Answer:
0.5%
Step-by-step explanation:
A coin is tossed 10 times. given that the first 9 tosses were heads, find the percent chance of getting 10 heads in a row?
Answer:
1/2
Step-by-step explanation:
Assume the coin is a fair coin.
Since we already know that the first 9 tosses were heads, the probability of 9 straight heads in the first 9 tosses is 1.
It all depends on the last toss. There is an equal probability of heads and tails in a single toss of a fair coin.
p(heads) = 1/2
p(10 heads) = 1/2
Ok so the answer is 1/2
A boat sails on a bearing of 63 for 124 miles and then turns and sails 201 miles on a bearing of 192. Find the distance of the boat from its starting point.
The distance of the boat from its starting point is 156.226 .
According to the question
A boat sails on a bearing of 63 degree for 124 miles
i.e
By making 63 degree covers 124 miles
therefore ,
In figure below
AC = 124 miles
Then turns and sails 201 miles on a bearing of 192 degree
therefore ,
In figure below
CD = 201 miles
Now,
According to the sum of triangle
∠ACB + ∠ABC + ∠BAC = 180°
∠ACB + 90° + 63° = 180°
∠ACB = 27°
CE = 180° (Straight line )
therefore,
∠DCE = 192° - 180°
= 12°
As ∠C = 90°
therefore
∠ACD = ∠C - ∠DCE - ∠ACB
= 90° - 12°- 27 °
= 51°
Now,
The distance of the boat from its starting point = AD
By using Law of Cosines
As
The Law of Cosines can be used to find the unknown parts of an oblique triangle(non-right triangle), such that either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are given.
The Law of Cosines (also called the Cosine Rule) says:
c² = a² + b² − 2ab cos(C)
As we have 2 sides and one angle available we can use Law of Cosines
Therefore,
by substituting the value
(AD)² = (AC)² + (CD)² − 2(AC)(CD) cos(∠ACD)
(AD)² = (124)² + (201)² − 2*124*201 cos(51)
AD = 156.226
Hence, the distance of the boat from its starting point is 156.226 .
To know more about Law of Cosines here:
https://brainly.com/question/17289163
#SPJ4
On a map, point C is 4.3km due east of point B , and point B is 2.7km on a bearing of 143° from point A . Give your answer to 2 decimal places for the following. a Find how far east point B is from A. b Find how far east point C is from A. c Find how far south point C is from A
Based on the bearings of the direction and the distances given, the distance of point B from A is 1.62 km. Point C's distance from A is 5.92 km east and 2.16 km south.
How far are points B and C from A?To find the distance from point B to point A, the Cos function should be used.
Point A's distance from B can be found as:
= Cos (143 - 90) x distance from point A
= Cos (53°) x 2.7
= 1.62 km
The distance of C from A eastward is:
= 1.62 + 4.3
= 5.92 km
As C is southward from point A, the function to be used is the Sin function.
The distance southward of c from A is:
= Sin(53°) x 2.7
= 2.16 km
Find out more on calculating distance at https://brainly.com/question/14364020
#SPJ1
The volume of a pyramid that fits exactly inside a cube is 18 cubic feet. what is the volume of the cube? 6 cubic feet 18 cubic feet 54 cubic feet 72 cubic feet
The volume of the cube that perfectly fits an 18 ft³ pyramid is calculated as (C) 54 ft³.
What is a cube?A cube is a three-dimensional solid object with six square faces, facets, or sides, three of which meet at each vertex. The cube is one of the five Platonic solids and the only regular hexahedron. It has six faces, twelve edges, and eight vertices.To find the volume of the cube that perfectly fits an 18 ft³ pyramid:
We have been provided that:
18 cubic feet is the volume of the pyramid.Now, in order for this pyramid to fit exactly into a cube, the base of the pyramid must be square, and the height of the pyramid must be equal to the height of the cube.We can conclude from this that the volume of a cube equals three times the volume of a pyramid.So, the volume of the cube = 3 × 18The volume of Cube = 54 ft³Therefore, the volume of the cube that perfectly fits an 18 ft³ pyramid is calculated as (C) 54 ft³.
Know more about a cube here:
https://brainly.com/question/1972490
#SPJ4
The correct question is given below:
The volume of a pyramid that fits exactly inside a cube is 18 cubic feet. what is the volume of the cube?
(A) 6 cubic feet
(B) 18 cubic feet
(C) 54 cubic feet
(D) 72 cubic feet
he system of equations below has no solution.
StartLayout enlarged left-brace 1st row two-thirds x + five-halves y = 15 2nd row 4 x + 15 y = 12
Which equation could represent a linear combination of the system?
a linear combination can be:
(a + b)*(4x + 15y) = a*12 + b*15
How to solve the given system of equations:Here we have the system of equations:
(2/3)*x + (5/2)*y = 15
4x + 15y = 12
To solve the system of equations, we first need to isolate one of the variables in one of the equations, I will isolate x on the second equation.
4x = 12 - 15y
x = (12 - 15y)/4
Now we can replace that in the other equation:
(2/3)*x + (5/2)*y = 15
(2/3)* (12 - 15y)/4 + (5/2)*y = 15
Now we can solve that for y.
2 - (10/4)*y + (5/2)*y = 15
2 = 15
That is a false equation, then we conclude that the system of linear equations has no solutions.
This means that the two lines are parallel lines, then a linear combination can be:
(a + b)*(4x + 15y) = a*12 + b*15
Where a and b are two real numbers.
If you want to learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
Answer:Your answer is
There are no solutions.
Step-by-step explanation:Brainliest Please?
find the perimeter ( will mark u brainliest for right answer)
The perimeter of the triangle is 56.4 units.
How to find the perimeter of a triangle?The perimeter of the triangle can be found as follows:
The perimeter of a figure is the sum of the whole sides. Therefore, the perimeter of a triangle is the sum of the three sides.
perimeter of a triangle = x + y + z
where
x, y and z are the three sides of the triangle.Therefore,
perimeter of the triangle = 19.8 + (9.8 + 8.4) + (8.4 + (19.8 - 9.8))
perimeter of the triangle = 19.8 + 18.2 + 18.4
perimeter of the triangle = 56.4
perimeter of the triangle = 56.4 units
learn more on perimeter here: https://brainly.com/question/16950569
#SPJ1
Which expression is equivalent to the given expression?
Assume the denominator does not equal zero.
a^3b^5 / a^4b
A. b^4 / a
B. a / b^4
C. 1 / ab^4
D. ab^4
The expression which is equivalent to the given expression by means of evaluation using the laws of indices is; Choice A; b⁴/a.
Which of the answer choice represents an expression which is equivalent to the given expression?The given expression according to the task content is; a³b⁵/a⁴b.
It therefore follows from the laws of indices that each variable can be evaluated by means of their exponents as follows;
a^(3-4)b^(5-1)
Consequently we have;
b⁴/a.
Read more on equivalent expressions;
https://brainly.com/question/11352551
#SPJ1
Trigonometry Question
(ASAP PLEASE) Peter had some triangular tiles with sides 3 cm long. He placed them side by side to make a trapezium. If the perimeter of the trapezium was 27 cm, how many tiles did Peter use?
Answer:
She used 9 tiles which are 3 cm long
Step-by-step explanation:
cuz 3x9=27 and yea
Write the following in interval notation
x < 8
Answer:
Yup Yup
Step-by-step explanation:
yessah
Inequalities help us to compare two unequal expressions. The given inequality x<8 can be written in the interval notation as x=(-∞,8).
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways. They do not, however, intend to indicate any particular location. Instead, they serve as a concise approach to expressing an inequality or a set of inequalities.
The given inequality x<8 can be written in the interval notation as,
x = (-∞,8)
Hence, The given inequality x<8 can be written in the interval notation as x=(-∞,8).
Learn more about Inequality here:
https://brainly.com/question/19491153
#SPJ2
please help if u can! greatly appreciated
don't answer if u dont know PLEASE
a. log₈8 = 1
b. log₇6/5
c. log₉3¹
The solution to the problem are1. log₈ 2 * 4 would produce an integer
= log₈8 = 1
The output is an integer
2. log₇6/5 would give us an irrational number
= log₇1.2
This would give us an irrational number
3. log₉3¹ would give us a rational number
= log₉9^[tex]^\frac{1}{2}[/tex] = 1/2 log⁹9
= 1/2
Read more on rational numbers here: https://brainly.com/question/12088221
#SPJ1
Quick algebra 1 question for some points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]let \: the \: number \: be \: denoted \: by \: p \\ five \: times \: a \: number = 5p \\ square\: of \: a \: number = p {}^{2} [/tex]
[tex] \gamma - p {}^{2} = 5p - p {}^{2} [/tex]
What is the probability that a class of 50 has an average midterm mark that is less than 75?
The probability that a class of 50 has an average midterm mark that is less than 75 is value=0
Average is the mathematics mean, and is calculated by means of adding a group of numbers and then dividing with the aid of the count of these numbers. for instance, the average of 2, three, three, five, 7, and 10 is 30 divided with the aid of 6, that is five.
The common is described as the implied value that is identical to the ratio of the sum of the number of a given set of values to the whole wide variety of values gift within the set.
There are three primary sorts of common: imply, median, and mode. each of those techniques works slightly differently and frequency effects in barely specific regular values. The suggestion is the maximum normally used average. To get the suggested fee, you add up all of the values and divide this total by using the number of values.
The probability that a class of 50 has an average midterm mark that is less than 75
n = 50
P(<75)=P(Z<75)
P(Z<75−786√50)
P(Z<−3.5355)
We will look for the value in the StandardNormal able. We will get the value=0
Learn more about average here https://brainly.com/question/20118982
#SPJ4
one adult ticket for a school play costs 10 dollars and one student ticket costs 6 dollars. one evening,750 people attended the play and the total receipts were 6860. how many of each type of ticket were sold? A full algebraic solution is required.
The algebraic solution to the situation is as follows:
x + y = 750
10x + 6y = 6860
The number of adult and student are 590 and 160 respectively.
How to find and solve an algebraic equation?One adult ticket for a school play costs 10 dollars and one student ticket costs 6 dollars.
One evening,750 people attended the play and the total receipts were 6860.
Therefore,
let
x = number of adult ticket
y = number of student tickets
Therefore,
x + y = 750
10x + 6y = 6860
10x + 10y = 7500
10x + 6y = 6860
4y = 640
y = 640 / 4
y = 160
Hence,
x = 750 - y
x = 750 - 160
x = 590
learn more on algebraic expression here: https://brainly.com/question/14934521
#SPJ1
the x and y intercept
Answer:
Step-by-step explanation:
X-INTERCEPT
Plug y=0 into the equation and solve the resulting equation −6x=−7 for x.
The x-intercept:
[tex]\left(\frac{7}{6},0\right)\approx \left(1.16666666666667,0\right)[/tex]
Y-INTERCEPT
Plug x=0 into the equation and solve the resulting equation 3y=−7 for y.
The y-intercept:
[tex]\left(0, - \frac{7}{3}\right)\approx \left(0,-2.33333333333333\right)[/tex]
Answer:
[tex]x[/tex]-intercept = ([tex]-\frac{7}{6}[/tex] , 0)
[tex]y[/tex]-intercept = (0 , [tex]-\frac{7}{3}[/tex])
Step-by-step explanation:
[tex]6x + 3y = -7[/tex]
• The x-intercept is the point at which the line crosses the x-axis, that is, where y = 0.
∴ [tex]6x + 3(0) = -7[/tex]
⇒ [tex]6x = -7[/tex]
⇒ [tex]x = \bf -\frac{7}{6}[/tex]
∴ The x-intercept is at the point ([tex]-\frac{7}{6}[/tex] , 0).
• Similarly, the y-intercept is the point at which the line crosses the y-axis, that is, where x = 0.
∴ [tex]6(0) + 3y = -7[/tex]
⇒ [tex]3y = -7[/tex]
⇒ [tex]y = \bf - \frac{7}{3}[/tex]
∴ The y-intercept is at the point (0 , [tex]-\frac{7}{3}[/tex]).
Beth is going to enclose a rectangular area in back of her house. the house wall will form one of the four sides of the fenced in area, so beth will only need to construct three sides of fencing. beth has 48 feet of fencing. she wants to enclose the maximum possible area. what amount of fence should beth use for the side labeled x?
The maximum possible area would have a length of 24 feet and width of 12 feet.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let x represent the length and y represent the width, hence:
Since beth has 48 ft fencing and cover 3 sides, hence:
x + 2y = 48
x = 48 - 2y (1)
Also:
Area (A) = xy
A = (48 - 2y)y
A = 48y - 2y²
The maximum area is at A' = 0, hence:
A' = 48 - 4y
48 - 4y = 0
y = 12 feet
x = 48 - 2(12) = 24
The maximum possible area would have a length of 24 feet and width of 12 feet.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Consider the interval [2, 3) = {x € r : 2 <= x < 3}. Find the complement of this interval where the universal set is taken to be r, the set of real numbers.
The complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
According to the given question.
We have an interval [2, 3).
Let A = [2, 3)
Which is defined as
[2, 3) = {x ∈ r : 2 ≤ x < 3}
This means that the interval [2, 3) contains all the real numbers which are greater and equal to 2 and less than 3.
And, here it is also given that the universal set is r ( set of real numbers).
As we know that " the complement of an interval is a set A of real numbers that conatins all the elements of universal set U except the number that lying between the given two numbers in the inerval" i.e.
[tex]A^{c} = U - A[/tex]
Where,
[tex]A^{c}[/tex] is the complement of interval A
Thereofre, the complement of the given interval [2, 3) will be all the elements of universal set i.e real numbers except 2 and the real numbers which lies in between 2 and 3.
So, we can say that
[tex]A^{c} = (-\infty, 2) \cup(3, \infty)[/tex]
Where, [tex]A^{c}[/tex] is the complement of the interval A.
Hence, the complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
Find out more information about complement of an interval here:
https://brainly.com/question/13202631
#SPJ4
If these two shapes are similar, what is the measure of the missing length w 20 in 15 in 12 in
Answer:
Step-by-step explanation:
Please helpp with my math hw I’ll give brainlest
Answer:
20 percent
40 percent
20 percent
20(.008) percent
Step-by-step explanation:
6) 54 - 45 = 9
45 / 9 = 5
100 / 5 = 20
20 percent
7) 60 - 36 = 24
60 / 24 = 2.5
100 / 2.5 = 40
40 percent
8) 30 - 24 = 6
30 / 6 = 5
100 / 5 = 20
20 percent
9) 24.99 - 19.99 = 5
24.99 / 5 = 4.998
100 / 4.998 approx. = 20.008
20.008 percent (or rounded 20 percent)
Briefly describe each of the eight guidelines for evaluating statistical studies.
8 Guidelines for Critically Evaluating a Statistical Study
1. Identify the Goal, Population, and Type of Study
2. Consider the Source
3. Examine the Sampling Method
4. Look for Problems in Defining or Measuring the Variables of
Interest
5. Watch Out for Confounding Variables
6. Consider the Setting and Wording of Any Survey
7. Check That Results Are Fairly Represented in Graphics or
Concluding Statements
8. Stand Back and Consider the Conclusions
Learn more about Statistical Study here
https://brainly.com/question/16859876
#SPJ4
Evaluate the expressions. 32) 12+ 32÷3-6
Answer:
16.66666667
Step-by-step explanation:
=12+10.66666667-6
=22.66666667-6
=16.66666667
What is the sign of s^67/t^9 when s < 0 and t > 0?
possible answers:
. positive
. negative
. zero
Answer:
negative
Step-by-step explanation:
[tex]s^{67}<0 \\ \\ t^9>0 \\ \\ \implies \frac{s^{67}}{t^9}<0
[/tex]
Answer:
negativeStep-by-step explanation:
The sign of a product or quotient cannot be determined by the positive number (t), so we can ignore it. The sign of the expression will be negative if and only if there are an odd number of negative factors.
Here, there are 67 (an odd number) negative factors, so the expression will be negative.
- 5x - 5 = 3x + 19 what would X be?
-5x - 5 = 3x + 19
---Move the x's to one side
-5x - 3x - 5 = 3x - 3x + 19
-8x - 5 = 19
---Isolate the -8x by removing the -5 from the left side
-8x - 5 + 5 = 19 + 5
-8x = 24
---Divide both sides by -8 to get x by itself
x = -3
Hope this helps!
-5x-5= 3x+19
= > -5x-3x= 19+5
= > -8x= 24
= >-x=24/8
= >x= -3
What are the solutions of the system of equations y = –(x 2)2 1 and y = 4x 9? (–2, 1) and (6, –15) (–2, 1) and (–6, –15) (2, 1) and (6, –15) (2, 1) and (–6, –15)
The equations exist [tex]$y =-(x+2)^2+1[/tex] and [tex]y =4x+9[/tex] then the value of
x = -6, x = -2 and y = -15, y = 1.
How to solve the system of equations [tex]$y =-(x+2)^2+1[/tex] and
[tex]y =4x+9[/tex] ?
The given equations are [tex]$y =-(x+2)^2+1[/tex] and [tex]y =4x+9[/tex]
[tex]$-\left(x\:+\:2\right)^2\:+\:1\:=\:4x\:+\:9[/tex]
[tex]$-x^{2}-4 x-3=4 x+9[/tex]
Subtract 9 from both sides, we get
[tex]$-x^{2}-4 x-3-9=4 x+9-9[/tex]
Simplifying the equation, we get
[tex]$-x^{2}-4 x-12=4 x[/tex]
Subtract 4x from both sides
[tex]$-x^{2}-4 x-12-4 x=4 x-4 x[/tex]
[tex]$-x^{2}-8 x-12=0[/tex]
Solve with the quadratic formula
[tex]$x_{1,2}=\frac{-(-8) \pm \sqrt{(-8)^{2}-4(-1)(-12)}}{2(-1)}[/tex]
[tex]$\sqrt{(-8)^{2}-4(-1)(-12)}=4[/tex]
[tex]$x_{1,2}=\frac{-(-8) \pm 4}{2(-1)}[/tex]
Separate the solutions
[tex]$x_{1}=\frac{-(-8)+4}{2(-1)}, x_{2}=\frac{-(-8)-4}{2(-1)}[/tex]
[tex]$x=\frac{-(-8)+4}{2(-1)}=-6[/tex]
[tex]$x=\frac{-(-8)-4}{2(-1)}= \quad-2[/tex]
The solutions to the quadratic equation are x = -6, x = -2
From the above equation [tex]y =4x+9[/tex],
substitute the value of x, then we get
Put, x = -6 then y = 4(-6) + 9 = -15
Put, x = -2 then y = 4(-2) + 9 = 1
The system of equations exists (–2, 1) and (–6, –15).
Therefore, the correct answer is (–2, 1) and (–6, –15).
To learn more about quadratic equations refer to:
https://brainly.com/question/1214333
#SPJ4
Answer:
(–2, 1) and (–6, –15)
Step-by-step explanation:
flvs testing (i am not completely sure btw)
just substitute that into a last equations (seperatly if you understand=== -2 and 1 as x and y; -6 and -15 as x and y)
Worth 15 points!!!!!!!!!!!!!!
A and b are monomials where a = 125 and b = 27p12. what is the factored form of a – b?
The factored form of a - b is [tex]\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)[/tex].
What is monomial factorization ?A monomial is an expression that is the product of constant and non-negative integer powers of x, like [tex]3x^{2}[/tex]..
A monomial is expressed as a product of two or more other monomials when it is factored.
Here,
a = 125
[tex]$b=27 p^{12}$[/tex]
To find: a - b
a - b = 125 - [tex]27 p^{12}$[/tex]
a - b = [tex]5^{3}-\left(3 p^{4}\right)^{3}$[/tex]
We know that,
[tex]$x^{3}-y^{3}=(x-y)\left(x^{2}+x y+y^{2}\right)$[/tex]
Finding the factored form of a - b using this method:
[tex]$a - b=\left(5-3 p^{4}\right)\left(5^{2}+5\left(3 p^{4}\right)+\left(3 p^{4}\right)^{2}\right)$[/tex]
[tex]$a-b=\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex]
So, factored form of a - b is [tex]$\left(5-3 p^{4}\right)\left(25+15 p^{4}+9 p^{8}\right)$[/tex].
Learn more about monomial factorization here:
https://brainly.com/question/26278710
#SPJ4
The booster club sold 36,276 tickets on Friday, 34,012 tickets on Saturday, and 29,879 tickets on Sunday. If you were going to find out how many fewer tickets were sold on Sunday than Saturday, which operation would you perform?
Answer:subtraction
Step-by-step explanation: to find out how many fewer tickets were sold on Sunday you would need to subtract 34012 by 29879. The solution would be how many fewer tickets were sold on Sunday compared to Saturday.
please help with algebra 2 question! arithmetic sequence
erica is playing a card game with her friend marquis. her points are shown in the following table:
round 1: 30 pts
round 2: 42 pts
round 3: 58.8 pts
marquis’s points in each round are represented by the following sequence:
50, 75, 112.5,…
in the table below, determine whether each row applies to eeica’s points or marquis’s points. select erica, marquis, or neither option.
(answers attached in pic) pls help!
Answer:
neitherMarquisEricaMarquisStep-by-step explanation:
The matching of exponential functions to table values involves matching both initial values and rate of growth. The value of a geometric series can be calculated from its formula, or can be shown by a calculator or spreadsheet.
Function determinationThe starting values of the two sequences are different, as are all of the starting values of the answer choices. Matching starting values is sufficient to identify which sum goes with which player.
The series ...
[tex]\displaystyle S=\sum_{k=1}^n{AB^{k-1}}[/tex]
gives the sum of a geometric sequence with first term A and common ratio B.
The first term of Erica's series is A=30. The ratio is B=42/30 = 1.4.
The first term of Marquis's series is 50. The ratio is B=75/50 = 1.5.
Using these values in the series formula, the total score after n rounds will be ...
[tex]\displaystyle \text{Erica:}\quad \sum_{k=1}^n{30(1.4)^{k-1}}\qquad\text{matches Row 3}\\\\\text{Marquis:}\quad \sum_{k=1}^n{50(1.5)^{k-1}}\qquad\text{matches Row 2}[/tex]
Total scoreThe explicit expression for these sums is ...
[tex]S=A\dfrac{B^n-1}{B-1}[/tex]
Then the total scores after 6 rounds are ...
Erica: 30(1.4^6 -1)/0.4 = 489.7152
Marquis: 50(1.5^6 -1)/0.5 = 1039.0625 . . . . . matches row 4
TableThen the required table gets filled in ...
neitherMarquisEricaMarquis__
Additional comment
The values in the attached table are total scores after each round. One must subtract the previous round's total to find the points scored in a given round.
The purpose of showing totals is to permit matching the value seen in Row 4 of the table.
18 times the quantity g plus 5
Answer:
Step-by-step explanation:
Comment
The first thing you should notice once you have read it, is there is a plus sign required. That means you are likely to get a binomial (two different things that won't reduce or combined).
So what you get is
18*g + 5
Notice where the place sign is. It is between 18g and 5. The result cannot be simplified any further.
Answer
18g + 5
can someone help with this algebra problem?
Answer:
g(1) = 1
Step-by-step explanation:
Since 1 ≠ -2 and 1 ≠ -1
Then we must use the expression:
g(x) = x³ - x² + 1 ,to calculate g(1).
Therefore
g(1) = (1)³ - (1)² + 1
= 1 - 1 + 1
= 0 + 1
= 1