end{bmatrix} = \begin{bmatrix} 1 \\ \frac{1}{5} \\ 1 \end{bmatrix}.
(a) Let $a^1 = \begin{bmatrix} 1 \\ 1 \\ 2 \\ 1 \end{bmatrix}, a^2 = \begin{bmatrix} -1 \\ 2 \\ 0 \\ -2 \end{bmatrix},$ and $a^3 = \begin{bmatrix} 1 \\ 4 \\ 4 \\ 0 \end{bmatrix}.$ Write the matrix $A = \begin{bmatrix} a^1 & a^2 & a^3 \end{bmatrix}$ in the form $A = QR$ by using the Gram-Schmidt process. (b) Use the QR factorization of $A$ in part (a) to solve the equation $Ax = b,$ where $b = \begin{bmatrix} 3 \\ 1 \\ 2 \\ 1 \end{bmatrix}.$The Gram-Schmidt algorithm is a numerical method to produce orthonormal basis of a subspace in Hilbert space that spans the same space, which makes the basis more convenient to work with. As for the first part of the question, let us begin by applying the Gram-Schmidt algorithm to $a^1, a^2, a^3.$ We begin by defining $q_1 = a^1 / \|a^1\|.$ Hence,$$q_1 = \frac{1}{3}\begin{bmatrix} 1 \\ 1 \\ 2 \\ 1 \end{bmatrix} = \begin{bmatrix} 1/3 \\ 1/3 \\ 2/3 \\ 1/3 \end{bmatrix}.$$Next, we define $v_2 = a^2 - \langle q_1, a^2 \rangle q_1.$ Therefore,$$v_2 = a^2 - \frac{-1}{3}(1/3)q_1 = \begin{bmatrix} -7/9 \\ 8/9 \\ -2/9 \\ -4/9 \end{bmatrix}.$$Now, we can define $q_2 = v_2 / \|v_2\|.$ Thus,$$q_2 = \frac{1}{3}\begin{bmatrix} -7 \\ 8 \\ -2 \\ -4 \end{bmatrix}.$$Finally, we define $v_3 = a^3 - \langle q_1, a^3 \rangle q_1 - \langle q_2, a^3 \rangle q_2.$ Then,$$v_3 = a^3 - \frac{5}{9}q_1 - \frac{7}{27}q_2 = \begin{bmatrix} -1/27 \\ 5/9 \\ 22/27 \\ -5/27 \end{bmatrix}.$$Lastly, we can define $q_3 = v_3 / \|v_3\|,$ so$$q_3 = \frac{1}{3}\begin{bmatrix} -1 \\ 5 \\ 22 \\ -5 \end{bmatrix}.$$Now, we can write $A = QR$ as $$\begin{bmatrix} a^1 & a^2 & a^3 \end{bmatrix} = \begin{bmatrix} q_1 & q_2 & q_3 \end{bmatrix} \begin{bmatrix} r_{11} & r_{12} & r_{13} \\ 0 & r_{22} & r_{23} \\ 0 & 0 & r_{33} \end{bmatrix}.$$We can obtain the entries of the $R$ matrix by calculating the inner product of each $q_i$ with $a^j.$ Thus,$$r_{11} = \|a^1\| = \sqrt{7},$$$$r_{12} = \langle q_1, a^2 \rangle = \frac{-1}{3}\sqrt{7},$$$$r_{13} = \langle q_1, a^3 \rangle = \frac{5}{9}\sqrt{7},$$$$r_{22} = \|v_2\| = \frac{5}{3}\sqrt{2},$$$$r_{23} = \langle q_2, a^3 \rangle = \frac{-7}{9}\sqrt{2},$$$$r_{33} = \|v_3\| = \frac{2}{3}\sqrt{6}.$$Therefore,$$\begin{bmatrix} a^1 & a^2 & a^3 \end{bmatrix} = \begin{bmatrix} q_1 & q_2 & q_3 \end{bmatrix} \begin{bmatrix} \sqrt{7} & -\frac{1}{3}\sqrt{7} & \frac{5}{9}\sqrt{7} \\ 0 & \frac{5}{3}\sqrt{2} & -\frac{7}{9}\sqrt{2} \\ 0 & 0 & \frac{2}{3}\sqrt{6} \end{bmatrix}.$$Now, let us solve the equation $Ax = b$ by using the QR factorization of $A.$ We can write $Ax = QRx = b.$ Since $Q$ is orthogonal, we can multiply both sides of the equation by $Q^T$ to obtain $Rx = Q^Tb.$ Note that $Q^Tb$ is easy to compute since $Q^T$ is just the matrix with the $q_i$'s as rows. Thus,$$\begin{bmatrix} \sqrt{7} & -\frac{1}{3}\sqrt{7} & \frac{5}{9}\sqrt{7} \\ 0 & \frac{5}{3}\sqrt{2} & -\frac{7}{9}\sqrt{2} \\ 0 & 0 & \frac{2}{3}\sqrt{6} \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} \frac{2}{3} \\ \frac{1}{3} \\ \frac{2}{3} \end{bmatrix}.$$This gives the system of equations$$\begin{cases} \sqrt{7}x_1 - \frac{1}{3}\sqrt{7}x_2 + \frac{5}{9}\sqrt{7}x_3 = \frac{2}{3}, \\ \frac{5}{3}\sqrt{2}x_2 - \frac{7}{9}\sqrt{2}x_3 = \frac{1}{3}, \\ \frac{2}{3}\sqrt{6}x_3 = \frac{2}{3}. \end{cases}$$Solving the last equation for $x_3,$ we obtain $x_3 = 1.$ Substituting this into the second equation, we obtain $x_2 = \frac{1}{5}.$ Finally, substituting these values into the first equation gives us $x_1 = 1.$ Therefore,$$x = \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ \frac{1}{5} \\ 1 \end{bmatrix}.$$
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Train wheels are designed to slope inward toward the track to keep the train stable as it goes around curves. However, as the slope of the wheels increases, it becomes less efficient at producing speed. How might making changes in the slope of a train's wheels affect the train overall?
There is a trade-off between stability and speed when it comes to the slope of a train's wheels.
What is slope ?
Slope is a measure of the steepness of a line or a surface. In mathematics, slope is often represented by the letter "m" and is calculated as the change in the vertical direction (y-axis) divided by the change in the horizontal direction (x-axis) between two points on the line or surface.
Changing the slope of a train's wheels can have both positive and negative effects on the train's overall performance.
On the positive side, increasing the slope of the wheels can improve the train's stability and safety as it goes around curves. This is because the inward slope of the wheels helps to counteract the centrifugal force that pushes the train outward as it goes around curves. By increasing the slope of the wheels, this counteracting force can be increased, which can help prevent derailments and improve the overall safety of the train.
On the negative side, increasing the slope of the wheels can decrease the train's efficiency at producing speed. This is because the slope of the wheels creates additional friction between the wheels and the track, which can slow the train down and require more energy to maintain speed. As the slope of the wheels increases, this friction also increases, which can make the train less efficient at producing speed and more costly to operate.
Therefore, there is a trade-off between stability and speed when it comes to the slope of a train's wheels. Train designers must find the optimal balance between these two factors to ensure that the train is both stable and efficient.
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the perimeter of a rectangular window is 654 inches if the length of the window is 205 inches what is the width of the window?
Answer:
The width of the window is 122 inches
Step-by-step explanation:
654- known two sides(410) =244
divide 244/2, to get both unknown sides of the rectangular window, 122 inches
please help asap i will give brainliest
Answer:
perfect square therefore rational
non perfect square therefore irrational
cuberoot
5
Step-by-step explanation:
the topic is about perfect squares and rationality of numbers
What is the true solution to the equation below? ln e^lnx + on e ^lnx2 = 2 on 8
After solving the given equation In [tex]e^{lnx} +[/tex] in [tex]e ^{lnx2}[/tex] = 2 in 8, we know that the value of x is (B) 4.
What are equations?The equals sign is a mathematical symbol that indicates that two expressions in a formula are equal.
A mathematical statement known as an equation is one that uses the word "equal to" between two expressions with the same value.
As in 3x + 5 = 15, for example.
Equations can be of many different types, such as linear, quadratic, cubic, and others.
So, we have the equation:
[tex]Ine^{inx} + Ine^{Inx2}[/tex] [tex]= 2In8,[/tex]
Now, solve the following equation as follows:
[tex]Inx * Ine +Inx^2 * Ine = 2In8[/tex]
[tex]e^{Inx}+Ine^{Inx2} = 2in8[/tex]
[tex]Inx+Inx^2 = In8^2[/tex]
[tex]In* (x*x^2) In64[/tex]
[tex]x^2 = 64 =4^3[/tex]
[tex]x=4[/tex]
Therefore, after solving the given equation In [tex]e^{lnx }[/tex] + in[tex]e ^{lnx2}[/tex] = 2in8, we know that the value of x is (B) 4.
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Correct question:
What is the true solution to the equation below? In [tex]e^{lnx}[/tex]+ in [tex]e ^{lnx2}[/tex] = 2 in 8
a x = 2
b x = 4
c x = 8
d x = 64
List in order from least to greatest.
Answer:
56%, 4/5, 1.07, 5/4
Step-by-step explanation:
5/4=1.25
56%=0.56
1.07
4/5=0.8
so the order is
56%, 4/5, 1.07, 5/4
-3y=2x-7
graphing linear equations in 2 variables
By solving the given equation, we can plot these two points on a coordinate plane, and then connect the points with a line. The formed line is the graph of the linear equation 3y=2x-7.
What is a coordinate plane?The coordinate plane is made up of two perpendicular lines called the x-axis and the y-axis. The x-axis, which is horizontal, is used to measure the distance of a point from the left and right side of the plane. The y-axis, which is vertical, is used to measure the distance of a point from the top and bottom of the plane.
To graph the equation 3y=2x-7, we first need to identify two points that satisfy the equation. We can do this by plugging in different values for x and solving for y. For example, when x=0, the equation becomes 3y=-7. Thus, one point that satisfies the equation is (0,-7). We can find a second point by plugging in a different value for x. For example, when x=2, the equation becomes 3y=-3. Thus, the second point that satisfies the equation is (2,-3).
Now, we can plot these two points on a coordinate plane, and then connect the points with a line. The formed line is the graph of the linear equation 3y=2x-7.
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Find all the real solutions of the equation using the rational root theorem. x^(3)-2x^(2)-5x+6=0
All the real solutions of the equation are x=3, x=1, and x=-2. The rational root theorem states that any rational root of the equation x³-2x²-5x+6=0 can be written in the form p/q, where p is a factor of the constant term (6) and q is a factor of the leading coefficient (1). Therefore, the possible rational roots of the equation are: ±1, ±2, ±3, ±6
We can use synthetic division to test each of these possible roots until we find one that gives a remainder of 0.
1 | 1 -2 -5 6
| 1 -1 4
|_____________
| 1 -1 -6 10
The remainder is not 0, so 1 is not a root of the equation.
-1 | 1 -2 -5 6
| -1 3 2
|_____________
| 1 -3 -2 8
The remainder is not 0, so -1 is not a root of the equation.
2 | 1 -2 -5 6
| 2 0 10
|_____________
| 1 0 -5 16
The remainder is not 0, so 2 is not a root of the equation.
-2 | 1 -2 -5 6
| -2 8 14
|_____________
| 1 -4 3 20
The remainder is not 0, so -2 is not a root of the equation.
3 | 1 -2 -5 6
| 3 3 0
|_____________
| 1 1 -2 6
The remainder is 0, so 3 is a root of the equation. We can use the quotient (1x²+1x-2) to find the remaining roots of the equation.
1x²+1x-2=0
Using the quadratic formula, we can find the remaining roots:
x = (-1 ± √(1²-4(1)(-2)))/(2(1))
x = (-1 ± √(1+8))/2
x = (-1 ± √9)/2
x = (-1 ± 3)/2
x = 1 or x = -2
Therefore, the real solutions using rational root theorem and quadratic formula are of the equation are x=3, x=1, and x=-2.
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When given a problem such as (5 + 3i)(7 – 4i), what are 2 important processes to remember to simplify your answer?
To simplify the expression (5 + 3i)(7 – 4i), two important processes to remember are to use the distributive property to multiply the real parts and imaginary parts separately and simplify the resulting expression by combining any like terms.
Use the distributive property:
For the expression (5 + 3i)(7 – 4i),
(5 + 3i)(7 – 4i) = 5(7) + 5(-4i) + 3i(7) + 3i(-4i)
= 35 - 20i + 21i - 12i^2
Note that i^2 = -1,
35 + i(21 - 20) - 12(-1) = 47 + i(41)
Simplify the resulting expression:
After using the distributive property to expand the expression, we can simplify the resulting expression by combining any like terms. In this case, there are no like terms to combine, so our final answer is:
(5 + 3i)(7 – 4i) = 47 + 41i
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ACTIVITY (EXPERIMENTAL PROBABILITY) 50 trials
The dice i roll: 2, 3, 4, 4, 4, 4, 6, 5, 2, 4, 2
What is the probability of rolling a sum of even number?
What is the probability of rolling a sum of odd number?
What is the probability of rolling a sum of greater than 5?
This is for statistics ok? Ty!U,,w,,U
The probability of rolling a sum greater than 5 is 13/18.
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.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
There are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
a) The probability of rolling a sum of even number
Number of favorable outcomes = 9
Total number of outcomes = 36
Now, probability = 9/36
= 1/4
b) The probability of rolling a sum of odd numbers
Number of favorable outcomes = 9
Total number of outcomes = 36
Now, probability = 9/36
= 1/4
c) The probability of rolling a sum of greater than 5
Number of favorable outcomes = 26
Total number of outcomes = 36
Now, probability = 26/36
= 13/18
Therefore, the probability of rolling a sum greater than 5 is 13/18.
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11. The distance round a circular hut is 17.6 m. What is the area of its floor?
12.A string measures 220 cm. Its two ends are joined to form a circle. What area
does the string enclose?
13. The area of a circular mat is 1.54 m². What is its circumference?
11. The area of the floor is 24. 62 m²
12. The area of the enclosed string is 3, 853. 09cm²
13. The circumference of the circular mat is 4.39m
How to determine the areaThe formula for the area of a circle is expressed with the equation;
A = πr²
Where;
A is the area.π takes the value 3.14r is the radius of the circle.Also, circumference of a circle is 2πr
For a circumference of 17. 6m, we have
17. 6 = 2×3.14r
r = 2. 80
Substitute the value
Area = 3.14 × (2. 80)²
Area = 24. 62 m²
For the string, circumference = 220cm
220 = 2× 31.4r
r = 35. 03 cm
Area of the enclosed string = 3.14 × (35. 03)²
Area = 3, 853. 09cm²
For the circular mat
1.54 = 3.14r²
r² = 0. 49
Take the square root
r = 0. 7m
Circumference = 2× 3.14 × 0. 7 = 4.39m
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I need help with this question! I'll give 20 points!
Answer:
Step-by-step explanation:multiply x by y to the power of 67000 and then you will get 730000000.
The cost of 4 shirts is $36. At this rate, what is the cost of 9 shirts?
Answer:
$81
Step-by-step explanation:
36/4 = 9
We can deduce that each shirt costs $9 so...
9x9 = 81
I’ll mark brainliest
Answer:
θ = 78.69°
Step-by-step explanation:
As this is a right angle triangle we use trigonometric ratios/
The perpendicular i.e the height of the mast = 50 ft
The base i.e the shadow = 10 ft
tanθ = perpendicular / base
tanθ = 50/10
θ = [tex]tan^{-1}[/tex] (50/10)
θ = 78.69°
Julie and Barry Spinos purchased a house for $96,400. They made a 25 percent down payment and financed the remaining amount at 5. 50 percent for 30 years. Their monthly payment is $410. 66. How much of the first monthly payment is used to reduce the principal?
The first monthly charge has about $78.78 allotted in the direction of reducing the principal.
The total buy charge of the house is $96,400 and the Spinoses made a 25% down payment, because of this they paid $96,400 x 0.25 = $24,100 in advance.
Therefore, the final quantity that they financed is $96,400 - $24,100 = $72,300.
They financed this amount at 5.50% for 30 years, which gives us the following method for calculating the monthly payment (P):
P = (r * PV) / (1 - (1 + r)^(-n))
in which:
r = month-to-month interest rate PV = present value n = overall range of paymentsSubstituting the values, we get:
P = (0.00458 * 72,300) / (1 - (1 + 0.00458)^(-360))
P ≈ $410.66
We recognise that the monthly payment is $410.66 and we will calculate the interest portion of the primary monthly price as follows:
interest = balance * monthly interest price
interest = $72,300 * (5.50% / 12) ≈ $331.88
To calculate the amount of the primary monthly charge this is used to lessen the fundamental, we subtract the interest component from the total monthly payment:
$410.66 - $331.88 ≈ $78.78
Thus, the first monthly charge has about $78.78 allotted in the direction of reducing the principal.
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A printing company charges $5,000 for the first 400 page printed. For each page printed over 400, the customer is charged an additional $0.01 per page which equation could be used to calculate the total cost, t, to copy p pages when p is greater than 400
If more than 400 sheets are duplicated, this equation will provide us with the overall expense, t.
What does a basic equation mean?A method that describes how two lines along both side of a sign connect each other. It typically contains an equal symbol and one variable. Similarly, 2x - 4 = 2. The variable x is present in the particular circumstance.
The equation that could be used to calculate the total cost, t, to copy p pages when p is greater than 400 is:
t = $5,000 + ($0.01 × (p - 400))
The base cost for copying the first 400 pages is $5,000. For each additional page above 400, the customer is charged $0.01 per page. Therefore, to calculate the total cost for copying p pages, we need to subtract 400 from p to determine the number of pages that are being charged at the additional rate, and then multiply that by $0.01 to determine the additional cost. This gives us:
Additional cost = $0.01 × (p - 400)
The total cost is then the sum of the base cost and the additional cost:
t = $5,000 + ($0.01 × (p - 400))
This equation will give us the total cost, t, for any number of pages greater than 400 that are copied.
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Write
tanz
in terms of
secz
using the Pythagorean Identity for: Part: 0 / 2 Part 1 of 2 (a)
z
in Quadrant II.
tanz=
Part:
1/2
Part 2 of 2 (b)
z
in Quadrant IV.
We can write tanz in terms of secz using the Pythagorean Identity as:
tanz = -sqrt(sec^2z - 1)
Part 1 of 2:
The Pythagorean Identity states that sin^2z + cos^2z = 1. We can use this identity to write tan^2z in terms of sec^2z.
First, let's rearrange the Pythagorean Identity to isolate cos^2z:
cos^2z = 1 - sin^2z
Next, we can divide both sides of the equation by cos^2z to get:
1 = sec^2z - (sin^2z)/(cos^2z)
Since tan^2z = (sin^2z)/(cos^2z), we can substitute this into the equation:
1 = sec^2z - tan^2z
Finally, we can rearrange the equation to isolate tan^2z:
tan^2z = sec^2z - 1
Now, let's consider the case when z is in Quadrant II. In this quadrant, tanz is negative and secz is negative. Therefore, we can write:
tanz = -sqrt(sec^2z - 1)
Part 2 of 2:
In the case when z is in Quadrant IV, tanz is negative and secz is positive. Therefore, we can write:
tanz = -sqrt(sec^2z - 1)
So, in both cases, we can write tanz in terms of secz using the Pythagorean Identity as:
tanz = -sqrt(sec^2z - 1)
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A tree three-foot tall grows 8% every five years. How tall will the tree be at the
end of 90 years?
Answer:
21.6 feet?
Step-by-step explanation:
8 percent of 3 is 0.24
0.24 x 90 is 21.6
A loaf of bread weighs about 1 pound. Choose all of the metric measures that are less than 1 pound
As one loaf of bread weighs about 1 pound, the metric measures that are less than 1 pound are:
450g100gIn which system is pound is the unit of weight?The pound means the unit of measurement used in the U. S. customary system and the British imperial system to measure weight. One familiar use of pounds is measuring how much a person weighs.
A pound is approximately 0.4535 kilogrammes, so 453.5 grammes. With this information, we can determine that answers 450 grammes and 100 grammes are the only correct ones because they are lesser than 453.5 grammes.
Full question "A loaf of bread weighs about 1pound. Chose all of the metric measures that are less than 1pound. 1kg 0.5kg 500g 450g 100g"
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determine the volume of the cone
[tex] \: [/tex]
_________
Given:-[tex] \tt \: Radius=9cm[/tex][tex] \: [/tex]
[tex] \tt \: Height = 12cm[/tex][tex] \: [/tex]
To find:-[tex] \tt \: volume \: of \: cone \: = \: ?[/tex][tex] \: [/tex]
By using formula:-[tex] \small{\star \boxed{ \tt \color{blue} volume \: of \: cone \: = \frac{1}{3}h\pi {r}^{2} }}[/tex]
[tex] \: [/tex]
Solution:-[tex] \tt \: v = \frac{1}{3}h\pi {r}^{2} [/tex][tex] \: [/tex]
[tex] \tt \: v = \frac{1}{3} \times 12 \times \pi \times ( {9})^{2} [/tex][tex] \: [/tex]
[tex] \tt \: v = \frac{1}{3} \times 12\pi \times 81[/tex][tex] \: [/tex]
[tex] \tt \: v = \frac{1}{ \cancel{3} } \times \cancel{972\pi}[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \tt{ \color{hotpink} \: 324\pi \: {cm}^{3} }}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━
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Which equation best represents the relationship between x and y in the graph?
Ay = 3x - 2
- ¹x +3
-8-7-6-5
9
8
-7
6
S
-1
-2
-3
4
-5
-6
-7
-8
-9
4 5 6 7 8
X
An equation that best represents the relationship between x and y in the graph is: A. y = -3x/4 - 3.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (-4, 0), an equation of this line can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 0 = (-3 - 0)/(0 + 4)(x + 4)
y - 0 = -3/4(x + 4)
y = -3x/4 - 3.
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27. The rodent population p in a large city is being controlled by a new poison that kills half the population every 2 months m. If there are currently 1,000,000 rodents in the city, how many will there be in 12 months?
Step-by-step explanation:
Since the new poison kills half the population every 2 months, we can say that the remaining half will survive for another 2 months. Therefore, after 2 months, the rodent population will be half of 1,000,000, which is 500,000.
After another 2 months, the remaining half of the 500,000 will survive, which is 250,000.
After another 2 months, the remaining half of the 250,000 will survive, which is 125,000.
After 6 months, the rodent population will be 125,000.
Since 12 months is six 2-month periods, we can repeat this process again. After another 2 months, the rodent population will be 62,500.
After another 2 months, the rodent population will be 31,250.
After another 2 months, the rodent population will be 15,625.
Therefore, after 12 months, the rodent population will be 15,625.
The table represents a linear equation. answers?
Option (c) has the same equation as above after simplification, so the answer is (c):y-8=-0.2(x+10).
What is simplification?Simplification involves reducing an expression, equation, or problem to a simpler form. This can involve performing operations such as combining like terms, factoring, or canceling out common factors.
What is point-slope form?Point-slope form is a way of writing the equation of a straight line in two-dimensional space, using a given point on the line and the line's slope.
The point-slope form equation for a line passing through a point (x1, y1) with slope m is:y - y1 = m(x - x1).
In the given question,
To write the equation of a line in point-slope form, we need to use the formula:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is any point on the line.
We are given two points on the line: (-10, 8) and (10, 4). We can use these points to find the slope of the line:
m = (y2 - y1) / (x2 - x1)
= (4 - 8) / (10 - (-10))
= -0.15
Now we can use the point-slope form with the point (-10, 8) and slope -0.15:
y - 8 = -0.15(x - (-10))
Simplifying this equation, we get:
y - 8 = -0.15(x + 10)
Option (c) has the same equation as above after simplification, so the answer is (c):
y-8=-0.2(x+10).
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The cafeteria needs 815 onions. There are 8 onions in each bag. How many bags should the cafeteria buy?
815 ÷ 8 = 101.875 ≈ 102
∴ The cafeteria should buy 102 bags.
Answer:
102 bags.
Step-by-step explanation:
You divided 815 by 8. The answer is 101.875 and you can't have half a bag so you round it up to the nearest whole number.
On its own 2c is a product with
We deduced the following from the given phrase:
1) The supplied expression is a sum with the four terms a, b, l, and c.
2) 2c is the result of the factors 2 and c on its own.
Describe a function?A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. For each function, there is a corresponding range, codomain, and domain.
What follows is:
A + (b+1) + 2c is the function that has been discovered and written in the question.
As we can see, three distinct terms—a, b+1, and 2c—have been demonstrated to be a part of this function.
As a result, we deduced the following from the above formula:
1) With the four terms a, b, 1 and 2c, the complete equation is a sum.
2) 2c is the result of the factors 2 and c on its own.
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The complete question is:
On its own 2c is a product with
NEED HELP DUE TODAY!!!!!!!!!!!!
Circle B is a dilation of circle A. What is the scale factor of dilation?
The scale factor of dilation is 3.
What is Dilation of a circle?
Dilation is the process of altering an object's or shape's size by reducing or enlarging its dimensions by a certain amount of scale. A circle with a radius of 10 units, for instance, is reduced to a circle with a radius of 5 units. This technique is applied in art and craft, photography, and logo design, among other fields.
Given : Radius of original circle A = 3
Radius of Dilation circle B = 9
We know that, Scale factor of dilation =
Dimension of Dilation shape / Dimension of original shape
So, Scale factor of given dilation = Radius of Circle B / Radius of Circle A
= 9/3
= 3.
Hence, Scale factor of dilation of circle B on Circle A is 3.
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A labour economist aims to estimate the variance of unemployed workers' mathematic test scores. Assume that a random sample of 18 scores had a sample standard deviation of 10.4.
Using the information above, form a 90% confidence interval for the population variance.
To have a full mark, you NEED to show your calculation and solution (with all the STEPS) in the midterm exam file posted under Assessment-Assignment (Similar to Weekly Quizzes).
Do NOT use EXCEL
a) The confidence interval is exactly between 46.64 and 202.07
b) The confidence interval is exactly between 26.64 and 182.07
c) The confidence interval is exactly between 86.64 and 222.07
d) The confidence interval is exactly between 66.64 and 212.07
e) None of the answers are correct
A labour economist aims to estimate the variance of unemployed workers' mathematic test scores. Assume that a random sample of 18 scores had a sample standard deviation of 10.4. To form a 90% confidence interval for the population varianceis The confidence interval is exactly between 46.64 and 202.07. The correct answer is option (a)
Find the degrees of freedom (df) by subtracting 1 from the sample size:
df = n - 1 = 18 - 1 = 17
Find the chi-square values for the 90% confidence interval using a chi-square table or calculator. The lower value corresponds to the 5th percentile (0.05) and the upper value corresponds to the 95th percentile (0.95):
χ² lower = 27.488
χ² upper = 8.672
Calculate the lower and upper limits of the confidence interval using the formula:
CI lower = (df * s²) / χ²_upper
CI upper = (df * s²) / χ²_lower
Where s² is the sample variance (the square of the sample standard deviation):
s² = 10.4² = 108.16
Plugging in the values:
CI lower = (17 * 108.16) / 27.488 = 46.64
CI upper = (17 * 108.16) / 8.672 = 202.07
The 90% confidence interval for the population variance is between the lower and upper limits:
CI = (46.64, 202.07)
Therefore, the correct answer is option (a) The confidence interval is exactly between 46.64 and 202.07.
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NEED HELP PLEASE. Graph
The graph of the functions are added as an attachment
How to graph the function using their periodsThe graphs are sinusoidal functions such that they are mathematical functions that exhibit a repetitive pattern over time or space
From the question, we have the following parameters that can be used in our computation:
y = 4cot(4x)
y = -1/2cot(2x - π/4)
To plot y = 4cot(4x) using two periods, we make use of the domain
{0 < x < π/2}
To plot y = 4cot(4x) using two periods, we make use of the domain
{0 < x < π}
See attachement for the graphs of the functions
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You have $39,000 you would like to invest in two different stocks, Stock Boll and Stock Coff. The buying limit on Stock Coff is $12,900 and you want to spend at least twice as much money on Boll as Coff. If Stock Boll earns 5% annual interest and Stock Coff earns 8% annual interest, how much money should you invest in each stock to maximize your annual interest earned? What is the maximum annual interest?
You should invest $26,100 in Stock Boll and $12,900 in Stock Coff to maximize your annual interest earned, and the maximum annual interest is $2,337.
To maximize your annual interest earned, you should invest as much money as possible in the stock with the higher interest rate, which is Stock Coff. However, there are two constraints that you need to consider: the buying limit on Stock Coff and the requirement to spend at least twice as much money on Stock Boll as Stock Coff.
Let's use algebra to solve this problem. Let x be the amount of money you invest in Stock Boll and y be the amount of money you invest in Stock Coff. Then we have the following equations:
x + y = $39,000 (the total amount of money you have to invest)
y <= $12,900 (the buying limit on Stock Coff)
x >= 2y (the requirement to spend at least twice as much money on Stock Boll as Stock Coff)
To maximize your annual interest earned, you want to maximize the expression 0.05x + 0.08y (the sum of the interest earned from Stock Boll and Stock Coff).
If you invest the maximum amount of money in Stock Coff ($12,900), then you have $39,000 - $12,900 = $26,100 left to invest in Stock Boll. This satisfies the requirement to spend at least twice as much money on Stock Boll as Stock Coff ($26,100 >= 2 * $12,900).
So the optimal solution is to invest $26,100 in Stock Boll and $12,900 in Stock Coff. The maximum annual interest earned is 0.05 * $26,100 + 0.08 * $12,900 = $1,305 + $1,032 = $2,337.
Therefore, you should invest $26,100 in Stock Boll and $12,900 in Stock Coff to maximize your annual interest earned, and the maximum annual interest is $2,337.
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Draw the image of the indicated translation of the given pre image please
The new points after the translation are (0, -4), (0, 0), (5, -5) and (5, 0) and the image is added as attachment
Calculating the image of the figureTranslation is the movement of a point either up, left, right or down on the coordinate plane.
If a point A(x, y) is translated a units left and b units down, the new point is A'(x - a, y - b)
From the question, the vertices of the rectangle are (2, 3), (2, 7), (7, 2) and (7, 7).
The translation T<-2, -7>; is a translation of 2 units left and 7 units down.
This means that
The new points are (0, -4), (0, 0), (5, -5) and (5, 0).
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Create a number sequence with 5 terms involving fractions with a common difference of 1/3 from one term to the next starting from 1/3
Answer:This free number sequence calculator can determine the terms (as well as the sum of all terms) of the arithmetic, geometric, or Fibonacci sequence.
Step-by-step explanation: