Let's take the first term as a and the common difference be d
The formula to find the nth term of an arithmetic progression is given by :
an = a + ( n - 1 ) dAccording to question, we have :
16th term of an AP is three times the 5th term.➝ a16 = 3 ( a5 )
➝ a + ( 16 - 1 )d = 3 ( a + ( 5 - 1 )d )
➝ a + 15d = 3 ( a + 4d )
➝ a + 15d = 3a + 12d
➝ 15d - 12d = 3a - a
➝ 3d = 2a
➝ 2a = 3d
➝ a = 3d/2ㅤㅤㅤ⸻ ( 1 )
And, the 12th term is 20 more the 7th term.➝ a12 - ( a7 ) = 20
➝ a + ( n - 1 )d -( a + ( n - 1 )d ) = 20
➝ a + ( 12 - 1 )d - + a + ( 7 - 1 )d ) = 20
➝ a + 11d - ( a + 6d ) = 20
➝ a - a + 11d - 6d = 20
➝ 5d = 20
➝ d = 20/ 5
➝ d = 4
Using equation ( 1 )➝ a = 3d / 2
➝ a = ( 3 × 4 ) / 2
➝ a = 12 / 2
➝ a = 6
hey peeps help with this
A country’s population in 1991 Was 211 million in 1998 it was 215 million estimate the population in 2012 using the exponential growth formula
Answer:
The population in 2012 is estimated in approximately 223 million people
Step-by-step explanation:
Exponential Growth
The formula for exponential growth of a variable P at the growth rate r, as time t goes on in discrete intervals, or at integer times 0, 1, 2, 3, ..., is :
[tex]\displaystyle P(t)=P_0(1+r)^{t}[/tex]
Where Po is the value of P at time 0.
The country’s population in 1991 was 211 million, and in 1998 it was 215 million. We have two discrete times to define the equation and set the year 1991 as t=0. Thus, the year 1998 is t=7.
The preliminary equation is:
[tex]\displaystyle P(t)=211(1+r)^{t}[/tex]
To find the value of 1+r, we use the second point (7,215):
[tex]\displaystyle 215=211(1+r)^{7}[/tex]
Dividing by 211:
[tex]\displaystyle \frac{215}{211}=(1+r)^{7}[/tex]
Solving:
[tex]\displaystyle (1+r)=\sqrt[7]{\frac{215}{211}}[/tex]
Calculating:
[tex](1+r)=1.002686[/tex]
The complete equation is:
[tex]\displaystyle P(t)=211(1.002686)^{t}[/tex]
Estimate the population in 2012 (t=21):
[tex]\displaystyle P(21)=211(1.002686)^{21}[/tex]
[tex]P(21)\approx 223[/tex]
The population in 2012 is estimated in approximately 223 million people
please help me figure out how to solve the problem below:
the problem below is asking how to find the surface area of the cylinder. please leave an explanation on how to solve it.
formula: 2(3.14)(r)^2 + 2(3.14)(r)
r: radius
Answer:
3315.84mm^2.
Step-by-step explanation:
We calculate the diameter of the base of the cylinder using Pythagoras:
40^2 = d^2 + 32^2
d^2 = 40^2 - 32^2 = 576
d = sqrt 576 = 24 mm.
So the radius = 1/2 diameter = 12 mm.
The surface area
= 2(3.14)(12)^2 + 2(3.14)(12)(32)
= 904.32 + 2411.52
= 3315.84.
Soccer cleats cost $45.52 per pair. How much will it cost for four pairs?
Answer:
182.08
Step-by-step explanation:
A statistics teacher gives a multiple-choice exam with 20 questions. The teacher wants to discourage guessing on the exam, so for each question the student earns 1 point for a correct answer, 0 points for no answer, and -1 point for a wrong answer. Consequently, if a student answered every question incorrectly the student would earn a score of -20 on the exam. However, if a student answered every question correctly, the student would earn a score of 20 on the exam. After the exam, the teacher distributes the list of test scores and asks the class to calculate the standard deviation. The first student to finish the calculations says that the standard deviation is -1.8.
a. True
b. False
Answer:
b. False
Step-by-step explanation:
The answer is false because the standard deviation was miscalculated.
We can compute the formula for calculating the standard deviation as:
[tex]\sigma = \sqrt{\dfrac{\sum (x_i-\overline x)^2}{n}}[/tex]
As a result of the square in the numerator of the summation, the square [tex]\sum (x_i-\overline x)^2[/tex] is usually non-negative.
Even if the data is positive, negative or zero, as a result of the above claim, the standard deviation is always non-negative.
Thus, the fact that the first student who finishes the calculation first and claim that the standard deviation is -1.8 is false.
A cylinder has a base diameter of 8 centimeters and a height of 7 centimeters. What is its volume in cubic centimeters, to the nearest tenths place
Answer:
Step-by-step explanation:
Answer: 351.9 cm^3
d = diameter = 8 cm
r = radius = diameter/2 = 4 cm
h = height = 7 cm
volume = (pi)r^2h
volume = (3.14159)(4 cm)^2(7 cm)
volume = 3.14159(16 cm^2)(7 cm)
volume = 351.858 cm^3
Answer: 351.9 cm^3
Answer:
Step-by-step explanation:
Answer: 351.9 cm^3
d = diameter = 8 cm
r = radius = diameter/2 = 4 cm
h = height = 7 cm
volume = (pi)r^2h
volume = (3.14159)(4 cm)^2(7 cm)
volume = 3.14159(16 cm^2)(7 cm)
volume = 351.858 cm^3
Answer: 351.9 cm^3
Simplify 3 - 2 / 4/5 + 1/2
Answer:
1
Step-by-step explanation:
PLEASE MARK AS BRAINLIEST
Answer:
1
Step-by-step explanation:
Division first
2÷4/5= 2 1/2
3-2 1/2= 1/2
1/2+1/2=1
A point has the coordinates (m, 0) and m ≠ 0.
Which reflection of the point will produce an image located at (0, –m)?
a reflection of the point across the x-axis
a reflection of the point across the y-axis
a reflection of the point across the line y = x
a reflection of the point across the line y = –x
Therefore the reflection of the point (m,0)and m≠0 will produce an image located at (0,-m) when reflection occurs across the line y=(-x).
Answer:
a reflection of the point across the line y = –x
Step-by-step explanation:
Let m = 5.
Graph (5, 0).
Then graph (0, -5).
Then draw the line y = -x.
You will see that the line y = -x is the axis of symmetry for the two points.
Answer:
a reflection of the point across the line y = –x
Help pls!! Determine whether each value is greater for function Q, the same for both functions, or greater for function R
The following conclusion about both functions are:
The initial value for function R (3) is greater than that for function Q (-2).The rate of change for function Q (3) is greater than that for function R (1/3).What is a Linear Function?A linear function is modelled as, y = mx + b
b is initial valuem is the rate of change = change in y/change in x.Function Q:
y = 3x - 2
Initial value (b) = -2
Rate of change (m) = 3
Function R:
Initial value = 3
Rate of change = 1/3
Therefore, the following conclusion about both functions can be made:
The initial value for function R (3) is greater than that for function Q (-2).The rate of change for function Q (3) is greater than that for function R (1/3).Learn more about linear functions on:
https://brainly.com/question/1254134
the price of a 2-pack shopkin should not be more then 4$. choose an inequality for this situation
The required inequality for the price of a 2-pack shopkin should not be more than $4 is ≤ 4.
The price of a 2-pack shopkin should not be more than $4. Inequality in the situation is to be determined.
What is inequality?Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
The price of a 2-pack shopkin should not be more than $4.
Let the price of 2 - pack shopkin is x and it should not be more than $4 it impise the price of 2 pack shopkin canno be set up more than 4 but it could be 4 or less so, Inequality for 4 or less of price of 2 pack shopkin is given by,
x ≤ 4.
Thus, the required inequality for the price of a 2-pack shopkin should not be more than $4 is ≤ 4.
Learn more about inequality here:
brainly.com/question/14098842
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The mixed number 1 2/5 and the decimal number 1.4 can be used to represent the same value.
True or False
B – 4 1/4 = 2 2/3 what is B?
Answer:
83/12
Step-by-step explanation:
To find B, simply add 4 1/4 to 2 2/3.
Hope that helps!
In a probability histogram, there is a correspondence between?
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Bananas are 3 for a dollar. Jen has $3. How many bananas can Jen buy?
1 dollar for 3 bananas
so with
3 dollars we will get 3x3 = 9 bananas
If her income is 210 marks, how many bananas can she buy if ... is 4 dollars each and the cost of bananas is 3 dollars per bunch.
Step-by-step explanation:
15/20 + 12 /20 = 27/20 =
Answer:
1 7/20
Step-by-step explanation:
So, you added the 15/20 and 12/20 to get 27/20
Then to simplify 27/20 you have to see how many times 27 can go into 20
27 can go into 20 with a remainder of 7 which then will lead you to the answer of 1 7/20 and you can't simplify it anymore.
Hopefully, that helps.
Which expression is equivalent to 5( 9 + 7)
Answer:80
Step-by-step explanation: Distribute the 5 to the 9 and 7 to get 35+45 and add to get 80
Variables y and x have a proportional relationship, where y = 18 when x = 2.
What is the value of x when y = 36?
Answer:
[tex]\huge\boxed{\sf x = 4}[/tex]
Step-by-step explanation:
Given that:
[tex]y \propto x[/tex]
Converting proportionality into equality
[tex]y = kx[/tex] ----------------(1)
y = 18 when x = 2
Put it in Eq. (1)
[tex]\displaystyle 18 = k(2)\\\\Divide \ both \ sides \ by\ 2\\\\\frac{18}{2} = k\\\\9 = k\\\\ \boxed{k = 9}[/tex]
Now,
x = ? when y = 36
Put it in Eq. (1)
[tex]36 = (9) x\\\\Divide \ both \ sides \ by \ 9\\\\36 / 9 = x\\\\4 =x \\\\\boxed{x = 4}\\\\\rule[225]{225}{2}[/tex]
what is the slope of a line that is perpendiculer to y=2/9x+9/2?
Answer:
Step-by-step explanation:
the slope of a line that is perpendicular is -9/2
The following is an excerpt from a paper published in BMJ (formerly the British Medical Journal) in 1994:
Charig et al undertook a historical comparison of success rates in removing kidney stones. Open surgery had a success rate of 78% (273/350) while a minimally invasive procedure called percutaneous nephrolithotomy had a success rate of 83% (289/350), an improvement over the use of open surgery. However, the success rates looked rather different when stone diameter was taken into account. This showed that, for stones of <2 cm, 93% (81/87) of cases of open surgery were successful compared with just 83% (234/270) of cases of percutaneous nephrolithotomy. Likewise, for stones of >/=2 cm, success rates of 73% (192/263) and 69% (55/80) were observed for open surgery and percutaneous nephrolithotomy respectively.
The main reason why the success rate reversed is because the probability of having open surgery or percutaneousnephrolithotomy varied according to the diameter of the stones. In observational (nonrandomized) studiescomparing treatments it is likely that the initial choice of treatment would have been influenced by patients'characteristics such as age or severity of condition; so any difference between treatments could be accounted for bythese original factors. Such a situation may arise when a new treatment is being phased in over time. Randomizedtrials are therefore necessary to demonstrate any treatment effect.
This is an example of Simpson's paradox because:
a. when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).
b. when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them).
c. when the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).
d. when the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them).
Answer: a. when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).
Step-by-step explanation: Simpson's Paradox happens when a group of data shows a relationship in each group but it is reversed when the group is combined.
In the BMJ paper, percutaneous nephrolithotomy had a bigger successful rate than open surgery. But, the rates are reversed when the diameter (size) of the stone is included in the research. So, an individual group of data had a relationship and a factor reversed the relationship. This is an example of Simpson's Paradox.
Excerpt form the paper in BMJ.
The excerpt is taken from the paper that got published in the british medical journal of 1994. Ths journal was understand for a historical comparison of the success rates in kidney stone removal. As the success rate of the surgery was about 83%.
Hence the answer is lurking variable is introduced, the conclusions are reversed.
As per the excerpt of the Simpsons paradox the such as rate of 78% and minimal invasive procedure called the percutaneous has a success rate of 83% thus better over open surgery.Thus the option A is correct. The variable size of stone and conclusion was the opposite.Learn more about the undertook a historical.
brainly.com/question/12653054.
Natalie painted three portraits of a 15 minutes at that rate how many would she paint in 10 minutes
Answer:
2 portraits
Step-by-step explanation:
since she painted 3 in 15 minutes, it means that she took 5 minutes on each portrait. If Natalie were to paint portraits for 10 minutes she would paint 2 portraits
3p in 15min = 1p in 5min = 2p in 10min
need help asap Write the equation of a line passing through the points(-6, -2) and (4, -12) in slope intercept form
Answer:
y=-1x-8
Step-by-step explanation:
A(n) ____________ is a metric unit used to measure mass.
A) liter
B) inch
C) meter
D) gram
I am stuck on a question I would like some help with
Answer:
m<3 = 80
Step-by-step explanation:
We know that the sum of all the angles in a triangle is 180.
Thus, we can find the m<3 using the equation 180 - (70 + 30) = m<3
Simplifying gives us m<3 = 80
Answer:
B .80
Step-by-step explanation:
all interior angles in a triangle=180
180-(70+30)
180-100
=80
Write an inequality that represents the verbal expression.
3 more than a number tis greater than or equal to 21.
Answer:
3x≥21
Step-by-step explanation:
triangle BCD is a right triangle the length of the hypotenuse is 20 cm the length of one of the legs is 15 cm what is the length of the other leg
Answer:
13.22
Step-by-step explanation:
The eqtn is
hypotenuse^2 = leg^2 + leg^2
20^2 = 15^2 + L^2
400 = 225 + L^2
L^2 = 400 - 225 = 175
L = √175 = 13.22
Prove triangle congruence.
Answer:
Step-by-step explanation:
Find the value:
cos -1 ( - √3/2 )
Answer:
The value is undefined.
please help MEEE i need this to be done
Answer:
NO
Step-by-step explanation:
There is an odd number of students so one team would have 7 students while the other would have only 6
Answer:
Step-by-step explanation:
No she can't divide them equally because the total of the both classes is 13 which is an odd number and it is not possible to divide an old number equally.
Hope this helps
I need help on this problem
Answer:
D
Step-by-step explanation:
In women's softball the pitcher stands about 13 meters from the batter's box. In men's softball the pitcher stands about 1,400 centimeters from the batter's box. About how many more centimeters is it from the men's pitcher to the batter's box than from the women's pitcher to the batter's box?
Answer:
About 100 centimeters.
Step-by-step explanation:
1,400 - (13 * 100) = 100