A population of values has a normal distribution with μ=208.4 and σ=23.2. If a random sample of size n=15 is selected,Find the probability that a single randomly selected value is greater than 192.2. Round your answer to four decimals.P (X > 192.2) =?Find the probability that a sample of size n=15 is randomly selected with a mean greater than 192.2. Round your answer to four decimals.P (M > 192.2) =?
Answers
The probability that a single randomly selected value is greater than 192.2. is 0.698
A population of values has a normal distribution with μ=208.4
Standard deviation of the population is σ=23.2
The random sample size of the population n = 15
P(X > 192.2)
P((x - μ)/σ) > (192.2 - 208.4)/23.2
P(z > -0.698)
Therefore, the probability that a single randomly selected value is greater than 192.2. is 0.698
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Related Questions
Consider the probability that no less than 95 out of 152 registered voters will vote in the presidential election. Assume the probability that a given registered voter will vote in the presidential election is 61%. Approximate the probability using the normal distribution. Round your answer to four decimal places.
Answers
Answer:
0.3821 = 38.21% probability that no less than 95 out of 152 registered voters will vote in the presidential election.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
\(E(X) = np\)
The standard deviation of the binomial distribution is:
\(\sqrt{V(X)} = \sqrt{np(1-p)}\)
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).
Assume the probability that a given registered voter will vote in the presidential election is 61%.
This means that \(p = 0.61\)
152 registed voters:
This means that \(n = 152\)
Mean and Standard deviation:
\(\mu = E(X) = 152*0.61 = 92.72\)
\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{152*0.61*0.39} = 6.01\)
Probability that no less than 95 out of 152 registered voters will vote in the presidential election.
This is, using continuity correction, \(P(X \geq 95 - 0.5) = P(X \geq 94.5)\), which is 1 subtracted by the pvalue of Z when X = 94.5. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{94.5 - 92.72}{6.01}\)
\(Z = 0.3\)
\(Z = 0.3\) has a pvalue of 0.6179
1 - 0.6179 = 0.3821
0.3821 = 38.21% probability that no less than 95 out of 152 registered voters will vote in the presidential election.
The water usage at a car wash is modeled by the equation W(x) = 5x3 + 9x2 − 14x + 9, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours. Write a function, C(x), to model the water used by the car wash on a shorter day. C(x) = 5x3 + 7x2 − 14x − 6 C(x) = 4x3 + 7x2 − 14x + 6 C(x) = 4x3 + 7x2 − 14x − 6 C(x) = 5x3 + 7x2 − 14x + 6
Answers
W(x) - C(x) = 2(W(x) - C(x))
Solving this equation for C(x), we get:
C(x) = (W(x) - 2W(x))
= W(x)(1 - 2)
= (5x3 + 9x2 - 14x + 9)(1 - 2)
= (5x3 + 7x2 - 14x + 6)
Therefore, the function C(x) to model the water used by the car wash on a shorter day is:
C(x) = (5x3 + 7x2 - 14x + 6)
The HCF of three numbers is 8 and the sum of these numbers is 80. List the possible set of such three numbers.
Answers
Let's denote the three numbers A, B, and C.
Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.
Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.
Let's list the possible combinations:
(8, 16, 56): In this case, A = 8, B = 16, and C = 56. All three numbers are divisible by 8, and their sum is 8 + 16 + 56 = 80.(16, 8, 56): Here, A = 16, B = 8, and C = 56. Again, all three numbers are divisible by 8, and their sum is 16 + 8 + 56 = 80.(24, 8, 48): In this combination, A = 24, B = 8, and C = 48. All three numbers are divisible by 8, and their sum is 24 + 8 + 48 = 80.(8, 24, 48): Similarly, A = 8, B = 24, and C = 48. All three numbers are divisible by 8, and their sum is 8 + 24 + 48 = 80.These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).
Find the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0. Also, show in the graph.
Answers
The inversion point of (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).
Finding the inversion pointTo find the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0, we need to follow these steps:
Step 1: Write the equation of the given circle in standard form by completing the square for x and y: (x - 2)² + (y - 3)² = 16.
Step 2: Find the radius of the circle by taking the square root of the constant term: r = √16 = 4.
Step 3: Find the distance between the given point (4, 5) and the center of the circle (2, 3) using the distance formula: d = √[(4 - 2)² + (5 - 3)²] = √8.
Step 4: Use the formula for inversion point to find the coordinates of the inversion point (x', y'): (x', y') = (h + r²/d² * (x - h), k + r²/d² * (y - k)), where (h, k) is the center of the circle and r is the radius.
Plugging in the values, we get: (x', y') = (2 + 4²/8 * (4 - 2), 3 + 4²/8 * (5 - 3)) = (6, 7).
Therefore, the inversion point of the given point (4, 5) with respect to the circle x² + y² - 4x - 6y - 3 = 0 is (6, 7).
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URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100
POINTS!!!!!
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The given statement is false: vertical angle do not depend on the line being parallel. A pair of vertical angles are always congruent.
Vertical angle:
Vertical angle means that the angles opposite each other when two lines cross.
Given,
Here we have the diagram and we also know that angle 7 is congruent to angle 5.
Now we need to find the given statement is true or not.
Through the given diagram, we have identified that, the eight angles will together form four pairs of corresponding angles.
Angles 1 and 5 constitutes one of the pairs.
We know that all the corresponding angles are congruent.
All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.
Through that we know that basically, the vertical angles are always congruent, which means that they are equal. So, it is not necessary for them to be parallel.
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Help me, I will give the brainlyest to the smartest and the fastest!
Answers
Answer:
{(1,4) (2,8) (3,12) (4,16)}
In an arithmetic sequence, a3=15 and a8=0. What is the value of a5?
Answers
Answer:
a3=15 , n=3
a8=0, n=8
a5 = ?
an = a1+ (n-1)d
a3 = a1 + (3-1) d
a3=a1+2d
and a8 = a1 + (8-1 )d
a8= a1+ 7d
15 = a1 + 2 d-------1
0= a1 +7 d----------2
substacting eq 2 from eq 1
15= - 5d
- 5d = 15
divide by - 5
d = -3
putting the value of d in eq 1
15 = a1 + 7 (-3)
15 = a1 -21
adding 21 on both sides
a1-21+21= 15+21
a1 = 36
a5 = ?, n=5, d= -3, a1=36
a5 = 36 + (5-1) (-3)
= 36+(4)(-3)
= 36-12
= 24
HELPPPPPPPPP 80 POINTS!!!
Complete the table, and then use the drawing tools to create the graph representing the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x.
Answers
Answer:
The y-axis is at 72 with a negative slope
Step-by-step explanation:
Searching will help you by making a graph if you search for " f(x) =72-12x" aka the equation you have :D
what is the answer and how do I figure it out
Answers
Answer:
\(\frac{3}{7}\) < \(\frac{3}{5}\)
Step-by-step explanation:
\(\frac{3}{7}\) ? \(\frac{3}{5}\)
We have to get both fractions with the same denominator to compare them.
\(\frac{3}{7}\) = \(\frac{15}{35}\)
\(\frac{3}{5}\) = \(\frac{21}{35}\)
\(\frac{15}{35} < \frac{21}{35}\)
So, \(\frac{3}{7}\) < \(\frac{3}{5}\)
Which is the correct equation for a line that passes through the points (-2,7) and (2,-5)?
y=3x+5
y=1/3x+3
y= -3x-12
y= -3x+1
Answers
Answer:
y= -3x+1
Step-by-step explanation:
x1= -2 x2=2 y1=7 y2=-5
using the formula
(y-y1)/(x-x1)=(y2-y1)/(x2-x1)
(y-7)/(x-(-2))=(-5-7)/(2-(-2))
(y-7)/(x+2)=(-5-7)/(2+2)
(y-7)/(x+2)=(-12)/4
(y-7)/(x+2)=-3
cross multiply
y-7=-3(x+2)
y-7=-3x-6
y=-3x-6+7
y=-3x+1
Principle money = $750. Interest rate = 6% What is the end of year balance?
Answers
The end of the year balance would be = $795
What is interest rate?An interest rate is defined as the percentage of money an individual receives from a particular principal amount of money that was invested by the same individual.
The principle money invested(P) = $750
The rate of interest( R) = 6%
Time (T)= 1 year
Simple interest (SI) = P × T × R /100
= 750 × 1 × 6/100
= 4,500/100
= $45
The amount that would be received would be = 750 + 45 = $795.
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Hi! I need help with this one problem.I have the answer but I need to go through the steps and explain how I got the answer.Please help! The problem is:
a/5-2=9
Answers
Answer:
Move all terms not containing a to the right side of the equation:
a/5 = 11
Multiply both sides of the equation by 5:
5 x a 5 = 5 x 11
Simplify both sides of the equation:
a=55
Step-by-step explanation:
Step by step-
1. Find common denominator
2. Combine fractions with common denominator
3. Multiply the numbers
4. Multiply all terms by the same value to eliminate fraction denominators
5. Cancel multiplied terms that are in the denominator
6. Multiply the numbers
7. Add 10 to both sides of the equation
8. Simplify
(THE PHOTOS SHOW YOU HOW TO DO IT STEP BY STEP IM SORRY, ITS ALOT!)
y=√x Can you please give a graph use color for function, asymptotes, etc.A short table of easy pointsThe domain and rangePlease identify and label the asymptotes (Please work this as if you didn’t have a calculator)
Answers
SQUARE ROOT FUNCTION
Given the parent function:
\(f(x)=\sqrt[]{x}\)Table
\(\begin{gathered} \text{When x}=0,f(x)=\sqrt[]{0}=0\implies(0,0) \\ \text{When x}=1,f(x)=\sqrt[]{1}=1\implies(1,1) \\ \text{When x}=4,f(x)=\sqrt[]{4}=2\implies(4,2) \\ \text{When x}=9,f(x)=\sqrt[]{9}=3\implies(9,3) \\ \text{When x}=16,f(x)=\sqrt[]{16}=4\implies(16,4) \end{gathered}\)First, we prepare a table of easy points:
Graph
The graph of the function is attached below:
Domain and Range
As can be seen from the graph, the domain and range of the square root parent function are:
• Domain: [0, ∞)
,• Range: [0, ∞)
Asymptotes
The square root parent function has NO ASYMPTOTES.
The radius of a circle is 17 centimeters. What is the circle's circumference?
Answers
Answer:
The circle's circumference is approximately 106.81 centimeters.
Explanation:
The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is pi (approximately 3.14), and r is the radius of the circle.
So, for a circle with a radius of 17 centimeters, its circumference can be found by:
C = 2πr
C = 2 x 3.14 x 17
C ≈ 106.81 cm
Therefore, the circumference of the circle is approximately 106.81 centimeters.
What is the population standard deviation?
{5,8,8,5}
Enter your answer as a decimal, rounded to the nearest tenth, like this: 4.2.
Answers
5, 8, 8, 5 has a population standard deviation of 3
Given,
The population is
{5, 8, 8, 5}
The population's mean is calculated as follows:
Sum of terms / Number of terms
Calculate the values and then replace them in the equation.
Sum equals 5 + 8 + 8 + 5 = 26
Number of terms = 4
The population's average is 26 / 4 = 6.5
The population's variance is equal to (5 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (5 - 6.5)²
= (-1.5) (-1.5)² + (1.5) (1.5)² + 1.5² + (-1.5) (-1.5)²
= 2.25 + 2.25 + 2.25 + 2.25
= 9
The population's standard deviation is equal to
= 3
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a vehicle purchased for $25,000 depreciates at a constant rate of 5%. determine the approximate value of the vehicle 12 years after purchase. round to the nearest whole dollar.
Answers
The value of the vehicle after 12 years of purchase will be $13,500.
Here, we are given that a vehicle purchased for $25,000 depreciates at a constant rate of 5%.
Therefore, the value of the vehicle after 1 year will reduce by-
25,000 × 5/100
= 250 × 5
= 1250
Thus, the value after 1 year will become = 25,000 - 1250 = 23750
In the same manner, the value will keep on reducing every year. Thus, the value after 12 years will become-
25,000 \((1- 5/100)^{12}\)
= 25,000 \((1 - 0.05)^{12}\)
= 25,000 \((0.95)^{12}\)
= 25,000 × 0.54
= 250 × 54
= 13,500
Thus, the value of the vehicle after 12 years of purchase will be $13,500.
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Four times a number plus three times a second number is negative nine. Twice the first number plus the second number is three.
Call the first number m and the second number n.
Answers
Answer:
m=9
n=-15
Step-by-step explanation:
If you set it up in a systems of equations way, ou would have
4m+3n=-9
+ . 2m+n=3
-------------------
You would need to cancel out a variable and in my opinion, canceling m out is easier.
4m+3n=-9
+-4m-2n=-6
-------------------
0m+n=-15
n=-15
you then plug this into one of the equations, (in my opinion the 2nd one is easier)
2m-15=3
2m=18
m=9
this gives you m so you can get the answer
m=9 and n=-15
4x² + 24x + 20
common factor =
Answers
how many 3-inch pieces can you cut from 5 yards of cloth?
Answers
Answer:
60 pieces
Step-by-step explanation:
1 yard = 36 inches
5 yard = 180 inches
180inches ÷ 3inches pieces = 60pieces
We can cut 60 pieces of cloth of 3 inches each from a 5-yard cloth.
What are yards?A measurement that is 3 feet or 36 inches long (or wide) in US units. In the metric system, a yard is equal to 0.9144 meters (the yard is defined that way).Yards to inches:1 yard = 36 inches
Solution -1 yard = 36 inches
5 yards = \(5(36)\) inches
5 yards = 180 inches
Now, divide 180 by 3 to get the number of cloth.
\(\frac{180}{3} =60\)
Therefore, you can cut 60 pieces of cloth.
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A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1080 feet of fencing material, what should be the length and width of the field?
Answers
The width of the field is 230 feet and the length is 310 feet.
Let's denote the width of the field as "x" feet.
The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.
To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:
2(length) + 2(width) = perimeter
Substituting the given values:
2(x + 80) + 2(x) = 1080
2x + 160 + 2x = 1080
4x + 160 = 1080
4x = 920
x = 920/4
x = 230
Therefore, the width of the field is 230 feet.
Now we can find the length by adding 80 feet to the width:
Length = Width + 80 = 230 + 80 = 310 feet.
So, the width of the field is 230 feet and the length is 310 feet.
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Vertices A(a, -6, 2), B(4,b,-9), C(3,5,c) and D(-2,-5,11) form a parallelogram. Determine the values of a,b,c.
Answers
Let's do a quick draw to help us visualize the problem:
That's a generic parallelogram, to verify that it's a parallelogram we can see that
\(\begin{gathered} AB=CD \\ \\ BC=AD \end{gathered}\)The opposite lengths are equal, then, let's do something similar here, let's say that
\(\vec{AB}=\vec{CD}\)then
\(\begin{gathered} \vec{AB}=B-A=(4,b,-9)-(a,-6,2)=(4-a,b+6,-9-2) \\ \\ \vec{AB}=(4-a,b+6,-11) \end{gathered}\)And the vector CD
\(\begin{gathered} \vec{CD}=D-C=(-2,-5,11)-(3,5,c)=(-2-3,-5-5,11-c) \\ \\ \vec{CD}=(-5,-10,11-c) \end{gathered}\)Let's impose our condition
\(\begin{gathered} \begin{equation*} \vec{AB}=\vec{CD} \end{equation*} \\ \\ (4-a,b+6,-11)=(-5,-10,11-c) \\ \\ \end{gathered}\)Then
\(\begin{gathered} 4-a=-5 \\ \\ b+6=-10 \\ \\ 11-c=-11 \end{gathered}\)By solving that equations we get
\(\begin{gathered} a=9 \\ \\ b=-16 \\ \\ c=22 \end{gathered}\)
Cuál es el valor de la siguiente expresión?
(6 + 27) / (5 - 2)
Answers
Answer: 11
Step-by-step explanation:
6+27=33
33/3 = 11
50
Select the correct answer.
S
The spread of data set X is greater than the spread of data set Y, and the data sets are normally distributed. Which statement is true?
OA. The mean of data set X is greater than the mean of data set Y.
The median of data set X is less than the median of data set Y.
The standard deviation of data set X is greater than the standard deviation of data set Y.
The range of data set X is less than the range of data set Y.
The mode of data set X is greater than the mode of data set Y.
B.
O C.
O D.
OE
entum. All rights reserved.
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If the spread of data set X is greater than the spread of data set Y, and the data sets are normally distributed. The statement that is true is: C. The standard deviation of data set X is greater than the standard deviation of data set Y.
What is data set?A data set standard deviation is often used to calculate its spread. As a result the standard deviation of data set X will be higher than the standard deviation of data set Y if the spread of data set X is bigger than the spread of data set Y.
The standard deviation may or may not have the same distribution as the the following :
The meanThe medianThe range and mode based on the fact that they are not directly related to the dispersion of a data collection.Therefore the correct option is C.
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Someone, please help! I really don't understand congruent triangles
Answers
Answer:
D. (CPCTC)
Step-by-step explanation:
Your proof that the triangles are congruent is complete at the 4th step. In Step 5, you are asked to draw a conclusion about corresponding angles in those congruent triangles.
__
what is congruence?Two geometric objects are congruent if they are identical in size and shape by any measure. If they are not labeled, you cannot tell them apart. Every measure of one is identical to the corresponding measure of the other. The location and orientation of congruent figures does not affect their congruence. You can move them, rotate them, flip them over, and they remain congruent.
This property, "corresponding parts of congruent triangles are congruent," is abbreviated "CPCTC." Once you have demonstrated objects are congruent, you can use this fact to relate measures of the objects that may not have been part of the demonstration.
proving congruencegeneral
We generally work with plane geometric figures that are polygons or have well-defined curved edges. Polygon figures are comprised of straight sides of fixed length. At each vertex, where sides meet, an angle is formed. Corresponding sides form corresponding angles.
The sides are generally named by the vertices at either end. The angles may be named by the vertex where it is located, or by the names of the sides that make it up.
In triangle ABC, for example, the vertices have labels A, B, and C. The sides are AB, AC, and BC. And the angles are A, B, and C, or BAC, ABC, ACB. (The vertex of the angle is the middle letter.)
To prove polygons are congruent, you must show corresponding angles are congruent, and corresponding sides are congruent. Generally, the number of sides will put constraints on the size of the angles. (A 6-sided polygon will have 6 angles that total 720°, for example.)
triangles
When the polygon is a triangle, the constraints on side lengths and angles generally mean there are shortcuts to proving congruence. The postulates that tell you what these are have been given mnemonic abbreviations. When we say, "angle" or "side" in this context, we are referring to congruent corresponding angles in the two triangles, or congruent corresponding sides.
AAS -- two consecutive angles and a side adjacent to one of them will prove congruenceASA -- two angles and the side between them will prove congruenceSAS -- two sides and the angle between them will prove congruenceSSS -- three sides will prove congruenceThese can also be applied to right triangles, where one angle is known to be 90°. In addition, there is a theorem that only applies to right triangles:
HL -- the hypotenuse and one leg will prove congruence. (Note that the hypotenuse is opposite the known 90° angle, so this is effectively an SSA congruence statement, only applicable to right triangles.)your proof
The triangles in your figure have a side marked with a single hash mark. This means those corresponding sides in the two triangles are congruent to each other.
There is an angle marked with two (2) arcs in each triangle. This marking means those corresponding angles are congruent. Likewise for the angles marked with three (3) arcs. You will notice the 3-arc angle, 2-arc angle, and 1-hash mark side are in the same order in the two triangles. This means the AAS congruence postulate applies, as is claimed on line 4 of your proof.
using congruenceAs you have seen, we only need to show some parts of a triangle are congruent in order to show all parts of the triangle are congruent. When we make a claim about corresponding parts that weren't an explicit part of the proof, we are essentially relying on the definition of congruent polygons. For triangles, that definition is summarized by the abbreviation CPCTC.
Line 5 of your 2-column proof is making a claim about corresponding angles of the triangle. That claim is supported by CPCTC.
_____
Additional comment
Choices A and C refer to congruence postulates, as discussed above. Those have no relation to the claim regarding angles ACB and XZY.
The "corresponding angles theorem" tells you corresponding angles are congruent where a transversal crosses parallel lines. It has no relation to the angles in this problem.
Given that the height of a particular object at time t is
h(t) = 50t - 4.9t^2, find h when t = 2h (2)
40
Answers
If the Time taken by object is 2 hour then the height will be 80.4 feet.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
We have Given the function as
h(t) = 50t - 4.9t²
If time = 2 hours then put the value of t=2 in the above Equation we get
h(t) = 50t - 4.9t²
h(t) = 50(2) - 4.9(2)²
h(t) = 100 - 4.9 x 4
h(2) = 100 - 19.6
h(2)= 80.4
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In Exercises 11-18, use analytic methods to find the extreme values of the function on the interval and where they occur. Identify any critical points that are not stationary points.
15. f(x) = sin(x + π/4), 0 ≤ x ≤ 7π/4
Answers
Answer:
Absolute maximum of 1 at x = pi/4 ; \((\frac{\pi}{4}, \ 1)\)
Absolute minimum of -1 at x = 5pi/4 ; \((\frac{5\pi}{4} , \ -1)\)
Local maximum of √2/2 at x = 0 ; \((0, \ \frac{\sqrt{2} }{2} )\)
Local minimum of 0 at x = 7pi/4 ; \((\frac{7\pi}{4}, \ 0)\)
No critical points that are not stationary points.
Step-by-step explanation:
\(f(x)=sin(x+\frac{\pi}{4} ), \ 0 \leq x\leq \frac{7 \pi}{4}\)
Take Derivative of f(x):Let's start by taking the derivative of the function.
Use the power rule and the chain rule to take the derivative of f(x).
\(f'(x)=\frac{d}{dx} [sin(x+\frac{\pi}{4})] \times \frac{d}{dx} (x+\frac{\pi}{4})\)The derivative of sin(x) is cos(x), so we can write this as:
\(f'(x)=cos(x+\frac{\pi}{4})\times \frac{d}{dx} (x+\frac{\pi}{4})\)Now, we can apply the power rule to x + pi/4.
\(f'(x)=cos(x+\frac{\pi}{4} ) \times 1\) \(f'(x)=cos(x+\frac{\pi}{4} )\)Critical Points: Set f'(x) = 0Now that we have the first derivative of \(f(x)=sin(x+\frac{\pi}{4})\), let's set the first derivative to 0 to find the critical points of this function.
\(0=cos(x+\frac{\pi}{4})\)Take the inverse cosine of both sides of the equation.
\(cos^-^1(0) = cos^-^1[cos(x+\frac{\pi}{4})]\)Inverse cosine and cosine cancel out, leaving us with x + pi/4. The inverse cosine of 0 is equal to 90 degrees, which is the same as pi/2.
\(\frac{\pi}{2} = x +\frac{\pi}{4}\)Solve for x to find the critical points of f(x). Subtract pi/4 from both sides of the equation, and move x to the left using the symmetric property of equality.
\(x=\frac{\pi}{2}- \frac{\pi}{4}\)\(x=\frac{2 \pi}{4}-\frac{\pi}{4}\) \(x=\frac{\pi}{4}\)Since we are given the domain of the function, let's use the period of sin to find our other critical point: 5pi/4. This is equivalent to pi/4. Therefore, our critical points are:
\(\frac{\pi}{4}, \frac{5 \pi}{4}\) Sign Chart(?):Since this is a sine graph, we don't need to create a sign chart to check if the critical values are, in fact, extreme values since there are many absolute maximums and absolute minimums on the sine graph.
There will always be either an absolute maximum or an absolute minimum at the critical values where the first derivative is equal to 0, because this is where the sine graph curves and forms these.
Therefore, we can plug the critical values into the original function f(x) in order to find the value at which these extreme values occur. We also need to plug in the endpoints of the function, which are the domain restrictions.
Let's plug in the critical point values and endpoint values into the function f(x) to find where the extreme values occur on the graph of this function.
Critical Point Values:\(f(\frac{\pi}{4} )=sin(\frac{\pi}{4} + \frac{\pi}{4} ) \\ f(\frac{\pi}{4} )=sin(\frac{2\pi}{4}) \\ f(\frac{\pi}{4} )=sin(\frac{\pi}{2}) \\ f(\frac{\pi}{4} )=1\)There is a maximum value of 1 at x = pi/4.
\(f(\frac{5\pi}{4} )=sin(\frac{5\pi}{4} + \frac{\pi}{4} ) \\ f(\frac{5\pi}{4} )=sin(\frac{6\pi}{4}) \\ f(\frac{5\pi}{4}) = sin(\frac{3\pi}{2}) \\ f(\frac{5\pi}{4} )=-1\)There is a minimum value of -1 at x = 5pi/4.
Endpoint Values:\(f(0) = sin((0) + \frac{\pi}{4}) \\ f(0) = sin(\frac{\pi}{4}) \\ f(0) = \frac{\sqrt{2} }{2}\)There is a maximum value of √2/2 at x = 0.
\(f(\frac{7\pi}{4} ) =sin(\frac{7\pi}{4} +\frac{\pi}{4}) \\ f(\frac{7\pi}{4} ) =sin(\frac{8\pi}{4}) \\ f(\frac{7\pi}{4} ) =sin(2\pi) \\ f(\frac{7\pi}{4} ) =0\)There is a minimum value of 0 at x = 7pi/4.
We need to first compare the critical point values and then compare the endpoint values to determine whether they are maximum or minimums.
Stationary Points:A critical point is called a stationary point if f'(x) = 0.
Since f'(x) is zero at both of the critical points, there are no critical points that are not stationary points.
Express 31% as a fraction in its lowest form- I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!
Answers
Answer:
31/100
Step-by-step explanation:
31% as a fraction can be represented as 0.31 as a decimal. 0.31 as a decimal can be represented as 31/100 as a fraction. Since 31 is a prime number, it cannot be simplified.
The simplest form 31% is 0.31.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
31% is number
Now, to convert the percent into fraction
=31 /100
As, 31 is prime number having no factor other than 31 and 1 .
So, 31/100= 0.31
Hence, the simplest form 31% is 0.31.
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Pedrobuysawheelbarrowpricedat$86.Shippingandhandlingareanadditional30%oftheprice.HowmuchshippingandhandlingwillPedropay?
Answers
The price of the wheelbarrow is $86, and Pedro will need to pay an additional 30% of the price for shipping and handling.
To calculate the shipping and handling cost, we can first find 30% of the price of the wheelbarrow:
30% of $86 = 0.3 x $86 = $25.80
Therefore, Pedro will need to pay $25.80 for shipping and handling.
4lb 7oz; oz
1 pound = 16 oz
Answers
Answer:
71 oz
Step-by-step explanation:
components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 87% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 26% of all defective components. what is the probability that the following occur?
Answers
The probability that a defective component will be detected only by the first inspector is 0.19
The probability that a defective component will be detected by exactly one of the two inspectors is 0.38
The probability that all three defective components in a batch escape detection by both inspectors is 0.
It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.
Therefore P(A)=P(B)=81%=0.81
At least one inspector does not detect a defect on 38% of all defective components.
Therefore, bar P(A∩B)=0.38
As we know:
bar P(A∩B)=1-P(A∩B)=0.38
P(A∩B)=1-0.38=0.62
A defective component will be detected only by the first inspector.
P(A∩barB)=P(A)-P(A∩B)
=0.81-0.62
P(A∩barB)=0.19
The probability that a defective component will be detected only by the first inspector is 0.19
Part (B) A defective component will be detected by exactly one of the two inspectors.
This can be written as: P(A∩barB)+P(barA∩B)
As we know:
P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)
Substitute the respective values we get:
P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)
=0.81+0.81-2(0.62)
=1.62-1.24
P(A∩ barB)+P(bar A∩B)=0.38
The probability that a defective component will be detected by exactly one of the two inspectors is 0.38
Part (C) All three defective components in a batch escape detection by both inspectors
This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)
As we know bar P(A∩B)=P(bar A∪ bar B)=0.38
From part (B): P(bar A∩B)+P(A∩bar B)=0.38
This can be written as:
P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0
The probability that all three defective components in a batch escape detection by both inspectors is 0
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