The total height gained from start to finish is 58m and the average gradient from start to finish is 29/210
What is an average gradient?
The gradient of a straight line drawn between two points is the average gradient between the two points.
Here, we have
A road has a gradient of 1/5 for 90 m.
Horizontal section 130 m long
The final section has a gradient of 1/5 for 200 m.
First, we will find the total height gained from start to finish
Total height from start to finish = 90 ×1/5 +200 × 1/5
= 18 + 40
Total height from start to finish =58 m
The average gradient from start to finish = 58/(90 + 130 +200)
= 58/420
= 29/210
Hence the total height gained from start to finish is 58m and the average gradient from start to finish is 29/210
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y=−16x ^2 +240x+115 ?
Answer:
Step-by-step explanation:
$y = -16x^2 + 240x + 115$
$= -16x^2 + 240x + 120 - 5$
$= -16x^2 + 240x + 120 - 5x - 5x$
$= -16x^2 + 240x + 120 - 10x - 5x$
$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2$
$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x$
$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x + x -x$
$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x + x -x + 3 - 3$
$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x + x -x + 0
in the picture below, we have a triangle DEF that has been dilated from center 0 by the scale factor r = 4. It is noted by D'E'F'. Describe the sequence of a dilation followed by a congruence that would map triangle D''E''F'' onto triangle DEF
HELP!!!!
The transformations that would map triangle D''E''F'' onto triangle DEF are given by:
Dilation centered at the origin with a scale factor of 1/4.Translation of 1 unit up and 2 units right.What are the transformations?The transformations to map triangle DEF into triangle D''E''F'' is given by:
Dilation centered at the origin with a scale factor of 4.Translation of 4 units down and 8 units left.The dilation means that the coordinates of each vertex of the figure are multiplied by the scale factor.
The dilation from DEF to D'E'F' has a scale factor of 4, hence the inverse dilation will have a scale factor of:
1/4.
Then the inverse translation is applied, as follows:
4 units x 1/4 = 1 unit, inverse of down is up.8 units x 1/2 = 2 units, inverse of left is right.More can be learned about transformations at https://brainly.com/question/29211183
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Simplify the complex expression to the standard form (a+bi). 8(5-9i)+2(5+2i)
The simplest form of complex expression is (a+bi) = 50+(-68)i.
What is complex expression?
A complex number is a number that is written as a + ib, in which “a” is a real number, and “b” is an imaginary number. The complex number contains a symbol “i” which satisfies the condition i^2 = −1.
Given,
8(5-9i)+2(5+2i)
= 40 - 72i +10 +4i
=50 - 68i
or we can write it as
= 50 + (-68i)
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What number is 76 more than the product of 13 and 8 Number sentence?.
Answer:
180
Step-by-step explanation:
13 X 8 = 104 --> 104 + 76 = 180
The following are airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport. 269 255 267 285 274 275 266 258 271 281
(a) Compute a 90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles. (Round your answers to three decimal places.)
(b) Give an interpretation of the 90% confidence level associated with the interval estimate in part (a).
a) If we were to take a large number of random samples of size 10, 10% of the resulting confidence intervals would contain the true mean airborne time.
b) If we were to take a large number of random samples of size 90, 10% of the resulting confidence intervals would contain the true mean airborne time.
c)If we were to take a 10 random samples of size 10, 10% of the resulting confidence intervals would contain the true mean airborne time.
d) If we were to take a large number of random samples of size 10, 90% of the resulting confidence intervals would contain the true mean airborne time.
90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles is (264.639, 275.5066), if 10 randomly selected flights from San Francisco to Washington Dulles airport.
Define confidence interval.In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability.
Given,
Airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport.
269 255 267 285 274 275 266 258 271 281
Sample mean = 270.10
Standard deviation = 9.326
Sample size = 10
Confidence level = 90%
Formula:
Confidence interval
= x ± tₐ₎₂(s/√n)
= 270 ± 1.833(9.326/√10)
= 270.1 ± 5.4066
= (264.639, 275.5066)
90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles is (264.639, 275.5066), if 10 randomly selected flights from San Francisco to Washington Dulles airport.
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In the coordinate plane, the point X(0,2) is translated to the point X(1,-3) . Under the same translation, the points Y(-2,4) and Z(4,5) are translated to Y and Z , respectively. What are the coordinates of Y and Z?
The new coordinates of Y and Z will be (-3, 9) and (3, 10), respectively.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
In the direction plane, point X(0,2) is meant the point X(1,- 3).
The rule of the transformation is written as,
(1, -3) ⇒ (0, 2)
(1, -3) ⇒ (1 - 1, -3 + 5)
(x', y') ⇒ (x - 1, y + 5)
Then the translation of the point Y(-2, 4) will be given as,
(x'', y'') ⇒ (-2 - 1, 4 + 5)
(x'', y'') ⇒ (-3, 9)
Then the translation of the point Y(4, 5) will be given as,
(x''', y''') ⇒ (4 - 1, 5 + 5)
(x''', y''') ⇒ (3, 10)
The new coordinates of Y and Z will be (-3, 9) and (3, 10), respectively.
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Which statement is true? A. A ray is a set of points that extends infinitely in both directions. B. A line consists of two endpoints and all the points between them. C. A line segment consists of two endpoints and all the points between them. D. A line has two endpoints.
The true statements are:
C. . A line segment consists of two endpoints and all the points between
D. A line has two endpoints.
What is a line segment?A line segment is bounded by two distinct points on a line.
How to know which statement is true?
From the definition,.
Also, we know that through two points one and only one line can pass .
Therefore, A line has two endpoints.
So, option C and D are correct.
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How many positive integers are there between 100 and 999 (both included) that are divisible by 3 or 4?.
There are 450 positive integers between 100 and 999 (both included) that are divisible by 3 or 4.
According to the question,
We have the following information:
Positive integers between 100 and 999 including both these integers which are divisible by 3 or 4
Now, the number of positive integers between 100 and 999 is (999-100+1) or 900.
Now, the numbers divisible by 3 will be in multiplication of 3.
So, number which are divisible by 3:
900/3 = 300
Now, the numbers divisible by 4 will be in multiplication of 4:
So, the numbers which are divisible by 4:
900/4 = 225
Now, there are also numbers in numbers divisible by which are divisible by 3. So, they are 1/3 of the numbers divisible by 4:
225/3
75
Now, total numbers divisible by 4:
225-75
150
Now, total numbers divisible by 3 or 4:
300+150
450
Hence, there are 450 positive integers between 100 and 999 (both included) that are divisible by 3 or 4.
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13 points) find the area of the largest rectangle that can be inscribed in a right triangle with legs of length 3 and 4 if two sides of the rectangle lie along the legs
The area of the largest rectangle will be 3.
By using properties of similar triangles we can say that
[tex]\frac{EF}{FB} - \frac{AC}{CB}[/tex]
B / (3 - a) = 4/3
3b = 12 - 4a
4a = 12 - 3b
a = (12 - 3b) / 4
Now as we know area of a rectangle is length * width. let us find the area
A = l * w
A = b * ( (2 - 3b) / 4 )
A = 3b - 3[tex]b^{2}[/tex]/4
Now to find maximum value we will differentiate the area and put it equal to zero.
[tex]D^{1}[/tex] = 3 - 6b/4 = 0
6b/4 = 3
6b = 12
b = 2
and
a = (12 - 3b) / 4
a = 6/4
a = 3/2
So, area will be = 3/2 * 2
Therefore maximum are of the triangle will be 3.
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A 40 inch board i to be cut into three piece o that the econd piece i 3 time a long a the firt piece and the third piece i 4 time a long a the firt piece. X equal the length of the firt piece, find the length of all three piece
The length of the first piece is 5 inches , the length of second piece is 15 inches and the length of third piece is 20 inches .
In the question ,
it is given that
the second piece is given to be 3 times as long as the first piece ,
and the third piece is given to be 4 times as long as the first piece .
let the length of the first piece [tex]=[/tex] x ,
So , the length of second piece [tex]=[/tex] 3x
and the length of the third piece [tex]=[/tex] 4x ,
total length of the board = 40 inch ,
So the equation becomes , x + 3x [tex]+[/tex] 4x [tex]=[/tex] 40
8x = 40
x = 40/8
x = 5
the first piece = 5 inches
second piece = 3*5 = 15 inches
third piece = 4*5 = 20 inches
Therefore , The length of the first piece is 5 inches , the length of second piece is 15 inches and the length of third piece is 20 inches .
The given question is incomplete , the complete question is
A 40 inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. X equal the length of the first piece, find the length of all three pieces ?
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Write the point-slope form of the equation of the horizontal line that passes through the point (2, 1).
a. Using variables, write out the formula for the point-slope form of the equation.
b. Identify the values for m, x1, and y1.
c. Fill these values into the point-slope form of the equation from part (a), and simplify as needed.
Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
SHOW WORK!!1
Answer:
y - 1 =0 (x-2)
Step-by-step explanation:
We are given that a horizontal line which is passing through the point (2,1).
We have to find the equation in point -slope form of the line .
We know that equation of horizontal line is given by
It means y does not vary with x therefore, Slope of line= Slope of horizontal line =0
Point- slope form equation of line
We have,
Substitute the values in the given formula
Then, we get the equation of horizontal line which is passing through the point (2,1) is given by
Hence, the equation of horizontal line which is passing through the point (2,1) is given by y - 1 =0 (x-2)
Let sin A = 1/3, with A in quadrant II, and let cos B =3/4, with B in quadrant I. Find sin(A - B). Give an exact, simplified answer.
The Trigonometric function sin(A - B) = (3 - 2[tex]\sqrt{14}[/tex]) ÷ 12
What is trigonometry?The study of correlations between triangles side lengths and angles is known as trigonometry.In geometric figures, unknown angles and distances are derived from known or measured angles using trigonometric functions. The need to calculate angles and distances in disciplines like astronomy, mapmaking, surveying, and artillery range finding led to the development of trigonometry.The easiest way is to use the Pythagorean Identity to find both cos A and sin B. Then use the sum/difference angle identity for sine.
The trigonometric Pythagorean identity tells us that,
[tex]Sin^{2}[/tex]θ + [tex]cos^{2}[/tex]θ = 1
which follows directly from the geometric identity for right triangles and the fact that,
sinθ = y/r and cosθ = x/r
If r is the distance (x,y) is from the origin, then
[tex]x^{2}[/tex] + [tex]y^{2}[/tex] = [tex]r^{2}[/tex]
[tex](x/r)^{2}[/tex] + [tex](y/r)^{2}[/tex] = 1(divide both sides by [tex]r^{2}[/tex])
[tex]cos^{2}[/tex]θ + [tex]Sin^{2}[/tex]θ = 1
Anyway, if we know sin A (and which quadrant it ends in), we can solve for cos A and vice versa:
[tex]Sin^{2}[/tex]θ + [tex]cos^{2}[/tex]θ = 1
[tex](1/3)^{2}[/tex] + [tex]cos^{2}[/tex]θ = 1
⇒ cos A = [tex]\sqrt{1-(1/3)^{2} }[/tex] = [tex]\frac{2\sqrt{2}}{3}[/tex]
cosθ is always negative in this quadrant.
Therefore,
cos A = -[tex]\frac{2\sqrt{2} }{3}[/tex]
Similar reasoning can be done with cos B = [tex]\frac{3}{4}[/tex] to show that sin B = -[tex]\frac{\sqrt{7} }{4}[/tex]
Now that we have all the necessary elements, we can use the sum/difference angle identity:
Sin(A-B) = sin A cos B - cos A sin B
= ( [tex]\frac{1}{3}[/tex] × [tex]\frac{3}{4}[/tex] ) - ( (-[tex]\frac{2\sqrt{2} }{3}[/tex] ) × (-[tex]\sqrt{7[/tex]/4) )
= (3 ÷ 12) - (2[tex]\sqrt{14}[/tex] ÷ 12)
= (3 - 2[tex]\sqrt{14}[/tex]) ÷ 12
We get sin(A - B) = (3 - 2[tex]\sqrt{14}[/tex]) ÷ 12
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Arianys runs a farm stand that sells grapes and apples. Each pound of grapes sells for
$3.75 and each pound of apples sells for $4. Arianys made $251.75 from selling a
total of 64 pounds of grapes and apples. Determine the number of pounds of grapes
sold and the number of pounds of apples sold.
The number of pounds of grapes is 24 sold and the number of pounds of apples sold is 30.
Given that,
Apples and grapes are sold at Arianys' farm stand. The price per pound for apples is $4 while the price per pound for grapes is $3.75. 64 pounds of apples and grapes were sold for a total profit of $251.75 for Arianys.
We have to find the number of the sold apples and pounds of grapes should be calculated.
What are the equation?a declaration that two mathematical expressions' values are equal (represented by the symbol =).
We get the equations as,
3.75x+4y=251.75
y=-0.93x+62.93---->equation(1)
x+y=64
y=-x+64------>equation (2)
We get the points as
For equation (1),
(0,62.93) and (67.66,0)
For equation (2),
(0, 64) and (64,0)
If we draw a graph we get 2 lines intersect at a point (24, 30).
Therefore, The number of pounds of grapes is 24 sold and the number of pounds of apples sold is 30.
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help asaap
There are 4 yellow, 3 blue, 5 green, 7 red and 2 orange sweets in my bag.
3.1.1 What is the probability of taking out a red sweet? Show all your steps.
3.1.2 What is the probability of taking out a green, blue or orange sweet? Show all your steps.
The probability of taking out a red sweet is; 1/3. The probability of taking out a green, blue or orange sweet is; 10/21
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We are given that there are 4 yellow, 3 blue, 5 green, 7 red and 2 orange sweets in my bag.
The total sweets = 4+3+5+7+2 = 21
1. the probability of taking out a red sweet is;
7/21 = (7:7)/(21:7)
= 1/3
2. The probability of taking out a green, blue or orange sweet is;
= (5+3+2)/21
= 10/21
Hence, The probability of taking out a red sweet is; 1/3. The probability of taking out a green, blue or orange sweet is; 10/21
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How much is this and i need to know the answer to this and then i need to know waht it is 8x 10⁹
8 * 10^9 is 8000000000
just 9 zeros to the 8
the distance from Huntington park to Promenade in Downey is 9 1/3 miles. if you were to walk at a steady 4 2/3 mph, how much time would be needed for the trip? Help please.!
The time that would be needed for the trip is 2 hours.
How to calculate the time?It is important to note that the formula that can be used for calculating the time taken will be:
Time = Distance / Speed
where
Distance = 9 1/3
Speed = 4 2/3
Therefore time will be:
Time = Distance / Speed
= 9 1/3 ÷ 4 2/3
= 28/3 ÷ 14/3
= 28/3 × 3/14
= 2 hours
The time is 2 hours.
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Round 8.7025 into two decimal places
Answer: the answer is 8.70.
Step-by-step explanation:
Since were rounding to the 2 decimal places(hundredths) we can immediately drop the 5. since 2 is not greater than 5 we do not round to 8.71. So, the answer is 8.70!
karen works 40 hours a week at a popular tourist attraction and earns a weekly salary of $400. this week, due to fourth of july crowds, she was asked to work another 10 hours. having worked 50 hours this week, how much can karen expect to earn for the week?
Answer:
$500
Step-by-step explanation:
400/40 = 10. This gives us her hourly rate
50 x 10 = 500
Drag all of the values to the box that round to 56.8 when rounded to the nearest tenth.
56.85
56.809
Drag all of the values to the box that round to 56.8 when rounded to the nearest tenth.
56.85
56.809
56.749
56.08
56.795
56.832
Drag all of the values to the box that round to 56.8 when rounded to the nearest tenth.
56.85
56.809
56.749
56.08
56.795
56.832
56.72
Numbers that round to 56.8
The numbers round to 56.8 when rounded to the nearest tenth are 56.809, 56.795, and 56.832 respectively.
What is rounding decimals?
The term "rounding decimals" describes the accurate rounding of decimal figures. To the nearest whole, tenth, or hundredth, we can round decimals.
The next place value on the right should be used to round a number to the closest tenth (the hundredths). Simply take away all the digits to the right if it's 4 or fewer. Remove all the digits to the right after adding 1 to the digit in the tenth position if the number is 5 or above.
We need to find the value that rounds to the nearest tenth which results in 56.8
Now, we check all options one by one and rounded them to the nearest tenth
56.85 = 56.9 (rounded to the nearest tenth)
56.809 = 56.8 (rounded to the nearest tenth)
56.749 = 56.7 (rounded to the nearest tenth)
56.08 = 56.1 (rounded to the nearest tenth)
56.795 = 56.8 (rounded to the nearest tenth)
56.832 = 56.8 (rounded to the nearest tenth)
56.72 = 56.7 (rounded to the nearest tenth)
Hence, the required answers are 56.809, 56.795, and 56.832.
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what is the y and x intercept of 2x+y=-3
Answer:The x-intercept is
(-3/2)
The y-intercept is
(0,-3)
Step-by-step explanation:
to find the x and y intercept you have to make x and y equal zero then solve.
finding x
2x+0=-3
2x/2=-3/2
x=-3/2
finding y
2(0)+y=-3
-2 -2
y= -5
Please heeeeelp I don’t understand
Answer:
A. y = 62x
Step-by-step explanation:
A.
y = 186/3x + b
y = 62x + b
186 = 62*3 + b
186 = 186 + b
b= 0
Write your answer as an integer or as a decimal round to the nearest 10th
m∠W = 33.8° , using inverse trignometric ratio.
What do you mean by inverse trignometric functions?
The sine, cosine, tangent, cotangent, secant, and cosecant functions are the fundamental trigonometric functions. Inverse trigonometric functions are just the inverse functions of these functions. They can also be referred to as cyclometric functions, antitrigonometric functions, or arcus functions. Trigonometry's inverse functions are used to find the angle for any trigonometric ratio.
It is given that VU = 2 units and VW = 3 units and VUW is a right angle triangle , right angled at V.
Using the ratio of tanW,
As we know tanA = P/B where P is the perpendicular and B is the base
In the given triangle VUW,
tanW = VU/VW = 2/3
W = [tex]tan^{-1}[/tex](2/3) = [tex]tan^{-1}[/tex](0.67) = 33.8 degree
Therefore, m∠W = 33.8°
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15 7 ÷ 15 4 is equal to _____.
15 3
1
15 11
Answer:
102
7.43 Answer by question
A gaming system costs $600 and is on sale for 15% off. After the discount, there is a 5% tax. What is the final price of the gaming system?
$90.00
$94.50
$510.00
$535.50
Answer:
535.50
Step-by-step explanation:
hope this helps :)
Answer:
535.50
Step-by-step explanation:
Hope this helps : )
Richard's Bakery recently spent a total of $594 on new equipment, and their average hourly operating costs are $5. Their average hourly receipts are $23. The bakery will soon make back the amount it invested in equipment. How many hours will that take? What would the total expenses and receipts both equal?
Answer:
33 Hours.
Step-by-step explanation:
Their hourly receipts are $23, and their hourly operating costs are $5. So you would subtract the hourly receipts from the hourly operating costs.
23 - 5 = 18
Then you would take the new number and divide the money spent on equipment by the money earned an hour.
594 / 18 = 33
Hope this helps! :)
8. Use point-slope form to write the equation of a line that passes through the point (18, -3) with slope -1.
The equation of the line that passes through the point (18,-3) with slope -1 is y = -x+15.
According to the question,
We have the following information:
The line passes through the point (18,-3) with slope -1.
We know that the following formula is used to find the equation of the line passing through a point with the slope which is denoted by m:
(y-y') = m(x-x')
In this case, we have the following values:
m = -1
x' = 18 and y' = -3
Putting these values in the above formula:
y-(-3) = -1(x-18)
y+3 = -x+18
Subtracting 3 from both sides of the equation:
y = -x+18-3
y = -x+15
Hence, the equation of the line that passes through the point (18,-3) with slope -1 is y = -x+15.
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pls help
50 points pls don't guess ty
Number of steps that he needed to walk to achieve the goal is 3141 steps
The goal of the Jayden = 10000 steps
The number of steps that he walked = [tex](\frac{1}{19} )^{-3}[/tex] steps
Here we have to convert the given number of steps to the suitable form for calculation
The number of steps that he walked
[tex](\frac{1}{19} )^{-3}[/tex] steps = [tex]19^3[/tex] steps
Find the power of the number
[tex]19^3[/tex] steps = 6859 steps
Number of steps that he needed to walk to achieve the goal = The goal of the Jayden - The number of steps that he walked
Substitute the value in the equation,
Here we have to sue the subtraction
Number of steps that he needed to walk to achieve the goal = 10000 - 6859
= 3141 steps
Hence, number of steps that he needed to walk to achieve the goal is 3141 steps
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Hello i really need help answering this question
Step-by-step explanation:
Problem #1:
A number is divisible by 4 if the last 2 digits of that number are multiple of 4 . So for example the number 2316 is a multiple of 4 because it ends with " 16 " and " 16 " is a multiple of 4 .
Write a program that prompts the user to enter an integer and displays whether the number is a multiple of 4 or not. The program stops reading integers, when the user inputs a negative value. It shows at the end the total number of values entered which are multiple of 4 .
Sample Run:
Enter an integer: 4
4 is a multiple of 4
Enter another integer: 213
213 is not a multiple of 4
Enter an integer: 2316
2316 is a multiple of 4.
Enter an integer: -20
The total number of integers entered which are multiple of 4 is 2 .
I'm not sure how to solve this
What is the ½ of ¾?.
The value of fraction 1/2 multiplied by 3/4 is 3/8 by multiplication of fractions.
What is fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. A fraction only informs us of the number of components that make up the total. The slash that is inserted between the two numbers identifies a fraction. The numerator is the highest number, while the denominator is the lowest number. 1/2, for instance, is a fraction. A fraction is a number that is a component of a whole.
Here,
1/2 of 3/4
=1/2*3/4
=3/8
By using fractional multiplication, the result of 1/2 times 3/4 is 3/8.
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