Answer:
this is tricky
Step-by-step explanation:
Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, four green ones, three white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She does not have all the red ones.
Answer:
0.8586 = 85.86% probability that she does not have all the red ones.
Step-by-step explanation:
The marbles are grabbed without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
Bag has 4 + 4 + 3 + 1 = 12 marbles, which means that \(N = 12\)
She grabs eight of them, which means that \(n = 8\)
Four are red, which means that \(k = 4\)
Probability that she does not have all the red ones.
This is
\(P(X < 4) = 1 - P(X = 4)\)
In which
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)
\(P(X = 4) = h(4,12,8,4) = \frac{C_{4,4}*C_{8,0}}{C_{12,8}} = 0.1414\)
Then
\(P(X < 4) = 1 - P(X = 4) = 1 - 0.1414 = 0.8586\)
0.8586 = 85.86% probability that she does not have all the red ones.
A jar contains 24 blue marbles, 16 red marbles, and 14 white marbles. Find the simplified ratio of total marbles to red marbles.
The simplified ratio of total marbles to red marbles is 27 to 8
How to determine the ratio of the marbles?In this question, we have the following parameters
Blue marbles = 24
Red marbles = 16
White marbles = 14
The above parameters mean that
Total marbles = sum of the individual marbles
Substitute the known values in the above equation, so, we have the following representation
Total marbles = 24 + 16 + 14
Evaluate
Total marbles = 54
The ratio is then represented as
Ratio = Total : Red
This gives
Ratio = 54 : 16
Simplify ratio
Ratio = 27 : 8
Hence, the simplified ratio is 27 : 8
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3. Do these three points create a right triangle?
A(2,2) B(-2-1) C(-3, 2)
Answer:
they do NOT create a right-angled triangle
Step-by-step explanation:
to make a right-angled triangle the side lengths must comply with Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
the side lengths in this ABC triangle are :
AB² = (2 - -2)² + (2 - -1)² = 4² + 3² = 16 + 9 = 25
AB = 5
BC² = (-2 - -3)² + (-1 - 2)² = 1² + (-3)² = 1 + 9 = 10
BC = sqrt(10)
CA² = (-3 - 2)² + (2 - 2)² = (-5)² + 0² = 25
CA = 5
so, this is an isoceles triangle (2 equal legs).
the side lengths 5, 5, sqrt(10) do NOT create a right-angled triangle.
no matter how we combine their squares in the Pythagoras formula, it does not work :
10 = 25 + 25 = 50 no.
25 = 10 + 25 = 35 no.
Matthew examines the relation shown in the below.
{(4,-11), (3,1), (0,1), (2,6), (3, -1)}
Is the relation a function? Why or why not?
No. There are x values which map to more than 1 y-value.
Yes. Every y-value maps to exactly 1 x-value.
No. There are y-values which map to more than 1 x-value.
Yes. Every x-value maps to exactly 1 y-value.
No, there are x values which map to more than 1 y-value.
Given that Matthew examines the relation as shown in the below.
{(4, -11), (3,1), (0,1), (2,6), (3, -1)}
We need to check whether the relation is a function or not,
So, we know that,
A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.
If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.
Here we can see that the y values are repeated, so it is not a function.
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Please help!
Whoever answers right gets brainliest!!!!
Answer:
\(y - 4 = - 3(x - 2)\)
Priya is buying raisins and almonds to make trail mix. Almonds cost $5.20 per pound and raisins cost $2.75 per pound. Priya spent $11.70 buying almonds and raisins. The relationship between pounds off almonds a, pounds of raisins r, and the total cost is represented by the equation 5.20a + 2.75r = 11.70
How many pounds of raisins did Priya buy if she bought the following amounts of almonds?
2 pounds of almonds:
1.06 pounds of almonds:
0.64 pounds of almonds:
a pounds of almonds:
Answer:
A. 1.42 Lbs of raisins
B. 2.25 lbs of raisins
C. 1.28 lbs of raisins
D. 5.20a+2.15r=11.70
Step-by-step explanation:
Put the pounds of almonds in for a and solve each questions.
What is the volume of the pyramid?
A solid oblique pyramid has an equilateral triangle as a base
with an edge length of 4/3 cm and an area of 12/3 cm.
O 12/3 cm3
16/3 cm
24/3 cm3
32/3 cm3
Answer:
16/9 cm³Step-by-step explanation:
Volume of a triangular pyramid = 1/3 * Base area * height
Given the Base area = area of the equilateral triangle = 12/3 cm
Height of the pyramid = length of its edge = 4/3 cm
Substituting this values in the formula we have;
V = 1/3 * 12/3 * 4/3
V = 48/27
V = 16/9 cm³
The volume of the given triangular pyramid is; B: 16/3 cm²
What is the Volume of the Pyramid?
Formula for volume of a triangular pyramid is;
V = ¹/₃ * Base area * height
We are given;
Base area = area of the equilateral triangle = 12 cm²
Height of the pyramid = length of its edge = 4/3 cm
Thus;
V = ¹/₃ * 12 * (4/3)
V = 16/3 cm³
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A restaurant stores flour, rice, and sugar in three different cylindrical containers.
The height of the rice cylinder is 12in.
The volume of the flour cylinder is 50.24 in.
What is a cylinder?A cylinder is a 3-D figure that has a radius and a height.
The volume of a cylinder is given as πr²h.
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume.
= 3.14 x 2 x 2 x 5
= 62.8 cm³
We have,
Sugar cylinder:
radius = 2.5 in
height = 8 in
Volume.
= πr²h
= 3.14 x 2.5 x 2.5 x 8
= 157 in²
Rice cylinder:
radius = 2.5 in
height = h
Volume = πr²h
Volume = 235.5 in²
πr²h = 235.5
3.14 x 2.5 x 2.5 x h = 235.5
196.26 x h = 235.5
h = 12 in
Flour cylinder:
Area of base = 12.56 in²
height = 4 in
Volume = x
Area of base = πr²
12.56 = 3.14 x r²
r² = 12.56/3.14
r² = 4
r = 2
Now,
Volume.
= πr²h
= 3.14 x 2 x 2 x 4
= 50.24 in²
Thus,
The solution for each cylinder is given above.
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A book is bought for 350 and sold for R490. Calculate the percentage profit.
well, the profit is clearly just 490 - 350 = 140.
Now, if we take 350(origin amount) to be the 100%, what is 140 off of it in percentage?
\(\begin{array}{ccll} Amount&\%\\ \cline{1-2} 350 & 100\\ 140& x \end{array} \implies \cfrac{350}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{5}{2} ~~=~~ \cfrac{100}{x}\implies 5x=200\implies x=\cfrac{200}{5}\implies x=40\)
Find the midpoint of AB when A=(1,-2) B=(1,-1)
Answer:
Midpoint Of AB = ( 1+1/2 , -2-1/2)
= (2/2 , -3/2)
= ( 1 , -1.5)
Hope this helps
Please mark Branliest.
Answer:
-2,0
Step-by-step explanation:
the first and last term arithmetic sequence are 9 and 165 respectively.if the sum of all the terms of the arithmetic sequence is 3480,find the number of terms and the common difference of this arithmetic sequence
Answer:
40 termsStep-by-step explanation:
Sum of n terms formula:
Sn = 1/2n(a1 + an)Solving for n
3480 = 1/2n(9 + 165)3480 = 87nn = 3480/87n = 40Answer:
Required Answer:-first term =a=9Last term =l=165 Sn=3480As we know that in a AP
\({:}\longrightarrow\)\(\sf S_n={\dfrac {1}{2}}(a+l)n\)
Substitute the values\({:}\longrightarrow\)\(\sf 3480={\dfrac {1}{2}} (9+165)n\)
\({:}\longrightarrow\)\(\sf 3480={\dfrac {1}{2}}(174)n\)
\({:}\longrightarrow\)\(\sf 3480={\dfrac {174}{2}}n \)
\({:}\longrightarrow\)\(\sf 3480=87n \)
\({:}\longrightarrow\)\(\sf n={\dfrac {3480}{87}}\)
\({:}\longrightarrow\)\(\sf n=40\)
\(\therefore\)Number of terms=40.
anyone wanna help me with this??
Answer:
1.c
2.b
3. c
4.d
Step-by-step explanation:
leave an brainlest!
x-intercept of 3 and y-intercept of 8
How do you write a lunar equation given this information and how do you write the equation in slope form
Answer:
y = -8/3x + 8
Step-by-step explanation:
Step 1: Identify which values we have and need to find in the slope-intercept form:
The general equation of the slope-intercept form of a line is given by:
y = mx + b, where
(x, y) is any point,m is the slope,and b is the y-intercept.Since we're told that the y-intercept is 8, this is our b value in the slope-intercept form.
Step 2: Find m, the slope of the line:
Since the x-intercept is 3, the entire coordinates of the x-intercept are (3, 0)Thus, we can find m, the slope of the line by plugging in (3, 0) for (x, y) and 8 for b:
0 = m(3) + 8
0 = 3m + 8
-8 = 3m
-8/3 = m
Thus, the slope is -8/3.
Therefore, the the equation of the line in slope-intercept form whose x-intercept is 3 and whose y-intercept is 8 is y = -8/3x + 8.
Optional Step 3: Check the validity of the answer:
We know that the entire coordinates of the x-intercept are (3, 0) and the entire coordinates of the y-intercept are (0, 8).Thus, we can check that we've found the correct equation in slope-intercept form by plugging in (3, 0) and (0, 8) for (x, y), -8/3 for m, and 8 for b and seeing if we get the same answer on both sides of the equation when simplifying:
Plugging in (3, 0) for (x, y) along with -8/3 for m and 8 for b:
0 = -8/3(3) + 8
0 = -24/3 + 8
0 = -8 = 8
0 = 0
Plugging in (0, 8) for (x, y) along with -8/3 for m and 8 for b;
8 = -8/3(0) + 8
8 = 0 + 8
8 = 8
Thus, the equation we've found is correct as it contains the points (3, 0) and (0, 8), which are the x and y intercepts.
1. Line A ang Line B are parallel lines cut by Transversals x and y. 2 = 57° and 3 = 85°, Find the measure of 5.
Answer:
Step-by-step explanation:
∠1 = 180° - ∠2 - ∠3 = 38°
∠5 = ∠1 = 38°
solve for the inequality ᵏ⁄₄ ≥ 6
Answer:
k ≥ 24
Step-by-step explanation:
ᵏ⁄₄ ≥ 6
Multiply each side by 4
ᵏ⁄₄ *4 ≥ 6*4
k ≥ 24
Answer:
k≥24
Step-by-step explanation:
k/4≥6
Use the multiplication property of equality by multiplying both sides by 4 to get
k≥24
If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem
Thank you
Exercise 1 (7 points)
The following data represent the scores of students in an Inferential
Statistics examination 5-12-8-14-11.
1. Determine the mean, variance and standard deviation of this population
2. How many simple random samples of size 2 can be constructed in an
exhaustive manner?
3. The sampling distribution of the sample means is studied, determine
the mean, variance and standard error of this sampling distribution.
4. Determine the variance of this sampling distribution.
5. This is considered to be data from a simple random sample, determine a
point estimate of the population mean and variance.
Answer: 1.To find the mean, we sum up all the scores and divide by the number of scores:
Mean = (5 + 12 + 8 + 14 + 11) / 5 = 50 / 5 = 10
To find the variance, we first find the deviation of each score from the mean:
5 - 10 = -5
12 - 10 = 2
8 - 10 = -2
14 - 10 = 4
11 - 10 = 1
We square each deviation and sum them up:
(-5)^2 + 2^2 + (-2)^2 + 4^2 + 1^2 = 26
Then, we divide by the number of scores to find the variance:
Variance = 26 / 5 = 5.2
Finally, we find the standard deviation by taking the square root of the variance:
Standard deviation = √5.2 = 2.28
2. To construct a simple random sample of size 2, we can choose any two scores from the population. The number of ways to do this is given by the combination formula:
C(5,2) = 5! / (2! * (5 - 2)!) = 10
Therefore, there are 10 simple random samples of size 2 that can be constructed.
3.The mean of the sampling distribution of the sample means is equal to the population mean, which we found to be 10. The variance of the sampling distribution is equal to the population variance divided by the sample size:
Variance of sampling distribution = Variance / Sample size = 5.2 / 2 = 2.6
The standard error of the sampling distribution is the square root of the variance:
Standard error = √2.6 = 1.61
4.The variance of the sampling distribution is 2.6, as we found in part
5. Since this is considered to be data from a simple random sample, we can use the sample mean as a point estimate of the population mean. Therefore, the point estimate of the population mean is 10.
Similarly, we can use the sample variance as a point estimate of the population variance. However, we need to correct for the bias in the sample variance by dividing by (n-1) instead of n:
Point estimate of population variance = Variance * (n / (n-1)) = 5.2 * (5 / 4) = 6.5
Step-by-step explanation:
The half-life of a radioactive substance is one day, meaning that every day half of the substance has decayed. Suppose you have 95 grams of this substance. Construct an exponential model for the amount of the substance remaining on a given day. Use your model to determine how much of the substance will be left after 4 days
Answer:
Exponential model
Y = y0e-0.693(t½)
Amount remaining after 4 days
5.9413 grams
Step-by-step explanation:
The formula will he given by
Y = y0e-k(t½)
The half life t½ for this radioactive substance is a day.
Initial mass y0 = 95 grams
Mass after one day = 95/2
Mass after one day = 47.5
.
Value of the decay constant k is not given, let's look for k.
Y = y0e-k(t½)
47.5= 95e-k(1)
47.5/95= e-k(1)
0.5= e-k(1)
In 0.5 = -k
-0.693= -k
0.693 = k
Y = y0e-0.693(t½)
Amount remaining after 4 days
Y = y0e-0.693(t½)
Y = 95e-0.693(4)
Y= 95e-2.772
Y= 95(0.06254)
Y= 5.9413 grams
Ana works 25 hours a week at the library. If she is paid $10 an hour, and her net salary each week is $212.50, what percent of her salary is withheld for taxes?
Approximately 17.65% of Ana's salary is withheld for taxes.
To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.
Number of hours worked per week (H) = 25 hours
Hourly wage (W) = $10
Net salary (S) = $212.50
Calculate the total earnings before taxes:
Total earnings = Hours worked * Hourly wage
Total earnings = 25 hours * $10/hour
Total earnings = $250
Determine the amount of tax withheld:
Tax withheld = Total earnings - Net salary
Tax withheld = $250 - $212.50
Tax withheld = $37.50
Calculate the percentage of salary withheld for taxes:
Percentage withheld = (Tax withheld / Net salary) * 100
Percentage withheld = ($37.50 / $212.50) * 100
Percentage withheld ≈ 17.65%
Therefore, approximately 17.65% of Ana's salary is withheld for taxes.
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Noah and Andre are 15 miles apart on a bike path when they start biking toward each other. Nosh rides at a constant speed of 4 miles per hour and Andre rides at a constant speed of 2 miles per hour. How long does it take until Noah and Andre meet?
The time that it will take until Noah and Andre meet is; 2.5 hours
How to solve Distance Time problems?Let t represent the time it would take for Noah and Andre to meet.
Formula to find distance is;
Distance = speed × time
Noah rides at a constant speed of 4 miles per hour. This tells us that the distance that Noah would cover in t hours is expressed as 4t.
Andre rides at a constant speed of 2 miles per hour. This tells us that the distance that Andre would cover in t hours is 2t
Since the total distance is 15 miles, then we can form the equation as;
4t + 2t = 15
6t = 15
t = 15/6
t = 2.5 hours
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PLEASE HELP FAST ILL FIVE YOU ALL THE REST OF MY POINTS FOR THIS ONE ANSWER CHEKC IT FIRST BEFORE YOU ANSWER!!!
Answer:
They intersect at (-4,-3)
Step-by-step explanation:
hope that helps
Please help me whoever gets the answer right first will get brainliest
Answer:I believe its this
Step-by-step explanation:
you can see the step by step in the attached image as well as the result
Winston is making a model of a statute using a scale where 2 inches equals 6 feet. If the actual height of
the statue is 20 feet, how tall is the model, in inches?
Answer:
6 2/3 inches
Step-by-step explanation:
2 inches / 6 feet * 20 feet = 6 2/3 inches
Fill in the blank for this question!
While an absolute value may be any number, the output from an absolute value expression is always greater than or equal to zero
How to Interpret an Absolute Value Function?The absolute value | x | of a real number x is defined as the non-negative value of x without regard to its sign. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero along real number line.
The absolute value of any number is seen to be always greater than or equal to zero. Both a number and its opposite are the same distance from zero on the number line. Since they have the same distance from zero, they have the same absolute value.
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find the equation of the line through point (4,-7) and parallel to y = -2/3x + 3/2.
Answer:
y = -2/3 x - 13/3
Step-by-step explanation:
y = -2/3 x + 3/2
y = mx + b
m = -2/3
The slope of the given line is -2/3. Parallel lines have equal slopes, so our line also has slope -2/3.
m = -2/3
y = mx + b
y = -2/3 x + b
Substitute the given point for x and y and solve for b.
-7 = -2/3 (4) + b
-21/3 = -8/3 + b
b = -13/3
Answer: y = -2/3 x - 13/3
B. What is each piece measurement if the angle is cut into 9 equal
lengths? Kerf width is 0.125.
Each piece Measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.
When a particular angle is cut into nine equal parts, the measure of each piece needs to be calculated.
Therefore, it is essential to first calculate the total angle measure and then divide it by the number of parts into which it is being cut.
What is an Angle?
An angle is a geometrical shape that consists of two rays sharing a common endpoint. The common endpoint is known as the vertex, and the two rays are known as the arms of the angle. An angle can be measured in degrees, radians, or gradians. Degrees are the most commonly used unit of measuring angles.How to Calculate Each Piece Measurement of an Angle if Cut into 9 Equal Lengths
To determine each piece measurement of an angle if cut into nine equal lengths, we will need to carry out the following steps:
Step 1: Calculate the total angle measure Suppose the angle being cut into nine equal lengths is an obtuse angle measuring 120 degrees. In that case, the total angle measure will be 120 degrees.
Step 2: Divide the total angle measure by the number of parts into which it is being cut.120 degrees ÷ 9 = 13.3333 degrees
Step 3: Add the kerf width to the piece measurements.0.125 x 9 = 1.125 degrees13.3333 + 1.125 = 14.4583 degrees
Therefore, each piece measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.
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what does 2/5y-4+7-9/10y=
answer this guys i will give brainliest! have a good day !!!
The ratios are;
Sin θ = 5/6
Cos θ = √11/6
Tan θ = 5√11/11
Sec θ = 6√11/11
Cosec θ = 6/5
Cot θ = √11/5
What are the six trigonometric ratios?These trigonometric ratios are used to relate the angles of a right triangle to the lengths of its sides
We can see that the hypotenuse is obtained from;
x =√\((10)^2 + (2\sqrt{} 11)^2\)
x = √100 + 44
x = 12
Then;
Sin θ = 10/12 = 5/6
Cos θ = 2√11/12
= √11/6
Tan θ = 10/2√11
= 20√11/44
= 5√11/11
Sec θ = 1/Cos θ
= 6/√11
= 6√11/11
Cosec θ = 1/Sin
θ = 6/5
Cot θ = 1/tan θ
= 11/ 5√11
= 55√11/275
= √11/5
Sinβ = 2√11/12
= √11/6
Cos β = 10/12
= 5/6
Tan β = 2√11/10
= √11/5
Sec β = 6/5
Cosec β = 6√11/11
Cot β = 5√11/11
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(i) Write the zeroes of the polynomial by using above graph.
(ii)Form a quadratic polynomial for above graph.
(iii)If a,1/a are the zeroes of polynomial 2x² -x +8k, then find the value of k.
please answer
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There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.
(i) Zeroes of the polynomial:
In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:
From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.
We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:
We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.
The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a
Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,
we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0
Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))
Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.
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What are the rectangular coordinates of the polar coordinates?
The rectangular coordinate from the given polar coordinate is (2.73, -0.73)
What are the rectangular coordinatesTo find the rectangular coordinate from the polar coordinates, we can rewrite this as;
x = r cosθ
y = r sinθ
r = The distance from the origin to the pointθ = The angle the line segment connects with the point and the origin makes along the positive axis.x = r cosθ
Let's substitute the values into it;
x = (2√2)* cos(-π/12)
x =(2√2)cos(-15)
x = √3 + 1
x = 2.73
y = r sin θ
y = (2√2)sin(-π/12)
y = (2√2) * sin (-15)
y = -√3 + 1
y = -0.73
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Consider this function.
f(x) = |x – 4| + 6
If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?
If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.
The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.
If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.
The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).
The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.
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