your job is to design a staircase that has a total rise of 11 feet and meets these design guidelines:
1) the slope of the staircase is between 0.55 and 0.85
2) twice the rise plus the run must be between 24 and 25 inches
3) there can be no irregular steps
4) each step must be the same size
how many risers and treads?
what size are they?
EXPLAIN DESIGN AND INCLUDE CALCULATIONS.
show how each design guideline is met.
Answers
Then the total run of the stair case is between
[tex] \frac{11}{0.85} = 12.94 \ feet \ and \ \frac{11}{0.55}=20 \ feet[/tex] . . . (1)
Given that twice the rise plus the run must be between 24 and 25 inches
Let the size of each run be x and the size of each rise, y, then
24 / 12 < x + 2y < 25 / 12
2 < x + 2y < 2.08 . . . (2)
Also, let the number of risers and treads be n, then
12.94 < nx < 20 . . . (3)
and
ny = 11 . . . (4)
From (2), 2 < x + 2y < 2.08, thus, we have
2 - 2y < x < 2.08 - 2y . . . (5)
Multiplying through by n, we have:
2n - 2ny < nx < 2.08n - 2ny . . . (6)
From (4), ny = 11, so we have
2n - 2(11) < nx < 2.08n - 2(11)
2n - 22 < nx < 2.08n - 22 . . . (7)
Comparing (3) and (7), we have
2n - 22 = 12.94 or 2.08n - 22 = 20
2n = 12.94 + 22 = 34.94 or 2.08n = 20 + 22 = 42
n = 17.47 or 20.19
Thus n is approximately 17 or 20.
From (4), ny = 11, so we have
y = 11/17 or 11/20
y = 0.65 or 0.55
From (2), 2 < x + 2y < 2.08, so we have
2 < x + 2(0.65) < 2.08
2 < x + 1.3 < 2.08
0.7 < x < 0.78
or
2 < x + 2(0.55) < 2.08
2 < x + 1.1 < 2.08
0.9 < x < 0.98
Therefore, we can conclude that we will have 20 risers and treads with each riser measuring 6.6 inches and each tread measuring 11 inches.
Related Questions
Thad and his four family members are going to the fair. Admission to the fair costs $8. Books of ride tickets are $15. THad has 200$. How much will he have for food and souvenirs?
Part 1: Define your variables and write an inequality that models the situatio.
Part 2: After paying for all family members to get into the fair, Thad buys books of ride tickets for 3 of them. Use the in equality from Part 1 to solve for the amount of money Thad has left for food and souvenirs. Show your work.
Answers
Answer:
Given,
Total number of members = 5,
Also, admission to the fair costs $8,
So, the total fair cost = $ 40
Part A: Let x represents the number of people who ride, and y represents the amount ( in dollars ) needed for food and souvenirs,
Since, ride cost for each person = $ 15,
So, the total ride cost = 15x dollars,
Thus, the total spending = ( 40 +15x + y ) dollars
According to the question,
The budget is of $ 200,
That is, total spending can not exceed $ 200,
⇒ 40 +15x + y ≤ 200
⇒ 15x + y ≤ 160
Which is the required inequality that represents the given situation,
Part B : If x = 3
15(3) + y ≤ 160
45 + y ≤ 160
y ≤ 115
Hence, $ 115 would left for food and souvenirs.
A player's goal was to score at least 150 points this season. So far, she has scored 123 points. If there is one game left, how many points must she score to reach her goal?
A) Write an inequality that represents this word problem.
Answers
The inequality that represents this word problem will be 150 - 123 = 27.
From the information given, the player's goal was to score at least 150 points this season but the player already has scored 123 points.
Therefore, since there is one game left, the number of points that must be scored to reach her goal will be:
= 150 - 123 = 27
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Which parking lot is less expensive if Mr. Lujan returns after 2 days and 3 hours?
Answers
What is the conversion factor used to convert inches to yards a.12 inches in 1 yard b.24 inches in 1 yard c.3inches in 1 yard d.36 inches in 1 yard
Answers
The conversion-factor used to convert inches to yards is : (d) 36 inches in 1 yard.
This means that for every 36 inches, there is 1 yard. By dividing the number of inches by 36, you can obtain the equivalent length in yards.
Conversion-Factors are ratios that express the relationship between different units of measurement.
In this case, using the conversion factor of 36 inches in 1 yard allows for a direct-conversion from inches to yards. It is derived from the information that there are 12 inches in a foot and 3 feet in a yard, giving a total of 36 inches in 1 yard.
Therefore, the correct option is (d).
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The given question is incomplete, the complete question is
What is the conversion factor used to convert inches to yards
(a) 12 inches in 1 yard,
(b) 24 inches in 1 yard,
(c) 3 inches in 1 yard,
(d) 36 inches in 1 yard.
Destiny combines 6.42 liters of red paint with 6.87 liters of blue paint to make purple paint. she pours the paint equally into 3 containers, and has 2.64 liters of paint left over. how many liters of paint are in each container?
Answers
(13.29 - 2.64) / 3 =
10.65/3 =
3.55 liters per container <=
Quantity of paint in each container will be 3.55 liters
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Quantity of red paint = 6.42 liters
Quantity of blue paint = 6.87 liters
And, she pours the paint equally into 3 containers, and has 2.64 liters of paint left over.
Now,
Total quantity of paint = 6.42 + 6.87
= 13.29 liters
Thus, The quantity in each container = 13.29 - 2.64 / 3
= 10.65 / 3
= 3.55 liters.
Therefore, Quantity of paint in each container will be 3.55 liters
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5+4g+8=1 (g=-3;g =-1; g =2)
Answers
Form the intersection for the following sets.
R = {10, 15, 20}
S = {20, 25}
R ∩ S =
A.{ }
B.{10, 15, 25}
C.{20}
D.{10, 15, 20, 25}
Answers
Arrange the complex numbers in order according to the quadrant in which they appear, starting with the first quadrant.
1. 3 − 4i
2. -1 − 3i
3. 4 + i
4. -2 + 2i
Answers
Answer:
The order of the complex numbers, numbered from the first quadrant are
4 + i
-2 + 2i
-1 - 3i
3 - 4i
Answer:
The previous answer was correct
Step-by-step explanation:
Consider 7 x 10 to the third power. Write a pattern to find the value of the expression
Answers
What is the product written in scientific notation? (5.91×10^−3)⋅(8.7×10^10)
a) 14.61 × 10^−30
b) 5.1417 × 10^8
c) 14.61 × 10^7
d) 5.1417 × 10^7
Answers
(5.91 * 8.7) * (10^-3 * 10^10) =
51.417 * 10^7.....which is the same as 5.1417 * 10^8
The product written in scientific notation will be; 5.1417 × 10^8
How do scientific notations work?Scientific notations have some of the profits as Better readability due to compact representation. Its value in terms of the power of 10 is known, which helps in the easy comparison of quantities differing by a large value.
We have been given that (5.91 × [tex]10^{-3}[/tex])⋅(8.7 × [tex]10^{10}[/tex])
Required to find the product written in scientific notation;
(5.91 × [tex]10^{-3}[/tex])⋅(8.7 × [tex]10^{10}[/tex])
(5.91 x 8.7) ( [tex]10^{-3}[/tex]× [tex]10^{10}[/tex])
51.417 × [tex]10^7[/tex]
which is the same as; 5.1417 × [tex]10^8[/tex]
Hence, the product written in scientific notation will be; 5.1417 × [tex]10^8[/tex]
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WILL GIVE 20 POINTS
Write the expression 44(4–7)(4) using a single exponent.
A) 4^–28
B) 4^–4
C) 4^–3
D) 4^–2
Answers
Answer:
D) 4^-2
Step-by-step explanation:
Given: 4^4*4^-7*4
If the base is the same, we can add the powers.
a^m * a^n = a^(m + n)
4^4*4^-7*4 = 4^(4 - 7 + 1)
= 4^(5 - 7)
= 4^-2
Answer: D) 4^-2
Hope this will helpful.
Thank you.
In which case is it legal to drive through a crosswalk?
A. When pedestrians are crossing but you have a green light
B. When all pedestrians are in lanes other than yours
C. When you can safely avoid pedestrians in your lane
D. None of the above
Answers
A. is wrong because pedestrians have right of way
B. is wrong because you could be turning right but they are in the far away, you are not allowed to turn because pedestrians have right of way
C. no because pedestrians have right of way
D is the answer
What property of multiplication do we use to find equivalent fractions?
Answers
The equivalent fractions for 2/3 are 6/9, 10/15, and 12/18; the multiplicative identity is a feature of multiplication which is used to find equivalent fractions.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
Given that 2/3 by multiplying by 3/3, 5/5, and 6/6.
= (2/3)(3/3)
= 6/9
= (2/3)(5/5)
= 10/15
= (2/3)(6/6)
= 12/18
The multiplicative identity is a feature of multiplication which is used to find the equivalent fractions.
Hence, the equivalent fractions for 2/3 are 6/9, 10/15, and 12/18; the multiplicative identity is a feature of multiplication which is used to find equivalent fractions.
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Point M is the midpoint of AB. What are the coordinates of B if A is (-8, 3) and if M is (-4, 2).
Answers
If a data set has an even number of data, is it true or false that the median is never equal to a value in the data set? explain.
Answers
The median is never equal to a value in the data set when the data set has an even number of data points.
The statement is true - if a data set has an even number of data points, the median will never be equal to a value in the data set. The median is the middle value in an ordered set of data. When there is an even number of points, there are two middle values, so the median is the average of those two values.
For example, if we have the data set (2, 4, 6, 8), the median would be (4 + 6)/2 = 5. As you can see, the median is not equal to any of the values in the data set.
In conclusion, the median is never equal to a value in the data set when the data set has an even number of data points.
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you are baking muffins for your class. there are 17 total students in your class and you have baked 5 muffins. write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. write your equation so that the units on each side of the equation are muffins per student
Answers
Answer:
Additional muffins required, x = 29
The equation so that the units on each side of the equation are muffins per student
[tex]\frac{5+x}{17}=2[/tex]
Step-by-step explanation:
Let the additional number x of muffins you need to bake in order to have 2 muffins for each student.
We have total number of students = 17
Number of muffins already baked = 5
So total number of muffins made = Number of muffins already baked + Additional muffins to be made
Total number of muffins made = 5 + x
We know that each student need to get 2 muffins
Total muffins needed = 17 x 2
Equating both
5 + x = 17 x 2
x = 34 - 5 = 29
Additional muffins required, x = 29
[tex]\frac{5+x}{17}=2[/tex]
This is the equation so that the units on each side of the equation are muffins per student
Work out the equation of the line which has a gradient of 2 and passes through the point (1,4)
Answers
Answer:
The equation would be y = 2x + 2
Step-by-step explanation:
We know that the equation of a line can be represented as:
(y - y1) = m ( x - x1)
where (x1, y1) is a point that belongs to the line and m is the gradient.
For this particular problem we would have (x1,y1) = (1,4) and m = 2.
If we substitute this data in the formula we get:
(y - y1) = m (x - x1)
y - 4 = 2(x - 1)
y - 4 = 2x - 2
y = 2x - 2 + 4
y = 2x + 2
Therefore, the equation would be y = 2x + 2
The equation of the line which has a gradient of 2 and passes through the point (1,4) is:
y = 2x + 2
What is gradientGradient also known as slope is the defined as
Gradient (m) = change in y coordinate / change in x coordinate
The equation of a line passing through a given point is given by the following equation:
y – y₁ = m(x – x₁)
How to determine the equation of the line passing through point (1,4)x coordinate (x₁) = 1y coordinate (y₁) = 4Gradient (m) = 2Equation =?y – y₁ = m(x – x₁)
y – 4 = 2(x – 1)
Clear bracket
y – 4 = 2x – 2
Make y the subject by adding 4 to both side
y – 4 + 4 = 2x – 2 + 4
y = 2x + 2
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write the sentence as a proportion
5 is to 7 as 15 is to X
9 is to 3 as X is to 12
g is to 9 as 16 is to 12
6 is to 18 as y is to 3
Answers
5:7 as 15:21 (x = 21)
9:3 as 36:12 (x = 36)
12:9 as 16:12 (g = 12)
6:18 as 1:3 (y = 1)
Let g(x) be the reflection of f(x) = x 2 + 3 in the x-axis. What is the function rule for g(x)?
A.
g(x) = -x^ 2 - 3
B.
g(x) = -x ^2 + 3
C.
g(x) = x ^2 - 3
D.
g(x) = x ^2 + 3
please show your work
Answers
refelction meand g(x) would equal -(fx)
so the answer would be C g(x) = -x^2 - 3
"More than 60% of the students scored below the mean on the last test." Can this statement be true? Why or why not?
Answers
So if the remaining 40% of students score 100 points, and the 60% score like 50 points, then the mean would still be 70 points because of the 40% of students that scored super high.
So yes, it can be true.
This can be true if the 60% of students scored really low and the 40% that didn't score below scored really high. Example: 20 kids in the class. 12 of the kids (60%) got 10% on their last test. 8 of the kids got 100%. The mean: ((10x12)+(100x8)) / 20 = 48. The mean is 48, but 60% of students got 10.
Answer: Yes
Zach is 23 years old. Zach's age is 3 years older than twice Maya's age. Let m represent Maya's age.
Which equation can be used to solve for Maya's age?
23 = 2m + 3
23 = 3m + 2
23 = m + 3
23 = 2m
Answers
To get to Zach's age, you have to double it and add 3.
So 2m + 3 = 23. That's the first answer.
Answer:
The correct option is A) [tex]23=2m+3[/tex].
Step-by-step explanation:
Consider the provided information.
Zach is 23 years old. Zach's age is 3 years older than twice Maya's age.
Let m represent Maya's age.
Twice of Maya's age can be written as:
[tex]2m[/tex]
3 years older than twice Maya's age can be written as:
[tex]2m+3[/tex]
It is given that Zach is 23 years old and Zach's age is 3 years older than twice Maya's age.
Thus, the above expression equal to 23.
[tex]23=2m+3[/tex]
Hence, the correct option is A) [tex]23=2m+3[/tex].
Explain how knowing 5 divided by 8 = 0.625 helps you write the decimal for 4 5/8
Answers
You only need to add 4 because it's a whole number, making the end result 4.625.
What is the relationship between 5.34×105 and 5.34×10−2 ?
Answers
and
5.34 x 10⁻² = 0.0534
so the relationship between these two numbers are first one is greater than the other number. the numbers or digits before the power of ten is same but when we the whole as with power of ten, that powers change the values of numbers.
Answer:
5.34×105 and 5.34×10−2
Step-by-step explanation:
the first is greater than the scoend and the second is less then
A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height. The total vertical distance the ball has traveled when it hits the ground the fifth time is meters.
Answers
[tex](10 + 5 + 5 + 2.5 + 2.5 + 1.25 + 1.25 + 0.625 + 0.625) = 28.75 [/tex]
A weather forecast predicts that the temperature in antarctica will decrease 8 degrees fahrenheit each hour for the next 6 hours. write and solve an inequality to determine how many hours it will take for the temperature to drop at least 36 degrees fahrenheit
Answers
It will take at least 5 hours for the temperature to drop by 36 degrees Fahrenheit.
To determine how many hours it will take for the temperature in Antarctica to drop at least 36 degrees Fahrenheit, you can set up an inequality. Let's call the number of hours it takes for the temperature to drop x.
Given that the temperature decreases 8 degrees Fahrenheit each hour, you can represent the temperature drop as:
8x
Now, you want this temperature drop to be at least 36 degrees Fahrenheit, so you can write the inequality:
8x ≥ 36
To solve for x, divide both sides of the inequality by 8:
x ≥ 36 / 8
x ≥ 4.5
So, it will take at least 4.5 hours for the temperature in Antarctica to drop by at least 36 degrees Fahrenheit.
Since time is typically measured in whole hours, it will take at least 5 hours for the temperature to drop by 36 degrees Fahrenheit.
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It will take at least 4.5 hours for the temperature in Antarctica to drop at least 36 degrees Fahrenheit.
Explanation:To determine how many hours it will take for the temperature in Antarctica to drop at least 36 degrees Fahrenheit, we can write and solve an inequality:
Let x be the number of hours it takes for the temperature to drop.
The temperature decreases 8 degrees Fahrenheit each hour for the next 6 hours:
8x ≥ 36
Divide both sides of the inequality by 8:
x ≥ 4.5
Therefore, it will take at least 4.5 hours for the temperature to drop at least 36 degrees Fahrenheit.
how is the decimal 2.4 written as a mixed number in its simplest form
Answers
2 2/5
That's the answer
The mixed number in their simplest form can be represented as
[tex]2\dfrac{2}{5}[/tex]
What are real numbers?Real numbers are defined as the value of a continuous quantity that can represent a distance along a line a real number in mathematics. Rational and irrational numbers are both real numbers. Rational numbers such as integers (-7, 0, 4), fractions(5/2,7/2, 4.2), and irrational numbers such as √5, π, etc., are all real numbers.
we have to determine the decimal 2.4 written as a mixed number in its simplest form.
Given that the decimal as:
⇒ 2.4
⇒ 2 + 0.4
Convert decimals into a fraction.
⇒ 2 + 4/10
⇒ 2 + 2/5
Thus, mixed number in their simplest form is
[tex]2\dfrac{2}{5}[/tex]
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B. if the two surge protectors are arranged in parallel, what is the probability that a voltage surge will not damage the television?
Answers
explain how you can use a straightedge and a protractor to show that each angle you formed by a bisector is one-half the original angle
Answers
You can measure the angle by following these steps:
1- Place the straightedge on the base of the angle.
2- Slide the protractor over it until the vertex of the angle is at the zero of the protractor.
3- Measure the angle.
What is the measure of angle ABD in trapezoid ABCD?
A. 24°
B. 40°
C. 64°
D. 92°
Answers
116+24=140
180-140=40
∠ABD=40
B. 40
Answer:
The answer is B.40
Step-by-step explanation:
The product of numbers on the diagonal when comparing two ratios