Brett wants to paint the exterior of his two-story home but does not know what length ladder he should buy. The top of his roof is 29 ft above ground level, and (for safety reasons) the ladder should not be at more than an 80° angle from the ground. How long, rounded up to the nearest foot, is the shortest ladder that Brett should buy?
Answers
so after rounding is 30 ft
Answer:
Brett should buy a ladder of minimum 30 ft length.
Step-by-step explanation:
Brett wants to paint his exterior of a double story home.
Height of the roof of the second story from the ground = 29 feet
Maximum angle between the ground and the ladder should be = 80°
Now from the figure,
sin 80° = [tex]\frac{AB}{AC}[/tex]
0.9848 = [tex]\frac{29}{AC}[/tex]
AC = [tex]\frac{29}{0.9848}[/tex]
AC = 29.45
≈ 30 ft
Therefore, Brett should buy a ladder of minimum 30 ft length.
Related Questions
What would a monthly payment be on a purchase of a $10,000 car at a 5.9% for 4 years?
Answers
A=p(1/r/100)^n
A=10000
r=5.9/12=0.5%
10000=p(1+0.5/100)^(4*12)
10000=p(1.005)^48
p=10000/(1.005)^48
p=7,871
the monthly payment will be:
7871/12
=$655.92
Answer:
$234.39
Step-by-step explanation:
What is the following sum in simplest form? sqrt 8 + 3 sqrt2 + sqrt 32
\
Answers
Answer:-[tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
Explanation:-
Given sum :- [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}[/tex]
To simplify, rewrite the numbers inside the root in the product of primes, we get
[tex]\Rightarrow\sqrt{2\times2\times2}+3 \sqrt{2}+ \sqrt{2\times2\times2\times2\times2}\\\\\Rightarrow\sqrt{2^2\times2}+3 \sqrt{2}+ \sqrt{4\times4\times2}\\\\\Rightarrow\sqrt{2^2}\sqrt{2}+3 \sqrt{2}+ \sqrt{4^2\times2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+\sqrt{4^2}\sqrt{2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+4\sqrt{2}=9\sqrt{2}[/tex]
Thus [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
Benny bought 5 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 43 cards left. How many cards did Benny start with?
Answers
PLEASE HELP!!!
The first two steps in determining the solution set of the system of equations, y = –x2 + 4x + 12 and y = –3x + 24, algebraically are shown in the table. Which represents the solution(s) of this system of equations? (3, 15) (–4, 36) (3, 15) and (4, 12) (–3, 33) and (–4, 36)
Answers
y = –3x + 24
so
–x2 + 4x + 12 = –3x + 24
x^2 -7x + 12 = 0
(x - 4)(x - 3) = 0
x - 4 =0; x =4
x - 3 = 0; x= 3
y = –3x + 24 = -3(3) + 24 = -9+24 = 15 (when x = 3)
y = –3x + 24 = -3(4) + 24 = -12+24 = 12 (when x = 4)
answer
(3, 15) and (4, 12)
Answer:
C
Step-by-step explanation:
or (3, 15) and (4, 12)
The sum of two consecutive integers is 111. find the largest of these integers
Answers
divide 111 in half
111/2 = 55.5
take the whole number above and below 55.5
so you get 55 and 56
55 + 56 = 111
56 is the larger one
identify the graph of the equation. What is the angle of rotation for the equation? 13x^2+6sprt3xy+7y^2-16=0
Answers
13x^2 + 6√3 xy + 7y^2 - 16 = 0
Based on the general equation of conic sections:
Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0,
A = 13
B = 6√3
C = 7
D = 0
E = 0
F = -16
So we can find the graph of the equation by solving for the discriminate B^2 - 4AC
B^2 - 4AC, substitute given:
(6^2 * 3) - 4 (13 * 7) = -256
since the discriminate is less than zero, the graph could be a circle or a parabola. In this case, the values of A and C are not equal, then our graph is a parabola.
Answer:
The answer is ellipse; 30° ⇒ answer (d)
The sum of two numbers is 61.61. if three times three times the smaller number is subtracted from the larger? number, the result is 5.5. find the two numbers.
Answers
y - 3x = 5...y = 3x + 5
x + (3x + 5) = 61
4x + 5 = 61
4x = 61 - 5
4x = 56
x = 56/4
x = 14
y - 3x = 5
y - 3(14) = 5
y - 42 = 5
y = 42 + 5
y = 47
ur 2 numbers are 14 and 47
What is the 7th term of the geometric sequence where a1 = -5 and a5 = -1,280?
Answers
a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number.
Here we are give the initial term so we have to solve to solve for the common ratio...
a(5)=-1280 and a(1)=-5 so
-1280=-5r^(5-1)
-1280=-5r^4
256=r^4
256^(1/4)=r
4=r, so our sequence is:
a(n)=-5(4^(n-1)), so the 7th term is:
a(7)=-5(4^6)
a(7)= -20480
A randomly generated list of numbers from 0 to 4 is being used to simulate an event, with the number 4 representing a success. What is the estimated probability of a success?
A.75%
B.60
C.25%
D.40%
Answers
The solution would be like this for this specific problem:
Given:
{0, 1, 2, 3, 4}
Success = 2, 3, and 4
Solution:
Success = 3 numbers
Sample = 5
= 3 / 5
= .6
= .6 * 100%
= 60%
So, the estimated probability of a success based from the randomly generated list of numbers being used to simulate an event is 60%.
To add, the measure of the likelihood that an event will occur is called probability and it is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty.
If you start with a number divide it by 4 then multiply it by two you end up with 8 squared
Answers
8 squared = 64
so
(x/4)*2 = 64
divide x/4 by 2 to get x/2=64
now multiply both sides by 2 to get x=128
x = 128
Corrugated Specialties produces boxes of all kinds, and they manufacture an average of 67,000 shirt-size boxes per month. In November, they were told to increase production by 35%. How many shirt-size boxes will they produce in November? Hint: This question requires two calculations. A. 91,125 B. 23,625 C. 23,450 D. 90,450
Answers
67,000×0.35=23,450
So they will produce in November
67,000+23,450=90,450....answer
A restaurant offers a choice of 2 soups, 3 entrees, and 5 desserts. how many different meals consisting of a soup, an entree, and a dessert are possible?
Answers
solve for b, then find the value of b when a = 3.
4a=2b-7
a. -9/2
b. 5/2
c. 19/2
d. 17
Answers
4(3) = 2b - 7
12 = 2b - 7
2b = 12 + 7
2b = 19
b = 19/2
answer
c. 19/2
How to convert decimal to binary by hand?
Answers
10 : 2 = 5 | 0
5 : 2 = 2 | 1
2 : 2 = 1 | 0
1 : 2 = 0 | 1
↑
Finally: 10 ( decimal ) = 1010 ( binary )
(15 POINTS) A student is chosen at random from a school. Why are the events "choosing a student of age group 5−10" and "choosing a student of age group 11−15" mutually exclusive?
a) They are independent.
b) They are dependent.
c) A student can belong to only one age group.
d) A student can belong to both the age groups.
Answers
Hence, the answer to this question is letter C.
Solve each proportion. Show your work
Answers
2x/7 = 12/14
x=6
I don't know b i am sorry
cross multiply
(2x)(14) = (7)(12)
28x = 84
x = 84/28
x = 3
3 / (x - 1) = 5/7
cross multiply
5(x-1) = (7)(3)
5x - 5 = 21
5x = 21 + 5
5x = 26
x = 26/5 or 5.2
Find the product of 543.1187 and 100
Answers
the price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what year will the price reach $4? use formula P(t)=1.1*e^0.047t A.)2007 B.)2005 C.)2003 D.)2009
Answers
40/11=e^(0.047t) take the natural log of both sides
ln(40/11)=0.047t divide both sides by 0.047
t=ln(40/11)/0.047
t≈24.5
1980+24.5
2007.5
So during 2007 the price will reach $4.
Answer:
The option A.) 2007 is correct
Step-by-step explanation:
The formula which is to be used is given :
[tex]P(t) = 1.1\cdot e^{0.047t}[/tex]
where P(t) is the function of time t and t is the time in years after January 1 , 1980
Now, we need to find the year when the price will reach $4
So, substituting P(t) = 4 and finding the value of t from the given equation.
[tex]\implies 4=1.1\cdot e^{0.047t}\\\\\implies 3.64=e^{0.047t}\\\\\text{Taking natural log ln on both the sides}\\\\\implies \ln 3.64=\ln e^{0.047t}\\\\\implies 1.29=0.047\cdot t\\\\\implies t = 27.49[/tex]
So, t = 27.49 which is approximately equals to 27.5 years
So, 27.5 years after January 1, 1980 is the year 2007
Hence, The price will reach $4 in the year 2007
Therefore, The option A.) 2007 is correct
Joshua is 25 years old and has a high risk job making $72,000 a year. The insurance company charges him an extra 20% on top of his premium rate because of his job. If Joshua wants a policy that will replace five years of his salary, what is the annual premium for the cheapest policy?
Answers
PLEASE HELP
Probability allows a person to effectively measure the risks in selecting one alternative over others.
True
False
Answers
What can you say about the function that generated the following table of values
Answers
best answer is b = it has exactly 1 x intercept
Answer:
B.
Step-by-step explanation:
We know that for x-intercept the graph crosses x-axis i.e the value of y = 0.
As in the table, the value of y is changing from negative to positive, so it will obtain the value y = 0 for some vale of x.
Therefore, this function will have only one x-intercept.
Hence, option A, C, D are discarded and option B is correct.
-x+3+5(2x-6)+9(3x+11) will you answer with work shown and answer
Answers
[tex]#-x + 3 + 5(2x - 6) + 9(3x + 11)# #-x + 3 + 10x - 30 + 27x + 99# Put the common terms together #-x + 10x + 27x + 3 + 99# #36x + 72#[/tex]
3. what is the simplified form of x+4/7 - x+3/x+5
Answers
------- * ----- - ----------- * --- = --------------------
7 (x+5) (x + 5) 7 7( x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
Simplify the expression, then we have
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
⇒ [(x + 4)(x + 5) - 7(x + 3)] / [7(x + 5)]
⇒ [x² + 9x + 20 - 7x - 21] / [7(x + 5)]
⇒ (x² + 2x - 1) / 7(x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
More about the Algebra link is given below.
https://brainly.com/question/953809
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Given the equation 2x + 4 = 4x − 2, select the reasoning that correctly solves for x.
Add 2, subtract 2x, then divide by 2.
Add 2, subtract 4x, then divide by −2.
Subtract 4, subtract 2x, then divide by −2.
Subtract 4, subtract 4x, then divide by 2.
Answers
Answer:
Number One / Letter A
Step-by-step explanation:
Add 2, subtract 2x, then divide by 2.
Hope This Helps!
Am I doing this right?
Answers
Aiden calculated the area of triangle QRS below by finding half the product of 1.5 and 1.1.
Answers
Aiden should have calculated
area = (1.1 * 5.4) / 2
because triangle area = half the base times the altitude.
Answer: The correct option is
(B) Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Step-by-step explanation: Given that Aiden calculated the area of triangle QRS by finding half the product of 1.5 and 1.1.
We are to select the correct option which states the error made by Aiden.
The AREA of a triangle is given by
[tex]A=\dfrac{1}{2}\times \textup{base}\times \textup{altitude},[/tex]
where the altitude is perpendicular to the base.
In ΔQRS, the length of the base is given by
b = QS = 0.9 + 4.5 = 5.4 units
and
the length of the altitude is given by
h = 1.1 units.
So, the area of the triangle QRS will be
[tex]A=\dfrac{1}{2}\times b\times h=\dfrac{1}{2}\times 5.4\times 1.1[/tex]
Therefore, the area of ΔQRS will be calculated by finding half the product of 1.1 and 5.4.
So, Aiden made the error by finding half the product of 1.5 and 1.1, because 1.5 line is not perpendicular to 1.1 line.
Thus, Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Option (B) is correct.
Simplify the expression 3^5*6^-6/3^3*6^-4
A. 180
B. 5/2
C. 1/4
D. 3/20
Answers
= 3^(5-3) 6^(-6+4)
=3^2 6^-2
= 9/36
= 1/4
answer
C. 1/4
Slope (12,-18),(11,12)
Answers
x2-x1. You will get the fraction -30/1 or -30 which is your slope. Hope that made sense!
The slope of the line passing through the points (12, -18) and (11, 12) is calculated using the formula for slope (y2 - y1) / (x2 - x1). The result is -30.
Explanation:The subject of this question is Mathematics, more specifically the topic of 'Slope of a Line'. The grade level appears to be High School.
To answer the question 'Find the slope for the given coordinates (12,-18) and (11,12)', we use the formula to calculate the slope between two points which is (y2 - y1) / (x2 - x1). Let's take (12, -18) as (x1, y1) and (11, 12) as (x2, y2). Now we just input the values into the formula:
Slope (m) = (12 - (-18)) / (11 - 12).
This simplifies to Slope (m) = 30 / -1 = -30.
So, the slope of the line passing through the points (12, -18) and (11, 12) is -30.
Learn more about Slope of a Line here:https://brainly.com/question/14511992
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The value of the cumulative standardized normal distribution at z is 0.8770. the value of z is
Answers
Final answer:
To find the z-score corresponding to a cumulative area of 0.8770 in a standard normal distribution, one can look up this area in a z-table or use statistical software, yielding a z-score of approximately 1.15.
Explanation:
The question involves finding the value of z in a standard normal distribution given that the cumulative area to the left of z is 0.8770.
The z-score is a measure that describes the position of a raw score in terms of its distance from the mean, measured in standard deviations.
To find the value of z corresponding to an area of 0.8770, one would typically use a z-table or statistical software. The z-table lists areas to the left (cumulative probabilities) for different z-values.
For an area of 0.8770, the z-score is approximately 1.15. This calculation is based on the standard normal distribution, where the mean is 0 and the standard deviation is 1.
Braces are used in interval or roster notation?
Answers
While parenthesis is used in interval notation.