The interval on which function f is increasing is (0, e^(-1/7)). The interval on which function f is decreasing is (e^(-1/7), ∞).
To find the intervals on which the function f(x) = x^7 ln(x) is increasing or decreasing, we need to find the first derivative of f(x) and determine its sign on different intervals.
First, we use the product rule and the chain rule to find the derivative of f(x):
f'(x) = (x^7)' ln(x) + x^7 (ln(x))'
f'(x) = 7x^6 ln(x) + x^6
Next, we find the critical points of f(x) by setting the derivative equal to zero and solving for x:
7x^6 ln(x) + x^6 = 0
x^6 (7ln(x) + 1) = 0
x = 0 or x = e^(-1/7)
Note that x = 0 is not in the domain of f(x) since ln(x) is undefined for x <= 0.
Now we can test the sign of f'(x) on different intervals:
Interval (-∞, 0): f'(x) is undefined since x is not in the domain of f(x).
Interval (0, e^(-1/7)): f'(x) is positive since both terms in f'(x) are positive.
Interval (e^(-1/7), ∞): f'(x) is negative since 7ln(x) + 1 < 0 for x > e^(-1/7).
Therefore, f(x) is increasing on the interval (0, e^(-1/7)) and decreasing on the interval (e^(-1/7), ∞).
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a typist can type 495 words in 15 minutes. How many words can she type in 25 minutes?
Answer:
They can type 825 words in 25 minutes.
Step-by-step explanation:
First, we need to find how many words they can type per minute. To do that, we need to divide 495 by 15.
[tex]495 \div 15 = 33[/tex]
Now, we know how many words per minute, and the question is how many words they can type in 25 minutes. So to find our answer, we need to multiply 33 by 25, since 33 is how many words in one minute.
[tex]33 \times 25=825[/tex]
So now we know our answer: 825 words in 25 minutes.
2. The prices of several different cereals are given below. Find the mean, median, mode, MAD, and IQR of these values. Which measure of center and which measure of variability best describe the data? $3.50, $4.25, $6, $4.75, $5.80, $4
I need this with explanation please:(
Mean = $ 4. 72
Median = $ 4. 5
Mode = No mode
MAD = $ 4. 8
IQR = $ 0. 5
Measure of center = $ 4. 5
Measure of variability = $ 2. 50
How to determine the valuesGiven the data;
$3.50, $4.25, $6, $4.75, $5.80, $4
Mean = sum of data/ number of data values
Mean = [tex]\frac{3. 50 + 4. 25 + 6 + 4. 75 + 5. 80 + 4}{6}[/tex]
Mean = $ 4. 72
Median is the number in the center when the data is arranged in an ascending order
$3. 50, $4, $4. 25, $4. 75, $5. 80, $6
Median = [tex]\frac{4. 25 + 4. 75}{2}[/tex]
Median = $ 4. 5
Mode is the number with the highest repeats.
From the given data, none of the numbers was repeated.
Thus, there is no mode.
MAD, mean absolute deviation = |data value - mean|
MAD = [tex]|(3. 50 - 4. 72) + (4. 25 - 4. 72) + (6 - 4. 72) + (4. 75 - 4. 72) + (5. 80 - 4.72) + (4- 4. 72) |[/tex]
MAD = [tex]1. 22 + 0. 47 + 1. 28 + 0. 03 + 1. 08 + 0. 72[/tex]
MAD = $ 4. 8
IQR, interquartile range = Quartile 3 - quartile 1
IQR = 4. 75 - 4. 25
IQR = $0. 5
Note that the mean and median are the most common measures of center.
A measure of variability is a single number that is used to describe the spread of a data set
The measure of the center best for the data is the median = $4. 5
Measure of variability = range = highest value - lowest value = $6 - $3. 50 = $2. 50
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Which digit in 125 734 016 has a value of 20 000 000?
Step-by-step explanation:
in a number like 125,734,016
the right most position has the weight 10⁰ = 1
so, 6×1 = 6.
the second right most position has the weight 10¹ = 10.
so, 1×10 = 10
the third right most position has the weight 10² = 100.
so, 0×100 = 0
the 4th right most position has the weight 10³ = 1000.
so, 4×1000 = 4,000
the 5th right most position has the weight 10⁴ = 10000.
so, 3×10000 = 30,000
the 6th right most position has the weight 10⁵ = 100000.
so, 7×100000 = 700,000
the 7th right most position has the weight 10⁶ = 1000000.
so, 5×1000000 = 5,000,000
the 8th right most position has the weight 10⁷ = 10000000
so, 2×10000000 = 20,000,000
and so on.
as we can see, the 2 (the 8th most position from the right or the second position from the left) has the value of 20,000,000.
Simplify the following expression. (2x-3)(5x^4-7x^3+6c^2-9)
The simplification of the expression (2x - 3)(5x⁴ - 7x³ + 6x² - 9) is 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27
Simplification(2x - 3)(5x⁴ - 7x³ + 6x² - 9)
= 10x^5 - 14x⁴ + 12x³ - 18x - 15x⁴ + 21x³ - 18x² + 27
= 10x^5 - 14x⁴ - 15x⁴ + 12x³ + 21x³ - 18x² - 18x + 27
= 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27
The simplified expression is 10x^5 - 29x⁴ + 33x³ - 18x² - 18x + 27
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What is the term for breaking a larger number apart into smaller numbers that can be multiplied together to get a specific result?.
Answer:
factoring
Step-by-step explanation:
A fishing trawler sails 30 km from port on a bearing of 120° until it reaches a submerged reef.
How far (to the nearest km) is the port north of the reef?
From rectangular component, the distance of the port north of the reef is 25.9808 km.
What is the distance of the given point by rectangular component analysis ?It is given that a fishing trawler sails 30 km from port on a bearing of 120° until it reaches a submerged reef.
Thus the direction of the fishing trawler is given to be 120° with respect to the movement of the trawler.
Resolving the direction by the horizontal and vertical components, we get
The horizontal component of distance is |30*cos(120°)| = 15 km
The vertical component of distance is |30*sin(120°)| = 25.9808 km
Thus as we have to find the north direction or the vertical component, the distance is 25.9808 km.
Therefore, from rectangular component, the distance of the port north of the reef is 25.9808 km.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
A, B, F
- The radius of the circle is 3 units
- The center of the circle lies on the x-axis
- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9
Step-by-step explanation:
The first option is correct because the standard equation of the circle is:
[tex](x - 1)^{2} + {y}^{2} = 9[/tex]
making the radius equal to 3.
The center is at (-1,0), therefore it lies on the x-axis.
And lastly, the last option is correct because both options have the radius of 3.
The volume of a rectangular box is 1.0 ft3. what is the length if the width is 1.0 ft and the height is 1.5 ft?
The length of the rectangular box is 0.67 feet
How to determine the length of the box?The given parameters are:
Length = ??
Width = 1.0 ft
Height = 1.5 ft
Volume = 1.0 ft^3
The volume is calculated as:
Volume = Length * Width * Height
Substitute the known values in the above equation
1 = Length * 1 * 1.5
Evaluate the product
1 = Length * 1.5
Divide both sides by 1.5
Length = 0.67
Hence, the length of the rectangular box is 0.67 feet
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please answer all of them with a clear answer
See below for the solution to the questions
The parallel side of the trapezoidThe given parameters are:
Area = 138
a = 4x - 1
b = x - 4
Height = 12
The area is calculated as:
Area = 0.5 * (a + b) * height
So, we have:
0.5 *(4x - 1 + x - 4) * 12 = 138
This gives
5x - 5 = 23
Add 5 to both sides
5x = 28
Divide by 5
x = 5.6
Recall that:
a = 4x - 1 = 4 * 5.6 - 1 = 21.4
b = x - 4 = 5.6 - 4 = 1.6
Hence, the short base length is 1.6 meters and the long base length is 21.4 meters
The largest angle in the triangleThe sides are given as:
x = 22
y = 24
z = 25
The largest angle always opposite the largest side.
This means that the largest angle is Z
The CircumferenceThe radius is given as:
r = 29
The circumference is calculated as:
[tex]C = 2\pi r[/tex]
So, we have:
[tex]C = 2\pi *29[/tex]
Evaluate
C = 182.21
Hence, the circumference is 182.21 inches
Measure of angle from arcThe measure of the arc is given as:
[tex]\theta = 69^o[/tex]
The angle LIK is calculated as:
[tex]m\angle LIK = \frac{\theta}2[/tex]
So, we have:
[tex]m\angle LIK = \frac{69^o}2[/tex]
Evaluate the quotient
[tex]m\angle LIK = 34.5^o[/tex]
Hence, the measure of the angle is [tex]m\angle LIK = 34.5^o[/tex]
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A machine fills bags with sweets there are 4275 sweets there are 28 sweets in each full bag the machine fills as many bags as possible how many sweets are left must show your working
19 sweets are lefted.
Lets simplify the problem,
Maximum no. of bag filled by 4275 sweets
Through Simple Division we get,
4275/28 ~=152
Therefore , there is 4256 sweets in 152 bags
Therefore, 4275-4256=19 sweets are left
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Pls help me
Here is a sequence of numbers
Answer:
a) Perfect square.
b) 9
Step-by-step explanation:
The given numbers are perfect squares.
64 = 8*8
49 = 7*7
36 = 6*6
25 = 5*5
16 = 4*4
So, the next number will be 3 *3 = 9
If a car travels 368.5 miles on 50 liters of gas, how many liters of gas will it take to go 691 miles if the car travels at the same rate? (Round to the nearest tenth)
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer: [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.
Step-by-step explanation:
Finding the third angle in triangle XYZ,
[tex]m\angle YXZ=180^{\circ}-77^{\circ}-48^{\circ}=55^{\circ}[/tex],
Thus, [tex]\triangle XYZ \sim \triangle GFH[/tex] by AA.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Find the factors of function f, and use them to complete this statement. From left to right, function f has zeros at , , , and .
The factorized form of the given function, f(x) = 2x⁴ - x³ - 18x² + 9x, is, f(x) = x(2x - 1)(x + 3)(x - 3), and the complete statement is, From left to right, function f has zeros at x = -3, x = 0, x = 1/2, and x = 3.
In the question, we are asked to find the factors of the function f, and complete the given statement.
The function f, given to us is:
f(x) = 2x⁴ - x³ - 18x² + 9x.
To factor the function, we first group the terms as follows:
f(x) = (2x⁴ - 18x²) - (x³ - 9x).
Now, we take common terms out of the group as follows:
f(x) = 2x²(x² - 9) - x(x² - 9).
Now, we again take common terms, as follows:
f(x) = (2x² - x)(x² - 9),
or, f(x) = x(2x - 1)(x + 3)(x - 3).
This is the factored form of the given function, f.
The statement given to us is:
From left to right, function f has zeros at x = _, x = _, x = _, and x = _.
To find the zeroes of the function, we equate the factorized form to 0.
x(2x - 1)(x + 3)(x - 3) = 0.
By zero-product rule, the zeroes are at:
x = 0,
2x - 1 = 0, or, x = 1/2,
x + 3 = 0, or, x = -3,
x - 3 = , or, x = 3.
Arranging these in ascending order, the zeroes are at: -3, 0, 1/2, and 3.
Thus, the factorized form of the given function, f(x) = 2x⁴ - x³ - 18x² + 9x, is, f(x) = x(2x - 1)(x + 3)(x - 3), and the complete statement is, From left to right, function f has zeros at x = -3, x = 0, x = 1/2, and x = 3.
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For the complete question, refer to the attachment.
Answer: Edmentum/plato
Step-by-step explanation:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer:
[tex]x^2+(y-3)^2=36\\[/tex] and [tex]x^2+(y+8)^2=36[/tex]
Step-by-step explanation:
So the general formula for a circle is usually represented as: [tex](x-h)^2+(y-k)^2=r^2[/tex] where (h, k) is the center of the circle and r is the radius of the circle.
Since the diameter is 12, the radius is going to be 6, because the radius is half the diameter. We now square that value (since it's squared in the equation), you get 36, which is going to be on the right side.
The last thing to know is since it's on the y-axis, that means h=0, since if h didn't equal 1, it would either be to the right or left of the y-axis. So the equation should look something like this: [tex]x^2+(y-k)^2=36[/tex] where k can be any real number.
So this gives you the two equations:
[tex]x^2+(y-3)^2=36\\[/tex] and [tex]x^2+(y+8)^2=36[/tex]
Find the measures of the numbered angles in each rhombus.
Answer:
Step-by-step explanation:
2=27
3=27
5=27
1=126
4=126
Trigonometry. What's x? Dont know how to do it
Answer:
12.11069457
Step-by-step explanation:
You start by using sin(48) = 9/x
You then multiply both sides by x to give you
xsin(48) = 9
you then divide both sides by sin(48) to get x by itself
x = 9/sin(48)
this gets you
x=12.11069457
g(x) = (x ^ 3 - 9x)/(x ^ 2 - 6x + 9)
The expression is simplified to x
How to simplify the expressiong(x) = (x ^ 3 - 9x)/(x ^ 2 - 6x + 9)
First, we simplify the numerator
= [tex]\frac{x (x^2 - 3^2)}{x^2 - 6x + 9}[/tex]
Now, let's solve the quadratic equation in the denominator
= [tex]\frac{x(x^2 - 3^2)}{x^2 - 3x - 3x + 9}[/tex]
= [tex]\frac{x(x^2 - 3^2)}{x(x-3) - 3(x - 3)}[/tex]
= [tex]\frac{x(x - 3) (x -3)}{(x -3) ( x-3)}[/tex]
Divide the like factors
= x
The answer is x
Thus, the expression is simplified to x
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Given Circle G with radius r, what is the formula for the area of the segment (unshaded region)
Answer:
Option D
Step-by-step explanation:
The triangle ABJ is equitorial
So area
√3/4r²Then mBJ is a arc which is 1/6th of circle
Area.
π/6r²So area of unshaded region
πr²/6-√3/4r²r²(π/6-√3/4)Answer:
[tex]\textsf{d.} \quad r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)[/tex]
Step-by-step explanation:
To find the area of the unshaded region, subtract the area of ΔJGB from the area of sector JGB.
The measure of an arc is equal to its corresponding central angle measure. Therefore, the central angle of sector JGB is 60°.
As the two sides of ΔJGB adjacent the central angle are the radii of the circle (and therefore equal in length), ∠GJB = ∠GBJ.
Interior angles of a triangle sum to 180°. Therefore, all interior angles of ΔJGB are 60° which makes it an equilateral triangle.
Area of an equilateral triangle:
[tex]\sf A=\dfrac{\sqrt{3}}{4}a^2 \quad \textsf{(where a is the side length)}[/tex]
As the side length of the given equilateral triangle is the radius (r):
[tex]\implies \sf Area\:of\:triangle=\dfrac{\sqrt{3}}{4}r^2[/tex]
To find the area of the sector, first convert degrees to radians by multiplying the degrees by π/180 :
[tex]\implies 60^{\circ}=60 \times \dfrac{ \pi}{180}=\dfrac{\pi}{3}\:\:\sf radians[/tex]
Area of a sector of a circle
[tex]\textsf{A}=\dfrac12 r^2 \theta \quad \textsf{(where r is the radius and the angle }\theta \textsf{ is in radians)}[/tex]
Substituting the angle in radians, the area of the sector is:
[tex]\implies \sf A=\dfrac{1}{2}r^2\left(\dfrac{\pi}{3}\right)[/tex]
[tex]\implies \sf A=\dfrac{\pi}6}r^2[/tex]
Area of the unshaded region:
[tex]\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\\\& = \dfrac{\pi}{6}r^2 - \dfrac{\sqrt{3}}{4}r^2\\\\& = r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)\end{aligned}[/tex]
Therefore, the solution is option D.
PLEASE HELP!!!
Review the table of values for function k(x).
x
k(x)
–19.1
37.5
–19.01
37.95
–19.001
37.995
–19.0001
37.9995
–19
undefined
–18.9999
43.9995
–18.999
43.995
–18.99
43.95
–18.9
43.5
What is Limit as x approaches negative 19 plusk(x)?
37.5
38
43.5
44
#12Writethe converse, inverse, and contrapositive of the following statement. Find the truth value of each.“If Brielle drives at exactly 0 mi/h, then she travels 10 mi in 0 mins
See below for the converse, inverse, and contrapositive of the statement
How to write the conditional statements?The statement is given as:
If Brielle drives at exactly 30 mi/h, then she travels 10 mi in 20 mins
The speed is calculated as:
Speed = Distance/Time
So, we have:
Speed = 10 mi/20 mins
This gives
Speed = 10 mi/1/3 h
Speed = 30 mi/h
The converse
To do this, we simply switch the hypothesis and the conclusion
So, the converse is:
If Brielle travels 10 mi in 20 mins, then she drives at exactly 30 mi/h
The above statement is true
The inverse
To do this, we simply negate the hypothesis and the conclusion
So, the inverse is:
If Brielle did not drive at exactly 30 mi/h, then she did not travel 10 mi in 20 mins
The above statement is false
The contrapositive
To do this, we simply negate the hypothesis and the conclusion, and then switch them
So, the contrapositive is:
If Brielle did not travel 10 mi in 20 mins, then she did not drive at exactly 30 mi/h
The above statement is false
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The marks obtained by 10 student in a test are as follows: 3,7,6,2,8,5,9,1,4 and 10. find the mean mark
Answer:
[tex]5.5[/tex]
Step-by-step explanation:
Mean:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is
[tex]\mu = \frac{{\sum}x}{N}[/tex]
The formula for the mean of a sample is
[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:
[tex]\frac{55}{10} = 5.5[/tex]
A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented by the x-axis and the base of the house is at the origin. There are two trees on the property. One tree is 8 feet from the base of the house and is 16 feet tall. The other tree is 11 feet from the base of the house and is 9 feet tall. What is the distance from the base of the house to the closest treetop? Round your answer to the nearest tenth. Need answer ASAP.
The distance from the base of the tree to the tallest would be 14.21 cm
We have the following data points in this questionX1 = 8 feet
y1 = 16 feet
x2 = 11 feet
y2 = 9 feet
To proceed with the solution we have to
We have to solve for the shorter tree
[tex]\sqrt{(y2 -y1)^2 + (x2-x1)^2} \\\\= \sqrt{9-0^2 + 11-0^2}[/tex]
= 9² + 11²
= √81 +121
= 14.21
For the taller tree we would have√8² + 16²
= √64 +256
= 17.89
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I don't understand any recursive sequences please help explain so
The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 units. Which statement about the domain and range of each function is correct?
A).Both the domain and range of the transformed function are the same as those of the parent function.
B).Neither the domain nor the range of the transformed function are the same as those of the parent function.
c).The range of the transformed function is the same as the parent function, but the domains of the functions are different.
D).The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.
The statement that is true about the domain and range of each function is; A) Both the domain and range of the transformed function are the same as those of the parent function.
How to interpret reflection of a function?We are told that the graph of f(x) = |x| is reflected across the y-axis. Thus;
|-x| = x
Now, the function is translated to the left by 5 units and so the transformed function is; g(x) = |x + 5|
Thus, from the graph, we get;
Domain of both functions is the set of all real numbers.
Range of both functions is the set {y|y ≥ 0}
Thus, we conclude that Both the domain and range of the transformed function are the same as those of the parent function.
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A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
Answer Options:
A.11.65
B.50.00
C.171.65
D.210.00
The time it took the rider to reach the ground level is 171.651seconds
Quadratic functionsQuadratic functions are functions that has a leading degree of 2.
Given the equation that represents roller coaster’s height as shown
h = –0.025t^2 + 4t + 50
The coaster will reach the ground when h = 0
Substitute
0 = –0.025t^2 + 4t + 50
Factorize
On factorizing, the time it took the rider to reach the ground level is 171.651seconds
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Answer:
171.65 seconds
Step-by-step explanation:
did the test and got it right
which of the answer choices could be the one missing data item for the following set, if the mode is 12? 7, 12, 9, 15, 12, 7, 9, 7, 12, 15 a. 15 b. 9 c. 7 d. 12
Answer: D. 12
Step-by-step explanation: The mode is the most popular number in a set of numbers. In this set, there are 3 sevens, 3 twelves, 2 nines, and 2 fifteens. If the mode is twelve, you need one more 12 because there are the same amounts of twelves and sevens. So that means the answer is 12!
The following table shows Kamal’s bank account balance after 7 months.
*TABLE IN THE FILE ATACHED BELOW*
a) What is the rate of change? Show your work.
b) What does the rate of change mean in Kamal’s scenario?
c) What is the initial value?
d) What does the initial value represent in Kamal’s scenario?
e) Determine the equation of the linear relation which represents his bank account balance.
PLEASE HELP I DON'T HAVE ANY TIME
a. The rate of change = -25/month
b. Kamal's account balance reduces by 25$ per month.
c. To find the $725.
d. Kamal's opening balance or initial deposit.
e. The linear equation is: A = -25n + 725.
How to Find the Rate of Change and Initial Value of a Linear Relation?The rate of change (m) = change in y/change in x.
a. The rate of change (m) = change in A / change in n = (700 - 650)/(1 - 3) = -25/month.
b. -25 dollar per month means every month, Kamal's account balance reduces by 25$
c. To find the initial value (b), substitute m = -25 and (7, 550) = (n, A) into A = nm + b:
550 = 7(-25) + b
550 = -175 + b
550 + 175 = b
b = 725.
Initial value is: 725.
d. The initial value, $725, is Kamal's opening balance or initial deposit.
e. To write the linear equation, Substitute m = -25 and b = 725 into A = nm + b:
A = -25n + 725
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.
Which equation represents a circle with a center (-5, -6) and a radius of 5?
The equation of the circle with a center (-5, -6) and a radius of 5 is (x + 5)² + (y + 6)² = 25.
How to Write the Equation of a Circle?The standard equation for writing the equation of a circle is: (x - h)² + (y - k)² = r².
Given the following:
Center (-5, -6) = (h, k)
Radius = 5 = r
Plug in the values into the formula
(x + 5)² + (y + 6)² = 5²
(x + 5)² + (y + 6)² = 25
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An angle has turn through 15 one-degree angle. what is a measurement of this angle in degrees
The measurement of the angle is 15° (if initial angle is 0°).
Turning Through One-degree Angles
An angle is said to have an angle measure of n degrees if it rotates across n one-degree angles. Since turning through one degree means making an angle of one degree, every time you take a turn of one degree, you rotate through one degree more. Thus, turning through n one-degree angles give rise to an angle of n degrees.
Measurement of the Angle
It is given that the angle has turned through 15 one-degree angles. Thus, the angle will turn through 15°.
Let us assume the initial angle to be x°.
Then, the new angle after 15 one-degree turns would be (x+15)°
If initial angle, x = 0°, the measurement of the angle formed is 15°.
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PLS HELP ITS DUE IN 9 MIN AND IM CONFUSED AND I DON’T WHAT TO DO ANSWER ASAP ILL GIVE BRAINIESTTTTT
A financial planner has three portfolios: A, B, and C. Because investors have different tolerances for risks, 20% of people are likely to invest in portfolio A, 30% are likely to invest in B, and 50% are likely to invest in C. Each portfolio has both stocks and bonds, and investors are equally likely to choose either.
This is a tree diagram that represents the probability of investors choosing the different financial products.
What is the probability of an investor choosing either stocks or bonds from portfolio C?
Considering the given tree diagram, there is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
At each node, the sum of the probabilities is of 1, hence:
0.2 + 0.3 + Z = 1.
Z = 0.5.
There is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.
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