The probability that the balls drawn are red, green, and black in that order will be 3/78.
What will the probability be?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
The box contains 4 black balls, 7 red balls, and 3 green balls. The total number will be:
= 4 + 7 + 3
= 14 balls.
The probability that the balls drawn are red, green, and black in that order will be:
= P(red) × P(green) × P(black)
= 7/14 × 3/13 × 4/12
= 1/2 × 3/13 × 1/3
= 3/78
The probability is 3/78.
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If
you
invest $100 in an index fund that earns an average annual rate of
return of 12.3% compounded monthly. You make a regular monthly
contributions of $25, how much will your investment be worth in 52 years?
Answer Interest rate = 12.3%
The compound interest formula is given by:
Where
A = Future amount
P = Present amount (Principal amount)
r = Interest rate in decimal form
n = No. of times compounded per year
t = time in years.
We can say that if:
Present amount = P
Future amount = 3P
r = 12.3/100 = 0.123
n = 1
t = ?
Substitute the values in the formula of compound interest:
Taking log on both sides.
Round off to nearest option
t ≅ 9 years
Find the value of .
X
100°
Y
130°
x
66°
w
Z
The measure for angle W is 80 degree.
What is Trapezium?A unrestricted polygon or figure with four sides, four corners, and four angles is called a trapezium. Each brace of a trapezium's opposing sides is resemblant to the other.
Similar to other quadrilaterals, the trapezium's four angles add up to 360°. Two of the sides of a trapezium are parallel, and the other two are not. Regular trapezium diagonals cut each other in half.
Given:
We have angles <X= 100, <Y = 130 and <Z= 66.
As, we know that in Trapezium the sum of adjacent angle is 180.
So, <X + <W = 180
100 + <W =180
<W= 180- 100
<W = 80 degree.
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Tim wants to create a circle graph showing the number of physicians whose specialty is aerospace medicine. He knows the following information.53 male physicians are under 35 years of age. 8 female physicians are under 35 years of age. 155 male physicians are between 35 and 44 years of age. 17 female physicians are between 35 and 44 years of age. 145 male physicians are between 45 and 54 years of age. 10 female physicians are between 45 and 54 years of age. 98 male physicians are over 54 years of age. 2 female physicians are over 54 years of age. If he wants to include each of the eight groups in his graph, how many degrees would he use for the central angle of the "45-54 year-old Males" sector? Express your answer to the nearest whole number.
Answer:
107 :)
Step-by-step explanation:
In total there are 53+8+155+17+145+10+98+2=488 physicians of aerospace medicine. 45-54 year-old males account for 145/488 of this population, so they should account for that fraction of the central angle of the circle graph also. Since there are 360 degrees in the central angle to divide up among the groups, the 45-54 year-old male group should get 145/488 x 360 which rounds to about 107 degrees.
Write the inequality
The inequalities which the number lines represent are as follows;
x > 3x <= 2.While writing inequalities represented on a number line;
We must observe the direction of the line; and also observe the shading on the starting point of the line.
In case 1:
The set of x values are represented as greater than 3; Therefore, the inequality is; x > 3In case 2:
The set of value are represented as less or equal to 2;Therefore, the inequality is; x <= 2The number line to represent the street sign is as in the attached image;
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Express (8 - 3sqrt(2))/(4 + 3sqrt(2)) in the form of a + b * sqrt(2) where a and b are integers.
Answer: [tex]\boldsymbol{-25+18\sqrt{2}}[/tex]
The expression is in the form [tex]a+b\sqrt{2}[/tex] where a = -25 and b = 18
==========================================================
Work Shown:
Let [tex]x = 3\sqrt{2}[/tex] and then square both sides
[tex]x = 3\sqrt{2}\\\\x^2 = \left(3\sqrt{2}\right)^2\\\\x^2 = \left(3\right)^2*\left(\sqrt{2}\right)^2\\\\x^2 = 9*2\\\\x^2 = 18\\\\[/tex]
We'll use both x and x^2 later on.
---------------------
The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.
[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}}\\\\\frac{8-x}{4+x}\\\\\frac{(8-x)(4-x)}{(4+x)(4-x)}\\\\\frac{32-8x-4x+x^2}{16-x^2} \ \text{ difference of squares rule}\\\\\frac{32-12x+x^2}{16-x^2}\\\\[/tex]
[tex]\frac{32-12*3\sqrt{2}+18}{16-18} \ \text{ plug in } x = 3\sqrt{2} \text{ and } x^2 = 18\\\\\frac{50-36\sqrt{2}}{-2}\\\\\frac{-2(-25+18\sqrt{2})}{-2}\\\\\boldsymbol{-25+18\sqrt{2}}[/tex]
Therefore,
[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}}=\boldsymbol{-25+18\sqrt{2}}[/tex]
-------------------------------------
Checking the answer:
Use a calculator to find that,
[tex]\frac{8-3\sqrt{2}}{4+3\sqrt{2}} \approx 0.45584412271571 \\\\-25+18\sqrt{2} \approx 0.45584412271571[/tex]
We get the same decimal approximation, which helps confirm the correct answer.
Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.
Y=x+3 please helppppppppppol
Answer:
(-1, 2), (0,3), (1,4)
slope= 1
y-intercept= (0,3)
Step-by-step explanation:
Determine if the data below represents a function. Explain your reasoning. (3, 2), (4,7), (8, 12). (10, 15)
Answer:
the data that is shown represents a function
Step-by-step explanation:
the easiest way to know is by looking at the x-variable. Each y-variable needs one x-variable. the x-variable should not be seen paired with another y-variable.
Does anyone know how to solve this?
Which product is negative?
Answer:
it is (3/8)( -5/7)(-1/4)
if ot it should be the one that is all postitive
WILL GIVE BRAINLIEST
Answer:
It has no solution because, 14x cancels out -14x when you move the variables to the left and leaves the equation as 0 = -12, however we know that 0 does not equal -12 which means this solution is false; therefore this equation has no solution since 0 does not equal -12.
Step-by-step explanation:
5 - 4x - 7 - 10x = -8x - 4 - 6x - 10 (Given)
-2 - 14x = -14x - 14 (Combine like terms)
0 = -12 (Move variables(x) to the left and the constants to the right)
Learning Task 2 B. Perform the indicated operations. Write your solution in the box below. Add Subtract: 1. (5x4 - 3x2 + 4) + (6x3 - 4x2 - 7) 6. (5x3 - 7x2 + 3x - 4) -(873 + 2x2 32-7) 2.-7x3y + 4x2y2 - 2 and 4x3y + 1 - 8x2y2 7. (2x2y - 5xy + 3y2 -- (7xy -- 672 - 5729) 3. (5 + 24y3 - 7y2) + (-6y3 + 7y2 + 5) 8. (9x5 - 623 + 712) - (773 4. (2xs - 6x3 - 12x2 - 4) + (-11x + 8x + 2x2 + 6) 9. Subtract 4x3.5x - 8 from 672 - 3x + 8 5. (3y5 - 2y + y* + 2y3 + 5) and (238 + 3y8 + 2+ 7) 10. (1.599 + 4.8y2 + 12) - (ya - 1.742 + 2y) Solution and Answer 67 + 2x2) -
WARNING: I need any worker or student to be aware that there are alt accounts going around and posting gore on answers. Some of them have the picture of the devil and other disturbing types of images and things. Please be aware of your questions if you see these accounts. Ive just encountered one and I am not putting its username so others won't see his posts. Be careful and aware
Describe what is meant by the operation of division using the terms dividend , divisor , and quotient
Answer:
Dividend: Number on top
Divisor: Number on bottom
Quotient: Answer
Dividend ÷ Divisor = Quotient
use the quadratic formula to solve 4x²-9x=2x²-2x-4
[tex]4x^2-9x = 2x^2 -2x -4\\\\\implies 4x^2 -9x -2x ^2 +2x +4 =0\\\\\implies 2x^2 -7x +4=0\\\\\text{Apply quadratic formula,}~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}.\\\\\text{In this case,} ~a =2, b = -7 ~ \text{and}~ c =4\\\\\\x =\dfrac{-(-7) \pm \sqrt{(-7)^2 - 4 \cdot 2 \cdot 4}}{2(2)}\\\\\\\implies x = \dfrac{7 \pm \sqrt{17}}4\\\\\\\text{Hence,}~ x = \dfrac{7 +\sqrt{17}}4~ \text{and}~x = \dfrac{7 -\sqrt{17}}4[/tex]
Solve for x.
9x + 1 = 7x - 8x + 4
Therefore, the answer is 3/10.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Answer:
9x + 1 = 7x - 8x + 4
9x + 1 = -x + 4
9x + 1 - 1 = -x + 4 - 1
9x = -x + 3
9x + x = -x + 3 + x
10x = 3
x = 3/10
Apollo110Assume that police estimate that 30% of drivers do not wear their seatbelts. They set up a safety roadblock, stopping cars
to check for seatbelt use. They stop 40 cars during the first hour.
a. Find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts. Use the
fact that the mean of a geometric distribution is j = and the variance is 02 - 9
1
р
2
b. How many cars do they expect to stop before finding a driver whose seatbelt is not buckled?
=
물
...
The mean is
(Round to the nearest tenth as needed.)
The variance is
(Round to the nearest tenth as needed.)
The standard deviation is
(Do not round until the final answer. Then round to the nearest tenth as needed.)
They expect to stop cars before finding a driver whose seatbelt is not buckled.
(Round to the nearest tenth as needed.)
Using the binomial distribution, it is found that:
a)
The mean is of 12.The variance is of 8.4.The standard deviation is of 2.9.b) They expect to stop 3.3 cars before finding a driver whose seatbelt is not buckled.
For each driver, there are only two possible outcomes, either they wear their seatbelts, or they do not. The probability of a driver wearing their seatbelt is independent of any other driver, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The variance of the binomial distribution is:
[tex]V(X) = np(1-p)[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem:
30% of drivers do not wear their seatbelts, hence [tex]p = 0.3[/tex].They stop 40 cars during the first hour, hence [tex]n = 40[/tex].Item a:
[tex]E(X) = np = 40(0.3) = 12[/tex]
[tex]V(X) = np(1-p) = 40(0.3)(0.7) = 8.4[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{40(0.3)(0.7)} = 2.9[/tex]
Hence:
The mean is of 12.The variance is of 8.4.The standard deviation is of 2.9.Item b:
The number of trials until q successes of a binomial variable is modeled by a geometric distribution, with expected value given by:
[tex]E(X) = \frac{q}{p}[/tex]
In this problem, one success, hence [tex]q = 1[/tex] and:
[tex]E(X) = \frac{q}{p} = \frac{1}{0.3} = 3.3[/tex]
They expect to stop 3.3 cars before finding a driver whose seatbelt is not buckled.
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At the Shelby Ski Resort, it snowed
5 4/5 feet yesterday and 4 2/5 feet
today. How much more did it snow
yesterday than today?
Answer:
it would have snowed 1 2/5 feet more the previous day than the current day.
Find the inverse function.
2x + 5
f(x) =
=
4
I need help urgently
Answer:
y=2x-5/2
Step-by-step explanation:
f(x)=(2x+5)/4
y=(2x+5)/4
-----------------
x=(2y+5)/4
2y+5=4*x
2y+5=4x
2y=4x-5
y=4/2x-5/2
y=2x-5/2
Pencils are on sale for 25 for $1.25. Based on this rate, how much would one pencil cost?
Answer:
$0.05
Step-by-step explanation:
1.25/25=0.05
C is the midpoint of PQ, if P is (4,m) , C is (n,-1) and Q is (-2,4) then m & n respectively are
Given points are P(4,m) and Q(-2,4)
Let (x1, y1) = P(4,m)
Where, • x1 = 4 and • y1 = m
Let (x2, y2) = Q(-2,4)
Where, • x2 = -2 and • y2 = 4
We know that
The coordinates of the mod point of the linesegment joining the points (x1, y1) and (x2, y2)
is M(x,y) = ( {x1+x2}/2 , {y1+y2}/2 )
Mid point of the linesegment PQ
⇛M(x,y) = ( { 4+(-2)}/2 ,{m+4}/2)
⇛M(x,y) = {(4-2)/2 , {m+4}/2)
⇛M(x,y) = (2/2,{m+4}/2)
⇛M(x,y) = (1,{m+4}/2)
According to the given problem
Mid point of PQ = C(n,-1)
M(x,y) = C(n,-1)
(1,{m+4}/2) = (n,-1)
On Comparing both sides then
1 = n and (m+4)/2 = -1
n = 1 and m+4 = -2
n = 1 and m = -2-4
n = 1 and m = -6
Hence, the value of m&n will be (1&-6) respectively.
Additional comment:
The coordinates of the mod point of the linesegment joining the points (x1, y1) and (x2, y2)
is M(x,y) = ( {x1+x2}/2 , {y1+y2}/2 )
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I need help doing this
how many 5 letter code words can be formed from the letters of the word MATRICES
113
Hope this helped you- have a good day bro cya)
During the first year with a company, Finley was paid an annual salary of $57,000, with a 4% raise for each following year. Which equation represents Finley's annual salary, f (n), during the nth year?
f (n) = 57,000(0.04n – 1)
f (n) = 57,000(1.04n)
f (n) = 57,000(1.04n – 1)
f (n) = 57,000(0.96n)
Answer:
Step-by-step explanation:
C I took the test
The equation of Finley's annual salary represents 57,000(1.04n – 1) during the nth year.
What is the percentage?The percentage is defined as ratio expressed as a fraction of 100.
Finley was paid an annual salary of $57,000
with a 4% raise for each following year
Finley's annual salary, during the 2th year
⇒ 4% of 57,000 + 57,000
⇒ (0.04)57,000 + 57,000
⇒ 2280 + 57,000
⇒ 59280
Finley's annual salary, during the 2th year
Determine the difference between year 2 and year 1 salary.
Rate of change = 4% of 57,000 - 57,000
Rate of change = (0.04)57,000 - 57,000
Rate of change = 57,000(0.04 - 1)
Finley's annual salary, during the 5th year
Determine the difference between year 5 and year 4 salary
⇒ 57,000(0.04(5) - 1)
That's the constant.
Finley's annual salary, during the nth year
So, f (n) = 57,000(1.04n – 1)
Hence, the equation of Finley's annual salary represents 57,000(1.04n – 1) during the nth year.
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On a number line, where would
7/10 be located? Choose all answers that make
a true statement.
Answer:
Step-by-step explanation:
find the value of p-8 when p=14
Answer:
6
Step-by-step explanation:
If p = 14
rewrite the equation
so replace the variable with 14.
now do basic subtraction.
14 - 8
= 6
help me pls
sssssssssssssssssssss
Amanda invests $5,000 in a CD at an annual interest rate of 2%. What will her investment be worth at the end of three years
132.16 divided by 16
Answer: 8.26
Step-by-step explanation:
Should I Explain How I got it?
132.16 divided by 16 is equal to 8.26.
Here, we have,
given that,
132.16 divided by 16
so, we have, 132.16 ÷ 16
To find the quotient of 132.16 divided by 16,
we can perform long division:
8.26
____________
16 | 132.16
112
____________
20
Therefore, 132.16 divided by 16 is equal to 8.26.
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Evaluate 40x40x402x2x2
Answer:
2,572,800
Step-by-step explanation:
I hope this helps!
Answer: 40 x 40 x 402 x 2 x 2 =128,640
In 2 + In 8 - In 4
In 4
In 6
In 74
Answer:
in8− in4+ in2
Step-by-step explanation:
thats the aswer