You have a 20-foot ladder that you are using as you paint your house. You place the ladder so that it forms an angle of 30 at the point of contact between the ladder and the ground. How high will the top of the ladder be above the ground
Answers
Answer:
The Ladder is 10 ft high.
Step-by-step explanation
According to the question we have a 20 ft ladder inclined against a wall at a 30° angle, and are asked to find how high the top of the ladder is from the ground. I have added a visual representation to help you better understand the situation. As you can see we need to solve for x. Since we are given one angle and the hypotenuse we can solve for x using the SIN operator.
[tex]sin(a) = \frac{opposite}{hypotenuse}[/tex]
Since we have the angle (a) and the hypotenuse we can just plug the information into the sin equation and solve for the opposite (x).
[tex]sin(30) = \frac{x}{20ft}[/tex]
[tex]sin(30)*20ft = x[/tex]
[tex]0.5*20ft = x[/tex]
[tex]10ft = x[/tex]
So now we can see that the height of the top of the ladder to the ground is 10 ft
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Related Questions
2/3 of a number is 32, what is the number?
Answers
a=32×3/2
a=96/2
a=48
The number is 48
Integers:- 3/2•2/3 = 32/1 = 3/2 = 96/2 = 48
On average, Donna's Cafe has 18 customers, which represents 36% of the total approved occupancy by the fire department. a. What is the total approved occupancy of the cafe by the fire department? Total approved occupancy = customers b. According to the fire department's occupancy approval, what percentage of the cafe is still available for customers? Available occupancy percentage = % c. According to the fire department's occupancy approval, how many seats are still available for customers? Seats still available =
Answers
Because this number is 36% of total approved occupancy. the maximum number of customers is
18/0.36 = 50
Part a.
Total approved occupancy = 50 customers
This means that available seats for customers are 50 - 18 = 32.
The available occupancy is
32/50 = 0.64 = 64%
Part b.
Available occupancy percentage for customers = 64%
Part c.
Number of seats still available for customers = 32
an actor gains 20pounds for a part and then losses 15 pounds during the filming of the movie to go along with the story.who do you write a addition expression to describe this situation
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He is then gaining 20 pounds. The clue is in the word 'gaining' as it means 'increasing' or in Mathematics can be related as 'plus'
The expression is: x+20
He then loses 15 pounds. The clue is in the word 'losses' as it means 15 pounds is to be subtracted from the last value
Last value is x + 20
The weight now is x + 20 - 15 = x + 5
Name the three different types of proof in math and give a description of each
Answers
If prices Increase at a monthly rate of 2.3%, by what percentage do they increase in a year?
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The calculation would be (100%+2.3%)^12= 131.37344984%
That would be about 31.37% a year.
A company uses a variable percentage markup of 35% .if the total cost of a product is $15,what is its selling price
Answers
The selling price of a product with a 35% markup on a cost of $15 is calculated by adding the markup amount of $5.25 to the cost, resulting in a selling price of $20.25.
Explanation:To calculate the selling price of a product using a variable percentage markup, you first need to determine the amount of markup by converting the percentage to a decimal and multiplying by the cost of the product. In this case, with a 35% markup on a product that costs $15, the calculation is as follows:
$15 × 0.35 = $5.25
This $5.25 represents the amount of markup on the product. To find the selling price, you simply add the markup to the cost:
$15 + $5.25 = $20.25
Therefore, the selling price of the product would be $20.25.
Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −1 s (s − 5)(s − 6)(s − 30)
Answers
Based on the given, the useful transformation equation is shown in the attached picture. The given equation is
[tex] \frac{-1}{s(s-5)(s-6)(s-30)} [/tex]
Breaking it into partial fractions,
[tex] \frac{-1}{s} * \frac{1}{s-5} * \frac{1}{s-6} * \frac{1}{s-30} [/tex]
From the given transformation equation:
-1/s ⇔ -e^0t ⇔ 1
1/(s-5) ⇔ e^-(-5t) ⇔ e^5t
1/(s-6) ⇔ e^-(-6t) ⇔ e^6t
1/(s-30) ⇔ e^-(-30t) ⇔ e^30t
Therefore, the laplace equation is equal to 1*e^5t*e^6t*e^30t which is simplified into e^41t,
A pharmacist has 40% and 80% iodine solutions on hand .How many liters of each iodine solutions will be required to produce 6 liters of a 50% iodine mixture?
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[tex]\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentration\\ amount \end{array}\\ &-----&-------&-------\\ \textit{40\% sol'n}&x&0.4&0.4x\\ \textit{80\% sol'n}&y&0.8&0.8y\\ -----&-----&-------&-------\\ mixture&6&0.5&3 \end{array}[/tex]
so... whatever "x" and "y" may be, we know the must add up to 6 liters.
and whatever 0.4x and 0.8y are, we also know, they must add up to a 3 of concentrated amount.
thus [tex]\bf \begin{cases} x+y=6\implies \boxed{y}=6-x\\ 0.4x+0.8y=3\\ ----------\\ 0.4x+0.8\left( \boxed{6-x} \right)=3 \end{cases}[/tex]
solve for "x", to see how much of the 40% solution will be needed.
what about "y"? well, y = 6 - x.
True or false: the difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.
Answers
Sampling error is an error which is calculated by finding the difference between the lower limit or upper limit of a confidence interval and the point estimate used in constructing the confidence interval.
As we can calculate the difference, so sampling error can be positive or negative.
which algebraic expression represents the phase
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A product is the result when multiplying.
Therefore, the answer here is B.
Multiply and Dividing Rational Numbers
8/9 ÷ 2/3
7/8 × 1/4
3/4×1/6
Answers
[tex]\bf \cfrac{8}{9}\div \cfrac{2}{3}\implies \cfrac{8}{9}\cdot \cfrac{3}{2}\implies \cfrac{8\cdot 3}{9\cdot 2}\implies \cfrac{24}{18}\implies \cfrac{4}{3} \\\\\\ \cfrac{7}{8}\cdot \cfrac{1}{4}\implies \cfrac{7\cdot 1}{8\cdot 4}\implies \cfrac{7}{32} \\\\\\ \cfrac{3}{4}\cdot \cfrac{1}{6}\implies \cfrac{3\cdot 1}{4\cdot 6}\implies \cfrac{3}{24}\implies \cfrac{1}{8}[/tex]
How can I use context clues and keywords to translate situations into inequalities? Explain with an example of your own.
Answers
Mira and Lola are looking to hire a hall for their 18th birthday party. They are expecting at least 50 guests and want a hire that will accommodate the party. Write this requirement as an inequality
Solution: the keyword here is 'at least' because it means that the hall must be able to accommodate a minimum of 50 people. It is a clue that Mira and Lola are expecting more than 50 guests. The inequality symbol for this context is 'more than or equal to' and as inequality, we have x ≥ 50
To translate situations into inequalities, use context clues and keywords. Start by understanding the relationships and factors involved. Then, represent the situation with variables and create an inequality based on the context clues. For example, if Bob earns $10 more than Alice, the inequality would be 'a < a + 10'.
Explanation:In order to use context clues and keywords to translate situations into inequalities, it's important to understand the relationships and factors involved. Let's take an example:
Scenario: Suppose you have two friends, Bob and Alice. Bob earns $10 per hour more than Alice. In this case, we can use the following context clues:
The relationship between Bob and Alice: Their wealth is unequal.The factor involved: The difference in their earnings.We can now translate this situation into an inequality:
Let's say Alice's earnings are represented by 'a'.Bob's earnings would be 'a + 10' (since he earns $10 more).The inequality can be represented as 'a < a + 10' (Alice's earnings are less than Bob's earnings).By using the context clues and the keywords (earnings, difference), we were able to translate the situation into the inequality 'a < a + 10'.
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Can anyone help me solve a trigonomic identity problem and also help me how to do it step by step?
it's ((cos theta) * (cot theta))/(1-sin theta) - 1 = csc theta
Answers
[tex]\bf \cfrac{cos(\theta )cot(\theta )}{1-sin(\theta )}-1=csc(\theta )\\\\ -------------------------------\\\\ \cfrac{cos(\theta )\cdot \frac{cos(\theta )}{sin(\theta )}}{1-sin(\theta )}-1\implies \cfrac{\frac{cos^2(\theta )}{sin(\theta )}}{\frac{1-sin(\theta )}{1}}-1\implies \cfrac{cos^2(\theta )}{sin(\theta )}\cdot \cfrac{1}{1-sin(\theta )}-1 \\\\\\ \cfrac{cos^2(\theta )}{sin(\theta )[1-sin(\theta )]}-1\implies \cfrac{cos^2(\theta )-1[sin(\theta )[1-sin(\theta )]]}{sin(\theta )[1-sin(\theta )]}[/tex]
[tex]\bf \cfrac{cos^2(\theta )-1[sin(\theta )-sin^2(\theta )]}{sin(\theta )[1-sin(\theta )]}\implies \cfrac{cos^2(\theta )-sin(\theta )+sin^2(\theta )}{sin(\theta )[1-sin(\theta )]} \\\\\\ \cfrac{cos^2(\theta )+sin^2(\theta )-sin(\theta )}{sin(\theta )[1-sin(\theta )]}\implies \cfrac{\underline{1-sin(\theta )}}{sin(\theta )\underline{[1-sin(\theta )]}} \\\\\\ \cfrac{1}{sin(\theta )}\implies csc(\theta )[/tex]
Which quantity is proportional to 20/5?
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jim sold 200 litters of soda at baseball game.How much is this in milliters?
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1000 * 200 = 200000
So, 200000 milliliter is the answer.
One liter is 1000 milliliters. To convert between them, multiply 200 by 1000 to get 200,000
What's the next value?
1 I 2 L 3 F 4
Answers
Brainliest answer plzzzz
let f(x)=4x-1 and g(x)=2x^2+3. perform the function operation and then find the domain. To
f(x) + g(x)
Answers
F(x)=4x-1 and g(x)=2x²+3.
f(x) + g(x) = 2x²+4x+2
the domain oh : f+g is : R
HELP!! A spherical ball just fits inside a cylindrical can, 16 centimeters tall, with a diameter of 16 centimeters. Which expression gives the volume of the sphere in cubic centimeters?
Answers
formula for volume of a sphere is V=4/3 x pi x R63
if diameter = 16 than radius = 16/2 = 8
so the equation would be 4/3 x pi x 8^3
Convert decimal +49 and +29 to binary, using the signed‐2’s‐complement representation and enough digits to accommodate the numbers. then perform the binary equivalent of (+29) + (-49), (-29) + (+49), and (-29) + (-49). convert the answers back to decimal and verify that they are correct.
Answers
To solve this problem, let us first find for the binary equivalents of the numbers. They are:
Decimal --> Binary
+ 29 --> 00011101
+ 49 --> 00110001
- 29 --> 11100011
- 49 --> 11001111
Now we apply the normal binary arithmetic to these converted numbers:
(+ 29) + (- 49) ---> 00011101 + 11001111 = 11101100 ---> - 20 (TRUE)
(- 29) + (+ 49) ---> 11100011 + 00110001 = 00010100 ---> + 20 (TRUE)
(- 29) + (- 49) ---> 11100011 + 11001111 = 10110010 ---> - 78 (TRUE)
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the second equation is substituted into the first equation.
2x – 7y = 4
3x + y = –17
Answers
Equation 2: [tex]3x+y=-17[/tex]
Rearranging equation 2 to make 'y' the subject
[tex]y = -17 - 3x[/tex] ⇒ Call this Equation 3
Substituting Equation 3 into Equation 1
[tex]2x-7(-17-3x)=4[/tex]
[tex]2x+119+21x=4[/tex]
[tex]23x+119=4[/tex]
[tex]23x=4-119[/tex]
[tex]23x=-115[/tex]
[tex]x=-5[/tex]
Then substitute x = -5 into either Equation 1 or Equation 2 to solve for 'y'
[tex]2x-7y=4[/tex]
[tex]2(-5)-7y=4[/tex]
[tex]-10-7y=4[/tex]
[tex]-7y=4+10[/tex]
[tex]-7y=14[/tex]
[tex]y=-2[/tex]
Note: the original question did not attach the option for the equation after substitution so you might want to follow the working out here carefully and match it with the options given.
Madison deposited a total of $5,000 between two saving accounts bearing simple interest. One of the accounts has an interest rate of 4% while the other rate is 5%. If the total interest earned after one year is $220, find the amount deposited into each of the accounts.
Answers
Solve for x to find the amount invested at 4%
0.04x+250-0.05x=220
0.04x-0.05x=220-250
-0.01x=-30
X=30÷0.01
X=3,000 invested at 4%
5000-3000=2000 invested at 5%
A home pregnancy test is not always accurate. suppose the probability that the test indicates that a woman is pregnant when she actually is not is 0.02, and the probability the test indicates that a woman is not pregnant when she really is, is 0.03. assume that the probability that a woman who takes the test is actually pregnant is 0.7. what is the probability that a woman is pregnant if the test yields a not pregnant result?
Answers
T=tests positive~T=tests negativeP=subject is pregnant~P=subject is not pregnant
We are givenP(T n ~P)=0.02P(~T n P)=0.03P(P)=0.7
recall by definition of conditional probabilityP(A|B)=P(A n B)/P(B)
Need to find P(P|~T)
First step: make a contingency diagram of probabilities (intersection, n)
P ~P sum
T 0.67 0.02 0.69=P(T)
~T 0.03 0.28 0.31=P(~T)
sum 0.70 0.30 1.00
=P(P) =P(~P)
therefore
P(P|~T)=P(P n ~T)/P(~T)=0.03/0.31 [ both read off the contingency table ]
=0.0968
The probability of a woman being pregnant if a home pregnancy test yields a negative result can be calculated using conditional probabilities and Bayes' theorem. From the provided probabilities, we can substitute into Bayes' theorem to calculate this probability.
Explanation:The subject of this question is based on conditional probabilities. From the question we know that:
The probability of the test indicating a woman is pregnant when she's not (false positive) is 0.02 i.e., P(Positive|Not Pregnant) = 0.02 The probability of the test indicating a woman is not pregnant when she actually is (false negative) is 0.03 i.e., P(Negative|Pregnant) = 0.03 The probability that a woman who takes the test is actually pregnant is 0.7 i.e., P(Pregnant) = 0.7
From the above, we can find the probability of a woman being pregnant even though the test results are negative. To find this we need to use Bayes' theorem, which states:
P(A|B) = P(B|A) * P(A) / P(B)
So, to calculate the probability of a woman being pregnant given a negative test result P(Pregnant|Negative), we need the probability of getting a negative result when pregnant P(Negative|Pregnant), the probability of a woman actually being pregnant P(Pregnant), and the total probability of getting a negative test result P(Negative).
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PLEASE HELP WITH SOME GEOMETRY
Prove the following statement by contradiction using an indirect proof. In a triangle angle A = 90°, then the triangle is a right triangle. Which of the following choices would be the first step to temporarily assume?
angle A = 90°
the triangle is a right triangle
the triangle is not a right triangle
angle A is not 90°
Answers
"The triangle is not a right triangle angle and A is not 90°"
Then you proof that this statement is false
A study of sleep patterns randomly selected participants in the study to sleep in either a dark room or a room with light.
Which element of experiment design is known to be a part of this study?
A.
blinding
B.
replication
C.
randomization
Answers
Answer:
C. randomization
Step-by-step explanation:
We are told that the study randomly selects participants in the study to sleep in either a dark room or a room with light. This means that randomization is part of the study.
Gabrielle's age is three times Mikhail's age. The sum of their ages is 44. What is Mikhail's age?
Answers
m=micsdjfsdf's age
g=3m
sum is add
g+m=44
subsitute 3m for g
3m+m=44
4m=44
divide by 4 both sides
m=11
mikhail is 11 year old
How to solve 7.86 x 4.6
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An apple farmer has planted 0.3 of his orchard with cherry trees. The orchard is 8.59 acres in size. How many acres are planted with cherry trees
Answers
amy has 72 sweets in bag.she keeps 1/4 of them for herself,but shares the remainder between 6 of her friends.how many sweets will she give to each of her friends?
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she has 54 left to share
54 divided by 6 is how many sweets each friend will get
Each friend gets 9 sweets
Find the area of a triangle with legs that are: 15mm,10mm,20mm
Answers
Area=sqrt(s(s-a)(s-b)(s-c))
where:
s=(a+b+c)/2
thus,
s=(15+10+20)/2
=22.5
hence the area will be:
Area=sqrt(22.5(22.5-15)(22.5-10)(22.5-20))
Area=sqrt(22.5*7.5*12.5*2.5)
=sqrt5273.4375
=72.62 mm^2
The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is [tex]72.618 mm^{2}[/tex]
Further Explanation;Area Area is a measure of how much space is occupied by a given shape. Area of a substance is determined by the type of shape in question.For example;
Area of a rectangle is given by; Length multiplied by width Area of a circle = πr². where r is the radius of a circle, Area of a square = S², Where s is the side of the square.etc.Area of a triangle The area of a triangle is given based on the type of the triangle in question.Right triangle.The area of a right triangle is given by;= 1/2 x base x height
Scalene triangleIt is a triangle that with sides and angles that are not equal.Area of a scalene triangle depends on the features of the triangle given.For example;
Sine FormulaArea of a triangle = 1/2 ab sin θ, when given two sides of the triangle and the angle between themHeron's formulaArea of a triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex] when given all the sides of the triangle. where [tex]s =\frac{(a+b+c)}{2}[/tex]In this case we are given, a = 15 mm, b = 10 mm, c = 20 mm
Therefore, we use the Heron's formula;
Area= [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]s =\frac{(a+b+c)}{2}[/tex]
[tex]s= \frac{(15+10+20)}{2} \\s= 22.5[/tex]
Therefore;
Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]
= [tex]22.5\sqrt{22.5(22.5-15)(22.5-10)(22.5-20)}[/tex]
=[tex]\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}[/tex]
[tex]= 72.618 mm^{2}[/tex]
Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.
Learn more about: Perimeter: https://brainly.com/question/12905000 Area: https://brainly.com/question/12905000 Area of a triangle: https://brainly.com/question/4125306Heron's Formula: https://brainly.com/question/10713495Level: Middle school
Subject; Mathematics
Topic: Area
Sub-topic: Area of a triangle
Find the area under the standard normal curve between z = −2.57 and z = 1.27. Round your answer to four decimal places, if necessary.
Answers
P(Z ≤ 1.27) = 0.8980
P(Z ≤ -2.57) = 1 - P(Z ≤ 2.57) = 1 - 0.99488 = 0.00512
P(-2.57 ≤ Z ≤ 1.27) = 0.8980 - 0.00512 = 0.89288
0.8929 (4 d.p.)
The area under the standard normal curve between z = −2.57 and z = 1.27 is, 0.8929
What is meant by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to give that,
To find the area under the standard normal curve between z = −2.57 and z = 1.27.
Now, the area under the standard normal curve is between z = −2.57 and z = 1.27 is,
P(-2.57 ≤ Z ≤ 1.27) = P(Z ≤ 1.27) - P(Z ≤ -2.57)
Since, P(Z ≤ 1.27) = 0.8980
And, P(Z ≤ -2.57) = 1 - P(Z ≤ 2.57)
= 1 - 0.99488
= 0.00512
Hence,
P(-2.57 ≤ Z ≤ 1.27) = 0.8980 - 0.00512
= 0.89288
= 0.8929
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