Answers
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.
Related Questions
Barbara puts $500.00 into an account to use for school expenses. the account earns 14% interest, compounded annually. how much will be in the account after 7 years?use the formula A= P ( 1 + ).where A is the balance (final amount), p is the principal ( starting amount), r is the Internet rate express as a decimal, n is number of time per year that the interest is compounded, and T is the time in years. Round, your answer to the nearest cent
Answers
the formula is:
A = P( 1 + r/n )^nt
then solve:
[tex]undefined[/tex]Identify the rate, base, and portion.
21% of what number is 57?
Question content area bottom
Which values are given? Select the correct choice below and fill in any answer boxes in your choice. (Type an integer or a decimal. Do not perform the calculation.)
A.The base is (enter your response here) and the portion is (enter your response here). The rate is not given.
B.The rate is (enter your response here % ) and the portion is (enter your response here). The base is not given.
C. The rate is (enter your response here %) and the base is (enter your response here).
Answers
Given:
21% of what number is 57
Let the number = x
So, 21% of x = 57
so, the rate = 21%
and the base = x
and the portion = 57
So, the base is not given
so, the answer will be option B
B) the rate is 21% and the portion is 57. the base is not given.
A gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. How many different options are available at this store?
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If a gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. The number of different options that are available at this store is 1344.
How to find the different options?Using this formula to determine the number of different options
Number of different options available = Number of shapes of boxes × Number of wrapping paper × Number of different bowl
Let plug in the formula
Number of different options available = 8 × 14 × 12
Number of different options available = 1,344
Therefore we can conclude that 1,344 different options are available.
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A cattle train left the station and traveled toward New York at an average speed of 41.4 mph. A passenger train left 5.6 hours later and traveled in the opposite direction with an average speed of 22.5 mph. How long does the passenger train need to travel before the trains are 513 mi. apart?
Answers
You have the following information:
- Average speed of cattle train to New York: 41.4 mph
- Average speed of passenger train: 22.5 mph
- The passenger train left in the opposite direction, 5.6 hour after cattle train started its travel.
In order to determine how long does the passenger need to travel before the trains are 513 mi apart, you take into account that you can express the previous situation in an algebraic way. If you consider x as the distance traveled by cattle train in a time t, the you have:
x = vt = (41.4)t = 41.4 t
Now, if you consider x' as the distance traveled by the passenger train in the opposite direction in a 5.3h after the left of cattle train, you have:
x' = v't = (22.5)(t + 5.3) = 22.5 t + 119.25
Next, if you are interested in the time on which passengers and cattle train will be separated by 513 mi, then you can write:
x - (-x') = 513 Here, you specify the distance between both trains are 513
x + x' = 513
The minussign of -x' is due to the fact the passengers trains goes in the opposite direction.
Then, by replaacing the expressions for x and x' you obtain:
(41.4t) + (22.5t + 119.25) = 513
Now, you can simplify the previous expression, and solve it for t:
41.4t + 22.5t + 119.25 = 513
63.9t = 513 - 119.25
63.9t = 393.75
t = 393.75/63.9
t = 6.16
Hence, both trains will be at a distance of 513 mi apart between them, after 6.16 hours
What is the product?(4y − 3)(2y2 + 3y − 5)8y3 + 3y + 158y3 − 23y + 158y3 − 6y2 − 17y + 158y3 + 6y2 − 29y + 15
Answers
We need to find the product of :
[tex]\mleft(4y-3\mright)\mleft(2y2+3y-5\mright)[/tex]So, the result as following:
[tex]\begin{gathered} \mleft(4y-3\mright)\mleft(2y^2+3y-5\mright) \\ =4y\cdot(2y^2+3y-5)-3\cdot(2y^2+3y-5) \\ =8y^3+12y^2-20y-(6y^2+9y-15) \\ =8y^3+12y^2-20y-6y^2-9y+15 \\ \\ =8y^3+6y^2-29y+15 \end{gathered}[/tex]So, the answer is the option 4. 8y3 + 6y2 − 29y + 15
relation and functionFunction OperationComposition of functionsymmetryfunction Inversesrate of change scartterplotsMINIMUM STEPS PLEASE!
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In order to find f(2) we just have to replace x by 2 in its equation:
f(x) = 3x - 1
↓
f(2) = 3 · 2 - 1
f(2) = 6 - 1
f(2) = 5
Finding g(x) = f(2)Since g(x) = f(2) is
g(x) = 5
using the equation of g, we have that
2x - 3 = 5
In order to find x we just solve the previous equation
2x - 3 = 5
↓ adding 3 both sides of the equation
2x - 3 + 3 = 5 + 3
2x = 8
↓ dividing by 2 both sides of the equation
2x/2 = 8/2
x = 4
Answer- D: x = 4
Lines PQ and Rs are parallel. Find y. P(2, -5); Q(5, 6); R(3, -1); S(6, y)y = ?
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To answer this question it is necessary to find the equation of the given lines
Find the equation for PQ. To do it, find the slope of the equation:
[tex]m=\frac{6-(-5)}{5-2}=\frac{11}{3}[/tex]Now, use the point slope formula to find the equation of the line:
[tex]\begin{gathered} y-6=\frac{11}{3}(x-5) \\ y=\frac{11}{3}x-\frac{55}{3}+6 \\ y=\frac{11}{3}x-\frac{37}{3} \end{gathered}[/tex]Parallel lines have the same slope, it means PQ and RS have the same slope, then RS has a slope of 11/3
Use the point slope formula to find the equation of the line RS:
[tex]\begin{gathered} y-(-1)=\frac{11}{3}(x-3) \\ y+1=\frac{11}{3}x-11 \\ y=\frac{11}{3}x-12 \end{gathered}[/tex]Now, use this equation to find y when x is 6 (which corresponds to point S):
[tex]\begin{gathered} y=\frac{11}{3}x-12 \\ y=\frac{11}{3}(6)-12 \\ y=22-12 \\ y=10 \end{gathered}[/tex]y has a value of 10.
Your $8800 investment grows to $15600 over the course of 5 years compounded quarterly. What interest rate did you receive on your investment? (Write your answer with at least four decimal points) Your interest rate is r =
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Given:
The initial amount is $8800.
The Future value is $15600.
Number of year = 5 years compounded quarterly .
The interest rate is calculated as,
[tex]\begin{gathered} FV=P(1+\frac{r}{4})^{4\times n} \\ 15600=8800(1+\frac{r}{4})^{4\times5} \\ \frac{39}{22}=(1+\frac{r}{4})^{20} \\ \sqrt[20]{\frac{39}{22}}=1+\frac{r}{4} \\ \frac{r}{4}=\sqrt[20]{\frac{39}{22}}^{}-1 \\ r=4(\sqrt[20]{\frac{39}{22}}-1) \\ r=0.1162 \end{gathered}[/tex]Answer: the interest rate is 0.1162.
Speeding tickets provide a significant source of revenue for many American cities. For one city in South Florida, the average annual speeding ticket revenue per police officer is $300,000. The standard deviation for these annual speeding ticket revenues is $58,000. If these amounts have a normal distribution, find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue generating officers from the other ninety-five percent.
Answers
Explanation
To find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue-generating officers from the other ninety-five percent.
We will need to find
[tex]P\left(x>z\right)=0.05[/tex]Therefore; using a z score calculator, this gives;
[tex]z=1.645[/tex]We can then find the cutoff amount z using the formula below;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \end{gathered}[/tex]Since
[tex]\begin{gathered} \mu=$ 300,000. $ \\ \sigma=58,000 \end{gathered}[/tex]Therefore, we will have
[tex]\begin{gathered} 1.645=\frac{x-300000}{58000} \\ \mathrm{Switch\:sides} \\ \frac{x-300000}{58000}=1.645 \\ crossmutiply \\ x-300000=58000\times1.645 \\ x=300000+95410 \\ x=395410 \end{gathered}[/tex]Answer: 395410
help meeeeeeeeee pleaseee !!!!!
Answers
The value of the composition (g ° f) (x) between the linear equation g(x) and the quadratic equation f(x) evaluated at x = 5 is equal to 6.
How to find and evaluate a composition between two functions
In this problem we find a quadratic equation f(x) and a linear equation g(x), of which we must derive a composition consisting in substituting the input variable of the linear equation with the quadratic equation. Later, we evaluate the resulting expression at x = 5.
Now we present the complete procedure:
(g ° f) (x) = - 2 · (x² - 6 · x + 2)
(g ° f) (x) = - 2 · x² + 12 · x - 4
(g ° f) (5) = - 2 · 5² + 12 · 5 - 4
(g ° f) (5) = - 50 + 60 - 4
(g ° f) (5) = 6
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Choose the correct equation in point slope form for the line through the given points or through the given point with the given slope
Answers
Answer:
[tex]y-3=-1(x+2)[/tex]Explanation:
The point-slope form of the equation of a line is generally given as;
[tex]y-y_1=m(x-x_1)[/tex]where m = the slope of the line
y1 = y-coordinate of the one point
x1 = x-coordinate of the one point
Given the slope of the line as m = -1 and the point (-2, 3) where x1 = -2 and y1 = 3, let's go ahead and substitute these given values into the point-slope formula to obtain the required equation as seen below;
[tex]\begin{gathered} y-3=-1\lbrack x-(-2)\rbrack \\ y-3=-1(x+2) \end{gathered}[/tex]In a survey, 300 adults and children were asked whether they preferredhamburgers or pizza. The survey data are shown in the relative frequencytable.
Answers
Answer:
Step-by-step explanation:
From the data in the table given
frequency of people who like pizza 0·36 +0·29=0·65
percentage of people who like pizza
0.65 × 100
=65%
A polynomial function with degree 5 can have a maximum of how many turning points? It would be 5 right?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
polynomial function
Step 02:
turning points:
The maximum number of turning points of a polynomial function is always one less than the degree of the function.
5th degree polynomial function and has 4 turning points.
The answer is:
5th degree polynomial function and has 4 turning points.
ABCD is a rectangle. Find the coordinates of P, the midpoint of AC. [B is (18,12) ]
Answers
the coordinates of P is (9, 6)
Explanation:Coordinate of B = (18, 12)
In a rectangle, the opposite parallal sides are equal
AB = DC
AD = BC
We need to find the coordinates of A and C inoder to get P:
Since the x coordinate of B is 18, the x coordinate of C will also be 18
C is on the y axis, this means its y coordinate will be zero
Coordinate of C (x, y) becomes: (18, 0)
The y coordinate of B is 12, the y coordinate of A will also be 12
A is on the y axis. This means the x coordinate of A will be zero
Coordinate of A (x, y becomes): (0, 12)
To get P, we will apply the midpoint formula:
[tex]\text{Midpoint = }\frac{1}{2}(x_1+x_2),\text{ }\frac{1}{2}(y_1+y_2)[/tex]Using the points A (0, 12) and C (18, 0) to get coordinates of P:
[tex]\begin{gathered} x_1=0,y_1=12,x_2=18,y_2\text{ = 0} \\ \text{midpoint = }\frac{1}{2}(0+18),\text{ }\frac{1}{2}(12+0) \\ \text{midpoint = }\frac{1}{2}(18),\text{ }\frac{1}{2}(12) \\ \text{midpoint = (9, 6)} \end{gathered}[/tex]Hence, the coordinates of P is (9, 6)
I need help with this practice problem solving This is the subject trigonometry
Answers
Given the fucntion:
f(x) = tanx
Let's graph the function and input the correct values in the box.
• To find the y-intercept of the function, input 0 for x and solve:
[tex]\begin{gathered} f(0)=\tan 0 \\ \\ f(0)=0 \end{gathered}[/tex]Therefore, the y-intercept is:
(0, 0)
• The period of the function:
The fundamental period of a tangent function is π.
Now, let's find points on the graph:
Therefore, the points are:
[tex]\mleft(-\frac{\pi}{3},-\sqrt{3}\mright),\mleft(-\frac{\pi}{4},-1\mright),\mleft(0,0\mright),\mleft(\frac{\pi}{4},1\mright),\mleft(\frac{\pi}{3},\sqrt{3}\mright)[/tex]ANSWER:
The tangent function's period is π . The y-intercept of the function is (0, 0).
The points are:
[tex](-\frac{\pi}{3},-\sqrt[]{3}),(-\frac{\pi}{4},-1),(0,0),(\frac{\pi}{4},1),(\frac{\pi}{3},\sqrt[]{3})[/tex]write a ratio that is equivalent to the ratio 25:10
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25:10 can be writen as
[tex]\frac{25}{10}[/tex]Since the numerator and the denominator are divisible by 5, then we have
[tex]\frac{25}{10}=\frac{5\times5}{5\times2}=\frac{5}{2}[/tex]Then, an equivalent ratio of 25:10 is 5:2
3.50 divide by 24.50
Answers
Answer:
1/7 or 0.143
Step-by-step explanation:
i hope this helps
A grocery store sells sliced cheddar cheese by weight. The relationship between the amount of cheddar cheese in pounds, and the time in dollars of cheddar cheese in pounds, x, and the total cost in dollars of the sliced cheddra cheese, y, is represented by a graph drawn in the xy-planeIf the point (8, 44) lies on the graph, what does the point (8, 44) indicate?
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Remember that the pair of coordinates
[tex](x,y)[/tex]of a point that lies on the graph of the function tells us the x-value and the
y-value related to that value.
Therefore, the point
[tex](8,44)[/tex]Represents that 8 pounds of cheddar cheese cost $44 in total (y represents the total cost, not the cost per pound)
(Correct answer is option B)
eric is giving a presentation about average rainfall in the united states and wants to create a graph that shows how yearly rainfall has changed over the past decade. what type of chart should he use?
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To represent the yearly rainfall in a graph, eric should use the Bar Graph
which is commonly used worldwide
Bar Graph:
The graphic representation of data in the form of vertical or horizontal bars or rectangular strips having uniform width is called bar graphs.
A bar graph is used to give the comparison between two or more groups. It comprises of two or more parallel vertical (or horizontal) rectangles.
With bar graphs, we can compare data sets from different groups. The graph depicts groups on one axis and a discrete value on the other. The main purpose is to display the relationship between the two axes.
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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
please help me solve this no tutor can ahelp me
Answers
Solution:
Since the confidence interval width is inversely proportional to n , the answer is the smallest n.
CORRECT OPTION: 36
For each angle, determine the measure of the arc subtended by the angle's ray in units of 1/10th of the circumference of the given circle.Measurement for the diagram below:
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Assuming you want the measure of the arc (in red) shown:
The circumference is divided into 10 equal parts. The red color arc is 1 and a half part.
The circumference is 360 degree and each part is 360/10 = 36 degrees
Thus, 1 and a half part will be:
[tex]1.5\times36=54\degree[/tex]Measure of Arc (in red) is:
54 degrees
Match the following. Match the items in the left column to the items in the right column.1. divisor2. decimal fraction3. algorithm4. fraction5.quotient6. reminder7. doidonsa. the result of dividing two numbersb. the number being dividedc. a set of rules to be followed tosolve a problemd. the number of equal parts a number is being divided intoe. a fraction in which the denominator is 10 or a power of 10f. the amount left over after Chivisiong. a number that expresses the portiona whole
Answers
We can match as follows:
1. divisor ----> d. the number of equal parts a number is being divided into
2. decimal fraction ----> e. a fraction in which the denominator is 10 or a power of 10
3. algorithm ----> c. a set of rules to be followed to solve a problem
4. fraction ----> g. a number that expresses the portion
5. quotient ----> a. the result of dividing two numbers
6. reminder ----> f. the amount left over after Division
Find the equations (in terms of x) of the line through the points (-2,-3) and (3,-5)
Answers
The general equation of a line passing through two points (xb₁,y₁)Pxb₂,y₂) is expressed as
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ m\Rightarrow slope\text{ of the line, expr}essed\text{ as }m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)\Rightarrow coordinate_{}\text{ of point P} \\ (x_2,y_2)\Rightarrow coordinate_{}\text{ of point Q} \end{gathered}[/tex]Given that the coordinates of the two points are (-2, -3) and (3, -5), we have
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(-2,\text{ -3)} \\ (x_2,y_2)\Rightarrow(3,\text{ -5)} \end{gathered}[/tex]Step 1:
Evaluate the slope o the line.
The slope is thus evaluated as
[tex]\begin{gathered} m\text{ = = }\frac{y_2-y_1}{x_2-x_1} \\ \text{ = }\frac{\text{-5-(-3)}}{3-(-2)} \\ =\frac{-5+3}{3+2} \\ \Rightarrow m\text{ = -}\frac{2}{5} \end{gathered}[/tex]Step 2:
Substitute the values of x₁,
Thus, we have
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ x_1=-2 \\ y_1=-3 \\ m\text{ =- }\frac{2}{5} \\ \text{thus,} \\ y-(-3)\text{ = -}\frac{2}{5}(x-(-2)) \\ y+3\text{ =- }\frac{2}{5}(x+2) \end{gathered}[/tex]Step 3:
Make .
[tex]\begin{gathered} y+3\text{ =- }\frac{2}{5}(x+2) \\ \text{Multiply both sides of the equation by 5 } \\ 5(y+3)\text{ = -2(x+2)} \\ \text{open brackets} \\ 5y\text{ + 15 =- 2x - 4} \\ \Rightarrow5y\text{ =- 2x - 4 -15} \\ 5y\text{ = -2x-1}9 \\ \text{divide both sides of the equation by the coefficient of y, which is 5.} \\ \text{thus,} \\ \frac{5y}{5}=\frac{-\text{2x-1}9}{5} \\ \Rightarrow y\text{ =- }\frac{2}{5}x\text{ - }\frac{19}{5} \end{gathered}[/tex]Hence, the equation of the line is
[tex]y\text{ = -}\frac{2}{5}x\text{ - }\frac{19}{5}[/tex]y₁ and m into the general equation of the line.
FIRST OPTIONS ARE THE NUMBER OF CONVERTIBLES SOLD BY PLATO CARSTHE REVENUE FROM SALES OF CONVERTIBLE CARS BY PLATO CARSTHE REVENUE FROM SALES OF SEDANS BY PLATO CARSTHE TOTAL SALES REVENUE OF PLATO CARS SECOND OPTIONS 0.1070.2250.290.33
Answers
Given:
The number in the highlighted cell is 18.
The total sales revenue of pluto cars is 80.
To find the relative frequency from the sales of sedans by Plato cars to the total sales revenue of Plato cars:
The formula for relative frequency is,
[tex]\begin{gathered} RF=\frac{subgroup\text{ fr}equency}{\text{Total frequency}} \\ =\frac{18}{80} \\ =0.225 \end{gathered}[/tex]So, the relative frequency is 0.225.
Hence, the answer is,
The number in the highlighted cell is 18. The relative frequency from the sales of sedans by Plato cars to the total sales revenue of Plato cars is 0.225
Three ships, A, B, and C, are anchored in the atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 miles, and from C to A is 11.164 miles. Find the angle measurements of the triangle formed by the three ships.A. m∠A=88.28267; m∠B=17.22942; m∠C=74.4879B. m∠A=74.4879; m∠B=17.22942; m∠C=88.28267C. m∠A=17.22942; m∠B=74.4879; m∠C=88.28267D. m∠A=88.28267; m∠B=74.4879; m∠C=17.22942
Answers
Question: Three ships, A, B, and C, are anchored in the Atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 miles, and from C to A is 11.164 miles. Find the angle measurements of the triangle formed by the three ships.
Solution:
Note: In finding the angles of a triangle given its three sides, we will use the Cosine Law.
[tex]\begin{gathered} c^2=a^2+b^2\text{ -2abcosC} \\ or\text{ it can be written as:} \\ \text{Cos(C) = }\frac{a^2+b^2-c^2}{2ab} \end{gathered}[/tex]
In finding angle C, we use the formula given above.
[tex]\begin{gathered} \text{Cos(C) = }\frac{37.674^2+11.164^2-36.318^2}{2\cdot37.674\cdot11.164} \\ \text{Angle C = 74.4879 degrees} \end{gathered}[/tex]Note: Side a is the side opposite Angle A, side b is the side opposite Angle B, and side c is the side opposite Angle C.
Let's find the next angle.
[tex]\begin{gathered} \text{Cos(B) = }\frac{a^2+c^2-b^2}{2ac} \\ \text{Cos(B) = }\frac{37.647^2+36.318^2-11.164^2}{2\cdot37.647\cdot36.318} \\ \text{Angle B = 17.2294}2\text{ degrees} \end{gathered}[/tex]Note: We can still use the cosine law in finding Angle A. But another solution is subtracting the Angles A and B from 180 degrees. The measure of the internal angle of a triangle is always 180 degrees no matter what type of triangle it is.
[tex]\begin{gathered} \text{Angle A = 180-74.4849 -17.22942} \\ \text{Angle A = 88.28 degrees} \end{gathered}[/tex]ANSWER:
A. m∠A=88.28267; m∠B=17.22942; m∠C=74.4879
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
Answers
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD:
15.70(d-3)=2.30
3d - 15.70 = 2.30
15.70d-3=2.30
3(d-15.70)=2.30
help meeeee pleaseeeee!!!
thank you
Answers
The value of x is -2.
We are given a graph of a function f(x).
We have to find the value of x when the value of f(x) is -3.
We know that x- axis represents x and the y-axis shows f(x).
Hence, the x and y coordinates of a point on the line will be (x, f(x)).
To find the value of x , I will check the coordinates of the point (x, -3) because it is given that f(x) is -3.
Using the graph, we found the coordinates of that point to be (-2,-3).
Hence, we can say that,
x = -2
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A plane flies from Oahu and back. Flying to Oahu the plane is flying against the wind and the trip takes 6 hours. On the way back the plane flies with the wind and it takes 5 hours. If the distance one way is 900 miles, what is the speed of the plane in still air and the speed of the wind?
Answers
Answer:
Plane: 165 miles per hour
Wind: 15 miles per hour
Explanation:
Let's call x the speed of the plane in still air and y the speed of the wind.
Additionally, the velocity is equal to distances over time. So, when the plane is flying against the wind, we can write the following equation:
[tex]\begin{gathered} x-y=\frac{\text{distance}}{\text{time}} \\ x-y=\frac{900\text{ miles}}{6\text{ hours}} \\ x-y=150 \end{gathered}[/tex]Because x - y is the total velocity of the plane when it is flying against the wind.
On the other hand, when the plane flies with the wind, we get:
[tex]\begin{gathered} x+y=\frac{900\text{ miles}}{5\text{ hours}} \\ x+y=180 \end{gathered}[/tex]So, we have the following system of equations:
x - y = 150
x + y = 180
Adding both equations, we get:
x - y = 150
x + y = 180
2x + 0 = 330
Solving for x:
2x = 330
2x/2 = 330/2
x = 165
Finally, Replace x by 165 on the second equation and solve for y as:
x + y = 180
165 + y = 180
165 + y - 165 = 180 - 165
y = 15
Therefore, the speed of the plane in still air is 165 miles per hour and the speed of the air is 15 miles per hour.
which of these is a formula that can be used to determine the nth term of the arithmetic sequence 15,27,39,51,....?
Answers
For an arithmetric progression, we need to find the common difference in the sequence
common difference = d = 2nd term - 1st term = 3rd term - 2nd term = 4th term - 3rd term
2nd term - 1st term = 27 -15 = 12
3rd term - 2nd term = 39-27 = 12
The result are the same.
Hence, d = 12
The first trm = 15
The formula for arithmetric sequence:
The nth term = 1st term + d(n - 1)
Replacing with the values we got above:
The nth term = 15 + 12(n - 1)
Since none of the options have the above, we would expand the parenthesis.
The nth term = 15 + 12×n - 12×1
The nth term = 15 + 12n - 12
= 15 -12 + 12n
The nth term = 3 + 12n = 12n + 3
From the options:
The nth term = 12n + 3 (option B)
[tex]a_n=\text{ }12n+3\text{ (}optionB)[/tex]