Find the value of x.
In the figure of circle provided. the value of x is
161 degreesHow to find the value of xIn a circle, equal chords subtends equal arc length.
In the problem it was given that:
chord SU is equal to chord ST hence we have that
x + x + 38 = 360 (angle in a circle)
collecting like terms
2x + 38 = 360
2x = 360 - 38
2x = 322
Isolating x by dividing both sides by 2
2x / 2 = 322 / 2
x = 161
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Help me find the slope of the line and it’s ok if you don’t know all of them
Slope of each graph are [tex]\frac{6}{5}[/tex],[tex]\frac{-1}{3}[/tex] and 1 respectively.
What is a Slope?Slope of a line in mathematics is defined as the ratio of the change in the y coordinate w.r.t the change in the x coordinate.
Both the change in the y-coordinate and the net change in the x-coordinate are denoted by y₂-y₁ and x₂-x₁, respectively.
Thus, the formula for the change in y-coordinate with regard to the change in x-coordinate is
m=y₂-y₁/ x₂-x₁
In the figure 1Taking two points as per observation
Point1: (x₁ y₁)=(0,-3)
Point2:(x₂, y₂)=(5/2,0)
Slope of line=y₂-y₁/ x₂-x₁
=[tex]\frac{0+3}{5/2-0}[/tex]
=[tex]\frac{6}{5}[/tex]
In the figure2Taking two points as per observation
Point1: (x₁ y₁)=(0,3)
Point2:(x₂, y₂)=(2,2)
Slope of line=y2-y1/x2-x1
=[tex]\frac{2-3}{2-0}[/tex]
=-⅓
In the figure 3Taking two points as per observation
Point1: (x₁ y₁)=(-2,0)
Point2:(x₂, y₂)=(0,2)
Slope of line=y2-y1/x2-x1
=[tex]\frac{2-0}{0+2}[/tex]
=1
Hence, Slope of each graph are 6/5,-⅓ and 1 respectively.
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math help needed detailed explanation
The percentage of 8th graders who send more than 50 texts is 56.15%
How to find the percentage?Here we want to find the percentage of eight grades who send more than 50 texts, and to get that we need to use the values in the table.
The formula for that percentage is:
P = 100%*(number that send more than 50 texts)/(total number)
On the table we can see that the total number of 8th gradesr is 130, and the number that send more than 50 messages is 73, then the percentage is:
P = 100%*(73/130)
P = 56.15%
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If Julie drives from york to Corby via Dorby how many miles will she have driven?
The answer to this question is 289 miles. The sum of 89 + 73 + 127 is 289, so Julie will have driven a total of 289 miles.
What is sum?Sum is the total of two or more numbers added together. It is a mathematical operation used to find the aggregate of two or more numbers or amounts. Sum is calculated by adding the numbers together to get the total.
This is because Julie will be driving a total of 89 miles from York to Derby, then 73 miles from Derby to Corby, for a total of 162 miles. She will then have to drive 127 miles from Derby back to York, giving a total of 289 miles.
Once these distances are determined, the total number of miles is simply the sum of the three distances. The sum of 89 + 73 + 127 is 289, so Julie will have driven a total of 289 miles.
To further illustrate this answer, it can be thought of as a triangle, where each location is a vertex and the lines connecting them are the distances between the locations.
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a box contains 4 white and 6 red chips. one chip is drawn at random and, without looking at its color, is discarded. a second chip is then drawn and the color is recorded. a. what is the probability that the second chip drawn is red?
The probability that the second chip drawn is red is 1/3.
The probability of drawing a red chip on the first draw is 6/10, or 3/5. After one chip is discarded, there are 9 chips remaining, 3 of which are red. So the probability of drawing a red chip on the second draw, given that a chip has already been discarded, is 3/9, or 1/3.
Therefore, the probability that the second chip drawn is red is 1/3. This is because the first chip drawn could be either white or red, so there are two possible scenarios. If the first chip drawn is white, there will be 6 red chips and 3 white chips left, so the probability of drawing a red chip on the second draw will be 6/9 or 2/3. If the first chip drawn is red, there will be 5 red chips and 4 white chips left, so the probability of drawing a red chip on the second draw will be 5/9. To get the overall probability of drawing a red chip on the second draw, we need to take the average of these two probabilities, weighted by the probability of the first chip being white or red, respectively.
The probability of the first chip being white is 4/10, or 2/5, and the probability of the first chip being red is 6/10, or 3/5. So the overall probability of drawing a red chip on the second draw is
(2/5) x (2/3) + (3/5) x (5/9) = 4/15 + 1/3 = 3/9 = 1/3.
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Elyse has a gift card to a local movie theater. the graph shows the amount of money remaining on her gift card based on the number of movies she has seen.
a. write an equation to represent the situation.
b. interpret the slope and y-intercept in the context of the situation.
a. The equation to represent the situation is y = -12x + 120, where x is the number of movies and y is the amount of money remaining on the gift card.
What is money?Money is a medium of exchange that is widely accepted as a way to pay for goods and services or to settle debts. Money also serves as a store of value, providing a way for people to save for the future. Money is generally created through government-backed fiat currencies, such as the U.S. dollar, which are issued and regulated by central banks. Money can also be created in the form of crypto-currencies, such as Bitcoin, which are not issued by any single government or central bank. Money is essential for economic growth and stability, as it allows for efficient exchanges of goods and services. Money can also be a source of financial security, providing people with a way to manage their finances and plan for the future.
b. The slope of -12 indicates that for every movie that Elyse sees, she will spend $12 from her gift card. The y-intercept of 120 indicates that if Elyse has not seen any movies, she will have $120 remaining on her gift card.
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The situation is,
a) The line equation is [tex]y = -3x - 6[/tex]
b) The line's y-intercept is -6, which indicates that when the amount of movies x = 0 , the amount on gift y = -6
c) The slope of the line is -3, indicating that as the number of movies x increases, the rate of change of the amount on the gift is declining.
What is an Equation of a line?a). The equation provides the line's slope.
Slope,
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Changing the numbers indicated in the slope equation,
Slope,
[tex]m=\frac{(6-12)}{(4-2)}[/tex]
Slope m = -6/2
Slope m = -3
The slope is -3
The equation of the line is,
[tex]y - y_1 = m ( x - x_1 )[/tex]
Substitute the given values in the equation,
[tex]y - 12 = -3 ( x - 2 )[/tex]
Simplify the equation,
[tex]y - 12 = -3x + 6[/tex]
Adding 12 on both sides
[tex]y = -3x - 6[/tex]
The equation of line is [tex]y = -3x - 6[/tex]
b). The y-intercept of the equation of line [tex]y = -3x - 6[/tex] is [tex]-6[/tex], when [tex]x=0[/tex]
c). The slope of the line [tex]y = -3x - 6[/tex] is [tex]m = -3[/tex] and the value is decreasing
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The completr question and graph attached below,
c. What is the slope, and what does it mean in the context of the situation?
julie the jeweler has two gold necklaces worth $105, seven silver necklaces valued at $100, twenty-seven plated necklaces valued at $55, and twenty-two beaded necklaces worth $25. what is the average value of a necklace at julie's shop? express your answer rounded to the nearest cent.
The average value of a necklace at Julie's shop is $4.90. For further explanation;-
Julie the jeweler has two gold necklaces worth $105, seven silver necklaces valued at $100, twenty-seven plated necklaces valued at $55, and twenty-two beaded necklaces worth $25. The average value of a necklace at Julie's shop can be calculated by finding the sum of the values of all the necklaces and dividing it by the total number of necklaces.
The total value of all the necklaces is $105 + $100 + $55 + $25 = $285. The total number of necklaces is 2 + 7 + 27 + 22 = 58.
Therefore, the average value of a necklace is $285 / 58 = $4.90. This answer should be rounded to the nearest cent, giving an average value of $4.90 per necklace at Julie's shop.
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Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one eighth to create polygon A′B′C′D′. If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′.
A′(3.5, −5.25), B′(1.75, −1.75), C′(−3.5, 1.75), D′(−3.5, −3.5)
A′(3.2, −4.8), B′(1.6, −1.6), C′(−3.2, 1.6), D′(3.2, 3.2)
A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5)
A′(−12, 14), B′(−10, 10), C′(12, −14), D′(12, 12)
The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).
What is Dilation:In geometry, dilation is a transformation that changes the size of a figure but not its shape. It is a type of similarity transformation.
When a figure is dilated, each point of the figure moves away or towards the center of dilation by a certain scale factor.
Here we have
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one-eighth to create polygon A′B′C′D′.
To dilate polygon ABCD using a scale factor of one-eighth i.e 1/8 multiply the coordinates of each vertex by the scale factor of 1/8.
The coordinates of A are (-4, 6), multiply each coordinate by 1/8
A' = (-4/8, 6/8) = (-1/2, 3/4) = (-0.5, 0.75)
The coordinates of B are (-2, 2), multiplying each coordinate by 1/8
B' = (-2/8, 2/8) = (-1/4, 1/4) = (-0.25, 0.25)
The coordinates of C are (4, -2), multiplying each coordinate by 1/8
C' = (4/8, -2/8) = (1/2, -1/4) = (0.5, - 0.25)
The coordinates of D are (4, 4). Multiplying each coordinate by 1/8
D' = (4/8, 4/8) = (1/2, 1/2) = (0.5, 0.5)
Therefore,
The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).
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I need help with this question
The value of the sides are;
h = 2√3
c = 4√2
How to determine the valueTo determine the value, we need to note that the trigonometric identities are represented with the fraction;
sin θ = opposite /hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the diagram shown, we have that;
Using the sine identity
sin 60 = 3/h
Now, cross multiply the values, we have;
h = 3/sin 60
find the sine value
h = 3/√3/2
divide the values
h = 6√3/3 = 2√3
For the second triangle.
sin 45 = 4/c
cross multiply
c = 4/1/√2
c = 4√2
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Answer:
[tex]h = \boxed{2\sqrt{3}}\\\\c = \boxed{4\sqrt{2}}[/tex]
Step-by-step explanation:
We can use the law of sines to determine the sides indicated
Law Of Sines
The ratio of the sides of a triangle to the sine of the angle opposite to that side is the same for all sides
In the triangle on the leftwe have side of length 3 opposite 60° and side of length h opposite 90°
So
[tex]\dfrac{h}{\sin 90} = \dfrac{3}{\sin 60}\\[/tex]
sin 90 = 1
[tex]\sin 60 = \dfrac{\sqrt{3}}{2}[/tex]
Therefore we get
[tex]\dfrac{h}{1} = \dfrac{3}{\dfrac{\sqrt{3}}{2}}\\\\h = 3 \times \dfrac{2}{\sqrt{3}}\\\\h = \dfrac{6}{\sqrt{3}}\\\\[/tex]
Rationalizing the denominator by multiplying by √3 we get
[tex]h = \dfrac{6\sqrt{3}}{3} = \boxed{2\sqrt{3}}[/tex]
(Answer)
-----------------------------------------------------------------------------------------
For the triangle on the right we have
[tex]\dfrac{c}{\sin 90} = \dfrac{4}{\sin 45}\\\\\sin 90 = 1\\\sin 45 = \dfrac{1}{\sqrt{2}}\\\\c = \dfrac{4}{\dfrac{1}{\sqrt{2}}}\\\\c = 4 \times \sqrt{2}\\\\c = \boxed{4\sqrt{2}}[/tex]
(Answer)
-----------------------------------------------------------------------------------------
In the both above computations we are using the fact that dividing by a fraction involves flipping the denominator fraction and multiplying
The angle of elevation to an airplane viewed from the air traffic control tower is 7 degrees. The tower is 200 feet tall, and the plane is at an altitude of 5127 feet. How far is the plane from the air traffic control tower?
The plane is approximately 44,197 feet away from the air traffic control tower.
What does elevation angle mean?An illustration of an angle of elevation
Between the horizontal line and the line of sight, an angle called the angle of elevation is created. When the line of sight is upward from the horizontal line, an angle of elevation is created.
Trigonometry can be used to resolve this issue. Let's illustrate:
P (plane)
/|
/ |
/ | h = altitude of plane = 5127 ft
/ |
/ θ |
T-----X
d = ?
In the illustration, T stands for the air traffic control tower, P for the aircraft, for the angle of elevation, X for the location on the ground directly beneath the aircraft, and d for the desired distance.
We can see that the tower, the spot on the ground just beneath the plane, and the actual plane itself make up the right triangle TPX. The triangle's opposite and adjacent sides can be related to the angle by using the tangent function:
tan θ = h / d
where d is the desired distance and h is the plane's altitude.
To find d, we can rearrange this equation as follows:
d = h / tan θ
Inputting the values provided yields:
d = 5127 feet / 7° of tan
Calculating the answer, we obtain:
d ≈ 44,197 ft
Thus, the distance between the aircraft and the air traffic control tower is 44,197 feet.
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A 3 3/4 feet is cut from a 10 feet plywood how much of the plywood is left
[tex]3\frac{3}{4}[/tex] feet is 2.25 feet. 7.75 feet of plywood left out of 10 feet when [tex]3\frac{3}{4}[/tex] feet of plywood is cut off.
[tex]3\frac{3}{4}[/tex] feet is a mixed fraction, first we need to convert it into a fraction and then we need to find the point value of the number.
therefore [tex]3\frac{3}{4}[/tex] feet = 3 x 3 / 4
= 3 x 0.75 = 2.25 feet
now we need to find the plywood left when [tex]3\frac{3}{4}[/tex] feet is cut from 10 feet,
therefore, now that we know [tex]3\frac{3}{4}[/tex] feet is 2.25 feet we can subtract it from 10 we get:
10 - 2.25 = 7.75
therefore, we know that there is 7.75 feet of plywood left out of 10 feet when [tex]3\frac{3}{4}[/tex] feet of plywood is cut off.
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I need the answer help pls
Answer:
Step-by-step explanation:
what is the area of the composite figure to the nearest square centimeter?
Based on the information in the image, we can infer that the surface area is 863.5cm³.
How to find the surface of the figure?To find the surface of the figure we must divide the figure in two, into the cone and the cylinder and find the surface of each one separately and then add it.
Cylinder surface area:
To calculate the surface area of a cylinder we must apply the following formula:
[tex]A = 2\pi r h ++ 2 \pi r^{2} \\A = 2 * \pi * 5 * 15 + 2 * \pi * 5^{2} \\A = 471 + 157\\A = 628cm^{3}[/tex]
Cone surface area:
[tex]A = \pi rh + \pi r^{2} \\A = \pi * 5 * 10 + \pi * 5^{2} \\A = 157 + 78.5 \\A = 235.5 cm^{3}[/tex]
Surface area of the entire figure:
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Ross is trying to make the target number 10. Using the numbers 6,7,8, and 9, how can ross make an equation out of those numbers that equals 10? Each number can be used only once, in any order, with any operations
One possible equation Ross can make is 9 - 7 + 8 = 10
Ross is given the numbers 6, 7, 8, and 9, and is asked to make an equation that equals 10. The equation can use each number only once, and can use any arithmetic operations (such as addition, subtraction, multiplication, and division) in any order.
One way Ross can approach this problem is to first think about what pairs of numbers can be combined to make 10. Ross could quickly see that there are no pairs of numbers that add up to 10, since the highest pair is 8 + 9 = 17.
Next, Ross could think about using subtraction or division to create a 10. However, there are no pairs of numbers that can be subtracted or divided to get 10 either.
Therefore, Ross needs to use a combination of addition, subtraction, and/or multiplication to create an equation that equals 10.
One possible equation Ross can make is:
9 - 7 + 8 = 10
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What is fifteen divided by two hundred and eighty nine?
15 divided by 289 is approximately equal to 0.0519 or 519/10000. Fifteen divided by two hundred and eighty nine is a division problem that involves dividing 15 by 289. To solve this problem, we can use long division or a calculator.
Using long division, we start by dividing the first digit of the dividend (2) by the divisor (15). Since 2 is less than 15, we add a decimal point and a zero to the dividend and continue the process. We bring down the next digit (8) and divide 28 by 15, which gives us a quotient of 1 with a remainder of 13. We add a decimal point after the quotient and bring down the next digit (9) to get 139 as the new dividend. We divide 139 by 15, which gives us a quotient of 9 with a remainder of 4. We add a decimal point after the quotient and bring down the last digit (0) to get 40 as the new dividend. We divide 40 by 15, which gives us a quotient of 2 with a remainder of 10. Finally, we add a decimal point after the last quotient and write the remainder as a fraction over the divisor to get the final answer:
15 divided by 289 is approximately equal to 0.0519 or 519/10000.
In summary, fifteen divided by two hundred and eighty nine is a division problem that can be solved using long division or a calculator. The answer is a decimal or a fraction, depending on how the division is carried out.
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Yeidalis needs three pieces of wood as shown to create a new work of art. The pieces of wood she is going to use are sold in 15-inch-wide boards. What is the minimum length board that Yeidalis must buy in order to have enough to complete her artwork?
The longest piece of wood we need is the bottom left piece, which requires a board of at least 15 inches in length
How to determine the minimum length board that Yeidalis must buy in order to have enough to complete her artworkBased on the dimensions provided in the image, we can see that Yeidalis needs a board that is at least as long as the longest piece of wood required.
The longest piece of wood required is the diagonal of the rectangle with dimensions 12 inches and 9 inches.
Using the Pythagorean theorem, we can calculate the length of this diagonal as:
sqrt(12^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15 inches
So Yeidalis needs a board that is at least 15 inches long to create her artwork.
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we learned in exercise 3.25 that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. we now consider a random sample of fifty 18-20 year olds. a) how many people would you expect to have consumed alcoholic beverages? do not round your answer.
Rounding off the value of X to the nearest whole number, we get that approximately 35 people would be expected to have consumed alcoholic beverages among 50 randomly selected 18-20 year-olds.
In exercise 3.25, it was learned that about 69.7% of 18-20 year-olds consumed alcoholic beverages in 2008.
Now, consider a random sample of fifty 18-20 year-olds.
It is required to calculate the number of people who would be expected to have consumed alcoholic beverages.
Let X be the number of people who have consumed alcoholic beverages out of 50 randomly selected 18-20 year-olds.
Let p be the proportion of 18-20 year-olds who consumed alcoholic beverages in 2008.
Therefore, the sample proportion is given as \hat{p}
Hence, p=0.69 \hat{p}=X/50
Now, by the properties of the sample proportion, E(\hat{p})=p
Therefore,
E(\hat{p})=E(X/50)
Thus, p=E(X/50) Or, X=50p
Substituting the value of p, we have
X=50(0.697)=34.85
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find a basis for the subspace of consisting of all vectors such that . hint: notice that this single equation counts as a system of linear equations; find and describe the solutions. answer:
A basis for the subspace of all vectors satisfying the equation x + y + z = 0 is {(-1, 0, 1), (0, 1, -1)}.
SOLUTION:
A basis for the subspace of all vectors (x, y, z) satisfying the single equation x + y + z = 0 can be found by solving this system of linear equations.
Step 1: Choose two variables to express in terms of the remaining variable.
Let's express x and y in terms of z. From the given equation, we get:
x = -y - z
y = -x - z
Step 2: Choose two independent vectors that satisfy the equations.
We can choose two independent vectors by setting z = 1 and z = -1:
When z = 1:
x = -y - 1
y = -x - 1
Let y = 0, then x = -1, so one vector is (-1, 0, 1).
When z = -1:
x = -y + 1
y = -x + 1
Let x = 0, then y = 1, so the other vector is (0, 1, -1).
Therefore, a basis for the subspace of all vectors satisfying the equation x + y + z = 0 is {(-1, 0, 1), (0, 1, -1)}.
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One - third of a number y is 14.
Answer:
42
Step-by-step explanation:
Answer:
Step-by-step explanation:
If one-third of a number y is 14, we can express this mathematically as:
1/3 y = 14
To solve for y, we can isolate y on one side of the equation by multiplying both sides by 3:
1/3 y * 3 = 14 * 3
Simplifying, we get:
y = 42
Therefore, the number is 42.
In circle R with the measure of minor arc
QS= 120°, find m/QTS.
Answer:180
Step-by-step explanation:
in practice, the most frequently encountered hypothesis test about a population variance is a .
In practice, the most frequently encountered hypothesis test about a population variance is an F-test.
In statistics, hypothesis tests provide us with a tool to evaluate evidence about a population. Hypothesis testing is a crucial part of statistical inference, in which an analyst tests hypotheses using statistical methods such as t-tests, chi-squared tests, and analysis of variance (ANOVA).
In practice, the most commonly used hypothesis test for population variance is the F-test. This test can be used to test the null hypothesis that two population variances are equal. F-tests have a wide range of uses, including in quality control, financial analysis, engineering, and more. The F-test statistic is calculated by dividing the sample variance of one sample by the sample variance of another sample. The F-test requires that the data come from populations that follow normal distributions, and it is sensitive to outliers in the data.
Therefore, in practice, the most frequently encountered hypothesis test about a population variance is an F-test.
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.
The rate of the jetstream is 300 mph traveling with the jetstream an airplane can fly 3000 miles in the same amount of time as it takes to fly 1000 miles against the jetstream. What is the airplanes, average rate in calm air?
The airplane's average rate in calm air is 600 mph.
What is an average?
In mathematics, the average is a measure of the central tendency of a set of numerical values, which is computed by adding all the values in the set and dividing them by the total number of values. The average is also known as the mean, and it is one of the most commonly used measures of central tendency in statistics
Let's denote the airplane's average rate in calm air by x mph.
When the airplane is flying with the jetstream, its ground speed (speed relative to the ground) is x + 300 mph. We know that it can fly 3000 miles in the same amount of time it takes to fly 1000 miles against the jetstream, so we can set up the following equation:
3000 / (x + 300) = 1000 / (x - 300)
We can cross-multiply to simplify:
3000(x - 300) = 1000(x + 300)
Expanding the brackets gives:
3000x - 900000 = 1000x + 300000
Simplifying and rearranging terms gives:
2000x = 1200000
x = 600
Therefore, the airplane's average rate in calm air is 600 mph.
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Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if
The distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.
Describe Distance?Distance can be calculated using a variety of methods, depending on the context. For example, the distance between two points in a straight line can be calculated using the Pythagorean theorem in two dimensions or the distance formula in three dimensions. In more complex situations, such as when the two points are not in a straight line, distance may be calculated using other mathematical methods or by estimating the distance based on contextual information.
Distance is often used in everyday life to describe how far apart objects or locations are from each other, such as the distance between two cities, the distance from home to work, or the distance between two landmarks. It is also used in many scientific fields to describe the separation between celestial objects, the distances traveled by particles in a chemical reaction, or the distances between neurons in the brain.
We can solve this problem using the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C:
a/sin A = b/sin B = c/sin C
Let's label the distance from point A to the boat as a, the distance from point B to the boat as b, and the distance from point C to the opposite bank as c. We are given that AB = 50 meters, angle ABC = 68 degrees, and angle BCA = 73 degrees. We want to find a and b.
First, we can find the measure of angle ACB by using the fact that the sum of angles in a triangle is 180 degrees:
angle ACB = 180 - angle ABC - angle BCA
angle ACB = 180 - 68 - 73
angle ACB = 39 degrees
Next, we can use the Law of Sines to find a and b:
a/sin 68 = c/sin 39
b/sin 73 = c/sin 39
Solving for c in both equations gives:
c = a sin 39 / sin 68
c = b sin 39 / sin 73
We can set these two equations equal to each other and solve for b:
a sin 39 / sin 68 = b sin 39 / sin 73
b = a (sin 39 / sin 73) * (sin 68 / sin 39)
b = a (sin 68 / sin 73)
We know that a + b = 50, so we can substitute the expression for b into this equation:
a + a (sin 68 / sin 73) = 50
Solving for a gives:
a = 50 / (1 + sin 68 / sin 73)
a ≈ 23.3 meters
Substituting this value of a into the expression for b gives:
b ≈ 26.7 meters
So the distance from point A to the boat is approximately 23.3 meters, and the distance from point B to the boat is approximately 26.7 meters, rounded to the nearest foot.
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The complete question is
Two landing points, A and B, lie on the straight bank of a river and are separated by 50 meters. Find the distance from each landing point to a boat pulled ashore on the opposite bank at a point C if angle ABC=68 degree and angle BCA=73 degree. Round to the nearest foot.
Work out the length of side BC in each triangle
Give your answers correct to 3 significant figures
In triangle ABC as per given measurements the measure side length BC is equal to 7.26cm (Rounding to three significant figures).
In triangle ABC,
Measure of angle A = 36 degrees
Measure of angle B = 90 degrees
length of AB = 8.7cm
Use trigonometry to solve for the length of BC.
First, Measure of angle C,
In triangle ABC,
Measure of (Angle A + Angle B + Angle C ) = 180
⇒ 36 + 90 + Measure of angle C = 180
⇒ Measure of angle C = 54 degrees
Now , use the sine function to solve for BC,
sin(C) = opposite side /hypotenuse
Substitute the values we have,
⇒ sin(54) = BC/AB
⇒BC = AB × sin(54)
⇒ BC = 8.7 × 0.834
⇒ BC = 7.2558
Rounding to three significant figures, we get,
BC ≈ 7.26 cm.
Therefore, the measure of length BC in triangle ABC is equal to 7.26cm.
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The above question is incomplete, the complete question is:
ABC is a right-angled triangle. Angle B = 90. Angle A = 36. AB = 8.7 cm. Work out the length of BC. Give your answer correct to 3 significant figures.
Which expression was factored completely using the GCF, if the original expression was
16x² + 8x?
4(4x²+2x)
4x(4x+2)
8(2x²+x)
8x(2x+1)
Answer:
It's D
Step-by-step explanation:
[tex]1. \: gcf = 8x \\ 2. \: 8x( \frac{16x {}^{2} }{8x} + \frac{8x}{8x} ) \\ 3. \: 8x(2x + 1)[/tex]
GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
Answer:
x>7
Step-by-step explanation:
The circle is open so seven is not included which eliminates the second and fourth choice.
x<7 means x is less than seven which is wrong.
x> means x is greater than seven.
Answer:
x > 7
Step-by-step explanation:
We see that the arrow is going to the right, signaling greater than.
We know that it is not greater than or equal to, since the dot is not shaded.
So, the answer is x > 7.
Kim's hourly wage is $14. She works 37 hours per week. What is her monthly income?
Answer:
2072
Step-by-step explanation:
Multiply 14 x 37
518 x 4
2072
Answer: $2,072 a month
Step-by-step explanation:
multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply 518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072
A dental student is conducting a study on the number of people who visit their dentist regularly. Of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year.Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n=60.Round all answers to 3 decimal places.p=Up=Op=
Answer:
Step-by-step explanation:
312/520 equals 60%
other people 40%
z score of 0.28 and corresponding z score
Step-by-step explanation:
Mathematics for Social Science 1011 PDF
in the inspection of tin plate by continous electrolytic process, .15 imperfections are spotted on one minute average. find the probability that three imperfection plates are spottwd in three minutes
The probability of spotting 3 imperfections plates in 3 minutes is .3352.
The probability of spotting 3 imperfections plates in 3 minutes can be calculated using the binomial probability formula. This formula is used to calculate the probability of getting a certain number of successes in a certain number of trials (n), given a certain probability of success (p) for each trial.
In this case, the probability of success (p) is .15 and the number of trials (n) is 3. The formula for this is:
[tex]P(X = 3) = 3C3(.15)^3(1-.15)^(3-3)[/tex]
P(X = 3) = .3352
Therefore, the probability of spotting 3 imperfections plates in 3 minutes is .3352.
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