Answers
Check the picture below.
so the base of the pyramid is a triangle whose base is 12 and altitude is "x", and the pyramid has a height/altitude of 15, so
[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(12)(x)\\[1em] h=15\\ V=240 \end{cases}\implies 240=\cfrac{1}{3}\left[\cfrac{1}{2}(12)(x) \right](15) \\\\\\ 240=30x\implies \cfrac{240}{30}=x\implies 8=x[/tex]
Related Questions
What is the value of 6 = 3 × 2³? 2/03/0 16 64
Answers
The value of 6 = 3 × 2³ is 24 by using PEMDAS operations, the correct option is (d).
To understand why, we can simplify the equation using the order of operations, which is PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction). To evaluate the expression 3 x 2³, we first need to simplify the exponent, which means multiplying 2 by itself three times:
2³ = 2 x 2 x 2
2³ = 8
Now we can substitute the value of 2³ into the original expression:
3 x 2³ = 3 x 8
3 x 2³ = 24
However, the value of 6 = 3 x 2³, is equal to 24 the correct option is (d).
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The complete question is:
What is the value of 6 = 3 × 2³?
a. 16
b. 64
c. 42
d. 24
14. Find mMK
16. Find mJPK.
Answers
The measures of arcs and segments are
NK = 12, MLK = 41.5 degrees, JK = 24 and JPK = 277 degrees
How to determine the measures of arcs and segmentsLength NK
Given the triangle as the parameter.
Using the Pythagoras theorem, we have
NK = √(KL² - LN²)
So, we have
NK = √(15² - 9²)
Evaluate
NK = 12
The arc measure MK
Here, we start by calculating the central angle MLK
This is done using the following cosine ratio
cos(MLK) = NK/KL
cos(MLK) = 9/12
cos(MLK) = 0.75
Evaluate
MLK = 41.5 degrees
This means that
Arc MK = 41.5 degrees
Length JK
This is calculated as
JK = NK * 2
So, we have
JK = 12 * 2
JK = 24
The arc measure JPK
This is calculated as
JPK = 360 - 2 * MK
So, we have
JPK = 360 - 2 * 41.5 degrees
Evaluate
JPK = 277 degrees
Hence, the arc measure is 277 degrees
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help me solve this homework
Answers
The volume of the triangular prism is 42 in³.
What is a triangular prism?In geometry, a triangular prism is a three-sided polyhedron with a triangle base, a translated copy, and three faces joining equal sides. A right triangular prism is oblique if its sides are not rectangular.
We know that
Volume of Prism (V) = Area of triangle * Height of Prism
Area of triangle = (Base * Height) / 2
Area of triangle = (4 * 3) / 2
Area of triangle = 12 / 2
Area of triangle = 6 in²
Using this, we get
⇒V = 6 * 7
⇒V = 42 in³
Hence, the volume of the triangular prism is 42 in³.
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Since there are multiple questions so the question answered above is attached below
Let A, B, C be three sets such that A U B = C & A ∩ B = φ then how do you prove that A = C – B?
Answers
When A U B = C & A ∩ B = φ, then A = C - B. The solution has been obtained by using properties of sets.
What is a set?
In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Curly brackets are typically used to represent sets.
We know that
A - B = (A ∪ B) - B
On substituting A U B = C in this, we get
A - B = C - B ...(1)
Similarly,
A - B = A - (A ∩ B)
On substituting A ∩ B = φ in this, we get
A - B = A ...(2)
From (1) and (2), we get
A = C - B
Hence, when A U B = C & A ∩ B = φ, then A = C - B.
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Find the
1. End behavior
2. X-intercepts
3. Positive/negative
4. Multiplicity
Answers
The end behavior is as x approaches negative infinity, f(x) approaches negative infinity as x approaches positive infinity, f(x) approaches negative infinity The only x-intercept of f(x) is x = 3.
What is the end behavior and x - intercepts of the functionThe given function is f(x) = -x³ + 2x² + 3
1. End behavior:
As the leading coefficient of f(x) is negative, -x^3 dominates the behavior of the function as x approaches negative or positive infinity. Therefore, the end behavior of the function is:
As x approaches negative infinity, f(x) approaches negative infinity.As x approaches positive infinity, f(x) approaches negative infinity.2. X-intercepts:
To find the x-intercepts of f(x), we need to solve the equation f(x) = -x^3 + 2x^2 + 3 = 0. We can factor out a common factor of -1 to simplify the equation:
-x^3 + 2x^2 + 3 = 0
x^3 - 2x^2 - 3 = 0
Using synthetic division or long division, we can find that one of the roots of this equation is x = 3. We can then factor out (x - 3) using polynomial division to find the other two roots:
x^3 - 2x^2 - 3 = (x - 3)(x^2 + x + 1)
The quadratic factor x^2 + x + 1 has no real roots, so the only x-intercept of f(x) is x = 3.
3. Positive/negative:
To determine the sign of f(x) for different values of x, we can look at the sign of each factor in the polynomial:
The leading coefficient of f(x) is negative, so for very large negative or positive values of x, f(x) is negative.The factor -x^3 is negative for negative values of x and positive for positive values of x.The factor 2x^2 is positive for all values of x.The constant term 3 is positive.Putting these together, we can make the following sign chart for f(x):
x f(x)
x < 0 -
0 < x < 3 +
x > 3 -
4. Multiplicity:
The only root of f(x) is x = 3, which has multiplicity 1. This means that the graph of f(x) crosses the x-axis at x = 3 and changes sign at that point.
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Pls give simple working
Answers
Answer:
Step-by-step explanation:
sum of all angles in quadrilateral = 360
So, x+48+48+132 =360
x =132
Vocabulary Matching
1. apathy
2. competent
3. expectations
4. value
positive or negative
fear of failure or success
Ahmein doesn't care if he does well
or not.
Javier knows he is able to build a
birdhouse.
Answers
The correct matches for the vocabulary would be :
Apathy - Ahmein is unconcerned with his academic performance.Competent - Javier is aware that he can construct a birdhouse.Expectations - Fear of failure or success Value - Positive or negative How to explain the vocabulary ?Apathy is a lack of interest or passion for anything. The line "Ahmein doesn't care if he does well or not" describes apathy since Ahmein is apathetic about whether he succeeds or fails.
Being competent is having the knowledge and skills required to complete a task successfully which describes Javier as he is aware that he can construct a birdhouse.
Expectations are convictions or presumptions regarding future events. Value is a term used to describe something's importance or worth.
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Answer:
1. apathy = Trudy doesn't care about doing well in school.
2. competent = Javier knows he is able to build a birdhouse.
3. expectations = fear of failure or success
4. autonomy = Alfonzo likes to make choices on his own.
5. stress = Quincy feels anxious and distressed about a test.
-2y=5x-6 in standard form
Answers
Answer: 5x + 2y = 6
Step-by-step explanation:
The standard form is Ax + By = C
Subtract 5x from each side:
- 5x - 2y = - 6
The first term in the standard form must be positive, so multiply by -1 to change the sign.
5x + 2y = 6
Hope this helps!
Write an equation in standard form using integers Y= X/5
Answers
To write an equation in standard form using integers, we need to eliminate any fractions by multiplying both sides of the equation by the least common multiple of the denominators.
In this case, the denominator is 5. So we can multiply both sides of the equation by 5 to get:-
5Y = X
Now, we can rearrange the equation so that the variables are on the left-hand side and the constants are on the right-hand side, in the form of Ax + By = C.
X - 5Y = 0 (subtracted X from both sides)
Therefore, the equation in standard form using integers is -X - 5Y = 0.
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24kg in the ratio 3 : 5 ?????
Answers
Answer: Your welcome!
Step-by-step explanation:
The ratio of 24kg is 3:5, which means 3 parts of 24kg is 3 times the 5th part of 24kg.
Therefore, 3 parts of the 24kg is 18kg and 5 parts of the 24kg is 6kg.
Determine algebraically whether the function is even, odd or neither: g(x) = x/x^2+3
Answers
The function [tex]g(x) = \frac{x}{x^2+3}[/tex] is neither even nor odd.
To determine if a function is even, we can use the following test:
f(x) = f(-x)
If this is true, then the function is even.
For the given function, [tex]g(x) = \frac{x}{x^2+3}[/tex], let's plug in -x for x and see if the function is equal to itself:
[tex]g(-x) = \frac{-x}{(-x)^2+3} = \frac{-x}{x^2+3}[/tex]
As we can see, g(x) does not equal g(-x), so the function is not even.
To determine if a function is odd, we can use the following test:
f(x) = -f(-x)
If this is true, then the function is odd.
For the given function, let's plug in -x for x and see if the function is equal to the negative of itself:
[tex]g(x) = \frac{-x}{(-x)^2+3} = \frac{-x}{x^2+3}\\\\ -g(-x) = \frac{x}{-x^2+3}[/tex]
As we can see, g(x) does not equal -g(-x), so the function is not odd.
After the algebraic analysis, we can conclude that the function g(x) is neither, i.e., it is neither even nor odd.
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ive been trying to do this since this morning and can't, I need help
a.) Use the table below to calculate the average percent change in population in California from 2000-2009.
b.) If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
Answers
The exponential growth equation is x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶ , where x ( t ) is the population in the year 2015 = 40,115,896
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units'
Given data ,
Let the exponential growth equation be represented as x ( t )
Now , the average percentage change from the year 2000 - 2009 is calculated by
The total percentage = ( 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93 )
The total number of years = 9 years
So , the average percentage change = total percentage / number of years
On simplifying , we get
The average percentage change = 12.21 / 9 = 1.35667 %
b)
The population in 2009 was 37,000,000
So , the population growth rate r = 1.35667 %
And , the population in the years 2015 is given by
The number of years n = 6 years
x ( t ) = 37,000,000 ( 1 + 1.3567% )⁶
On simplifying , we get
x ( t ) = 37,000,000 ( 1.013567 )⁶
x ( t ) = 40,115,896
Hence , the population in the year 2015 is 40,115,896
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Question 1: a. Suppose that f(x)=2 x^{2}-5 x-8, g(x)=9-x and ( k(x)=2 x+4 ) Perform the following combination functions, then simplify your results as much as you can: (I Mark) 1. ( 4(f+k){x}
Answers
1. 4(f+k)(x)=4(2x^2 - 5x - 8 + 2x + 4) = 8x^2 - 20x - 32.
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Determine if the triangles are similar.
A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar
Answers
The triangles are similar by SSS and the scale factor is 0.625
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔJKT
Let the second triangle be represented as ΔKLS
Now , the measure of side JT = 20
The measure of side JK = 14
The measure of side KS = 32
The measure of side KL = 22.4
The corresponding sides of similar triangles are in the same ratio
So , on simplifying , we get
JT / KS = JK / KL
20 / 32 = 14 / 22.4
On further simplification , we get
0.625 = 0.625
Hence , the triangles are similar
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The angle of elevation of the top of the building at a distance of 55 m from its foot on a
horizontal plane is found to be 60°. Find the height of the building rounded to the nearest
tenth of a meter.
The height of the building is _______ meters.
Need help
Answers
Let's call the height of the building "h". We can use trigonometry to solve for "h" using the angle of elevation and the horizontal distance from the foot of the building to the point where the angle of elevation is measured.
In this case, we have a right triangle with the height of the building as one leg, the horizontal distance as the adjacent leg, and the angle of elevation as the angle opposite the height. So we can use the tangent function:
tan(60°) = h/55
Solving for "h", we get:
h = 55 tan(60°)
h ≈ 95.1
Rounded to the nearest tenth of a meter, the height of the building is approximately 95.1 meters.
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Select the graph that represents the system of equations.
y=−3x−13 y=2x+2
Answers
In answering the question above, the solution is As a result, (x,y) = is the system of equations' answer (-3,8).
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The equations in the system are:
[tex]y = -3x - 13 \sy = 2x + 2[/tex]
We may put the two equations equal to one another and get x to solve this system:
-3x - 13 = 2x + 2
3x added to both sides results in:
-13 = 5x + 2
By taking 2 away from both sides, we arrive at:
-15 = 5x
When we multiply both sides by 5, we get:
x = -3
We may use either of the original equations to calculate y now that we know x:
y = -3(-3) - 13 = 8
As a result, (x,y) = is the system of equations' answer (-3,8).
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Please answer this question
Answers
160 student tickets were sold.
Describe Equation?Equations are used to model a wide range of phenomena, from physical laws in science to economic models in finance. They are also used in solving problems and making predictions in various fields.
Let's start by setting up a system of equations to represent the given information:
a + s = 200 (equation 1: total number of tickets sold)
7a + 5s - 210 = 870 (equation 2: profit after paying back Mr. Shum's investment)
We can simplify equation 2 by adding 210 to both sides:
7a + 5s = 1080 (equation 3)
Now we can use equation 1 to solve for one variable in terms of the other:
s = 200 - a (equation 4)
Substitute equation 4 into equation 3 and solve for a:
7a + 5(200 - a) = 1080
7a + 1000 - 5a = 1080
2a = 80
a = 40
So 40 adult tickets were sold. We can use equation 4 to find the number of student tickets sold:
s = 200 - a = 200 - 40 = 160
Therefore, 160 student tickets were sold.
To check our answer, we can verify that the total revenue from ticket sales is equal to the initial investment plus the profit:
7(40) + 5(160) = 210 + 870
280 + 800 = 1080
This checks out, so our answer is correct.
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Julia's dog Toby had 5 puppies. Each pup eats 0. 13 pounds of dog food every day. How much dog food do puppies eat in 1 day?
Answers
Answer:
0.65
Step-by-step explanation:
0.13 * 5 = 0.65
Can someone answer this
Answers
Answer:
16
Step-by-step explanation:
g(x)=-5x+1
g(-3)
x=-3
-5(-3) +1
15+1
16
Answer:
See below.
Step-by-step explanation:
For this problem, we are asked to find the value of g(-3).
We are given a Linear Function.
What is a Linear Function?A Linear Function is a Polynomial Function that is commonly graphed. This function most of the time will simply be represented as a straight line when graphed.
For this problem;
[tex]g(x)=-5x+1 \ Find \ g(-3).[/tex]
We simply need to substitute -3 in for x.
[tex]g(-3)=-5(-3)+1[/tex]
Simplify:
[tex]g(-3)=16.[/tex]
Our final answer is g(-3) = 16.
When Sarah runs the 400 meter dash, her finishing times are normally distributed with a mean of 63 seconds and a standard deviation of 1. 5 seconds. Using the empirical rule, what percentage of races will her finishing time be between 61. 5 and 64. 5 seconds?
Answers
Based on the given mean and standard deviation of Sarah's finishing times, we can estimate that approximately 68% of her races will have finishing times between 61.5 and 64.5 seconds.
The empirical rule, also known as the 68-95-99.7 rule, is a useful tool for estimating the percentage of data that falls within a certain number of standard deviations from the mean in a normal distribution.
In this case, Sarah's finishing times in the 400-meter dash are normally distributed with a mean of 63 seconds and a standard deviation of 1.5 seconds. To use the empirical rule, we need to first calculate the z-scores for the lower and upper bounds of the range we're interested in.
For the lower bound of 61.5 seconds:
z = (61.5 - 63) / 1.5 = -1
For the upper bound of 64.5 seconds:
z = (64.5 - 63) / 1.5 = 1
These z-scores tell us how many standard deviations are away from the mean each time. Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Since the range we're interested in is within one standard deviation of the mean, we can estimate that approximately 68% of Sarah's finishing times will be between 61.5 and 64.5 seconds.
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a car headlight reflector is cut by a plane along its axis. the section is a parabola having the light center at the focus. if the distance of focus from the vertex is 3/4cm and if the diameter of the reflector is 10 cm, find its depth.
A. 22/3
B. 25/3
C. 23/3
D. 27/3
Answers
The correct answer is B. 25/3.
We can use the equation of a parabola with a focus at (h, k) and a directrix at y = k + p to find the depth of the reflector. The equation is:
(y - k)² = 4p(x - h)
Since the focus is at the light center, we can set h = 0 and k = 0. The distance of the focus from the vertex is 3/4 cm, so p = 3/4. The diameter of the reflector is 10 cm, so the x-coordinate of the vertex is 5 cm. We can plug in these values to find the depth of the reflector:
(y - 0)² = 4(3/4)(x - 0)
y² = 3x
y = √(3x)
When x = 5, we can find the depth of the reflector:
y = √(3*5)
y = √15
y = 3.87 cm
The depth of the reflector is 3.87 cm, or 25/3 cm.
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When a car headlight reflector is cut by a plane along its axis, the section obtained is a parabola. This parabola is such that the light center is at the focus. The distance of focus from the vertex is 3/4 cm and the diameter of the reflector is 10 cm. The depth of the reflector comes out to be CD = VC - VF = (10/3) - (3/4) = 27/4 cm
The vertex of the parabola is the midpoint of the diameter of the reflector. Let V be the vertex of the parabola and let F be the focus. The distance between V and F is given as 3/4 cm.The reflector is such that light rays from the source (headlamp) placed at the focus of the parabola are reflected by the parabola in such a way that the rays are parallel to the axis of the parabola. This is known as the reflecting property of the parabola.
This is equal to CD.Let P be the point on the parabola, as shown in the diagram below, such that PF is equal to the diameter of the reflector. Then, by the definition of the parabola, the distance from P to the vertex C is the same as the distance from the focus F to P, i.e., PF = PC. Since PF is equal to the diameter of the reflector, it is given that PF = 10 cm.Therefore, PC = 10 cm. It is also given that VF = 3/4 cm. Therefore, VC = PC - PV = 10 - 20/3 = 10/3 cm.
Hence, the depth of the reflector is CD = VC - VF = (10/3) - (3/4) = 27/4 cm. Therefore, the depth of the reflector is 27/4 cm, which is the correct option among the given choices.
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(4,3); y = 3x² - x + 7
Answers
Answer:13
Step-by-step explanation:
because when you
Write an equation of the line passing through the point (8,3) that is parallel to the line y=-3/4+4
Answers
The equation of the line passing through the point (8,3) that is parallel to the line y=-3/4+4 is y = (-3/4)x + 9.
The slope of the given line is -3/4. The desired line will likewise have a slope of -3/4 because it is parallel to this line.
The equation of the line travelling through the point (8,3) with a slope of -3/4 may be found using the point-slope form of a line's equation:
y - y1 = m(x - x1)
where the provided point is (x1, y1), and m is the slope.
When we change the values, we obtain:
y - 3 = (-3/4)(x - 8)
Making the right side simpler:
y - 3 = (-3/4)x + 6
To each sides, add 3:
y = (-3/4)x + 9
Hence, y = (-3/4)x + 9 is the equation of the line going through the point (8,3) that is parallel to the line y=-3/4+4.
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At the Livingston Zoo's bug exhibit, Marcy watches a millipede crawl for 1 4/8 minutes, stay still for a while, and then crawl for 2 1/8 minutes more. How much total time did Marcy spend watching the millipede crawl?
Answers
Marcy spent 2.125 minutes of total time watching the millipede crawl.
How to the total time Marcy spent watching the millipede crawl?To find the total time Marcy spent watching the millipede crawl, we need to add up the time it crawled during the first period and the time it crawled during the second period.
1 4/8 minutes is the same as 1 2/4 minutes, or 1.5 minutes.
2 1/8 minutes is the same as 2.125 minutes.
So the total time the millipede crawled is:
1.5 minutes + 2.125 minutes = 3.625 minutes
Therefore, Marcy spent a total of 3.625 minutes watching the millipede crawl.
We know that Marcy watched the millipede crawl for 1 4/8 minutes, which can be simplified to 1 2/4 minutes, or 1.5 minutes.
Next, the millipede stayed still for a while, and then crawled for 2 1/8 minutes. We can convert 2 1/8 minutes to a decimal by adding the whole number (2) to the fraction (1/8) converted to a decimal (0.125). So:
2 + 0.125 = 2.125 minutes
Marcy spent 2.125 minutes of total time watching the millipede crawl.
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One year, a company sales increased by 15%. The following year the company's sales increased by 18%. Calculate the overall percentage increase
Answers
The overall percentage increase is approximately 35.7%.
What is the overall percentage increase of the company sales?Given that, a company sales increased by 15% in year one and 18% in the following year.
To calculate the overall percentage increase, we need to find the combined effect of the two increases.
One way to do this is to use the formula for compound interest, which is:
A = P(1 + r₁)(1 + r₂)
where:
A = the final amountP = the initial amountr₁ = the first interest rate (as a decimal)r₂ = the second interest rate (as a decimal)In this case, let's assume that the initial sales amount is 100 (you could use any amount as long as you keep it consistent throughout the calculation).
Then, the first year's increase of 15% would result in a new amount of:
100(1 + 0.15) = 115
In the second year, the 18% increase would be applied to this new amount of 115, resulting in:
115(1 + 0.18) = 135.7
Hence, we have an overall increase of:
(135.7 - 100)/100
= 0.357 × 100%
= 35.7%
Therefore, the increase is approximately 35.7 percent.
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8 + (9-1) ÷ 4 =? 10 or 4
Answers
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
The Kangaroo Lodge of Madison County has 10 members (A, B, C, D, E, F, G, H, I, and J). The club has five working committees: the Rules Committee (A, C, D, E, I, and I), the Public Relations Committee (B, C, D, H, I, and J), the Guest Speaker Committee (A, D, E, F, and H), the New Year's Eve Party Committee (D, F, G, H, and I), and the Fund Raising Committee (B, D, F, H, and J). (a) Suppose we are interested in knowing which pairs of members are on the same committee. Draw a graph that models this problem. (Hint: Let the vertices of the graph represent the members.) (b) Suppose we are interested in knowing which commit- tees have members in common. Draw a graph that models this problem. (Hint: Let the vertices of the graph represent the committees.)
Answers
1.Solve the system of equations [8] 2x + 6y + 62 = 6 2x + 7y + z = 7 2x + 7y + 72 = 8 - using the inverse of the coefficient matrix.(Compute inverse by inversion algorithm)
Answers
The solution to the system of equations is:
x = -6.552
y = -1.655
z = 1.276
To solve the system of equations using the inverse of the coefficient matrix, we will first need to find the inverse of the coefficient matrix using the inversion algorithm. The coefficient matrix is:
A = [[2, 6, 6], [2, 7, 1], [2, 7, 7]]
To find the inverse of A, we will use the inversion algorithm:
1. Find the determinant of A:
|A| = 2(7*7 - 1*7) - 6(2*7 - 1*2) + 6(2*7 - 2*7) = 14 - 72 + 0 = -58
2. Find the matrix of minors:
M = [[(7*7 - 1*7), -(2*7 - 1*2), (2*7 - 2*7)], [-(6*7 - 6*1), (2*7 - 6*2), -(2*6 - 6*2)], [(6*1 - 7*6), -(2*1 - 7*2), (2*6 - 7*6)]]
M = [[42, -12, 0], [-36, 2, -12], [-36, 12, -30]]
3. Find the matrix of cofactors:
C = [[42, 12, 0], [36, 2, 12], [-36, -12, -30]]
4. Find the adjugate matrix:
adj(A) = [[42, 36, -36], [12, 2, -12], [0, 12, -30]]
5. Find the inverse of A:
A^-1 = (1/|A|)adj(A) = (1/-58)[[42, 36, -36], [12, 2, -12], [0, 12, -30]]
A^-1 = [[-0.724, -0.621, 0.621], [-0.207, -0.034, 0.207], [0, -0.207, 0.517]]
Now, we can use the inverse of the coefficient matrix to solve the system of equations. The system of equations can be written in matrix form as:
AX = B
Where A is the coefficient matrix, X is the matrix of unknowns, and B is the matrix of constants:
A = [[2, 6, 6], [2, 7, 1], [2, 7, 7]]
X = [[x], [y], [z]]
B = [[6], [7], [8]]
Multiplying both sides of the equation by the inverse of A, we get:
A^-1AX = A^-1B
IX = A^-1B
X = A^-1B
Substituting the values of A^-1 and B, we get:
X = [[-0.724, -0.621, 0.621], [-0.207, -0.034, 0.207], [0, -0.207, 0.517]] * [[6], [7], [8]]
X = [[-6.552], [-1.655], [1.276]]
Therefore, the solution to the system of equations is:
x = -6.552
y = -1.655
z = 1.276
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Suppose you deposit $1100 in an account with an annual interest rate of 8 % compounded quarterly: Use the formula 4 = P(1+#)" and round each answer to 2 decimal places, if necessary: Find an equation that gives the amount of money in the account after t years: A(t) Preview Find the amount of money in the account after 8 years After 8 years_ there will be $ in the account: c How many years will it take for the account to contain $2200? It will take years for there to be S2200 in the account: d. If the same account and interest were compounded continuously, how much money would the account contain after 8 years? With continuous compounding interest; there would be in the account after 8 years
Answers
a) A(t) = 1100(1 + 0.08/4)^(4t)
b) After 8 years, there will be $2203.99 in the account.
c) It will take approximately 8.03 years for there to be $2200 in the account.
d) With continuous compounding interest, there would be $2219.54 in the account after 8 years.
A(t) = P(1 + r/n)^(nt)
Where:
A(t) = the amount of money in the account after t years
P = the initial deposit
r = the annual interest rate
n = the number of times interest is compounded per year
t = the number of years
Find an equation that gives the amount of money in the account after t years:
A(t) = 1100(1 + 0.08/4)^(4t)
Find the amount of money in the account after 8 years:
A(8) = 1100(1 + 0.08/4)^(4*8)
A(8) = 1100(1.02)^32
A(8) = 2203.99
After 8 years, there will be $2203.99 in the account.
How many years will it take for the account to contain $2200?
2200 = 1100(1 + 0.08/4)^(4t)
2 = (1.02)^4t
log(2) = 4t*log(1.02)
t = log(2)/(4*log(1.02))
t = 8.03
It will take approximately 8.03 years for there to be $2200 in the account.
If the same account and interest were compounded continuously, how much money would the account contain after 8 years?
A(t) = Pe^(rt)
A(8) = 1100*e^(0.08*8)
A(8) = 1100*e^0.64
A(8) = 2219.54
With continuous compounding interest, there would be $2219.54 in the account after 8 years.
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In 2017, were an estimated 8,888,543 people living in New Jersey and there was a total of 74,846 deaths of NJ residents reported. Of those deaths, 1,908 were due to diabetes.
a. Calculate the crude mortality rate in NJ in 2017
b. Calculate the cause-specific mortality rate due to diabetes in NJ in 2017
c. What additional variable (piece of information) would I need to calculate the case-fatality percent of diabetes?
Answers
Answer: a. To calculate the crude mortality rate in NJ in 2017, we need to divide the total number of deaths (74,846) by the total population (8,888,543) and then multiply by 1,000 to express the result per 1,000 population.
Crude Mortality Rate = (Total deaths / Total population) x 1,000
Crude Mortality Rate = (74,846 / 8,888,543) x 1,000
Crude Mortality Rate = 8.42 per 1,000 population
b. To calculate the cause-specific mortality rate due to diabetes in NJ in 2017, we need to divide the number of deaths due to diabetes (1,908) by the total population and then multiply by 1,000 to express the result per 1,000 population.
Cause-specific Mortality Rate due to Diabetes = (Deaths due to diabetes / Total population) x 1,000
Cause-specific Mortality Rate due to Diabetes = (1,908 / 8,888,543) x 1,000
Cause-specific Mortality Rate due to Diabetes = 0.21 per 1,000 population
c. To calculate the case-fatality percent of diabetes, we would need to know the number of people diagnosed with diabetes who died during the same time period. Specifically, the case-fatality percent of diabetes would be calculated by dividing the number of people with diabetes who died (numerator) by the total number of people with diabetes (denominator) and then multiplying the result by 100 to express the percentage. Therefore, the additional variable required is the number of people with diabetes in the population.
Step-by-step explanation: