find the area of following figure...?
Answer:
33600 m²
Step-by-step explanation:
The top and bottom horizontal sides are parallel, so this is a trapezoid with bases DC and AB. The height is BC.
area of trapezoid = (a + b)h/2
where a and b are the lengths of the bases, and h is the height.
We need to find the height, BC.
Drop a perpendicular from point A to segment DC. Call the point of intersection E. E is a point on segment DC.
DE + EC = DC
EC = AB = 360 m
DC = 600 m
DE + 360 m = 600 m
DE = 240 m
Use right triangle ADE to find AE. Then BC = AE.
DE² + AE² = AD²
DE² + 240² = 250²
DE² = 62500 - 57600
DE² = 4900
DE = √4900
DE = 70
BC = 70 = h
area = (a + b)h/2
area = (600 m + 360 m)(70 m)/2
area = 33600 m²
Answer:
33,600 m^2.
Step-by-step explanation:
This is a trapezium, so
Area = (h/2)(a + b)
= (h/2) ( 360 + 600)
= 960h / 2
= 480h,
We find the value of h using Pythagoras:
250^2 = h^2 + (600-360)^2
h^2 = 250^2 - 240^2 = 4900
h = 70.
So the Area = 70 * 480
= 33,600 m^2
find the missing length indicated 144 and 60
The missing length in the right triangle as given in the task content is; 156.
What is the missing length indicated?It follows from the complete question that the triangle given is a right triangle and the missing length (longest side) can be evaluated by means of the Pythagoras theorem as follows;
x² = 144² + 60²
x² = 20736 + 3600
x² = 24,336
x = √24336
x = 156.
Remarks: The complete question involves a right triangle and the missing length is the longest side.
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Paul has four paper strips of the same length. He glues two of them together with 4 cm overlap, and the new strip is 36 cm long. He wants to make a 30cm long strip with the other two strips how long should the overlap be?
Answer:
maybe the answer ris 36×4 and then 30×4 and subtract the result?!?!
explian GOLDEN RATION singinficane
[tex]\large\bold\blue{ANSWER:-}[/tex]
Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.
1/2a+2/3b=50 when b=30?
The given equation is (1/2)a + (2/3) b = 50
and b = 30
Substituting the given value of b is above the equation we get
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a+\left(\frac{2}{3}\right)\times30=50 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow \left(\frac{1}{2}\right)a+20=50 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a=50-20=30 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow a = 30 \times 2 = 60 } \end{gathered}$}[/tex]
Therefore, a = 60 and b = 30 is a solution of the given equation.
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https://brainly.com/question/12950748In 2016, Alberta had about 4.2 million people.
Assuming they follow the same population
growth rate, it is predicted they will have 6.65
million people in 20 years. At what rate is the
province's population growing?
the population of province is growing at the rate of 2.91%
What is the formula of the rate of growth of a population?the formula of the rate of growth of a population =
[(future population- initial population/initial population)*100]/time
population in 2016 = 4.2 milllion = 4200000
Population predicted in 20 years = 6.65 million = 6650000
so, initial population = 4200000
future population = 6650000
rate of growth = {(6650000- 4200000/4200000)*100]/20
= 58.33/20
= 2.91%
the population is growing at the rate of 2.91%
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Sampling distribution. a quarterback threw 1 interception in his first game, 2 interceptions in his second game, 5 in terceptions in his third game, and then he retired. consider the values of 1, 2, and 5 to be a population. assume that samples of size 2 are randomly selected (with replacement) from the population
a. list the 9 different possible samples and find the mean of each sample
b. what is the mean of the sample means from part a?
c. is the mean of the sampling distribution from part t equal to the mean of the population of the three listed values? are those means always equal?
(a) The Sample mean of each sample is 1, 2, 5, 1.5, 3, 3.5, 3, 1.5,3,3.5.
(b) The mean of the sample means from part (a) is 8/3.
(c) Yes, The mean of the sample distribution is always equal to the mean of the Population.
According to the questions,
Game number 1 2 3 Total
Number of interceptions 1 2 5 8
a) Element 1 Element 2
1 1
2 2
5 5
1 2
1 5
2 5
2 1
5 1
5 2
Sample mean of each sample is 1, 2, 5, 1.5, 3, 3.5, 3, 1.5,3,3.5.
b) The mean of the sample means from part a.
(1+2+5+1.5+3+3.5+1.5+3+3.5)/9 = 8/3
The mean of the sample means from part (a) is 8/3
c) Mean of the populations = (1+2+5)/3 = 8/3
The mean of the sample distribution from part b. is 8/3
Yes, The mean of the sample distribution is always equal to the mean of the Population
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Select the correct answer from each drop-down menu.
Consider the function represented by this graph.
As the value of x increases, the value of f (x)........ increases or decreases
The x-intercept is the point......
As the value of x increases and the function of f(x) also increases since it is moving in the upward direction. The x-intercept is (-3,0)
What is the function?A function is a set of input values into a program that produces the desired output. In mathematical terms, we can say a function is a set of x values that maps to a set of y values.
Functions can also be represented on the graph called graphical representation.
From the given graphical information, as the value of x increases, the function of f(x) also increases since it is moving in the upward direction.
The x-intercept is the value where the line cuts the horizontal x-axis when y is zero, therefore the x-intercept is (-3,0)
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Outside temperature over a day can be modelled using a sine or cosine function. Suppose you know the high temperature for the day is 72 degrees and the low temperature of 62 degrees occurs at 3 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
The equation which represents the equation for the temperature, D , in terms of t is D(t)=5°cos{(π/3)t}+67°.
Given that the high temperature is 72 degrees and low temperature is 62 degrees at 3 A.M.
We know that temperature is the intensity of the heat present around us.
We know that,
Maximum temperature=72 degrees,
Minimum temperature=62 degrees, which occurs at t=3 hours
Now we can write the equation as:
D(t)=A cos(ct)+B
Where A, c, B are constants.
We have a minimum at t=3 a minimum means cos(ct)=-1
then we have that D(3)=A cos(c*3)+B
=A*(-1)+b
=35°
Here we solve that ,
Cos(c*3)=-1
this means that
c*3=-1
c*3=π
c=π/3
We also know that the maximum temperature is 72°, the maximum temperature is when cos(c*t)=1
D(t)=0=A(t)+B=72
With this we can find that values of A and b
-A+B=62
A+B=72
B=67
A=5
Equation will be D(t)=5 cos{(π/3)t}+67°.
Hence the equation for the temperature is D(t)=5 cos{(π/3)t}+67°..
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the current value of a new car is 18,000. the car will depreciate 15% per year over the next 5 year. which exponential equation models this situation
The exponential equation that models this situation is:
[tex]V(t) = 18000(0.85)^t, 0 \leq t \leq 5[/tex].
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.For this problem, the parameters are:
A(0) = 18000, r = 0.15.
Hence the equation for the value of the car over the next 5 years is:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 18000(1 - 0.15)^t[/tex]
[tex]V(t) = 18000(0.85)^t, 0 \leq t \leq 5[/tex].
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What is the common difference in this
recursive definition?
common is 1 because 3-2 is 1
m is inversely proportional to the square of (p-1).
When p = 4, m = 5.
Find m when p = 6.
Answer:
9/5
Step-by-step explanation:
First we have to find the constant k
m = k/(p-1)^2 (p-1)^ goes on the bottom of the fraction because of the inverse.
5 = k/(4-1)^2
5 = k/3^2
5 = k/9 Multiply both side by 9
45 = k We know can use this constant to solve our problem
m = 45/(6-1)^2
m = 45/5^
m = 45/24
m = 9/5
Graph f(x)=2x+1 and g(x)=−x+7 on the same coordinate plane.
What is the solution to the equation f(x)=g(x) ?
Answer:
x = 2
Step-by-step explanation:
To solve the equation, you need to set both functions equal to each other and simplify to find the value of "x".
f(x) = 2x + 1
g(x) = -x + 7
f(x) = g(x) <----- Given equation
2x + 1 = -x + 7 <----- Insert functions
3x + 1 = 7 <----- Add "x" to both sides
3x = 6 <----- Subtract 1 from both sides
x = 2 <----- Divide both sides by 3
Find the surface area of the composite solid. Round your answer to the nearest hundredth.
A. 424.11 ft²
B. 438.00 ft²
C. 449.00 ft²
D. 549.78 ft²
The surface area of the composite solid is 579.84 square feet
How to determine the surface area of the solid?The composite solid that completes the question is added as an attachment
From the attached figure, we have the following figures:
Rectangular prismCylinderThe surface area of a rectangular prism is
A = 2(lw + lh + wh)
Using the dimensions of the prism, we have:
A = 2(6 * 11 + 6 * 8 + 8 * 11)
This gives
A = 404
The surface area of a cylinder is
A = 2πr^2 + 2πrh
Using the dimensions of the cylinder, we have:
A = 2 * 3.14 * 4^2 + 2 * 3.14 * 4 * 5
Evaluate
A = 226.08
The area of the circle between both shapes is
A = πr^2
This gives
A = 3.14 * 4^2
A = 50.24
The surface area of the composite solid is then calculated as:
Surface area = Area of rectangular prism + Area of cylinder - Area of circle
This gives
Surface area = 404 + 226.08 - 50.24
Evaluate
Surface area = 579.84
Hence, the surface area of the composite solid is 579.84 square feet
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30 points please help i dont understand
Answer:
502.4 ft²
Step-by-step explanation:
To find the individual area of the ring, you first need to find the area of the white circle. Then, you need to find the area of the circle and the ring (which can be found by adding the width of the ring to the radius of the circle). Finally, you can find the area of the ring through subtraction.
Area (White Circle)
radius = 1/2 diameter
radius = (1/2) x 36 ft
radius = 18 ft
Area = πr²
Area = π(18 ft)²
Area = π(324 ft²)
Area = 1017.36 ft²
Area (White Circle + Ring)
radius = 1/2 diameter + width of ring
radius = (1/2 x 36 ft) + 4 ft
radius = 22 ft
Area = πr²
Area = π(22 ft)²
Area = π(484 ft²)
Area = 1519.76 ft²
Area (Ring)
Area (Ring) = Area (White Circle + Ring) - Area (White Circle)
Area (Ring) = 1519.76 ft² - 1017.36 ft²
Area (Ring) = 502.4 ft²
44. The table below lists the tallest waterfalls in the world, in feet.
Name/Location Height (ft.)
Mutarazi - Zimbabwe 24.99 x 102
Gocta Cataracts - Peru 2.532 x 103
Utigord - Norway 2,625 x 100
Angel - Venezuela .3212 x 104
Espelands - Norway 2.307 x 103
Yosemite - California (USA) 2,425
Monge - Norway 25.4 x 102
Tugela - South Africa 3.11 x 103
**Heights are approximations**
[Part 1]
List the waterfalls from tallest to shortest.. Show all of your work and/or explain your reasoning.
[Part 2]
What is the difference between the tallest and shortest heights? Show your work.
The difference between the tallest and shortest heights is 0.787 × 10
StatisticsMutarazi - Zimbabwe 24.99 x 10²Gocta Cataracts - Peru 2.532 x 10³Utigord - Norway 2,625 x 10^0Angel - Venezuela .3212 x 10⁴Espelands - Norway 2.307 x 10⁴Yosemite - California (USA) 2,425Monge - Norway 25.4 x 10²ugela - South Africa 3.11 x 10³From tallest to shortest:
Angel - Venezuela 3.212 x 10⁴Espelands - Norway 2.307 x 10⁴ugela - South Africa 3.11 x 10³Utigord - Norway 2,625 x 10^0Monge - Norway 25.4 x 10²Gocta Cataracts - Peru 2.532 x 10³Mutarazi - Zimbabwe 24.99 x 10²Yosemite - California (USA) 2,425Difference between tallest and shortest heights =
3.212 x 10⁴ - 2,425
= 3.212 x 10⁴ - 2.425 × 10³
= (3.212 - 2.425) × 10^4 - 3
= 0.787 × 10
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In 2016, 5,200 parking permits were issued in a city. The number of parking permits increases by 5% every year. Let y represent the number of parking permits issued x years since 2016. Which type of sequence does the situation represent? A.The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
B.
The situation represents an arithmetic sequence because the successive y-values have a common difference of 1.5.
C.
The situation represents a geometric sequence because the successive y-values have a common ratio of 1.5.
D.
The situation represents an arithmetic sequence because the successive y-values have a common difference of 1.05.
The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
How to determine the situation?The given parameters are:
Initial = 5200
Rate = 5%
Because the population by 5% every year, then the situation is a geometric sequence.
The common ratio is then calculated as:
Ratio = 1 + Rate
This gives
Ratio = 1 + 5%
Evaluate
Ratio = 1.05
Hence, the situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.
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The length of time needed to complete a certain test is normally distributed with mean 44 minutes and standard deviation 8 minutes. Find the probability that it will take less than 34 minutes to complete the test.
The probability that it willtake less than 34 minutes to complete the test is 0.1056
Given mean of 44 minutes and standard deviation of 8 minutes.
We have to find the probability that it will take less than 34 minutes to complete the test.
The probability lies between 0 and 1. The formula to calculate probability is number of items divided by total items but it can also be found through z test calculations.
We are using z test to find the probability.
Z=X-μ/σ
Where μ is sample mean and
σ= standard deviation
Z is z value
First we will find the p value from 34 to 44.
Z=34-44/8
=-10/8
=-1.25
P value for X<34=P(Z<-1.25)
=0.5-0.3944
=0.1056.
Hence the probability that it will take less than 34 minutes is 0.1056.
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the ratio of peters money to henrys money is 4 : 3 there at first. after perter spent 12 dollars they had an equal amount of money each. How much money id peter have at first
Using a system of equations, it is found that Peter had $48 at first.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Peter's money.Variable y: Henry's money.The ratio of peters money to henrys money is 4 : 3, hence:
[tex]\frac{x}{y} = \frac{4}{3}[/tex]
After Peter spent $12, they had the same amount, hence:
y = x - 12.
Then, replacing in the ratio:
[tex]\frac{x}{y} = \frac{4}{3}[/tex]
[tex]\frac{x}{x - 12} = \frac{4}{3}[/tex]
4(x - 12) = 3x
x = 48.
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Sean tried to drink as fast as he could. He drank the slushy at a constant rate. There were originally 275 milliliters of slushy in the cup. After 13 seconds, 210 milliliters of slushy remained. (Please help and explain.)
How fast did Sean drink?
How long did it take Sean to drink all the slushy?
The rate at which Sean drank the slushy is 5 milliliters per second.
The time it would take to drink all the slushy is 55 seconds.
How fast did Sean drink?In order to determine the speed at which the slushy was drank, divide the slushy drank in 13 seconds by 13 seconds.
Speed = slushy drank in 13 seconds / time
(275 - 210) / 13
65 / 13 = 5 milliliters per second
Time it would take to drink all the slushy =total milliliters of the slushy / speed
275 / 5 = 55 seconds.
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LaQuinta is in the French club with 25 other students. Three exchange
students will be attending her school from France. If the French teacher
chooses a student at random to guide each of the visiting students, what is
the probability that LaQuinta will NOT be picked as a guide?
Answer: 23/26
Step-by-step explanation:
Let’s say we have 3 spots, one for each of the three exchange students. It doesn’t matter who goes with who, we’re just going to choose people.
If LaQuinta is NOT one of the people chosen, then there are 25 possible people left to become tour guides. We will need to choose 3 of them, so there are (25 choose 3) = 2,300 ways.
With no restrictions, there are 26 people to choose from and 3 spots to fill. Therefore there are (26 choose 3) = 2,600 ways to fill these 3 spots with no restrictions.
The total probability is 2,300/2,600, which simplifies to 23/26.
Riley bought a 7 1/2 pounds of clay for the students in her pottery class. She then divided the clay into 4 equal pieces for her students to use for making vases and pots. How much did each piece weigh?
Answer:
1.857 pounds
Step-by-step explanation:
If the clay is divided into 4 equal parts, we divide 7.5lbs by 4: 7.5/4 = 1.857 lbs
Nakeisha read 2 and 3/5 pages in 6 minutes at what rate, in pages per hour, did she read?
The rate at which she reads is 26 pages per hour
How to determine the rate?The given parameters are
Pages = 2 and 3/5
Time = 6 minutes
Convert the time from minutes to hour
Time = 6/60 hour
This gives
Time = 0.1 hour
The rate at which she reads is calculated as:
Rate = Page/Time
This gives
Rate = (2 and 3/5)/0.1 hour
Rewrite as:
Rate = 2.6 pages/0.1 hour
Divide
Rate = 26 pages per hour
Hence, the rate at which she reads is 26 pages per hour
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Clarice was late paying her credit card bill of $249. She was charged a 5% late fee. What was the amount of the late fee?
Answer:
You subtract 249 minus 5
Which statement can you use to conclude that quadrilateral xyzw is a parallelogram
Answer: Option (4)
Step-by-step explanation:
A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.
From Andys house to Billys hometown you can travel by 3 roads. And to get from Billys hometown to Willies's house you can travel by 5 roads. How many possible wats are there to travel from andys house to willies house?
3 roada andy to billy
5 road billy to willies
3×5 =15 it's the answer 15
Drag the tiles to the correct boxes to complete the pairs. Match the systems of equations with their solutions.
The systems of linear equations have been matched with their respective solutions as shown in the image attached below.
What is a system of linear equations?A system of linear equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).
In this exercise, you're required to match the systems of linear equations with their respective solutions as shown in the image attached below.
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Determine the present value of quarterly payments of $450 for 6 years at 7.5% annual interest, compounded quarterly. PV= R[(1+i)^-n]/i
Using it's formula, the present value of the amount is: $288.
What is the present value formula?The present value formula is:
[tex]PV = \frac{R}{(1 + r)^n}[/tex]
In which the parameters are:
R is the future value.r is the interest rate.n is the number of periods.Considering quarterly compounding, the parameters for this problem are as follows:
R = 450, r = 0.075/4 = 0.01875, n = 6 x 4 = 24.
Hence the present value is:
[tex]PV = \frac{R}{(1 + r)^n}[/tex]
[tex]PV = \frac{450}{(1.01875)^{24}}[/tex]
PV = $288
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Hi Guys!
I need help ASAP
Answer:
8.
Step-by-step explanation:
P/Q = 3.125 = 3 1/8
- looks like the denominator Q could be 8.
It could not be any of the other choices.
25/8 = 3.125.
What is the solution to this equation? (1/4)^x+1 =31
A. -7/2
B. 2
C. 3/2
D. -2