.A 15 m ladder rests against a wall at an angle of 60° with the ground. How far is the
foot of the ladde from the wall?
Answers
9514 1404 393
Answer:
7.5 m
Step-by-step explanation:
The cosine relation applies.
Cos = Adjacent/Hypotenuse
cos(60°) = (distance to wall)/(15 m)
distance to wall = (15 m)cos(60°) = (15 m)(1/2) = 7.5 m
The foot of the ladder is 7.5 m from the wall.
Related Questions
Solve the following quadratic equations using factoring.
C. X^2-10=9x
Answers
we can easily solve this one by splitting theiddle term
x2 - 9x -10
x2 -10x + x - 10
x(x - 10) 1( x - 10)
(x + 1) (x-10)
x = -1 or 10
is y = -x a proportional relationship
Answers
Answer:
For any proportional relationship, k=yx (such as a line that passes through the origin). Find the equation of the line by solving for y in the constant of proportionality equation. This equation y=kx is another representation of a proportional relationship.
Step-by-step explanation:
Answer:
Yes kdsjsbahajajsjsbsbsbsnsn
a rectangle is constructed with its base on the diameter of a semicircle with radius 29 and with its two other vertices on the semicircle. what are the dimensions of the rectangle with maximum area?
Answers
The dimensions of the rectangle with maximum area are 58 for the length and 29 for the width, resulting in a maximum area of 1,682 square units.
Let's consider the construction of the rectangle within the semicircle. The diameter of the semicircle is twice the radius, which is 58. Thus, the length of the rectangle should be equal to this diameter. To find the width of the rectangle, we need to analyze the relationship between the rectangle and the semicircle. The two other vertices of the rectangle lie on the semicircle. As a rectangle has opposite sides equal in length, the width of the rectangle will be equal to the radius of the semicircle, which is 29.
Therefore, the dimensions of the rectangle with maximum area are 58 for the length and 29 for the width. To maximize the area of the rectangle, we use the formula for the area of a rectangle, which is given by length multiplied by width. Substituting the dimensions we found, the maximum area of the rectangle is 58 * 29 = 1,682 square units.
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Alberto started out bench pressing 60 pounds. He then added 5 pounds every week. Determine whether the situation is linear or nonlinear, and proportional or nonproportional
Answers
Answer
linear
nonproportional
Step-by-step explanation:
Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.
At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.
Answer:
linear
nonproportional
order to create the box plot:
Answers
Answer:
b
Step-by-step explanation:
Use the method of undetermined coefficients to find a particular solution to the given higher-order equation. 2y'"' + 6y + y' - 5y = e-t A solution is yp(t) =
Answers
Using the method of undetermined coefficients particular solution to the given higher-order equation 2y''' + 6y'' + y' - 5y = \(e^{-t}\) is \(y_p\)(t) = (-1/2)\(e^{(-t)}\).
To find a particular solution to the higher-order equation 2y''' + 6y'' + y' - 5y = \(e^{(-t)}\) using the method of undetermined coefficients, we assume a particular solution of the form \(y_p\)(t) = A\(e^{(-t)}\), where A is a constant to be determined.
Taking the derivatives of \(y_p\)(t), we have:
\(y_p\)'(t) = -A\(e^{(-t)}\)
\(y_p\)''(t) = A\(e^{(-t)}\)
\(y_p\)'''(t) = -A\(e^{(-t)}\)
Substituting these into the original equation, we get:
2(-A\(e^{(-t)}\)) + 6(A\(e^{(-t)}\)) + (-A\(e^{(-t)}\)) - 5(A\(e^{(-t)}\)) = \(e^{(-t)}\)
Simplifying this equation, we have:
(-2A + 6A - A - 5A)\(e^{(-t)}\) = \(e^{(-t)}\)
Combining like terms, we get:
(-2A + 6A - A - 5A)\(e^{(-t)}\) = \(e^{(-t)}\)
(-2A)\(e^{(-t)}\) = \(e^{(-t)}\)
Dividing both sides by -2\(e^{(-t)}\), we find:
A = -1/2
Therefore, a particular solution to the given equation is:
\(y_p\)(t) = (-1/2)\(e^{(-t)}\)
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The question is -
Use the method of undetermined coefficients to find a particular solution to the given higher-order equation.
2y''' + 6y'' + y' - 5y = e^{-t}
A solution is y_p(t) = _____
a car factory made 18 cars with a sunroof and 20 cars without a sunroof. what is the ratio of the numbers of cars without a sun roof to the number of cars with a sunroof
Answers
Answer:
20:8 please give me brainliest
Answer:
10:9
Step-by-step explanation:
So you would take the 20 cars without sunroofs and put those next to the 20 cars with sunroofs
20:18
But this can be simplified so divide each by 2 to get
10:9
Show that the equation x ^ 3 + 6x - 10 = 0 has a solution between x = 1 and x = 2
Answers
So all we have to do is plug in 1 and 2 for x and prove one is negative and the other is positive.
If we plug in 1, we get -3. If we plug in 2, we get positive 10. This means there is a solution!
If my score goes up 20,000 a day how long will it take me to reach 2,000,000
Answers
Answer:
It would take 100 days
Step-by-step explanation:
2,000,000 divided by 20,000 equals 100
So it would take 100 days
HELP ME PLEASE I NEED A GOOD GRADE
Answers
Answer:
rectangles
Step-by-step explanation:
They are rectangles because all paralellograms have 4 sides and right angles. All objects or shapes with 4 sides and corners, are rectangle. Even squares are catorized as rectangles.
Plzz help will mark brainiest Don't do it for the points plzz i really need help
Answers
Answer:
A
Step-by-step explanation:
(-3,13) and (4,-15) have a slope of 11.
The mean number of days that the midge Chaoborus spends in its larval stage is 14. 1 days, with a standard deviation of 2. 2 days. This distribution is skewed toward higher values. What is the z-score for an individual midge that spends 12. 7 days in its larval stage?
Answers
The z-score for an individual midge that spends 12. 7 days in its larval stage is -0.636
Given,
The mean number of days that the midge Chaoborus spends in its larval stage = 14.1 days
Standard deviation = 2.2 days
We have to find the z-score for an individual midge that spends 12. 7 days in its larval stage;
Now,
z score = (x - μ) / σ
Here,
x = 12.7
Mean, μ = 14.1
Standard deviation, σ = 2.2
Then,
z score = (x - μ) / σ = (12.7 - 14.1) / 2.2 = -0.636
That is,
The z-score for an individual midge that spends 12. 7 days in its larval stage is -0.636
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The average grade on a Probability Statistics Final Exam is 77%. a) Use Markov's inequality to estimate the probability that some will score an 83% or lower on the Final Exam. b) The average grade on a Probability Statistics Final Exam is 77%, and the variance of the Final Exam is known to be 9%. Its distribution is unknown. Use Chebyshev's inequality to obtain an interval that includes 97.5% of stack sizes of this assembler. c) Compare the results in (b) with what you would get if you knew that the distribution of the Final Exam grades was a normal distribution. Problem 5) The average grade on a Probability Statistics Final Exam is 77% with a known variance of 9%. APUS wants to design a criterion that requires as least 90% of all Probability Final Exams not differ from the mean by more than 4.5% a) Use Chebyshev's inequality to establish whether the design criterion is satisfied. b) Would the design criterion be satisfied if it were known that the retrieval time is normally distributed with a mean of 77% and a variance of 9% ?
Answers
At least 90% of the retrieval time should be within 3.465 of the mean. This criterion would be satisfied if the retrieval time is normally distributed with a mean of 77% and a variance of 9%.
(a)We need to estimate the probability that someone will score an 83% or lower on the Final Exam using Markov's inequality. Markov's inequality states that for a non-negative variable X and any a>0, P(X≥a)≤E(X)/a.Assuming that E(X) is the expected value of X. We are given that the average grade is 77%.
Therefore E(X) = 77%.P(X≤83) = P(X-77≤83-77) = P(X-77≤6).Using Markov's inequality,P(X-77≤6) = P(X≤83) = P(X-77-6≥0) ≤ E(X-77)/6 = (σ^2/6), where σ^2 is the variance.So, P(X≤83) ≤ σ^2/6 = 9/6 = 3/2 = 1.5.So, the probability that someone will score an 83% or lower on the Final Exam is less than or equal to 1.5.
(b)Using Chebyshev's inequality, we can find the interval that includes 97.5% of stack sizes of this assembler. Chebyshev's inequality states that for any distribution, the probability that a random variable X is within k standard deviations of the mean μ is at least 1 - 1/k^2. Let k be the number of standard deviations such that 97.5% of the stack sizes lie within k standard deviations from the mean.
The interval which includes 97.5% of stack sizes is given by mean ± kσ.Here, E(X) = 77 and Var(X) = 9, so, σ = sqrt(Var(X)) = sqrt(9) = 3.Using Chebyshev's inequality, 1 - 1/k^2 ≥ 0.9750. Then, 1/k^2 ≤ 0.025, k^2 ≥ 40. Therefore, k = sqrt(40) = 2sqrt(10).The interval which includes 97.5% of stack sizes is [77 - 2sqrt(10) * 3, 77 + 2sqrt(10) * 3] ≈ [69.75, 84.25].
(c)If we assume that the distribution of Final Exam grades is a normal distribution, then we can use the Empirical Rule which states that approximately 68% of the data falls within 1 standard deviation of the mean, 95% of the data falls within 2 standard deviations of the mean, and 99.7% of the data falls within 3 standard deviations of the mean.
Therefore, if the Final Exam grades are normally distributed with a mean of 77% and a variance of 9%, then 97.5% of the stack sizes would fall within 2 standard deviations of the mean.
The interval which includes 97.5% of stack sizes would be given by [77 - 2 * 3, 77 + 2 * 3] = [71, 83].(a)Using Chebyshev's inequality, we can establish whether the design criterion is satisfied or not. Let μ be the mean of the Probability Final Exams, and σ be the standard deviation of the Probability Final Exams. Let X be a random variable that denotes the probability of the Final Exam that is within 4.5% of the mean. Then, P(|X - μ|/σ ≤ 0.045) ≥ 0.9.Using Chebyshev's inequality, we have,P(|X - μ|/σ ≤ 0.045) ≥ 1 - 1/k^2, where k is the number of standard deviations of the mean that includes at least 90% of the stack sizes.
Then, 1 - 1/k^2 ≥ 0.9, 1/k^2 ≤ 0.1. Thus, k ≥ 3. Therefore, at least 90% of the Probability Final Exams should be within 3 standard deviations of the mean by Chebyshev's inequality.So, P(|X - μ|/σ ≤ 0.045) ≥ 0.9.(b)If we know that the retrieval time is normally distributed with a mean of 77% and a variance of 9%, then we can use the Empirical Rule to find the percentage of retrieval time that is within 4.5% of the mean.
According to the Empirical Rule, 68% of the data falls within 1 standard deviation of the mean, 95% of the data falls within 2 standard deviations of the mean, and 99.7% of the data falls within 3 standard deviations of the mean. So, 4.5% of the mean is 4.5% of 77 = 3.465. Therefore, at least 90% of the retrieval time should be within 3.465 of the mean. This criterion would be satisfied if the retrieval time is normally distributed with a mean of 77% and a variance of 9%.
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-5x-35=-2x+31 i needa solve work
Answers
move the variable to the left-hand side and change its side (-5x-35+2x=31)
collect the like terms (-3x=31+35)
divide both sides of the equation by -3 (x=-22)
Answer:
x=-22
Step-by-step explanation:
first you're going to move the terms , move -2x over to the left side and move -35 over to the right side , you're also going to change their signs , so they're not negative anymore .
next you're going to collect like terms so -5x+2x=3x and then add the numbers 31+35=66
lastly you're going to divide both sides by -3
x=-22 is what you should get
-3 belongs to the set of
Answers
Answer: integers
Step-by-step explanation:
Find z_1 x z_2 for z_1 = 9(cos225° + isin225°) and z_2 = 3(cos45° + isin45°).The 'z' is all subscript.
Answers
Using Euler's Formula:
\(re^{i\theta}=r(\cos (\theta)+i\sin (\theta))\)Since:
\(\begin{gathered} z1=9(\cos (225)+i\sin (225)) \\ z2=3(\cos (45)+i\sin (45)) \\ \end{gathered}\)We can rewrite them as:
\(\begin{gathered} z1=9e^{225i} \\ z2=3e^{45i} \end{gathered}\)So:
\(\begin{gathered} z1\times z2=(9e^{225i})(3e^{45i})=27e^{225i+45i}=27e^{270i} \\ so\colon \\ z1\times z2=27(\cos (270)+i\sin (270)) \end{gathered}\)\(\begin{gathered} a=r\cos (\theta) \\ b=r\sin (\theta) \\ where \\ r=27 \\ \theta=270 \end{gathered}\)So:
\(undefined\)if you can figure this out correctly I will give you thanks five stars and brainliest promise!!!
Answers
Answer 1,260 Cards.
Step-by-step explanation: 210 x 2 = 420, 420 + 210 = 630+210+420 = 1,260.
Hope this helps? :)
Answer:
they have 1,260 because anna had 420, ronald had 210 and erika had 630 add them together you get 1,260
so sorry if this is wrong
A bag contains hair ribbons for a spirit rally. The bag contains 18 black ribbons and 2 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. What is the probability that Lila selects a black ribbon and Jessica selects a green ribbon?
Answers
EXPLANATION:
Given;
We are told that a bag contains the following;
\(\begin{gathered} Black\text{ }ribbons=18 \\ \\ Green\text{ }ribbons=2 \\ \\ Total=20 \end{gathered}\)Lila selects a ribbon at random and then Jessica selects a ribbon at random from the remaining ones.
Required;
Calculate the probability that Lila selects a black ribbon and Jessica selects a green ribbon.
Step-by-step solution;
The probability of an event is calculated by the formula given below;
\(P[Event]=\frac{number\text{ }of\text{ }required\text{ }outcomes}{number\text{ }of\text{ }all\text{ }possible\text{ }outcomes}\)For Lila to select a black ribbon, we have;
\(\begin{gathered} P[black]=\frac{18}{20} \\ \\ P[black]=\frac{9}{10} \end{gathered}\)Now we have 19 ribbons left, note that Jessica had to select from the remaining ribbons.
For Jessica to select a green ribbon, we have;
\(P[green]=\frac{2}{19}\)Next to calculate the probability that Lila selects a black ribbon and Jessica selects a green ribbon we have a product of probabilities;
\(\begin{gathered} P[black]\text{ }and\text{ }P[green]=\frac{9}{10}\times\frac{2}{19} \\ \\ P[black]\text{ }and\text{ }P[green]=\frac{9}{95} \end{gathered}\)Therefore,
ANSWER:
The probability that Lila selects a black ribbon and Jessica selects a green ribbon is,
\(\frac{9}{95}\)5. Line 1 passes through the point D(2, 4) and has the same slope as the line segment joining
M(4, 5) and N(6, -19). Determine the equation of Line 1 in the form y = mx + b.
Answers
The equation of Line 1 in the form y=-12x+28
What is a Line Segment?A measurable path between two places is referred to as a line segment. Line segments may make up the sides of any polygon since they have a set length.
Coordinates of Line 2 M(4,5) and N(6,-19)
Slope of Line 2 is =(-19-5)/(6-4)
=-24/2=-12
Slope of line 1 and line 2 are same
Cordinate of Line 1 is D(2,4)
D(2,4) must pass through line 1, so it must satisfy the equation
y=mx+b
4=2(-12)+b
4+24=b
b=28
the equation of Line 1 in the form y=-12x+28
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We have 4 3/4 pounds of apple in each bag. If there are four bags, how many pounds of apples are there in all
Answers
HELP PLEASE ILL MARK BRAINLIST HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
1. RTS
2. RTS
3. 85, 180
4. 19
Step-by-step explanation:
1. The vertical angles are equal to each other.
2. The sum of the interior angle in a triangle is always 180 degrees.
Sam found a tent in his garage, and he needs to find the center height. the sides are both 5 feet long, and the bottom is 6 feet wide. what is the center height of sam’s tent, to the nearest tenth? 3 feet 4 feet 5.5 feet 7.8 feet
Answers
The centre height of Sam's tent to the nearest tenth = 7.8 feet.
Calculation of the center heightThe length of both sides of the tent (a) = 5ft
The base of the tent is (b)= 6ft
The centre height (c) = ?
Using the Pythagorean theorem
c² = a² + b²
c² = 5² + 6²
c² = 100 + 36
c² = √136
c² = 7.8 feet
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6. Solve P = C + rC for r.
Answers
Answer:
r=c2pi ok
Step-by-step explanation:
that the answer
Answer:
\(p = c + rc \\ p - c = rc \\ \frac{p - c}{c} = r \: or \: r = \frac{p - c}{c} \)
8.G.C.9
Which formula will find my volume?
Answers
The formula to find the volume of attached figure: V = πr²h
The correct answer is an option (d)
In the attached image we can observe that the figure is of cylinder with radius 'r' and height 'h'
This means that we need to find the volume of cylinder.
We know that the formula for tha cylinder is:
Volume of cylinder = Base area × height of cylinder
As we know that the base of cylinder is circular in shape.
so, the base area of cylinder would be,
A = πr²
when we say height of the cylinder then it means the perpendicular distance between two parallel bases of cylinder. It is also known as length of the cylinder.
So, the formula for volume would be,
V = πr²h
Therefore, the correct answer is an option (d)
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do all square numbers have an odd number of factors
Answers
No, not all square numbers have an odd number of factors. In fact, square numbers can have either an odd or an even number of factors, depending on their prime factorization.
A square number is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a square number because it can be written as 2 * 2.
When we analyze the factors of a square number, we find that each factor has a corresponding pair that multiplies to give the square number. For instance, the factors of 4 are 1, 2, and 4. We can see that the pairs are (1, 4) and (2, 2). Thus, 4 has an even number of factors.
However, there are square numbers that have an odd number of factors. Consider the square number 9, which is equal to 3 * 3. The factors of 9 are 1, 3, and 9. In this case, 9 has an odd number of factors.
In conclusion, while some square numbers have an odd number of factors (like 9), others have an even number of factors (like 4). The determining factor is the prime factorization of the square number.
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The probability distribution histogram shows the number of trees in yards in a certain neighborhood.
What is the probability that a randomly selected yard will have 6 or more trees?
Answers
Answer:
45%
Step-by-step explanation:
Here, we want to know the probability of a randomly selected yard having 6 or more than 6 trees
To get this, we simply add up the probability of 6 yards and above
That is the probability of 6, 8 , 10 and 12 yards
This is obtainable from the histogram
We then proceed to add up from the graph
What we have is;
0.05 + 0.25 + 0.10 + 0.05
= 0.10 + 0.10 + 0.25 = 0.45
This is same as 45/100 which is otherwise 45%
The probability that a randomly selected yard will have 6 or more trees is 45%.
Probability of having 0-2 tree = 0.35
Probability of having 2-4 tree = 0.20
Probability of having 4-6 tree = 0.05
Probability of having 6-8 tree = 0.20
Probability of having 8-10 tree = 0.10
Probability of having 10-12 tree = 0.05
What is the probability?Probability is to quantify the possibilities or chances.
So, probability of having 6 or more trees
= (2*0.05 + 2*0.25 + 2*0.10 + 2*0.05)/(0.35*2+0.20*2+2*0.05 + 2*0.25 + 2*0.10 + 2*0.05)
=0.9/2
=0.45
=45%
So, probability of having 6 or more trees =45%
Therefore, the probability that a randomly selected yard will have 6 or more trees is 45%.
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If (x)²√³ = (x√x)², where x * 0, then the value of x is
Answers
Answer:
We can simplify both sides of the equation using the rules of exponents:
(x)²√³ = (x^(2/3))^2 = x^(4/3)
(x√x)² = (x^(3/2))^2 = x^3
Now we can set the two expressions equal to each other and solve for x:
x^(4/3) = x^3
Divide both sides by x^(4/3):
x^3 / x^(4/3) = x^(9/3 - 4/3) = x^5/3 = 1
Taking the cube root of both sides:
x = 1^(3/5) = 1
Therefore, the value of x is 1.
In a school, 4/5 of the students study a language.
Of those students who study a language, 1/3 study German
What is the ratio of students who study German to the students who do not study German?
Answers
Answer:
I agree with Emma
Step-by-step explanation:
above
Answer:
4 12
--- : ---
15 15
I think this might be the answer, but fair warning there is a high chance I am wrong.
Consider the same open-top box, which is to have volume 216 in^3. Suppose the cost of the material for the base is 20$/in^2 and the cost of the material for the sides is 30$/in^2 and we are trying to minimize the cost of this box. Write the cost as a function of the side lengths of the base. (Let 3 be the side length of the base and y be the height of the box.) Hint If the cost of one of the sides is 30°/in^2, the cost of that side is 0.30 xy dollars
Answers
The cost of the box can be expressed as a function of the side length of the base as C(x) = 20x^2 + 0.6xy + 12.96/x dollars.
How to find a function that expresses the cost of the box in terms of the side length of the base and the height of the box, using the given material cost?Let x be the length of the base and y be the height of the box.
The volume of the box is given by:
V = x^2y = 216 in^3
Solving for y, we get:
y = 216/(x^2)
The cost of the material for the base is 20$/in^2, so the cost of the base is:20x^2 dollars
The cost of the material for the sides is 30$/in^2, and the four sides of the box have the area:
2xy + 2yx = 2xy + 2x(216/x^2) = 2xy + 432/x
Therefore, the cost of the material for the sides is:
(0.30)(2xy + 432/x) dollars = 0.6xy + 12.96/x dollars
The total cost of the box is the sum of the cost of the base and the cost of the sides, which is:
C(x) = 20x^2 + 0.6xy + 12.96/x dollars
Hence, the cost of the box can be expressed as a function of the side length of the base as C(x) = 20x^2 + 0.6xy + 12.96/x dollars.
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Help I suck at math
Answers
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
We can use this formula to find the equation of the line
(y-y1)/(y2-y1) = (x-x1)/(x2-x1)
(y - 11)/(23-11) = (x-1)/(3-1)
(y-11)/12 = (x-1)/2
y-11 = 6x-6
y = 6x + 5
the rate of change is the slope of the line, while the constant (5) is the y intercept