cos 36 × cos 72 = 0.25
cos 36 × cos 72 =
0.309 x 0.809 = 0.249 = 0.25
The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2. (a) What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2
Answer:
0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.
This means that [tex]\mu = 14, \sigma = 2[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex]
What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?
This is 1 subtracted by the p-value of Z when X = 14.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{14.2 - 14}{0.2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
1 - 0.8413 = 0.1587
0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.
The following dot plot shows the number of chocolate chips in each cookie that Shawn has. Each dot represents a different cookie. Which of the following is a typical amount of chocolate chips in one of Shawn's cookies?
Choose 1 answer:
Please help me!!!!
Using the dot plot, it is found that a typical amount of chocolate chips in one of Shawn's cookies is around 4.56.
What is a dot plot?The dot plot is a graph shows the number of times each measure appears in the data-set.
Researching this problem on the internet, the dot plot states that:
2 cookies have 2 chips.2 cookies have 3 chips.5 cookies have 4 chips.4 cookies have 5 ships.3 cookies have 6 ships.2 cookies have 7 chips.The mean is given by:
M = (2 x 2 + 2 x 3 + 5 x 4 + 4 x 5 + 3 x 6 + 2 x 7)/(2 + 2 + 5 + 4 + 3 + 2) = 4.56.
Hence, a typical amount of chocolate chips in one of Shawn's cookies is around 4.56.
More can be learned about dot plots at https://brainly.com/question/24912483
Answer:
5 chocolate chips
Step-by-step explanation:
did on khan
George would like to build a garden this year, George measure out his proposed garden and would like to know how many square feet of space he will have to use . Calculate the area of the garden from the picture below
Answer:
The area is 105.5ft^2
Step-by-step explanation:
Required
The area of the composite figure
The figure can be divided to 2 shapes
(1) Rectangle: Length = 6ft and Width = 8ft
(2) Trapezoid: Height = 5ft (i.e. 8 - 3), Parallel sides = 9ft and 14ft (i.e. 20 - 6)
The area of the rectangle is:
[tex]Area = 6 * 8 = 48[/tex]
The area of the trapezoid is:
[tex]Area = \frac{1}{2}(9 + 14) * 5[/tex]
[tex]Area = \frac{1}{2}(23) * 5[/tex]
[tex]Area = 11.5 * 5[/tex]
[tex]Area = 57.5[/tex]
So, the area of the garden is:
[tex]Total = 48 + 57.5[/tex]
[tex]Total = 105.5[/tex]
Need help please with end behavior!
I'll focus on problem 2.
For these types of problems, I recommend graphing the functions to see how the end behavior looks.
The graph of y = x^2 has a parabola where both endpoints aim upward. So each end goes to positive infinity (regardless if x is going to positive or negative infinity).
In short, the graph rises to the left and it rises to the right.
Increasing the leading coefficient will not change this fact. We can pick any leading coefficient we want and the end behavior will stay the same. All that matters is the leading coefficient is positive.
If the leading coefficient becomes negative, then everything flips: the endpoints will aim down. The other terms we add on (such as a 3x+3) will not change the end behavior. The leading term, with the largest exponent, is what directly and solely determines the end behavior.
The graph is shown below. I used GeoGebra to make the graph. Desmos is another handy tool you could use.
if ABCD is a cyclic quadrilateral and A,B,C,D are its interior angles , then prove that
tanA/2+tanB/2=cotC/2+cotD/2
answer the question plz
dont spam or else i will report that
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Explanation:
In a cyclic quadrilateral, opposite angles are supplementary. This means ...
A + C = 180° ⇒ A/2 +C/2 = 90° ⇒ C/2 = 90° -A/2
B + D = 180° ⇒ B/2 +D/2 = 90° ⇒ D/2 = 90° -B/2
It is a trig identity that ...
tan(α) = cot(90° -α)
so we have ...
tan(A/2) = cot(90° -A/2) = cot(C/2)
and
tan(B/2) = cot(90° -B/2) = cot(D/2)
Adding these two equations together gives the desired result:
tan(A/2) +tan(B/2) = cot(C/2) +cot(D/2)
Anempt 1012
Find the mean for the given set of data.
-4,-3,-1,-1, 0,1
Answer:
-1 1/3
Step-by-step explanation:
To find the mean, add up all the numbers
(-4+-3+-1+-1+0+1) =
-8
Then divide by the number of terms
-8/6
-4/3
-1 1/3
Answer A is your answer
Step-by-step explanation:
Please help ASAP!!!
Answer:
C.
Step-by-step explanation:
When you replace x with x - h, the graph shifts h units horizontally.
Here, x is replaced by x - 12.
Compare x - 12 to x - h.
h = 12
The graph shifts 12 units to the right.
Answer:
answer maybe A..not sure but it might be in my opinion..
90 dollars ratio in 1:2:3
Answer:
3:6:9
Step-by-step explanation:
1/1+2+3 × 90 = 15
2/1+2+3 × 90 = 30
3/1+2+3 × 90 = 45
If i Bahraini dinar = £2.13, convert 4000 dinar to pounds. show your working.
Answer:
£8520
Step-by-step explanation:
1 Bahraini dinar = £2.13
Multiply both sides of the equation by 4000.
4000 * 1 Bahraini dinar = 4000 * £2.13
4000 Bahraini dinar = £8520
A block of wood has the shape of a triangular prism. The bases are right triangles. Find its surface area. 4.5 in 6 in 16 in 7.5 in
Answer:
315 in²
Step-by-step explanation:
the surface area is the sum of the areas of all the individual shapes in the surface.
so, we have the 2 triangular bases and 3 rectangles as is sides.
the area of a rectangular triangle is a×b/2
we need them twice, so that is then a×b
a=4.5
b=6
a×b = 27 in²
one rectangle is 16×7.5 = 120 in²
one rectangle is 16×6 = 96 in²
one rectangle is 16×4.5 = 72 in²
total surface area is therefore
A = 27+120+96+72 = 315 in²
Suppose you have a regular hexagon with all side lengths equal to1. Prove that if you pick seven points from the interior of the hexagon, there is a pair of two points that are distance at most 1 apart.
Answer:
Proved
Step-by-step explanation:
Given
[tex]n = 6[/tex] --- sides of hexagon
[tex]l = 1[/tex] --- side length
Required
Prove that for 7 points picked from the interior, 2 points are at most 1 unit apart
1. Draw a hexagon (see attachment)
2. Divide the hexagon into 6 triangles
3. Select 7 points on the hexagon
You will notice that at least 2 points will be in one of the triangle.
The maximum distance between these two points is 1 unit. This is because
1. The triangle is equilateral (all sides equal)
2. The length of each is 1 unit (in other words, the distance between points, cannot exceed the side length)
Rewrite the given equation in logarithmic form. Then, select all of the equations with an equivalent solution.
8e^x - 5 = 0
Answer:
ans: ln (5/8) , ln5 - ln8
Step-by-step explanation:
8e^x -5 = 0
e^x = 5/8
x = ln (5/8)
x = ln5 - ln8
Find the value of x.
68°
110°
135°
Answer:
47
Step-by-step explanation:
Answer:
hi, the answer is 47°
Step-by-step explanation:
68+135+110=313 360-313=47
Question 10 (1 point)
After a certain drug is injected into a patent, the concentration C of the drug in the
bloodstream is monitored. At time t > 0 (in minutes since the injection) the
concentration (in mg/L) is given by
5
30t
c(t)
t2 + 2
9
What will the concentration of the drug eventually be in the bloodstream? Do not
enter any units with your answer.
Answer:
From the values obtained, we can see that after the initial 10mg/L values obtained in the first 1 and 2 minutes, the concentration has been dipping and it will continue to do so.
Step-by-step explanation:
The concentration monitored ar time, t > 0 is represented by :
C(t) = 30t / (t² + 2.)
At, t = 1
C(1) = 30(1) / (1 + 2) = 30/3 = 10
At t = 2
C(2) = 30(2) / (2² + 2) = 60/(4+2) = 60/6 = 10
At t = 3
C(3) = 30(3) / (3² + 2) = 90/ 11 = 8.18
At t = 4
C(4) = 30(4) / (4²+2) = 120/18 = 6.67
At t = 5
C(5) = 30(5) / (5²+2) = 150/ 27 = 5.55
At t = 10
C(10) = 30(10) / (10²+2) = 300/102 = 2.94
From the values obtained, we can see that after the initial 10mg/L values obtained in the first 1 and 2 minutes, the concentration has been dipping and it will continue to do so.
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)
[1 0 0 1]
[0 0 1 0]
[0 0 0 0]
(x1, x2, x3, x4) = _________
Answer:
[tex]x_1 = -t[/tex]
[tex]x_2 = s[/tex]
[tex]x_3 = 0[/tex]
[tex]x_4 = t[/tex]
Step-by-step explanation:
Given
[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]
Required
Determine x1 to x4
First, we write the augmented matrix
[tex]\left[\begin{array}{cccc}1&0&0&1\\0&0&1&0\\0&0&0&0\end{array}\right] = \left[\begin{array}{c}0&0&0\end{array}\right][/tex]
Taking the position of each column, we have:
[tex]x_1 + 0 + 0 +x_4 = 0[/tex]
[tex]0 + 0 + x_3 +0 = 0[/tex]
[tex]0 + 0 + 0 + 0 = 0[/tex]
There is no explicit equation for [tex]x_2[/tex]
So: [tex]x_2 = s[/tex] ----- arbitrary variable
[tex]x_1 + 0 + 0 +x_4 = 0[/tex] implies that:
[tex]x_1 + x_4 = 0[/tex]
[tex]0 + 0 + x_3 +0 = 0[/tex] implies that
[tex]x_3 = 0[/tex]
[tex]0 + 0 + 0 + 0 = 0[/tex] implies that
[tex]0 = 0[/tex]
So, we have:
[tex]x_1 + x_4 = 0[/tex]
[tex]x_3 = 0[/tex]
[tex]x_1 + x_4 = 0[/tex] becomes
[tex]x_1 = -x_4[/tex]
Let
[tex]x_4 = t[/tex]
So:
[tex]x_1 = -x_4[/tex]
[tex]x_1 = -t[/tex]
Where t , s are real numbers
14x^4y^6/7x^8y^2 assume the denominator does not equal zero
Answer:
(y/x)⁴
Step-by-step explanation:
14x^4y^6/7x^8y^2
= 2x^(-4)/2y^(-4)
= (y/x)⁴
Answer:
2y^4/x^2
Step-by-step explanation:
4x^4y^6 ÷ 7x^8y^2
you will find the GCF of the equation which is: 7x^4y^2 . Then, you will divide both of the equation by the GCF and it will become
14x^4y^6 ÷ 7x^4y^2 = 2y^4
7x^8y^2 ÷ 7x^4y^2 = x^2
then you'll get the answer 2y^4/x^2
Identify the vertex, focus, and directrix of the graph. Which of the following equations represents the parabola in the graph?
need help with this, i’ll mark you brainliest!!
Answer:
Equation: [tex](x-2)^2=16(y-2)[/tex]
Vertex: [tex](2,2)[/tex]
Directrix: [tex]y=-2[/tex]
Focus: [tex](2,6)[/tex]
Step-by-step explanation:
Standard Form of Vertical Parabola:
Equation -> [tex](x-h)^2=4p(y-k)[/tex] where [tex]p\neq 0[/tex]Vertex -> [tex](h,k)[/tex]Directrix -> [tex]y=k-p[/tex]Focus -> [tex](h,k+p)[/tex]We know that our vertex is [tex](h,k)[/tex] -> [tex](2,2)[/tex], therefore, we can determine the value of [tex]p[/tex] by selecting a point from the parabola as [tex](x,y)[/tex]:
[tex](x-h)^2=4p(y-k)[/tex]
[tex](x-2)^2=4p(y-2)[/tex]
[tex](6-2)^2=4p(3-2)[/tex]
[tex](4)^2=4p(1)[/tex]
[tex]16=4p[/tex]
[tex]4=p[/tex]
Therefore:
Directrix -> [tex]y=k-p[/tex] -> [tex]y=2-4[/tex] -> [tex]y=-2[/tex]Focus -> [tex](h,k+p)[/tex] -> [tex](2,2+4)[/tex] -> [tex](2,6)[/tex]Conclusion:
Equation -> [tex](x-2)^2=16(y-2)[/tex]Vertex -> [tex](2,2)[/tex]Directrix -> [tex]y=-2[/tex]Focus -> [tex](2,6)[/tex]Review the graph for a visual
Shawna reduced the size of a rectangle to a
height of 2 in. What is the new width if it
was originally 24 in wide and 12 in tall?
Answer: 10 in
Step-by-step explanation:
PLEASE HELP ASAP!! The graph of the equation y = 3x + 1 is shown below.
9514 1404 393
Answer:
A. y = 3^-x +1
Step-by-step explanation:
Reflection across the y-axis replaces x with -x. The reflected curve is described by ...
y = 3^-x +1 . . . . matches choice A
Natural logs can be written as _______.
Answer:
Step-by-step explanation:
The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.
Answer:
Ln x as opposed to log x
Step-by-step explanation:
i need help with this question on my homework
Answer:
the angle would be 64°
Step-by-step explanation:
since the other angle is already 296° having the other angle would add to complete the 360 degrees of the circle
Answer:
Step-by-step explanation:
64 because you subtract 360 by 296
a basketball team playd 64 games they won 28 more than they lost
Find the area of the following circle.
plz I need this fast!
------11m------
379.94 m 2
34.54 m 2
94.985 m 2
17.27 m 2
Answer:
[tex]A=379.94\ m^2[/tex]
Step-by-step explanation:
Given that,
The radius of a circl is 11 m
We need to find the area of the circle. The forcemula for the area of a crcle is given by :
[tex]A=\pi r^2[/tex]
Put all the values,
[tex]A=3.14\cdot11^{2}\\A= 379.94\ m^2[/tex]
So, the area of the circle is equal to [tex]379.94\ m^2[/tex].
Answer:94.985 m 2
Step-by-step explanation:
SOLVE THIS PROBLEM PLEASE 20 POINTS
Answer:
x=5
y=0
Step-by-step explanation:
KL = JM
3x-y = 15
and JK = LM
4x -4y = 20
Divide this equation by 4
x-y= 5
Multiply by -1
-x+y =-5
Add this to the first equation
3x-y = 15
-x+y =-5
-----------------
2x = 10
Divide by 2
2x/2 = 10/2
x =5
x-y = 5
5-y = 5
-y = 0
y =0
Answer:
x=5,y=0
Step-by-step explanation:
KL=JM [Opposite sides of rectangle are equal]
3x-y=15-> eq 1
JK=LM
4x-4y=20
=>4(x-y)=20
=>x-y=5-> eq 2
From eq 1 and 2,
3x-y=15
x-y=5
=>2x=10
=>x=5
x-y=5
y=x-5
=>y=5-5
=>y=0
please answer yes i give brainliest
A.
B .
C.
OR
D.
Answer:
D. its the only straight line
Step-by-step explanation:
by the way, they are all functions
If "u" varies directly with "v," and u = 6
when v = -7, what is "u" when v = 4
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Answer:
u = -3 3/7
Step-by-step explanation:
The new value of v is 4/-7 = -4/7 of the old value. Because u varies directly, its new value will also be -4/7 of the old value.
u = -4/7(6) = -24/7
u = -3 3/7
In parallelogram HJKL if HM=12 find HK.
K
M
M
H
L
Answer:
HK = 24
Step-by-step explanation:
HK and JL are diagonals of the parallelogram.
Recall that diagonals of a parallelogram bisect each other. This implies that, they divide each other into equal parts.
Therefore,
HK = 2(HM)
HM = 12
Thus,
HK = 2(12)
HK = 24
Two expressions of the equation
Step-by-step explanation:
let the expression of the equation be :
x+y=0
x²+y²= 5
hope it is helpful to you
Suppose x and y are sets such that XuB=(-8,-4,-2,0,2,4,6,8), XnY =(-2,0,2) and X/Y =(-8,8) on this basis which of the following is not true
Answer:
I need points
Step-by-step explanation:
Rico can walk 3 miles in the same amount of time that Donna can walk 2 miles. Rico walks at a rate 2 miles per hour faster than Donna. At that rate, what is the number of miles that Rico walks in 2 hours and 10 minutes?
Answer:
[tex]13[/tex]
Step-by-step explanation:
Donna's Rate is [tex]R[/tex]
Rico's Rate is [tex]R+2[/tex]
[tex]\frac{R}{R+2}=\frac{2}{3}[/tex]
Cross-Multiply
[tex]2(R+2)=32[/tex]
[tex]2R+4=3R[/tex]
[tex]4=R[/tex]
Donna's Rate is [tex]R=4[/tex]
Rico's Rate is [tex]R+2=6[/tex]
[tex]\frac{6(130)}{60} = \frac{130}{10}=13[/tex]