The scale ratio for this map is 0.0000063.
What is scale ratio?
Scale ratio is the ratio between the measurements of an object or distance on a map or drawing and the actual measurements of the object or distance it represents in real life. It allows us to compare and relate the sizes or distances of objects in a drawing or map to their actual sizes or distances in the real world.
The scale ratio can be found by dividing the distance on the map by the corresponding distance in reality:
scale ratio = distance on map / distance in reality
In this case, the distance from Wellspring to Red Creek is 4 inches on the map and 10 miles in reality. So the scale ratio is:
scale ratio = 4 inches / 10 miles
To simplify this ratio, we need to convert the units so that they are the same. Let's convert inches to miles:
1 mile = 63,360 inches
So, we can convert the inches on the map to miles as follows:
4 inches * (1 mile / 63,360 inches) = 0.000063 miles
Now we can rewrite the scale ratio as:
scale ratio = 0.000063 miles / 10 miles
Simplifying this ratio by canceling out the units of miles, we get:
scale ratio = 0.0000063
Therefore, the scale ratio for this map is 0.0000063.
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a drug company has developed a test to detect steroid use by athletes. the test is accurate 95% of the time when the athlete took steroids and 97% of the time when the athlete did not take steroids. we know that 10% of the athletes tested a certain day have taken steroids. if we know the test is accurate what is the probability that they did not take steroids.
The probability that an athlete who tests negative actually did not take steroids is approximately 0.926 or 92.6%.
How to find the probability of athlete that they did not take steroids?Let's assume that 100 athletes were tested that day. Of these, 10 are expected to have taken steroids, and 90 are expected to have not taken steroids.
Of the 10 athletes who took steroids, the test is accurate 95% of the time, so 9 of them are expected to test positive for steroids, and 1 is expected to test negative.
Of the 90 athletes who did not take steroids, the test is accurate 97% of the time, so 87 of them are expected to test negative for steroids, and 3 are expected to test positive.
Therefore, out of the 100 athletes tested, a total of 90 + 1 + 3 = 94 are expected to test negative for steroids.
Since we know that the test is accurate, the probability that an athlete who tests negative actually did not take steroids is:
(Probability that athlete did not take steroids and tested negative) / (Probability of testing negative)
= 87 / 94
= 0.9255 (rounded to four decimal places)
Therefore, the probability that an athlete who tests negative actually did not take steroids is approximately 0.926 or 92.6%.
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PLEASE HELP AND SHOW YOUR WORK! ALSO EXPLAIN HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST!
Answer:3.6
Step-by-step explanation:
Step 1: Calculate
We calculate the square root of 13
√13 = 3.60555127546399
Step 2: simplify
Reduce the tail of the answer above to two numbers after the decimal point which is :
3.60
Step 3: Round
Round 3.60 so you only have one digit after the decimal point to get the answer:
3.6
Ok, so I have a test on equations of circles in 2 days, so I need help with some of the lessons. The main lesson I'm VERY confused about is general forms and standard forms and how to convert them. The formula that I was given for general form was:
x^2+y^2+Dx+Ey+F=0
and the formula for standard form was:
(x-h)^2+(y-k)^2=r^2
I need help understanding how to go from general form to standard form when you don't have all the variables in the general form equation.
FYI, from the standard form, I also need to know how to go back to general form. If someone can give me an example, that would be great! Worth 50 points, will mark brainliest.
The explanation of how to convert a general form equation to a standard form equation is given below:
How to solveLet's first look at how to convert a general form equation to a standard form equation. Given a general form equation:
x^2 + y^2 + Dx + Ey + F = 0
Complete the square for both x and y:
a. Divide the coefficients D and E by 2, and square the results. Let's call these values Cx and Cy:
Cx = (D/2)^2
Cy = (E/2)^2
b. Add and subtract Cx and Cy on both sides of the equation:
x^2 + Dx + Cx + y^2 + Ey + Cy = -F + Cx + Cy
Rearrange the equation to form the standard form equation:
a. Group the x and y terms and rewrite as perfect squares:
(x + D/2)^2 + (y + E/2)^2 = -F + Cx + Cy
b. Now, compare this to the standard form equation:
(x - h)^2 + (y - k)^2 = r^2
c. Identify the values of h, k, and r:
h = -D/2
k = -E/2
r^2 = -F + Cx + Cy
Now let's see how to convert a standard form equation to a general form equation. Given a standard form equation:
(x - h)^2 + (y - k)^2 = r^2
Expand the squares:
(x^2 - 2hx + h^2) + (y^2 - 2ky + k^2) = r^2
Rearrange the equation to form the general form equation:
x^2 + y^2 - 2hx - 2ky + h^2 + k^2 - r^2 = 0
Compare this to the general form equation:
x^2 + y^2 + Dx + Ey + F = 0
Identify the values of D, E, and F:
D = -2h
E = -2k
F = h^2 + k^2 - r^2
Now you can convert equations between the general form and the standard form. If you're missing some variables in the general form equation, just treat them as zero and proceed with the same steps.
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Which of these expressions are equivalent to p/3
Answer:
B) 3p/9
D)1/3p
Step-by-step explanation:
6. ____ tales and _____ tales
folk tales are storues with no known creator. they were originally passed down from one generation to another by word of mouth.
fairytales were often created to teach children behavior in an entertaining way.
what is the blank fictions/nonfictions?
The complete statement is folk tales and fairy tales
Both folk tales and fairy tales are types of fiction because they are imaginative stories that are not based on factual events or characters.
Explaining fictions and nonfictions?Folk tales
Folk tales are stories with no known creator. They were originally passed down from one generation to another by word of mouth. Folk tales are a type of traditional literature that is deeply rooted in the culture of a particular region or community.
They often feature supernatural elements, and their origins can be traced back many centuries.
Because they were passed down orally, different versions of the same tale may have developed in different regions, with variations in characters, plot, and theme.
Fairy tales
Fairy tales were often created to teach children behavior in an entertaining way. Fairy tales are a type of story that typically features magical creatures or events and often have a moral or lesson to teach. They were originally intended for both adults and children and were used as a way to teach moral values, societal norms, and important life lessons in an entertaining way.
The fairy tale genre has evolved over time, and modern fairy tales may have different themes and messages than traditional ones.
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Identify the graph of 4y^4 + 12x^3 for T(-1,4) and write and equation of the translated or rotated graph in general form
The general form of the equation as:
(x/2)⁴ + (y/4)³ = 1
Explain equation
An equation is a statement that shows the equality between two mathematical expressions. It consists of variables, constants, and mathematical operators and is used to represent relationships between different quantities or variables. Equations are fundamental in mathematical modelling and problem-solving.
According to the given information
To get the general form of the equation of the translated or rotated graph, we can use the following steps:
1. Start with the equation of y=x⁴
2. Translate the graph horizontally by 2 units to the left by replacing x with (x+2).
3. Rotate the graph 90 degrees clockwise by replacing x with y and y with -x.
4. Scale the graph horizontally by a factor of 1/2 and vertically by a factor of 1/4 to get a better fit.
This gives us the general form of the equation as:
(x/2)⁴ + (y/4)³ = 1
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Which inequality is true when the value of w is -3?
Four friends want to play a game. In how many ways can the friends from teams, if both team dont have name
The friends can form teams in 6 different ways.
If the four friends want to form two teams, we can count the number of ways they can do this using combinations.
The number of ways to choose two people out of four is given by the combination formula,
C(4,2) = 4! / (2! * (4-2)!) = 6
We can list them as follows, where each team is represented by the letters A and B,
AB | CD
AC | BD
AD | BC
BC | AD
BD | AC
CD | AB
This means that there are 6 different ways the four friends can be split into two teams.
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optimal garden a rectangular flower garden with an area of 30 m2 is surrounded by a grass border 1 m wide on two sides and 2 m wide on the other two sides (see figure). what dimensions of the garden minimize the combined area of the garden and borders?
If the rectangular "flower-garden" has area of 30 m², then dimensions of garden to minimize the combined area of garden and borders is length is √15 m and width is √60 m.
Th area of the rectangular garden is 30m²,
So, rectangular garden area is expressed using the equation
⇒ 30 = L×W, where L is length and W is width.
So, We can express "L", in terms of W, by equation,
⇒ L = 30/W.
We need to minimize the "combined-area" of garden and it's borders.
The equation for the combined area is ⇒ A = (L + 1)(W + 2).
We minimize area by first expressing the function in terms of "W", and then differentiate the function for "combined-area" and then equate the derivative to 0.
The dimension which satisfies the equation optimizes the combined area.
⇒ A = (L+1)×(W+2)
⇒ A = (30/W + 1)×(W + 2)
⇒ A = 30 + W + 60/W + 2
⇒A = 32 + W + 60/W,
Differentiating the area with the width,
We get,
⇒ dA/dW = 1 − 60/W²
⇒ 0 = 1 − 60/W²
⇒ 1 = 60/W²
⇒ W² = 60, ⇒ W = √60.
So, garden's width is √60 m and length "L" = 30√60 = √15 m.
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The given question is incomplete, the complete question is
A rectangular flower garden with an area of 30 m² is surrounded by a grass border 1 m wide on two sides and 2 m wide on the other two sides. What dimensions of the garden minimize the combined area of the garden and borders?
Alex had 8. 8 meters of string. Suni had 36 decimeters of string. Juanita had 672 centimeters of string. What is the order of string lengths from the longest to the shortest? 8. 8 meters, 672 centimeters, 36 decimeters 8. 8 meters, 36 decimeters, 672 centimeters 36 decimeters, 8. 8 meters, 672 centimeters 672 centimeters, 36 decimeters, 8. 8 meters
The order of string lengths from the longest to the shortest is:
8.8 meters, 36 decimeters, 672 centimeters. So the correct option is : 2
To compare these lengths, we need to convert them to the same units.
8.8 meters is the longest length.
36 decimeters is equivalent to 3.6 meters.
672 centimeters is equivalent to 6.72 meters.
1 meter = 10 decimeters = 100 centimeters
Now converting ,
So, 8.8 meters = 88 decimeters = 880 centimeters
36 decimeters = 360 centimeters
Now we can see that the order from longest to shortest is:
8.8 meters = 880 centimeters
36 decimeters = 360 centimeters
672 centimeters
Therefore the correct option is : 2.
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--The complete Question is, Alex had 8. 8 meters of string. Suni had 36 decimeters of string. Juanita had 672 centimeters of string. What is the order of string lengths from the longest to the shortest?
8. 8 meters, 672 centimeters, 36 decimeters 8. 8 meters, 36 decimeters, 672 centimeters 36 decimeters, 8. 8 meters, 672 centimeters 672 centimeters, 36 decimeters, 8. 8 meters --The angle of elevation from point A to the top of a hill is 49°. If point A is 400 feet from the base of the hill, how high is the hill? Round to the nearest tenth.
1. 460.1 ft
2. 301.9 ft
3. 262.4 ft
4. 459.3 ft
The height of the hill for the given angle of elevation through which the given condition is satisfied is 460.1 ft
What about angle of elevation?
The angle of elevation is the angle between the horizontal plane and the line of sight or the direction of the observer's line of sight above the horizontal plane. It is measured upwards from the horizontal plane to the object being viewed. The angle of elevation is typically used in trigonometry and geometry to calculate the height, distance, or length of an object or location.
According to the given information:
Given, The given angle of elevation from point A to the top of a hill is [tex]49^{0}[/tex].
As, we know tan (x) = [tex]\frac{perpendicular}{base}[/tex]
tan [tex]49^{0}[/tex] = [tex]\frac{unknown}{400}[/tex]
1.15 x 400 = unknown
So, the unknown = 460.1 ft
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Use the image below to complete 1-3.
1. What is the length of XW?
2.What is the length of WV?
3. Which angle must be congruent to
Angles VYX and ZVX are alternate interior angles and are congruent.
Length of XW = 13 * 54 / WV, Length of WV = 702 / XW.
XW/YZ = VZ/WV (by similarity of triangles WYX and VZX).
What is congruency?Congruency refers to the property of two geometric figures that have exactly the same size and shape, so that they can be superimposed on one another. In other words, if two geometric figures are congruent, then all corresponding sides and angles of the figures are equal in measure.
1. To find the length of XW, we can use the fact that VZ is parallel to WY to set up a proportion. Since VZ and WY are parallel, we know that angles VZW and WYX are alternate interior angles and are therefore congruent. Similarly, angles VYX and ZVX are alternate interior angles and are congruent. Thus, we have:
XW/YZ = VZ/WV (by similarity of triangles WYX and VZX)
XW/13 = 54/WV (substituting the given values)
We can solve for XW by multiplying both sides by 13:
XW = 13 * 54 / WV
2. To find the length of WV, we can use the same proportion we set up in part 1 and substitute the given values:
Copy code
XW/YZ = VZ/WV
XW/13 = 54/WV
We can solve for WV by multiplying both sides by 54 and then dividing both sides by XW:
54 / (XW/13) = WV
WV = 702 / XW.
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What is the answer to this question? (Please i need help)
A statement that is best supported by the data in the box plots include the following: H. the interquartile range of the data for the community college is greater than the interquartile range of the data for the university.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.
How to calculate the interquartile range (IQR)?Mathematically, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):
Interquartile range (IQR) of university = Q₃ - Q₁
Interquartile range (IQR) of university = 15 - 9
Interquartile range (IQR) of university = 6.
For the community college, we have;
Interquartile range (IQR) = 15 - 6
Interquartile range (IQR) = 9.
Therefore, 9 is greater than 6.
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Last Friday, AT&T closed at $41.68. AT&T pays an annual dividend of $1.98. Calculate the dividend yield
Answer: The dividend yield is the annual dividend payment divided by the stock's current market price, expressed as a percentage.
Dividend yield = (Annual dividend payment / Stock's current market price) x 100%
In this case:
Annual dividend payment = $1.98
Stock's current market price = $41.68
Dividend yield = ($1.98 / $41.68) x 100% = 4.75%
Therefore, the dividend yield for AT&T is 4.75%.
Step-by-step explanation:
Find the 49th term.
-15, -10, -5, O, 5, ...
49th term = [?]
1st term + common difference(desired term - 1)
Enter
Answer:
49th term = 225
Step-by-step explanation:
The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.
An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.
The general formula, for the nth term of an arithmetic progression, is thus:
Tn = a + (n - 1)d, where a = first term, and d = common difference.
In the sequence: -15, -10, -5, 0, 5...,
a = -15, and d = -10--15 = 5
T49 = -15 + (49 - 1)5 = 225
∴ 49th term = 225
Find the length of AC.
Round your answer to the nearest tenth.
By Pythagorean theorem, the length of chord AC is approximately 46.6 units.
How to find the length of a chord AC in a circle
In this question we find a geometric system, in which we need to determine the length of the chord AC within the circle. The system indicates that chord AC is perpendicular to radius DB, then we can obtain the length of the chord by Pythagorean theorem:
AC = 2 · √(DB² - DM²), where M is the midpoint of chord AC.
If we know that DB = 25 and DM = 9, then the length of chord AC is:
AC = 2 · √(25² - 9²)
AC = 8√34 (approx. 46.6)
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An analyst is interested in testing the hypothesis that stock betas are higher in a down market (when the market index returns are negative) than otherwise.
Write the regression equation you would employ to test the analyst’s hypothesis.
This supports the analyst's hypothesis that betas are higher in down markets.
What is the meaning of equations?In algebra, the definition of an equation, in its simplest form, is a mathematical statement that shows that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two expressions separated by the equation.
To test the hypothesis that stock betas are higher in bear markets, we use the following regression equation:
Ri = αi + βi(Rm) + εi
where,
Ri = return on ith stock
Rm = market return
αi = intercept (constant term) of the regression equation of the ith stock.
βi = slope of the market return of the ith stock (regression coefficient).
εi = error period of the ith stock
To test the hypothesis, we include an additional variable in the regression equation that describes the effect of the market return when it is negative. This variable would be a dummy variable that takes the value 1 if the market return is negative and 0 otherwise. Let's call this variable D. So the modified regression equation would be:
Ri = αi + βi(Rm) + γiD + εi
where,
γi = the excess regression coefficient of the ith stock that describes the effect of the market return when it is negative
The coefficient γi measures the difference between the beta value of a stock between a falling market and a non-falling market. If γi is significantly greater than 0, this supports the analyst's hypothesis that betas are higher in down markets.
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Bus stops A,B,C, and D are on a straight road. The distance from A to D is exactly 1 km. The distance from B to C is 2 km. The distance from B to D is 3 km, the distance from A to B is 4 km, and the distance from C to D is 5 km. What is the distance between stops A and C?
Answer:
The answer is: 1+4+2+3+4+5=19 km
The distance between stops A and C is 11 km.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the distance between stops A and C, we can use the fact that the distance from A to D is 1 km and the distance from B to C is 2 km.
We can also use the fact that the distance from A to B is 4 km, the distance from B to D is 3 km, and the distance from C to D is 5 km.
We can start by finding the distance from A to B to C to D as follows:
Distance from A to B: 4 km
Distance from B to D: 3 km
Distance from D to C: 5 km
Total distance from A to C:
distance from A to B + distance from B to C + distance from C to D
So, the total distance from A to C is:
4 km + 2 km + 5 km = 11 km
Therefore,
The distance between stops A and C is 11 km.
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The right triangle shown is enlarged such that each side is multiplied by the value of the hypotenuse, 3y. Find the expression that represents the perimeter of the enlarged triangle. TRIANGLE AND ANSWER CHOICES BELOW!
Answer:
c.
Step-by-step explanation:
The original triangle has two sides with length 4x each, and the hypotenuse has length 3y.
After the enlargement, each of the sides with length 4x becomes 3y × 4x = 12xy, and the hypotenuse becomes 3y × 3y = 9y^2.
Therefore, the perimeter of the enlarged triangle is the sum of the lengths of its three sides:
12xy + 12xy + 9y^2 = 24xy + 9y^2 = 9y^2 + 24xy
So the answer is (C) 9y^2 + 24xy.
Chelsea is buying mini candy bars for her classmates. She has four different options for buying the candy bars. The list below gives different options for quantity and price.
If Chelsea wants to spend the lowest amount per mini candy bar, then which option should she buy?
Answer:
small
Step-by-step explanation:
You can divide the number of mini candy bars over the price, and the lowest would be the smallest one, with 8.33.
During a busy day last week, Pam made 8 pots at a piece rate of $11 per pot and five vases at a piece rate of $17 per vase. Her pay for the day was $____.00.
Pam's pay for the day was $173.00, found by using arithmetic operations.
What is an arithmetic operation?Arithmetic operation refers to the basic mathematical operations that involve numerical values and follow the rules of arithmetic. The four main arithmetic operations are Addition, Subtraction, Multiplication, and Division.
According to the given information:
To calculate Pam's pay for the day, we need to multiply the number of pots she made by the piece rate for pots, multiply the number of vases she made by the piece rate for vases, and then add the two amounts together.
Given:
Number of pots made (p) = 8
Piece rate for pots (r1) = $11 per pot
Number of vases made (v) = 5
Piece rate for vases (r2) = $17 per vase
Calculation:
Pay for pots = Number of pots made × Piece rate for pots = 8 × $11 = $88
Pay for vases = Number of vases made × Piece rate for vases = 5 × $17 = $85
Total pay for the day = Pay for pots + Pay for vases = $88 + $85 = $173
So, Pam's pay for the day was $173.00.
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In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student who did not complete the homework passed the test?
The probability that a student who did not complete the homework passed the test is 0.25.
In a sample of 200 people, 150 said they would vote for Davis. What are the odds against Davis winning the election?
The requried odds against Davis winning the election is 0.33 or 33%.
We can find the odds against Davis winning the election by using the formula:
odds against Davis = (number of people not voting for Davis) / (number of people voting for Davis)
Out of the 200 people, 150 said they would vote for Davis. So the number of people not voting for Davis is:
200 - 150 = 50
Therefore, the odds against Davis winning the election are:
odds against Davis = 50 / 150 = 1/3 or 0.33 (rounded to two decimal places)
This means that for every person who thinks Davis will win, there are three people who think he will lose.
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PLEASE HELP. Lesson 15.3 Tangents and Circumscribed Angles
Proof of Circumscribed Angle Theorem
Given: ZAXB is a circumscribed angle of circle C.
Prove: ZAXB and ZACB are supplementary.
Complete the proof.
A
B
C
If ZAXB is a circumscribed angle of circle C, XA and XB are
Select an answer to the circle
The assumption that AXB is a bounded angle is false, as a result, if AXB is a circumscribed angle of circle C, then AXB and ACB are supplementary.
How to prove circumscribed angles?To complete the proof of the Circumscribed Angle Theorem, use the fact that an inscribed angle of a circle is equal to half of the central angle that intercepts the same arc.
Since angle ∠AXB is circumscribed by the circle, point X lies on the circumference of the circle. Therefore, angles ∠CXA and ∠CXB are inscribed angles that intercept the same arc AB.
By the Inscribed Angle Theorem:
∠CXA = ½∠CAB
∠CXB = ½∠CAB
Adding these two equations:
∠CXA + ∠CXB = ½∠CAB + ½∠CAB
∠CXA + ∠CXB = ∠CAB
Now, observe that angles ∠CAB and ∠ACB form a linear pair, since they are adjacent angles that together make a straight line. Therefore, they are supplementary, which means:
∠CAB + ∠ACB = 180°
Substituting ∠CAB with ∠CXA + ∠CXB:
∠CXA + ∠CXB + ∠ACB = 180°
Finally, ∠AXB and ∠CXB form a linear pair, since they are adjacent angles that together make a straight line. Therefore, they are supplementary, which means:
∠AXB + ∠CXB = 180°
Substituting ∠CXB with ∠CAB - ∠CXA:
∠AXB + ∠CAB - ∠CXA = 180°
Adding ∠CXA to both sides:
∠AXB + ∠CAB = ∠ACB + 180°
Substituting ∠AXB + ∠CAB with 180° (since they are adjacent angles that together make a straight line):
180° = ∠ACB + 180°
Simplifying:
∠ACB = 0°
This is a contradiction, since we know that ∠ACB is a non-zero angle. Therefore, our assumption that ∠AXB is a circumscribed angle must be false. Hence, we have proved that if ∠AXB is a circumscribed angle of circle C, then ∠AXB and ∠ACB are supplementary.
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Imma give h Brainliest!!!
Answer:
Yes, because of the Angle-Angle Theorem
Step-by-step explanation:
The sum of the interior angles of a triangle are 180.
Triangle on the left
180 - 90 - 42 = 48
Triangle on the right:
180 - 90 - 48 = 42
Since the angles measurements are the same, the triangles are similar.
Helping in the name of Jesus.
Answer: Yes, because of the Angle-Angle Theorem
Step-by-step explanation:
The two triangles have the same angles, so they are similar by the Angle-Angle Theorem.
Please help me with this, i am stuck on it ever since yesterday. Thank you :)
Answer:
Opposite and Adjacent
Step-by-step explanation:
Tanegnt is a function where you take the side lengths of the opposite side from the angle and the adjacent sides of the angle. opp/adj is the commonly used formula.
A helicopter hovering above a command post shines a spotlight on an object on the ground 250 feet away from the command post as shown in the diagram how far is the object from the helicopter to the nearest foot
The distance of the object from the helicopter is 698 ft.
What is distance?Distance is the length between two points.
To calculate how far the object is above the helicopter, we use the formula below.
Formula:
Sin∅ = O/H..................... Equation 1Where:
∅ = AngleO = OppositeH = Hypotenus = Distance of the object from the HelicopterFrom the question,
Given:
O = 250 ft∅ = 21°Substitute these values into equation 1 and solve for H
H = 250/Sin21°H = 697.61 ftH ≈ 698 ftHence, the distance is 698 ft.
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Given f(x)= raiz 6x and g(x)= 1/x-6 Which value is in the domain of f g
The domain of the composition function fog(x) when f(x)= √6x and g(x)= 1/ (x-6) is equal to (-∞, 6) U (6, ∞).
Function f(x) = √6x
And g(x)= 1/ (x-6
Composition function fog is ,
fog(x) = f(g(x))
Domain of fog(x),
First, find the domain of g(x),
Here,
g(x) = 1/(x-6)
The denominator of g(x) cannot be equal to zero,
So we must exclude x = 6 from the domain of g(x).
The domain of g(x) is equal to ,
domain of g(x) = {x | x ≠ 6}
The range of g(x) is,
As x approaches 6 from the left, g(x) approaches negative infinity,
And as x approaches 6 from the right, g(x) approaches positive infinity.
Range of g(x) = (-∞, 0) U (0, ∞)
Now, the domain of fog(x),
fog(x)
= f(g(x))
= √6g(x)
=√ 6 (1 /(x - 6 ) )
Square root sign must be non-negative.
Since the range of g(x) does not include zero,
Exclude the part of the range that is less than zero.
The domain of fog(x) is,
domain of fog(x)
= {x | g(x) > 0}
= {x | x < 6} U {x | x > 6}
The domain of fog(x) consists of all real numbers except x = 6.
Therefore, the domain of fog(x) is (-∞, 6) U (6, ∞).
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The above question is incomplete, the complete question is :
Given f(x)= √6x and g(x)= 1/ (x-6) Which value is in the domain of fog.
at what rate is the base of the triangle changing when the altitude is 20 cm and the area is 120 cm2?
The rate at which the base of the triangle is changing when the altitude is 20 cm and the area is 120 cm^2 is 0 cm/s.
To solve this problem, we need to use the formula for the area of a triangle, which is:
A = (1/2)bh
Where A is the area, b is the base, and h is the altitude.
We know that the area is 120 cm^2 and the altitude is 20 cm. So we can plug in these values and solve for the base:
120 = (1/2)b(20)
240 = 20b
b = 12 cm
Now we need to differentiate both sides of the equation with respect to time (t):
dA/dt = (1/2)(db/dt)h
We are given the value of dh/dt (which represents the rate at which the altitude is changing) is 3 cm/s. We need to find db/dt (which represents the rate at which the base is changing).
Plugging in the values we know, we get:
dA/dt = (1/2)(db/dt)(20)
Solving for db/dt, we get:
db/dt = (2dA/dt)/h
Plugging in the values we know, we get:
db/dt = (2)(0)/20
db/dt = 0 cm/s
Since the area is constant (120 cm²) and the altitude is constant (20 cm), the base of the triangle is not changing. Therefore, the rate at which the base is changing is: 0 cm/s
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describe how the shape, center, and spread of the sampling distribution of the sample proportion change as sample size increases. group of answer choices as the sample size increases, the shape of the distribution approaches the normal distribution, and the spread of the sam
As the sample size increases, the shape of the distribution approaches the normal distribution, and the spread of the sampling distribution increases. The correct answer is option D.
As the sample size increases, the shape of the sampling distribution of the sample proportion approaches the normal distribution, and the spread of the sampling distribution decreases. The mean of the sampling distribution is always equal to the true proportion of that population, regardless of the sample size.
This phenomenon is due to the Central Limit Theorem (CLT), which states that as the sample size increases, the sampling distribution of the sample proportion becomes increasingly normal in shape, even if the population distribution is not normal.
The spread of the distribution decreases because larger sample sizes lead to more precision in estimating the true proportion.
Moreover, the mean of the sampling distribution of the sample proportion is equal to the true proportion of the population, regardless of the sample size. This property is known as unbiasedness. As the sample size increases, the variance of the sampling distribution decreases, resulting in a more precise estimate of the true proportion.
In conclusion, the larger the sample size, the more accurately the sample proportion represents the true proportion of the population. This result is due to the combination of the CLT and the unbiasedness of the sample proportion as an estimator of the population proportion.
The correct answer is option D.
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Complete question is:
Describe how the shape, center, and spread of the sampling distribution of the sample proportion change as sample size increases.
A) As the sample size increases, the shape of the distribution approaches the normal distribution, and the spread of the sampling distribution decreases. Regardless of the sample size, the mean of the sampling distribution is equal to the true proportion of that population.
B) As the sample size increases, the shape of the distribution becomes right skewed, and the spread of the sampling distribution increases. Regardless of the sample size, the mean of the sampling distribution is not equal to the true proportion of that population.
C) As the sample size increases, the shape of the distribution approaches the normal distribution, and the spread of the sampling distribution decreases. Regardless of the sample size, the mean of the sampling distribution is not equal to the true proportion of that population.
D) As the sample size increases, the shape of the distribution approaches the normal distribution, and the spread of the sampling distribution increases. Regardless of the sample size, the mean of the sampling distribution is equal to the true proportion of that population.
E) As the sample size increases, the shape of the distribution becomes left skewed, and the spread of the sampling distribution increases. Regardless of the sample size, the mean of the sampling distribution is not equal to the true proportion of that population.
