In a school of 450 people 110 are in the choir 240 are in a band and 60 are in both
What is the probability
Answers
The question doesn't require any specific probabilities, but I'm adding my own calculations to make it easier for you to solve your own problem
Answer:
Questions added and answered below
Step-by-step explanation:
Venn Diagram
When we have different sets, some of them belong only to one set, some belong to more than one, some don't belong to any of them. This situation can be graphically represented by the Venn Diagrams.
Let's analyze the data presented in the problem and fill up the numbers into our Venn Diagram. First, we must use the most relevant data: there are 60 people in both the choir and the band. This number must be in the common space between both sets in the diagram (center zone, purple).
We know there are 110 people in the choir, 60 of which were already placed in the intersection zone, so we must place 110-60=50 people into the blue zone, belonging to C but not to B.
We are also told that 240 people are in a band, 60 of which were already placed in the intersection zone, so we must place 240-60=180 people into the red zone, belonging to B but not to C.
Finally, we add the elements in all three zones to get all the people who are in the choir or in the band, and we get 50+60+180=290. Since we have 450 people in the school, there are 450-290=160 people who are not in the choir nor in the band.
The question doesn't ask for a particular probability, so I'm filling up that gap with some interesting probability calculations like
a) What is the probability of selecting at random one person who is in the band but not in the choir?
The answer is calculated as
[tex]\displaystyle P(A)=\frac{180}{450}=0.4[/tex]
b) What is the probability of randomly selecting one person who belongs only to one group?
We look for people who are in only one of the sets, they are 50+180=230 people, so the probability is
[tex]\displaystyle P(B)=\frac{230}{450}=0.51[/tex]
b) What is the probability of selecting at random one person who doesn't belong to the choir?
We must add the number of people outside of the set C, that is 180+160=340
[tex]\displaystyle P(C)=\frac{340}{450}=0.76[/tex]
Related Questions
"If two lines intersect, then the intersection is a point." What is the hypothesis? Two lines intersect
Intersection is a point
Points have intersection
Intersection happens at a point
Answers
Answer:
Hypothesis is: Intersection happens at a point
Step-by-step explanation:
A hypothesis in science is a suggested explanation of something that has a consequence or leads to an occurrence. Usually it will be written in the form of an "if and then" statement.
Such statement explains what would occur, or follow if the possibility enunciated in the "if" part of the statement happens.
In this case the hypothesis is that if there is intersection of lines, it has to occur at a point. Therefore the closest to that statement among the options given in the problem is the last one: "Intersection happens at a point"
Answer:
Two Line Intersect
Step-by-step explanation:
I got it right on the test :)
Simplify each expression, and then arrange them in increasing order based on the coefficient of n2. -5(n3 – n2 – 1) + n(n2 – n) (n2 – 1)(n + 2) – n2(n – 3) n2(n – 4) + 5n3 – 6 2n(n2 – 2n – 1) + 3n2
Answers
To simplify the expressions and arrange them based on the coefficient of n², combine like terms and perform necessary operations. The expressions, in increasing order, are: 3n + 2, 2n³ - n² + 2n, -5n³ + 6n² - n + 5, and 6n³ - n² + n - 6.
Explanation:To simplify each expression and arrange them in increasing order based on the coefficient of n², we need to combine like terms and perform any necessary operations. Let's go through each expression:
-5(n³ – n² – 1) + n(n² – n) = -5n³ + 6n² - n + 5(n² – 1)(n + 2) – n²(n – 3) = 3n + 2n²(n – 4) + 5n³ – 6 = 6n³ - n² + n - 62n(n² – 2n – 1) + 3n² = 2n³ - 4n² + 2n + 3n² = 2n³ - n² + 2nArranging them in increasing order based on the coefficient of n², we have:
3n + 22n³ - n² + 2n-5n³ + 6n² - n + 56n³ - n² + n - 6Learn more about Simplifying Expressions here:https://brainly.com/question/29003427
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is y=5x+7 liner, nonlinear, or both
Answers
[tex](1 \times 10^{5)(6 \times {10}{4} [/tex]
Answers
Note that [tex]10^a\cdot10^b=10^{a+b}[/tex] or more general form, [tex]a^b\cdot a^c=a^{b+c}[/tex].
[tex]10^5\cdot6\cdot10^4=\boxed{6\cdot10^9}[/tex]
Hope this helps.
I need help on this problem
Answers
Answer: [tex]QR=4.04[/tex]
Step-by-step explanation:
For this exercise you must use the followinG Trigonometric Identity:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
In this case, given the right triangle PQR, you can identify that:
[tex]\alpha=60\°\\opposite=PR=7.0\\adjacent=QR[/tex]
Then, the next step is to substitute those values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex]:
[tex]tan(60\°)=\frac{7.0}{QR}[/tex]
And the final step is to solve for "QR" in order to find its value.
So you get that this is:
[tex](QR)(tan(60\°))=7.0\\\\QR=\frac{7.0}{tan(60\°)}\\\\QR=4.04[/tex]
What is the equation of the line that passes through the point
(
−
6
,
−
6
)
(−6,−6) and has a slope of
2
3
3
2
?
Answers
Answer:
y+6=2(x+6)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-6)=2(x-(-6))
y+6=2(x+6)
What equation represents the proportional relationship displayed in the table? x=2,4,6,8 y=10,20,30,40 Enter your answer in the box to complete the equation. y = ? x
Answers
The answer is y = 5x.
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Answer:
y=5x
Step-by-step explanation:
I did the test
The graph of a system of inequalities is shown.
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 6, negative 1) and (0, negative 4). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 2, negative 4) and (0, 0). Everything to the left of the line is shaded.
Which system is represented by the graph?
y > 2x
x + 2y ≤ –8
y ≥ 2x
x + 2y < –8
y < 2x
x + 2y ≥ –8
y ≤ 2x
x + 2y > –8
Answers
Answer:
The system is
[tex]x+2y \leq -8[/tex]
[tex]y> 2x[/tex]
Step-by-step explanation:
Part 1
Find the equation of the first inequality
we know that
The first line is a solid line with negative slope passing through the points (-6,-1) and (0,-4)
The slope is equal to
[tex]m=(-4+1)/(0+6)\\m=-0.5[/tex]
The equation of the solid line in slope intercept form is
[tex]y=-0.5x-4[/tex]
Everything below the line is shaded
so
The inequality is
[tex]y \leq -0.5x-4[/tex]
Convert to standard form
Adds 0.5x both sides
[tex]0.5x+y \leq -4[/tex]
Multiply by 2 both sides
[tex]x+2y \leq -8[/tex] -----> First inequality
Part 2
Find the equation of the second inequality
we know that
The second line is a dashed line with positive slope passing through the points (-2,-4) and (0,0)
This line represent a proportional relationship, because the line passes through the origin
The slope is equal to the constant of proportionality
[tex]k=(-4)/(-2)=2[/tex]
The equation of the dashed line is
[tex]y=2x[/tex]
Everything to the left of the line is shade
so
The inequality is
[tex]y> 2x[/tex] -----> Second inequality
see the attached figure to better understand the problem
The system of inequalities represented by the given graph is y > 2x and x + 2y ≤ –8.
Explanation:The system of inequalities represented by the given graph is:
y > 2xx + 2y ≤ –8We can determine the equations of the lines using the given points:
Line 1: y = mx + b, where m is the slope and b is the y-intercept. Using the points (–6, –1) and (0, –4), we can calculate the slope: m = (–4 – (–1)) / (0 – (–6)) = –3 / 6 = –1/2. Thus the equation of Line 1 is y = –(1/2)x – 3.
Line 2: Using the points (–2, –4) and (0, 0), we can calculate the slope: m = (0 – (–4)) / (0 – (–2)) = 4 / 2 = 2. Thus the equation of Line 2 is y = 2x – 4.
By looking at the graph, we can see that everything below Line 1 (shaded area) satisfies y > 2x, while everything below or on Line 2 (including the line itself) satisfies x + 2y ≤ –8.
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Your second mortgage of $31,200 is at a rate of 10.7% compounded quarterly for 8 years. What total will you have paid for your second mortgage after 8 years?
Answers
Answer:
The Amount paid after 8 years is $72611.76
Step-by-step explanation:
Given as :
The principal mortgage = p = $31,200
The rate of interest = r = 10.7% compounded quarterly
The time period of mortgage = t = 8 years
Let The Amount paid after 8 years = $A
Now, According to question
From Compounded Interest method
Amount = Principal × [tex](1+\dfrac{\textrm rate}{4\times 100})^{\textrm 4\times time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{4\times 100})^{\textrm 4\times t}[/tex]
Or, A = $31,200 × [tex](1+\dfrac{\textrm 10.7}{4\times 100})^{\textrm 4\times 8}[/tex]
Or, A = $31,200 × [tex](1.02675)^{32}[/tex]
Or, A = $31,200 × 2.3273
∴ A = $72611.76
So, The Amount paid after 8 years = A = $72611.76
Hence, The Amount paid after 8 years is $72611.76 Answer
What is the equation of the line that passes through the point (-1, -3) and has a slope of -5?
answers y = -5x -16
y = -5x -8
y = -5x +8
y = -5x + 16
Answers
Answer:
y = -5x -8
Explanation:
Find b in equation y = mx + b
Insert numbers to find b
-3 = -5· -1 + b
Step 1: Simplify both sides of the equation.
−3=(−5)(−1)+b
−3=5+b
−3=b+5
Step 2: Flip the equation.
b+5=−3
Step 3: Subtract 5 from both sides.
b+5−5=−3−5
b=−8
Insert into equation
y = -5x - 8
Let’s start by writing out the model equation for slope-intercept
y=mx+b
M: Slope
X: Variable
B: Y-intercept
Now we know that m is slope. Let’s fill in the slope provided to us, which is -5
y=mx+b
y=-5x+b
Now let’s solve for b. We’ll do this by taking the point given to us and substituting it into the equation and solving.
y=-5x+b
*substitute the y and x of the point*
-3=-5(-1)+b
*multiply -5 and -1*
-3=5+b
*subtract 5 on both sides*
-8=b
Now you know b! Let’s put this into our equation
y=mx+b
y=-5x+b
y=-5x-8
This is your answer! Hope this helps comment below for more questions :)
Find the number, if d 12/13 of it is 24
Answers
Answer:
26 is the number
Step-by-step explanation:
12/13 x = 24
Multiply by 13 on both sides
12x = 24 * 13
12x = 312
Simplify
x = 26
26
Hope this helps :)
10 points!
Find the shape resulting from the cross-section of the cylinder.
Answers
Answer:
Triangle
Step-by-step explanation:
cross section through the cone perpendicular will be a triangle with the base of the cone's base diameter.
[tex] {x}^{2} - 1 < 18[/tex]
Answers
[tex]
x^2-1 < 18 \\
x^2 < 19 \\
x < \sqrt{19}
[/tex]
Hope this helps.
What is a reasonable distance between two cities? A. 200 km B. 200 m C. 200 cm D. 200 mm
Answers
Answer:
A would be best
Step-by-step explanation:
200 km is roughly 124.2 miles
200 m is about 0.12 miles
200 cm and 200 mm is way too small to be distances between cities because 200 cm is like 78.7 inches
200 mm is like 7.8 inches
124.2 miles or 200 km would be a reasonable distances between two cities.
Answer:
A. 200km is your answer
Step-by-step explanation:
How do you graph x-y-3=0
Answers
Answer:
see explanation
Step-by-step explanation:
To graph the line, we require 2 points
Find the intercepts, that is where the graph crosses the x and y axes
To find the x- intercept let y = 0 in the equation and solve for x
x - 3 = 0 ( add 3 to both sides )
x = 3 ⇒ (3, 0 ) ← x- intercept
To find the y- intercept let x = 0 in the equation and solve for y
- y - 3 = 0 ( add 3 to both sides )
- y = 3 ( multiply both sides by - 1 )
y = - 3 ⇒ (0, - 3 ) ← y- intercept
Plot the points (3, 0) and (0, - 3) and draw a straight line through them
5% tax on $1.50 What us total cost
Answers
Answer:
$1.58
Step-by-step explanation:
1.50 multiplied by 1.05
answer is 1.575
rounded is 1.58
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Answer:
2.25
Step-by-step explanation:
just multiply .05 by 1.50 so that would be .075, so then add that by original price so 2.25. Don't Quote me on this its been awile.
A credit card issuer charges an APR of 19.66%, and its billing cycle is 30 days
long. What is its periodic interest rate?
O
A. 21.72%
OB. 1.62%
O C. 21.53%
O D. 1.22%
SUBMIT
Answers
Answer:
The periodic interest rate is 1.62 %
Step-by-step explanation:
Given:
Annual percentage rate = 19.66%
Time period = 30 days
To Find:
Periodic interest rate =?
Solution:
The periodic interest rate r is calculated using the following formula:
r = (1 + \frac{i}{m})^{\frac{m}{n}} - 1
Where,
i = nominal annual rate
n = number of payments per year i.e., 12 for monthly payment, 1 for yearly payment and so on.
m = number of compounding periods per year
The period interest rate per payment is integral to the calculation of annuity instruments including loans and investments.
Now substituting the values we get
[tex]r = (1 + \frac{19.66}{12})^{\frac{12}{12}} - 1[/tex]
[tex]r = (1 + \frac{19.66}{12})^1 - 1[/tex]
r = (1 +1.638 ) - 1
r = (2.638 ) - 1
r = 1.638 %
ILL GIVE BRAINLEST AND EXTRA POINTS
Answers
Answer:
it's (-3,9 i hope in prey so
Step-by-step explanation:
Answer:
(- 2, - 5 )
Step-by-step explanation:
Note that y = 1 is a horizontal line passing through all points with a y- coordinate of 1
The point (- 2, 7 ) is 6 units above y = 1 (7 - 1 = 6 ), thus
The reflection is 6 units below y = 1, (1 - 6 = - 5 ), hence
P(- 2, 7 ) → P'(- 2, - 5 )
Round 0.566 to the nearest tenth
Answers
Answer:
0.06
Step-by-step explanation:
If you round 0.566 to the nearest tenth it would be 0.06
pls rate and thank me
Answer:
To round 0.566 to the nearest tenth consider the hundredths' value of 0.566, which is 6 and equal or more than 5. Therefore, the tenths value of 0.566 increases by 1 to 6.
=0.6
Step-by-step explanation:
comment how this helps
Please help!!
1. Solve the following system of equations by graphing.
x + 2y = 8
x + 2y = -4
What is the solution?
(3, 5), no solution, infinite solutions, none of the above
2. The ordered pair (4,2) is a solution to the system of inequalities below.
y>-3x+2
y<2x+1
True or False
3.When solving the system by substitution, what would you plug into the second equation for the letter x?
x+2y=4
2x+2y=6
x = 2, x = 4-2y, x = 4, x = 2y+4
4. There is no solution to the system below.
2x + 4y = 8
x + 2y = 6
True or False
Answers
Answer:
(Q.1) No solution
(Q.2) True
(Q.3) x = 4 - 2y
(Q.4) True
========================================
Step-by-step explanation:
(Q.1) As shown in the first attached figure.
By graphing. x + 2y = 8 & x + 2y = -4
The two lines are parallel, there is no intersection points between the lines.
So, there is no solution to the system of equations.
Also, we should note the parallel lines have the same slope
to find it make the equation similar to y = mx + c where m is the slope
at this situation m = -1/2
===================================================
(Q.2) As shown in the second attached figure.
By graphing the system of inequalities y> -3x+2 & y<2x+1
The Shaded area represents the solution of the system of inequalities
And the point (4,2) is inside the shaded area
So, The ordered pair (4,2) is a solution to the system of inequalities.
====================================================
(Q.3) solving the system { x+2y=4 & 2x+2y=6 } by substitution
From the first equation x + 2y = 4
we will find x in terms of y then plug it into the second equation
So, x + 2y = 4 ⇒ x = 4 - 2y
=====================================================
(Q.4) As shown in the third attached figure.
By graphing. 2x + 4y = 8 & x + 2y = 6
The two lines are parallel, there is no intersection points between the lines.
So, there is no solution to the system of equations.
Also, we should note the parallel lines have the same slope
to find it make the equation similar to y = mx + c where m is the slope
at this situation m = -1/2
Madison’s monthly salary is $1348. If her budget for rent is 32% of salary, then how much is budgeted for rent?
Answers
Answer:
$431.36 is budgeted for rent.
Step-by-step explanation:
Given:
Madison’s monthly salary is $1348.
Her budget for rent is 32% of salary.
Now, to find the amount budgeted for rent.
So, salary = $1348.
And, budget for rent = 32% of $1348.
Thus, the budgeted for rent is:
[tex]32\%\ of\ \$1348.[/tex]
[tex]=\frac{32}{100} \times 1348[/tex]
[tex]=0.32\times 1348[/tex]
[tex]=\$431.36.[/tex]
Therefore, $431.36 is budgeted for rent.
runner is compared with the world record
holder during a race. A negative number means the
runner is ahead of the time of the world record holder.
A
positive number means that the runner is behind
the time of the world record holder. The table
shows the time difference between the runner and
the world record holder for each lap. What time
difference does the runner need for the fourth lap
to match the world record?
Answers
Answer:
-0.42
Step-by-step explanation:
To match the world record, the runner needs a time difference for the fourth lap that brings the total time difference from all laps to zero. This time difference is calculated based on the sum of time differences of the first three laps.
Explanation:This question is asking about the time difference that the runner needs for the fourth lap in order to match the world record.
Assuming that the total time difference after the first three laps is provided in the table, what you'll do is add these three time differences to get the total difference for the first three laps.
Let's say, for instance, the total after three laps is +15 seconds. Since a positive number means the runner is behind the world record holder's time, we want the fourth lap to compensate for that and bring the total time difference to zero to match the world record. Therefore, the runner will need a -15 seconds time difference on the fourth lap.
Remember that a negative number means the runner ran the lap faster than the world record holder.
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The area of a square is 144 square centimeters. Find the length of the diagonal. Write your answer in simplest radical form.
Answers
Answer:
[tex]12\sqrt{2}\ cm[/tex]
Step-by-step explanation:
step 1
Find the length side of the square
we know that
The area of a square is equal to
[tex]A=b^{2}[/tex]
where
b is the length side
we have
[tex]A=144\ cm^2[/tex]
substitute in the formula of area
[tex]144=b^{2}[/tex]
solve for b
square root both sides
[tex]b=12\ cm[/tex]
step 2
Find the length of the diagonal
Applying the Pythagorean Theorem
[tex]d^2=b^2+b^2[/tex]
see the attached figure to better understand the problem
substitute the given values
[tex]d^2=12^2+12^2[/tex]
[tex]d^2=288[/tex]
square root both sides
[tex]d=\sqrt{288}\ cm[/tex]
simplify
[tex]d=12\sqrt{2}\ cm[/tex]
Dave's sister baked $3$ dozen pies of which a third contained chocolate, a quarter contained marshmallows, a sixth contained cayenne, and one twelfth contained salted soy nuts. What is the smallest possible number of pies that had none of these ingredients?
Answers
Step-by-step explanation:
As Dave's sister baked 3 dozen pies.
So, total number of pies = 3 × 12 = 36
Number of pies = 3×12 = 36
Pies which contained chocolate = 1/3×36 = 12
Pies which contained marshmallows = 1/4×36 = 9
Pies which contained cayenne = 1/6×36 = 6
Pies contained soy nut = 1/12×36 = 3
So,
Pies that had none of these ingredients = 36 - (12+9+6+3)
= 36 - 30
= 6 pies
So, total 6 pieces are left that had none of these ingredients.
i.e. 1, 2, 3, 4, 5, 6
Therefore,
The largest possible number of pies that had none of thees ingredients = 6 piecesThe smallest possible number of pies that had none of thees ingredients = 1 pieceKeywords: smallest possible number
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She baked 36 pies. Of these
1/3*36=12 contained chocolate
1/4*36=9 contained marshmallows
1/636=6 contained cayenne
1/12*36=3 contained salted soy nuts.
In order to make the number of pies with none of these ingredients as small as possible, Dave's sister should put all of these ingredients in different pies so that only one of the ingredients is in any pie. If she does this, then 12+9+6+3=30 of the pies will have one of these ingredients. The other 6 pies will have none of these ingredients. At least 6 pies have none of these ingredients.
-Alcumus AoPS Staff
Brainliest would be great!!!
The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. [-5, 5] by [-5, 5]
a. r = 2 - 2 sin θ
b. r = 3 - 2 sin θ
c. r = 2 + 2 sin θ
d. r = 1 - 3 sin θ
Answers
Answer:
A
Step-by-step explanation:
A limacon curve passes trough the point [tex]\left(\dfrac{\pi}{2},0\right)[/tex], this means when [tex]\theta =\dfrac{\pi}{2},[/tex] the distance [tex]r=0.[/tex]
Note that
[tex]\sin \dfrac{\pi}{2} =1,[/tex]
so, if [tex]r=a+b\sin \theta,[/tex]
then
[tex]r\left(\dfrac{\pi}{2}\right)=a+b=0\\ \\a=-b[/tex]
The only option which shows a = -b is option A.
Answer:
b
Step-by-step explanation:
o find the minimum value of the quadratic expression −4x2+8x−25,
−
4
x
2
+
8
x
−
25
,
Marla used the following steps to complete the square:
Step 1: −4(x2+8x)−25
−
4
(
x
2
+
8
x
)
−
25
Step 2: −4(x2+8x+16−16)−25
−
4
(
x
2
+
8
x
+
16
−
16
)
−
25
Step 3: −4(x2+8x+16)+64−25
−
4
(
x
2
+
8
x
+
16
)
+
64
−
25
Step 4: −4(x+4)2+39
−
4
(
x
+
4
)
2
+
39
Did Marla use the correct steps to complete the square?
Answers
Answer:
Marla didn't use the right steps to complete the square. Maria made a mistake in step 1, she put 8x instead of -2x
Step-by-step explanation:
we have
[tex]-4x^{2}+8x-25[/tex]
This is a vertical parabola open downward
The vertex is a maximum
Find the vertex
step 1
Factor the leading coefficient -4
[tex]-4(x^{2}-2x)-25[/tex]
step 2
Complete the square
[tex]-4(x^{2}-2x+1-1)-25[/tex]
step 3
[tex]-4(x^{2}-2x+1)-25+4[/tex]
[tex]-4(x^{2}-2x+1)-21[/tex]
step 4
Rewrite as perfect squares
[tex]-4(x-1)^{2}-21[/tex]
the vertex is the point (1,-21)
so
The maximum value of the quadratic equation is (1,-21)
therefore
Marla didn't use the right steps to complete the square. Maria made a mistake in step 1, she put 8x instead of -2x
Marla correctly completed the square for the expression −4x2+8x−25, arriving at the simplified form −4(x+4)2 + 39 to find the minimum value.
Explanation:To find the minimum value of the quadratic expression −4x2+8x−25, Marla completed the square. Her steps are as follows:
Factor out the coefficient of x2: −4(x2+∼2x−∼) -25Add and subtract (b/2a)2 inside the parentheses: −4(x2+8x+16−16) −25Combine the added 16 with the −4 outside and subtract from −25: −4(x2+8x+16) + 64 −25Factor the perfect square trinomial and simplify: −4(x+4)2 + 39
Marla used the correct steps to complete the square, which simplifies to −4(x+4)2 + 39.
HELP
Find the area of the semicircle.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
Answers
Area of complete circle with radius of 2 is about 12.56
Divided by 2 is 6.28
The area of the semicircle if the radius is 2 in terms of π is 2π.
What is the area of the semicircle?Area of a circle = πr²
Where,
r = radius
A semicircle is half of a circle.
So,
Area of a semicircle = ½πr²
If r = 2
Area of a semicircle = ½ × π × 2²
= ½ × Π × 4
= 4/2π
= 2π
Hence, the area of the semicircle is 2π.
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The 3rd term of a geometric sequence is -2 and the 7th is -32. Find the common ratio,the first term, the explicit formula, and the 10th term.
Answers
Answer:
see explanation
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Both a and r have to be found
Given a₃ = - 2, then
ar² = - 2 → (1)
Given a₇ = - 32, then
a[tex]r^{6}[/tex] = - 32 → (2)
Divide (2) by (1)
[tex]\frac{ar^6}{ar^2}[/tex] = [tex]\frac{-32}{-2}[/tex], that is
[tex]r^{4}[/tex] = 16 ( take the fourth root of both sides )
r = 2 ← common ratio
Substitute r = 2 into (1)
a × 2² = - 2, that is
4a = - 2 ( divide both sides by 4 )
a = - [tex]\frac{1}{2}[/tex] ← first term
Hence
[tex]a_{n}[/tex] = - [tex]\frac{1}{2}[/tex][tex](2)^{n-1}[/tex] ← explicit formula
and
[tex]a_{10}[/tex] = - [tex]\frac{1}{2}[/tex] × [tex]2^{9}[/tex] = - 0.5 × 512 = - 256
A survey of all beings on planet Tott found that 12 beings preferred
hab juice to all other juices. If 40 beings were surveyed altogether,
what percent of them preferred hab juice?
(step by step)
Answers
Answer:
30% of them preferred hab juice.
Step-by-step explanation:
Given:
A survey of all beings on planet Tott found that 12 beings preferred hab juice to all other juices.
40 beings were surveyed altogether.
Now, to find percent of them preferred hab juice.
Total beings surveyed = 40.
Number of beings preferred hab juice = 12.
So, to get the percent:
[tex]\frac{Total\ beings\ surveyed}{Number\ of\ beings\ preferred\ hab\ juice} \times 100.[/tex]
[tex]=\frac{12}{40} \times 100[/tex]
[tex]=0.3\times 100[/tex]
[tex]=30\%.[/tex]
Therefore, 30% of them preferred hab juice.
Given that V= πr^2h. Make r the subject of the formula.
Using the result from the above,find r when V = 81 cm3, π = 4 and h = 9cm
Answers
Answer:
The answer is [tex]r=\frac{3}{2}\ cm.[/tex]
Step-by-step explanation:
Given:
V= πr²h.
V = 81 cm3,
π = 4 and
h = 9cm.
Now, making r the subject of the formula using the result from the above, find r.
So, to get the value of r:
[tex]V=\pi r^2h[/tex]
[tex]81=4\times r^2\times 9[/tex]
[tex]81=36r^2[/tex]
Dividing both sides by 36 we get:
[tex]\frac{81}{36} =r^2[/tex]
Using square root on both sides we get:
[tex]\frac{9}{6} =r[/tex]
[tex]\frac{3}{2} =r[/tex]
[tex]r=\frac{3}{2}.[/tex]
Therefore, the answer is [tex]r=\frac{3}{2}\ cm.[/tex]