Answer:
a) 400 meters
b) 67 meters
c) 124.790 meters
Step-by-step explanation:
Given data :
g1 = - 0.4 %
g2 = +2 %
change of grade of sag curve ( a ) = 0.6 %
Elevation of PVI ( h2 ) = 124.80 m
a) compute the length of the curve using the relation below
a = [tex]\frac{g2-g1}{L}[/tex] . hence ; L = ( g2 - g1 ) / a
L = ( 2 -(-0.4 ) / 0.6
= 2.4 / 0.6 = 4
= 400 meters
b) compute the elevation of the lowest point of the curve
slope of the vertical curve = 0
0 = 2ax l + b
= 2( [tex]\frac{g2-g1}{L}[/tex] ) x + g1
∴ x = [tex]\frac{-g1L}{(g2-g1)}[/tex] = ( 0.4 * 4 ) / ( 2 + 0.4 ) = 1.6 / 2.4 = 0.67 stations
therefore x ( elevation of the lowest point ) = 67 meters
C) compute the elevation at Sta. 12 + 125.60
Given that the rate of change of elevation is the same at all points
= [tex]\frac{h2 - h1 }{PVI -P0}[/tex] = 0.4 -------- ( 1 )
where h2 = 124.80
h1 = ? ( elevation of p0 ) at 12 + 125.60
PVI = 12 + 150.06
p0 = 12 + 125.60
back to the above equation
- h1 = 0.4 ( PVI - P0 ) - h2
= 0.4 ( 12.150 - 12.1256 ) - 124.80
-h1 = -124.790
hence h1 = 124.790 m
The design for a small counter top
is shown. What is the perimeter and
area of the counter top?
Answer:
P = 22 ft
A = 18 ft²
See picture
Step-by-step explanation:
The perimeter is all the sides added together. You have to find the missing values. The missing vertical value is 2.5 (4-1.5). The missing horizontal value is 4 (7-3).
Add all the sides together for the perimeter.
Split the shape into 2 rectangles to find the area. Find the area of each rectangles, then add them together to find the total area.
Find the height. Write the answer in terms of pi.
Researchers published a study in which they considered the incidence among the elderly of various mental health conditions such as dementia, bi-polar disorder, obsessive compulsive disorder, delirium, and Alzheimer's disease. In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study. Calculate the probability that fewer than 320 out of the n
Answer:
The step-by-step procedure to solve this question is given, using the normal approximation to the binomial distribution.
Step-by-step explanation:
We use the normal approximation to the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study.
This means that [tex]p = 0.45[/tex]
Mean and standard deviation for the approximation, for a sample of n:
[tex]\mu = E(X) = np = 0.45n[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{0.45*0.55n}[/tex]
Calculate the probability that fewer than 320 out of the n
Using continuity correction, this is [tex]P(X < 320 - 0.5) = P(X < 319.5)[/tex], which is the pvalue of Z when X = 319.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{319.5 - 0.45n}{\sqrt{0.45*0.55n}}[/tex]
Just have to replace the value of n, find Z, and then find its pvalue.
5. Point C (3, -4) is reflected on the line y = -x, then reflected again on the X axis.
the reflection composition of point C is ....
a. C "(4, 3)
b. C '(4, -3)
C.
C "(- 4, 3)
d. C "(- 4, -3)
Answer:
[tex]C" = (4,3)[/tex]
Step-by-step explanation:
Given
[tex]C = (3,-4)[/tex]
Transformation 1: y = -x reflection
Transformation 2: x axis reflection
Required
The new coordinates of C
[tex]C = (3,-4)[/tex]
Transformation 1: y = -x reflection
This gives: (-y,-x)
So:
[tex]C = (3,-4)[/tex]
[tex]C' = (4,-3)[/tex]
[tex]C' = (4,-3)[/tex]
Transformation 2: x axis reflection
This gives: (x,-y)
So:
[tex]C' = (4,-3)[/tex]
[tex]C" = (4,3)[/tex]
A shopkeeper marks the price of an article
30% above its cost price and gives a customer discount of
15%. A customer bought that article including 13% VAT at
Rs. 1872.975. Find the marked price of the article and the
gain of shopkeeper
Answer:
The gain percent made by shopkeeper is 10.5%.
Step-by-step explanation:
Given:
Price at which goods are marked = 30%
Discount on the marked price = 15%
To Find:
Gain percentage of the shopkeeper
Solution:
Let the cost price of the product be = 100
Therefore,
MP = 30 + 100 = 130
Since discount is 15%. thus -
Discount = 15/100 x 130
= 19.5
Selling price = MP - Discount
SP = 130 - 19.5
= 110.5
Profit = SP - CP
= 110.5 - 100
= 10.5
Calculating the gain%
Gain% = 10.5/100 x 100
= 10.5
Answer: The gain percent made by shopkeeper is 10.5%.
Great Falls is at approximately 47.5 degrees N, and 111.3 degrees W. Lemhi is approximately 45.5 degrees N, and 113.5 degrees W. (We will assume the rivers flow straight from Great Falls to Lemhi on the surface of Earth). Apply the Law of Cosines for Sides of a spherical triangle to find the angle between Great Falls and Lemhi.
Answer:
The angle between Great Falls and Lemhi is approximately 3.02°
Step-by-step explanation:
The location parameters are;
The Great Falls location = 47.5° N, 111.3° W
The location of Lemhi = 45.5 °N and 113.5 °W
Therefore, we have;
The angle between the Great Falls and the poles, AP = 90° - 47.5° = 42.5°
The angle between Lemhi and the poles, PB = 90° - 45.5° = 44.5°
The angle between the lines of longitude, P = 113.5° - 113° = 0.5°
By the law of cosines for Sides of a spherical triangle, we have;
CosAB = cos AP·cosPB + sinAP·sinPB·cosP
Where;
AB = The angle between Great Falls and Lemhi
∴ CosAB = cos(47.5°) × cos(44.5°) + sin(47.5°) × sin(44.5°) × cos(0.5°) ≈ 0.9986
AB ≈ arccos(0.9986) ≈ 3.02°
The angle between Great Falls and Lemhi ≈ 3.02°
PLEASE HELP!!!! ILL GIVE BRAINLIEST!
Explain why the two figures below are not similar. Use complete sentences and provide evidence to support your explanation.
Answer: because the figure on the left is negative and more wide open while the other one is not only smaller but also positive and it’s more shut
Step-by-step explanation:
So the X-axis of the Figure on the left is going form point -3 to 0 while the other figure on the right is going form 3 to 5. And the Y- axis of the figure on the left is 2 while the right is 1 which proves that the figure on the left is bigger then the other
Your Also supposed to add all the point like first look for the Y and the X of I with J Then look for H and K then look for G and L the look for the slope of all those and then add them,then do the same with the left one and see which ones more and how much more
Answer the question in the picture please and if you don't know please just don't answer it <3
9514 1404 393
Answer:
340 quarters1020 dimes1031 nickels2062 penniesStep-by-step explanation:
x is the number of quarters
__
a) d = 3x . . . . . . the number of dimes is 3 times the number of quarters
b) n = d + 11 = 3x +11 . . . . there are 11 more nickels than dimes
c) p = 2n = 2(3x +11) = 6x +22 . . . . there are twice as many pennies as nickels
d) The total number of coins is ...
x + d + n + p = 4453
x + (3x) +(3x +11) +(6x +22) = 4453
13x +33 = 4453
13x = 4420
x = 4420/13 = 340 . . . . number of quarters collected
3x = 1020 . . . . . . . . . . . .number of dimes collected
1020 +11 = 1031 . . . . . . . number of nickels collected
2·1031 = 2062 . . . . . . . . number of pennies collected
There were 340 quarters, 1020 dimes, 1031 nickels, and 2062 pennies collected.
_____
Check
340 +1020 +1031 +2062 = 4453 . . . as required
giving brainliest ! *easy*
Answer:
19π/15
Step-by-step explanation:
Answer:
θ + 19π / 15 this is my answer
A floor is 7 m long and 5 m wide. A square carpet of side 4 m is laid on the floor. Find
the area of the floor that is not carpeted?
Answer:
the area of the floor that is not carpeted 19 m squared
Step-by-step explanation:
7x5 =35 m squared = area of the floor
4x4 = 16 squared =(area of the carpeted floor)
35-16 = 19
Is 307,404 divisible by 3?
How are zero identified in a rational expression??? Please help
0x0
Step-by-step explanation:
Answer:
look at the y and x intercept
Step-by-step explanation:
Help meeeeeeeee please!!!!
Answer:
C
Step-by-step explanation:
Amella bought roast beef for $6.85 per pound. Find the total cost Amelia bought 4
pounds of roast beef.
She bought $27.40 worth of roast beef.
A population has a standard deviation of 11. What is the approximate standard error of the mean for a sample size of 150?
Answer:
the approximate standard error is 0.90
Step-by-step explanation:
The computation of the approximate standard error is shown below:
As we know that
Standard error is
= Standard deviation ÷ √mean
= 11 ÷ √150
= 11 ÷ 12.247
= 0.90
Hence, the approximate standard error is 0.90
SOMEONE HELP ME PLEASE I BEG YOU
Answer:
x=40 mark brainlist please
Step-by-step explanation:
5/6 + (-4/9) - (-2), is this right??
Answer:
YES SIR OR I MEANT YES MAM
2028.863 rounded to the nearest hundredth
Answer:
2028.863 to the nearest hundredth
The Number In The Hundredth Place Is 6 And The The Number Following Is 3 And Because Its Less Than 5, The 6 Will Remain.
So Its 2028.86
Answer:
2,028.86
Step-by-step explanation:
this is the correct answer to your question
PLZ HELP I GIVE BRAINLIEST!!! (Plz show work)
Answer:
800 × ( 3.87 ÷ 100 ) × 1
= 30.96
A light bulb consumes 17100 watt-hours in 4 days and 18 hours. How many watt-hours does it consume per day?
Answer:
3600
Step-by-step explanation:
17100 in a total of 114 hrs (24*4+18)
Find it hourly
17100/114=150
Then, multiply by 24 to get the amount it consumers in the day.
150*24=3600
Answer:
first multiply 4 with 18
then divide the answer with 17100
So,
4x18=72
17100 /by 72=237.5
It uses 237.5 watts per day
Checking= 237.5x72=17100
So it is true.
Step-by-step explanation:
Guys I need help, if a couch costs 200 dollars and is marked up 300 percent, what is the cost?
Answer:
200 X 300% =$600.00
Step-by-step explanation:
Which of the following functions is graphed below ?
Answer:
A. y = |x + 4| - 2.
Step-by-step explanation:
The graph of y = |x| is V shaped and passes through the origin and the slope is 1 (like the given graph).
y = |x + 4) moves the V shaped graph 4 units to the left so the tip of the V is at x = -4.
Now subtracting 2 from this graph will bring the graph to the point where x = -4 and y = -2.
So the given function is y = |x + 4| - 2.
Express each rate below as a unit rate.
975 calories in 13 brownies
Answer:
Step-by-step explanation:
975/13=75
75 calories per brownie
Plz help me!!
I am timed!
Answer:
4 is the length
5 is the width
3 is the height
60 cubes
60m is the volume
c. Add two cube numbers and
one square
number.
Answer:
Step-by-step explanation:
Add two cube numbers and
one square
number.
PLEASE HELP will give right answer brainiest
Answer:
48 -52 and 64 - 66
Step-by-step explanation:
sence it dosent give exact numbers on the graph ur going to have to estimate then to find when it increases look for an interval were it goes up reading from left to right and for decreasing look for an interval that is going down reading the graph left to right
Use mental math to simplify.
(4.55 + 27) + 5.45
Answer:
31.55+5.45
Step-by-step explanation:
4.55+27 would go to 31.55
31.55+5.45
Answer: 37
Step-by-step explanation:
4.55 + 27 = 31.55
31.55 + 5.45 = 37
Please help me
I give u brainliest answer if correct and all those
Answer:
3) 23.32
4) 11.12
5) 2.06
6) 20.69
..................
Answer:
Step-by-step explanation:
3. 12+3.04+8.28= 23.32
4. 6.97+4.15= 11.12
5. 9.04-6.97= 2.07
6. 4.02+0.19+16.48= 20.69
Sorry if I'm wrong hope it helps!
what is V50+V32 please help.
Answer:
82V
Step-by-step explanation:
regroup terms 50V+V×32
regroup terms 50V+32V
simpfly 82V
what is 2/3 + 1/4 as a fraction
Answer:
[tex] \frac{11}{12} [/tex]
Can I be brainliest pls
