If the matrix xt x is not invertible, then its determinant is equal to 0. A determinant of 0 implies that the matrix is singular, meaning that its columns are linearly dependent.
This means that one of the columns of x can be expressed as a linear combination of the other columns, which implies that there is only one way in which the invertibility problem may arise: when the columns of the matrix x are linearly dependent.
If the determinant of xt x is equal to 0, then at least one column of x can be expressed as a linear combination of the others. For example, if column c can be expressed as a linear combination of columns a and b, then we can write:
c = k1a + k2b
where k1 and k2 are constants. This means that the information in column c is already represented in columns a and b, and so it is redundant.
This is the only way in which the invertibility problem of xt x may arise. If the columns of the matrix are linearly independent, then the determinant of xt x will be non-zero, and the matrix will be invertible.
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Your question is incomplete, but most probably, the full question was:
Proof that [tex]X^{T} X[/tex] is not invertiblethen at least one column of x is a linear combination of the others. This implies that there is only one way in which a problem with the invertibility of xt x may arise
6 The figure shows the dimensions of a compost bin. Can the expression
below be used to find the surface area of the compost bin? Explain.
Include a net in your explanation.
6.5 +4.5 +3.5+5.5+ 2[3.4+ (3•4)]
The surface area of the composite bin can be found using the expression 6·5 + 4·5 + 3·5 + 5·5 + 2·[3·4 + (1/2)·(3·4)]
Please find attached the drawing of the net of the composite bin, created with MS Word
What is the surface area of a composite figure?The surface area of a composite figure can be found finding the sum of the individual exposed surface area of the composite figure.
Please find attached the possible drawing of the diagram in the question, created with MS Word
The possible complete expression in the question, obtained from a similar, online question, is presented as follows;
6·5 + 4·5 + 3·5 + 5·5 + 2·[3·4 + (1/2)·(3·4)]
The surface area of the figure consists as follows;
Two trapezoidal faces (in front and on the rear
Four rectangular faces, orthogonal to the trapezoidal faces
Please find attached the net of the composite bin created with MS Word
The area of the trapezoidal faces = (3 + 6)×4/2 = ((1/2)·(3·4) + ((1/2)·(6·4))
((1/2)·(3·4) + ((1/2)·(6·4)) = ((1/2)·(3·4) + (3·4)
((1/2)·(3·4) + ((3·4)) = 3·4 + (1/2)·(3·4)
Therefore, the area of the two trapezoidal faces = 2 × (3·4 + (1/2)·(3·4))
The area of the four rectangular faces are;
Face [tex]{}[/tex] Area
Orthogonal rear face = 6 × 5
Orthogonal front face = 3 × 5
Face at the bottom of the figure = 4 × 5
The slant face at the top = 5 × 5
The area is therefore;
The surface area of the composite bin, A, is therefore;
A = 6 × 5 + 3 × 5 + 4 × 5 + 5 × 5 + 2 × (3·4 + (1/2)·(3·4))Learn more about the surface area of composite figures here: https://brainly.com/question/28167393
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How do you do this? I’m very confused
On solving the provided question, we can say that an explicit equation for the geometric sequence t(n) = [tex]t^2+ 6t - 8[/tex] and a recursive equation for the geometric sequence; t(1) = -1
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
an explicit equation for the geometric sequence.
t(n) = [tex]t^2+ 6t - 8[/tex]
a recursive equation for the geometric sequence.
t(1) = -1
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The formulas for total revenue and total cost, in hundreds of dollars, for selling and producing q hundred Items are: total revenue: TR(q) = 30q total cost: Tc(q) = q^3-15q^2+75q+10. (a) Find the smallest quantity at which marginal cost is equal to 15 dollars per Item. (b) Recall: Fixed cost is given by FC = TC(0). Variable cost is given by VC(q) = TC(q) - FC. Average variable cost is given by AVC(q) = VC(q)/q. Find a positive value of q at which average variable cost is equal to marginal cost. (c) Find the longest interval on which marginal revenue exceeds marginal cost. (d) Recall that profit is given by P(q) = TR(q)-TC(q) and On an interval of quantities where MR(q) < MC(q), profit is decreasing. On an interval of quantities where MR(q) > MC(q), profit is increasing Use the sketch you drew in part (c) to find the quantity at which profit is greatest. What is the maximum value of profit?
(a). The smallest quantity at which marginal cost is equal to 15 dollars per item is 2.76. (b). The positive value of q at which average variable cost is equal to marginal cost is [tex]\frac{15}{2}[/tex]. (c). The longest interval on which marginal revenue exceeds marginal cost is (1.8377, 8.1622). (d). The profit is increasing at 8.1622 at p(q) is maximum. (e). The maximum value of profit is 78.2455 dollars.
The total revenue: TR(q) = 30q
The total cost: Tc(q) = [tex]q^3-15 q^2+75 q+10$[/tex]
The change in cost is referred to as the change in the cost of production when there is a need for change in the volume of production.
(a). Marginal cost MC[tex]=\frac{\partial}{\partial q}(T C)$[/tex]
[tex]$$=3q^2-30 q+75 \text {. }$$[/tex]
According to question.
[tex]$$\begin{aligned}& 3 q^2-30 q+75=15 \\& 3 q^2-30 q+60=0 \\& q^2-10 q+20=0 \\& q= \frac{10 \pm \sqrt{100-80}}{2} \\&= \frac{10 \pm 2 \sqrt{5}}{2}=5 \pm \sqrt{5}\end{aligned}[/tex]
[tex]$$$\therefore \quad q=5+\sqrt{5} \quad$ and $q=5-\sqrt{5}$[/tex]
we have to find smallest quantity.
[tex]$$\therefore \quad q=5-\sqrt{5}=2.76 \text {. }$$[/tex]
b)
[tex]$$\begin{aligned}& F C=T C(0)=10 \\& V C(q)=T C(q)-F C \\& =q^3-15 q^2+75 q . \\& \text { AVC(q) }=\frac{V C(q)}{q}=q^2-15 q+75 .\end{aligned}$$[/tex]
When AVC(q)=MC(q)
[tex]$$\begin{array}{ll}\Rightarrow & q^2-15 q+7 ;=3 q^2-30 q+75 \\\Rightarrow & 2 q^2-15 q=0 .\ \Rightarrow q(2 q-15)=0 . \\\Rightarrow & q=0, \frac{15}{2} \quad \Rightarrow \quad q=\frac{15}{2}\end{array}$$[/tex]
Therefore, the positive value of q at which average variable cost is equal to marginal cost is [tex]\frac{15}{2}[/tex].
(c).
[tex]& M R(q)=\frac{d}{d q}(T R)=30 . \\[/tex]
[tex]& M C(q)=3 q^2-30 q+75 . \\[/tex]
Let MR(a)>MC(q)
[tex]& \Rightarrow \quad 30 > 3 q^2-30 q+75 \text {. } \\[/tex]
[tex]& \Rightarrow \quad 3 q^2-3 p q+45 < 0 \\[/tex]
[tex]& \Rightarrow \quad q^2-10 q+15 < 0 \text {. } \\[/tex]
[tex]& \because \quad q=\frac{10 \pm \sqrt{100-60}}{2} \Rightarrow q=\frac{10 \pm 2 \sqrt{10}}{2} \\[/tex]
[tex]& q=(5 \pm \sqrt{10}) \\[/tex]
[tex]& \Rightarrow \quad(q-5+\sqrt{10})(q-5-\sqrt{10}) < 0 . \\[/tex]
[tex]& \Rightarrow \(q-5+\sqrt{10}) < 0 \quad \& \quad(q-5-\sqrt{10}) > 0 \text {. } \\[/tex]
[tex]& \text { or } \quad(q-5+\sqrt{10}) > 0 \quad \& \quad(q-5-\sqrt{10}) < 0 \text {. } \\[/tex]
[tex]& \therefore \quad \text { other } q < 5-\sqrt{10}=1.8377 ., q > 5+\sqrt{10}=8.1622 \text {. } \\[/tex]
[tex]& \Rightarrow \quad q < 1.8377 \& q > 0.1622 \text {. } \\[/tex]
[tex]& \text { or } q > 5-\sqrt{10} \quad \& \quad q < 5+\sqrt{10} \text {. } \\[/tex]
[tex]& \Rightarrow q > 1.8377 \quad < q < 8.1622 \text {. } \\[/tex]
The Interval is (1.8377, 8.1622).
(d). P(q) =TR(q)-TC(q)
[tex]& =30 q-\left(q^3-15 q^2+75 q+10\right) \\& =-q^3+15 q^2-75 q-10+30 q \\& =-q^3+15 q^2-45 q-10 .[/tex]
on (1.8377,8.1622). we have to find a point such that p"(q)=0 and p"(q)<0.
[tex]& p^{\prime}(q)=-3 q^2+30 q-45 \\[/tex]
[tex]& \Rightarrow \quad-3\left(q^2-10 q+15\right)=0 \\[/tex]
[tex]& \Rightarrow \quad q^2-10 q+15=0 . \\[/tex]
[tex]& \quad q=1.8377 \text { and } \quad q=8.1622 . \\[/tex]
[tex]& \Rightarrow \quad p^{\prime \prime}(q)=-6 q+30 . \\[/tex]
[tex]& p^{\prime \prime}(1.8377)=-6(1.8377)+30 \\[/tex]
[tex]&=18.9738 \\[/tex]
[tex]& p^{\prime \prime}(8.1622)=-6(8.1622)+30 . &=-18.9732 < 0 .[/tex]
at 8.1622, p(q) is maximum.
(e).
Max profit-P(8.1622)
=78.2455 dollars
Therefore, the maximum value of profit is 78.2455 dollars.
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a rectangle is drawn so the width is 2 inches longer than the height. if the rectangle's diagonal measurement is 24 inches, find the height.
Answer:
15.94
Step-by-step explanation:
(2+h)² + h² =24²
4+4h+h²+ h² =24²
2+2h+h²= 576/2
h²+2h-286=0
solve h=15.94
In the 2018 winter Olympics there were 240 athletes from the USA and 7 /20 of them were skiers. How many Olympic skiers were there?
Answer:
84
Step-by-step explanation:
Number of skiers = Number of athletes * Fraction of skiers
= 240 * 7/20
= 84 skiers
Answer:
84
Step-by-step explanation:
240/20=12
12*7=84
1/4 divided by 6? I really would like to know. Thank you in advance.
Answer:
[tex] \frac{1}{24} [/tex]
Step-by-step explanation:
When you're dividing a fraction, you multiply the denominator
For example, taking this question
[tex] \frac{1}{4} \div 6[/tex]
The dominator is 4
You're dividing by 6
So multiply the denominator and what you're dividing by
[tex]4 \times 6 = 24[/tex]
Now that you have that, 24 will be the new denominator
[tex] \frac{1}{24} [/tex]
started business with cash 200000 and furnitur 500000
As an asset account, the furniture account is debited as its balance increases.
What is the journal entry for cash furniture?Cash and bank amount are assets accounts as well, and when furniture is purchased percentage , they are credited for the amount that has been deducted from them.
Record in journal
A/C for furniture is $50,000.
A/C Cash: DR 2,000,000.
To Capital, 2.5 million
(The beginning of a business with money and furniture)
Note: Since cash and furniture are investments in the business, they are capital, and when capital increases, it is credited. Furniture is our asset, and if it increases, it will be debited. Cash is also our asset, and as it is arriving in the firm, it is increasing, therefore it will be debited.
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The complete question is " Explain Journal entry for started business with cash Rs 200000 and furniture Rs 50000. "
Hello :) Could you please check and help to answer it?
A rectangular piece of metal is 15 in longer than it is wide. Squares with sides
3 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1350 in3, what were the original dimensions of the piece of metal?
Let the width be [tex]w[/tex] inches and the length be [tex]w+15[/tex] inches.
So, the dimensions of the box are [tex]w-6[/tex], [tex]w+9[/tex], and [tex]3[/tex] inches.
[tex]3(w-6)(w+9)=1350 \\ \\ (w-6)(w+9)=450 \\ \\ w^2+3w-54=450 \\ \\ w^2+3w-504=0 \\ \\ (w+24)(w-21)=0 \\ \\ w=-24,21[/tex]
Rejecting the negative case, [tex]w=21[/tex].
So, the dimensions are 21 by 36 inches.
Which fraction is closest to 1/2
?
The fraction which is closest to 1/2 is, 3/8. So option B is correct
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
A fraction number 1/2
In decimal form = 0.5
Closest fraction number = ?
Most closest number is that number from which we subtract the given number and the magnitude of result we get is very less,
Lets take, A fraction 1/6
In decimal form it can written as, 0.167
Difference 1 = 0.5 - 0.167
= 0.333
Similarly, For numbers 3/8, 3/4, -1/2
Difference 2 = 0.5 - 0.375 = 0.125
Difference 3 = 0.5 - 0.75 = -0.25
Difference 4 = 0.5 - (-0.5) = 1.0
It can be seen that,
Magnitude of difference in case of 3/8 is very less
Hence, the closest number is 3/8
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The table below shows Bashir's earnings on the job. Time (hours) Time (hours) Earnings (dollars) Earnings (dollars) 15 $ 228 $228 23 23 $ 349.60 $349.60 33 33 $ 501.60 $501.60 How much does he make in 15.5 15.5 hours?
Bashir earns $235.6 in 15.5 hours.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Slope= 501.60-349.60/33-23
=152/10
=15.2
Now let us find the y intercept
228=15.2(15)+b
228=228+b
b=0
Now let us find how much he earns in 15.5 hours.
y=15.2(15.5)
y=235.6
Hence, Bashir earns $235.6 in 15.5 hours.
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Can someone please answer this question?
Answer:
40 dollars per hour
Kevin was solving for the area of the triangle below.
8 in
5 in
The formula for area of a triangle is A = bh. Kevin's answer
for the area of this triangle was 40 inches².
Is Kevin's Colution correct? Why or why not?
If not, what was his mistake?
If not, what is the correct solution for the area of this
triangle?
The correct solution for the area of this triangle is 20 inches².
Describe Area of Triangle?The area of a triangle is a measure of the amount of two-dimensional space enclosed by its three sides. It is represented by the symbol A and is calculated by multiplying the base of the triangle by its height and dividing the result by 2.
A = (1/2)b×h
In other words, the height of the triangle is a line segment perpendicular to the base that divides the triangle into two smaller triangles of equal area. The area of a triangle is important in many real-world applications, such as in construction and architecture, where it is used to determine the amount of material needed for a project, and in geometry, where it is used to solve problems related to triangles.
No, Kevin's solution is not correct. The formula for the area of a triangle is
A = (b×h)/2, not A = b×h.
To find the area of this triangle, you would use the formula:
A = (8 × 5)/2 = 20 inches²
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Find the equation of circle passing through point (3,4) and having equation of its diamter x+y-14=0 and 2x-y-4=0
Answer:
The equation of a circle can be represented in the form (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius.
A diameter of a circle is a straight line passing through the center of the circle and has endpoints on the circle.
Given that the equation of the diameter of a circle is x+y-14=0 and 2x-y-4=0, we can find the center of the circle by solving for the intersection of these two lines.
We can find the intersection point of these lines by solving the system of equations using the substitution method:
x+y-14=0 and 2x-y-4=0
x = 14/3, y = 10/3
So the center of the circle is (14/3, 10/3)
Since we know that the point (3,4) lies on the circle, we can use the distance formula to find the radius of the circle.
r = sqrt((x-h)^2 + (y-k)^2)
r = sqrt((3-(14/3))^2 + (4-(10/3))^2) = sqrt(5)
Therefore, the equation of the circle is (x-14/3)^2 + (y-10/3)^2 = 5^2
or (x-14/3)^2 + (y-10/3)^2 = 25
So, the equation of the circle passing through point (3,4) and having equation of its diameter x+y-14=0 and 2x-y-4=0 is (x-14/3)^2 + (y-10/3)^2 = 25
What's the area of this?
Answer:
5 units^2
Step-by-step explanation:
IREADY MATH AREA pls help ty!
The area of the shaded region is πr² - (2 × 13.5π).
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a shaded region inside a circle.
The area of each section is -
A{S} = 13.5π
We can write the area of the shaded region as -
πr² - (2 × 13.5π)
Therefore, the area of the shaded region is πr² - (2 × 13.5π).
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what fraction of clockwise revolution does the hour hand of clock turn through when it goes from 3 to 9
Answer:
1/2
Step-by-step explanation:
On the clock from 3 to 9, the hour hand turns clockwise 1/2 of the revolution. On the clock from 4 to 7, the hour hand turns clockwise 1/4 of the revolution
Question
Add.
7 2/6 + 3 2/6
Enter your answer in the box as a mixed number in simplest form.
Answer:
10 4/6 = 10 2/3
Step-by-step explanation:
dude this is easy and not for college but thanks anyway
A recent survey of 2500 college students revealed that during any weekend afternoon, 1364 receive a text message, 857 receive an e-mail and 470 receive both a text message and an e-mail . Suppose a college student is selected at random, what is the probability that he/she neither receives a text message nor an email during any weekend afternoon? Round your answer to four decimal places.
For this example, use the function 1 () 1 2 fx x = + and an initial value of 4. Note that
with each successive iteration, you can use the previous output as your new input
to the function.
• 1 (4) 4 1 3 2 f = ⋅+=
• 2 1 (4) (3) 3 1 2.5 2 f f = = ⋅+=
• 3 1 (4) (2.5) 2.5 1 2.25 2 f f = = ⋅ +=
Questions
3. What happens to the value of the function as the number of iterations
increases?
4. Choose an initial value that is less than zero. What happens to the value of
the function as the number of iterations increases?
5. Come up with a new linear function that has a slope that falls in the range
−< < 1 0 m . Choose two different initial values. For this new linear function,
what happens to the function’s values after many iterations? Are the
function’s values getting close to a particular number in each case?
6. Use the function gx x () 2 =− + with initial values of 4, 2, and 1. What happens
after many iterations with all three initial values? How do the results of all
three iterations relate to each other?
a) for initial value 4 function oscillate between 4 and -2
b) for a initial value of 2 function oscillate between 2 and 0
c) for a initial value of 1 function value is constant = 1
What is a function?A function is a relationship between a set of inputs that each have one output. A function, in simple terms, is a relationship between inputs, with each input corresponding to exactly one output. Each function has a domain as well as a co-domain or range. The general notation for a function is f(x), where x is the input. A function is generally represented as y = f. (x).
In math, there are various types of functions. Among the most important types are:
Injective function: When there is a mapping for a range for each domain between two sets.Surjective functions, also known as Onto functions, are used when there are multiple elements mapped from domain to range.A polynomial function is a function made up of polynomials.Inverse Functions: A function that has the ability to invert another function.f(x) = 1/2.x + 1
f(4) = 1/2*4+1=3
f(4) = 1/2*3+1=2.5
f(4) = 1/2*2.5+1=2.25
f(4) = 1/2*2.25 + 1 = 2.125
f(4) = 1/2*2.125+1 = 2.0625
f(4) = 1/2*2.0625 + 1 = 2.0123
As the iteration increases function value converges to 2
You can write a simple MATLAB program to check it
matlab code:
clc;
clear all;
close all;
syms x;
f=-x+2;
y(1)=4;
g(1)=2;
h(1)=1;
for n=1:20
y(n+1)=subs(f,x,y(n));
g(n+1)=subs(f,x,g(n));
h(n+1)=subs(f,x,h(n));
end
t=[y',g',h'];
output :
t =
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
a) for initial value 4 function oscillate between 4 and -2
b) for a initial value of 2 function oscillate between 2 and 0
c) for a initial value of 1 function value is constant = 1
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Find two solutions of each equation. Give your answers in degrees
(0° ≤ < 360°)
and in radians
(0 ≤ < 2).
Do not use a calculator. (Do not enter your answers with degree symbols. Enter your answers as comma-separated lists.)
(a)
sin() = 1/2
degrees
radians
(b)
sin() = − 1/2
degrees
radians
Answer:
(a) sin() = 1/2
degrees: 30, 150
radians: π/6, 5π/6
(b) sin() = − 1/2
degrees: 210, 330
radians: 7π/6, 11π/6
Note that these solutions are in the interval of 0 to 360 degrees or 0 to 2 radians. Also note that these are the primary solutions, there are infinitely many solutions that can be obtained by adding multiples of 360 degrees or 2π radians to these values.
Ratio for 63 inches to 4 yards
Answer:
The ratio for 63 inches to 4 yards is 1:16. To calculate this, divide 63 inches by 4 yards, which is equal to 48 inches per yard. Therefore, the ratio for 63 inches to 4 yards is 1:16.
A seven-character database password is formed from 10 digits and 26 upper-case letters. What is the probability that a randomly selected password has no digits? SHOW ALL YOUR WORK and Round your answer to four decimal places.
The probability that a randomly selected password has no digits is 10.24%.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Given that, a seven-character database password is formed from 10 digits and 26 upper-case letters.
Number of characters in passwords: 7
The possible number of ways to formed the first value of passwords is sum of 26 (upper letters) and 10 (0 to 9 numbers).
The required number of possible passwords is 36⁷
= 78364164096
Favorable out comes is 26⁷
= 8031810176
Now, probability of an event = 8031810176/78364164096
= 0.1024
= 10.24%
Therefore, the probability that a randomly selected password has no digits is 10.24%.
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Which is the equation of the circle that has a diameter with endpoints located at (5, –3) and (11, 5)?
(x – 5)2 + (y + 3)2 = 25
(x – 7)2 + y2 = 100
(x – 8)2 + (y – 1)2 = 25
(x – 11)2 + (y + 5)2 = 100
The equation of the circle that has a diameter with endpoints located at (5, –3) and (11, 5) is; (x – 8)² + (y – 1)² = 25
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
The midpoint of the diameter of a circle is it's center.
As such; the coordinates of its center are;
x = (5+11)/2
x = 8
y = (-3 + 5)/2
y = 1
The coordinates of the center are then; (8, 1)
The radius of a circle is half the length of the diameter;
Radius, r = d/2
where; d = √(11-5)² + (5-(-3))²
d = √36 + 64
d = √100
d = 10
Therefore, radius, r = 10/2 = 5.
Therefore, the equation of the circle usually takes the form;
(x -f)² + (x -g)² = r²
In this scenario; the equation is;
(x – 8)² + (y – 1)² = 25.
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ANSWER FAST!!! U WILL GET BRAINLEST WHEN U ANSWER!!
Answer: 31
Step-by-step explanation:
You need to find the perimeter of something, you just add the numbers of the sides.
6 + 9 = 15
15 + 5 = 20
20 + 3 = 23
23 + 5 = 28
28 + 3 = 31
Perimeter = 31 in.
Step-by-step explanation:1. Remember the concept of perimeter.A perimeter of any shape is just the total length of all its sides. In other words, is the distance around the edge of the shape.
2. Add up all the measures.Perimeter = 5 in + 3 in + 5 in + 9 in + 6 in + 3 in = 31 in.
3. Conclude.Perimeter = 31 in.
During one eight-week period, a particular mutual fund outperformed the S&P 500 index 29 out of 40 days. Find the
probability that it would perform as well or better again.
What is The probability?
On solving the provided question we can say that probability, P' = 1 - P( P' < 0.80 ) = 1 - P( P'- 0.80/0.06235 < 0.80-0.80/0.06235 ) => P' = 0.5
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
the proportion of days when particular mutual fund out performed the S&P 500 index = 29/40 = 0.0.725 = 0.8
Let P' denotes the sample proportion for random sample size of n = 40
now, probability, P' = 1 - P( P' < 0.80 ) = 1 - P( P'- 0.80/0.06235 < 0.80-0.80/0.06235 )
P' = 1 - P(Z)
P' = 1 - 0.5
P' = 0.5
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2) Mary's parents ask her to pick up as many boxes of shoes as she
can. Each box is 12" x 8" x 6" (volume: 576 cu in). If Mary used
volume as an estimate, how many boxes would fit, if her trunk is 44"
wide x 46" long x 20" tall (volume: 40,480 cu in)?
O 7 boxes
O 70 boxes
O 70.3 boxes
The number of boxes that would fit into the trunk is 70.
How many boxes would fit into the trunk?The box is known as a cuboid. A cuboid is a three-dimensional shape that has six faces, 12 sides and 6 vertices.
In order to determine the number of boxes that would fit into the trunk, divide the volume of the trunk by the volume of one box.
Volume is the product of the length, width and height of an object. It measures how much space is in object.
Number of boxes that can fit into the trunk = volume of the trunk / volume of one of the boxes
40,480 / 576 = 70.28 boxes or 70 boxes
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prove that, given a nonnegative integer , there is a unique nonnegative integer such that m^2 < sqrt n < (m 1)^2
It is proved that m = √n.
To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:
m^2 ≤ n < (m + 1)^2.
So, after taking the square root, it will be:
m ≤ √n < m + 1
From that we can see m = √n is the unique m.
What is a nonnegative integer?A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.
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Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.
Find the equation of the linear function represented by the table below in slope-intercept form. x y -2 -2 2 6 6 14 10 22
The equation of the linear function represented by the table in slope intercept form is f(x) = 2x + 2.
What is Linear Function?
A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.
Equation of the linear function in slope intercept form can be represented as y = mx + d, where m is the slope and d is the y intercept.
Slope is the change in y coordinates divided by the change in x coordinates.
y intercept is the point on the line where the line touches the Y axis.
Given points are (-2, -2), (2, 6), (6, 14) and (10, 22).
Consider the points (-2, -2) and (2, 6).
Slope, m = (6 - -2) / (2 - -2) = 8 / 4 = 2
So the equation becomes y = 2x + d
Substituting one of the points (2, 6) in the above equation,
6 = (2 × 2) + d
d = 2
So the equation is y = 2x + 2.
Hence the given linear function can be represented as f(x) = 2x + 2.
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Independent and Dependent Variable examples.
Answer:
Independent variable: The variable that is changed or manipulated in an experiment to observe its effect on the dependent variable. Example: The number of hours of studying (Independent variable) and the test score (Dependent variable)
Dependent variable: The variable that is being measured or observed in an experiment. Its value is dependent on the independent variable. Example: The temperature of water (Independent variable) and the volume of the water (Dependent variable)
Answer:
y=5x
Here y is dependent variable because it's depend on x but x is not depend on any other variable. So, it's independent variable.
If 4 is added to the quotient of 24 and -8, what
number results?
Answer:
1
Step-by-step explanation:
Quotient of 24 and -8 gives you -3. Hence, 4 added to -3 is 1, which is the answer.
