Using it's concept, it is found that the probability that the first three balls are drawn out of the box alternated in colour is of 0.1541 = 15.41%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering the situation described, the ways that alternate colored balls can be taken, and their probabilities, are given as follows:
R(5/8) - W(3/9) - R(5/11).W(3/8) - R(5/10) - W(5/11).Hence the probability is given by:
[tex]p = \frac{5}{11} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex]
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A school is watching students as they enter the football game for students who are dressed
inappropriately. they estimate that 7% of all students are dressed inappropriately. out of a group
of 40 students, what is the probability that exactly 2 are dressed inappropriately? round to 3 decimal places.
Using the binomial distribution, it is found that there is a 0.242 = 24.2% probability that exactly 2 are dressed inappropriately.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 40, p = 0.07.
The probability that exactly 2 are dressed inappropriately is given by P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{40,2}.(0.07)^{2}.(0.93)^{38} = 0.242[/tex]
0.242 = 24.2% probability that exactly 2 are dressed inappropriately.
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If y varies inversely as x, and y = 58 when x = 9, find y when x = 261.
Answer:
2
Step-by-step explanation:
y=k/x
58=k/9
k=58×9
k=522
y=522/x
when x=261
y=522/261
y=2
The vertical line test can be used to determine the given relation/graph is a
What was k? 200 400 600
Answer:
pls yo give the full question
An ongoing promotion at a department store gives customers 20\%20%20, percent off the portion of their bill that is over \$100$100dollar sign, 100. Ruby's total bill at the department store after the promotion has been applied is \$250$250dollar sign, 250. If xxx represents the amount of money Ruby would have spent on the same purchase at the department store without the promotion, which of the following equations best models the situation?
The equation best models the situation 100 + 0.8(x - 100) = 250.
The correct option is (D)
What is equation?
An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.
The complete question is:
An ongoing promotion at a department store gives customers 20% off the portion of their bill that is over $100. Ruby's total bill at the department store after the promotion has been applied is $250. If x represents the amount of money Ruby would have spent on the same purchase at the department store without the promotion, which of the following equations best models the situation?
A. 0.2x + 100 = 250
B. 0.8x + 100 = 250
C. 100 + 0.2(x - 100) = 250
D. 100 + 0.8(x - 100) = 250
Given:
Department store gives 20 % off the portion of the bill that is over 100 dollars.
Total bill = 250
let x is the amount of money she would have spent without the promotion.
Then, cost after discount applies = 0.8 ( x - 100 ).
Hence, the equation is 100 + 0.8 (x - 100) = 250.
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Peter's garden is in the shape of a rectangle whose width is 15 inches and length is twice the width. Find the area of the garden.
Answer:
450 in^2
Step-by-step explanation:
Width = 15 Length is twice as much = 30 in
Area = L * W = 15 * 30 = 450 in^2
can anyone give me answer for this question -
[tex] \frac{ {3}^{6} \times {5}^{3} }{ {9}^{2} \times {5}^{2} } \\ \\ \frac{ {3}^{6} \times {5}^{3 - 2} }{ {3}^{4} } \\ \\ {3}^{6 - 4} \times {5}^{1} \\ \\ {3}^{2} \times 5 \\ \\ 9 \times 5 \\ \\ 45.[/tex]
The first term of an arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the last term is 81.
Answer:
n = 53
Step-by-step explanation:
the sum to n terms of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 3 and a₅ = 9 , then
3 + 4d = 9 ( subtract 3 from both sides )
4d = 6 ( divide both sides by 4 )
d = 1.5
then solving for n
3 + 1.5(n - 1) = 81 ( subtract 3 from both sides )
1.5(n - 1) = 78 ( divide both sides by 1.5 )
n - 1 = 52 ( add 1 to both sides )
n = 53
there are 53 terms in the progression
Answer:
53 terms
Step-by-step explanation:
Finding common difference :
a = 3a + 4d = 94d = 6d = 1.5Solving :
a_{n} = a + (n - 1)d81 = 3 + 1.5n - 1.579.5 = 1.5nn = 533 connecting lines are shown. Line D F is horizontal. Line D E is about half the length of line D F. Line F E is about one-third of the length of line D F.
Which inequality explains why these three segments cannot be used to construct a triangle?
EF + FD > DE
ED + EF < DF
ED + EF > DF
EF + FD < DE
Answer:
ED + EF < DF
Step-by-step explanation:
shorter side lengths added together > larger side length
however, smaller side lengths are < larger
So ED + ED < DF means that this cannot be a triangle
Answer:
ED + EF < DF
(second option listed)
Step-by-step explanation:
for a triangle, the sum of the two shorter side lengths must be greater than the larger side length
so we know that the two smaller lengths (DE and FE) would have to add up to be greater than the larger side length (DF)
because this is not the case, we know that we cannot construct a triangle
[to construct a triangle:]
smaller + smaller > bigger
DE + FE > DF; which is false/not the case
so because DE + FE < DF, we cannot form a triangle
so, ED + EF < DF explains why these three segments cannot construct a triangle
How many cubes are needed to build this figure?
4
6
5
3
Answer:
3
Step-by-step explanation:
because I sense three and You need
1/5 divided by 4 equals to what
Answer:
1/5 divided by 4 equals to 0.05
answer both questions please
Answer: The two imaginary solutions with rational coefficients are +/- 4i and the two imaginary solutions with irrational coefficients are +/- 1.414213562i.
Step-by-step explanation:
I would recommend using pascal's triangle to solve this problem.
*Note: This is more of a quick answer, I can show a detailed step-by-step procedure if you need, just comment.
The circle graph shows the results of a survey of registered voters the day of an election.
The error given in the graph means that the actual percentage could be 2% more or 2% less than the parent reported by the survey.
What are the minimum and maximum percentages of voters who could vote Republicans? Green?
How can you use absolute value equations to represent your answers in part (a)?
One candidate receives 44% of the vote, Which party does the candidate belong to? Explain.
The minimum and maximum percentages of voters who could vote Republicans are 40% and 44% respectively, while Green are 0% and 4%
The minimum and maximum percentages of voters in Republicans? Green?The attached circle graph represents the missing information in the question.
From the graph, we have:
Republicans = 42%
Green = 2%
The actual percentage is given as: ±2%
So, we have:
Republicans = 42% ± 2% = (40%, 44%)
Green = 2% ± 2% = (0%, 4%)
Hence, the minimum and maximum percentages of voters who could vote Republicans are 40% and 44% respectively, while Green are 0% and 4%
The absolute value equations of part (a)?We have:
The actual percentage is given as: ±2%
Let the number of votes be on the circle graph be x and the range be y.
So, we have:
y - x = ±2%
Express as absolute value equation
|y - x| = 2%
For Republicans, we have:
|y - 42%| = 2%
For Green, we have:
|y - 2%| = 2%
Hence, the absolute value equations are |y - 42%| = 2% and |y - 2%| = 2%
The party of candidate that receives 44% voteIn (a), we have:
Republicans = 42% ± 2% = (40%, 44%)
Hence, the party of candidate that receives 44% vote is Republican
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PLEASE HELP ASAP
The file is attached
The trigonometric function for an angle [tex]\dfrac{\pi}{4}[/tex] is
[tex]tan\theta =1\ \ \ \ Cos \theta=\dfrac{\sqrt{2}}{2}\ \ \ \ Sin\theta = \dfrac{\sqrt{2}}{2}[/tex]
The trigonometric function for an angle [tex]\dfrac{\pi}{6}[/tex] will be:-
[tex]tan\theta = \dfrac{1}{\sqrt3}}\ \ \ \ \ Sin\theta = \dfrac{1}{2} \ \ \ \ \ Cos \theta = \dfrac{\sqrt{3}}{2}[/tex]
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
The trigonometric function for an angle [tex]\dfrac{\pi}{4}[/tex] is
[tex]tan\theta = tan\dfrac{\pi}{4}=1\ \ \ \ Cos \theta=Cos\dfrac{\pi}{4}=\dfrac{\sqrt{2}}{2}\ \ \ \ Sin\theta =Sin\dfrac{\pi}{4}= \dfrac{\sqrt{2}}{2}[/tex]
The trigonometric function for an angle [tex]\dfrac{\pi}{6}[/tex] will be:-
[tex]tan\theta=tan \dfrac{\pi}{6}= \dfrac{1}{\sqrt3}}\ \ \ \ \ Sin\theta =Sin\dfrac{\pi}{6}= \dfrac{1}{2} \ \ \ \ \ Cos \theta = Cos\dfrac{\pi}{6}= \dfrac{\sqrt{3}}{2}[/tex]
Therefore the trigonometric function for an angle [tex]\dfrac{\pi}{4}[/tex] is
[tex]tan\theta =1\ \ \ \ Cos \theta=\dfrac{\sqrt{2}}{2}\ \ \ \ Sin\theta = \dfrac{\sqrt{2}}{2}[/tex]
The trigonometric function for an angle [tex]\dfrac{\pi}{6}[/tex] will be:-
[tex]tan\theta = \dfrac{1}{\sqrt3}}\ \ \ \ \ Sin\theta = \dfrac{1}{2} \ \ \ \ \ Cos \theta = \dfrac{\sqrt{3}}{2}[/tex]
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Consider the graph of the function f(x) = 25
-10-8-6-4-2
10
8-
6-
4
2
02 4 6 8 10
2
-4
6
-8
-10
Which statement describes a key feature of function gif 9(a) = 2f(x)?
Considering it's horizontal asymptote, the statement describes a key feature of function g(x) = 2f(x) is given by:
Horizontal asymptote at y = 0.
What are the horizontal asymptotes of a function?They are the limits of the function as x goes to negative and positive infinity, as long as these values are not infinity.
Researching this problem on the internet, the functions are given as follows:
[tex]f(x) = 2^x[/tex].[tex]g(x) = 2f(x) = 2(2)^x[/tex]The limits are given as follows:
[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 2(2)^x = \frac{2}{2^{\infty}} = 0[/tex]
[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 2(2)^x = 2(2)^{\infty} = \infty[/tex]
Hence, the correct statement is:
Horizontal asymptote at y = 0.
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angle A and angle B are a linear pair. If measure of angle A = 4x-10 and measure of angle B = 3x+43, find the measure of angle A and measure of angle B
Answer:
See below ~
Step-by-step explanation:
Linear pairs add up to 180 degrees.
⇒ 4x - 10 + 3x + 43 = 180
⇒ 7x + 33 = 180
⇒ 7x = 147
⇒ x = 21
∠A = 4(21) - 10
∠A = 84 - 10
∠A = 74°
∠B = 3(21) + 43
∠B = 63 + 43
∠B = 106°
What is the sum of the polynomials?
(7x³-4x²) + (2x³-4x²)
5x³
9x3
O5x³-8x²
O9x³8x²
[tex](7 {x}^{3} - 4 {x}^{2} ) + (2 {x}^{3} - 4 {x}^{2} ) \\ 7x ^{3} - 4 {x}^{2} + 2 {x}^{3} - 4 {x}^{2} \\ 7 {x}^{3} + 2 {x}^{3} - 4 {x}^{2} - 4 {x}^{2} \\ 9 {x}^{3} - 8 {x}^{2} [/tex]
PLEASE GIVE BRAINLIEST
Therefore , the solution of the given problem of equation comes out to be 9x³ - 8x².
What is the equation?A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra.
Here, we have,
Polynomial function total
Polynomial functions are those that have a leading degree of three or higher. given the total;
(7x^3-4x^2)+(2x^3-4x^2)
Expand => (7x 3-4 times) + (2x 3-4 times)
= > 7x^3-4x^2 + 2x^3-4x^2
assemble similar terms
=> 7x^3 + 2x^3 - 4x^2 -4x^2
=> 9x^3 - 8x^2
Therefore , the solution of the given problem of equation comes out to be 9x³ - 8x².
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given triangle PQR with QR = 8, PQ = 6, and m p = 90 degrees, which of the following choices is used to determine m r
The value of the angle R in the right triangle PQR is sin⁻¹ 6 / 8
The situation forms a right angle triangle.
How to find an angle in a right triangle?The angle R can be found as follows:
using trigonometric ratios,
sin R = opposite / hypotenuse
Therefore,
opposite sides = 6
hypotenuse = 8
sin R = 6 / 8
R = sin⁻¹ 6 / 8
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The graph of a function f(x) is shown. What is the value of x where f(x) = -5? And f(0)?
Answer:
x = -3 when f(x) = -5
f(0) = 3
Step-by-step explanation:
When f(x) = -5, that means they have told you the y value. When y = -5, x = -3.
If the number is in the parentheses of the function, they are giving you the x value. When x = 0, y = 3
A triangle has two sides of lengths 10 and 14 what value could the length of the third side be
Answer:
17.20465053
Step-by-step explanation:
17.20465053 or
17.2 (to 1 dp)
Answer:
Third side has to be greater than 4 and less than 24.
Step-by-step explanation:
A triangle is valid if the sum of two sides is greater than the third side. That has to be the case for each of the sides. So let the sides of triangle be a, b and c.
a + b > c
a + c > b
b + c > a
Given:
a = 10
b = 14
We are looking for the third side, c.
First inequality:
a + b > c
10 + 14 > c
24 > c
This tells us that c has to be less than 24.
Second inequality:
a + c > b
c > b - a
c > 14 - 10
c > 4
This tells us that c has to be grater than 4.
Third inequality:
b + c > a
c > a - b
c > 10 - 14
c > -4
This tells us that c has to be greater than -4. But we also know that c has to be greater than 4, so we take 4 as the minimal value for c.
Final answer:
4 < c < 24
Third side has to be greater than 4 and less than 24.
[tex]2^{x^2-5x}=\frac{1}{64}[/tex]
Answer:
2, 3
Step-by-step explanation:
See attached images for work.
Choose the function whose graph is given below.
The graph represents the trigonometric function y = cotx option (C) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have shown a trigonometric graph in the picture.
As we know:
At x = 0
tan0 = 0
But cotx at x = 0 does not defined.
The csc x and sec x are the reciprocal of sinx and cosx and the sinx and cos have a sinusoidal graph.
Thus, the graph represents the trigonometric function y = cotx option (C) is correct.
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The number of gallons of gas Connie’s car, g, uses is directly proportional with the number of miles she drives, m. Last week, she drove 469.8 miles and used 14.5 gallons of gas. Which equation would best represent the problem?
The equation which represent the problem is 14.5 = 469.8k.
What is Equation?An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.
Here, As given in question
The number of gallons of gas Connie’s car, g, uses is directly proportional with the number of miles she drives, m.
g α m
g = km ............(i)
g = 14.5 gallons of gas m = 469.8 miles
14.5 = k X 469.8
14.5 = 469.8k
Thus, the equation which represent the problem is 14.5 = 469.8k.
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the roots of x+1/x=3 are: (x not equal to 0)
Answer:
x^2-2x-3
Step-by-step explanation:
(x+1)(x-3)
x(x-3)+1(x-3)
The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 240 bacteria, and the population after 9 hours is double the population after 1 hour. How many bacteria will there be after 4 hours? (Round your answer to the nearest whole number.)
Answer:
339
Step-by-step explanation:
Exponential Function
General form of an exponential function: [tex]y=ab^x[/tex]
where:
a is the initial value (y-intercept)b is the base (growth/decay factor) in decimal formx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
Given information:
a = 240 (initial population of bacteria)x = time (in hours)y = population of bacteriaTherefore: [tex]y=240b^x[/tex]
To find an expression for the population after 1 hour, substitute x = 1 into the found equation:
[tex]\implies y=240b^1[/tex]
[tex]\implies y=240b[/tex]
We are told that the population after 9 hours is double the population after 1 hour. Therefore, make y equal to twice the found expression for the population after 1 hour, let x = 9, then solve for b:
[tex]\implies 2(240b)=240b^9[/tex]
[tex]\implies 480b=240b^9[/tex]
[tex]\implies 480=240b^8[/tex]
[tex]\implies 2=b^8[/tex]
[tex]\implies b=\sqrt[8]{2}[/tex]
[tex]\implies b=2^{\frac{1}{8}}[/tex]
Therefore, the final exponential equation modelling the given scenario is:
[tex]\implies y=240(2^{\frac{1}{8}})^x[/tex]
[tex]\implies y=240(2)^{\frac{1}{8}x}[/tex]
To find how many bacteria there will be after 4 hours, substitute x = 4 into the found equation:
[tex]\implies y=240(2)^{\frac{1}{8}(4)}[/tex]
[tex]\implies y=240(2)^{\frac{1}{2}}[/tex]
[tex]\implies y=339 \:\: \sf (nearest\:whole\:number)[/tex]
Therefore, there will be 339 bacteria (rounded to the nearest whole number) after 4 hours.
Indigo earned a grade of 93% on her multiple choice history final that had a total of
200 problems. How many problems on the final exam did Indigo answer correctly?
Answer:
186
Step-by-step explanation:
x/200 = 0.93
x = 200(0.93)
x = 186
The number of problems that Indigo did answer correctly in the final exam is 186.
Given that:
Indigo earned a grade of 93% on her multiple-choice history final which had a total of 200 problems.
Total number of problems = 200
So, 100% grade = 200 problems
Let x be the number of problems which is answered correctly to get 93%.
Using the proportional concept,
[tex]\frac{x}{200} =\frac{93}{100}[/tex]
Cross multiply,
100x = 93 × 200
Dividing whole by 100,
x = 93 × 2
x = 186
Hence, the number of problems that are answered correctly is 186.
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It took for 4 butterflies to give birth to 4 larvae. how many larvae would 12 butterflies give birth to in 12 days
12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
It took 4 days for 4 butterflies to give birth to 4 larvae. After 4 days, each butterfly produces a larvae
Hence for 12 butterflies in 12 days:
number of larvae = 12 butterflies * (12 days /4 days per larvae) = 36 larvae
12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.
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Peter uses the equation y = StartFraction 13 over 4 EndFraction x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by Peter’s equation?
The statement C is true about the proportional relationship that is modeled by Peter’s equation. Peter walks at a rate of 13/4 miles per hour.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
The complete question is
"Peter uses the equation Y=13/4x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by the peat there's the equation?
A: Peter walks a rate of 4/13 miles per hour.
B: Peter walks at a rate of 4 miles per hour.
C: Peter walks at a rate of 13/4 miles per hour.
D: Peter walks at a rate of 13 miles per hour."
Given equation;
Y=13/4x
Where,
y represents the number of miles
x is the time period
The equation shows Peter walks at a rate of 13/4 miles per hour.
Hence statement C is true about the proportional relationship that is modeled by Peter’s equation.
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You work for a lending institution and are tasked with whether or not to approve a home loan, using the standard 28/36 ratio. the loan application is for $230,000. you see that the applicant has an annual salary of $83,000. the applicant also has a car payment of $315, a student loan of $140 and a boat loan of $96. how likely are you to approve the loan? a. very likely; recurring debt is considerably less than what is allowed. b. somewhat likely; recurring debt is very close to what is allowed. c. not likely; recurring debt is higher than what is allowed. d. there is not enough information given to determine the answer.
You work for a lending institution and are tasked with whether or not to approve a home loan, its Somewhat likely; that recurring debt is very close to what is allowed. Option B.
What is recurring debt?Generally, any payment that is utilized to repay debt obligations that occur on a continuous basis is said to be recurrent debt.
In conclusion, Recurring debt consists of payments that cannot be readily canceled at the request of the payer. Examples of this kind of debt include alimony, child support, and loan installments.
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Answer:
its B
Step-by-step explanation:
Hey I need to point of rotation for this question. Need the answer asap :)
Answer:
see explanation
Step-by-step explanation:
the vertices of S under the translation [tex]\left[\begin{array}{ccc}0\\-3\\\end{array}\right][/tex] are
(2, 3 ) → (2, 0 )
(6, 3 ) → (6, 0 )
(4, 5 ) → (4, 2 )
Under an anticlockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) then the above coordinates become
(2, 0 ) → (0, 2 )
(6, 0 ) → (0, 6 )
(4, 2 ) → (- 2, 4 )
which are the coordinates of the vertices of the image T
then the rotation is 90° anticlockwise about the origin , point (0, 0 )
Answer:
Below
Step-by-step explanation:
the vertices of S under the translation are
(2, 3 ) → (2, 0 )
(6, 3 ) → (6, 0 )
(4, 5 ) → (4, 2 )
Under an anticlockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) then the above coordinates become
(2, 0 ) → (0, 2 )
(6, 0 ) → (0, 6 )
(4, 2 ) → (- 2, 4 )
which are the coordinates of the vertices of the image T
then the rotation is 90° anticlockwise about the origin , point (0, 0 )