A 20-foot ladder is placed against a tree. The bottom is located 5 feet from the base of the tree and the top of the ladder is 5√15 feet up the tree. Use tangent to find the angle created between the ladder and tree. Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a degree.
Answer:
14.5°
Step-by-step explanation:
The sketch results in an angle of depression problem.
In this case, the opposite side of the triangle formed is 5 ft
The hypotenuse side is 20 ft
The adjacent side is the [tex]5\sqrt{15}[/tex] ft
Using tangent θ = opp/adj
tangent θ = 5/[tex]5\sqrt{15}[/tex] = [tex]\frac{1}{\sqrt{15} }[/tex] = 0.258
θ = [tex]tangent^{-1}[/tex] 0.258 = 14.5°
A sandman earns a commission of 26%. One week he had sales of $24400. Find the commission for the week.
Answer:
6344
Step-by-step explanation:
Find 26% of 24400
24400 * 26%
24400 * .26
6344
A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.
Answer:
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]Sections = 10[/tex]
[tex]n(Gray) = 5[/tex]
[tex]n(Blue) = 5[/tex]
Required
Determine P(Gray and Blue)
Using probability formula;
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
Calculating P(Gray)
[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]
[tex]P(Gray) = \frac{5}{10}[/tex]
[tex]P(Gray) = \frac{1}{2}[/tex]
Calculating P(Gray)
[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]
[tex]P(Blue) = \frac{5}{10}[/tex]
[tex]P(Blue) = \frac{1}{2}[/tex]
Substitute these values on the given formula
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
Simple geometry please help
Find KL. Round to the nearest hundredth.
Answer:
KL ≈ 1.94
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos48° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{JL}{KL}[/tex] = [tex]\frac{1.3}{KL}[/tex] ( multiply both sides by KL )
KL × cos48° = 1.3 ( divide both sides by cos48° )
KL = [tex]\frac{1.3}{cos48}[/tex] ≈ 1.94 ( to the nearest hundredth )
Question 1 of 10
What is the measure of ZXYZ shown in the diagram below?
Y
S
(369
7
Х
1140
Plz help
Answer:
B
Step-by-step explanation:
Secant-secant with vertex outside the circle
1/2(larger-smaller arc)
1/2(114-36)
1/2(78)
39
The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information.
Store's Card Major Credit Card
Sample size 64 49
Sample mean $140 $125
Population standard deviation $10 $8
A point estimate for the difference between the means is:________
a. 18
b. 265
c. 15
d. 2
Match each polynomial on the left with its two factors on the right.
Answer:
Hello
Step-by-step explanation:
[tex]Formula: \\\\\boxed{\Large a^3\pm b^3=(a \pm b)(a^2 \mp ab+b^2)}\\\\8x^3+1=(2x)^3+1^3=(2x+1)(4x^2-2x+1)\\\\8x^3-1=(2x)^3-1^3=(2x-1)(4x^2+2x+1)\\[/tex]
The factors of the expression 8x³ + 1 and 8x³ - 1³ will be (2x + 1) & (4x² – 2x + 1) and (2x – 1) & (4x² + 2x + 1), respectively.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The expression is given below.
8x³ + 1 and 8x³ - 1³
(2x)³ + 1³ and (2x)³ - 1³
We know that the formula is given as,
a³ + b³ = (a + b) (a² – ab + b²)
a³ – b³ = (a – b) (a² + ab + b²)
Then the expression is written as,
(2x)³ + 1³ = (2x + 1) [(2x)² – 2x + 1²]
(2x)³ + 1³ = (2x + 1) (4x² – 2x + 1)
(2x)³ – 1³ = (2x – 1) [(2x)² + 2x + 1²]
(2x)³ – 1³ = (2x – 1) (4x² + 2x + 1)
The factors of the expression 8x³ + 1 and 8x³ - 1³ will be (2x + 1) & (4x² – 2x + 1) and (2x – 1) & (4x² + 2x + 1), respectively.
More about the polynomial link is given below.
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you write a short story, but you want to make sure your work is protected before you post it online. what should you do to help protect your copyright?
Answer:
Hey there!
Here are a few steps:
Make sure your work is properly marked, because then it will be protected under law.
Register your work.
Keep or register supporting evidence.
Let me know if this helps :)
A triangle has a base that is increasing at a rate of 18 mm per minute with the height being held constant. What is the rate of change of the area of the triangle if the height is 7 mm
Answer:
63mm/minStep-by-step explanation:
Area of a triangle = 1/2 * base * height
A = 1/2bh
Rate of change of area is expresssed as dA/dt = dA/db * db/bt
db/dt is the rate at which the base is increasing.
Given db/dt = 18mm/min
A = 1/2*7b
A = 7b/2
dA/db = 7/2
The rate at which the area is changing dA/dt = dA/db * db/bt
dA/dt = 7/2 * 18
dA/dt = 7*9
dA/dt = 63mm/min
Hence the rate at which the area of the triangle is changing is 63mm/min
name all sets of numbers to which each real number belongs
Answer:
1. Natural Number
2. Integer
3. Rational Number
4. Rational Number
5. Irrational Number
6. Rational Number
7. Rational Number
8. Natural Number
9. Irrational Number
10. Integer
11. Irrational Number
12. Natural Number
Type the missing number in this sequence:
1,
4,
,64, 256,
1,024
Answer:
16
Step-by-step explanation:
The sequence is 1, 4,...,64, 256, 1024
Notice that:
● 1 = 2^0
● 4 = 2^2
● 64 = 2^6
● 256 = 2^8
● 1024 = 2^10
Notice that we add 2 each time to the exponent so the missing number is:
● 2^(2+2) = 2^4 = 16
find the value of x, circles and angles
Answer:
x = 50
Step-by-step explanation:
When two secants intersect in the interior of a circle, the angles formed are the average of the arc an angle and its vertical intercept. In this case, our angle, 73, should be the average of x and 96. We can translate this to an equation and solve:
[tex]\frac{x+96}{2} = 73[/tex]
x + 96 = 146
x = 50
The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:\
Answer: Expected value
Step-by-step explanation: The expected value of a random variable refers to a predicted variable which is obtained from the summation of the product of all possible values and the probability of occurrence of each value. The expected values gives the mean or average possible value over the cause of a certain experiment or scenario. It is thus the probability weighted average of all possible values or outcomes of an experiment.
The expected value could be represented mathematically as thus;
E(x) = [Σ(x * p(x)]
Where x = all possible values or outcomes of x;
p(x) = corresponding probability of each x value.
What is the volume of a cone below?
What is the domain of the function represented by the graph
Answer:
C
Step-by-step explanation:
Domain of the function is the whole R
Pls Help ASAP..................
Answer:
1. 8+(30/(2+4)) = 8+(30/6) = 8+5 = 13
2. ((8+30)/2)+4 = (38/2)+4 = 19+4 = 23
Step-by-step explanation:
:)
Answer:
Step-by-step explanation:
23:
(8 + 30) ÷ 2 + 4
13:
8 + 30 ÷ (2 + 4)
please give me the brainliest if u can
A solid is formed by rotating the region bounded by y = x − x^2 and y = 0 about the line x = 2 . Use the shell method to find the volume of the solid.
Answer:
The volume of the resulting solid is π/2 cubic units.
Step-by-step explanation:
Please refer to the diagram below.
The shell method is given by:
[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]
Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.
From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:
[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]
The volume of the resulting solid is π/2 cubic units.
Answer:
pi/2
Step-by-step explanation:
I always like to draw an illustration for these problems.
For shells method think volume of cylinder=2pi×r×h
Integrate(2pi(2-x)(x-x^2) ,x=0...1)
Multiply
Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)
Combine like terms
Integrate(2pi(2x-3x^2+x^3) ,x=0...1)
Begin to evaluate
2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1
2pi(x^2-x^3+x^4/4), x=0...1
2pi(1-1+1/4)
2pi/4
pi/2
Define limit and it's types.
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.
g(x) , one may look at how big f(x) and g(x) are. For example: If f(x) is close to some positive number and g(x) is close to 0 and positive, then the limit will be ∞. If f(x) is close to some positive number and g(x) is close to 0 and negative, then the limit will be −∞.
what is the definition of a sequence
Answer:
the process of combining things in a particular order, or discovering the order in which they are combined: A common sign of dyslexia is that the sequencing of letters when spelling words may be incorrect. biology specialized.
Step-by-step explanation:
Solve the following equation algebraically:
3x^2=12
a.+3
b. +2
C.+3.5
d. +1.5
Answer:
Step-by-step explanation:
answer is c just took test
A study was conducted to explore the effects of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 got only water (control). Treatment 2 got 1g of ethanol per kg of body weight, and treatment 3 got 2g/kg. The amount of REM sleep in a 24hr period was recorded, in minutes. Data are below:
Treatment 1: 63, 54, 69, 50, 72
Treatment 2: 45, 60, 40, 56
Treatment 3: 31, 40, 45, 25, 23, 28
Required:
a. Calculate 90% confidence intervals for all pairwise comparisons of treatment means using the uncorrected method. Create a letter code table to summarize your results, then interpret the results in context.
b. Now calculate 90% confidence intervals for all pairwise comparisons using the Bonferroni correction. Create a letter code table, and interpret your results in context. Do any of the results differ from part (a)?
Answer:
the answer is A
Step-by-step explanation: i have calculated this problom
what number should be added to -5/8 to get -3/2
Answer:
-7/8
Step-by-step explanation:
-5/8+x=-3/2
x= -3/2+5/8=-12/8+5/8= -7/8
The number of values of xx in the interval [0,5π][0,5π] satisfying the equation 3sin2x−7sinx+2=03sin2x-7sinx+2=0 is/are
Answer:
6
Step-by-step explanation:
Given, 3sin2x−7sinx+2=03sin2x-7sinx+2=0
⇒(3sinx−1)(sinx−2)=0⇒3sinx-1sinx-2=0
⇒sinx=13 or 2⇒sinx=13 or 2
⇒sinx=13 [∵sinx≠2]⇒sinx=13 [∵sinx≠2]
Let sinα=13,0<α<π2,sinα=13,0<α<π2, then sinx=sinαsinx=sinα
now x=nπ+(−1)nα(n∈I)x=nπ+(−1)nα(n∈I)
⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α⇒x=α,π−α,2π+α,3π−α,4π+α,5π−α Are the solution in [0,5π][0,5π]
Hence, required number of solutions are 6
Simplify, write without exponents.
[tex]2*4^{2} *(128\frac{1}{4})[/tex]
[tex]_\sqrt[_]{_}[/tex]
a.) 8
b.) 20
c.) 2
d.) 64
e.) 4
f.) 16
it is helpful to you
Which expression is equivalent to x+y+x+y+3(y+5)
Answer:
2x + 5y + 15
Step-by-step explanation:
add like terms
(x+x) + (y+y)+3y+15
2x+2y+3y+15
2x + 5y + 15
i hope this helps!
Nick needs one more class to complete his schedule. There are 5 writing classes, 3 history classes, and 4 mathematics classes that can fit into his schedule. If Nick chooses a class at random, what is the probability that he chooses a history class? Give your answer as a fraction.
Answer:
1/4
Step-by-step explanation:
Probability = 3/(5+3+4)
= 3/12 or 1/4
a number is divisible by 10 if it has ____ in ones place .
Answer:
A number is divisible by 10 if it has a zero in ones place.
Step-by-step explanation:
We know that 10= 2 x 5 .So to be divisible by 10 we have to be divisible by both 2 and 5As we know ,Numbers divisible by 2 are even numbers and numbers divisible by 5 if it has a zero or a five in ones place . From that, we have A number is divisible by 10 if it has a zero in ones place.If y = 4x -2, what are possible inputs and outputs of the function?
Complete the ordered pairs:
(0, __)
(-2, __)
(___, 14)
(___, -14)
Graph the data, what type of function is it?
Answer:
(0,-2), (-2,-10), (4,14), (-3,-14)
Step-by-step explanation:
y(0)=-2, y(-2)=-10, y(x) = 14 so x=16/4=4, y(x) = - 14, x=-12/4=-3.
Find f (3) for the following function:
f (x) = 4x+3/x^2
Answer: [tex]12.333[/tex] or [tex]12\frac{1}{3}[/tex] or [tex]\frac{37}{3}[/tex]
Step-by-step explanation:
Replace every x with (3)
[tex]f(x) = 4x+3/x^2\\f(3) = 4(3)+3/3^2\\f(3) = 12+3/9\\f(3) = 12.333 or 12\frac{3}{9}or \frac{111}{9}\\f(3) = 12.333 or 12\frac{1}{3} or \frac{37}{3}[/tex]
Line L has a slope of 1/2 . The line through which of the following pair of points is perpendicular to L?
The line which crosses through L must have an intersect point with L to become perpendicular.
Gien slope is positive 1/2.
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the lineslope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.
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