The conditional probability, in a single roll of two fair 6 sided dice, that the sum is greater than 6, given that neither die is a two : 17/25
We know that the conditional probability is given by,
P(B | A) = probability of occurrence of event B, given that event A has
occurred
= P(A ∩ B) / P(A)
Here, P(A ∩ B) means the probability of happening two events A and B at the same time.
We also know that if P (B | A ) = P(B) i.e., P(A ∩ B) = P(A) × P(B) the two events A and B are independent of each other.
For this question, let the dice D1 and D2 are rolled once.
Let the numbers displayed on the dice be d1 and d2 respectively.
The dice D1 and D2 are independent.
We need to find the conditional probability that the sum is greater than 6, given that neither die is a two.
Let S represents the sum of the numbers displayed on the dice.
S = d1 + d2
The sum is even, if d1 = d2 is odd OR if d1 = d2 is even
P(d1 = even) = 3/6
=1/2
P(d2=even) = 1/2
P(d1 = odd) = 1/2
P(d2 = odd) = 1/2
So, P(S = even) = [P(d1=even) × P(d2 = even)] + [P(d1= odd) × P(d2=odd)]
= [1/2 × 1/2] + [1/2 × 1/2]
= 1/2
So, we can say that, the sum is either even or odd which are equally likely and hence its probability is 1/2.
First we find the probability for the sum is greater than 6 i.e., P(S > 6)
The possible combination of d1 and d2 for the sum greater than 6 would be,
{(1,6), (2,5), (2, 6), (3, 4), (3, 5), (3, 6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
⇒ n(S > 6) = 21
The number of all possible outcomes = 36
So, P(S > 6) = 21/36
= 7/12
Now we find the probability that neither die is a two
⇒ P(neither die is a two) = [P(1) ∪ P(3 ≤ d1 ≤ 6)] AND [P(1) ∪ P(3 ≤ d1 ≤ 6)]
⇒ P(neither die is a two) = 5/6 × 5/6
⇒ P(neither die is a two) = 25/36
Now, we find the probability that the sum S > 6 AND neither die is a two.
The possible combination for the sum S > 6 AND neither die is a two would be,
{(1,6), (3, 4), (3, 5), (3, 6), (4,3), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,1), (6,3), (6,4), (6,5), (6,6)}
⇒ n(S > 6 AND neither die is a two) = 17
So, P(S > 6 AND neither die is a two) = 17/36
Now we find the conditional probability P(S > 6 | neither die is a two)
⇒ P(S > 6 | neither die is a two) = P(S > 6 AND neither die is a two) ÷
(neither die is a two)
⇒ P(S > 6 | neither die is a two) = (17/36) / (25/36)
⇒ P(S > 6 | neither die is a two) = 17/25
Therefore, the conditional probability, in a single roll of two fair 6 sided dice, that the sum is greater than 6, given that neither die is a two : 17/25
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please help i dont understand
The box and whisker plot is a 71 and 53 and 89 which represent the
median, upper value and lower value.
According to the statement
we have given that the some data of the marks of 18 students and we have to make the plot of that data.
So, For this purpose, we have given that the
A box and whisker plot is a visual tool that is used to graphically display the median, lower and upper quartiles, and lower and upper extremes of a set of data.
And it is used to find the median and the lower value and the maximum value.
So, The median become:
median = n /2
median = 18/2
median = 9th term and
median value is 71.
And then the lower value of the data is a 53.
And the upper value of the data is a 89.
So, overall we can say that the combination of median, upper value and lower value is called the box and whisker plot.
So, The box and whisker plot is a 71 and 53 and 89 which represent the
median, upper value and lower value.
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A gardener wants to design a rectangular garden and has 100 feet of fencing available. A house is on one side of the garden, so no fencing will be needed there. What dimensions will give the maximum area?
Answer:
50 ft and 25 ft give the maximum area
Step-by-step explanation:
Let l and w be the dimensions of rectangle.
The length of fencing is 100 ft:
l + 2w = 100Then:
l = 100 - 2wThe area is:
A = lw = w(100 - 2w) = 100w - 2w²In order to have the maximum area we need to find the vertex of the quadratic function:
y = - 2w² + 100wThe vertex has x-coordinate:
w = - b/(2a) It comes from quadratic function y = ax² + bx + cor
w = - 100/(2*(-2)) = 25So the width is 25 ft.
Find the length:
l = 100 - 2*25 = 50 ftThe area is:
A = 50*25 = 1250 ft²See the attached graph.
pls help i don’t know how to do this
Answer: [tex]\displaystyle\\\frac{2\pi }{3},\ \frac{5\pi }{3} .[/tex]
Step-by-step explanation:
[tex]\displaystyle\\tan\theta=-\sqrt{3}\ \ \ \ 0\leq \theta\leq 2\pi \\\theta =\frac{2\pi }{3}+\pi N\ \ \ (N=0,\ 1,\ 2,\ 3\ ...)\\ N=0\\\theta=\frac{2\pi }{3} +\pi *0\\\theta=\frac{2\pi }{3}\ \ \ \ ( 0\leq \theta\leq 2\pi)\\ N=1\\\theta=\frac{2\pi }{3}+\pi *1 \\\theta=\frac{2\pi }{3} +\pi \\\theta=\frac{2\pi +3\pi }{3} \\\theta=\frac{5\pi }{3} \ \ \ ( 0\leq \theta\leq 2\pi)\\[/tex]
[tex]N=2\\\theta=\frac{2\pi }{3}+2\pi \\ \theta=\frac{2\pi +3*2\pi }{3}\\ \theta=\frac{2\pi +6\pi }{3} \\\theta=\frac{8\pi }{3} \\\theta=2\frac{2}{3} \pi \ \ \ \ (\notin0\leq \theta\leq 2\pi).\\[/tex]
A shape has an area of 37 mm², of which 60%
is green.
The shape is enlarged so that all its side lengths
increase by 45%.
Work out the area of the green part of the larger
shape.
If your answer is a decimal, give it to 1 d.p.
If the side are increased by 45% then the area of green part will be 26.6955 [tex]mm^{2}[/tex].
Given that area of a shape of 37 [tex]mm^{2}[/tex] in which 60% is green.
We are required to find the area of green region if the side is increased by 45%.
Area is basically part of a surface covered by a shape.
When the side is increased by 45% then the area will increase by 45%*45%=20.25%.
Increased area =37*20.25%=7.4925
New area=37+7.4925
=44.4925
We have been given that 60% is the area of green.
Area of green region=44.4925*60/100
=26.6955 [tex]mm^{2}[/tex]
Hence if the sides are increased by 45% then the area of green part will be 26.6955 [tex]mm^{2}[/tex].
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of
Given the triangle ABC at points A=(1,6) B=(-3,5) C=(7,1), and if the triangle is first reflected over the
y axis, and then over the x axis, find the new point A".
Select one:
O a. (1,-6)
Ob. (3,5)
Oc. (-1,-6)
O d. (1,6)
After reflected over the triangle the point a become A = (-1,-6). The option c is correct.
According to the statement
we have given that the a triangle ABC at the points A=(1,6) B=(-3,5) C=(7,1), and we have to find the points of a when the triangle is first reflected over the y axis.
So, For this purpose
we know that the when the triangle is at the x axis then the point A is A=(1,6).
But when the triangles reflected over the y - axis then the point A goes to the negative side of the graph. In other words whole of the triangle shift to the negative side of the graph. That's why the point become negative.
So, The option c is correct. After reflected over the triangle the point a become A = (-1,-6)
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Complete the equivalent ratio. How many ounces are in 2 cups?
StartFraction 48 ounces Over 6 cups EndFraction = StartFraction question mark ounces Over 2 cups EndFraction
Given the function f(x) = -5x²-x+ 20, find f(3).
O-28
O-13
O62
O64
Answer: [tex]\Large\boxed{First~Choice.~-28}[/tex]
Step-by-step explanation:
Given function expression
f(x) = -5x² - x + 20
Requirement of the question
Find the value of f(3)
Substitute the values into the function
f(x) = -5x² - x + 20
f(3) = -5(3)² - (3) + 20
Simplify the exponents
f(3) = -5(9) - 3 + 20
Simplify by multiplication
f(3) = -45 - 3 + 20
Simplify by subtraction and addition
f(3) = -48 + 20
[tex]\Large\boxed{f(3)=-28}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x 3y=108
For given f(x, y) the extremum: (12, 24) which is the minimum.
For given question,
We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108
We use the constraint to build the constraint function,
g(x, y) = 3x + 3y
We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:
[tex]f_x=8x[/tex]
[tex]f_y=4y[/tex]
[tex]g_x=3[/tex]
[tex]g_y=3[/tex]
Setting up the Lagrange multiplier equations:
[tex]f_x=\lambda g_x[/tex]
⇒ 8x = 3λ .....................(1)
[tex]f_y=\lambda g_y[/tex]
⇒ 4y = 3λ ......................(2)
constraint: 3x + 3y = 108 .......................(3)
Taking (1) / (2), (assuming λ ≠ 0)
⇒ 8x/4y = 1
⇒ 2x = y
Substitute this value of y in equation (3),
⇒ 3x + 3y = 108
⇒ 3x + 3(2x) = 108
⇒ 3x + 6x = 108
⇒ 9x = 108
⇒ x = 12
⇒ y = 2 × 12
⇒ y = 24
So, the saddle point (critical point) is (12, 24)
Now we find the value of f(12, 24)
⇒ f(12, 24) = 4(12)² + 2(24)²
⇒ f(12, 24) = 576 + 1152
⇒ f(12, 24) = 1728 ................(1)
Consider point (18,18)
At this point the value of function f(x, y) is,
⇒ f(18, 18) = 4(18)² + 2(18)²
⇒ f(18, 18) = 1296 + 648
⇒ f(18, 18) = 1944 ..............(2)
From (1) and (2),
1728 < 1944
This means, given extremum (12, 24) is minimum.
Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.
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d. If you double a certain number and subtrack 7 you get the same answer as when you add 5 to the number, Determine the number
Answer:
12
Step-by-step explanation:
Let n = the number.
2n - 7 = n + 5
n = 12
Let’s check if we got the right answer by substituting 12 for n into the original equation.
2*12 - 7 = 12 + 5
24 - 7 = 17
17 = 17
Prove the cofunction identity using the addition and subtraction formulas. sec 2 − u = csc(u) use a reciprocal identity, then apply a subtraction formula to simplify
Proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We have to prove that the cofunction identity using the addition and subtraction formulas.
sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We can prove this by using the identities given below:
[tex]sec(u)=\frac{1}{cos(u)}[/tex]
[tex]\frac{1}{sin(u)} =csc(u)[/tex]
cos(a-b) = cos a cos b + sin a sin b
Now the explanation,
[tex]sec(\frac{\pi }{2} -u) = csc(u)[/tex]
By using trignometric identities,
[tex]cos(u)=\frac{1}{sec(u)}[/tex] ∴[tex]sec(u)=\frac{1}{cos(u)}[/tex]
So,
[tex]\frac{1}{cos(\frac{\pi }{2}-u) } =csc(u)[/tex]
By substituting the given identities we get,
[tex]\frac{1}{cos(\frac{\pi }{2})cos(u)+sin(\frac{\pi }{2} )sin(u) }[/tex]
= [tex]\frac{1}{0.cos(u)+(1).sin(u)}[/tex]
=[tex]\frac{1}{sin(u)}[/tex]
= csc(u)
csc(u) = csc(u)
Here we proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]-u) = csc(u)
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A Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. Which Equations Can Be Used To Find The Numbers Of Miles Driven For A Truck That Cost A Total Of $42.50 To Rent For One Day?
A)$25m + 0.35m = $42.50
B)$0.35 + $25m = $42.50
C)$42.50 + $0.35m = $25
D)$0.35 = $42.50
The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50
According to the statement
we have given that the Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. and a Truck That Cost A Total Of $42.50 To Rent For One Day.
And we have to find the equation for this.
So, for given purpose,
we know that the A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
And from the given values the equation formed that the
In the equation the charges per mile is added to the original charges is equal to the total charges per day.
So, The equation become
$25m + 0.35m = $42.50
And by this equation we represent the all given conditions related charges.
So, The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50
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Question 3 of 10
Which of the following must be true for an expression to be a difference of
two squares?
a. all variables are raised to an even power
b. there are only two terms
c. both terms have negative coefficients
OA. a, b, and c
B. a and b
OC. a and c
D. b and c
Assume that each circle shown below represent one unit express the shaded amount as a single fraction and as a mixed number
One fraction: 5/2.
Mixed-fraction: 2 1/2.
In the question, we are asked to assume that each circle shown below represents one unit, and are asked to express the shaded amount as a single fraction and a mixed fraction.
The given circle is divided into 8 equal parts.
In the first circle, all 8 parts are shaded, shown by the fraction, 8/8.
In the second circle, all 8 parts are shaded, shown by the fraction, 8/8.
In the third circle, 4 parts are shaded, shown by the fraction, 4/8.
Thus, the total shaded part can be calculated by adding:
8/8 + 8/8 + 4/8,
= (8 + 8 + 4)/8
= 20/8
= 5/2 {Cancelling off by 4}.
Thus, one fraction is 5/2.
To convert this to a mixed fraction, we divide 5 by 2, write the quotient as the whole part, the remainder as the numerator, and 2 as the denominator.
5÷2 gives quotient 2, and remainder 1.
Thus, the mixed-fraction is 2 1/2.
For the complete question, refer to the attachment.
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Rewrite the function by completing the square. f(x) = x2 - 8x + 7
The function f(x) = x2 - 8x + 7 rewritten by completing the square is x² - 8x + 16 = 9.
Rewrite the function by completing the square?Given the function; f(x) = x² - 8x + 7
To rewrite by completing the square.
We simplify the function into a proper form to completing the square.
x² - 8x + 7 = 0
x² - 8x = -7
We create a trinomial square on the left side of the equation that is equal to the square of the half of b.
(b/2)² = (-4)²
Next, we add the term to both side of the equation.
x² - 8x + (-4)² = -7 + (-4)²
x² - 8x + 16 = 9
Therefore, the function f(x) = x2 - 8x + 7 rewritten by completing the square is x² - 8x + 16 = 9.
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solve for x
2^x,2^4=2^3x
Answer:
x=2
Step-by-step explanation:
2^x *2^4=2^3x
using law of indices
2^x+4=2^3x
x+4=3x
4=3x-x
4=2x
2=x
Several properties are used to evaluate this expression. identify the property used in each step. 21 + (19 + 36): (21 + 19) + 36:
21 + (36 + 0 + 19) Equals 76.
What is the property of addition?A final result is obtained by adding two or more integers together. Commutative, associative, distributive, and additive identity are the four major characteristics of b. b means that even if the order changes, the addition result will remain the same.
Equation to be used: 21 + (36 + 0 + 19)
The identity property of addition states that a + 0 = a.21 + (36 + 0 + 19) = 21 + (36 + 19)Using the commutative property of addition, a + b equals a + b.21 + (36 + 19) Equals 21 + (19 + 36)By using the associative property of addition, the formula is: a + (b + c) = a + b + c.21 + (19 + 36) Equals (21 + 19) + 36Put two more numbers within the bracket now.(21 + 19) + 36 = 40 + 36A + B Equals C, any number, using the closure property of addition.40 + 36 = 76Hence 21 + (36 + 0 + 19) Equals 76.To know more about property of addition visit:
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I understand that the you are looking for is :
Several properties are used to evaluate this expression. Identify the property used in each step.
21 + (36 + 0 + 19)
21 + (36 + 19):
21 + (19 + 36):
(21 + 19) + 36:
40 + 36
76
Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. if he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings? a. $40 b. $60 c. $74 d. $55
The total amount he puts towards emergency savings is $74
The correct option is C.
According to the given information:His total weekly deposits are as follows: 219+115+40+20+10+40+15 = 459
Now
that we are aware, his weekly deposits total $459 in total.
His total remuneration is $498 due to an error in his addition of the numbers.
The amount he has each week will be determined by deducting his deposits from his paycheck:
498-459 = 39
He contributes two equal payments of $20 and $15 to his emergency fund.
His entire contribution to emergency savings is = 20 + 15 = 35.
Only need to add the additional $39
To determine how much he can set aside each week for emergency savings, multiply his total emergency savings by 35 dollars:
39+35 = 74
the total per week that he can put towards emergency savings = $74
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I understand that the question you are looking for is:
Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Pictable) Education investment fund $10 Other (Pictable) Retirement investment fund $40 Other (Pictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings?
a. $40
b. $60
c. $74
d. $55
Answer: C. $74
Step-by-step explanation: C. $74.00
A die is rolled. if it rolls to a 1 or 2, you win 2 usd. if it rolls to a 3, 4, 5, or 6, you will lose 1 usd. what is the expected payoff from rolling this die?
The expected payoff from rolling the die is 0 usd.
According to the given question.
A die is rolled.
So, the possiblbe outcomes for a dice = {1, 2, 3, 4, 5, 6}
⇒ Total number of outcomes = 6
Also, it is given that
If a die is roll to a 1 or 2, we win 2usd and if it rolls to 3, 4, 5, or 6 we lose 1 usd.
As, we know that "Probability denotes the possibility of the outcome of any random event". And probability of any event can be calculated as
P(E) = total number of favorable outcomes/ Total number of outcomes
So,
The probability that die rolls 1 or 2 = 1/6 + 1/6 = 2/6 = 1/3
And, the probability thet die rolls 3, 4, 5, or 6
= 1/6 + 1/6 + 1/6 + 1/6
= 4/6
= 2/3
Therefore, the excepted payoff from rolling this die
= [tex]2\times\frac{1}{3} - 1\times\frac{2}{3}[/tex]
[tex]= \frac{2}{3} - \frac{2}{3}[/tex]
= 0 usd
Hence, the expected payoff from rolling the die is 0 usd.
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The graph of the function f(x)= 5/4 sin(x)+1 is shown. What are the key features of this function?
- The maximum value of the function is....(2pi,2.25,1)
- The minimum value of the function is...(pi/2,-0.25,-1)
- On the interval (0,pi/2), the function is...(increasing, decreasing)
-the range of the function is...([-0.25,2.24],all real numbers, [-1,1])
The answers to this question can be given as
The maximum value of the function is 2.25- The minimum value of the function is -0.25- On the interval (0,pi/2), the function is increasing-the range of the function is ([-0.25,2.25]What is the maximum value of a function?This is the point of the function while is it shown on the graph where it is said to be at its highest point or it is at its highest vertex.
When you trace the graph, the highest point is at 2.25.
What is the minimum value of a function?This is the point or the part of the function where it is at the vertex that is the lowest in the graph.
This is at -0.25
This is a function that can be said to be increasing from the behavior of this graph.
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Please answer quickly! Several questions from Algebra 2, on a unit about Sequences and Series, most of these have to do with Arithmetic and Geometric Series-screenshots of the questions are linked below. It would be great if you could include the question # and the answer in the answer section, and then explain it below. Thank you in advance!
The sum of the geometric series is 2199; option E.
The 36th term of the arithmetic series is -60.5 option CThe sum of the arithmetic series is 2547; option EThe missing geometric sequence are; 1.614375, 3.30946875, 6.7844109375. option EArithmetic and Geometric seriesa1 = 1458r = 1/3a6 = 6S6 = a(rⁿ - 1) / r -1
= 1468(1/3^6 - 1) / (1/3 - 1)
= 1468(0.00137174211248 - 1) / -2/3
= 1468(-0.9986282578875) / -0.66666666666666
= -1,465.98628257885 / -0.66666666666666
= 2198.97942386829
Approximately,
S6 = 2199
Arithmetic series
a36a1 = 27d = -5/2Sn = n/2{2a + (n -1)d}
= 36/2 {2×27 + (36-1)-5/2}
= 18{54 + (35)-5/2}
= 18(54 + 175/2)
= 18(54 + 87.5)
= 18(141.5)
s36 = 2547
a36 = a + (n - 1) d
= 27 + (36 - 1)-5/2
= 27 + (35)-5/2
=27 + -175/2
= 27 - 87.5
= -60.5
S20 = n/2{2a + (n -1)d}
= 20/2{2×27 + (20-1)-5}
= 10(54 + (19)-5)
= 10{54 + (-95)}
= 10(54-95)
= 10(-41)
s20 = -410
Missing terms of the geometric sequence:
nth term = ar^n-1
448/135 = 63/80×r^(6-1)
448/135 = 63/80×r^5
r^5 = 448/135 ÷ 63/80
= 448/135 × 80/63
= 35,840/8,505
r = 5√35,840/5√8505
= 946.57/461.11
r = 2.05
Second term = a×r
= 63/80×2.05
= 1.614375
Third term = ar²
= 63/80×2.05²
= 63/80×4.2025
= 3.30946875
Fourth term = 63/80 × 2.05³
= 63/80×8.615125
= 6.7844109375
Therefore, none of these are correct
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please please please
The amount of water in each mug is 2 / 5 litres
How to find the litres of water in each mug?The water bottle has 4/5 litres of water.
The litre of water is poured equally in 2 mugs.
Therefore, the amount of water in each mug can be calculated as follows;
amount of water in each mug = 4 / 5 ÷ 2
amount of water in each mug = 4 / 5 × 1 / 2
amount of water in each mug = 4 / 10
amount of water in each mug = 2 / 5 litres
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6. If x is the largest of three consecutive integers, represent the sum of the three integers.
a) If x is the largest of three consecutive integers, how do we represent the three integers?
b) How do we convert this information into a solvable equation?
c) Find the sum
Answer:
See below
Step-by-step explanation:
x = largest
x-1 previous
x -2 smallest
sum = x + x-1 + x-2
sum = 3x -3
Based on these segment lengths, which group of segments cannot form a triangle? a. 12, 7, 8 b. 8, 7, 13 c. 1, 2, 3 d. 80, 140, 70
(D) 80°, 140°, and 70° group of segments cannot form a triangle.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC represents a triangle with vertices A, B, and C.In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. In other words, the triangle is contained in just one plane, and every triangle is contained in some plane. There is just one plane and all triangles are enclosed in it if the entire geometry is merely the Euclidean plane; but, in higher-dimensional Euclidean spaces, this is no longer true.To find which group of segments cannot form a triangle:
80°, 140°, and 70° cannot form a triangle because the sum of the three angles is 290°, whereas the sum of the angles in a triangle is 180°.Therefore, (D) 80°, 140°, and 70° group of segments cannot form a triangle.
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Answer:
80, 140, 70
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the properties to the regular polygons they describe.
A polygon is a figure that has a given number of sides.
What is a polygon?A polygon is an n - sided figure. The number of sides in a polygon is almost infinite. Let us now match the properties with the type of polygon.
a. 12.gon - An interior angle measures 150°
The polygon that has 12 sides is called the Dodecagon.
Given that the sum of the interior angles in a dodecagon is 1800, then each interior angle is; 1,800/12
= 150°
b. 15-gon - An exterior angle measures 24°
The polygon that contains 15 sides is called pentadecagon. Given that the sum of the exterior angles of polygon is 360 degrees and each exterior angle is 24° then;
360/ 24° = 15 sides
c. 16-gon - The sum of the interior angles is 2,520°
The polygon that contains 16 sides is called the hexadecagon. The sum of its interior angles is 2,520° hence each interior angle measures; 2,520°/16 = 157.5°
d. 18-gon - An interior angle measures 160°
A polygon that contains 18 sides is called an octadecagon .
We have;
160 = (n−2) × 180° / n
160n = 180n - 360
360 = 20n
n = 18
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Missing parts;
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the properties to the regular polygons they describe.
An interior angle measures 150".
An exterior angle measures 24.
The sum of the interior angles is 2520°.
An interior angle measures 160".
The sum of the exterior angles is 180º.
The sum of the interior angles is 2160°.
15-gon
16-gon
12.gon
18-gon
Answer:
15 gon = An exterior angle measure 2416 gon = The sum of the interior angles is 2,52012 = An interior angle measure 15018 = An interior angle measure 160Step-by-step explanation:
Need help with my math please. 31-41.
Step-by-step explanation:
31) the answer is (98765x9) +3=888888
why if u look at the equation is descending and if u verify the cinjecture u will find out is correct
41)½+¼+⅛+1/16+1/32=1-1/32
just d same reason with (31)
A vase in the shape of an oblique cylinder has the dimensions shown. What is the volume in the vase in liters?round nearest tenth
The volume of a vase with a radius of 1 m and height of 7 m is 22000 L
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Cylinder is solid geometrical figure with straight parallel sides and a circular or oval cross section
Let us assume that the vase has a base with radius of 1 m and height of 7 m, hence:
Volume of vase = π * radius² * height
Volume of vase = π * (1)² * 7 = 22 m³ = 22000 L
The volume of a vase with a radius of 1 m and height of 7 m is 22000 L
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Find the value of x.
OA. 66
OB. 122
OC. 98
O D. 76
SUBMIT
Answer:
C) 98
Step-by-step explanation:
Hope this helps! sry if I'm wrong
The value of x in the given equation 15x + 120 = 5x + 1100 is 98. Option C is correct.
An equation is a combination of numbers, variables, mathematical operations, and functions. It is basically a statement emphasising that the two or more expressions are equal to each other.
The given equation is
15x + 120 = 5x + 1100
Take the like terms together,
15x - 5x = 1100 - 120
10x = 980
x = [tex]\frac{980}{10}[/tex]
x = 98.
Thus, the option C is correct stating that the value of x in the given equation is 98.
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The complete question is as follows:
Find the value of x in the equation:
15x + 120 = 5x + 1100.
A. 66
B. 122
C. 98
D. 76
SUBMIT.
Find the m of
Find the m of
Can someone help I’m so very confused on how I even start this??
Both of these problems will be solved in a similar way, but with different numbers. First, we set up an equation with the values given. Then, we solve. Lastly, we plug into the original expressions to solve for the angles.
[23] ABD = 42°, DBC = 35°
(4x - 2) + (3x + 2) = 77°
4x+ 3x + 2 - 2 = 77°
4x+ 3x= 77°
7x= 77°
x= 11°
-
ABD = (4x - 2) = (4(11°) - 2) = 44° - 2 = 42°
DBC = (3x + 2) = (3(11°) + 2) = 33° + 2 = 35°
[24] ABD = 62°, DBC = 78°
(4x - 8) + (4x + 8) = 140°
4x + 4x + 8 - 8 = 140°
4x + 4x = 140°
8x = 140°
8x = 140°
x = 17.5°
-
ABD = (4x - 8) = (4(17.5°) - 8) = 70° - 8° = 62°
DBC =(4x + 8) = (4(17.5°) + 8) = 70° + 8° = 78°
Select the correct answer from each drop-down menu.
Given: W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3) are the vertices of quadrilateral WXYZ.
Prove: WXYZis a square.
Using the distance formula, I found that
…
A. all four sides have a length of 5
B. all four sides have different lengths
C. only 2 sides have the same length
D. all four sides have a length of 10
Answer: A
Step-by-step explanation:
[tex]WX=\sqrt{(-1-3)^2 +(1-4)^2}=5[/tex]
Since WXYZ must be a square, all the sides must have a length of 5.
A day care program has an average daily expense of $75.00. the standard deviation is $5.00. the owner takes a sample of 64 bills. what is the probability the mean of his sample will be between $70.00 and $80.00? step 1. calculate a z-score for $70.00 - step 2. give the probability for step 1. % step 3. calculate the z-score for $80.00 step 4. give the probability for step 3. % step 5. add the probabilities from steps 2
Answer:
B. 68
Step-by-step explanation:
x is a raw score to be standardized;
μ is the mean of the population;
σ is the standard deviation of the population.
Therefore the mean is zero. Seventy is -1z, or -1 standard deviation.
Step 2: 34.13% of the cases fall between -1 standard deviation and the mean. Thus there is a 34.13% chance that the score will fall between 70 and 75. This, of course, assumes a normal curve.
Step 3: An 80 is +1z or +1 standard deviation assuming a normal curve.
Step 4: Thirty four percent of the cases fall between +1 standard deviation and the mean. Thus there is a 34.13% chance that the score will fall between 75 and 80. This, of course, assumes a normal curve.
Step 5: Score between +1z and -1z, or +1 and -1 standard deviation account for 68.26% of the cases.
