The expression that shows the total attendance is 7 x 40 + 7 x 2.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
Given that,
Total number of rows = 8.
Number of seats in each row = 42.
Total number of seats = 42 x 8 = 336.
Since, an act needs to keep first row empty, but rest of the seats sold.
So the remaining seats = 336 - 42 = 294.
So, the expression for the total attendance can be given as,
7 x 40 + 7 x 2 = 280 + 14 = 294.
The required expression is 7 x 40 + 7 x 2.
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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
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:
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:
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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An equation was used to predict possible sales of phones for 6 months. The actual sales of phones are also listed. Actual sales 55 150 325 510 780 990 Predicted sales 40 150 300 500 800 1,000 The sum of the residuals is ______. Numerical Answers Expected!
Answer:
20
Step-by-step explanation:
The sum of (actual - predicted) is ...
{55, 150, 325, 510, 780, 990} - {40, 150, 300, 500, 800, 1,000}
= total({15, 0, 25, 10, -20, -10}) = 20
The sum of residuals is 20.
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:
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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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
A.) write an exponential expression: let 10 be the base and an even number between 1 and 10, be the exponent.
b.) then write the exponential expression in expanded form and standard form. (note: you may need to copy and paste the expression from a word document—use the insert equations button, or you may use a "^" to indicate the exponent)
Answer:
10^2 . . . . see below for additional information or versions of the answer(s)
Step-by-step explanation:
You seem to want 10^exponent, where exponent is an even single digit, not zero.
We choose exponent = 2, so your expression is ...
10^2
__
There are several versions of expanded form. One uses exponents. In that form, the expression above is the expanded form.
Another uses multipliers of 1, 10, 100, 1000, and so on. In that form, the expression expands as ...
10^2 = 1×100
Another expanded form uses individual digits of the expanded form with others set to zero
10^2 = 100
The standard form is ...
10^2 = 100.
_____
We suppose your exponential expression might have another multiplier, such as 2.98:
exponential expression: 2.98×10^2standard form: 298expanded form 1: 2×10^2 + 9×10^1 +8×10^0expanded form 2: 2×100 +9×10 +8×1expanded form 3: 200 + 90 + 8To write an exponential expression with a base of 10 and an even exponent between 1 and 10, we can use 10^2 as an example. By multiplying the base by itself the number of times indicated by the exponent, we find that the expanded form is 10 × 10 = 100. Therefore, the standard form of the expression is 100.
Explanation:a) The exponential expression with a base of 10 and an even number between 1 and 10 as the exponent would be:
102
b) To write the expression in expanded form, we would multiply the base (10) by itself the number of times indicated by the exponent (2):
10 × 10 = 100
The standard form of the expression would be 100.
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URGENT WILL GIVE BRAINLIEST 
Answer:
C.
Step-by-step explanation:
This can be written as
[tex]log_w\frac{(x^2-6)^4}{(x^2+8)^\frac{1}{3} }[/tex]
when you divide log you should subtract the terms
[tex]log_w(x^2-6)^4-log_w(x^2+8)^\frac{1}{3}[/tex]
Rewrite powers in the terms as below
[tex]4log_w(x^2-6)-\frac{1}{3} log_w(x^2+8)[/tex]
Answer:
C. [tex]4\cdot log_w(x^2-6)-\frac{1}{3}\cdot log_w((x^2+8)[/tex]
Step-by-step explanation:
We have been given an expression [tex]log_w\frac{(x^2-6)^4}{\sqrt[3]{x^2+8}}[/tex]. We are asked to choose the equivalent expression to our given expression.
Upon applying log rule [tex]log_c(\frac{a}{b})=log_c(a)-log_c(b)[/tex], we will get:
[tex]log_w(x^2-6)^4-log_w(\sqrt[3]{x^2+8})[/tex]
Using exponent rule [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex], we will get:
[tex]log_w(x^2-6)^4-log_w((x^2+8)^{\frac{1}{3}}[/tex]
Now, we will apply rule [tex]log_c(a^b)=b\cdot log_c(a)[/tex] to simplify our expression as:
[tex]4\cdot log_w(x^2-6)-\frac{1}{3}\cdot log_w((x^2+8)[/tex]
Therefore, option C is the correct choice.
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 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.
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]
Alice and Bob are playing a game. Alice starts first. On Alice's turn, she flips a coin. If she gets a heads, she wins. If not, it becomes Bob's turn. On Bob's turn, he flips a coin. If he gets a tails, he wins. If not, it becomes Alice's turn. What is the probability that Alice wins the game?
Final answer:
The probability that Alice wins the coin-flipping game is 2/3, or approximately 66.67%. This is calculated by summing the infinite geometric series of her winning probabilities over multiple rounds.
Explanation:
The student has asked about the probability that Alice wins a coin-flipping game against Bob where Alice needs a heads to win, and Bob requires a tails to win. Each has a turn to flip the coin if the previous person does not win.
Probability is the measure of the likelihood that an event will occur. To calculate Alice's probability of winning, we consider that she has the first opportunity to win with a 50% chance (heads). If she does not get heads, Bob has a turn, also with a 50% chance (tails), but this does not directly affect Alice's probability. What affects Alice's chances are the subsequent rounds where she will have another opportunity to flip the coin if Bob does not win on his turn.
To calculate her total probability of winning, we can sum up the probabilities of her winning on the first turn, plus the probability of her winning after each complete set of turns:
Alice's probability of winning on the first turn is simply 0.5 (50% for getting heads).
If both fail their first attempt, the game starts over with the same conditions, so the probability of Alice winning on the second set of turns is (0.5 x 0.5 x 0.5), since both need to fail their first flip (0.5 x 0.5) and then Alice must succeed on her second try (x 0.5).
This pattern continues indefinitely, with each complete set of turns reducing Alice's additional chance of victory by a factor of (0.5 x 0.5).
Thus, the sum of this geometric series gives us the total probability of Alice winning:
P(Alice) = 0.5 + ([tex](0.5^3[/tex]x[tex]0.5^5)[/tex] + ... = 0.5 / (1 - (0.5^2)) = 0.5 / (0.75) = 2/3
Alice has a 2/3 (approximately 66.67%) chance of winning the game.
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.
What is the midpoint of the segment below?
(3,5)(-6,-6)
Answer: (-1.5, -0.5)
Step-by-step explanation:
Turns out that I'm going to need help with this question. I wasn't able to figure it out on my own. Thanks for the help!
Answer:
r=1
Step-by-step explanation:
x^2 +y^2 =1
We know that x^2 + y^2 = r^2
Replacing that in the equation
r^2 =1
Taking the square root of each side
sqrt(r^2) = sqrt(1)
r =1
The other way is to replace x with r cos theta and y with r sin theta
(r cos theta)^2 + (r sin theta) ^2 =1
r^2 cos^2 theta + r^2 sin^2 theta = 1
Factor out r^2
r^2 (cos^2 theta + sin^2 theta) =1
We know cos^2 theta + sin^2 theta =1
r^2 (1) =1
r^2 =1
Answer:
r = 1
Step-by-step explanation:
The usual translation between rectangular coordinates and polar coordinates is ...
x = r·cos(θ)y = r·sin(θ)Substituting these into your equation, you get ...
(r·cos(θ))² + (r·sin(θ))² = 1
r²(cos(θ)² +sin(θ)²) = 1 . . . . . . factor out r²
r²(1) = 1 . . . . . . . . . . . . . . . . . . use the trig identity cos(θ)² +sin(θ)² = 1
r = 1 . . . . . . . take the square root
_____
It's that simple. Just as x=1 describes a line in Cartesian coordinates, r=1 describes a circle in polar coordinates.
2 questions thanks everyone:))
Answer:
[tex]\large\boxed{\bold{Q1.}\ \overline{WX},\ \overline{XY},\ \overline{YW}}\\\boxed{\bold{Q2.}\ \angle P,\ \angle Q,\ \angle R}[/tex]
Step-by-step explanation:
The longest side is opposite the largest angle, and the shortest is opposite the smallest one.
The largest angle lies opposite the longest side, and the smallest is opposite the smallest side.
Q1.
Calculate m∠Y.
We know: Measures of angles of triangle add up to 180°.
m∠Y + m∠W + m∠X = 180°
Substitute given angles:
m∠Y + 51° + 90° = 180°
m∠Y + 141° = 180° substitute 141° from both sides
m∠Y = 39°
39° < 51° < 90° → XW < XY < YW
Q2.
RQ < PR < PQ → ∠P < ∠Q < ∠R
How many complex roots exist for the polynomial in this equation F(X)=x3+4x2-16 A. 1 real root and 2 complex roots B. 2 real and 1 complex root C. 0 real roots and 3 complex roots D. 3 real roots and 0 complex roots
Answer:
A. 1 real root and 2 complex roots
Step-by-step explanation:
The one sign change among the coefficients tells you there is one positive real root. The rule of signs is inconclusive regarding the number of negative real roots. A graph shows there are none, so there are ...
1 real root and 2 complex roots
The given polynomial F(X)=x3+4x2-16 can have either 3 real roots and 0 complex roots if the discriminant is greater than zero, or 1 real root and 2 complex roots if the discriminant is less than zero. The standard cubic formulas or numeric methods can be used to solve it.
Explanation:The subject of your question is the roots of a cubic polynomial, a topic in mathematics. The given polynomial is not a quadratic equation, so the quadratic formula is not directly applicable. The roots of the polynomial F(X)=x3+4x2-16 can be complex or real numbers depending on the discriminant of the polynomial. If the discriminant of the polynomial is greater than zero, then there are 3 real roots and 0 complex roots, and if it is less than zero, there are 1 real root and 2 complex roots. Standard cubic formulas or numeric methods can be used to solve it, which is a more advanced topic usually covered in high school or college level algebra.
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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
What is the area of the two-dimensional cross section that is parallel to face ABC ?
Enter your answer in the box.
ft²
A right triangular prism containing dashed lines representing the hidden edges. The prism is resting on a triangular face, which is labeled D E F and contains right angle E. Side E F is labeled twelve feet. The top of the prism is labeled A B C and contains right angle B. Side A B is labeled five feet and side A C, which is the hypotenuse of the right triangular face, is labeled thirteen feet. The height of the prism is side C F labeled seventeen feet.
Answer:
The area of the two-dimensional cross section is 30 feet²
Step-by-step explanation:
* Lets explain what is the right triangular prism
- The right triangular prism has five faces
- Two right triangular bases (cross sections)
- Three rectangular faces
- Its volume V = area of its base × its height
- Its surface area SA = the sum of the areas of the five faces
- The area of the triangular bases = 1/2 × base of Δ × height of Δ
* Lets solve the problem
- ABCFED is a right triangular prism
- Its two parallel bases are ABC and DEF
- Its bases are congruent right triangles
∴ AB = DE , BC = EF , AC = DF
∵ AB = 5 feet
∴ DE = 5 feet
- The two-dimensional cross section that is parallel to face ABC
is the face DEF
∵ Δ DEF is right triangle , where angle E is a right angle
∴ DE and EF are the base and the height of Δ DEF
∵ DE = 5 feet ⇒ proved
∵ EF = 12 feet ⇒ given
∴ The area of Δ DEF = 1/2 × 5 × 12 = 30 feet²
∵ The two-dimensional cross section that is parallel to face ABC
is the face DEF
* The area of the two-dimensional cross section is 30 feet²
Answer:
The area of the cross section is 30 feet².
Step-by-step explanation:
The area is 30, because you want to multiply 5 and 12, then multiply that by 1/2 to find the area of a right triangle.
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
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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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.
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.
What is the square root property of:
The square root property seems to be another name for completing the square
x^2 + 5x + 6 = 0
We move the constant to the other side
x^2 + 5x = -6
We square half the linear coefficient and add that to both sides
x^2 + 5x + (5/2)^2 = -6 + 25/4
Now the left side is a perfect square,
(x + 5/2)^2 = 1/4
Here's the square root property part, we take the square root of both sides, remembering the ±
x + 5/2 = ± 1/2
x = -5/2 ± 1/2
Answer: x = -3 or x=-2
We check by plugging in these values to the original equation, and they work.
------
x^2 + 6x = 16
Again we add half the linear coefficient, squared, to both sides
x^2 + 6x + 3^2 = 16 + 9
(x + 3)^2 = 25
Here comes the square root property, taking the square root of both sides:
x + 3 = ±5
x = -3 ± 5
x = 2 or x = -8
Again we check by substitution, and they both work
Answer: x = 2 or x = -8
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
3
Step-by-step explanation:
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.
What is the product?
Answer:
=20s³+50s²+32s+6
Step-by-step explanation:
We multiply each of the term in the initial expression by the the second expression as follows:
4s(5s²+10s+3)+2(5s²+10s+3)
=20s³+40s²+12s+10s²+20s+6
Collect like terms together.
=20s³+50s²+32s+6
Answer: It's the same thing as multiplication.
Step-by-step explanation:
PLEASE HELP!! MULTIPLE CHOICE MATH QUESTION
Which monomials are divisible by 4xy?
A. x^2
B. -8y^2
C. None of the Above
Answer:
C. None of the Above
Step-by-step explanation:
None of the given monomials have all of 4 and x and y as factors.
___
They can all be divided, but the result will be a fraction--which is probably not what is intended. None can be divided "evenly" by 4xy.