Answers
Answer:
Step-by-step explanation:
First Identify what sides you have based on the angle given: 52
O = 13
H = x
This means we will use Sin
(Sin = O/H)
Sin (52) = 13/x
Multiply both sides by x
X Sin (52) = 13
Divide both side by Sin (52)
X = 13/Sin(52)
X = 13.176197
X = 13
Related Questions
Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^4, y=1 and the y-axis and whose cross-sections perpendicular to the x axis are semicircles.
Answers
The base of the solid - call it B - is the set of points
B = {(x, y) : 0 ≤ x ≤ 1 and x ⁴ ≤ y ≤ 1}
Recall the area of a circle with radius r is πr ²; in terms of the diameter d = 2r, the area is π (d/2)² = π/4 d ². Then the area of a semicircle with the same diamater is half of this, π/8 d ².
Cross sections of the solid in question are semicircles arranged perpendicular to the x-axis, which means the diameters of each cross section corresponds to the vertical distance between y = x ⁴ and y = 1 for any given values of x between 0 and 1. So d = 1 - x ⁴, which makes the area of each cross section come out to π/8 (1 - x ⁴)².
Split up the solid into very thin cross sections with "base" area π/8 (1 - x ⁴)² and thickness ∆x. Take the sum of these half-cylinders' volumes, then let ∆x converge to 0. In short, we get the total volume by integrating,
[tex]\displaystyle \int_0^1\frac\pi8(1-x^4)^2\,\mathrm dx = \frac\pi8\int_0^1(1-2x^4+x^8)\,\mathrm dx = \boxed{\frac{4\pi}{45}}[/tex]
Find the volume of this square based pyramid 8cm 6cm 6cm
Answers
Answer:
96cm3
Step-by-step explanation:
formula is
v=1/3×area of the base×height
area of base which is a square=l×l
which is equal to 6×6=36
therefore
v=1/3×(6×6)×8
=96cm3
I hope it helps
(2/3)^x-1=27/8, find x. Please add a step-by-step explanation.
[tex]( \frac{2}{3} ) {x - 1 = \frac{27}{8} }^{?} [/tex]
Answers
so basically after doing all the algebra, you will have to use the log function to solve. rearranging things and you will get the log expression that I obtained, then solve it using the change of base formula.
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→[infinity] ln(5x) 5x Step 1 As x → [infinity], ln(5x) → and 5x → .
Answers
Answer:
[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x} = \lim_{x \to \infty} \frac{1/x}{5} = \lim_{x \to \infty} \frac{1}{5x} = 0[/tex]
Step-by-step explanation:
L'Hopital's rule says that, if both numerator and denominator diverge, then we can look at the limit of the derivates.
Here we have:
[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x}[/tex]
The numerator is ln(5x) and when x tends to infinity, this goes to infinity
the denominator is 5x, and when x tends to infinity, this goes to inifinity
So both numerator and denominator diverge to infinity when x tends to infinity.
Then we can use L'Hopithal's rule.
The numerator is:
f(x) = Ln(5x)
then:
f'(x) = df(x)/dx = 1/x
and the denominator is:
g(x) = 5*x
then:
g'(x) = 5
So, if we use L'Hopithal's rule we get:
[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x} = \lim_{x \to \infty} \frac{1/x}{5} = \lim_{x \to \infty} \frac{1}{5x} = 0[/tex]
Match each set of vertices with the type of triangle they form.
A(2, 0), B(3, 2), C(5, 1)
obtuse scalene triangle
A(4, 2), B(6, 2), C(5, 3.73)
isosceles right triangle
A(-5, 2), B(-4, 4), C(-2, 2)
right triangle
A(-3, 1), B(-3, 4), C(-1, 1)
acute scalene triangle
A(-4, 2), B(-2, 4), C(-1, 4)
Answers
9514 1404 393
Answer:
rightacuteobtuserightobtuseStep-by-step explanation:
When the same problem is repeated, I like to solve it using a spreadsheet. That way, the formulas only need to be entered once, and the arithmetic is (almost) guaranteed to be done correctly.
A "form factor" computed from side lengths can be used to determine the type of triangle. Where 'c' is the long side, that factor can be computed as ...
f = a² +b² -c²
and interpreted as follows:
f = 0, right trianglef > 0, acute trianglef < 0, obtuse triangle(The sign of f matches the sign of the cosine of the largest angle computed using the law of cosines.)
Of course, a right triangle can also be identified by looking at the slopes of the sides of the triangle. If any pair of slopes has a product that is -1, or if any pair is 0 and "undefined", then the triangle will be a right triangle.
__
The attached spreadsheet is designed to accommodate a number of different problem requirements. It shows both side lengths and slopes, and it shows the "form factor" as described above. The final classification is shown at far right.
Please helpppp me I really confused
Answers
Answer:
The answer would be D
Step-by-step explanation:
This is a piecewise function, meaning that it is split into two parts. The right side is an exponential and that part is greater than one, the left side is a line less than or equal to one. The only equation that matches the criteria for that is D.
You throw two four-sided dice. Let the random variable X represent the maximum value of the two dice. Compute E(X). Round your answer to three decimal places.
Answers
Answer:
E(X)=3.125
Step-by-step explanation:
We are given that two four sided dice.
Then , the sample space
{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}
Total number of outcomes=16
Let the random variable X represent the maximum value of the two dice
Outcomes X P(X)
(1,1) 1 1/16
(1,2),(2,1),(2,2) 2 3/16
(1,3),(2,3),(3,1),(3,2),(3,3) 3 5/16
(1,4),(3,4) ,(2,4),(4,1),(4,2),(4,3),(4,4) 4 7/16
Using the probability formula
[tex]P(E)=\frac{Favorable\;outcomes}{Total\;number\;of\;outcomes}[/tex]
Now,
[tex]E(X)=\sum_{i=1}^{n}x_iP(x_i)[/tex]
[tex]E(x)=1(1/16)+2(3/16)+3(5/16)+4(7/16)[/tex]
[tex]E(x)=\frac{1+6+15+28}{16}[/tex]
[tex]E(x)=\frac{50}{16}=3.125[/tex]
Random samples of size 81 are taken from a population whose mean is 45 and standard deviation is 9. Calculate the probability that a sample mean is less than 42. (round to 4 decimal places)
HINT: When you randomly select a group (n > 1) then you need to re-calculate the standard deviation using the formula:
σ n
Answers
Answer:
Using z table
= 0.0013
The probability = 0.0013
Step-by-step explanation:
Given that,
mean = μ = 45
standard deviation = σ = 9
n=81
μT = μ =45
[tex]\sigma T = \sigma / \sqrt n = 9 / \sqrt81 =1[/tex]
[tex]P(T <42 )\\= P[(T - \mu T ) / \sigma T < (42-45) /1 ]\\\\= P(z <-3 )[/tex]
Using z table
= 0.0013
probability= 0.0013
Which of the statements is true for the two division problems below? A: (x^2-3x-18)/(x-6) B. (x^3-x^2-5x-3)/(x^2+2x+1)
Answers
Answer:
B is the right statement
Answer:
add the answer choices
Step-by-step explanation:
in one particular suburb slacks have been reduced to $36. This price is at 90% of the original price for slacks. Given this what is the original price of the slacks
Answers
40*90/100 = 36
You just have to be careful with the rest of the problem
(5,4) (3,7) find the equation for A+b=C
Answers
Answer:
Step-by-step explanation:
Slope of line through (5,4) and (3,7) = (7-4)/(3-5) = -1.5
Point-slope equation of line:
y-4 = -1.5(x-5)
Convert equation to standard form:
y-4 = -1.5x + 7.5
1.5x + y = 11.5
3x +2y = 23
Write the equation of a line in the slope-intercept form that has a slope of 4
and contains the point (4, 12).
Answers
Answer:
The equation of the point (4, 12) is y=4x+12
While planning a hiking trip, you examine a map of the trail you are going on hike. The scale on the map shows that 2 inches represents 5 miles.
If the trail measures 12 inches on the map, how long is the trail?
Answers
Answer:
30 miles
Step-by-step explanation:
Given that :
Scale = 2 inches represents 5 miles
This means that 2 inches in the map equals to 5 miles on ground ;
Hence, if the trail measures 12 inches on the map, the length on ground will be ; x
2 inches = 5 miles
12 inches = x miles
Cross multiply :
2x = (12 * 5)
2x = 60
x = 60 / 2
x = 30 miles
The ages of a group of 142 randomly selected adult females have a standard deviation of 18.1 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let σ=18.1 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 99% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population? The required sample size is
Answers
Answer:
Start with the formula for Z:
Z = (x-µ)/(σ/√n)
We want the sample mean to be within one-half year of the population mean, so we set x-µ=0.5. We are looking for a 99% confidence interval, so we set Z=2.7578. We are told to use σ=18.1. Plugging those values into the formula, we get:
2.5758 = 0.5(18.1/√n)
We can rearrange to solve for n:
((2.5758-18.1)/0.5)2 = n
Plugging that into our calculator, we get n = 964.003. Since we can't have a fraction of a person in our sample, it would be safest to round up to n=965. (But since .003 is so small, I'd also accept 964 as an answer.)Step-by-step explanation:
The required sample size for the given population distribution is; n = 8696 female ages
We are given;
Standard deviation; σ = 18.1
Confidence level; CL = 99%
Now, formula to find the margin of error is;
E = z(σ/√n)
Where;
E is margin of error
z is critical value at confidence level
σ is standard deviation
n is required sample size
Now we are told that the sample mean is within one-half year of the population mean.
Thus;
E = 0.5
z value at 99% Confidence level is;
z = 2.576
Thus, Making n the subject of the formula is;
n = (zσ/E)²
n = (2.576 × 18.1/0.5)²
n = 8695.78
Approximating to a whole number gives;
n = 8696 female ages
Read more about margin of error at; https://brainly.com/question/6650225
a sequence of numbers is given by 25,30,35..............,300. find the number of terms in the sequence
Answers
Answer:
56
Step-by-step explanation:
clearly, the sequence is built by adding 5 for every new term.
so, an = an-1 + 5
a1 = 25 (the starting value)
a2 = a1 + 5 = 25 + 5 = 30
a3 = a2 + 5 = a1 + 5 + 5 = a1 + 2×5 = 25 + 10 = 35
...
an = an-1 + 5 = a1 + (n-1)×5
now, we know, the last term is 300.
when we determine for which n we get an = 300, we know that n is the number of terms in the sequence.
so,
300 = a1 + (n-1)×5 = 25 + 5n - 5 = 20 + 5n
280 = 5n
n = 56
a56 = 300
so, we have 56 terms in this sequence
Answer:
56
Step-by-step explanation:
nth term = a+d(n-1) =25+5(n-1) = 25+5n-5 = 20+5n
300 = 20 + 5n
5n = 280
n = 56
since 300 is the last term in the sequence, the total number would be 36
Find the number of distinguishable arrangements of the letters of the word SEPTILLION
Answers
Answer:
10!
Step-by-step explanation:
Septillion-10 letters
1-s-10 places to be in
2-e-9
3-p-8
4-t-7
5-i-6
6-l-5
7-l-4
8-i-3
9-o-2
10-n-1
So, then
10×9×8×7×6×5×4×3×2×1=10!
or 3628800
The arrangement of the number will be equal to 3628800.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a way to choose items or numbers from a collection or group of items without worrying about the items' chronological order.
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
The given word is SEPTILLION. The word has 10 characters. The different ways of the arrangement will be calculated as,
Arrangement = 10!
Arrangement = 10×9×8×7×6×5×4×3×2×1
Arrangement = 3628800
Therefore, the arrangement of the number will be equal to 3628800.
To know more about permutation and combination follow
https://brainly.com/question/4658834
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rectangle a is dilated to form rectangle b. what is the scale factor used .
Answers
Answer:
5
Step-by-step explanation:
The scale factor is 5. Answered by Gauthmath
The length and the width of rectangle a are expanded 5 times respectively.
What is a scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.
According to the question
Rectangle a is dilated to form rectangle b.
By division operation, the ratio
[tex]\frac{20}{4} =\frac{30}{6} =5[/tex]
The length and the width of rectangle a are expanded 5 times respectively.
Find out more information about scale factor here
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Which of the binomials below is a factor of this trinomial?
x^2+8x+16
Answers
This is because the given expression factors to (x+4)(x+4), which condenses to (x+4)^2.
To factor, think of two numbers that A) multiply to 16, and B) add to 8. Those values would be 4 and 4
4+4 = 8
4*4 = 16
So that's how we end up with (x+4)(x+4). You can use the FOIL rule to expand that out and get x^2+8x+16 again to help verify you have the correct factorization.
Translate To An Algebraic Expression:
S% of 1/r
Answers
Answer:
S/100r
Step-by-step explanation:
S% of 1/r = (1/r x S) : 100
(1/r x S) : 100
S/r : 100
S/100r
Have a great day! Stay safe. Hope it helped
Mr Gardner is making 6 treat bags. He has 185 chocolate-covered raisins to share evenly among the treat bags.
Answers
Answer:
✎There will be 30 Chocolate-Covered raisins in each bag.
✎ And 5 Remaining.
Step-by-step explanation:
Take 185 and divide it by 6 and you should get 30 per bag with a remainder of 5 :)
B) 5 chocolate covered raisins will be left over
See the photo attached to see the long division.
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
A town recently dismissed 8 employees in order to meet their new budget reductions. The town had 9 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that at least 7 employees were over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Answer:
The probability that at least 7 employees were over 50 is 0.0073%.
Step-by-step explanation:
Given that a town recently dismissed 8 employees in order to meet their new budget reductions, and the town had 9 employees over 50 years of age and 16 under 50, if the dismissed employees were selected at random, to determine what is the probability that at least 7 employees were over 50, the following calculation must be performed:
9/25 x 8/24 x 7/23 x 6/22 x 5/21 x 4/20 x 3/19 = X
0.36 x 0.33 x 0.304 x 0.272 x 0.238 x 0.2 x 0.157 = X
0.000073 = X
100X = 0.0073
Therefore, the probability that at least 7 employees were over 50 is 0.0073%.
Find the interval in which f(x) = 3x2 - 2x is decreasing.
Answers
Answer:
Option (3)
Step-by-step explanation:
Given function is,
f(x) = 3x² - 2x
= [tex]3(x^{2} -\frac{2}{3}x)[/tex]
= [tex]3(x^{2} -\frac{2}{3}x+\frac{1}{9}-\frac{1}{9})[/tex]
= [tex]3(x^{2}-\frac{2}{3}x+\frac{1}{9})-\frac{1}{3}[/tex]
= [tex]3(x-\frac{1}{3})^2-\frac{1}{3}[/tex]
Vertex of the parabola → [tex](\frac{1}{3},-\frac{1}{3})[/tex]
Here, leading coefficient is positive (+3),
Therefore, parabola will open upwards.
In a parabola opening upwards function decreases from negative infinity to the x value of the vertex.
Function will decrease in the interval (-∞, [tex]\frac{1}{3}[/tex]).
Option (3) will be the answer.
In Riverview Middle school, 20 percent of the students participate in an after school club for every 100 students how many are in an afterschool club
Answers
Answer:
What is the diferentes between and red bolos celos ?
Step-by-step explanation:
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
Our soccer team lost 9 games this season. That was 3/8 of all they played. How many games did they play this season?
Answers
Answer:
15
Step-by-step explanation:
3/8 = 9
9÷3= 3
the remainder of 3/8 is 5/8 so
5x3=15
a test has 20 multiple-choice questions with 5 choices each, followed by 35 true/false questions. if a student guesses on each question, how many ways can he answer the questions on the test
Answers
Answer
There are 170 ways the student can answer the test.
Explanation
If there are 20 multiple-choice questions with 5 choices each, the student has 100 choices. The first question has 5 choices to pick from. The second has 5 as well. So does the third. Hopefully now you realize that you have to multiply the number of choices by the number of questions.
The same thing goes with the true/false questions. There are 2 choices for each true/false question, and there are 35 of those. 35×2 is 70. There are 70 ways to answer on the true/false questions.
Now combine the number of choices on the first part and the second part; 100+70 is 170.
Consider the function z(x,y) describing the paraboloid \[z = (2x - y)^2 - 2y^2 - 3y.\]Archimedes and Brahmagupta are playing a game. Archimedes first chooses $x.$ Afterwards, Brahmagupta chooses $y.$ Archimedes wishes to minimize $z$ while Brahmagupta wishes to maximize $z.$ Assuming that Brahmagupta will play optimally, what value of $x$ should Archimedes choose?
Answers
Answer: -3/8
Step-by-step explanation:
Expanding z we get
z = 4x^2 - 4xy + y^2 - 2y^2 - 3y
= -y^2 - (4x + 3) y + 4x^2.
After Archimedes chooses x, Brahmagupta will choose
y=-(4x+3/2) in order to maximize z
Then
z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2
z=8x^2+6x+9/4
To minimize this expression, Archimedes should choose x=-3/8
The coordinates of three points are A(- 1, - 3) , B(2, 3) and C(6, k) . If AB is perpendicular to BC find (i) the value of k, (ii) the gradient of AC (iii) the acute angle that AC makes with the x-axis.
Answers
9514 1404 393
Answer:
(i) k = 1
(ii) 4/7
(iii) arctan(4/7) ≈ 29.7°
Step-by-step explanation:
(i) A graph of the given points is helpful. It shows us the slope of AB is ...
mAB = rise/run = 2/1 = 2
so the slope of BC must be the opposite reciprocal, -1/2.
Point C is 6-2 = 4 units to the right of point B, so will be (-1/2)(4) = -2 units from point B in the vertical direction. That is, ...
k = 3 -2
k = 1
__
(ii) The gradient of AC is found from the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (1 -(-3))/(6 -(-1))
mAC = 4/7
__
(iii) The angle that line AC makes with the +x axis is the arctangent of the slope:
arctan(4/7) ≈ 29.7° . . . angle between AC and +x axis
3pt b) Suggest one way that is always under the control of the researcher of making the margin of error smaller.
Answers
Answer:
By making use of a lower confidence level
Step-by-step explanation:
The margin of error is also referred to as the confidence interval and it is the system in which we use to measure the error in the result of the survey or experiment.
Now, for us to reduce the margin of error, there are different things we can do such as;
- increasing sample size
- using less data variation
- making use of a lower confidence level
- making use of a one sided confidence interval rather than a two sided confidence interval.
Looking at the above different methods of making the margin of error smaller, the one that is always under the control of the researcher is "making use of a lower confidence level".
Every other means, he does not have as much control as he has to do to lower the confidence level. That one is strictly based on his jurisdiction.
porfavor se los agradeceria mucho y de corazon :D
Answers
Answer:
1=2p+3
2=
Step-by-step explanation:
If p = 1/2 and q = 4; evaluate 3p2q+pq2
Answers
Answer:
11
Step-by-step explanation:
3p²q+pq²=3×1/4×4+1/2×16=3+8=11
