"In order to meet ADA requirements, a wheelchair ramp must have an angle of elevation of no more than" the angle of elevation is mathematically given as
∅=3.434
What angle of elevation will this ramp have?Generally, the equation for the angle is mathematically given as
[tex]\theta=\frac{opp}{adj}\\\\Therefore\\\\tan\theta=\frac{1.5}{25}\\\\tan\theta=\frac{1.5}{25}\\\\\theta=tan^{-1}\frac{1.5}{25}\\\\[/tex]
∅=3.434
In conclusion, the angle of elevation
∅=3.434
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Rewrite \sqrt((1+cos45)/(2)) using a half-angle identity
[tex]\stackrel{\textit{Half-Angle Identities}}{cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}}} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos\left( \cfrac{45^o}{2} \right)\implies \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos(22.5^o)[/tex]
What percent of the first 20 natural numbers are one-diget numbers
Answer:
9/20 or forty five percent (45%)
tion of the process. You owe $1,568.00 on a credit card with a limit of $2,200.00 at an interest rate of 11.3% APR. You pay $300.00/month until it is paid off. How many months does it take you to pay it off and how much is the total interest you paid? Rocura
Answer:
Select four types of data demographers study to make predictions.
birth rate
death rate
employment
income
marriage
migration
kgf chapter 2
VOLINCE VOLINCE VOLINCE
pushpa RajJaime had ten posters, but only five could fit on his closet door. how many
different ways can he arrange the five posters out of the ten on his closet
door?
i accidentally chose a.
There are 30240 different ways can he arrange the five posters out of the ten on his closet door
How to determine the number of arrangements?The given parameters are:
Total, n = 10Posters to arrange, r = 5The number of ways is calculated as:
Ways =[tex]^nP_r[/tex]
This gives
Ways =[tex]^{10}P_5[/tex]
Apply the permutation formula
Ways = 30240
Hence, there are 30240 different ways can he arrange the five posters out of the ten on his closet door
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Question 3 of 21
The graphs below have the same shape. The equation of the blue graph is
f(x)=Ix. Which of these is the equation of the red graph, g(x)?
y f(x) = |x|
g(x) = ?
A. g(x) = x +5
B. g(x) = x+ 51
C. g(x) = 1x1-5
OD. g(x)=Ix-51
The equation of the red graph, g(x) is g(x) = |x| - 5
How to determine the equation of the red graph, g(x)?The graph that completes the question is added as an attachment
The function f(x) is given s:
f(x) = |x|
From the attached graph, we can see that the function f(x) is shifted 5 units down to get to g(x).
This means that:
g(x) = f(x) - 5
Substitute f(x) = |x|
g(x) = |x| - 5
Hence, the equation of the red graph, g(x) is g(x) = |x| - 5
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Look at the picture pls don't answer in pictures
Which of the following exponential regression equations best fits the data shown below?
X -4 -3 -2 -1 0 1 2 3 4
y 1.07 1.98 2.93 3 9 10 16 25 36
A. y 3.02 3.67*
B. y 6.61 1.55*
C. y 2.27 2.09*
D. y = 8.04.0.98*
The exponential regression equation that fits the data is D. y = 8.04.0.98ˣ.
How to depict the equation?The quickest way is probably to do direct substitution. First, let's try f(0). The values of y predicted by the four equations are, respectively, 3.14, 5.32, 10.84, and 8.46.
From here, it looks like C and D are the closest to the observed data. Let's try f(4) on C and D.
10.84(1.77)⁴ = 10.84 × 9.815 = 106.4
8.46(3.51)⁴ = 8.46 × 151.4 = 1284
Therefore, the exponential regression equation that fits the data is y = 8.04.0.98ˣ.
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You have a spinner with red and blue regions. When you spin, it comes up blue 60 percent of the time. You do an experiment where you spin the spinner 180 times, and it comes up blue 114 times. (a) What proportion of spins came up blue in your sample
Explanation:
Divide the number of times blue came up (114) over the number of spins total (180). Ignore the 60% given to you. That's a theoretical value that doesn't play any part in determining an experimental probability.
114/180 = 0.633 approximately
The '3's go on forever. Round that however your teacher instructs.
In a survey of 100 people, 60 like farming, 65 like civil service. Draw a venn-diagram and find the number of people who like farming as well as civil service.
Answer:
Ur question is wrong..
Step-by-step explanation:
In a survey of 100 people, 60 like farming and 65 like civil service?
60+65=125..?
how to find the volume of a room
multiply the height x the length x the width to find the volume of a room (or another 3d object)
This box plot shows information about the marks scored in a test.
Nobody gained exactly 30, 48 or 70 marks.
120 students gained less than 70 marks.
How many students gained more than 48 marks?
Which algebraic expression is equivalent to the expression below? 2(x - 5) + 13(x + 7) please help!!
Answer:
C
Step-by-step explanation:
What is the volume of a cylinder of radius 3.5m and height 12m ?
Answer:
462
Step-by-step explanation:
Base=π × r²
=> π × 3.5²
=>38.48
Volume:
Base times height
=>38.48 x 12
=>461.81
Answer:
426m²Step-by-step explanation:
Given ;
radius = 3.5m , hieght = 12mVolume of cylinder = π2²h
22/7 × ( 3.5 )² × 1222/7 × ( 7/2 )² × 12 22/7 × 7/2 × 7/2 × 12462m²Volume of the cylinder is 426m².
A line passes through the points (-3,-4) and (6,2)
What is the x intercept of this line?
Answer: x - int : (3,0)
Step-by-step explanation:
point-slope form: y - y1 = m(x - x1)
m = y2-y1/x2-x1
= -4-2/-3-6
=-6/-9
= 2/3
y1 = 2
x1 =6
y - 2 = 2/3(x-6)
x -int: when y = 0, what is x?
0-2 = 2/3(x-6)
-2 = 2/3x - 4
2 = 2/3x
x=3
~Hope this helps!~
Consider these dimensions for a cylindrical aquarium.
A cylinder with height 14 feet and radius 25 feet.
The measures have been substituted in the formula for the volume of a cylinder.
V = π252(14)
Approximately how much water will fill the tank?
Use the calculator to approximate the amount to the nearest hundredth.
cubic feet
The amount of water that will fill the tank is 11100 cu.ft to the nearest hundredth.
What is a Cylindrical figure ?A cylinder is a three dimensional figure with two identical circular faces at each end , and a curved surface.
It does not have an edges or vertices.
It is given in the question that
A cylinder with height 14 feet and radius 25 feet.
The volume of a cylinder.
V = π252(14)
The water than can be filled is equal to the volume of the cylinder
V = 11088 cu.ft
There the amount of water that will fill the tank is 11100 cu.ft to the nearest hundredth.
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Answer: 27,488.94 cubic feet
Step-by-step explanation:
A population of aardvarks is growing at a rate of 2% per year. This year there are 714 aardvarks. How many aardvarks were there last year
A population of aardvarks is growing at a rate of 2% per year, there are 714 aardvarks this year and 700 aardvarks were there last year.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the amount of aardvarks after x years.
It can be represented by the equation:
y = a(1.02)ˣ
If this year there are 714 aardvarks, the amount in the last year is:
714 = a(1.02¹)
a = 700
A population of aardvarks is growing at a rate of 2% per year, there are 714 aardvarks this year and 700 aardvarks were there last year.
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Bart had 36 marbles. he gives all of his marbles to four friends. he gives each friend the same number of marbles. how many marbles does each friend have?
Answer:
9
Step-by-step explanation:
He had 36 Marbles and he gives all to his four friends. And all friends get the same number of marbles so we will have to do division which will be :
36{marbles} divide by 4{friends}=9 so each friend got 9 marbles.
Each friend will have 9 marbles
What is division?
Division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing.
The division is an operation inverse of multiplication. If 3 groups of 4 make 12 in multiplication; 12 divided into 3 equal groups give 4 in each group in division.
Given that:
[tex]4x=36[/tex]
[tex]36[/tex] ÷ [tex]4[/tex] [tex]=9[/tex]
Therefore, each friend will have 9 marbles
KEYWORDS:
equaldivideshareremainderleft overLearn more about division here:
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If a line has a slope of 4 and contains the point (-2, 5), what is its equation in
point-slope form?
O A +5=4(x-2)
OB. J-5= 4(x-2)
C. + 2 = 4(x-5)
O D.y-5=4(x+2)
Answer:
y - 5 = 4(x + 2)
Step-by-step explanation:
Given:
Slope = 4Point = (-2,5)The point-slope form is in the form of [tex]\displaystyle \large{y-y_1=m(x-x_1)}[/tex]. Determine the followings:
m = slope = 4(x1,y1) = point = (-2,5)Therefore, input these in the formula.
[tex]\displaystyle \large{y-5=4[x-(-2)]}\\\\\displaystyle \large{y-5=4(x+2)}[/tex]
Therefore, the answer to this question is y - 5 = 4(x + 2)
Please let me know if you have any questions regarding my answer or explanation!
Michael plans to watch 3 movies each month. Write an equation to represent the total number of movies n that he will watch in m months.
n = 3m. Think of it this way: every month, this guy is watching 3 movies. So in 1 month, he's watched 3. In 2 months, he's watched 6. So the total number of movies that he's watched in months is 3 * however many months, which the problem is saying noting as 'm'
Write/Indicate the corresponding measures of 300- 600-900 right triangle.
2 ^ x = 3 ^ (x + 1) solve for x
Answer:
-2.71
Step-by-step explanation:
This exponential equation can be solved by rewriting it so there is only one base, then using logarithms.
__
solve for x2^x = 3^(x+1) . . . . . given
2^x = 3·3^x . . . . . . eliminate the constant in the exponent
(2/3)^x = 3 . . . . . . . divide by 3^x
x·log(2/3) = log(3) . . . . take logarithms
x = log(3)/log(2/3) ≈ -2.7095113
The value of x is about -2.71.
__
Alternate solution
Taking logarithms transforms this exponential equation to a linear equation.
x·log(2) = (x +1)·log(3) . . . . take logs
x(log(2) -log(3)) = log(3) . . . . . . subtract x·log(3)
x = log(3)/(log(2) -log(3)) = log(3)/log(2/3) . . . . . same result as above
_____
Additional comment
In the attached, we have used a graphing calculator to find the x-intercept of the function f(x) = 0, where f(x) = 2^x -3^(x+1). This is the solution to the given equation.
The applicable rules of logarithms are ...
log(a^b) = b·log(a)
log(a/b) = log(a) -log(b)
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each radical expression to the corresponding expression in rational exponent form.
The radical expressions and their corresponding expression in rational exponent form are
[tex]972^\frac 15 = 3\sqrt[5]{4}[/tex], [tex]448^\frac 13 = 4\sqrt[3]{7}[/tex], [tex]3528^\frac 12 = 42 \sqrt 2[/tex] and [tex]4050^\frac 14 = 3\sqrt[4]{50}[/tex]
How to match the tiles?We start by evaluating each expression as follows:
[tex]972^\frac 15[/tex]
Expand 972
[tex]972^\frac 15 = (243 * 3)^\frac 15[/tex]
Take the 5th root of 243
[tex]972^\frac 15 = 3* (4)^\frac 15[/tex]
Rewrite as:
[tex]972^\frac 15 = 3\sqrt[5]{4}[/tex]
Next, we have:
[tex]448^\frac 13[/tex]
Expand 448
[tex]448^\frac 13 = (64 * 7)^\frac 13[/tex]
Take the 3rd root of 64
[tex]448^\frac 13 = 4 * (7)^\frac 13[/tex]
Rewrite as:
[tex]448^\frac 13 = 4\sqrt[3]{7}[/tex]
Next, we have:
[tex]3528^\frac 12[/tex]
Expand 3528
[tex]3528^\frac 12 = (1764 * 2)^\frac 12[/tex]
Take the square root of 1764
[tex]3528^\frac 12 = 42 * (2)^\frac 12[/tex]
Rewrite as:
[tex]3528^\frac 12 = 42 \sqrt 2[/tex]
Lastly, we have:
[tex]4050^\frac 14[/tex]
Expand 4050
[tex]4050^\frac 14 = (81 * 50)^\frac 14[/tex]
Take the 4th root of 81
[tex]4050^\frac 14 = 3 (50)^\frac 14[/tex]
Rewrite as:
[tex]4050^\frac 14 = 3\sqrt[4]{50}[/tex]
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5/9 divided by 20/27 in its simplist form
Answer: 3/4
Step-by-step explanation: Find the reciprocal of the divisor
Reciprocal of 20/27: 27/20
Now, multiply it with the dividend So, 5/9 ÷ 20/27 = 5/9 × 27/20= 5 × 27/9 × 20 = 135/180
After reducing the fraction, the answer is
3/4
A bag contains 6 white marbles and 4 black
marbles. A marble is drawn from the bag
and then a second marble is drawn without
replacing the first one.
What is the probability of drawing a white
marble on the first draw, followed by a black
marble on the second?
The probability of drawing a white marble on the first draw, followed by a black marble on the second is 4/15
How to determine the probability?The distribution of the marbles is given as:
White = 6
Black = 4
When the white marble is drawn, the probability is:
P(White) = 6/10
Now, there are 9 marbles left.
When the black marble is drawn, the probability is:
P(Black) = 4/9
The required probability is:
P = 6/10 * 4/9
Evaluate
P = 4/15
hence, the probability is 4/15
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Which of the following best describes ZAOR?
R
142⁰
A
A major arc is an arc that is greater than 180 degrees.
A minor arc is an arc less than 180 degrees.
An acute angle is an angle less than 90 degrees.
What is the central angle?
A central angle is an angle created in the center of a circle with 2 sides being the radius.
Thus, we can see in the figure that we are talking about the angle so we can eliminate the major arc and minor arc.
Now, we clearly see that the angle is greater than 90 degrees so it cannot be an acute angle.
The correct answer is the central angle as it goes with the definition.
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Piece wise functions
Answer:
f(-5) = -6
f(-2.6) = 2.4
f(2.1) = 9.41
Step-by-step explanation:
In the question, we are told to find f(-5), f(-2.6), and f(2.1). The numbers in the parentheses represent x.
First, let's look at f(-5). Which equation should we use because x is -5? We should use the first equation because -5 is less than -3. Plug into the equation and solve:
f(-5) = -6 (We didn't have to do much because anything less than -3 equals -6)
Now, let's look at f(-2.6). We should use the equation in the middle because -2.6 is between -3 and 0. Plug -2.6 in the equation and solve:
f(-2.6) = -2.6 + 5
f(-2.6) = 2.4
Lastly, let's look at f(2.1). We should use the third equation because x is greater than 0. Plug 2.1 in the equation and solve:
f(2.1) = [tex](2.1)^{2} +5[/tex]
f(2.1) = 4.41 + 5
f(2.1) = 9.41
Therefore, the final answers are:
f(-5) = -6
f(-2.6) = 2.4
f(2.1) = 9.41
Hope this helps!! If you have questions about my work, please let me know in the comments!
A, B & C lie on a straight line.
D, C & E lie on a different straight line.
Angle y= 107° and angle z = 56°.
Work out x
Answer:
x = 129°
Step-by-step explanation:
∠ ABD and ∠ DBC are a linear pair and sum to 180° , then
y + ∠ DBC = 180°
107° + ∠ DBC = 180° ( subtract 107° from both sides )
∠ DBC = 73°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles , then
x = ∠ DBC + z = 73° + 56° = 129°
esi ran around a rectangular swimming pool 31 times if the distance around the pool is 800m. find the total distance covered by esi km and m
Answer:
24,800m or 24.8km or 24km 800m
Step-by-step explanation:
Perimeter of Rectangle (Given) = 800m or (800/1000)km = 0.8km
Total Distance covered by esi = Perimeter of Rectangle x Number of round ran
= 800m or 0.8km x 31
= 24,800m or 24.8km or 24km 800m
Not sure how you want the answer in so I came up with all possible answers.
Answer:
24.8km
24800m
Step-by-step explanation:
800 x 31 = 24800
24800m
to convert 24800m into km, we divide 24800 by 1000
24800/1000 = 24.8
24.8 km
hope this helps:)
What is the approximate distance between points A and B?
A
-4-3-2
06.32
06.95
07.62
08.56
B
432
052 37
-1
-4
12345
Answer: 7.62
Step-by-step explanation:
[tex]AB=\sqrt{(-2-1)^{2}+(-3-4)^{2}}=\sqrt{9+49}=\sqrt{58} \approx 7.62[/tex]
A book store is hosting a special night in which families can enjoy a story and craft time. Tickets to the event must be purchased ahead of time and are $1.50 for children and $2.50 for adults. So far, 45 children's tickets have been sold, which is 60% of the total tickets sold. How many tickets have been sold so far? Show your calculations or explain how you got your answer.
Need help pls
A book store is hosting a special night in which families can enjoy a story and craft time. The ticket have been sold so far would be 75.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have given that 45 children's tickets have been sold, being 60% of the total tickets having been sold.
So, we have to solve for x:
60% × x = 45
60/100 × x = 45
Multiplying both sides by 100 and dividing both sides by 60,
x = 45 × 100/60
x = 75
Thus, the ticket have been sold so far would be 75.
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