Answers
In order to get the volume of the irregular figure, let's cut it into two regular figures. See the cut below.
First, let's calculate the volume of the upper part.
The dimensions of the upper part are 7cm by 3 cm by 3 cm. Since the shape is a rectangular prism, let's multiply 7, 3, and 3.
[tex]V_{upper}=7cm\times3cm\times3cm=63cm^3[/tex]Hence, the volume of the upper figure is 63 cm³.
Let's now calculate the volume of the lower figure.
The dimensions of the lower figure are 5cm by 4 cm by 3 cm. Since this is a rectangular prism too, let's multiply the dimensions.
[tex]V_{lower}=5cm\times4cm\times3cm=60cm^3[/tex]The volume of the lower figure is 60 cm³.
Let's add the volume of the two figures to get the volume of the entire irregular figure.
[tex]V_{irregular}=V_{upper}+V_{lower}[/tex][tex]V_{irregular}=63cm^3+60cm^3=123cm^3[/tex]Therefore, the entire volume of the given irregular figure is 123 cm³.
Related Questions
2) a truck rental company rents a moving truck one day by charging $31 plus $0.13 per mile. write a linear equation that relates the cost c, in dollars, of renting the truck to the number x of miles driven. what is the cost of renting the truck if the truck is driven 180 miles? a) c(x)
Answers
The equation is c = 31 + 0.13x and total cost on driving 180 miles is $54.4.
Firstly we will form the equation using one time charge and the product of number of miles and charge per mile. Then we will keep the value in equation to find the total cost.
Forming the equation -
c = 31 + 0.13x
Keep the value of x in formula for calculation of total cost.
c = 31 + 0.13×180
Performing multiplication on Right Hand Side of the equation
c = 31 + 23.4
Performing addition on Right Hand Side of the equation
c = $54.4
Thus, the equation for calculation of total cost is c = 31 + 0.13x and total cost is $54.4.
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I need this answered please
Answers
Answer:
$2,000
Step-by-step explanation:
Amount invested in Fund A = 6000
Profit rate of return = 5%
Amount of profit = 6000 x 5% = 6000 x 0.05 = $300
Let amount invested in Fund B be $x
Profit amount = 0.01x
Total amount invested is 6000 + x
Total profit in $ = 300 + 0.01x
Total profit in percentage = Total Profit/Total investment x 100
= 4 %
So Total Profit/Total investment = 4/ 100 = 0.04
= (300 + 0.01x) / (6000 + x) = 0.04
Multiply both sides by (6000 + x)
=> 300 + 0.01x = 0.04(6000 + x)
=> 300 + 0.01x = 240 + 0.04x
==> 300 - 240 = 0.04x - 0.01x
=> 60 = 0.03x
x = 60/0.03
x = $2,000
Amount invested in Fund B = $2,000
Step-by-step explanation:
Fund A
$6000 returned a 5% profit. that means it had at the end 105% of the original investment
the formally correct way
100% = 6000
1% = 100%/100 = 6000/100 = $60
5% = 1%×5 = 60×5 = $300
in short, if we knew what we are doing, we could have simply calculated 6000 × 0.05 = $300.
and by the way, 6000 × 1.05 = $6300. which is the current balance of the account (investment plus the returned profit). but we don't need this here. this is just FYI.
Fund B
x returned 1% profit.
Fund A + Fund B
6000 + x returned 4% profit.
so, we have
6000×0.05 + x×0.01 = (6000 + x)×0.04
300 + 0.01x = 240 + 0.04x
60 + 0.01x = 0.04x
60 = 0.03x
x = 60/0.03 = $2000
so, he invested $2000 into fund B.
If 6 is an element in the domain of
f(x)=8–2x, what is its corresponding element
in the range
Answers
The corresponding element in the range when 6 is an element in the domain is f(6) = -4.
What are a function's domain and range?A function's domain and range are the set of all possible inputs and outputs, respectively. A function's domain and range are crucial components. The range includes all of the function's output values, whereas the domain includes all potential input values from the set of real numbers.Given function f(x) = 8–2x.
6 is an element in the domain of this function.
To find the corresponding element in the range of the function,
Substitute x = 6 in the given function f(x).
So,
f(6) = 8 - 2(6)
f(6) = 8 -12
f(6) = -4
Hence, the corresponding element in the range when 6 is an element in the domain is -4.
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a man receives extra money from two independent sources on the weekend: one a lottery which he wins 1 100 of the time; the other a friday night card game which he wins 1/3 of the time. what is the probability that he will win money from at least one of the sources this weekend?
Answers
Probability that the man wins money from at least one of the sources, a lottery and a card game, is equal to 17/50.
Probability that he wins from first source = 1/100
Probability that he doesn’t wins from first source = 99/100
Probability that he wins from second source = 1/3
Probability that he doesn’t wins from second source = 2/3
Probability that the man wins money from at least one of the sources = 1-(probability that the man wins no money from any of the sources)
[tex]=1-[(\frac{99}{100} )(\frac{2}{3} )] =1-(\frac{33}{50} )=\frac{17}{50}[/tex]
So, the required probability of winning the money by the man from at least one of the sources is 17/50.
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a triangle with a perimeter of 50 has side lengths x-1, 2x-3, and 3x "-6." what are the side lengths
Answers
The dimensions of the sides of the triangle is found as 9 units, 17 units and 24 units.
What exactly is the perimeter?Any closed shape's perimeter is just the total length of the its boundary.The perimeter of a shape is defined as the total length round the.It is the length of the outline or boundary of any two-dimensional geographic shape.The perimeters of different shape can be equal in size depending on the dimensions.For the given question,
The perimeter of the triangle is 50 units.
The three sides of the triangle is given as;
x-1, 2x-3, and 3x - 6The formula for finding the perimeter is;
Perimeter = sum of all sides.
Let 'P' be the perimeter of the triangle. Then,
P = x-1 + 2x-3 + 3x - 6
Simplifying.
P = x + 2x + 3x - 1 - 3 - 6
50 = 6x - 10
6x = 60
x = 10
For the measure of the side length, put x = 10 in the sides.
10-1 = 9 units2×10-3 = 17 units3×10 - 6 = 24 units.Thus, the dimensions of the sides of the triangle is found as 9 units, 17 units and 24 units.
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The simple interest charged on a 65 day loan of $1250 is $7.75. Find the annual simple interest rate in precent for this loan round to the nearest tenth of a percent. Use 360 days in 1 year
Answers
We have a loan of 65 days.
The principal is $1250 and the interest is $7.75.
We have to find the annual simple interest rate.
We can express the interest of a loan of this type as:
[tex]I=r\cdot\frac{t}{360}\cdot P[/tex]where r = annual interest rate, t = period of the loan in days, I = interest and P = principal.
Then, we can rearrange the equation and replace with the values:
[tex]\begin{gathered} I=r\cdot\frac{t}{360}\cdot P \\ r=\frac{I\cdot360}{t\cdot P} \\ r=\frac{7.75\cdot360}{65\cdot1250} \\ r=\frac{2790}{81250} \\ r\approx0.03433846 \\ r\approx3.4\% \end{gathered}[/tex]Answer: the annual simple interest rate is 3.4%.
I will give 100 points to anyone who can answer my question.
Answers
Answer:
A system of nonlinear equations is a system where at least one of the equations is not linear. Just as with systems of linear equations, a solution of a nonlinear system is an ordered pair that makes both equations true. In a nonlinear system, there may be more than one solution.
Answer:
The answers are (-10, -4) and (0, 1)
Step-by-step explanation:
The solution to a system of equations is the point where both lines intersect. In this case, all you have to do is mark the points of intersection and look at their coordinates.
Hope this helps!
39% of 80 74% of 240 91% of 82 66% of 160
9% of 71 126% of 80 234% of 145 97.9% of 39
52% of 57.9 33% of 15.3
Answers
Answer:
39% of 80 = 39.2
74% of 240 = 177.6
91% of 82 = 74.62
66% of 160 = 105.6
9% of 71 = 63.9
126% of 80 = 100.8
234% of 145 = 339.3
97.9% of 39 = 38.181
52% of 57.9 = 30.108
33% of 15.3 = 5.049
Step-by-step explanation:
In order to find the percentage of each equation, we will use the first one as an example. We take the 39%, and convert it to 0.39 and get rid of the %. Then, "of" means multiplication.
So, we have:
0.39 x 80 = 39.2
Hi, can y oh please me I’m stuck on this question.
Answers
The measure of angle 2 is 81° because angles 1 and 2 are corresponding angles.
Corresponding angles:
Corresponding angle means the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
Given,
Two electricity poles are built standing parallel to each other, as shown below. The measure of angle 1 is 81°.
Here we need to find the measure of the angle 2.
We know that,
If the lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet.
And as per the definition of corresponding angles, we know that, if any two lines are said to be parallel if the Corresponding angles so formed are equal.
Then the measure of the angle 2 is 81° because angle 1 and 2 are parallel.
Therefore, those angles are the corresponding angles also.
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If a train runs on a circular track of radius 400 meters through all four sections of the park, about how long is the part of the train track that runs through Water World?
Answers
The arc length is given by:
[tex]s=2\pi r(\frac{\theta}{360})[/tex]In this case the radius is 400 m and the angle is 36°, plugging these values we have:
[tex]\begin{gathered} s=2\pi(400)(\frac{36}{360}) \\ s=251.33 \end{gathered}[/tex]Therefore, the part of the train track that runs through water world is approximately 250 meters.
Solve for a, b, and c
Answers
Applying the law of indeces for the fraction with radicals, the value of A=3, b=14 and c=-5
What are radicals?In mathematics, the term radical expressions such that contain a square root. In this question, we have fractions at both sides of the equation with radicals.
To solve this question, let's see some laws below that will help us:
[tex] \sqrt[x]{a} = {a}^{ \frac{1}{x} } [/tex]
[tex] \frac{ {a}^{x} }{ {a}^{y} } = {a}^{x - y} [/tex]
[tex] \frac{1}{ {a}^{x} } = {a}^{ - x} [/tex]
From the given equation; the left hand side will be simplified as follows;
[3^(1/7)]÷[3^(1/2)]=[3^[(2-7)/14]=3^(-5/14)
And the right hand side will be simplified as follows;
1÷[A^(c/b)]=A^-(c/b)
Hence, by comparing both sides of the equation after simplifying the fractional radicals, the value of A is 3, b is 14 and c is -5.
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Two cylinders have the same volume. The first has a radius of 5cm and a height of 10 cm. The second has a radius of 10cm. The surface area of the first cylinder is and the surface area of the second i s
Answers
ANSWER
[tex]\begin{gathered} 1)150\pi \\ 2)250\pi \end{gathered}[/tex]EXPLANATION
For the first cylinder;
[tex]\begin{gathered} r=5 \\ h=10 \end{gathered}[/tex]Recall, the formula for calculating the surface area of a cylinder is;
[tex]A=2\pi rh+2\pi r^2[/tex]Now, substitute the values for the first cylinder;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times5\times10+2\times\pi\times5^2 \\ =100\pi+50\pi \\ =150\pi \end{gathered}[/tex]The volume of the first cylinder is calculated using the formula;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ \end{gathered}[/tex]Substitute the values of r and h for the first cylinder;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ =\pi\times5^2\times10 \\ =\pi\times25\times10 \\ =250\pi \end{gathered}[/tex]To get the surface area of the second cylinder, we need to calculate the height (h).
To get the height, we use the volume of the first cylinder to get the height of the second (since they have the same volume).
Hence;
[tex]\begin{gathered} V=250\pi \\ r=10 \\ V=\pi r^{2}h \\ 250\pi=\pi\times10^2\times h \\ h=\frac{V}{\pi \cdot \:r^2} \\ h=\frac{250\pi }{\pi 10^2} \\ =2.5 \end{gathered}[/tex]Substitute the height to calculate the surface area is calculated thus;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times10\times2.5+2\times\pi\times10^2 \\ =50\pi+200\pi \\ =250\pi \end{gathered}[/tex]Sara buys $30 of produce at the farmer's market. She spends $5more on green vegetables than she does on fruit. How much didSara spend on green vegetables? How much did she spend onfruit? Write and solve a system of equations.
Answers
Okay, here we have this:
Considering the provided information, we are going to write and solve the correspondinf system of equation, so we obtain the following:
According to the information given, we obtain the following system of equations, where we take x as money spent on fruit and y as money spent on green vegetables, so we have:
[tex]\begin{gathered} x+y=30 \\ x+(x+5)=30 \end{gathered}[/tex]Now let's solve for x in the second equation:
x+x+5=30
2x+5=30
2x=30-5
2x=25
x=25/2
x=12.5
Now from the value of x that we got, then we will plug it into the first equation to get the value of y:
[tex]\begin{gathered} x+y=30 \\ 12.5+y=30 \\ y=30-12.5 \\ y=17.5 \end{gathered}[/tex]Then, finally we obtain that she spend $12.5 on fruits and $17.5 on green vegetables.
A furniture store is having a 20% sale.
(a) A sofa usually costs £1200. Work out the sale price of the sofa.
(b) The sale price of a table is £480. Work out the original price of the table.
Answers
Answer:
a) £960
b) £576
Step-by-step explanation:
Hi!
Ok so since the store has a 20% sale we multiply 0.2 to the original amount it would have costed without the sale:
a) [tex]1200*0.2 = 240[/tex]
Then we subtract the number we got from the price:
1200 - 240 = 960
Now we do the same thing but this time add since we are trying to find the price of the table before the sale:
b) [tex]480*0.2 = 96[/tex]
480 + 96 = 576
Please ask me if you have any more questions!
and Have a great day! :)
PLS HELP DUE NOWWWWWWWWWW
Answers
The correct statement will be:
A. The rate of change is the number of inches grown per month, and the initial value is the starting height.
We can form the following equation from the given data:
H(m) = 13 + 41m,
Where H ( Height ) is a function of the number of months ( m ).
We can see that the height changes with respect to months i.e. as the number of months increases, the height of the sunflower also increases.
The initial value or the initial height of the sunflower remains constant throughout and has less impact on its height.
So, option A will be the ultimate explanation for the data given.
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Answer:
Step-by-step explanation:
This is a linear function of time, as mentioned.
A linear function is always in the form of:
[tex]y=mx+b[/tex]
The 'sunflower's height is a linear function of time', so the [tex]x[/tex] variable represents the time (which is in terms of months here), and the [tex]y[/tex] would represent the sunflower's height after time has passed.
The initial value is when [tex]x=0[/tex].
[tex]x=0[/tex] means at the very beginning.
At the very beginning, the height would be the starting height, so the initial value would be the starting height.
The rate of change means the change in [tex]y[/tex] in respect to [tex]x[/tex].
Since [tex]y[/tex] represents the height after [tex]x[/tex] months, the rate of change would be the change in height per month.
You could also write it as the number of inches grown per month.
The initial value is the starting height, and the rate of change is the number of inches grown per month, so the correct answer is (A).
Rewrite all 3 fractions with the least common denominator between them.
Answers
Answer:
To rewrite the given fraction with the least common denominator between them
The given fractions are,
[tex]\frac{1}{3},\frac{5}{10},\frac{7}{30}[/tex]we get, LCM of 3,10,30 is 30
The equivalent fractions for the above factions as common denominator 30 is as follows,
For 1/3,
Multiply and divide by 10, we get,
[tex]=\frac{1}{3}\times\frac{10}{10}=\frac{10}{30}[/tex]Using this we get,
[tex]\frac{1}{3}=\frac{10}{30}[/tex]For 5/10,
Multiply and divide by 3, we get,
[tex]\frac{5}{10}=\frac{5}{10}\times\frac{3}{3}=\frac{15}{30}[/tex]Using this we get,
[tex]\frac{5}{10}=\frac{15}{30}[/tex]For 7/30,
Since the denominator 30, we get same fraction,
[tex]\frac{7}{30}=\frac{7}{30}[/tex]Answer is:
[tex]\frac{1}{3}=\frac{10}{30}[/tex][tex]\frac{5}{10}=\frac{15}{30}[/tex][tex]\frac{7}{30}=\frac{7}{30}[/tex]find the slope of m and choose the correct letter
Answers
We can use the given points to find the slope
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{63_{}-49_{}}{_{}2009-1999_{}} \\ \\ m=\frac{14_{}}{_{}10_{}} \\ \\ m=1.4 \end{gathered}[/tex]It means that every year, there are 1.4 million MORE households with personal computers
the owner of a small deli is trying to decide whether to discontinue selling magazines. he suspects that only 8.4% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. assuming his suspicion that 8.4% of his customers buy a magazine is correct, what is the probability that exactly 3 out of the first 11 customers buy a magazine?
Answers
The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%
The proportion of customers that buy a magazine = 8.4%
If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%
Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;
probability = 8.4% × 27.27%
probability = (8.4/100) × (27.27/100)
probability = 0.084 × 0.2727
probability = 0.0223
Converting it into percentage as follows;
probability = 0.0223 × 100
probability = 2.23%
Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.
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A pet store makes a profit of $4.75 per bag on its line of organic dog food. The store wants to make a profit of no less than $5,700. Could selling 1,300 bags of dog food meet this goal?
Answers
I need help with this
Answers
Angle XBC is a corresponding angle to angle AXY.
The value of angle BXC is 30 degrees.
How to find measure of angles?When parallel lines are cut by a transversal line, angle relationships are formed such as alternate angles, corresponding angles, linear angles, vertically opposite angles etc.
Therefore, XY and BD are parallel lines and are cut by the transversal line AB and XC.
XBC forms an isosceles triangle.
∠AXY = 75 degrees.
∠XBC is a corresponding angle to ∠AXY.
Corresponding angles are congruent.
Therefore,
∠AXY = ∠XBC
Let's find the angle BXC.
The sum of angle in a triangle is 180 degrees.
The triangle BXC is an isosceles triangle. An isosceles triangle has base angles equal to each other.
Hence,
75 + 75 + ∠BXC = 180°
∠BXC = 180 - 150
∠BXC = 30°
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Hannah is solving 42×19. Hannah says, “That’s easy! I can just break up the numbers and do 40×10=400 and 2×9=18.” Is Hannah correct? In the space below, show or explain why he’s correct or incorrect.
Answers
No, Hannah is incorrect.
We are given the expression 42*19.
Hannah got the solution by multiplying 40*10 and 2*9 and then adding the values.
This can be done by using distributive property, which is given by:-
(a + b)(c + d) = ac + ad + bc + bd
We can write,
42*19 = (40 + 2)(10 + 9) = 40*10 + 40*9 + 2*10 + 2*9
Hence, the answer is not just 40*10 + 2*9 but 40*10 + 40*9 + 2*10 + 2*9.
Hannah did not add the remaining 40*9 + 2*10 to calculate the answer.
That is why Hannah was incorrect.
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Change 6.3 kg to grams pls it's urgent
Answers
Answer:
6,300 grams
Step-by-step explanation:
kg to g is multiply by 1,000
Answer:
Step-by-step explanation:
630%
pls explain with working out
Answers
Answer: 26m
Step-by-step explanation:
The area is 36m^2, the possible measurement that could've worked is 4m for width and 9m for length (4x9=36). Now just do 4+4+9+9 = 26m.
Hope this helped
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
= 6; = 2
P(5 ≤ x ≤ 9) =
Answers
The probability P(5 ≤ x ≤ 9) is 0.6847
Assume that x has a normal distribution
We have been the mean and standard deviation μ = 6; σ = 2.
To calculate this probability we use the standardized normal distribution and the z-value for 5 and 9.
z = (5 - 6)/2
= -0.5
and z = (9 - 6)/2
= 1.5
Then the probability is calculated as:
P(x ≤ 5) = 0.3085
P(x ≤ 9) = 0.9932
P(5 ≤ x ≤ 9) = 0.9932 - 0.3085
P(5 ≤ x ≤ 9) = 0.6847
Therefore, the probability P(5 ≤ x ≤ 9) is 0.6847
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Match each number to its opposite. 1. -8 8 2. -1 -11 3. -17 17 4. 31 -31 5. 11 1
Answers
The opposite for each number is: ( -8, 8), (-1,1), (-17,17), (31,-31) and (11,-11).
Number Classification Whole Numbers - They are the numbers represented by positive real numbers where the fractions and decimal numbers are not included. Integer Numbers - They are the whole numbers. They are represented by zero, positive and negative numbers. Opposite numbers - They are numbers that the distance to 0 is equal. The numbers are classified as the opposite when the sum between them is equal to zero (0).Thus, you can conclude that the opposite number of a positive number is a negative number. And the opposite number of a negative number is a positive number.
The question gives the follow numbers
1. -8 8
2. -1 -11
3. -17 17
4. 31 -31
5. 11 1
The opposite for:
-8 is the number 8-1 is the number 1-17 is the number 1731 is the number -3111 is the number -11Read more about number classifications here:
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Which of these equations is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2)?
Answers
The equation of the line perpendicular to the line line joining (-4,4) and (2,-2) will be → y = x + 2.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line that is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2),
The midpoint of line joining (-4,4) and (2,-2) will be -
x[m] = (- 4 + 2)/2 = -1
y[m] = (4 - 2)/2 = 1
Coordinates of the midpoint will be M(-1, 1)
Slope of the line joining (-4,4) and (2,-2) will be -
m = (- 2 - 4)/(2 + 4)
m = -6/6
m = - 1
Then, the slope of the line perpendicular to this line will be -
m[p] = -1/-1
m[p] = 1
Assume that the equation of the perpendicular line as -
y[p] = x + c
Since it passes though (-1, 1) so -
1 = -1 + c
c = 2
Therefore, the equation of the line perpendicular to the line line joining (-4,4) and (2,-2) will be → y = x + 2.
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Can anyone please answer this question, Ill give points.
Answers
Answer:
(0,1) and (-10.-4)
Step-by-step explanation:
To find the solutions, find the points where both the curve and line intersect and read off the coordinates
Kaj invests money in an account paying a simple interest of 1.2% per year. If she invests $90 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents?
Answers
Answer:
$91.08
Step-by-step explanation:
Interest = $90 × .012 = $1.08
Total amount = $90 + $1.08 = $91.08
if it is accepted that an observed association is a causal one, an estimate of the impact that a successful preventive program might have can be derived from:
Answers
The estimate of the impact that a successful preventive program might have can be derived from
attributable risk.
What is an attributable risk?In epidemiology, attributable risk or excess risk is a phrase equivalent with risk difference, which has also been used to express the attributable proportion among the exposed and the population.
Attributed risk assists in determining how much of an outcome is attributable to a certain risk factor (i.e., an estimate of the excess risk) in a population exposed to that factor.
The rate (percentage) of a health result (illness or death) in exposed persons that can be linked to the exposure is known as the attributable risk (AR). Attribitable risk measures how much more common a result is in absolute terms among the exposed than the non-exposed.
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According to the distributive property, a(5 + b) =
Answers
Answer:
From the bit that you have given , we can say = 5a + ab = to the rest of the equation