The graph of y = (x + 3)² is a transformation of the graph y = x². It is shifted left 3 units.
Describing the transformation of the functionsThe equation of the function is given as
y = x²
The transformed function is
y = (x + 3)²
This means that the parent function is y = x²
When compared, we can see that
x in y = x² is x + 3 in y = (x + 3)²
This means that y = x² is shifted left by 3 units to form y = (x + 3)²
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HELPPPPPPPPPPP
Nathaniel has 132 DVDs in his collection.
Each DVD case has the dimensions shown.
He plans to buy shelves for the collection
that are 31.5 inches wide and cost $15.75
each. How much will it cost Nathaniel to
shelve his DVD collection? Explain how you
found your answer.
The dimensions are 7.5in, 5.3in, 0.6in
The cost of shelving Nathaniel’s DVD collection is 15.75×27=$425.25.
We are given that;
Dimensions =7.5in, 5.3in, 0.6in
To find the cost of shelving Nathaniel’s DVD collection, we need to find how many shelves he needs and multiply that by the price of each shelf. To find how many shelves he needs, we need to find how many DVDs can fit on one shelf and divide that by the total number of DVDs.
Since the shelves are 31.5 inches wide and the DVDs are 5.3 inches wide, we can fit 5.331.5≈5.94 DVDs on one shelf. We round this down to 5 DVDs per shelf because we cannot fit a partial DVD on a shelf.
Since Nathaniel has 132 DVDs in his collection, he needs 5132=26.4 shelves. We round this up to 27 shelves because we cannot use a partial shelf.
Therefore, by algebra the answer will be 15.75×27=$425.25.
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certain game, a fair die is rolled and a player gains 20 points If the die shows a If the die does not show a 6the player loses 3 points die were to be rolled 100 times, what would be the expected total gain or loss for the player?
If player gains 20 points If die shows "6" and loses 3 points if die does not show "6", then there will be a gain of 83 points, Option(c) is correct.
To find the expected total gain or loss for the player, we need to find the expected value of the points earned or lost on each roll of the die and then multiply that by "number-of-rolls".
Let X be the random-variable representing the points earned on a single roll of the die.
If "6" appears on die, then , X = 20,
If "6" does not appear on die, then X = -3,
The probability of getting "6" is = 1/6, and
The probability of not getting "6" is = 5/6.
So, the expected-value of X is : E(X) = (1/6) × 20 + (5/6) × (-3) = 0.83,
It means that, on average, the player can expect to earn about 0.83 points per roll of the die.
To find the expected total gain or loss for 100 rolls of the die, we multiply the expected value of X by 100;
⇒ E(total) = 100 × E(X) = 100 × 0.83 = 83,
The "Expected-Value" is positive, the player can expect to gain about 83 points over 100 rolls of the die.
Therefore, the correct option is (c).
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The given question is incomplete, the complete question is
In a certain game, a fair die is rolled and a player gains 20 points if the die shows a "6." If the die does not show a "6," the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player?
(a) A gain of about 1,700 points
(b) A gain of about 583 points
(c) A gain of about 83 points
(d) A loss of about 250 points
(e) A loss of about 300 points
The table shows the distribution, by age and gender, of the million people in a certain region who live alone. Use the data in the table to find the probability that a randomly selected person living alone in the region is male.
The histogram represents data collected on the frequency of how far the tide rose, in feet, up the beach from the buoy. A histogram titled Tides For 15 Days with an x-axis labeled Measurement In Feet with intervals of 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25. The y-axis is labeled Frequency and starts at 0 with tick marks every one unit up to 7. There is a shaded bar above 1 to 5 that stops at 1, above 6 to 10 that stops at 3, above 11 to 15 that stops at 4, above 16 to 20 that stops at 4, and above 21 to 25 that stops at 3. Which statement best describes the spread and distribution of the data? The data is almost symmetric, with a maximum range of 24. This means that the tide frequently measured around 11 to 20 feet. The data is skewed, with a maximum range of 24. This means that the tide was frequently very high in the 16 to 25 feet range. The data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 21 to 25 feet. The data is symmetric, with a maximum range of 20. This means that the tide frequently measured around 1 to 5 feet.
The histogram is solved and the data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 16 and 20 feet.
Given data ,
Let the number of observations of each interval is:
1 to 5: 2 observations.
6 to 10: 5 observations.
11 to 15: 2 observations.
16 to 20: 6 observations.
21 to 25: 1 observations.
Let the maximum range be represented as M
And , there are two similarly high bins for the histogram , hence the distribution can be said to be bimodal, with maximum range given as follows
M = 25 - 5
M = 21 - 1
M = 20
Hence , the histogram is solved
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Paula is investing $5,000 in an account that earns 4.10% APR compounded quarterly. How much
money will she have in 25 years?
$15,556.84
Paulanwill have approx $15,556.84 if she investb$5k that earns 4.10% apr compound quarterly..
Answer:
I’m pretty sure it’s $11,780.60
Step-by-step explanation:
We can use the formula for compound interest to determine how much money Paula will have in 25 years:
A = P(1 + r/n)^(nt)where:A = the total amount of money after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = $5,000
r = 4.10% = 0.041 (as a decimal)
n = 4 (compounded quarterly)
t = 25 years
Plugging these values into the formula, we get:
A = $5,000(1 + 0.041/4)^(4*25)
A = $5,000(1 + 0.01025)^100
A = $5,000(1.01025)^100
A = $5,000(2.356)
A = $11,780.60
Therefore, Paula will have approximately $11,780.60 in her account after 25 years.
Mr. Oakley class surveyed 200 students about their favorite type of pie. The double bar graph below shows the result of the survey. What is the difference in the total number of students who chose peach pie as their favorite type of pie and the total number of students who chose apple pie? Show all your work. Explain why you did each step.
The difference in the students who chose peach pie and apple pie is 46
What is the difference in the students who chose peach pie and apple pie?From the question, we have the following parameters that can be used in our computation:
Number of students = 200Proportion of students that choose peach = 38%Proportion of students that choose apple = 15%From the above, we have the percentage difference to be
Difference = 38% - 15%
When the given values are substituted, we have
Difference = 23%
This means that
Students = 23% * 200
Evaluate
Students = 46
Hence, the number of students is 46
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Rectangle LMNP is similar to rectangle WXYZ.
The length of LM is 19 in, the area of rectangle LMNP is 140.6 in2, and the length of XY is 2.22 in.
What is the difference between the perimeters of the two rectangles?
A. 31.96 in
B. 36.96 in
C. 15.84 in
D. 41.96 in
The required, difference between the perimeters of the two rectangles is 46.03 in. None of the options is correct.
Since rectangles LMNP and WXYZ are similar, their corresponding sides are proportional. Let's denote the scale factor as k. Then:
k = XY / LM = 2.22 / 19
To find the value of k, we can divide 2.22 by 19:
k ≈ 0.117
The area of rectangle LMNP is given as 140.6 in^2. We can use this to find the length of NP:
LM * NP = area of LMNP
19 * NP = 140.6
NP ≈ 7.4 in
Since the sides of WXYZ are proportional to those of LMNP, we can find the length of YZ:
XY / YZ = LM / NP
2.22 / YZ = 19 / 7.4
YZ ≈ 1.167 in
Now we can calculate the perimeters of both rectangles:
Perimeter of LMNP = 2(LM + NP) = 2(19 + 7.4) = 52.8 in
Perimeter of WXYZ = 2(XY + YZ) = 2(2.22 +1.167) = 6.77in
The difference between the perimeters is:
52.8 - 6.77 = 46.03 in
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Which statement about a quadrilateral is true?
Responses
A. All rectangles are squares.
B. A rhombus has exactly one pair of parallel sides.
C. A trapezoid has two pairs of parallel sides.
D. Some rhombuses have four right angles.
The statement which is true about the quadrilateral is D. Some rhombuses have four right angles.
Quadrilaterals are four sided polygons which also have four vertices and four angles.
Sum of all the interior angles of a quadrilateral is 360 degrees.
Rectangles, squares, trapezium, parallelogram, rhombus are all quadrilaterals.
A. All squares are rectangles but all rectangles are not squares, since for squares, all sides need to be equal.
But for a rectangle, opposite sides only need to be equal.
B. A rhombus has all the sides equal and opposite sides are parallel.
So there are 2 pairs of parallel sides.
C. A trapezoid can have only one pair of sides parallel.
D. Some rhombuses have four right angles.
This is true since square is a rhombus and it has 4 right angles.
Hence the true option is D.
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With workings, please help
Answer:
Step-by-step explanation:
I need help with this please
Answer: C
Step-by-step explanation:
Right angles (or 90 degree angles) are indicated by little squares in the corners of the figures that have them.
For which equations below is x = -3 a possible solution? Select three options.
Ox| = 3
Ox| = -3
01-x| = 3
Ox|=-3
O-kx| = -3
From November to December of 2015, the price per share of BP Oil dropped from $90.75 to $82.75. Exxon shares also dropped from $87.25 to $61.25. In November, your rich cousin invested $97,918.25 into a combination of BP and Exxon shares. By December they sold their shares for $74,090.25 losing $23,828 from their investment. How many of each stock did they purchase?
By solving equations we get to know that your cousin bought 356 shares of BP and 1448 shares of Exxon.
Initial investment:
x shares of BP at $90.75 per share + y shares of Exxon at $87.25 per share = $97,918.25
Sale of shares:
x shares of BP at $82.75 per share + y shares of Exxon at $61.25 per share = $74,090.25
We now have two equations with two variables, which we can solve using either substitution or elimination
0.875x($90.75) + 0.875y($87.25) = $85,648.23
x($82.75) + y($61.25) = $74,090.25
0.875x($90.75) - x($82.75) = $11,558.98 - 0.875y($87.25) + y($61.25)
0.875x($8) = $11,558.98 - 0.875y($26)
7x = $11,558.98 - $22.75y
We can then substitute this expression for "x" into either of the original equations to solve for "y".
(7($11,558.98 - $22.75y))/$8 + y($87.25) = $97,918.25
$81,763.03 - $19.9375y + $87.25y = $97,918.25
$7.0125y = $10,155.22
y = 1448
and x = 356
Hence, your cousin bought 356 shares of BP and 1448 shares of Exxon.
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What is the difference between the median math test score in the morning and the afternoon?
The difference between the median math test score in the morning and the afternoon is 9.5
What is median?The median can simply be described as the middle number in a given set of data when the values are arranged in an order from least to the greatest values.
From the information given, we have that;
The math scores for the afternoon test were;
55, 70, 76, 85, 95
The math scores for the morning test were;
70, 80.5, 85.5, 90.5 and 95.5
Hence,
The median for the afternoon test = 76
The median for the morning test =85.5
The difference between the values would be = 85.5 - 76 = 9. 5
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PLEASE HELP ME SOLVE THIS!! I AM LOST! HELP ME PLEASE!!!! THANKS
The Cost of the blue paint that would cover the shaded area = $0.495
The Cost of the white paint that would cover the triangular shapes = $0.6678
How to Find the Area of a Circle and Triangle?Recall the following formulas:
Area of a circle = πr²
Area of a triangle = 1/2 * base * height.
Area the blue paint will cover = 2(1/2 * base * height) = 2(1/2 * 1.5 * 1)
= 1.5 ft²
Cost of the blue paint = 1.5 * 0.33 = $0.495
Area the blue paint will cover = πr² - area of the two triangles
= 3.14 * 1.5² - 1.5 = 5.565 ft²
Cost of the white paint = 5.565 * 0.12 = $0.6678
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A 105 kg halfback runs north and is tackled by a 156 kg opponent running south at 6 m/s. The collision is perfectly inelastic. Just after the tackle, both players move at a velocity of 3 m/s north. Calculate the velocity (m/s) of the 105 kg player just before the tackle. Answer to one decimal place.
We can solve this problem using the conservation of momentum and the law of conservation of energy. Here's how:
Let v be the velocity of the 105 kg player just before the tackle. Then the velocity of the 156 kg player just before the tackle is -6 m/s, since he is running south. After the tackle, the two players move at a velocity of 3 m/s north, so we have:
Total momentum before = Total momentum after
(105 kg)(v) + (156 kg)(-6 m/s) = (105 kg + 156 kg)(3 m/s)
Simplifying and solving for v, we get:
v = (105 kg + 156 kg)(3 m/s) + (156 kg)(6 m/s) / 105 kg
v = 2.85 m/s
Therefore, the velocity of the 105 kg player just before the tackle was 2.85 m/s north.
Two square carpets are used in the reception area of a hotel. The sum of the areas of the carpets is 720 square feet. The difference of the areas of the carpets is 432 square feet. Find the dimensions of each carpet.
Answer:
Let x be the length of one side of the first carpet in feet. Then, the area of the first carpet is x^2 square feet.
Let y be the length of one side of the second carpet in feet. Then, the area of the second carpet is y^2 square feet.
From the problem, we know that the sum of the areas of the two carpets is 720 square feet:
x^2 + y^2 = 720
We also know that the difference of the areas of the two carpets is 432 square feet:
x^2 - y^2 = 432
We can solve this system of equations by using the method of substitution. Solving for x^2 in the second equation, we get:
x^2 = y^2 + 432
Substituting this expression for x^2 into the first equation, we get:
y^2 + 432 + y^2 = 720
Simplifying and solving for y, we get:
2y^2 = 288
y^2 = 144
y = 12
Substituting this value of y into the equation x^2 + y^2 = 720 and solving for x, we get:
x^2 + 144 = 720
x^2 = 576
x = 24
Therefore, the dimensions of the first carpet are 24 feet by 24 feet, and the dimensions of the second carpet are 12 feet by 12 feet.
Step-by-step explanation:
An employee receives a 3% raise once per year. If the employee's initial salary is $65,800.00, what will the employee's salary be after 7 years?
Answer:
$79,618
Step-by-step explanation:
7 years x 3% = 21%
$65,800 x 21% = $13,818
$65,800 + $13, 818 = $79,618
Please help with my question!!!!!!!!
The perimeter of the regular nonagon will be; 840.7 units
The in-radius of the regular nonagon is given as:
Radius, r =17
The perimeter is then calculated by:
P = 18r/Tan(π/9)
Substitute 17 for r;
P = 18(17)/Tan(π/9)
Evaluate the product of 18 and 17;
P = 306/Tan(π/9)
Evaluate the quotient
P = 840.7
Hence, the perimeter of the regular nonagon = 840.7 units
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Based on its second derivative and given initial values, the function is equal to f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + 4.
How to determine and to evaluate the function related to its second integral
In this problem we find the definition of the second derivative of a function, whose form must be dertermined by integration and the use of initial values. First, write the second derivative:
f''(x) = 2 · x + 6 · sin x
Second, determine the first derivative of the function:
f'(x) = x² - 6 · cos x + C
2 = 0² - 6 · cos 0 + C
2 = - 6 + C
C = 8
f'(x) = x² - 6 · cos x + 8
Third, determine the function:
f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + C
4 = (1 / 3) · 0³ - 6 · sin 0 + 8 · 0 + C
4 = C
C = 4
f(x) = (1 / 3) · x³ - 6 · sin x + 8 · x + 4
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2×2 pleaseeee hellppppppp
i am need of help so very badly
100 points for the answer
4
add 2 and 2 together and you get 4.
Answer:
4
Step-by-step explanation:
2x2 is the same as 2+2, so 2+2 is 4.
Jamal and his dad went scuba diving. They went on a 54-foot dive, descending from a motor boat located on the Gulf of Mexico. The boat was located
at sea level.
Where on a number line would you plot a point to represent the boat's location?
Your answer is incorrect. A company makes wax candles in the shape of a rectangular prism. Each candle is 6 inches long, 3 inches wide, and 8 inches tall. How much wax will they need to make 288 candles?
The amount of wax needed to make 288 candles is 41472 inches³.
How to find the amount of candles wax ?A company makes wax candles in the shape of a rectangular prism. Each candle is 6 inches long, 3 inches wide, and 8 inches tall.
Therefore, the amount of wax to make 288 candles can be calculated as follows:
Hence,
volume of each rectangular prism = 6 × 3 × 8
volume of each rectangular prism = 18 × 8
volume of each rectangular prism = 144 inches cube
Therefore,
1 candle = 144 inches cube
288 candles = ?
cross multiply
volume of wax for 288 candles = 288 × 144
volume of wax for 288 candles = 41472 inches³
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In the coordinate plane, the point A (-2, -4) is translated to the point A' (-3, -1). Under the same translation, the points B (0, -7) and C (-5, -8) are translated to B' and C', respectively. What are the coordinates of B' and C'?
The coordinates of the points B' and C' are B' = (-1, 10) and C' = (-6, -5)
Calculating the coordinates of B' and C'?From the question, we have the following parameters that can be used in our computation:
A = (-2, -4)
This point is translated to
A' = (-3, -1)
This means that the rule of transformation is
(x, y) = (x - 1, y + 3)
Given that
B = (0, 7) and C = (-5, -8)
When this transformation is applied on B and C, we have
B' = (0 - 1, 7 + 3) and C' = (-5 - 1, -8 + 3)
Evaluate
B' = (-1, 10) and C' = (-6, -5)
Hence. the coordinates of B' and C' are B' = (-1, 10) and C' = (-6, -5)
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The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected giraffe adult. Round all answers to 4 decimal places.
D. What is the probability that a randomly selected giraffe will be shorter than 18.5 feet tall?
E. probability that a randomly selected giraffe will be between 19 and 19.9 ft tall?
F. 75th percentile for the height of giraffes.
D. The probability that a randomly selected giraffe will be shorter than 18.5 feet tall is given as follows: 0.7340 = 73.40%.
E. The probability that a randomly selected giraffe will be between 19 and 19.9 ft tall is given as follows: 0.0968 = 9.68%.
F. The 75th percentile for the height of giraffes is given as follows: 18.54 ft.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 18, \sigma = 0.8[/tex]
The probability that a randomly selected giraffe will be shorter than 18.5 feet tall is the p-value of Z when X = 18.5, hence:
Z = (18.5 - 18)/0.8
Z = 0.625
Z = 0.625 has a p-value of 0.7340.
The probability that a randomly selected giraffe will be between 19 and 19.9 ft tall is the p-value of Z when X = 19.9 subtracted by the p-value of Z when X = 19, hence:
Z = (19.9 - 18)/0.8
Z = 2.375
Z = 2.375 has a p-value of 0.9912.
Z = (19 - 18)/0.8
Z = 1.25
Z = 1.25 has a p-value of 0.8944.
Hence:
0.9912 - 0.8944 = 0.0968 = 9.68%.
The 75th percentile is X when Z = 0.675, hence:
0.675 = (X - 18)/0.8
X - 18 = 0.8 x 0.675
X = 18.54 ft.
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Find an equation of the line passing through the given points. Use function notation to write the equation.
(−2,−3) and (−4,−4)
Answer:
Step-by-step explanation:
Let A(-2,-3), B(-4,-4).
Line f(x) = y = ax + b (C)
The line passes through these points so when substituting their coordinates into (C), we get:
-3 = -2a + b
-4 = -4a + b
Solving this set of equations gives us a = 1/2; b = -2.
So the equation of this line is [tex]f(x)=\frac{1}{2}x-2[/tex]
Use the substitution u = 1/x and v = 1/y to rewrite the equations in the system in terms of the variables u and v. Solve the system in terms of u and v. Then substitute to determine the solution set to the original system in terms of x and y.
1/x + 2/y = 1
-1/x + 8/y = -6
Step-by-step explanation:
We have the system of equations:
1/x + 2/y = 1 -----(1)
-1/x + 8/y = -6 -----(2)
We can use the substitutions u = 1/x and v = 1/y to rewrite the equations in terms of u and v. Substituting, we get:
u + 2v = 1 -----(3)
-u + 8v = -6 -----(4)
Now we can solve the system in terms of u and v. Adding equations (3) and (4) gives:
2v = -5
Dividing both sides by 2, we get:
v = -5/2
Substituting this value of v into equation (3) gives:
u + 2(-5/2) = 1
Simplifying:
u - 5 = 1
u = 6
Therefore, we have u = 6 and v = -5/2.
To find the solution set in terms of x and y, we substitute back:
u = 1/x, so 6 = 1/x, and x = 1/6
v = 1/y, so -5/2 = 1/y, and y = -2/5
Therefore, the solution set to the original system is x = 1/6 and y = -2/5.
2. The million-dollar question! Suppose you
want to have $1,500,000 for retirement in
30 years. If you deposit the same amount
each month into an annuity that earns 6%
interest annually (and compounded
monthly),
what is the amount you need to
deposit each month?
Show your work
using the formula.
The formula to calculate the monthly payment needed to achieve a future value in an annuity is:
PMT = FV * (r / 12) / [(1 + r / 12)^(n * 12) - 1]
where PMT is the monthly payment, FV is the future value, r is the annual interest rate (as a decimal), and n is the number of years.
In this case, FV = $1,500,000, r = 0.06, and n = 30. Plugging these values into the formula, we get:
PMT = $1,500,000 * (0.06 / 12) / [(1 + 0.06 / 12)^(30 * 12) - 1]
PMT = $1,500,000 * 0.005 / [1.06^(360) - 1]
PMT = $1,500,000 * 0.005 / 5.743
PMT = $1,244.23 (rounded to the nearest cent)
Therefore, the amount that needs to be deposited each month to achieve a future value of $1,500,000 in 30 years is $1,244.23.
Answer:
the guys above me is correct
Step-by-step explanation:
because i did it and the answer was correct for me
select all the equations that are equivalent to 81x^2+180x-200=100
The factorized form of the equation is 3((3x + 10)(9x - 10) ) = 0.
What is the simplification of the equation?
The given quadratic equation is simplified as follows;
81x² + 180x - 200 = 100
Collect similar terms together;
81x² + 180x = 100 + 200
81x² + 180x = 300
81x² + 180x - 300 = 0
Factorize the equation by using a common factor;
3(27x² + 60x - 100) = 0
Factorize further as follows;
3(27x² + 90x - 30x - 100) = 0
3( 9x (3x + 10) - 10(3x + 10) )= 0
3((3x + 10)(9x - 10) ) = 0
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A city garden club is creating a green space as a community project on 5.5 acres of land for their citizens’ enjoyment. A local landscaping company is expected to donate somewhere between 2500 and 3000 seedlings for the project. What will the density be in trees per acre upon completion? Round your answers to the nearest whole number
The density in trees per acre upon completion will be 500 trees per acre.
How to calculate the densityIn this scenario, let's say the landscaping provider donates 2750 seedlings.
Density of trees per acre = Total number of trees / Total area of land
Hence, applying the formula leads us to:
Density of trees per acre = 2750 trees / 5.5 acres
The answer comes out to be roughly around 500 trees/acre. So when completed, approximately 500 trees are estimated to be present in each acre of the landscape.
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A cyclist is riding on a mountain trail. Her current elevation is 1.9 km, and she is riding at a constant speed of 25 km/hr. She is riding downhill, and her angle of
descent is 2° from the horizontal. See the figure below. (The figure is not drawn to scale.) Find her new elevation, h, after 0.50 hours. Carry your Intermediate
computations to at least four decimal places, and round your answer to the nearest tenth of a kilometer.
1.9 km
2°
- Cyclist after 0.50 hours
Ih km
Sea Level
After 0.50 hours, the cyclist's new elevation is h = 1.8 km.
Since the cyclist is riding downhill, we can use the formula h = h0 - Vt sin θ to calculate her new elevation. In this formula, h0 represents her initial elevation, V her speed, t her time, and θ her angle of descent. We are given h0 = 1.9 km, V = 25 km/hr, t = 0.50 hours, and θ = 2°.
h = 1.9 km - (25 km/hr)(0.50 hours)(sin 2°)
h = 1.9 km - (25 km/hr)(0.50 hours)(0.03492)
h = 1.8282 km
h ≈ 1.8 km
Therefore, after 0.50 hours, the cyclist's new elevation is h = 1.8 km.
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