Answers
Answer:
23 degrees
Step-by-step explanation:
We can use basic trigonometric equations to solve for the angle x because we are given a right triangle.
I will use the sin x = opposite / hypotenuse
sin x = 5 / 13
x = sin^-1 (5 / 13)
x = 22.61986 degrees
The question requires us to round to the nearest degree which is 23.
Other alternative methods you can use include the tangent and cosine functions or the law of cosines.
Answer:
x = 23°
Step-by-step explanation:
I will use
[tex]tanx=opposite/adjacent[/tex]
[tex]tanx=\frac{5}{12}[/tex]
[tex]x=tan^{-1} (\frac{5}{12} )=tan^{-1} (0.417)=22.62^{o}[/tex]
rounded to the nearest degree : 23°
Hope this helps
Related Questions
A support cable for a 56-foot tower forms a 67° angle with the ground.
What is the length of the cable to the nearest foot?
56 ft.
61 ft.
60 ft.
75 ft.
Answers
to find the length of the cable, you need to use trigonometry. So you have 56ft as the opp of 67degree and cable as hypotenuse of 67degree.
thus Sin(67)=OPP/HYP
=56/HYP
HYP=56/Sin(67)
=60.83618113
=61 ( nearest foot )
Therefore Ans: 61ft
If ∠ 1 = 26 o , find the measure of ∠ 4 .
Answers
The angle ∠4 of the given transversal shown in the diagram is gotten as; 26°.
How to find alternate angles?The alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
Now, we are told that ∠1 = 26° as seen in the attached diagram. However, it is clear that ∠2 is an alternate angle to ∠1. Thus, we can say that ∠2 = 26°.
Now, Corresponding angles are the pairs of angles that are found in the same relative position on different intersections.
From the diagram we see that ∠4 is a corresponding angle to ∠2. Thus;
∠4 = 26°.
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Which point is a solution to the system?
A. (0, -1)
B.(2, 3) C.(4,0)
D. (6,-6)
Answers
Answer:
(0;-1)
Step-by-step explanation:
for more details see the attachment.
The sum of two numbers is 32. One number is 3 times as large as the other. What are the numbers?
Answers
Answer: 8, 24
Step-by-step explanation:
Since the sum of two numbers is 32 and one number is 3 times as large as the other, the first number can be defined as x and the second number is 3x.
Divide 32 by (3+1) = 4 and you get 8, which is x.
The second number is 3(8) = 24.
Solve the system using substitution.
5x + 3y = -4
y - 2x = 6
([?], [? ])
Answers
Answer:
(-2,2)
Step-by-step explanation:
i tried sorry if it's wrong
The function ()=2f(x)=x2is transformed to
()=0.4(+1)2f(x)=0.4(x+1)2
Which statement describes the effect(s) of the transformation on the graph of the original function?
The parabola is narrower and shifted 1 unit to the right.
The parabola is narrower and shifted 1 unit to the left.
The parabola is wider and shifted 1 unit to the right.
The parabola is wider and shifted 1 unit to the left.
Answers
Answer:
StepWhat is the measure of z? Z X y 4 9 z = [ ? ]VI-by-step explanation:
Select one of the factors of 3x² + 4x - 4.
O (x + 4)
O (3x + 2)
O (3x - 2)
O(x - 2)
Answers
Answer:
(3x-2)
Step-by-step explanation:
3x² + 4x - 4
look for two factors whose product is (3)(-4)=-12 and sum is +4
The factors will be +6 and -2
substitute these factors inplace of 4x to get:
3x² - 2x + 6x - 4
then factorize:
x(3x-2)+2(3x-2)
finally we get factors: (3x-2)(x+2)
Two trains leave a station at the same time. One train is heading south at a rate that is 1.5 times faster than the other train, which is heading north. After 5 hours, the trains are 750 miles apart. At what speed, in mph, are the two trains getting farther away from each other?
Answers
Answer:
150 mph
Step-by-step explanation:
The relationship between time, speed, and distance is ...
speed = distance/time
ApplicationThe trains have separated 750 miles in 5 hours, so their rate of separation is ...
(750 mi)/(5 h) = 150 mi/h
The trains are separating at a speed of 150 mph.
Whih number produces a rational number multiplied by 0.5
Answers
The question is incomplete. Please find the full content below.
Which number produces a rational number multiplied by 0.5
(C) 2.22 produces a rational number multiplied by 0.5.
If a number can be expressed by p/q form where p and q are whole numbers and q does not equal to 0, is called a Rational number.
If a number cannot be expressed as above then that number is called Irrational Number.
In simple term, we can say that the never-ending decimal numbers and square roots of non perfect square numbers are Irrational Numbers.
Product of two rational numbers is always a rational and the product of one rational and one irrational is always an irrational number.
Here given that the number is 0.5 which is clearly a rational number.
In order to get a rational number, we have to multiply another rational number with that.
In the given choices,
[tex]\pi=3.14......[/tex]
is a never-ending decimal number that is irrational.
7 is not a perfect square so
[tex]\sqrt{7}[/tex]
is an irrational number.
2.020020002.... is also a never-ending decimal number hence it is irrational.
Only 2.22 is rational here.
So multiplication of 2.22 and 0.5 produces a rational number since the product of two rational numbers is always a rational number.
Hence option (C) is correct.
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Create both a tree diagram AND sample space of all possible boy/girl births in a family of three kids.
1. How many outcomes are there?
2. What is the probability of all three kids being boys?
3. What is the chance of only the middle kid being a girl?
4. What is the probability of there being at least two boys?
5. What is the chance of there being at most one girl?
Answers
Answer: Sample space: {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}
1. 8 outcomes in total
2. 1/8 or 0.125
3. 1/2 or 0.5
4. 1/2 or 0.5
5. 3/8 or 0.375
Step-by-step explanation:
1. As shown by the sample space and the tree diagram, there are 8 total possibilities.
2. There is only a 1/8 or 0.125 chance of there being all boys, which is BBB
3. There are 4 outcomes that allow the middle child to be a girl, and 4/8 = 1/2. There will only be a girl middle child with BGB, GGG, BGG, and GGB.
4. We can think of at least as meaning no less than two boys, which includes two to three boys. The only outcomes that have either two or three boys is BBB, BBG, BGB, GBB. 4/8 = 1/2.
5. We can think of at most as meaning no more than one girl. The only outcomes that have only one girl are BBG, BGB, and GBB, which is 3/8.
To access his bank’s ATM, Tom must choose a four-digit PIN. Any digit from 0 through 9 can be used in the PIN, but digits may not be repeated. How many possible PIN numbers are there?
Answers
Answer:
Try using the permutations formulae - nPr
n = 10
r = 4
you should get the answer. I don't have calculator on me and I'm lazy searching an online calculator. cheers
1. Simplify (7y²)
(3y³)
Answers
Answer:
21 y power 5
Step-by-step explanation:
3 A bag contains red and blue marbles, such that the probability of drawing a blue marble is 8 An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. What is the probability that both of the marbles drawn are blue? a. b. $ 24% * 39% C. d 0 14% 3 A bag contains red and blue marbles , such that the probability of drawing a blue marble is 8 An experiment consists of drawing a marble , replacing it , and drawing another marble . The two draws are independent . What is the probability that both of the marbles drawn are blue ? a . b . $ 24 % * 39 % C. d 0 14 %
Answers
Answer:
My answer: B
Step-by-step explanation:
The probability mass function of random variable X which represents the number of blue marbles drawn in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
The probability of drawing exactly one blue marble = 0.46875
Complete Question
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. an experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome.
To write the Probabilty mass function, we have to establish that in two draws with replacement, the possible number of blue marbles that can be drawn is 0, 1 and 2.
Probability of drawing a blue marble = P(B) = (3/8)
Probability of not drawing a blue marble = P(B') = 1 - (3/8) = (5/8)
- Probability of drawing 0 blue marbles in 2 draws with replacement = P(B') × P(B') = (5/8) × (5/8) = (25/64) = 0.390625
- Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
- Probability of drawing two blue marble in 2 draws with replacement = P(B) × P(B)
= (3/8) × (3/8) = (9/64) = 0.140625
The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
b) Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
So, B is the answer.
y is directly proportional to x and inversely proportional to the square of w. Give the equation:
Answers
Answer: y=kx/w^2
Step-by-step explanation:
y is directly proportional to x
y∝x
y=kx
y inversely proportional to the square of w.
y ∝ (1/(w)^2)
y=k/w^2
y=kx/w^2
What is the slope of a line parallel to the line whose equation is3x−4y=8?
−43
−34
34
43
Answers
The slope of the parallel line is 3/4
How to determine the slope?The equation is given as:
3x - 4y = 8
Rewrite as:
4y = 3x - 8
Divide through by 4
y = 3x/4 - 2
A linear equation is represented as:
y = mx + b
Where m represents the slope
By comparison:
m = 3/4
Parallel lines have equal slope
Hence, the slope of the parallel line is 3/4
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Factor the trinomial below.
x2 - 14x + 45
Answers
Answer:
(x-9) (x-5)
x = 9 x = 5
Step-by-step explanation:
find out which 2 numbers when multiplied give 45 and
when added give -14
they are -9 and -5
(x-9) (x-5)
x = 9 x = 5
Answer:
[tex]x_{1}=9, x_2=5[/tex]
Step-by-step explanation:
Recall a quadratic formula for quadratic equation [tex]ax^2+bx+c=0[/tex]: [tex]x_{1/2}=\frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
Notice the constant in the given equation [tex]x^2-14x+45[/tex]:
[tex]a=1, b=-14, c=45[/tex]
Substitute the values into the formula:
[tex]x_{1/2}=\frac{-(-14)\pm \sqrt{(-14)^2 -4\cdot 1\cdot 45}}{2\cdot 1}[/tex]
Calculate the values:
[tex]x_{1/2}=\frac{14\pm \sqrt{196 -180}}{2}=\frac{14\pm\sqrt{16}}{2}=\frac{14\pm 4}{2}[/tex]
It follows that there are two solutions:
[tex]x_1=\frac{14+4}{2}=\frac{18}{2}=9[/tex] and [tex]x_2=\frac{14-4}{2}=\frac{10}{2}=5[/tex].
Two bikers meet at a park. Biker A needs to stop at the store that is 12 miles east of the park. Biker B heads southeast at a 61° angle at the same time for 24 miles. Once biker A leaves the store he heads southwest at an angle of 89° for 21 miles. Do NOT use the law of cosines, use your knowledge from the content of this course.
a. Use your knowledge of triangles to figure out if the two bikers will be able to meet up if each biker travels the distance given.
b. If they do not meet up, how much farther would one of the bikers have to travel to meet the other?
c. What is the measure of the angle between the bikers?
d. What is the relationship between the measure of the angles and the paths the bikers took?
e. Classify the triangle the paths created.
f. How many miles did they travel together?
Answers
The bikers will meet at point N, all the questions have been answered below.
What is a Triangle?A triangle is a polygon with three sides, angles, and vertices.
The triangle MNO is formed on the basis of the data given in the question
If the triangle satisfies the sine-rule then the biker meets the other biker at point N
According to the sine rule
In a Triangle ABC of side length a,b and c respectively
a/ sin A = b/ sin B = c/sin C
NM/sin NOM =21/ sin 61°
NM/sin NOM = 24.01
NO/sin OMN =24/sin 89°
NO/sin OMN = 24.003
∠ONM = ( 180-61-89) = 30°
OM / sin ONM = 12/ sin 30 = 24
The ratio of the side and angles of the triangle are almost equal, therefore they satisfy the sine ruleand so, the bikers will meet at point N.
As they are meeting the distance between them will be zero.The measure of the angle between the bikers is as calculated above = 30°.The largest angle is opposite to the longer path.The triangle formed is an acute angle triangle.Total miles they travelled = 24+12+21 = 57 miles.To know more about Triangle
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Write 13.13.13.13.13 in exponential form?
Answers
13.13.13.13.13 in exponential form is 13^5
How to rewrite the expression?The expression is given as:
13.13.13.13.13
The factors of the above expression are 13.
And each factor is grouped by product
There are five 13s in the expression.
So, we have:
13.13.13.13.13 = 13^5
Hence, 13.13.13.13.13 in exponential form is 13^5
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Can anybody tell me how to solve this?
The real risk free rate is 2%. The inflation premium for the next three years is 4.0%. The maturity risk premium for three year bonds is 3.7%. Liquidity premium is 3% and default risk premium is 3.5%. What is the nominal rate on a three year Treasury Bond?
answer in % without the symbol
Answers
The nominal rate on a three year Treasury Bond, which is the risk-free rate plus the inflation premium, is 6%.
What are nominal rates?The nominal interest rate (also known as the money interest rate) is the percentage of interest that the borrower pays to the lender for a loan.
The nominal interest rate includes the real rate and the inflation premium.
Data and Calculations:Risk-free rate = 2%
Inflation premium = 4.0%
Maturity risk premium = 3.7%
Liquidity premium = 3%
Default risk premium = 3.5%
Nominal rate for Treasury Bond = Risk-free rate plus Inflation premium
= 6% (2% + 4%)
Thus, the nominal rate on a three year Treasury Bond is 6%.
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2x+15
4x + 5
x = [?]
X
O
Answers
Lenny bought x shares of stock for Sy per share last month. He paid
his broker a flat fee of $20. He sold the stock this month for Sp per
share, and paid his broker a 2% commission. Express Lenny's net
proceeds algebraically.
Answers
Lenny's net proceeds algebraically are found as;[tex]\rm |xy + 20 - \frac{98}{100} |[/tex]
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Let the bought share will be $ x, and $y is the price per share
Paid fees to the broker = $ 20
The total amount spent = $(xy+20)
The price at which each share sells = $ A
Broker commission = 2 %
The total amount obtained after selling the shares;
⇒ ax - 2% of ax
⇒ 98 % of ax
Hence, Lenny's net proceeds algebraically are found as;[tex]\rm |xy + 20 - \frac{98}{100} |[/tex]
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Answer:
Step-by-step explanation:
what were Laura net proceeds
if ABC is a isosceles triangle with sides(2a+b)cm, (6a+2b+1)cm and a base of 4a cm, if it's perimeter is 28 find sides
Answers
Answer:
a=1.5, b= 3
Step-by-step explanation:
sum of all sides will give us perimeter. Therefore
2a+b+6a+2b+1+4a=28
12a+3b+1=28
12a+3b=27....eqn1
since t two sides of this isosceles triangle are equal:
2a+b=4a
2a=b
[tex]a=\frac{b}{2}[/tex]
substituting [tex]\frac{b}{2}[/tex][tex].[/tex] in the first equation whenever we encounter a we will have:
[tex]12(\frac{b}{2})+3b=27\\[/tex]
6b+3b=27
9b=27
b=3
therefore [tex]a= \frac{b}{2} =\frac{3}{2} =1\frac{1}{2} or 1.5[/tex]
Compare the graph of g(x) = -0.3x² + 7 with the graph of p(x) = x².
The graph of g(x) is wider.
The graph of q(x) opens downward and the graph of p(x) op
Both have the axis of symmetry x = 0.
The vertex of q(x) is (0, 7); the vertex of p(x) is (0, 0).
O The graph of q(x) is narrower.
The graph of q(x) opens downward and the graph of p(x) op
Both have the axis of symmetry x = 1.
The vertex of q(x) is (1, 7); the vertex of p(x) is (1, 0).
The graph of q(x) is wider.
Both graphs open upward.
Both have the axis of symmetry x = 1.
The vertex of q(x) is (1, 7); the vertex of p(x) is (1, 0).
The graph of q(x) is narrower.
Both graphs open downward.
Both have the axis of symmetry x = 0.
The vartov nf n/v) is in 7) the vartav nf n/v) ie in my
Answers
Answer:
Step-by-step explanation:
Below is the graphs of the given g(x) and p(x)
g(x) is green
p(x) is blue
The graph of g(x) is wider.
The graph of g(x) opens downward
Both have the axis of symmetry x = 0
The vertex of g(x) is (0, 7); the vertex of p(x) is (0, 0).
The graph of g(x) opens downward and the graph of p(x) opens upward
The graph of g(x) is wider.
Classify the graph as a linear function, nonlinear function, or relation (non- function). -i0- O A. Nonlinear function O B. Linear function C. Relation
Answers
Answer:
I need to see the graph
No explanation
Find the area of a rectangle with
side lengths of in. and in.
2|3
in.
415
in.
Simplify your answer completely.
in.2
Answers
Answer:
Area = length * width
= 4/5 * 2/3
= 8/15
Answer:
[tex]area = \frac{8}{15} {in}^{2} [/tex]
Step-by-step explanation:
The solution is in the attached file
At a recent chess tournament, all 15 of the participants had to fill out a form that gave their names, address and age. The ages of the participants were recorded as follows: 36, 48, 54, 92, 57, 63, 66, 76, 66, 80, 82, 65, 39, 77, and 45. Use the data to construct a frequency table and histogram with 3 classes.(15 points) Classes Class Boundaries
Answers
The frequency table and histogram are shown in the attached picture.
What is a histogram?It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.
We have:
The ages of the participants were recorded as follows:
36, 48, 54, 92, 57, 63, 66, 76, 66, 80, 82, 65, 39, 77, 45
The classes can be made:
30-42, 43-55, 56-68, 69-81, and 82-94
The histogram is shown in the picture.
Thus, the frequency table and histogram are shown in the attached picture.
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2. Employed Women If 60% of all women are employed
outside the home, find the probability that in a sample
of 20 women,
aid sel
Mil
2
a. Exactly 15 are employed
b. At least 10 are employed
c. At most 5 are not employed outside the home
Answers
Using the binomial distribution, the probabilities are given as follows:
a) 0.0747 = 7.47%.
b) 0.8725 = 87.25%.
c) 0.1256 = 12.56%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are:
n = 20, p = 0.6.
Item a:
The probability is P(X = 15), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 15) = C_{20,15}.(0.6)^{15}.(0.4)^{5} = 0.0747[/tex]
Item b:
The probability is:
[tex]P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + \cdots + P(X = 20)[/tex]
Finding each value with the equation we used in item a, we have that:
[tex]P(X \geq 10) = 0.8725[/tex]
Item c:
At least 20 - 5 = 15 on the road, hence the probability is:
[tex]P(X \geq 15) = P(X = 15) + P(X = 16) + \cdots + P(X = 20)[/tex]
Then, using the same procedure as item b, we have that:
[tex]P(X \geq 15) = 0.1256[/tex]
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Can someone please tell me the answer to this question?
Answers
Answer:
D) 12pm
Step-by-step explanation:
8 pm = 20:00
20:00 + 16:00*4 = 20:00 + 64:00 = 84:00
subtract the 24 hours in 84:00
84:00 - 3 X 24:00 = 12:00
12:00 = 12pm
System A
x−4y=1
5x+6y=−5
System B
x=1+4y
5x+6y=−5
1) How can we get System B from System A?
CORRECT (SELECTED)
Replace one equation with itself where the same quantity is added to both sides
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
CORRECT (SELECTED)
Yes
Answers
1. System B from System A by replacing one equation with itself where the same quantity is added to both sides
2. Yes, both system A and system B are equivalent and therefore has the same solution
How to prove the statementsSystem A
x − 4y= 1
5x + 6y= −5
System B
x = 1+4y
5x + 6y= −5
1. System B can be gotten from system A by
from the first equation of A
x − 4y= 1
Make 'x' subject of formula
x = 1 + 4y
This makes it equal to tat of system B
Thus, replacing one equation with itself where the same quantity is added to both sides
2. System A
x = 1 + 4y
5x + 6y= −5
System B
x = 1 + 4y
5x + 6y= −5
From the above equations, we can see that both system A and system B are equivalent and therefore has the same solution.
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Which expression is equivalent to sin?
O sin-
sin
O sin 5
O sin 5
11
sin-
Answers
Answer: Option 4
Step-by-step explanation:
[tex]\sin \frac{7\pi}{6}=\sin \left(-\frac{\pi}{6} \right)=\sin \frac{11\pi}{6}[/tex]
Using equivalent angles, the equivalent expression to [tex]\sin{\left(\frac{7\pi}{6}\right)}[/tex] is:
[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]
What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, we have that [tex]\frac{7\pi}{6}[/tex] is on the third quadrant, as [tex]\pi < \frac{7\pi}{6} < \frac{3\pi}{2}[/tex]. Hence the equivalent angle on the first quadrant is:
[tex]\frac{7\pi}{6} - \pi = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{\pi}{6}[/tex]
The sine is negative on the third and fourth quadrants, hence the equivalent angle on the fourth quadrant is:
[tex]2\pi - \frac{\pi}{6} = \frac{11\pi}{6}[/tex]
Thus, the equivalent expression is:
[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]
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