100 POINTS!!! To find the distance AB across a river, a distance BC of 319 m is laid off on one side of the river. It is found that B = 104.6° and C = 14.4°. Find AB.
Answers
Answer: AB = 90.7 meter
Given following:
BC = 319 meterangle B = 104.6°angle C = 14.4°Find angle A :
⇒ 180° - (104.6° + 14.4°)
⇒ 61°
Now, use sine rule:
\(\sf \dfrac{AB}{BC} = \dfrac{sin(C^{\circ })}{sin(A^{\circ \:})}\)
\(\sf \dfrac{AB}{319} = \dfrac{sin(14.4) } {sin(61)}\)
\(\sf AB = \dfrac{319 \ sin(14.4) } {sin(61)}\)
\(\sf AB = 90.70464953 \quad \approx \quad 90.7 \ m \ (rounded \: to \: nearest \ tenth)\)
Related Questions
HELP PLZ IF I DON'T GET THIS RIGHT
Answers
Answer:
The one that you have marked is an improper fraction, the answer is 5/9
A proper fraction is a fraction that is less than one, with a numerator less than the denominator
Answer:
5/9 = \(\frac{5}{9}\)
Step-by-step explanation:
This is the answer because:
1) A proper fraction is a fraction having a lower numerator number than the denominator number.
Ex. 5/9
2) A improper fraction is a fraction having a higher numerator number than the denominator number.
Ex. 9/5
3) A mixed fraction is a fraction that contains whole number and a fraction combined into one mixed number.
Ex. 1 1/2
4) A whole number is a counting number
Ex. 3
Hope this helps!
250 gram as a percentage of 1 kg
Answers
Hey there!
Answer: 25%
\( \rightarrow \: (\sf{ \frac{250}{1000} ) \times 100}\)
\( \rightarrow \: ( \sf{0.25) \times 100}\)
\( \rightarrow \: \sf{ = 25\%}\)
Answer:
25%
Step-by-step explanation:
the quantities must have the same units
1 Kg = 1000 grams
express the quantities as a fraction and multiply by 100%
\(\frac{250}{1000}\) × 100% = 0.25 × 100% = 25%
let y1,y2 be independent random variables both having the uniform(0,1) distribution. re- call that the density function and distribution function of a uniform random variable y
Answers
A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function.
A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. Accordingly, the likelihood of any specific outcome of y is the same, and the likelihood of any range of outcomes is equal to the length of the range. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function. Accordingly, the length of the range multiplied by the likelihood of any specific occurrence yields the cumulative probability of any range of outcomes. Since the likelihood of any specific result in that range is 1 and the range's length is 0.5, for instance, the cumulative probability of 0 y 0.5 is 0.5. Since the likelihood of any given result within that range is still 1, but the range's length is 0.5, the cumulative probability of 0.5 y 1 is 0.75. The chance of any range of outcomes for y1 and y2 if they are independent random variables both having the uniform(0,1) distribution is just the sum of their respective cumulative probabilities.
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Pls help me I’ve been stuck on this question for almost 3 hours
Answers
The perimeter of the triangle is 24 units
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. Similar triangles have the same corresponding angle measures and proportional side lengths.
The perimeter of a triangle is calculated by adding all the sides of the triangle together.
Finding the sides of the triangle ;
10/5= 5+x+1)/x+2
10/5 = 6+x)/x+2
5( 6+x) = 10(2+x)
30 +5x = 20+10x
10 = 5x
x = 2
side AB = x+x+2
= 6
side BC = 10
Side AC = x+6
= 8
Perimeter of the triangle
= a+b+c
= 6+10+8
= 24 units
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help please!!!
13x - 12
B
с
E
(7x-6)
A
F
What is the value of x?
Answers
Answer:
Step-by-step explanation:
The sector of a circle has an area of 104pi/9
square inches and a central angle with measure 65 degree
. What is the radius of the circle, in inches?
Answers
Answer:
Given:
Area of the sector (A) = 104π/9 square inches
Central angle (θ) = 65 degrees
The formula for the area of a sector of a circle is:
A = (θ/360) * π * r^2
We can rearrange this formula to solve for the radius (r):
r^2 = (A * 360) / (θ * π)
Plugging in the given values:
r^2 = (104π/9 * 360) / (65 * π)
r^2 = (104 * 40) / 9
r^2 = 4160 / 9
r^2 ≈ 462.22
Taking the square root of both sides:
r ≈ √462.22
r ≈ 21.49
Therefore, the radius of the circle is approximately 21.49 inches.
Answer: 8 inches
Step-by-step explanation:
A plane flying with a constant speed of 360 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30°. At what rate (in km/h) is the distance from the plane to the radar station increasing a minute later? (Round your answer to the nearest whole number.)
Answers
The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).
To solve this problem, we can use the concepts of trigonometry and related rates.
Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.
Given:
The plane is flying with a constant speed of 360 km/h.
The plane passes over the radar station at an altitude of 1 km.
The plane is climbing at an angle of 30°.
We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.
We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:
sin(30°) = 1/D.
To find dD/dt, we can differentiate both sides of this equation with respect to time:
cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.
Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:
cos(30°) * 0 = -1/D^2 * dD/dt.
We can substitute the known values:
cos(30°) = √3/2,
D = 1 km.
Therefore, we have:
√3/2 * 0 = -1/(1^2) * dD/dt.
Simplifying further:
0 = -1 * dD/dt.
This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.
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Show all relevant steps.
If fire fighters response time to an emergency call is normally distributed with a mean of 9 minutes and a standard deviation of 2 minutes. Determine the percent of emergency calls with a firefighter response time:
(a) Between 7 and 11 minutes (b) Less than 12.2 mins (c) At least 7.8 minutes
Answers
Answer:
Step-by-step explanation:
A
write 819 in base five
Answers
819 in base five is equal to 13134.
Define base five.Base five is a positional numeral system used in mathematics, having 5 as its base or radix. This means that it represents any real number using five different symbols, often the digits 0, 1, 2, 3, and 4. The ones place is represented by the digit on the right, the place of the five by the digit to the left, the twenty-fives place by the digit after that, and so on. Each digit in base five represents a multiple of a power of five.
To write 819 in base five:
Find the largest power of 5 that is less than or equal to 819: 5^4 = 625.Divide 819 by 625 to find how many 5^4's are in 819: 819 / 625 = 1 with a remainder of 194.Write down the result (1) in the 5^4 place (leftmost digit).Repeat steps 1-3 with the remainder (194):
5^3 = 125194 / 125 = 1 with a remainder of 69Write down the result (1) in the 5^3 place (second digit from left).Repeat steps 1-3 with the remainder (69):
5^2 = 2569 / 25 = 2 with a remainder of 19Write down the result (2) in the 5^2 place (third digit from left).Repeat steps 1-3 with the remainder (19):
5^1 = 519 / 5 = 3 with a remainder of 4Write down the result (3) in the 5^1 place (second digit from right).The remainder (4) is less than 5, so write it down in the 5^0 place (rightmost digit).
Combine all the digits: 13134.
Therefore, 819 in base five is equal to 13134.
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Find the intersection of the three sets: A = {–2, 7, 8, 9}, B = {–2, 5, 9}, C = {–2, 5, 9}.
A {–2, 5, 7, 8, 9}
B null set
C {–2, 5, 8, 9}
D {–2, 9}
Answers
High School Geometry
Answers
Answer:
Step-by-step explanation:
310 is the answer.
Select the correct answer.
A figure shows the inscribed triangle ABC with center point O which bisects BO. An angle of C is 50 degrees.
In the diagram,
is a diameter of the circle with center O. If m∠
= 50°, what is m∠
?
A.
50°
B.
40°
C.
80°
D.
100°
Reset Next
Answers
Answer: C
Step-by-step explanation:
Please help!
A basketball has the radius of 13 inches
What is the volume?
Answers
Answer:
9203 in.³
Step-by-step explanation:
V = (4/3)πr³
V = (4/3) × 3.14159 × (13 in.)³
V = 9203 in.³
a student connects a battery to a wire and wraps and wraps the wire around an iron nail to produce an electromagnet. which action should the student take to increase the number of paper clips the electromagnet will pick up?
Answers
By increasing the number of wire turns, using a thicker wire, increasing the battery voltage, and using a soft iron core, the student can enhance the electromagnet's strength, allowing it to pick up more paper clips.
To increase the number of paper clips the electromagnet will pick up, the student should take the following actions:
1. Increase the number of wire turns: By wrapping the wire around the iron nail more times, the student will create a stronger magnetic field. This is because each wire turn generates a magnetic field, and when the turns are in close proximity, their fields add up, creating a stronger overall field.
2. Use a thicker wire: A thicker wire will allow more current to flow through it, which will result in a stronger magnetic field. The higher the current, the more powerful the electromagnet becomes.
3. Increase the voltage of the battery: By increasing the voltage of the battery, the student can cause more current to flow through the wire. This will enhance the magnetic field, making the electromagnet more effective at picking up paper clips.
4. Use a soft iron core: Soft iron materials have higher magnetic permeability than other materials, meaning they can easily be magnetized and demagnetized. When the wire is wrapped around a soft iron nail, the resulting electromagnet will have a stronger magnetic field, thus improving its ability to pick up paper clips.
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for the system shown below what are the coordinates of the solution that lies in quadrant 1 x^2+4y^2=100 4y-x^2=-20
Answers
The coordinates of the solution that lies in quadrant 1 for the given system are (-2, -5).
To find the coordinates of the solution that lies in quadrant 1 for the given system of equations, x^2 + 4y^2 = 100 and 4y - x^2 = -20, we need to solve the equations simultaneously.
Rearranging the second equation, we have x^2 = 4y + 20. Substituting this value of x^2 into the first equation, we get 4y + 20 + 4y^2 = 100.
Combining like terms, we have 4y^2 + 4y - 80 = 0.
Dividing the equation by 4, we obtain y^2 + y - 20 = 0.
Factoring the quadratic equation, we have (y + 5)(y - 4) = 0.
Setting each factor equal to zero, we find y = -5 and y = 4.
Substituting these values of y back into the second equation, we can solve for x.
When y = -5, we get 4(-5) - x^2 = -20, which gives x = -2.
When y = 4, we get 4(4) - x^2 = -20, which has no real solutions.
Therefore, the solution that lies in quadrant 1 is (x, y) = (-2, -5).
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Need some help with algebra
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Answers
Answer:
7 Bags of Popcorn and 8 Bags of Candy
Step-by-step explanation:
Please help if you can, this is due tomorrow.
In the diagram below, $\angle BAC=24^\circ$ and $AB=AC$.
If $\angle ABC=y^\circ$, what is the value of $y$?
[asy]
size(4.25cm);
pair a=(0,cos(pi/15)); pair b=(-sin(pi/15),0); pair c=-b; pair d=c+(1,0);
dot(a); dot(b); dot(c);
draw(c--a--b--c);
draw((2*a+3*b)/5-0.05*(cos(pi/15),-sin(pi/15))--(2*a+3*b)/5+0.05*(cos(pi/15),-sin(pi/15)));
draw((2*a+3*c)/5-0.05*(cos(pi/15),sin(pi/15))--(2*a+3*c)/5+0.05*(cos(pi/15),sin(pi/15)));
label(scale(0.75)*"$24^\circ$",a-(0,0.3),S);
label("$A$",a,N);
label("$B$",b,SSW);
label("$C$",c,S);
label(scale(0.85)*"$y^\circ$",b,NE);
[/asy]
Answers
The given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
What is equation?Equation is a mathematical expression that consists of variables, symbols, and numbers, and shows the relationship between different quantities. An equation can involve one or more unknowns, and can be represented as an equality or as an inequality. Solving an equation requires understanding the relationship between the different elements in the equation, and manipulating the equation to isolate the unknowns. Common types of equations include linear equations, quadratic equations, and polynomial equations.
From this diagram, we can conclude that $\angle ABC$ is an isosceles triangle. This is because the angles opposite equal sides of a triangle must be equal. Since $\angle BAC=24^\circ$, $\angle ABC$ must be $24^\circ$. Furthermore, the sides $AB$ and $AC$ are equal, so $ABC$ is an isosceles triangle.
This conclusion can be verified by using the Pythagorean Theorem. If $AB=AC$, then it follows that $BC = \sqrt{AB^2 + AC^2} = \sqrt{2AB^2}$. Since $AB=3$, it follows that $BC=\sqrt{2*3^2}=6$. Therefore, the triangle $ABC$ is a right triangle with legs of length 3 and hypotenuse of length 6. Since $\angle BAC = 24^\circ$, it follows that $\angle ABC = 24^\circ$, verifying that the triangle is isosceles.
In conclusion, the given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
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Answer:
78
Step-by-step explanation:
Find the geometric mean of 5 and 16.
Answers
Answer:
10.5
Step-by-step explanation:
To find mean, you add all the terms and divide your sum by the number of terms there are. Since the terms are 5 and 16, you would do 5+16=21. Then, since there are two terms, divide 21 by 2 and your mean is 10.5.
The geometric mean of 5 and 16 is √80 ≈ 8.94.
What is Geometric mean?Geometric mean of two or more numbers is defined as the square root of the product of all the numbers.
Simply, if the two numbers are a and b,
Geometric mean of those numbers = √(ab)
Here the given numbers are 5 and 16.
Geometric mean of 5 and 16 = √(5 × 16) = √80 ≈ 8.94
Hence the geometric mean is approximately 8.94.
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Solve for x. 9x + 7 - 3 - 4x = -26
Answers
Starting with the equation:
\(9x+7-3-4x=-26\)Rewrite using the commutative property of addition to bring together similar terms:
\(9x-4x+7-3=-26\)Add like terms on the left hand side of the equation:
\(5x+4=-26\)Substract 4 fom both sides of the equation:
\(\begin{gathered} 5x=-26-4 \\ =-30 \end{gathered}\)Divide both sides by 5:
\(\begin{gathered} x=-\frac{30}{5} \\ =-6 \end{gathered}\)Plug in the value of x=-6 into the original equation to check your answer:
\(\begin{gathered} 9x+7-3-4x=-26 \\ \Rightarrow9(-6)+7-3-4(-6)=-26 \\ \Rightarrow-54+7-3+24=-26 \\ \Rightarrow-26=-26 \end{gathered}\)Therefore:
\(x=-6\)In the figure below, AB is a diameter of circle P.
What is the arc measure of minor arc AC in degrees?
Answers
The arc measure of minor arc AC in degrees is 111 degrees
How to determine the measureTo determine the minor arc is defined as;
From the information given, we have that;
AB is the diameters
the circle is P
Then, we can say that
m<A = m<P + m< C
Substitute the values
We should know that angles on a straight line is 180 degrees
Then, we have that;
180 = 69 + m<C
collect the like terms, we have;
m<C = 180 - 69
Subtract the values, we get;
m<C = 111 degrees
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what is the square root of 1/121
Answers
Answer:
11
Step-by-step explanation:
example 11×11 = 121
therefore squreroots = 11
The pharmacy receives an order for a 1 L bag of 5% Dextrose how many grams of dextrose are in this bag
Answers
50 grams of dextrose are in a 1-litre bag of 5% dextrose.
EquationTo calculate the number of grams of dextrose in a 1-litre bag of 5% dextrose, we need to know the definition of "5% dextrose."
A 5% dextrose solution is a solution that contains 5 grams of dextrose per 100 mL of solution. Therefore, we can calculate the number of grams of dextrose in a 1 litre (1000 mL) bag of 5% dextrose as follows:
5 grams of dextrose per 100 mL of solution = x grams of dextrose per 1000 mL (1 L) of solution
Cross-multiplying, we get:
100 mL x 5 grams of dextrose = 1000 mL (1 L) x grams of dextrose
Simplifying the equation, we get the following:
x = (1000 mL x 5 grams of dextrose) / 100 mL
x = 50 grams of dextrose
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Can someone help find the surface area, then round the answer to the nearest whole number please?
Answers
The Surface Area of cylinders are: 100 yd² , 264 m², 226 mm²
The Surface Area of Can is 219 cm².
We know the formula for Surface Area of Cylinder
= 2πrh
1. Radius = 2 yd
Height = 8 yd
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 2 x 8
= 100 yd²
2. Radius = 7 m
Height = 6 m
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 6 x 7
= 264 m²
3. Radius = 3 mm
Height = 12 mm
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 3 x 12
= 226 mm²
4. Radius = 3.5 cm
Height = 10 cm
So, Surface Area of Can
= 2πrh
= 2 x 3.14 x 3.5 x 10
= 219 cm²
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3 Graph AB with endpoints A(-2,5) and B(4,2) and its image after the composition Reflection: in the line y = x Rotation: 90° about the origin
Answers
The segment A'B' is obtained after reflecting AB over the line y =x (in green)
The segment A''B'' is obtained after rotating A'B' clockwise 90° about the origin
An insurance company claims that in the population of homeowners, the mean annual loss from fire is u-$5000 with a standard deviation of o-$250
distribution of loss is strongly right-skewed: Many policies have $0 loss, but a few have large losses.
If we create a sampling distribution with a sample of 64 homeowners, what is the z-score that corresponds to a sample average of $5100?
Round to four decimals
Type your answer.
1 point
Answers
Answer:
To find the z-score, we use the formula:
z = (x - mu) / (sigma / sqrt(n))
where:
x = sample mean = $5100
mu = population mean = $5000
sigma = population standard deviation = $250
n = sample size = 64
Substituting the values, we get:
z = (5100 - 5000) / (250 / sqrt(64))
z = 2.56
Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).
Step-by-step explanation:
I clicked on the black picture. thought is was the box to enter the answer.
The points (4,10) and (s,0) fall on a line with a slope of 10. What is the value of s?
Answers
Answer:
s = 3
Step-by-step explanation:
Solving
10 = 0 - 10 / s - 410 (s - 4) = -10s - 4 = -1s = 3Answer:
-140
Step-by-step explanation:
What is the constant rate???
Answers
Answer:
The constant rate is 4
Step-by-step explanation:
40 ÷ 10 = 4
80 ÷ 20 = 4
120 ÷ 30 = 4
160 ÷ 40 = 4
They all equal 4 so that is the constant rate.
Brainliest???
PLEASE HELP!! a bag contains 10 marbles. four of them are red, three blue, two white, and one yellow. A mare ke drawn at random. What is the probability that it is blue?
Answers
Answer:
The probability that one marble drawn at random is not blue is 70%
a company that receives the majority of its orders by telephone conducted a study to determing how long customers were willing to wait on hold before ordering a product. The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 3 minutes. What proportion of customers having to hold more than 4.5 minutes will hang up before placing an order 0.51342 0.48658
Answers
Answer:
0.2231 = 22.31% of customers having to hold more than 4.5 minutes will hang up before placing an order
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
\(f(x) = \mu e^{-\mu x}\)
In which \(\mu = \frac{1}{m}\) is the decay parameter.
The probability that x is lower or equal to a is given by:
\(P(X \leq x) = \int\limits^a_0 {f(x)} \, dx\)
Which has the following solution:
\(P(X \leq x) = 1 - e^{-\mu x}\)
The probability of finding a value higher than x is:
\(P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}\)
The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 3 minutes.
This means that \(m = 3, \mu = \frac{1}{3}\)
What proportion of customers having to hold more than 4.5 minutes will hang up before placing an order?
This is:
\(P(X > 4.5) = e^{-\frac{1}{3}*4.5} = e^{-\frac{4.5}{3}} = e^{-1.5} = 0.2231\)
0.2231 = 22.31% of customers having to hold more than 4.5 minutes will hang up before placing an order
Your total monthly bill (T
) from the Electric and Gas Company depends on how much electricity and how much gas you use each month. For every kilowatt hour of electricity (k
) you use, you are charged $0.25
and for each therm (t
) of gas used you are charged $0.97
.
Which of the following equations represents the relationship between electricity and gas used and your bill?
Answers
The equation representing the relationship between Electricity and Gas used, and your Bill is:
T = 0.25 * k + 0.97 * t
Step-by-step explanation:
Make a plan:
We need to find the equation that represents the relationship between the total monthly bill (T), The Kilowatt Hours of Electricity used (k), and the Terms of Gas used (t).
T = 0.25 * k + 0.97 * t
Solve the problem:
1 - Write the Equation for the cost of Electricity:
0.25 * k
2 - Write the Equation for the Cost of Gas:
0.97 * t
3 - Combine the Equations to Represent the total Monthly Bill (T):
T = 0.25 * k + 0.97 * t
Draw the Conclusion:Hence, The equation representing the relationship between Electricity and Gas used, and your Bill is:
T = 0.25 * k + 0.97 * t
I hope that helps!