Consider the following triangle. A right triangle. The hypotenuse is 5 feet, the side opposite to angle theta is 3 feet, the side adjacent to angle theta is 4 feet. If sin Theta = three-fifths, what is the measure of the angle? a. 53.1º b. 36.9º c. 30.1º d. 59º
Answers
The measure of the angle is 36.9^o. Option B.
What is a right triangle?A right triangle is a form or type of triangle in which the measure of one of its internal angles is 90^o. As such, either the trigonometric functions or Pythagorean theorem can be applied to determine any of its properties as the case may be.
From the details given in the question, we can deduced that;
Sin θ = 3/5
= 0.6
So that,
θ = Sin^-1 0.6
= 36.87
θ = 36.9^o
The measure of the angle is 36.9^o. Option B.
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Related Questions
This morning the temperature was -5F. This afternoon the temperature rose 1F. What was the new temperature?
Answers
Answer:
-4f
Step-by-step explanation:
if it only went up by one it should be -4f. I guess -5 +1= -4 can be used as an explanation
I hope this answer helps you with your test and/or homework
A worker is paid $2,350 monthly and has $468 withheld from each monthly paycheck. Which of the following is her annual net salary
Answers
Answer:
Annual net salary = $22,584
Step-by-step explanation:
Given:
Monthly wage = $2,350
Withheld paycheck = $468
Find:
Annual net salary = ?
Computation:
Total net salary = Monthly wage - Withheld paycheck
Total net salary = $2,350 - $468
Total net salary = $1,882
Annual net salary = Total net salary × 12
Annual net salary = $1,882 × 12
Annual net salary = $22,584
which point is on the line 4y-2x=0
Answers
Answer:
(2,1)
Step-by-step explanation:
The line 4y - 2x = 0 can be written in slope-intercept form as y = 1/2x.
So any point that satisfies this equation will lie on the line. For example, the point (2,1) satisfies the equation:
4(1) - 2(2) = 0
So the point (2,1) is on the line.
look at attachment!!!!
Answers
Answer:
x = 5
Step-by-step explanation:
We know that BD = 2x - 1 and BC + CD = BD. Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:
BC + CD = BD
x - 3 + 7 = 2x - 1
x + 4 = 2x - 1
x + 5 = 2x
5 = x
Thus, x = 5
Checking the validity of our answer:
We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:
5 - 3 + 7 = 2(5) - 1
2 + 7 = 10 - 1
9 = 9
Thus, our answer is correct.
Challenge Question: 146.794/0.643 I bet u 100 bucks to do it!!!!!!
Answers
The answer would be 228.295489891
Rounded to the nearest tenth it would 228.3
A cylindrical drill with radius 5 is used to bore a hole through the center of a sphere of radius 7. Find the volume of the ring-shaped solid that remains.In this problem, we are asked to find the volume of the intersection of a cylinder and a sphere. To solve this problem, we must first set-up the equation of each object using three-dimensional coordinates
Answers
the equation of the sphere is: x{power}2 + y{power}2 + z{power}2 = 49 To solve this problem, we need to first visualize the objects involved: a cylinder with radius 5 and a sphere with radius 7.
The cylinder has a height that is infinite (i.e., it extends infinitely in the vertical direction), while the sphere is centered at the origin.
To set up the equation of the cylinder, we can use the cylindrical coordinate system. The equation of a cylinder with radius r and infinite height in cylindrical coordinates is given by:
r{power}2 + z{power}2 = R{power}2
where r is the radial distance from the z-axis, z is the height, and R is the radius of the cylinder. In our case, we have R = 5, so the equation of the cylinder is:
r{power}2 + z{power}2 = 25
To set up the equation of the sphere, we can use the Cartesian coordinate system. The equation of a sphere with radius R centered at the origin in Cartesian coordinates is given by:
x{power}2 + y{power}2 + z{power}2 = R{power}2
In our case, we have R = 7, so the equation of the sphere is:
x{power}2 + y{power}2 + z{power}2 = 49
Now, we want to find the volume of the ring-shaped solid that remains when we bore a hole through the center of the sphere using the cylinder. To do this, we need to find the volume of the intersection of the cylinder and the sphere.
To find the intersection, we can substitute the equation of the cylinder into the equation of the sphere and solve for z. This gives us:
x{power}2 + y{power}2 + (r{power}2 - 25) = 49
r{power}2 = 74 - x{power}2 - y{power}2
So the intersection is defined by the set of points (x, y, z) that satisfy both equations. To find the volume of the intersection, we can integrate over the region where the cylinder and sphere intersect. In cylindrical coordinates, the region of integration is defined by:
r{power}2 + z{power}2 ≤ 49
r{power}2 + z{power}2 ≥ 25
Using the equation we derived earlier for r{power}2, we can rewrite this region as:
25 ≤ r{power}2 ≤ 74 - x{power}2 - y{power}2
-sqrt(74 - x{power}2 - y{power}2) ≤ z ≤ sqrt(74 - x{power}2 - y{power}2)
Finally, we can use a triple integral to find the volume of the intersection:
V = ∫∫∫ (r dz dr dθ)
Over the limits of the region described above.
After computing the integral, the result will be the volume of the ring-shaped solid that remains.
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Use the information to answer the question. The table shows the amount of lemon juice and water that 4 students mix. Student Luca Kal Jenna Micah Lemon Juice Water (fluid ounces) (fluid ounces) 2 6 4 6 10 8 9 B Which two students mix the same ratio of lemon juice to water? Choose two students to show the answer.
Answers
The two students that mix the same ratio of juice to water is given as follows:
A. Luca.
D. Micah.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is given as follows:
a to b.
Which is also the division of the two amounts.
Hence the ratio of juice to water for each person is given as follows:
Luca: 2/6 = 1/3.Kal: 6/10 = 3/5.Jenna: 4/8 = 1/2.Micah: 3/9 = 1/3.Hence Luca and Micah used the same ratio, meaning that options A and D are correct.
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classify the following set of measurements as accurate, precise, both, or neither. checking for consistency in the weight of chocolate chip cookies: 17.27 g, 13.05 g, 19.46 g, 16.92 g
Answers
The dimensions listed above are thus neither exact nor precise.
In the given question the chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively and we have to classify the following set of measurements as accurate, precise, both, or neither.
It is the "value" that a buyer is prepared to pay for an object, particularly a used or second-hand car; typically, the "real worth" of any used car is a predetermined price tag after determining its value based on its condition and usage.
The chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively. This demonstrates that the weight of chocolate chips is not comparable to their actual worth.
The dimensions listed above are thus neither exact nor precise.
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find the unknown measures. round lengths to the nearest hundredth and angle measures to the nearest degree.
Answers
The unknown measures are from right angle triangle is
KM = 10.68
∠m = 35 and ∠k = 55
Given that
KL =6.2
LM =8.7
KM = x
The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
The triangle that is presented is a right angle triangle.
\(KM^{2}\) = \(LM^{2}\) + \(KL^{2}\)
KM = \(\sqrt{(8.7)^{2} + (6.2)^{2} }\)
KM = \(\sqrt{114.13}\)
KM = 10.68
Now figure out the angles.
∠m = sinm
= P/H
=6.2/10.2
∠m = 35
Again,
∠k = sink
=P/H
= 8.7/10.6
∠k = 55
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To make marbled paper, Shannon filled a rectangular 279/10cm by 178/10cm dish with water. Then they gently swirled paint on top of the water. let a represent the area of the dish.
Select 1 multiplication and 1 division equation to represent the relationship.
choose 2 answers
A) 178/10 x a = 279/10
B) 178/10 x 279/10 = a
C) 279/10 ÷ 178/10 = a
D) a ÷ 178/10 = 279/10
Answers
The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:
a = (279/10) cm x (178/10) cm
Simplifying this expression, we get:
a = 4953/100 cm^2
So, the correct equations are:
B) 178/10 x 279/10 = a
and
D) a ÷ 178/10 = 279/10
Math workshops and final exams: The college tutoring center staff are considering whether the center should increase the number of math workshops they offer to help students improve their performance in math classes. Faculty would like to know if requiring student attendance at these math workshops will improve overall passing rates for their students in their math classes. They plan to use the number of workshops attended to predict the final exam score and regression analysis to determine the effectiveness of the mandatory workshop attendance policy. Which is the response variable?
1. Whether the student attended a workshop.
a. yes.
b. no.
2. Number of workshops attended.
3. Whether the student passes the course.
a. yes.
b. no.
4. Final exam score Correlation.
Answers
Answer:
2. Number of workshops attended.
Step-by-step explanation:
The variable of interest for predicting the final exam score and doing regression analysis is workshop attendance. Therefore, the response variable should be the number of workshops attended by each student.
This also agrees with what the college tutoring center staff are considering, which forms the research question: "should the center increase the number of math workshops they offer to help students improve their performance in math classes?"
Jack is paid £2400 a month.
He spends half his money on rent,
He spends the rest on food, bills and savings in the ratio 3:5:4
How much does he spend on bills?
(I really need help with this) - TYSM if anyone is able to help) :)
Answers
Answer:
300+400+500=1200
Step-by-step explanation:
given total paid $2400
spend $1200 on a rent (half of his paid)
so rest he spend as a ratio of 3:4:5=1200
let x as a amount he using to pays rest of the bills so
3x+4x+5x=1200
12x=1200
x=1200/12
x=100
so he spends 3x=300
4x=400
5x=500
hope it helps you
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The graph to the right is the uniform probability density function for a friend who is x minutes late. (a) Find the probability that the friend is between 10 and 30 minutes late. (b) It is 10 A.M. There is a 20% probability the friend will arrive within how many minutes? part a) what is the probability that the friend is between 10 and 30 minutes late_?
Answers
The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.
Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.
The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.
The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.
Therefore, the probability of the friend being between 10 and 30 minutes late is:
P(10 < x < 30) = (height of rectangle) x (width of rectangle)
= (1/30) x 20
= 2/3
≈ 0.6667
So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.
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Mitchell’s dog is 1/3 as old as Katie’s cat. The sum of their ages is 12 years. How old is Mitchell’s dog?
Answers
Answer:
Mitchell's dog is 3 years old
Step-by-step explanation:
9 x 1/3 = 3
9 + 3 = 12
To solve this I just thought of the multiples of three under 12 that if added to 3 are equal to 12 to find Katie's cat age. The multiples of three under 12 are 3, 6 and 9. It couldn't be 3 and 6+3=9 so it had to be 9. So if Katie's cat is 9, you just multiply 9 by 1/3 or divide it by 3 to find Mitchell's dog age.
Solve 5ax + 3 ax = 4ax + 12 for x. Assume a + 0. A. x= 3a 3 O B. 1 c. F D. X= a a
Answers
So we have to solve the equation:
\(5ax+3ax=4ax+12\)Knowing that a isn't zero. Let's start:
\(\begin{gathered} 5ax+3ax=8ax=4ax+12 \\ 8ax-4ax=12 \\ 4ax=12 \end{gathered}\)Then, since a isn't zero we can divide the right side of the equation by 4a:
\(x=\frac{12}{4a}=\frac{3}{a}\)So correct option is B.
I need to know The value of f(1/2)
Answers
\(\huge\boxed{\textsf{a.)}\ 10}\)
Substitute \(\frac{1}{2}\) for \(x\).
\(f\left(\frac{1}{2}\right)=5\cdot4^\frac{1}{2}\)
Use \(a^\frac{m}{n}=\sqrt[n]{a^m}\).
\(\begin{aligned}f\left(\frac{1}{2}\right)&=5\cdot\sqrt[2]{4^1}\\&=5\cdot\sqrt[2]{4}\\&=5\cdot2\\&=\boxed{10}\end{aligned}\)
Find the volume of the solid.
Answers
Answer:
64cm³
Step-by-step explanation:
( 4 x 4 x 4) cm x cm x cm
4. Amy, Betty and Carol have 96 books altogether. Betty has 6 books less than Amy and Carol has half as many as Betty. How many books does each girl have?
Answers
The Amy has 42 books, Betty has 36 books, and Carol has 18 books.
Let's set up equations to represent the given information:
Let A represent the number of books Amy has.
Let B represent the number of books Betty has.
Let C represent the number of books Carol has.
Let's say Amy has x books.
Betty has 6 books less than Amy, so Betty has (x - 6) books.
Carol has half as many books as Betty, so Carol has (x - 6)/2 books.
According to the problem, the total number of books they have is 96.
So, we can write the equation:
x + (x - 6) + (x - 6)/2 = 96
To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:
2x + 2(x - 6) + (x - 6) = 192
2x + 2x - 12 + x - 6 = 192
5x - 18 = 192
5x = 210
x = 42
Amy has 42 books.
Betty has (42 - 6) = 36 books.
Carol has (36)/2 = 18 books.
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The Problem of the Points. Two players engage in a game. They are equally matched, and the chances of winning a point are the same for each player. The first player to score 10 points wins the $100 stakes. The game is interrupted suddenly when Player A has 7 points and Player B has 5 points. How should the stakes be divided fairly
Answers
Answer:
Player A receives $77.34375 of the sakes
Player B receives $22.65625 of the stakes
Step-by-step explanation:
Given that at the time the game was interrupted, we have;
The number of points player A has = 7 points
The number of points player B has = 5 points
The amount the first player to score 10 points wins = $100
The number of points remaining for player A to win the game = 3
The number of points remaining for player B to win the game = 5
Therefore, the number of trials remaining for a winner to emerge = 3 + 5 - 1 = 7 trials
We take the probability that Player A wins a point as success
We find the likelihood of Plater A winning by using binomial theory as follows;
\(P(S) = \sum\limits_{j=3}^7 \dbinom{7}{3} \cdot \dfrac{1}{2^7} = \dfrac{35}{128} + \dfrac{35}{128} + \dfrac{21}{128} + \dfrac{7}{128} + \dfrac{1}{128} = \dfrac{99}{128}\)
Therefore, given that the likelihood of Player A winning = 99/128
The stakes should be divided such that Player A gets 99/128 share of the stakes while Player B gets 1 - 99/128 = 29/128 share of the stakes
Therefore, Player A gets (99/128) × $100 = $77.34375
Player B gets (29/128) × $100 = $22.65625
To estimate 179% of 41 by rounding, use the expression
.
Using the distributive property, the expression is equivalent to
.
179% of 41 is about
Answers
The estimate of 179% of 41 by rounding is about 73.19.
To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.
Since we are rounding, we round this value to the nearest whole number, which is 73. Therefore, the direct answer is 179% of 41 is about 73.When estimating by rounding, we look at the decimal places. In this case, the hundredth place is 3. Since 3 is less than 5, we round down. Hence, the estimate is 73.19. It is important to note that rounding introduces some degree of error, as the actual value is 73.39. However, for most practical purposes, an estimate provides a close approximation that is quick and easy to calculate.For more similar questions on whole number
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Multiply 3.76 X.2
Show your work
Answers
Answer:
7.52
Step-by-step explanation:
Write it out: 3.76 × 23.76 × 2 = 7.52I hope this helps!
Find the slope of the line passing through (6,8) and (-10,3)
Answers
Answer:
5/16
Step-by-step explanation:
Use the formula to find slope when 2 points are given.
m = rise/run
m = y2 - y1 / x2 - x1
m = 3 - 8 / -10 - 6
m = -5 / -16
m = 5/16
The slope of the line is 5/16.
Answer: m=5/16
Step-by-step explanation:
2. The mean temperature in an area is 74 degrees Fahrenheit. The sum of the temperatures is
2,516. How many temperatures are in the set?
Answers
To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.
Number of temperatures = Sum of temperatures / Mean temperature
In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.
Number of temperatures = 2,516 / 74
Calculating the division:
Number of temperatures ≈ 34.05
Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.
Submit five "starters" for improv. They must be appropriate for school
Answers
Answer:
By "starters" what do you mean?
Find the perimeter of the figure.
O 1610 cm
O162 cm
O116 cm
O 81 cm
Answers
Answer:
162 cm
Step-by-step explanation:
Perimeter =35+35+46+46
=162cm
Perimeter is basically adding up all the sides of the length
What is the value of x? A. 36 B. 12 C. 32 D. 28
Answers
Answer:
the answer is D I hope this helps
Principal = $500 Interest rate =5% Time = 5 years What is the interest earned?
Answers
Answer:
125dollars
Step-by-step explanation:
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Reduce the fraction to lowest terms. Do not use spaces in your answer.
Answers
Answer:
-2x/yz
Step-by-step explanation:
You can cancel out terms using division and properties of exponents. x^a/x^b = x^a-b
Hope that helps a bit.
14 is an integer
True or false?
Answers
Answer:
trueeeeeeee!!!!!!!!!!!
Answer:
Yes, 14 is an integer
Step-by-step explanation:
An integer has to be a whole number, and 14 IS a whole number. So, yes. The answer is true
9. Determine the area of the figure below.
5.5 cm
8 cm
12 cm
6.8 cm
Answers
" Sum of area of Trapezoid and Semicircle "
Lets calculate the area of Trapezoid first ~its " 1/2 times (sum of parallel sides) times (perpendicular distance between them) "
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times ( 8+ 12) \times (5.5)\)
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times (20) \times (5.5)\)
\(\qquad\displaystyle \tt \dashrightarrow \: 10 \times 5.5\)
\(\qquad\displaystyle \tt \dashrightarrow \: 55 \: \: cm {}^{2} \)
Next, area of Semicircle ~\(\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi {r}^{2} }{2} \)
\( \textsf{[ diameter (d) = 8 cm, radius (r) = d/2 = 8/2 = 4 cm ]} \)
\(\qquad\displaystyle \tt \dashrightarrow \: \frac{3.14 \times ( {4)}^{2} }{2}\)
\(\qquad\displaystyle \tt \dashrightarrow \: 1.57 \times 16\)
\(\qquad\displaystyle \tt \dashrightarrow \: 25.12 \: \: cm {}^{2} \)
Now, Area of the composite figure :- Area of Trapezoid + Area of Semicircle
\(\qquad\displaystyle \tt \dashrightarrow \: 55 + 25.12 = 80.12 \: cm²\)