You are playing a game that uses two fair number cubes. If the total on the number cubes is either 11 or 2 on your next turn, you win the game. Whatpreitacility of wiring on your next turn? Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Answers
Given the word problem, we can deduce the following information:
1. The game uses two fair number cubes.
2. If the total on the number cubes is either 11 or 2 on your next turn, you win the game.
To determine the probability of winning the next turn, we note that the two cubes have 36 possible outcomes since each dice has six combinations which are independent.
Rolling a 2 would have one possible outcome: (1,1)
Rolling an 11 would have two possible outcomes: (5,6) and (6,5)
So there would be three possible outcomes out of 36:
[tex]\begin{gathered} P=\frac{3}{36} \\ =\frac{1}{12} \end{gathered}[/tex]The combined probability,P, is 1/12. We express this into percent by:
[tex]\begin{gathered} P=\frac{1}{12}(100) \\ =8.3 \end{gathered}[/tex]Therefore, the answer is 8.3%.
Related Questions
What is 8 percent of 15.4 ?
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Evaluate the value of 8 percent of 15.4 .
[tex]\begin{gathered} \frac{8}{100}\cdot15.4=0.08\cdot15.4 \\ =1.232 \end{gathered}[/tex]So value of 8 percent of 15.4 is 1.232.
Use a tree diagram to determine the probability of tossing a total of 7 using two regular dice.
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Solution
Use a tree diagram to determine the probability of tossing a total of 7 using two regular dice.
For the sum number hould be 7
First dice : 1 2 3 4 5 6
second dice 6 5 4 3 2 1
Probability = favourable outcomes /total outcomes
Pro(total sum of 7) = number of seven / Total number
[tex]Pr(sum\text{7\rparen =}\frac{6}{36}=\frac{1}{6}\text{ }[/tex]
A building inspector needs to determine if two walls in a new house are built at right angles, as the buildingcode requires. He measure and find the following information. Wall 1 measures 12 feet, wall 2 measures 14feet, and the distance from the end of wall 1 to the end of wall 2 measures 18 feet. Do the walls meet at rightangles? Explain
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A right triangle is made, where lengths of the walls are the legs and the distance from the end of wall 1 to the end of wall 2 is the hypotenuse.
If there is a right angle, the Pythagorean theorem must be satisfied.
12² + 14² = 18²
144 + 196 = 324
340 ≠ 324
Then, the walls don't meet at a right angle.
Solve: 3/5x +7/10 =19/10
Answers
Subtracting 7/10 from the given equation we get:
[tex]\begin{gathered} \frac{3}{5}x+\frac{7}{10}-\frac{7}{10}=\frac{19}{10}-\frac{7}{10}, \\ \frac{3}{5}x=\frac{12}{10}. \end{gathered}[/tex]Now, multiplying the above equation by 5/3 we get:
[tex]\begin{gathered} \frac{3}{5}x\times\frac{5}{3}=\frac{12}{10}\times\frac{5}{3}, \\ x=\frac{4}{2}, \\ x=2. \end{gathered}[/tex]Answer:
[tex]x=2.[/tex]the following data are an example of what type of regression?
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In this problem, we want to determine which type of function best represents the data.
The best way to do this is to graph the points and determine which functions makes the best model.
From the table, we will graph the points:
[tex]\begin{gathered} (1,10960) \\ (2,10808) \\ (3,10904) \\ (4,11286) \\ (5,11876) \\ (6,12553) \end{gathered}[/tex]We get the following graph:
We can typtically determine the correct graph by the shape of the curve. To do this, let's take a look at the parent function for each graph listed:
Since we see a graph similar to the middle graph, or the quadratic function, we can conclude that the best model is a quadratic regression model.
does the series 3+9+27+81+…. diverge or converge
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Given the series
[tex]3+9+27+81+\cdots[/tex]which is a geometric series with first term 3 and common ratio 3.
A geometric series conveges if and only if |r| < 1, where r is the common ratio. Here, r = 3 > 1. So, the given geometric series diverges.
Which of the following equations is an example of direct variation between variables x and y?A. y= x/9B. y= 9/xC. y= 9xD. y= x+9
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Given:
We have equations in options.
Required:
Which of the following equations is an example of direct variation between variable x and y.
Explanation:
The formula for direct variation is y = kx, where k is the constant of variation.
We have
[tex]y=\frac{1}{9}x\text{ and }y=9x\text{ is in form of direct variation.}[/tex]Answer:
Option A and C is correct.
A teacher is selecting students for a trivia bowl. If there are nine interested students and a trivia bowl team consists of three players, how many different teams can the teacher select? A 24 B. 84 C. 252 D. 504
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The number of different combinations of k elements in a set of n elements, is:
[tex]\frac{n!}{k!(n-k)!}[/tex]If we want to select three players from a group of 9 students, then the amount of different teams will be given by:
[tex]\begin{gathered} \frac{9!}{3!(9-3)!}=\frac{9!}{3!\cdot6!} \\ =\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2}{3\cdot2\cdot6\cdot5\cdot4\cdot3\cdot2} \\ =\frac{9\cdot8\cdot7}{3\cdot2} \\ =\frac{9}{3}\cdot\frac{8}{2}\cdot7 \\ =3\cdot4\cdot7 \\ =84 \end{gathered}[/tex]Therefore, the total amount of different teams that can be selected, is:
[tex]84[/tex]Drag each tile to the correct box. Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval. f(x) = x² + 3x interval: (-2, 3] f(x) = 3x - 8 interval: [4, 5] f(x) = x² - 2x interval: (-3,4) f(x) = x².5 interval: [-1.1)
Answers
To find the average rate of change, use the formula:
[tex]A=\frac{f(b)-f(a)}{b-a}[/tex][tex]\begin{gathered} f(x)=x^2+3x \\ \end{gathered}[/tex]Interval, (a, b) = (-2, 3]
Let's find the average rate of change:
[tex]\begin{gathered} f(a)=f(-2)=-2^2+3(-2)=4\text{ - 6 = -2} \\ \\ f(b)=f(3)=3^2+3(3)=9+9=18 \end{gathered}[/tex]Average rate of change is:
[tex]A=\frac{18-(-2)}{3-(-2)}=\frac{18+2}{3+2}=\frac{20}{5}=4[/tex][tex]f(x)=3x\text{ - 8}[/tex]Interval, (a, b) = [4,5]
Let's solve for f(a) and f(b):
[tex]\begin{gathered} f(a)=f(4)=3(4)-8=12-8=4 \\ \\ f(b)=f(5)=3(5)-8=15-8=7 \end{gathered}[/tex]Average rate of change =
[tex]A=\frac{f(b)-f(a)}{b-a}=\frac{7-4}{5-4}=\frac{3}{1}=3[/tex][tex]f\mleft(x\mright)=x^2-2x[/tex]interval, (a,b) = (-3, 4)
Solve for f(a) and f(b)
[tex]\begin{gathered} f(a)=f(-3)=-3^2-2(-3)=9+6=15 \\ \\ f(b)=f(4)=4^2-2(4)=16-8=8 \\ \\ A=\frac{8-15}{4-(-3)}=\frac{8-15}{4+3}=\frac{-7}{7}=-1 \end{gathered}[/tex][tex]f(x)=x^2(5)[/tex]interval, (a,b) =[-1, 1)
[tex]\begin{gathered} f(a)=f(-1)=-1^2(5)=5 \\ \\ f(b)=f(1)=1^2(5)=5 \\ \\ A=\frac{5-5}{1-(-1)}=\frac{0}{2}=0 \end{gathered}[/tex]"Jeff Bezos needs 1000 ft of fence to surround his backyard. Mr. Booth has a similar, but much smaller backyard with a scale factor of 3/5. How many feet of fence does Mr. Booth need?"
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ANSWER:
Mr. Booth need 600 feet
STEP-BY-STEP EXPLANATION:
The scale factor is the ratio of the length of one side of one figure to the length of the corresponding side of the other figure, therefore:
[tex]1000\cdot\frac{3}{5}=600[/tex]What is the volume of a cylinder, in cubic ft, with a height of 12ft and a base diameterof 12ft? Round to the nearest tenths place,
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To get the volume of a cylinder, we multiply its height by the base area:
[tex]V=A_b\cdot h[/tex]The area is a circle if diameter equals 12 ft, so, its radius is half that, 6 ft.
The area of a circle is:
[tex]\begin{gathered} A_b=\pi r^2 \\ A_b=\pi6^2=36\pi \end{gathered}[/tex]So, we input the area of the base to get the volume of the cylinder:
[tex]\begin{gathered} V=A_b\cdot h \\ V=36\pi\cdot12 \\ V=432\pi \\ V=1357.168\ldots\approx1357.2 \end{gathered}[/tex]So, the volume is approximately 1357.2 ft³
Which of the following is an equivalent form of the compound inequality[tex] - 44 \ \textgreater \ - 2x- 8 ⩾ -8[/tex] the options are below in picture
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Given the compound inequality:
[tex]-44>-2x-8⩾-8[/tex]Let's find the equivalent form of the inequality.
To find the equivalent form, let's simplify the inequality.
SInce it is a compund inequality, we are to seperate the inequalities.
Simplify the first two inequalities, then simplify the last two inequalities.
We have:
First two inequalities: -44 > -2x - 8
Last two inequalities: -2x - 8 ⩾ -8
Let's simplify both
[tex]\begin{gathered} -44>-2x-8 \\ \\ Rewrite\text{ the inequality and change the inequality sign:} \\ -2x-8<-44 \end{gathered}[/tex][tex]\begin{gathered} \text{Second inequality:} \\ -2x-8⩾-8 \\ \end{gathered}[/tex]Therefore, the equivalent form is:
[tex]-2x-8<-44\text{ and -2x - 8 }⩾\text{ -8}[/tex]ANSWER:
[tex]d.\text{ -2x - 8<-44 and -2x - 8 }⩾\text{ -8}[/tex]Consider the following line According to the information above, the line passes through the point and its director vector is
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Given:
[tex]L:\frac{x+10}{2}=y=\frac{z-1}{3}[/tex]Required:
We need to find the point that lies on the given line and director vector.
Explanation:
Consider the equation.
[tex]\frac{x+10}{2}=y[/tex]Set x =2 and substitute in the equation.
[tex]\frac{2+10}{2}=y[/tex][tex]\frac{12}{2}=y[/tex][tex]6=y[/tex]We get y =2
Consider the equation.
[tex]y=\frac{z-1}{3}[/tex]Substitute y =6 in the equation.
[tex]6=\frac{z-1}{3}[/tex]Multiply both sides by 3.
[tex]3\times6=3\times\frac{z-1}{3}[/tex][tex]18=z-1[/tex]Add 1 to both sides.
[tex]18+1=z-1+1[/tex][tex]19=z[/tex]We get z =19.
The given line passes through the point ( 2,6,19).
[tex]\text{ Set x =0 in the equation }\frac{x+10}{2}=y.[/tex][tex]\frac{10}{2}=y[/tex][tex]5=y[/tex][tex]\text{ Set y =0 in the equation }\frac{x+10}{2}=y.[/tex][tex]\frac{x+10}{2}=0[/tex][tex]x=-10[/tex][tex]Set\text{ y =0 in the equation }y=\frac{z-1}{3}.[/tex][tex]\frac{z-1}{3}=0[/tex][tex]z-1=0[/tex][tex]z=1[/tex]The director vector is (-10, 5.1).
Final answer:
The given line passes through the point ( 2,6,19).
The director vector is (-10, 5.1).
What number is 1/4 of 8
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The question given is
[tex]\frac{1}{4}of\text{ 8}[/tex][tex]of\text{ means multiplication (}\times)[/tex]Therefore,
[tex]\begin{gathered} \frac{1}{4}of\text{ 8} \\ =\frac{1}{4}\times8 \\ =\frac{8}{4} \\ =2 \end{gathered}[/tex]Hence,
The final answer is 2
Find the length of the diagonal of a square with perimeter 32.A.[tex]4 \sqrt{2} [/tex]B. 8C.[tex]2 \sqrt{2} [/tex]D. 45E.[tex]8 \sqrt{2} [/tex]
Answers
ANSWER
[tex]E.8\sqrt[]{2}[/tex]EXPLANATION
The square has a perimeter of 32.
The perimeter of a square is given as:
[tex]P=4\cdot L[/tex]where L = length of the side of the square
Therefore, we have that for the given square:
[tex]\begin{gathered} 32=4\cdot L \\ \Rightarrow L=\frac{32}{4} \\ L=8 \end{gathered}[/tex]The square has sides 8 units long.
To find the length of the diagonal, apply Pythagoras theorem, since the diagonal forms a right triangle with the sides of the square:
[tex]\text{hyp}^2=a^2+b^2[/tex]where hyp = hypotenuse of the triangle (diagonal)
a, b = legs of the triangle (side lengths of the square)
Therefore, we have that:
[tex]\begin{gathered} D^2=8^2+8^2 \\ D^2=64+64=128 \\ D=\sqrt[]{128} \\ D=8\sqrt[]{2} \end{gathered}[/tex]That is the length of the diagonal.
can you please help me I need quick answer please
Answers
1) - 5 x - 9 = 45
2) 21 / - 7 = - 3
3) - 7 x 7 = - 49
4) - 7 x- 4 = 28
5) - 18/- 6 = 3
6) 9/- 9 = - 1
7) - 48/6 = - 8
8) - 16 x - 4 = 64
9) 90/- 10 = - 9
10) 7 x - 6 = - 42
11) - 12 x - 7 = 84
12) - 72/- 8 = 9
13) 88/-8 = - 11
14) - 6/-6 = 1
15) 4 x - 7 = - 28
How many years did it take to earn $406.25 in interest given a principal of $650 and a simple interest rate of 2.5%?
Answers
Solution
For this case we can use the following formula:
A = P(1+rt)
And the interest is given by
I = Prt
And replacing we got:
406.25 = 650 * 0.025*t
And solving for t we got:
[tex]t=\frac{406.25}{650\cdot0.025}=25[/tex]And then the final answer is:
25 years
Equation attached Select all that apply1. Vertex:(4,-1)2.y-intercept (0,-17)3. X-intercept (5,0)4. Axis of symmetry:x=45.x-intercept (3,0)6. No x-intercepts
Answers
To answer this question we will use the graphical method.
The graph of f(x) is:
Therefore:
a) The vertex of the given parabola is (4,-1).
b) Its y-intercept is (0,-17).
c) Its axis of symmetry is at x=4.
d) The parabola has no x-intercepts.
Answer: Options 1, 2, 4, and 6.
Find the measure of angle x. Round to the nearest minute. X=___ ___a= 64° 16°
Answers
ANSWER:
25° 44'
STEP-BY-STEP EXPLANATION:
we know that the sum of x and a is equal to 90°, now we convert the minutes into decimals knowing that 60 minutes is equal to 1 degree, therefore:
[tex]\begin{gathered} \frac{16}{60}=0.266 \\ \\ 64.266+x=90 \\ \\ x=90-64.266 \\ \\ x=25.734 \end{gathered}[/tex]Now, we convert in minutes and we would have:
[tex]\begin{gathered} 0.734\cdot60=44 \\ \\ \text{ therefore:} \\ \\ x=25\degree44^{\prime} \end{gathered}[/tex]The value of x is 25° 44'
This probability distribution shows thedistribution for a Geometrytypical grade distributioncourse with 35 students.GradeABCD FFrequency510153 2Find the probability that a student earns agrade of D or F.p=[?
Answers
We are given a table of frequencies of each grade. To calculate the probabilities, we simply divide the reported number by the total number of students (35). So we have the table
Grade Pr(Grade)
A 5/35
B 10/35
C 15/35
D 3/35
F 2/35
As we want to calculate the probability that the student earns a grade D or a F, we simply add the probabilities of each grade. That is
[tex]Pr(D\text{ or F\rparen=Pr\lparen D\rparen+Pr\lparen F\rparen = }\frac{3}{35}+\frac{2}{35}=\frac{5}{35}=\frac{1}{7}[/tex]we also have that
[tex]\frac{1}{7}=0.142857143[/tex]which rounded to the nearest hundredth is 0.14. So the probability that a student earns a grade of D or F is 0.14
Write the equation of the line perpendicular to y = 5x + 1 that passes through the point (3,-1).
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What is the answer to 354x+-34(x)
Answers
Answer
320x
Explanation
We are asked to solve the expression
354x + (-34x)
Noting that,
plus × minus = minus
The expression becomes
354x + (-34x)
= 354x - 34x
= 320x
Hope this Helps!!!
[tex]354x+(-34x)[/tex]
Combine Like terms:
[tex](354x+-34x)[/tex]
[tex]=320x[/tex]
Hope this helps!
Please help A family has two cars. During one particular week, the first car consumed 40 gallons of gas and the second consumed 15 gallons of gas. The two cars drove acombined total of 1975 miles, and the sum of their fuel efficiencies was 65 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Answers
Let's define the following variables.
x = fuel efficiency of Car 1
y = fuel efficiency of Car 2
Therefore, 40x + 15y = a total of 1975 miles.
Another given data is that the sum of the fuel efficiency of the two cars is 65 miles per gallon, therefore, x + y = 65.
We now have two equations:
1. 40x + 15y = 1975
2. x + y = 65
To solve for x and y, let's use the substitution method. Let's equation the second equation into y. So, equation 2 becomes y = 65 - x. Using this, we'll substitute the value of y in the first equation,
[tex]\begin{gathered} 40x+15y=1975 \\ 40x+15(65-x)=1975 \\ 40x+975-15x=1975 \\ 40x-15x=1975-975 \\ 25x=1000 \\ \frac{25x}{25}=\frac{1000}{25} \\ x=40 \end{gathered}[/tex]Therefore, the fuel efficiency of Car 1 is 40 miles per gallon.
Since we now have the value of x, let's solve for the value of y.
[tex]\begin{gathered} y=65-x \\ y=65-40 \\ y=25 \end{gathered}[/tex]Therefore, the fuel efficiency of Car 2 is 25 miles per gallon.
Determine whether the given ordered pair is a solution to the system of equations. 6x−2y =34−3x+3y =15 and (11,16) ____Yes, it is a solution.____ No, it is not a solution.
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Given:
[tex]\begin{gathered} 6x-2y=34\ldots\ldots\ldots\text{.}\mathrm{}(1) \\ -3x+3y=15\ldots\ldots\ldots\text{.}(2) \end{gathered}[/tex]Sol:.
Mutiply by 2 in equation (2) then.
[tex]\begin{gathered} -3x+3y=15 \\ 2(-3x+3y)=2\times15 \\ -6x+6y=30 \end{gathered}[/tex]Add both equation then:
[tex]\begin{gathered} 6x-2y=34 \\ -6x+6y=30 \\ \text{Add both equation:} \\ 6x-2y+(-6x)+6y=34+30 \\ 6x-6x+6y-2y=34+30 \\ 6y-2y=64 \\ 4y=64 \\ y=\frac{64}{4} \\ y=16 \end{gathered}[/tex]Put the value of y for find the value od "x"
[tex]\begin{gathered} 6x-2y=34 \\ y=16 \\ 6x-2(16)=34 \\ 6x-32=34 \\ 6x=34+32 \\ 6x=66 \\ x=\frac{66}{6} \\ x=11 \end{gathered}[/tex]So the value of "x" is 11 and value of "y" is 16 then:
[tex]\text{solution =(11,16)}[/tex]Using the GCF factor the given expression: 4m - 204(m - 5)2(2m - 10)4(m - 20)2(2m - 20)
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Given:
The given expression: 4m - 20
Required:
Using the GCF factor the expression.
Explanation:
We will solve as:
[tex]\begin{gathered} 4(m-5)=4m-4(5)=4m-20 \\ 2(2m-10)=4m-2(10)=4m-20 \end{gathered}[/tex]Answer:
Hence, first and second is true.
Solve the following system of linear equations.3x – 2y +z = 124x – 3y - 5z = 114x + 3y + 3z = - 5-=AnswerX =y =z =
Answers
given
3x-2y+z=12 , 4x-3y-5z=11 , 4x+3y+3z=-5
3x-2y+z=12
3x=12-z+2y
x=(12-z+2y)/3 ....................(1)
4x-3y-5z=11
put the value of x in the above equation
4((12-z+2y)/3)-3y-5z=11
48-4z+8y-9y-15z=33
-19z-y=33-48
-19z-y=-15
-y=-15+19z
y=15-19z .....................(2)
4x+3y+3z=-5
put value of x and y in the given equation
[tex]\begin{gathered} 4(\frac{12-z+2(15-19z)}{3})+3(15-19z)+3z=-5 \\ 4(\frac{12-z+30+38z}{3})+45-5z+3z=-5 \\ 48-4z+120+152z+135-15z+9z=-15 \end{gathered}[/tex][tex]303+142z=-15[/tex]142z=288
z=2.02
put the value of z in equation in equation (2)
y=15-19*2.02
y=-23.38
put the value of value of y and z in equation (1)
[tex]\begin{gathered} x=(\frac{12-2.02+2\times-23.38}{3}) \\ =\frac{-36.78}{3} \\ =12.26 \end{gathered}[/tex]x=12.26
MEAN the mean A of two numbers, x and y, is given by A=x+y/2, solve for Y
Answers
- According to the Subtraction property of equalily, if:
[tex]a=b[/tex]Then:
[tex]a-c=b-c[/tex]- The Multiplication property of equality states that, if:
[tex]a=b[/tex]Then:
[tex]a\cdot c=b\cdot c[/tex]For this case, you have the following equation:
[tex]A=\frac{x+y}{2}[/tex]So, in order to solve for "y", you can follow these steps:
1. Apply the Multiplication property of equality by multiplying both sides of the equation by 2:
[tex]\begin{gathered} A(2)=(\frac{x+y}{2})(2) \\ \\ 2A=x+y \end{gathered}[/tex]2. Apply the Subtraction property of equality by subtracting "x" from both sides of the equation:
[tex]\begin{gathered} 2A-(x)=x+y-(x) \\ 2A-x=y \end{gathered}[/tex]Then, the answer is:
[tex]y=2A-x[/tex]Please help me solve it I’ve tried it many times and the answer is wrong the yellow is what I tried
Answers
Your solutions are correct: x= 3/2 or -8
Try writting the answer as: x=1.5 or -8
A textbook search committee is considering 18 books for possible adoption. The committee has decided to select 5 of the 18 for further consideration. In how many ways can it do so?
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In order to select 5 books from the 18 possible, we use combinations because the order, in this case, won't matter, this means that
[tex]\text{abcde}=\text{cbaed}[/tex]then, by definition
[tex]\text{nCr}=\frac{n!}{r!(n-r)!}[/tex]then,
[tex]\begin{gathered} 18C5=\frac{18!}{5!13!} \\ 18C5=\frac{18\cdot17\cdot16\cdot15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{5\cdot4\cdot3\cdot2\cdot1\cdot13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1} \\ 18C5=\frac{18\cdot17\cdot16\cdot15\cdot14}{5\cdot4\cdot3\cdot2\cdot1}=\frac{1028160}{120} \\ 18C5=8568 \end{gathered}[/tex]An inscribed angle with a diameter as a side has measure x. If the ratio of mAD to mDB is 1:5, what is mDB? (Round to the nearest tenth if necessary.) B mDB is
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_________________________________
m AD : m DB = 1:5
that means mDB= 5 mAD
This is a right triangle so then, using the Pythagorean theorem
(5 mAD)^2 = mAB^2 + mAD^2
mAB = x (the diameter)
___________________
(5 mAD)^2 = x^2 + mAD^2
25 mAD^2 - mAD^2 = x^2
24 mAD^2 = x^2
mAD= √ (x^2/ 24)
mAD= x / (2√6 )
mAD= x √6/ 12
________________
Answer
mDB= 5 (√6/ 12)* x
[tex]mDB=\frac{5\sqrt[]{6}}{12}x[/tex]_______________________________________________
Do you have any questions regarding the solution?