Sample size--
It is the collections of all the possible outcomes of an event.
(A)
It is given that:
Shona spins a spinner with three equal-sized spaces—red, green, and yellow and then rolls a six-sided die numbered from 1 to 6.
This means that the possible outcomes are given as follows:
(Red,1) (Green,1) (Yellow,1)
(Red,2) (Green,2) (Yellow,2)
(Red,3) (Green,3) (Yellow,3)
(Red,4) (Green,4) (Yellow,4)
(Red,5) (Green,5) (Yellow,5)
(Red,6) (Green,6) (Yellow,6)
This means that the total number of outcomes are: 18
Hence, the sample size for this compound event is: 18
(B)
If the spinner has four colored spaces.
Let the fourth color be: Blue
Then the possible outcomes are given by:
(Red,1) (Green,1) (Yellow,1) (Blue,1)
(Red,2) (Green,2) (Yellow,2) (Blue,2)
(Red,3) (Green,3) (Yellow,3) (Blue,3)
(Red,4) (Green,4) (Yellow,4) (Blue,4)
(Red,5) (Green,5) (Yellow,5) (Blue,5)
(Red,6) (Green,6) (Yellow,6) (Blue,6)
Hence, the total number of outcomes are: 24
The sample size of this compound event would be 24.
Answer:
a- 18
b- 24
Step-by-step explanation:
the first quartile of a data set is 2.5. which statement about the data values is true?
A) three-fourths of the values are less than or equal to 2.5, and one-fourth of the values are greater than or equal to 2.5.
B) Half of the values are less than or equal to 2.5, and half of the values are greater than or equal to 2.5.
C) One-fourth of the values are less than or equal to 2.5, and half of the values are greater than or equal to 2.5.
D) one-fourth of the values are less than or equal to 2.5, and three-fourths of the values are greater than or equal to 2.5.
Answer:
The correct option is D.
Step-by-step explanation:
In a data set we have three quartiles and the second quartile is known as median.
First quartile Q₁ divides the data set in 1:3. It means [tex]\frac{1}{4}[/tex] of the data set are less than or equal to Q₁ and [tex]\frac{3}{4}[/tex] of the data set are more than or equal to Q₁.
Second quartile Q₂ divides the data set in 1:1. It means [tex]\frac{1}{2}[/tex] of the data values are less than or equal to Q₂ and [tex]\frac{1}{2}[/tex] of the data values are more than or equal to Q₂.
Third quartile Q₃ divides the data set in 3:1. It means [tex]\frac{3}{4}[/tex] of the data values are less than or equal to Q₃ and [tex]\frac{1}{4}[/tex] of the data values are more than or equal to Q₃.
It is given that first quartile of a data set is 2.5. It means [tex]\frac{1}{4}[/tex] of the data set are less than or equal to 2.5 and [tex]\frac{3}{4}[/tex] of the data set are more than or equal to 2.5.
Therefore the correct option is D.
Answer:
D) one-fourth of the values are less than or equal to 2.5, and three-fourths of the values are greater than or equal to 2.5.
Step-by-step explanation:
Triangle ABC underwent a sequence of transformations to give triangle A'B'C' which transformations could not have taken place?
A
a reflection across the line y = x followed by a reflection across the line ya
B.
a reflection across the x-axis followed by a reflection across the yaxis
Answer:
The correct option is a rotation 180° clockwise about the origin followed by a reflection across the line y = x
Step-by-step explanation:
The correct option is missing from the given options:
Option A states that a reflection across the line y = x followed by a reflection across the line yaxis
These transformation map triangle ABC to triangle A'B'C' . So this option is in correct.
Option B states that a reflection across the x-axis followed by a reflection across the y-axis
This option is also incorrect because these transformation map triangle ABC to triangle A'B'C'.
Thus the correct option is a rotation 180° clockwise about the origin followed by a reflection across the line y = x ....
Answer:
A
Step-by-step explanation:
Use synthetic division to divide (x^ 3 + x^ 2 – 40x – 4) ÷ (x – 6)
For this case we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until reaching the remainder.
It must be fulfilled that:
Dividend = Quotient * Divider + Remainder
Looking at the attached image we have that the quotient is given by:
[tex]x ^ 2 + 7x + 2[/tex]
Answer:
Option C
The cost C, in dollars, of renting a moving truck for a day is given by the function C(x)=0.20x+45, where x is the number of miles driven.
(a) What is the cost if a person drives x=160 miles?
(b) If the cost of renting the moving truck is $120, how many miles did the person drive?
(c) Suppose that a person wants the cost to be no more than $200. What is the maximum number of miles the person can drive?
(d) What is the implied domain of C?
(e) Interpret the slope.
(f) Interpret the y-intercept.
To solve the problem we will substitute the value of x and C in the given function.
Given to us
The cost C, in dollars, of renting a moving truck for a day C(x)=0.20x+45,
What is the cost if a person drives x=160 miles?To find the cost if a person drives x=160 miles, simply substitute the value of x in the function of cost c,
[tex]C(x)=0.20x+45\\\\C(160)=0.20(160)+45\\\\C(160)=77[/tex]
Hence, the cost of the moving truck if a person drives x=160 miles is $77.
If the cost of renting the moving truck is $120, how many miles did the person drive?To solve the problem substitute the value of C as 120 in the given function,
[tex]C(x)=0.20x+45\\\\120 = 0.20x+45\\\\x = 375\rm\ miles[/tex]
Hence, If the cost of renting the moving truck is $120, the person drives 375 miles.
Suppose that a person wants the cost to be no more than $200. What is the maximum number of miles the person can drive?To solve the problem substitute the value of C as 200 in the given function,
[tex]C(x)=0.20x+45\\\\200 = 0.20x+45\\\\x = 775\rm\ miles[/tex]
Hence, if a person wants the cost to be no more than $200. The maximum number of miles a person can drive is 775.
What is the implied domain of C?Implied Domain is the value of C for which it is defined, since even if the truck is not moving a single mile it will still be costing $45, to a person, therefore, the domain of C is [45, +∞].
What is the slope of the function?If we look at the function it is a function of line therefore, the comparing the two equations,
[tex]y = mx+c\\C=0.20x+45[/tex]
we know that m is the slope of the function,
m = 0.20
therefore, the slope of the function is 0.20.
What is the y-intercept?We know that the intercept of y is the value of y at which it intersect the y axis.
when we put the value of x=0, we get the value of y as 45, therefore, the intercept of y is 45.
Hence, the intercept of y is 45.
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which fraction has terminaring decimal as its decimal expansion ?
A: 1/3
B: 1/5
C: 1/7
D: 1/9
Answer:
The correct answer option is B. 1/5.
Step-by-step explanation:
We are given four fractions in the answer options and we are to determine whether which one of them has terminating decimal as its decimal expansion.
Terminating decimal means a decimal value which has a finite amount of numbers and has an end to it.
[tex]\frac{1}{3} = 0.333333333[/tex]
[tex]\frac{1}{5} = 0.2[/tex]
[tex]\frac{1}{7} = 0.142357142[/tex]
[tex]\frac{1}{9} = 0.111111111[/tex]
Therefore, the correct answer is 1/5.
What's the dífference between paying $10,000 cash for a car or paying a loan of $200 per month for 60 months?
Answer:
The loan will cost you 2000 dollars more.
Step-by-step explanation:
If you pay 200 per month for 60 months, then you are paying 200(60) after the 60 months.
200(60)=12000.
So the loan will cost you 12000.
The difference between paying 12000 and 10000 is 2000.
The loan will cost you 2000 dollars more.
The simplified form of an expression is 1/256 t28 which expression was simplified?
Answer:
1/258 *(t^28)
= t^28 / 4^4
= t^28 4^-4
= (t^-7 * 4)^-4
= (4t^-7)^-4
Step-by-step explanation:
Answer:
so the answer is d
Step-by-step explanation:
Need help with a math question
Answer:
the coordinates of C' = (2,1)
Step-by-step explanation:
The coordinates of point C can be found by looking at the graph.
Coordinates of C are C= (6,3)
If ABCD is dilated by a factor of 1/3 then the coordinates of C' can be found by multiplying the coordinates of C by 1/3
C = (6,3)
C' =(1/3*6,1/3*3)
C' = (2,1)
So, the coordinates of C' = (2,1)
The GCD(a, b) = 9, the LCM(a, b)=378. Find the least possible value of a+b
[tex]\text{lcm}(a,b)=\dfrac{|a\cdot b|}{\text{gcd}(a,b)}\\\\378=\dfrac{|a\cdot b|}{9}\\\\|a\cdot b|=42\\\\a\cdot b=-42 \vee a\cdot b=42[/tex]
So, the least value is -42
Solve 4^x-5 = 6 for x using the change of base formula log base b of y equals log y over log b
Answer:
[tex]4^x-5=6[/tex] gives the solution [tex]x=\frac{\log(11)}{\log(4)}[/tex].
[tex]4^{x-5}=6[/tex] gives the solution [tex]x=\frac{\log(6)}{\log(4)}+5[/tex].
Step-by-step explanation:
I will solve both interpretations.
If we assume the equation is [tex]4^{x}-5=6[/tex], then the following is the process:
[tex]4^x-5=6[/tex]
Add 5 on both sides:
[tex]4^x=6+5[/tex]
Simplify:
[tex]4^x=11[/tex]
Now write an equivalent logarithm form:
[tex]\log_4(11)=x[/tex]
[tex]x=\log_4(11)[/tex]
Now using the change of base:
[tex]x=\frac{\log(11)}{\log(4)}[/tex].
If we assume the equation is [tex]4^{x-5}=6[/tex], then we use the following process:
[tex]4^{x-5}=6[/tex]
Write an equivalent logarithm form:
[tex]\log_4(6)=x-5[/tex]
[tex]x-5=\log_4(6)[/tex]
Add 5 on both sides:
[tex]x=\log_4(6)+5[/tex]
Use change of base formula:
[tex]x=\frac{\log(6)}{\log(4)}+5[/tex]
Answer:
6.292
Step-by-step explanation:
I got it right on the test.
The random numbers below represent 10 trials of a simulation. 2632, 1365, 9367, 2056, 0026, 6564, 1434, 8045, 4781, 8681 The numbers 0–7 represent students who watched television last night, and the numbers 8 and 9 represent students who did not. Based on the simulated data, what is the probability that exactly 2 out of a group of 4 randomly selected seventh-graders watched television last night? A. 5 10 B. 4 10 C. 9 10 D. 1 10
Answer:
D. 1/10
Step-by-step explanation:
The trial results (# who watched TV) are ...
4 4 3 4 4 4 4 3 3 2
Of the 10 trials, only 1 resulted in 2 in the group of 4 watching TV.
Your probability is 1/10.
A computer can sort x objects in t seconds, as modeled by the function below t=0.003x^2 + 0.001x how long in seconds will it take the computer to sort 12 objects
Answer:
[tex]t=0.444\ seconds [/tex]
Step-by-step explanation:
Let
x -----> the number of objects
t ----> the time in seconds
we have
[tex]t=0.003x^{2}+0.001x[/tex]
For x=12 objects
substitute in the formula and solve for t
[tex]t=0.003(12)^{2}+0.001(12)[/tex]
[tex]t=0.444\ seconds [/tex]
To find the time to sort 12 objects, we plug x = 12 into the equation t=0.003x^2 + 0.001x to get t = 0.444 seconds.
The student has asked for the time it will take for a computer to sort 12 objects, according to the function t=0.003x^2 + 0.001x.
Step 1: Plug in the value
The first step is to plug the value x = 12 into the given equation.
t = 0.003(12)^2 + 0.001(12)
Step 2: Calculate squares and products
We calculate (12)^2 which is 144, then multiply it by 0.003, which equals 0.432.
Next, we calculate 0.001 times 12, which equals 0.012.
Step 3: Solve for t
Finally, we sum the two products: t = 0.432 + 0.012, resulting in t = 0.444 seconds.
For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5. There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?
A. 0B. 1C. 2D. 3E. 4
Answer:
The correct option is D.
Step-by-step explanation:
Given information:
Total number of teams = 3
Total number of members in each team = 3
A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.
It means the points for 1st, 2nd, 3rd, 4th, and 5th place are 5, 4, 3, 2 and 1 respectively.
Total points that can earned = 5+4+3+2+1=15
There were no ties, disqualifications, or withdrawals.
No team earned more than 6 points.
To minimize the score of a team, we have to maximize the score of the other two teams.
Let two teams earn there maximum score. i.e. 6. So the score of third team is
[tex]15-6-6=3[/tex]
The least possible score a team could have earned is 3. Therefore the correct option is D.
Which statement is the correct interpretation of the inequality ?4 > ?5? On a number line, ?4 is located to the left of 0 and ?5 is located to the right of 0. On a number line, ?4 is located to the right of 0 and ?5 is located to the left of 0. On a number line, ?4 is located to the right of ?5. On a number line, ?4 is located to the left of ?5.
Answer:
On a number line, -4 is located to the right of -5
Step-by-step explanation:
Answer:
On a number line, -4 is located to the right of -5
Step-by-step explanation:
Amy and Alex are making models for their science project. Both the models are in the shape of a square pyramid. The
length of the sides of the base for both the models is 8 inches. Amy’s model is 5 inches tall and Alex’s model is 3 inches tall.
Find the difference in volume of the two models.
Answer:
128/3 cubic inches
Step-by-step explanation:
The formula for pyramid volume is (1/3)lwh. Using this we can calculate that the volume of each shape is 320/3 cubic inches and 192/3 inches. When these are subtracted, it reads 128/3 cubic inches.
Answer:
The answer is 42.67 cubic inches.
Step-by-step explanation:
Both the models are in the shape of a square pyramid.
The length of the sides of the base for both the models is 8 inches.
Amy’s model is 5 inches tall and Alex’s model is 3 inches tall.
The volume is given by :
[tex]a^{2}\frac{h}{3}[/tex]
So, Amy's figure volume is :
[tex]8^{2}\times \frac{5}{3}[/tex] = 106.67 cubic inches
And Alex's figure volume is:
[tex]8^{2}\times \frac{3}{3}[/tex] = 64 cubic inches
So, the difference between volumes is = [tex]106.66-64=42.67[/tex] cubic inches.
The answer is 42.67 cubic inches.
The intensity of a sound varies inversely where of its distance from the source at a distance of 1 meter the intensity of a jet engine noise is ten watts per square meter an air port cargo worker is 50 meters from the jet engine what is the sound intensity at this distance
Answer:
1/250 W/m² or 0.004 W/m² or 4 mW/m²
Step-by-step explanation:
The cargo worker is (50 m)/(1 m) = 50 times the reference distance. The intensity varies as the inverse of the square of the distance, so will be ...
(1/50)²×(10 W/m²) = 10/2500 W/m² = 1/250 W/m²
This might be more conveniently written as 4 mW/m².
Of the last 60 people who went to the cash register at a department? store, 14 had blond? hair, 17 had black? hair, 25 had brown? hair, and 4 had red hair. Determine the empirical probability that the next person to come to the cash register has redred hair.
Answer:
1/15 or 6.67%.
Step-by-step explanation:
Empirical Probability = number of red haired people in the last 60 people / 60.
= 4/60
= 1/15.
The empirical probability of the next customer at the department store having red hair is approximately 0.0667 or 6.67%, based on the hair color distribution of the previous 60 customers.
Explanation:The student is asking to determine the empirical probability that the next person to come to the cash register has red hair. Empirical probability is based on actual experiment results and calculated by the number of successful trials divided by the total number of trials.
In this case, the total number of people who went to the cash register is 60. Out of these, 4 people had red hair. Hence, the empirical probability of the next customer having red hair would be 4 out of 60 or 0.0667 when rounded to four decimal places. So, there's approximately a 6.67% chance that the next person to visit the cash register will have red hair assuming that the hair color distribution remains consistent.
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The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x) = 9x – 2. Which expression represents the profit, (k – h)(x), of producing soccer balls?
14x – 8
14x + 4
4x – 8
4x + 4
Answer:
4x - 8
Step-by-step explanation:
Cost of producing x soccer balls = h(x) = 5x + 6 in thousands of dollars
Revenue generated from x soccer balls = k(x) = 9x - 2 in thousands of dollars
We need to calculate the profit for x soccer balls.
Profit = p (x) = Revenue - Cost
p(x) = (9x - 2) - (5x + 6)
p(x) = 9x -2 - 5x- 6
p(x) = 4x - 8
Thus the profit from x soccer balls in thousands of dollars would be 4x - 8.
Answer:4x-8
Step-by-step explanation:
a falling object accerlates from -10.0m/s to -30.0m/s how much time does that take
Answer:
2.04 seconds
Step-by-step explanation:
Falling objects near the surface of the earth have an acceleration of -9.81 m/s².
Acceleration is the change in velocity over change in time:
a = (v − v₀) / t
-9.81 = (-30.0 − (-10.0)) / t
-9.81 = -20.0 / t
t = 2.04
It takes 2.04 seconds.
A manufacturer wants to make a ball bearing that is made of a mixture of zinc, iron, and copper and has come down to a choice of two alloys. Alloy A has a density of 7.5 grams per cubic centimeter and alloy B has a density of 8.5 grams per cubic centimeter.
Use the formula for the volume of a sphere, V=43πr3 , and the formula for density, D=mv , to write an equation for m as a function of r for each alloy.
Answer:
Alloy A: m = 10πr³ . . . . . . . . . . . . mass in grams; radius in cmAlloy B: m = (34π/3)r³Step-by-step explanation:
Solving the density equation for mass, we get ...
D = m/V
m = DV . . . . . multiply by volume
Substituting the volume formula gives ...
m = D(4/3π)r³
Alloy A
Substituting D = 7.5 gives ...
m = 7.5(4/3)πr³
m = 10πr³ . . . . . simplify
__
Alloy B
Substituting D = 8.5 gives ...
m = 8.5(4/3π)r³
m = (34π/3)r³ . . . . . simplify
At a farmers' market, Frederick buys 4 pounds of apples and 15 pounds of cherries for $36.93. At the same farmers' market, Wilhelmina buys 12 pounds of apples and 9 pounds of cherries for $30.51. Determine the price per pound of apples and cherries at the farmers' market.
The price per pound of apples and cherries can be calculated using a system of linear equations. This is based on the given information about how much Frederick and Wilhelmina spent on these fruits at the farmers' market.
Explanation:In order to find the price per pound of apples and cherries at the farmers' market, we will use a system of linear equations. We can assume the price per pound of apples is A and the price per pound of cherries is C. Frederick's purchases can be represented as 4A + 15C = 36.93 and Wilhelmina's purchases can be represented as 12A + 9C = 30.51. By using these equations, we can solve for A and C using any method you are comfortable with, such as substitution or elimination.
Note: The information regarding fruit consumption in 2001 and the cost calculation methodology is not directly relevant to the main question, but it provides a context of fun facts.
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A farmer wants to plant peas and carrots on no more than 400 acres of his farm. If x represents the number of acres of peas and y represents the number of acres of carrots for solution (x, y), then which is a viable solution?
A.) (−125, 500)
B.) (250, 150)
C.) (400, −10)
D.) (1, 400)
Answer:
B.
Step-by-step explanation:
It doesn't make sense for either x or y to be negative because we are talking about x representing the number of acres and y representing another number of acres and that they should add up to no more than 400.
So I'm not going to look at A or C.
B looks good 250+150=400
D almost looks good 1+400=401; the problem with this answer is that is more than 400
Option B (250, 150) is the only viable solution as it adheres to the constraints of the problem, summing to exactly 400 acres with both variables being non-negative.
The farmer has set a constraint for planting peas and carrots where the total acres used for planting both cannot exceed 400 acres.
Thus, we are looking for a solution where the sum of x (acres of peas) and y (acres of carrots) must be equal to or less than 400. The solution should also satisfy the requirement that both x and y must be non-negative since you cannot plant crops on a negative amount of land.
Among the options provided, option B (250, 150) is the viable solution. Here's why:
A.) (−125, 500): We cannot have negative acres for crops, so x cannot be negative. Also, y exceeds 400 acres on its own, violating the total area constraint.
B.) (250, 150): This solution sums up to 400 acres exactly, fitting within the constraint and with both x and y being non-negative.
C.) (400, −10): y cannot be negative, representing a nonsensical scenario for planting.
D.) (1, 400): The total acreage here is 401, which exceeds the maximum allowable acreage.
The windows of a downtown office building are arranged so that each floor has 6 fewer windows than the floor below it. If the ground floor has 52 windows, how many windows are on the 8th floor?
Answer:
10 windows are on the 8th floor
Step-by-step explanation:
1 = 52
2 = 46
3 = 40
4 = 34
5 = 28
6 = 22
7 = 16
8 = 10
What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?
3x − 4y = −17
3x − 4y = −20
4x + 3y = −2
4x + 3y = −6
Visible line: (0,3)(3,-1)
For this case we have that by definition, if two lines are parallel their slopes are equal.
The line given for the following points:
(0,3) and (3, -1). Then the slope is:
[tex]m = \frac {y2-y1} {x2-x1} = \frac {-1-3} {3-0} = \frac {-4} {3} = - \frac {4} {3}[/tex]
Then, the requested line will be of the form:
[tex]y = - \frac {4} {3} x + b[/tex]
To find "b" we substitute the given point:
[tex]2 = - \frac {4} {3} (- 3) + b\\2 = 4 + b\\2-4 = b\\b = -2[/tex]
Finally, the line is:
[tex]y = - \frac {4} {3} x-2[/tex]
By manipulating algebraically we have:
[tex]y + 2 = - \frac {4} {3} x\\3 (y + 2) = - 4x\\3y + 6 = -4x\\4x + 3y = -6[/tex]
Answer:
Option D
Answer: last option.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Knowing that the given line passes through the points (0,3) and (3,-1), we can find the slope:
[tex]m=\frac{-1-3}{3-0}=-\frac{4}{3}[/tex]
Since the other line is parallel to this line, its slope must be equal:
[tex]m=-\frac{4}{3}[/tex]
Substitute the slope and the point (-3, 2) into [tex]y=mx+b[/tex] and solve for "b":
[tex]2=-\frac{4}{3}(-3)+b\\\\2-4=b\\\\b=-2[/tex]
Then, the equation of the other line in Slope-Intercept form is:
[tex]y=-\frac{4}{3}x-2[/tex]
Rewriting it in Standard form, you get:
[tex]y+2=-\frac{4}{3}x\\\\-3(y+2)=4x\\\\-3y-6=4x\\\\4x+3y=-6[/tex]
I need help with this proof.
Answer:
My proof is in the explanation.
Step-by-step explanation:
This is a two-column proof.
One column for statements and the other for the reason for that statement.
Hopefully it shows up well on your screen. Let me know if it doesn't.
Statement | Reason
1) CD is the perpendicular 1) Given
bisector of AB
2) AD=DB 2) Definition of bisector
3) CD=CD 3) Reflexive property
4) mAngleCDA=90 4) Definition of perpendicular
5) mAngleCDB=90 5) Definition of perpendicular
6) mAngleCDA=mAngleCDB 6) Substitution property
7) Corresponding parts of each 7) SAS
triangle are congruent (side-angle-side)
8) AC=CB 8) The two triangles are ............................................................................congruent so
the corresponding parts ............................................................................are
congruent.
Suppose you have 3 jars with the following contents. Jar 1 has 1 white ball and 4 black balls. Jar 2 has 2 white balls and 1 black ball. Jar 3 has 3 white balls and 2 black balls. One jar is to be selected, and then 1 ball is to be drawn from the selected jar. The probabilities of selecting the first, second, and third jars are 1/2, 1/3, and 1/6 respectively. Find the probability the ball was drawn from Jar 1, given that the ball is white.
The probability is:
[tex]\dfrac{9}{38}[/tex]
Step-by-step explanation:We need to use the Baye's theorem in order to find the probability .
Jar 1: has 1 white ball and 4 black balls.
This means that the probability of white ball is: 1/5
( since there are a total of 1+4=5 balls out of which 1 is white)
Jar 2: has 2 white balls and 1 black ball.
This means that the probability of white ball is: 2/3
( since there are a total of 2+1=3 balls out of which 2 are white)
Jar 3 : has 3 white balls and 2 black balls.
This means that the probability of white ball is: 3/5
( since there are a total of 3+2=5 balls out of which 3 are white)
Hence, the probability the ball was drawn from Jar 1, given that the ball is white is:
Ratio of drawing jar 1 and a white ball from it to the sum of choosing each jar and a white ball from it.
i.e.
[tex]=\dfrac{\dfrac{1}{2}\times \dfrac{1}{5}}{\dfrac{1}{2}\times \dfrac{1}{5}+\dfrac{1}{3}\times \dfrac{2}{3}+\dfrac{1}{6}\times \dfrac{3}{5}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{1}{10}+\dfrac{2}{9}+\dfrac{1}{10}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{2}{10}+\dfrac{2}{9}}\\\\\\=\dfrac{\dfrac{1}{10}}{\dfrac{38}{90}}\\\\\\=\dfrac{9}{38}[/tex]
The probability that a drawn white ball came from Jar 1, given the stated conditions, is approximately 0.286 or 28.6%.
Explanation:This problem can be solved using the concept of conditional probability. Let's define the events as follows:
J1, J2, and J3 are the events of selecting Jars 1, 2, and 3 respectively.W is the event of drawing a white ball.The question requires us to find P(J1|W), that is, the probability that the ball came from Jar 1 given that it is white. Using Bayes' theorem, we can write this as:
P(J1|W) = [P(W|J1) * P(J1)] / P(W). Here, P(W|J1) is the probability of drawing a white ball from Jar 1, P(J1) is the probability of choosing Jar 1, and P(W) is the total probability of drawing a white ball.
We can find these probabilities as:
P(W|J1) = 1/5 (since Jar 1 contains 1 white and 4 black balls)P(J1) = 1/2 (given in the problem)P(W) should be calculated as: [P(W|J1) * P(J1)] + [P(W|J2) * P(J2)] + [P(W|J3) * P(J3)] = [(1/5) * (1/2)] + [(2/3) * (1/3)] + [(3/5) * (1/6)] = 0.35Substituting these values into the Bayes' theorem, we find P(J1|W) = [(1/5) * (1/2)] / 0.35 = 0.286 approximately. Therefore, there is approximately a 28.6% chance that the drawn white ball came from Jar 1.
Learn more about Conditional Probability here:https://brainly.com/question/10567654
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A diagonal of a parallelogram is also its altitude. What is the length of this altitude, if the perimeter of the parallelogram is 50 cm, and the length of one side is 1 cm longer than the length of the other?
Answer:
The length of this altitude is 5 cm.
Step-by-step explanation:
The length of the altitude = ?
Given the diagonal forms the altitude of the parallelogram. The figure is shown in image.
Given
The perimeter of the parallelogram = 50 cm
The length of one side is 1 cm longer than the length of the other.
Thus,
Let one side (a) is x cm, The other side (b) be (x + 1) cm
Perimeter of parallelogram = 2(a + b) = 2(x +(x + 1)) = 4x + 2 = 50 cm
Thus,
x = AB = CD = 12 cm
x + 1 = BC = AD = 13 cm
Using Pythagorean theorem to find the length of the altitude as:
ΔABC is a right angle triangle.
AB² + AC² = BC²
AC² = 13² - 12² = 5 cm
The length of this altitude is 5 cm.
After being rearranged and simplified, which of the following equations could
be solved using the quadratic formula? Check all that apply.
A. 5x + 4 = 3x^4 - 2
B. -x^2 + 4x + 7 = -x^2 - 9
C. 9x + 3x^2 = 14 + x-1
D. 2x^2 + x^2 + x = 30
Answer:
C and D
Step-by-step explanation:
The quadratic formula is
x= (-b±√b²-4ac)/2a
The formula uses the numerical coefficients in the quadratic equation.
The general quadratic equation is ax²+bx+c where a, b and c are the numerical coefficients
So, lets try and see;
A.
[tex]5x+4=3x^4-2\\\\=3x^4-5x-2-4\\=3x^4-5x-6\\a=3,b=-5,c=-6[/tex]
But due to the fact that in this equation you have x⁴, the equation is not a quadratic equation thus can not be solved using this formula
B
[tex]-x^2+4x+7=-x^2-9\\\\\\=-x^2+x^2+4x+7+9\\=4x+16[/tex]
C
[tex]9x+3x^2=14+x-1\\\\\\=3x^2+9x-x-14+1\\\\=3x^2+8x-13\\\\\\a=3,b=8,c=-13\\[/tex]
D.
[tex]2x^2+x^2+x=30\\\\\\=3x^2+x-30\\\\\\a=3,b=1,c=-30[/tex]
From the checking above, the equations will be C and D
Answer:
Option C and D
Step-by-step explanation:
To find : After being rearranged and simplified, which of the following equations could be solved using the quadratic formula? Check all that apply.
Solution :
Quadratic equation is [tex]ax^2+bx+c=0[/tex] with solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
A. [tex]5x+4=3x^4-2[/tex]
Simplifying the equation,
[tex]3x^4-2-5x-4=0[/tex]
[tex]3x^4-5x-6=0[/tex]
It is not a quadratic equation.
B. [tex]-x^2+4x+7=-x^2-9[/tex]
Simplifying the equation,
[tex]-x^2+4x+7+x^2+9=0[/tex]
[tex]4x+16=0[/tex]
It is not a quadratic equation.
C. [tex]9x + 3x^2 = 14 + x-1[/tex]
Simplifying the equation,
[tex]3x^2+9x-x-14+1=0[/tex]
[tex]3x^2+8x-13=0[/tex]
It is a quadratic equation where a=3, b=8 and c=-13.
[tex]x=\frac{-8\pm\sqrt{8^2-4(3)(-13)}}{2(3)}[/tex]
[tex]x=\frac{-8\pm\sqrt{220}}{6}[/tex]
[tex]x=\frac{-8+\sqrt{220}}{6},\frac{-8-\sqrt{220}}{6}[/tex]
[tex]x=1.13,-3.80[/tex]
D. [tex]2x^2+x^2+x=30[/tex]
Simplifying the equation,
[tex]3x^2+x-30=0[/tex]
It is a quadratic equation where a=3, b=1 and c=-30.
[tex]x=\frac{-1\pm\sqrt{1^2-4(3)(-30)}}{2(3)}[/tex]
[tex]x=\frac{-1\pm\sqrt{361}}{6}[/tex]
[tex]x=\frac{-1+19}{6},\frac{-1-19}{6}[/tex]
[tex]x=3,-3.3[/tex]
Therefore, option C and D are correct.
1. What is the value of x? Enter your answer in the box
2. What is the value of x? Enter your answer in the box
Answer:
X=5, X=9
Step-by-step explanation:
The first one has two sides that are equal length, so the angles opposite of those sides are equal. This means that there are 2 73 degree angles. A triangle only had 180 degrees, so the last angle is equal to 34 degrees. When you set 6x+4=34, x is equal to 5.
The second triangle is an equilateral triangle, so every angle is equal to 60 degrees. We can set 7x-3=60. Add 3 to isolate x. 7x=63. Divide by 7 to solve for x. x=9.
Answer:
Give Zdomi Brainliest now <3
Step-by-step explanation:
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
Arc length is [tex]\frac{14\pi}{3}[/tex] , or, 14.7
Step-by-step explanation:
AB is an arc intercepted by 140 degree angle. The formula for length of an arc is given by
[tex]AL=\frac{\theta}{360}*2\pi r[/tex]
Where
AL is the arc length
[tex]\theta[/tex] is the angle (in our case, 140)
r is the radius of the circle (which is 6)
Substituting, we get:
[tex]AL=\frac{\theta}{360}*2\pi r\\AL=\frac{140}{360}*2\pi (6)\\AL=\frac{7}{18}*12\pi\\AL=\frac{14\pi}{3}[/tex]
In decimal (rounded to tenths) - 14.7