The city planning committee is discussing making a bike path extension in its city park. They have a $5050 budget for the proposed project. The cost to construct the path is $2.20 per foot. The path would be a straight line from the fountain to the large oak tree. In the right triangle formed, the height is 880 ft and the base is 2112 ft. How much will the path cost? Will this work with the city planning budget?
Final answer:
After using the Pythagorean theorem to calculate the length of the bike path as approximately 2287 feet, and multiplying by the cost of $2.20 per foot, the total comes to $5031.40. This total cost fits within the city planning budget of $5050.
Explanation:
The city planning committee needs to determine if their $5050 budget is sufficient for the bike path extension, with construction costs at $2.20 per foot. To calculate the cost of the bike path, we first must find the length of the path, which will be the hypotenuse in a right triangle formed by the height (880 ft) and the base (2112 ft). Applying the Pythagorean theorem (a² + b² = c²), where a is the height and b is the base, the length of the path (c) can be calculated as follows:
c = √(880² + 2112²) = √(774400 + 4456444) = √5230844 ≈ 2287 ft.
Now, we can determine the total cost by multiplying the length of the path by the cost per foot:
Total Cost = 2287 ft × $2.20/ft = $5031.40
Thus, the total cost for constructing the path would be $5031.40, which is within the city planning budget of $5050.
when do we say that a real number, say r, is a root of a given polynomial equation in x?
Four letters to different insureds are prepared along with accompanying envelopes. the letters are put into the envelopes randomly. calculate the probability that at least one letter ends up in its accompanying envelope.
Final answer:
The probability that at least one of four randomly distributed letters ends up in its correct envelope is 62.5%. This calculation uses the complementary approach, subtracting the probability of no matches (9/24) from 1.
Explanation:
The question asks about the probability that at least one letter ends up in its accompanying envelope when four letters are randomly put into four envelopes.
To solve this, we employ the principle of complementary probability, which suggests that the probability of at least one match is 1 minus the probability of no letters matching their envelopes.
Calculating the probability of no matches directly can be complex due to numerous possible permutations, so using the complementary approach is more efficient.
We can calculate the total permutations of the four letters being distributed into four envelopes as 4!, which equals 24.
To find the probability of no letters matching their envelopes (a derangement of 4 items), we use a specific formula or recognition of known patterns, resulting in 9 derangements. Thus, the probability of no matches is 9/24.
The probability of at least one letter matching its corresponding envelope is then 1 - (9/24), which simplifies to 15/24 or 5/8. Therefore, the probability is 0.625 or 62.5%.
A 50 foot ramp makes an angle of 4.9° with the horizontal. to meet new accessibility guidelines, a new ramp must be built so it makes an angle of 2.7° with the horizontal as shown below. what is the length of the new ramp?
Abcd is a quadrilateral. three of the angles of abcd measure 100°, 87°, and 106°, respectively. find the measure of the missing angle.
a. 67°
b. 74°
c. 80°
d. 87°
Simplify the expression.
a. square root 6
b. square root 12
c. 9 square root 12
d. 9 square root 6
The expression is d) [tex]9 \sqrt{6}[/tex]
To simplify the given expressions involving square roots, follow these steps:
a. Square root 6
Since 6 is not a perfect square and has no perfect square factors, [tex]\sqrt{6} i[/tex]s already in its simplest form.
b. Square root 12
Break down 12 into its prime factors: 12 = [tex]2 \times 2 \times 3[/tex]. Therefore,[tex]\sqrt{12}[/tex]can be simplified as follows:
[tex]\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}[/tex]
c. 9 square root 12
We already know that [tex]\sqrt{12} = 2\sqrt{3},[/tex] so we substitute it into the expression:
[tex]9 \sqrt{12} = 9 \times 2\sqrt{3} = 18\sqrt{3}[/tex]
d. 9 square root 6
Since [tex]\sqrt{6[/tex]} is already in its simplest form, the expression remains:
[tex]9 \sqrt{6}[/tex]
Help me with this please
A long distance runner can run 9 miles per hour. how many hours will it take the runner to run 27 miles
The long-distance runner will take 3 hours to run 27 miles.
What is a unitary method example?In simple terms, the unitary method is used to find the price of a single unit from a given multiple.
Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
You divide 27 miles by 9 miles per hour, getting 27/9 (miles/(miles))hour.
The units cancel out to make hours
This runner takes 1 hr to run 9 miles.
So, to run 27 miles the runner will take
= 27/9
= 3 hours.
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In standard notation, 2.34 x 102 is 23,400. true or false
Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial function. f(x) = 5x + 4 h(x) = x2 + 8x + 24
x = -3
x = 3
x = 4
x = 5
The correct answer is x = 5.
Trust me, I just did the quiz.
Marla is looking for a new car. She has test-driven two cars but can only purchase one. The probability that she will purchase car A is 0.52, and the probability that she will purchase car B is 0.38. What is the probability that she will not purchase either car A or car B?
Answer: The required probability is 0.10.
Step-by-step explanation: Given that Marla is looking for a new car. She has test-driven two cars A and B but can only purchase one.
We are to find the probability that she will not purchase either car A or car B.
Let, 'C' denotes the event that Marla will purchase car A and 'D' denotes the event that Marla will purchase car 'B'.
Then, according to the given information, we have
[tex]P(A)=0.52,~~~P(B)=0.38.[/tex]
Since Marla cannot purchase both the cars, so the events A and B are disjoint.
That is,
[tex]A\cap B=\phi~~~~~\Rightarrow P(A\cap B)=0.[/tex]
Therefore, the probability that Marla will purchase either car A or car B is given by
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.52+0.38-0=0.90.[/tex]
Hence, the probability that she will not purchase either car A or car B will be
[tex]P^\prime(A\cup B)=1-P(A\cup B)=0-0.90=0.10.[/tex]
Thus, the required probability is 0.10.
How many numbers between 1 and 101 are evenly divisible by 4 but not by 8?
101/4 = 25.25
so 25 numbers are divisible by 4
101/8 = 12.625
so 12 numbers are divisible by 8
25-12 =13
so 13 numbers are divisible by 4 but not by 8
simplify the expression.
cos^2(pi/2-x)/sqrt1-sin^2(x)
a. tan(x)
b. cos(x)tan(x)
c. cos(x)cot(x)
d. sin(x)tan(x)
What is the exponential function modeled by the following table? x f(x) 2 10 3 28 4 82 f(x) = 2x f(x) = 2x + 1 f(x) = 3x f(x) = 3x + 1
A f(x) = 2x
B f(x) = 2x + 1
Cf(x) = 3x
D f(x) = 3x + 1
Answer:
D f(x) = 3x + 1
Step-by-step explanation:
The level of detail that infants can see at 20 feet is equivalent to the level of detail that adults can see at _____ feet.
Grace is planning a move to a different city. She contacts two local rental companies and obtains the following information for the one-day cost of renting a truck: Company A: $40.95 per day plus $0.19 per mile Company B: $19.95 per day plus $0.49 per mile Let n represent the total number of miles driven in one day. Write an inequality that can be used to determine for what number of miles it is less expensive to rent the truck from Company B.
PLEASE HELP IMAGE ATTACHED!! can u explain how to do it
A system of equations is shown below: x + 3y = 5 (equation 1) 7x − 8y = 6 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?
Answer:
The correct answer is B. Show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations"
Step-by-step explanation:
To solve the system of linear equations 3x+5y=2 and 6x+10y=8 by using the linear combination method, Laura correctly multiplied the first equation by –2 to get -6x-10y=-4 and then correctly added the equations -6x-10y=-4 and and then correctly added the equations -6x-10y=-4 and 6x+10y=8 to get 0 = 4. How many solutions are there to the system of equations?
A. 0
B. 1
C. 2
D. 4
Answer:
The two linear equation are
1. 3 x + 5 y =2
2. 6 x + 10 y = 8
If you will multiply equation (1), by number ,2 you will get
6 x + 10 y=4
or, if you will divide equation 2,by 2 you will get ,line
2 × (3 x + 5 y)=2 × 4
3 x + 5 y=4
→Slope of line 1
[tex]=\frac{-3}{5}[/tex]
→Slope of line 2
[tex]=\frac{-6}{10}=\frac{-3}{5}[/tex]
→→Slope of two lines are equal , so they are parallel.
Parallel lines never intersect. So,there is no solution.
Option A: 0
The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours:
A graph titled Distance Vs Time is shown with Time in hours labeled on x axis and Distance from Island in miles labeled on y axis. The scale on the x axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y axis shows the numbers 0, 25, 50, 75, 100, 125, 150, 175, 200, 225. The graph shows a straight line joining the ordered pairs 0, 25, and 1, 75, and 2, 125, and 3, 175, and 4,225.
What is the speed of the motorboat?
225 miles per hour
25 miles per hour
75 miles per hour
50 miles per hour
the graph is showing for every 1 hour the boat is 50 miles further away
so the speed of the boat is 50 miles per hour
The speed of the boat is 50 miles per hour.
We have given that,
The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours
A graph titled Distance Vs Time is shown with Time in hours labeled on the x-axis and Distance from Island in miles labeled on the y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 25, 50, 75, 100, 125, 150, 175, 200, 225. The graph shows a straight line joining the ordered pairs 0, 25, and 1, 75, and 2, 125, and 3, 175, and 4,225.
We have to determine the speed of the motorboat.
What is the speed?The speed of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time it is thus a scalar quantity.
The graph is showing for every 1 hour the boat is 50 miles further away
1hour=50 miles from the graph
So the speed of the boat is 50 miles per hour.
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Mountain officials want to know the length of a new ski lift from A to C , as shown in the figure below. They measure angle DAC to be 32° . They then move 960 feet to point B and measure angle DBC to be 18° . What is the length of the new ski lift from A to C ? Round your answer to the nearest tenth of a foot.
Knowing if trigonometry knowledge we can say that the distance will be 305.4 ft.
So knowing how sine and tangent work we can write the equals as:
[tex]sin (32) = CD / 960\\CD = 508.72[/tex]
[tex]tan (32) = 508.72 / AD\\AD = 814.13[/tex]
To calculate the distance, we will decrease the two values found, like this:
[tex]814.13 - 508.72 = 305.4 ft[/tex]
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The graph below shows the price, y, in dollars, of different amounts of pounds of almonds, x: A graph titled Almond Prices shows Number of Pounds on x axis and Price in dollars on y axis. The scale on the x axis shows numbers from 0 to 12 at increments of 2, and the scale on the y axis shows numbers from 0 to 84 at increments of 14. A straight line joins the ordered pairs 0, 0 and 12, 84 Which equation best represents the relationship between x and y? y = 7x y = x + 7 y = 14x y = x + 14
Answer:
my brain has exceeded the limit of cofusion
Step-by-step explanation:
Find the equation of the parabola whose vertex is the origin and whose directrix is x=-4
Answer:
D
Step-by-step explanation:
2020 2021
Equation of the parabola whose vertex is the origin and whose directrix is x=-4 is x=0.
What is Parabola?A parabola is a curve where any point is at an equal distance from: a fixed point (the focus ), and; a fixed straight line (the directrix )
As we have vertex at the origin i.e. (0,0) and directrix is x=-4 and a line parallel to y-axis,
it must have a focus at (4,0)
Equation of the parabola represents locus of a point (x, y), which moves so that its distance from x=-4 to (4,0) are equal.
Hence, equation of parabola is
(x-4)²+(y-0)²=(x+4)²
(x-4)²+y²=(x+4)²
x²+16-8x=x²+16+8x
-16x=0
x=0
Hence, equation of the parabola whose vertex is the origin and whose directrix is x=-4 is x=0.
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What expression represents the area of the triangle?
Option first is the answer.
Step-by-step explanation:
For finding the are of a right angle triangle, we use the base and the height of the triangle. The height is the right angle leg of the triangle. Hypotenuse is not considered here.
In the given diagram, the base or 'b' is = 10 units
And the height or 'h' is = 24 units
Area of a right triangle is given as :
[tex]A=\frac{bh}{2}[/tex]
So, in the given options the correct option is : Option first.
[tex]A= \frac{10*24}{2 }[/tex] or [tex]\frac{1}{2}(10*24)[/tex]
Solve 2 cos theta + 2 = 3 in the interval from 0 to 2pi. Round to the nearest hundredth.
Final answer:
The solutions to the equation 2 cos θ + 2 = 3 in the interval from 0 to 2π are θ = π/3 and θ = 5π/3, which approximate to 60 degrees and 300 degrees.
Explanation:
The equation given is 2 cos θ + 2 = 3. To solve this equation, first subtract 2 from both sides to get 2 cos θ = 1. Then, divide both sides of the equation by 2 to isolate cos θ, yielding cos θ = 0.5.
In the interval from 0 to 2π (0 to 360 degrees), cos θ = 0.5 occurs at θ = π/3 and θ = 5π/3 (60 degrees and 300 degrees), as these are the angles in the first and fourth quadrants where the cosine value is positive and equal to 0.5.
Therefore, the solutions to the equation are θ = π/3 (θ ≈ 1.05 radians) and θ = 5π/3 (θ ≈ 5.24 radians), or θ ≈ 60 degrees (θ ≈ 1.05) and θ ≈ 300 degrees (θ ≈ 5.24) when rounded to the nearest hundredth of a radian.
Determine the sample size required to estimate the mean score on a standardized test within 5 points of the true mean with 99% confidence. assume that s=17 based on earlier studies.
Based on the mean score and the confidence interval, the sample size required to estimate the mean score is 77.
What is the sample size required?This can be found as:
= (Z score for 99% interval² x Sample size²) / Points off the true mean ²
Solving gives:
= (2.576² x 17²) / 5²
= 76.7
= 77
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If wx = XZ, then WX = YZ
MN = 2AB, so 3MN = 6AB. This is an illustration of which property?
PLEASE HURRY!!! 30 POINTS
A rectangle has an area of 102 cm2. The length of the rectangle is 17 cm.
What is the perimeter of the rectangle?
Answer:
(Really really really sorry if this incorrect)... ok so it's 17 cm tall in length. That would be 17 blocks high, for example. The area is 102, so 102 cm2 divided in half equals 51, so the width would be 51 cm. So the perimeter is 17 + 17 + 51 + 51 = 136 cm.
The quotient of 13 ÷ 24 is a decimal number. Which digit in the quotient is overlined?
1
4
5
6
13/24 = 0.5416666
since 6 keeps repeating that would be the number that has the line over it.