Final answer:
The probability that a randomly selected blue marble came from the first box is 7/31, which is approximately 0.2258 when rounded to four decimal places.
Explanation:
The probability that the blue marble came from the first box can be found using Bayes' theorem and the concept of conditional probability. First, we need to determine the probability of drawing a blue marble from either box (P(Blue)). Then, we calculate the probability of drawing a blue marble from the first box (P(Blue|First box)). Finally, we apply Bayes' theorem to find the probability that the blue marble came from the first box (P(First box|Blue)).
Here are the relevant probabilities:
P(First box) = 1/2 (since there are only two boxes)
P(Second box) = 1/2
P(Blue|First box) = 3/5 (3 blue out of 5 total marbles)
P(Blue|Second box) = 2/7 (2 blue out of 7 total marbles)
Using these probabilities, we calculate P(Blue):
P(Blue) = P(Blue|First box) * P(First box) + P(Blue|Second box) * P(Second box) = (3/5) * (1/2) + (2/7) * (1/2) = 3/10 + 1/7 = 21/70 + 10/70 = 31/70
Now, we apply Bayes' theorem to get P(First box|Blue):
P(First box|Blue) = [P(Blue|First box) * P(First box)] / P(Blue) = [(3/5) * (1/2)] / (31/70) = (3/10) / (31/70) = (3/10) * (70/31) = 21/310 = 7/31 or approximately 0.2258 (rounded to four decimal places)
Therefore, the probability that the marble came from the first box is 7/31.
Find 3/7⋅9/10 . Write your answer as a fraction in simplest form.
The value of the multiplication of the fractions will be equal to 27 / 70.
What is multiplication?Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the fractions are 3/7 and 9/10. The multiplication of the number will be calculated as,
M = 3 / 7 x 9 / 10
M = 27 / 70
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convert 0.045 to a fraction
Twelve of the students in the school choir like to sing solos. These 12 students make up 24% of the choir. How many students are in the choir?
Answer:
The answer is 50 students
Step-by-step explanation:
4 1/2 + 8 3/4
A. 12 2/3
B. 12 1/3
C. 13 1/4
D. 13 2/3
4 1/2 + 8 3/4
4+8 = 12
1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4
12 + 1 1/4 = 13 1/4
Answer is C
Malia has 8 hamsters. That is 6 fewer than Sasha has. How many hamsters does Sasha have?
ax+3x=bx+5 what is the answer for x
Question 26(multiple choice worth 1 points) (02.02) simplify . −4 4
Solve the equation.
-3(y - 5) = 24
y = ______?
The value of Equation is y = -3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have Equation,
-3(y-5) = 24
Now, solving for y
Divide both side by (-3) we get
-3(y-5) / (-30= 24/ (-3)
y-5 = -8
Add 5 to both side
y- 5 +5 = -8 + 5
y = -3
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5/8 divided by 5 3/4
six people share 3/5 pound of peanuts equally. What fraction of a pound of peanuts does each person recieve?
The librarian, Ms. Barrett, wants to buy new books for the school library. She posts a sign in the library to raise money, and 75 students donate $0.50 each for the book drive. If she splits the money donated evenly between two genres (fiction and non-fiction), how much money does she have to spend on each genre? A) $18.75 B) $187.50 C) $28.50 D) $37.50
Answer:
A
Step-by-step explanation:
Find the critical numbers of the function. (Enter your answers as a comma-separated list.)
f(θ) = 8sec θ + 4tan θ, 0 < θ < 2π
The critical numbers of the function f(θ) = 8sec(θ) + 4tan(θ) are where the derivative is undefined, specifically at θ = π/2 and θ = 3π/2.
Explanation:To find the critical numbers of the function f(θ) = 8sec(θ) + 4tan(θ), we need to take its derivative and set it equal to zero or find where the derivative does not exist. First, we compute the derivative of the function. Recall that the derivative of sec(θ) is sec(θ)tan(θ) and the derivative of tan(θ) is sec2(θ).
Thus, the derivative f'(θ) is 8sec(θ)tan(θ) + 4sec2(θ). We look for where this derivative is undefined or equal to zero. The derivative is undefined when sec(θ) is undefined, which occurs at θ = π/2 and θ = 3π/2. To find where the derivative is zero, we can factor out 4sec(θ):
4sec(θ)(2tan(θ) + sec(θ)) = 0
The second factor will never be zero because sec(θ) and tan(θ) will not be zero for the same θ in the interval given. Therefore, the critical numbers are where the derivative is undefined, which is θ = π/2 and θ = 3π/2.
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28 is 32% of what number?
divide:
28 / 0.32 = 87.5
A vector a has a magnitude of 60m and directed as shown. find the x and y components of this vector
Final answer:
To find the x and y components of a vector, use the cosine and sine functions, respectively, with the given angle. For a vector of 60m at 38°, the components are approximately 47.28m (x) and 36.96m (y).
Explanation:
To find the x and y components of a vector given its magnitude and a direction, you can use trigonometric functions. Assuming the vector Δr is the one you're referring to, with a magnitude of 60m and an angle of 38° (from the x-axis, presumed direction), you can apply the cosine function for the x-component and the sine function for the y-component of the vector.
For the x-component: x = magnitude × cos(angle) = 60m × cos(38°) = 60m × 0.788 = 47.28m
For the y-component: y = magnitude × sin(angle) = 60m × sin(38°) = 60m × 0.616 = 36.96m
Therefore, the x and y components of the vector are approximately 47.28m and 36.96m, respectively.
Write each percent as a fraction in simplest form 47%=
The percentage of 47% can be expressed as the fraction 47/100 in simplest form. This means that 47 out of every 100 units can be represented by the fraction 47/100.
The percentage is given as 47%.
To write 47% as a fraction in simplest form, we can interpret the percent symbol as meaning "per 100."
Recognize that percent means "per 100." Therefore, 47% can be written as 47 per 100 or 47/100.
Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 47 and 100 is 1.
Divide both the numerator and denominator by their GCD to simplify the fraction:
(47 ÷ 1) / (100 ÷ 1) = 47/100
The resulting fraction, 47/100, is already in its simplest form.
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In isosceles ∆ABC the segment BD (with D ∈ AC ) is the median to the base AC . Find BD, if the perimeter of ∆ABC is 50m, and the perimeter of ∆ABD is 40m.
The length of the height triangle ABC is BD i.e., [tex]15\;units[/tex].
According to the question, In isosceles [tex]∆ABC[/tex] the segment BD is the median to the base AC . Also, the perimeter of ∆ABC is 50m, and the perimeter of the triangle [tex]ABD[/tex] is 40m.
Let the length of the equal sides of the isosceles triangle be [tex]x \;meters[/tex] and the length of the base of the isosceles triangle is [tex]2y\;meters[/tex].
[tex]Perimeter_{ABC}=x+x+2y\\2x+2y=50\\x+y=25\\x=25-y----(i)[/tex]
Also,
[tex]Perimeter_{ABD}=x+y+BD\\x+y+\sqrt{x^2-y^2}=40\\x+y+\sqrt{(25-y)^2-y^2}=40\\25+\sqrt{625-50y}=40\\\sqrt{625-50y}=15\\625-50y=225\\y=8\;units[/tex]
So,
[tex]x=25-8\\x=17\;units[/tex]
Now,
[tex]BD=40-x-y\\BD=40-17-8\\BD=15\;units[/tex]
Hence, the length of the height triangle ABC is BD i.e., [tex]15\;units[/tex].
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Yolanda's club has 50 members. It's rules require that 60% of them must be present for any vote. At least how many members must be present to vote?
Which equation correctly applies the distributive property?
A. 2.4⋅(−3.4)⋅(−1.25)=−3.4⋅2.4⋅(−1.25)
B. −3⋅(6.48)=(−3⋅6)+(−3⋅0.4)+(−3⋅0.08)
C. −2.5⋅(4⋅3.67)=(−2.5⋅4)⋅3.67
D. (42⋅3.5)+(42⋅1.3)+(42⋅5.2)=42+(3.5+1.3+5.2)
Answer:
B
Step-by-step explanation:
There are 691 students at Palmer Elementary School and 1,293 students at Palmer Middle School. About how many students are there in all at both school?
There are 1,984 students in total at Palmer Elementary School and Palmer Middle School combined, showing an example of increasing school enrollments. This is calculated by simply adding the number of students from both schools.
Explanation:Calculating the Total Number of Students
To find out how many students are in all at both Palmer Elementary School and Palmer Middle School, we add the number of students at each school together. Palmer Elementary School has 691 students, and Palmer Middle School has 1,293 students.
To determine the total, we perform the following addition:
691 (Palmer Elementary School students)+ 1,293 (Palmer Middle School students)= 1,984 students in totalTherefore, there are approximately 1,984 students in total at both schools combined. This calculation helps us understand the scale of student populations within a small section of the education system, reflecting broader national trends where school enrollments are increasing.
A 12 oz bottle of a new soda costs $2.49. What is the unit rate, rounded to the nearest tenth of a cent?
Daniel dives into a swimming pool. The height of his head is represented by the function h(t) = -8t2 - 28t + 60, where t is the time in seconds and h(t) is the height of his head, in inches.
How many seconds will it take for Daniel's head to reach the surface of the pool?
Whats the unit rate of $3.60
Write a number sentence to show the distributive property. 7x6=
Answer:
According to the distributive property of multiplication,
a . (b + c ) = (a . b) + (a . c)
Given: 7 × 6
which can be rewritten as: a) 7 . (4 + 2), b) 7 . (3 + 3), c) 7 . (1 + 5)
Rewriting the given expression using the distributive property of multiplication:
a) 7 . (4 + 2) = (7 . 4) + (7 . 2)
7 . (6) = 28 + 14
42 = 42
b) 7 . (3 + 3) = (7 . 3) + (7 . 3)
7 . (6) = 21 + 21
42 = 42
c) 7 . (1 + 5) = (7 . 1) + (7 . 5)
7 . (6) = 7 + 35
42 = 42
As the left hand side is equal to the right hand side in each case, therefore, it proves the distributive property.
The point (2, -3) lies in quadrant I II III IV
Using mental math, the approximate tip to leave for a bill of $81.79, if you tip 15% would be _____..
What is the sum of 1/3(9-6m) + 1/4(12m -8)?
Answer:
The sum of the given expression is (m+1).
Step-by-step explanation:
The given expression is
[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)[/tex]
Use distributive property to to simplify the given expression.
[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)=\frac{1}{3}(9)+\frac{1}{3}(-6m)+\frac{1}{4}(12m)+\frac{1}{4}(-8)[/tex]
[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)=3-2m+3m-2[/tex]
Add like terms.
[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)=(3-2)+(-2m+3m)[/tex]
[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)=(1)+(m)[/tex]
[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)=m+1[/tex]
The sum of the given expression is (m+1).
Given the points L(-2,5) and M(2,-3), point Q (6/5 m, -7/5) partitions LM in the ratio
Answer:
4:1
Step-by-step explanation:
We are given that
Point L(-2,5) and M(2,-3).
Point Q([tex]\frac{6}{5},\frac{-7}{5})[/tex] partitions LM .
We have to find the ratio in which Q divides the LM.
Let point Q divides the LM in the ratio K:1.
Section formula;[tex]x=\frac{m_1x_2+m_2x_1}{m_1+m_2},y=\frac{m_1y_2+m_2y_1}{m_1+m_2}[/tex]
Substitute the values in the given formula then we get
[tex]\frac{6}{5}=\frac{2k-2}{k+1}[/tex]
[tex]6k+6=10k-10[/tex]
[tex]6+10=10k-6k[/tex]
[tex]16=4k[/tex]
[tex]k=\frac{16}{4}=4[/tex]
Hence, the point Q divides the LM in the ratio 4:1.
Photography World has a portrait special. A three-pose portrait package has a sitting fee of $35, and a six-pose package has a sitting fee of $60. On a Saturday, $690 was collected in sitting fees. Which equation can be used to represent x, the number of three-pose portrait packages and y, the number of six-pose portrait packages?
The equation that can be used to represent the number of three-pose and six-pose portrait packages is: 35x + 60y = 690
What are word problems?Word problems in mathematics are methods and approaches applied in solving real-life scenarios. Data can be modeled from the certain information given.
From the parameters given, Let us assume that:
x represents a three-pose portrait package that has a sitting fee of $35y represents a six-pose package that has a sitting fee of $60Now, on Saturday a total amount of 690 was collected. This data can be modeled as:
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What is five times two
Twice the sum of a number and 3 is the same as 5 subtracted from the number. find the number.
Twice the sum of a number and 3 is the same as 5 subtracted from the number. Then the number will be -11.
Sum refers to the addition of terms, while subtraction means removal.
Let the number be x
Following the given information:
sum of a number and 3 = x+3
Expression 1
Twice the sum of a number and 3 =2(x+3)
Expression 2
5 subtracted from the number=x-5
On equating both the expressions as follows:
2(x+3)=x-5
Solving the equation to get the value of x:
2x+6=x-5
2x-x=-5-6
x=-11
Thus, the number is -11.
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