3)(x-3)}[/tex]Remember in order to sum a fraction the denominator must be the same
[tex]\frac{(x-2)(x-3)+10x}{(x+3)(x-3)}[/tex]then we solve the multiplications (x-2)(x-3)
[tex]\frac{x^2-3x-2x+6+10x}{(x+3)(x-3)}=\frac{x^2+5x+6}{(x+3)(x-3)}[/tex]then we can factorize the numerator
[tex]x^2+5x+6=(x+3)(x+2)[/tex]so the simplification will be
[tex]\frac{x^2+5x+6}{(x+3)(x-3)}=\frac{(x+3)(x+2)}{(x+3)(x-3)}=\frac{(x+2)}{(x-3)}[/tex]the final result is
[tex]\frac{(x+2)}{(x-3)}[/tex]An observer in a lighthouse 350 ft above sea level observes two ships directly offshore. The angles of depression to the shops are 4 degree and 6.5 degree. How far apart are the ships?
Answers
The two ships are 1933.32 ft apart
Explanation:Given:
The height of the lighthouse = 350 ft
The angles of depression to the ships are 4 degree and 6.5 degree
To find:
the distance between the two ships
To determine the distance, we will use an illustration of the situation
First we will find the value of y as we need to know this value to get x
To get y, we will apply tan ratio (TOA)
[tex]\begin{gathered} tan\text{ 6.5\degree = }\frac{opposite}{adjacent} \\ opp\text{ = 350 ft} \\ adj\text{ = y} \\ tan\text{ 6.5\degree = }\frac{350}{y} \\ y(tan\text{ 6.5\degree\rparen= 350} \\ y\text{ = }\frac{350}{tan\text{ 6.5}} \\ y\text{ = 3071.9106 ft} \end{gathered}[/tex]Next is to find x using tan ratio (TOA):
[tex]\begin{gathered} angle\text{ = 4\degree} \\ tan\text{ 4\degree= }\frac{opposite}{adjacent} \\ \\ opposite\text{ = 350 ft} \\ adjacent\text{ = y + x} \\ tan\text{ 4\degree= }\frac{350}{y\text{ + x}} \end{gathered}[/tex][tex]\begin{gathered} tan\text{ 4 = }\frac{350}{3071.9106+x} \\ \frac{350}{tan\text{ 4}}\text{ = 3071.9106 + x} \\ 5005.2332\text{ = 3071.9106 + x} \\ x\text{ = 1933.3226} \\ \\ The\text{ ships are 1933.32 ft apart \lparen nearest hundredth\rparen} \end{gathered}[/tex]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.
