Answer:
B
Step-by-step explanation: B is the only reasonable answer
3 x 4 divided by 110 + 60
Answer:
60.10
Step-by-step explanation:
3 x 4 = 12
12 / 110 = 0.109
0.109 + 60 = 60.109
Brady is selling candy bars for a school fundraiser to help pay for new sports uniforms. He gets paid $2 for every candy bar he sells, and he made a total of $90 on Saturday. Write an equation to show how many candy bars Brady sold on Saturday.
Answer: 2x = $90
Step-by-step explanation:
From the question, we are informed that Brady is selling candy bars for a school fundraiser to help pay for new sports uniforms and that he gets paid $2 for every candy bar he sells, and he made a total of $90 on Saturday.
The equation showing the number of candy bars Brady sold on Saturday goes thus:
Let the number of candy bars sold on Saturday be x.
Since each candy bar is sold for $2 and he made a total of $90, this means that the $90 gotten is the product of each candy bar and the amount sold which we represented by x. Therefore the equation will be:
2 × x = $90
2x = $90
We can further solve to get x.
2x = 90
x = 90/2
x = 45
That means 45 candy bars were sold.
Answer:
hi, so i belive the correct option to your question is:
2x = 90
Step-by-step explanation:
it just makes the most sense to me because 2x which could mean two times which in the equation it says he makes to dollars per candy bar sold, so it makes more sence for it to be 2x rather than 90x. and then it says he made a total of ninty dollars on saturday which is a key factor in solving this equation so think it would be 2x = 90$.
im really not sure if this logic makes sence, im not super good with algebra but i hope this helps you out.
a researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a ...
A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a prospective study.
Define prospective study.Individuals are tracked over time in prospective studies, and information is gathered about them as their characteristics or circumstances change. Prospective studies include things like birth cohort studies. In retrospective research, people are sampled, and details about their past are gathered. Always after a predetermined number of incidents, the analysis takes place. The fact that individuals were enrolled and baseline data was obtained before any subjects experienced an outcome of interest identifies a study as prospective.
Given,
A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a ...
Prospective study
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On a coordinate plane, triangles P Q R and S T U are shown. Triangle P Q R has points (4, 4), (negative 2, 0), (negative 2, 4). Triangle S T U has points (2, negative 4), (negative 1, negative 2), (negative 1, negative 4). Complete the statements to verify that the triangles are similar. StartFraction Q R Over T U EndFraction = StartFraction P R Over S U EndFraction = StartFraction P Q Over S T EndFraction = StartFraction StartRoot 52 EndRoot Over StartRoot 13 EndRoot EndFraction = Therefore, △PQR ~ △STU by the theorem.
Answer:
The answer is below
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion.
The distance between two points on the coordinate plane is given as:
\(Distance=\sqrt{(x_2-x_1}^2+(y_2-y_1)^2 \\\\Therefore\ in\ triangle\ PQR:\\\\|QR|=\sqrt{(-2-(-2))^2+(4-0)^2}=4\\\\|PQ|=\sqrt{(-2-4)^2+(0-4)^2}=\sqrt{52}=2\sqrt{13} \\\\|PR|=\sqrt{(-2-4)^2+(4-4)^2}=6\)
In triangle STU:
\(|ST|=\sqrt{(-1-2)^2+(-2-(-4))^2}=\sqrt{13}\\\\|SU|=\sqrt{(-1-2)^2+(-4-(-4))^2} =3\\\\|TU|=\sqrt{(-1-(-1))^2+(-4-(-2))^2}=2\)
|QR| / |TU| = 4/2 = 2
|PR| / |SU| = 6/3 = 2
|PQ| / |ST| = 2√13 / √13 = 2
Hence:
|QR| / |TU| = |PR| / |SU| = |PQ| / |ST|
Therefore, △PQR and △STU are similar triangles since the ratio of their sides are in the same proportion.
Similar triangles may or may not be congruent
Triangles PQR and STU are similar by SSS theorem.
The vertices of triangle PQR are given as:
\(P= (4, 4)\)
\(Q= (-2, 0)\)
\(R = (-2, 4)\)
The vertices of triangle STU are given as:
\(S = (2, -4)\)
\(T = (-1, -2)\)
\(U =(-1, -4)\)
Start by calculating the side lengths of the two triangles, using the following distance formula
\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\)
For triangle PQR, we have:
\(PQ = \sqrt{(4 --2)^2 + (4 -0)^2} = \sqrt{52}\)
\(PR = \sqrt{(4 --2)^2 + (4 -4)^2} = 6\)
\(QR = \sqrt{(-2 --2)^2 + (0 -4)^2} = 4\)
For triangle STU, we have:
\(ST= \sqrt{(2 --1)^2 + (-4 --2)^2} = \sqrt{13}\)
\(SU= \sqrt{(2 --1)^2 + (-4 --4)^2} = 3\)
\(TU= \sqrt{(-1 --1)^2 + (-2 --4)^2} = 2\)
Check if the side lengths of both triangles are similar, by dividing corresponding sides
\(k = \frac{PQ}{ST} = \frac{\sqrt{52}}{\sqrt{13}} = 2\)
\(k = \frac{PR}{SU} = \frac{6}{3} = 2\)
\(k = \frac{QR}{TU} = \frac{4}{2} = 2\)
Because the scale factors of the side lengths are the same, then both triangles are similar by SSS theorem.
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71/3 - 21/4 (2 1/5 × 3/4) with working
Use+the+information+in+scenario+4.2.+what+is+the+normal+time+for+this+job+element+if+the+rating+factor+is+75%?
Based on the rating factor of 75%, the normal time for the job element would be 11.19 seconds.
What is the job element's normal time?When given the rating factor, the normal time can be found as:
= Average time for the job element x Rating factor
Average time for the job factor is:
= [(10 x 18) + (15 x 25) + (20 x 17)] / (18 + 25 + 17)
= 14.92 seconds
The normal time for the job element is therefore:
= 14.92 x 0.75
= 11.19 seconds
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Desmond opened a savings account and deposited $600.00 as principal. The account earns
6% interest, compounded annually. What is the balance after 6 years?
Use the formula A = P(1+r/n)^nt
where A is the balance (final amount), P is the principal
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.
Answer:
$826.28
Step-by-step explanation:
Given:
\(P = 600\)
\(r = 6% or 0.06\)% or \(0.06\)
\(t = 6\)
Work:
\(A=Pe^{rt}\)
\(A=600e^{0.06*6}\)
\(A=600e^{0.36}\)
\(A=826.28\)
Therefore, the balance after 6 year is 826.28.
depending on the circumstances, the dequeue method of our linkedqueue class sometimes throws the queueunderflowexception. True or false?
True. depending on the circumstances, the dequeue method of our linkedqueue class sometimes throws the queueunderflowexception
The dequeue method of a LinkedQueue class throws a QueueUnderflowException when the queue is empty, and the user attempts to remove an element from it. This is because removing elements from an empty queue is not allowed and violates the basic properties of a queue data structure. Therefore, depending on the circumstances, the dequeue method may throw a QueueUnderflowException to indicate that the operation is invalid.
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find the volume of a right cylinder that has a diameter of 6 m and a height of 22 m. use straight pi equals 3.14 and round your answer to the nearest whole meter.
The volume of the cylinder is approximately 622 cubic meters.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height of the cylinder.
Given that the diameter of the cylinder is 6 m, we can calculate the radius by dividing the diameter by 2:
r = 6 m / 2 = 3 m
Using the value of π as 3.14, we can substitute the values into the volume formula:
V = 3.14 * (3 m)^2 * 22 m
Simplifying the expression:
V = 3.14 * 9 m^2 * 22 m
V = 3.14 * 198 m^3
V ≈ 621.72 m^3
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Judy's heart beats 70 times a minute. At this rate, how many times does it beat per hour?
Answer:
4200 timesStep-by-step explanation:
\(70\:times = 1\:minute\\x\:times\:= 60\:minute\\\\Cross\:multiply\\ x = 70 \times 60\\\\x = 4200\\\\= 4200 \:times\:in\:an\:hour\\\\Note: 60\:minutes = 1 \:hour\)
Answer:
4200 beat per hour
Step-by-step explanation:
70 beat per min to beat per hour
70 beat 60 min
------- x ----------- = 4200 beat per hour
min 1 hour
which value makes the equation 10x/2=15 true
[ give thanks and rate 5stars if this helps u po! welcome! ]
Step-by-step explanation:
To solve the equation 10x/2 = 15, we can simplify the left-hand side first by dividing 10x by 2, which gives us 5x. So the equation becomes:
5x = 15
To isolate x, we can divide both sides by 5:
x = 3
Therefore, the value that makes the equation true is x = 3.
Answer:X=
Step-by-step explanation:
1.1 Discuss how interactions involving dummy variables, impact on the results and interpretation of a regression model. Use your own example. 1.2 State the problems of using the linear probability model. In addition, briefly explain how some of these problems can be remedied 1.3 Critically assess the goodness-of-fit measures of logit models.
Interactions involving dummy variables can provide insights into the different effects of independent variables across categories.
1. Dummy variables are binary variables that represent categorical variables in a regression analysis. When interactions are included between dummy variables and other independent variables, it allows for differential effects of the independent variables based on the different levels of the categorical variable.
For example, let's consider a regression model to predict income based on education level and gender. We can include an interaction term between education level (represented by dummy variables for different levels) and gender. This interaction term allows us to examine whether the effect of education level on income differs between males and females. It helps capture any gender-specific differences in the relationship between education and income.
1.2 The linear probability model (LPM) is a common approach to estimate the probability of an event occurring using a linear regression framework. However, it has several problems:
1. The predicted probabilities from the LPM can fall outside the [0, 1] range: Since the LPM does not impose any restrictions on the predicted probabilities, they can sometimes exceed the valid probability range. This violates the assumption of probabilities being bounded between 0 and 1.
2. Heteroscedasticity: The LPM assumes constant error variance across the range of the predictors. However, in practice, the variability of the error term may change with different levels of the predictors, resulting in heteroscedasticity. This violates the assumption of homoscedasticity.
3. Non-linearity: The LPM assumes a linear relationship between the predictors and the probability of the event. However, this may not always be the case, and using a linear model can result in misspecification.
To remedy these problems, an alternative to the LPM is to use logistic regression or probit regression models. These models explicitly model the probability of an event occurring and address the issues mentioned above. They provide predicted probabilities that fall within the valid range of 0 to 1, account for heteroscedasticity, and allow for non-linear relationships between the predictors and the probability of the event.
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The diameter of a circle is 8 millimeters. What is the circle's circumference?
Step-by-step explanation:
The circumference of a circle can be calculated using the formula C = πd, where d is the diameter. Substituting d = 8 millimeters and using the approximation π ≈ 3.14, we get:
C = πd = 3.14 x 8 mm = 25.12 mm
Therefore, the circle's circumference is 25.12 millimeters.
Find the midpoint of the hypotenuse.
Write without negative exponents: (3xy^−3)^−2
The expression \((3xy^{-3})^{-2}\) without negative exponents is \(\frac{y^6}{9x^2}\).
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
Given, An expression in exponents \((3xy^{-3})^{-2}\).
Now, Changing the place of exponents from the numerator to the denominator or vice versa changes its sign.
Therefore, \((3xy^{-3})^{-2} = 3^{-2}x^{-2}y^{6}\).
\(3^{-2}x^{-2}y^{6} = \frac{y^6}{3^2x^2}\).
\(\frac{y^6}{3^2x^2} = \frac{y^6}{9x^2}\).
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function contains the ordered pairs (0, 3), (6, 1), and (9, 0). Which statement explains whether or not the function is linear?
A.The function is linear because it has both x- and y-intercepts.
B.The function is linear because it has a constant rate of change.
C.The function is not linear because the difference in the x-coordinates is not constant.
D.The function is not linear because the y-coordinate is not a constant multiple of the x-coordinate.
Is that the correct answer for it please help me. I want to past my ecam
Answer:
No answer is be 28%
5+9+7+4=25
7/25 + .28 =28%
Step-by-step explanation:
Pete is making decorations for a dinner party.
The instructions tell him to use 9 flowers for a medium-sized decoration.
Complete each statement to adjust the flowers for different-sized decorations based on these instructions.
Tiva earns $48 for 6 hours of babysitting.
Complete each statement if Tiva keeps earning her babysitting money at this rate.Tiva earns $48 for 6 hours of babysitting.
Complete each statement if Tiva keeps earning her babysitting money at this rate.
The daffodils flower Pate needs is 8, total number of flower when rose is 2, is 18 and the carnations to be needed for decoration is 15.
What is algebraic expression?Algebraic expression are the expression which consist the variables, coefficients of variables and constants.
The algebraic expression are used represent the general problem in the mathematical way to solve them.
Pete is making decorations for a dinner party. The instructions tell him to use 9 flowers for a medium-sized decoration which has 2 lilies, 1 rose, 3 carnations, 2 daffodils and 1 iris.
The ratio of daffodils to total flower is,
n=2/9.
To make a large decoration, Pete uses 36 flowers. Let suppose the daffodils flower he needs for this is x. Thus,
x=36*(2/9)
x=4*2
x=8
The rose flower is increased from 1 to 2. Thus, the total number of flower also be twice for decoration.
Flower=2*9
Flower=18
Now Pete uses 10 lilies instead of 2 which is 5 times the medium-sized decoration. Thus, the carnations to be needed is,
Carnations=3*5
Carnations=15
Hence, the daffodils flower Pate needs is 8, total number of flower when rose is 2, is 18 and the carnations to be needed for decoration is 15.
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Find the indefinite integral using the substitution x = 4 sin(). (use c for the constant of integration. ) 1 (16 − x2)3/2 dx
The indefinite integral of \(1/(16-x^2)^{(3/2)}\) dx using the substitution x = 4 sin(t) is (1/8) arcsin(x/4) - \((1/16)x(16-x^2)^{0.5}\) + C here C is the constant of integration.
Let us take x = 4 sin(t), then dx/dt = 4 cos(t), and x² = 16 sin²(t). Substituting these values in the integral, we get:
\(\int\limits 1/(16-x^{2})^{(3/2}) dx\) =\(\int\limits1/(16-16sin^{2}(t))^{(3/2)} * 4cos(t) dt\)
= ∫1/16cos³(t) dt
= (1/16) ∫sec³(t) dt
= (1/16) (1/2 sec(t) tan(t) + 1/2 ln|sec(t)+tan(t)| + C)
Substituting back x = 4 sin(t), we get:
\(\int\limits1/(16-x^2)^{(3/2)}\) dx = (1/8) \(arcsin(x/4) - (1/16)x(16-x^{2})^{0.5}\) + C
where C is the constant of integration.
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A regular polygon has angles that all measure 162 degrees. How many sides does the polygon have?
A regular polygon with angles that all measure 162 degrees has 20 sides.
Let's first consider a formula to find the measure of an interior angle of a regular polygon. We can use the formula:
Interior angle = (n-2) x 180 / n,
where n is the number of sides of the polygon.
If all angles of the polygon measure 162 degrees, then we can set up an equation:
(n-2) x 180 / n = 162
Multiplying both sides by n, we get:
(n-2) x 180 = 162n
Expanding the left side, we get:
180n - 360 = 162n
Subtracting 162n from both sides, we get:
18n - 360 = 0
Adding 360 to both sides, we get:
18n = 360
Dividing both sides by 18, we get:
n = 20
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Plz hel p me my class is counting on me(you)
Answer:
The correct answer is D because for example...
Step-by-step explanation:
If b squared minus 4ac is non-negative, so at 0 or greater, we have at least one real solution. If it's less than 0, if it's negative, we have no real solutions!
Hope I was able to help, and I hope you Have a good day! :)
For what value of x is the
quadrilateral a parallelogram?
2xº
(x + 30°)
Answer:
50°
Step-by-step explanation:
In a parallelogram, opposite angles are equal and all angles sum up to 360°.
So, 2x + 2x + x + 30 + x + 30 = 360
6x + 60 = 360
6x = 300
x = 50°
I think this is the answer.
a business computer system is designed with a backup computer system in place so that the system will work as long as either the system or the backup is working properly. in a 30-day period when no one is available to fix the systems, each computer system has a 98% chance of working properly. for this 30-day period, what is the probability that neither the system nor its backup are working properly at the end of the 30 days? assume that the systems work or fail independently of each other.
The probability of either the system or the backup working properly is 1 - 0.02 = 0.98. Which is 0.02 x 0.02 = 0.0004 or 0.04%. Therefore, the probability that neither the system nor its backup is working properly at the end of the 30 days is very low, only 0.04%.
To find the probability that neither the primary computer system nor the backup system is working properly at the end of the 30-day period, we'll need to use the given probability of each system working properly (98%) and the fact that the systems work or fail independently.
Step 1: Find the probability of each system failing
Since each system has a 98% chance of working properly, the probability of it failing is 100% - 98% = 2%.
Step 2: Calculate the probability that both systems fail
Since the systems work or fail independently, we can multiply the probabilities of each system failing together:
2% (primary failing) x 2% (backup failing) = 0.02 x 0.02 = 0.0004
Step 3: Convert the probability to a percentage
0.0004 x 100% = 0.04%
Therefore, the probability that neither the primary computer system nor its backup are working properly at the end of the 30-day period is 0.04%.
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an aircraft seam requires 27 rivets. the seam will have to be reworked if any of these rivets is defective. suppose rivets are defective independently of one another, each with the same probability. (round your answers to four decimal places.)
The probability of at least one defective rivet in a seam requiring 27 rivets, assuming they are independently defective with the same probability, is approximately 68.3%.
To solve this problem, we can use the concept of probability and the binomial distribution.
The probability of a rivet being defective is denoted by "p". Since each rivet is defective independently of the others, the probability of a rivet not being defective (i.e., being good) is 1 - p.
The seam will need to be reworked if any of the 27 rivets is defective. Therefore, we want to calculate the probability that at least one rivet is defective.
The probability of at least one defective rivet can be found using the complement rule: subtracting the probability of no defective rivets from 1.
The probability of no defective rivets is given by (1 - p) raised to the power of 27 (since each rivet is independent).
So, the probability of at least one defective rivet is:
P(at least one defective rivet) = 1 - P(no defective rivets)
P(at least one defective rivet) = 1 - (1 - p)^27
Now, we can substitute any desired value for the probability of a defective rivet, "p," to calculate the probability of at least one defective rivet.
For example, if we assume a defective rivet probability of p = 0.05 (5%), the calculation would be as follows:
P(at least one defective rivet) = 1 - (1 - 0.05)^27
P(at least one defective rivet) ≈ 0.683
Therefore, with a 5% probability of a rivet being defective, the probability of at least one defective rivet in the seam is approximately 0.683 or 68.3%.
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Which issue is least likely arise in machine learning (ml) and artificial intelligence (ai)?
The issue of too many proficient business-savvy programmers is least likely to arise in machine learning(ml) and artificial intelligence(ai).
What is machine learning?
The process by which computers learn to recognize patterns, or the capacity to continuously learn from and make predictions based on data, then make adjustments without being specifically programmed to do so, is known as machine learning (ML), a subcategory of artificial intelligence.
The operation of machine learning is quite complicated and varies according to the task at hand and the algorithm employed to do it. However, at its foundation, a machine learning model is a computer that analyzes data to spot patterns before using those realizations to better fulfill the work that has been given to it. Machine learning can automate any task that depends on a set of data points or rules, even the more difficult ones.
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a measure of meaningfulness that expresses the difference between the experimental and control group in standard deviation units is the
The measure you're referring to is called "Cohen's d." It expresses the difference between the experimental and control group in standard deviation units, providing an indicator of effect size and meaningfulness in a study.
The measure of meaningfulness that expresses the difference between the experimental and control group in standard deviation units is the effect size. Effect size is typically calculated by dividing the difference between the means of the two groups by the standard deviation of the control group. It is a useful tool for comparing the effectiveness of different interventions or treatments, as it allows researchers to assess the magnitude of the difference between the groups beyond just statistical significance.
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Find integers s,t such that 15s+34t=1. You must show your work.
The equation 15s + 34t = 1 has infinitely many integer solutions, which can be represented as (s, t) = (-7/15 - 2k, k), where k is an integer.
To find integers s and t such that 15s + 34t = 1, we can use the extended Euclidean algorithm.
We start by applying the Euclidean algorithm to the original equation. We divide 34 by 15 and get a quotient of 2 and a remainder of 4. Therefore, we can rewrite the equation as:
15s + 34t = 1
15s + 2(15t + 4) = 1
15(s + 2t) + 8 = 1
Now, we have a new equation 15(s + 2t) + 8 = 1. We can ignore the 8 for now and focus on solving for s + 2t. We can rewrite the equation as:
15(s + 2t) = 1 - 8
15(s + 2t) = -7
To find the multiplicative inverse of 15 modulo 7, we can use the extended Euclidean algorithm. We divide 15 by 7 and get a quotient of 2 and a remainder of 1. We then divide 7 by 1 and get a quotient of 7 and a remainder of 0.
Working backward, we can express 1 as a linear combination of 15 and 7:
1 = 15 - 2(7)
Now, we can substitute -7 with the linear combination of 15 and 7:
15(s + 2t) = 1 - 8
15(s + 2t) = 15 - 2(7) - 8
15(s + 2t) = 15 - 14 - 8
15(s + 2t) = -7
Since 15 is relatively prime to 7, we can divide both sides of the equation by 15:
s + 2t = -7/15
To find integer solutions for s and t, we can set t as a parameter, say t = k, where k is an integer. Then, we can solve for s:
s + 2k = -7/15
s = -7/15 - 2k
Therefore, for any integer value of k, we can find corresponding integer solutions for s and t:
s = -7/15 - 2k
t = k
This means that there are infinitely many integer solutions to the equation 15s + 34t = 1, and they can be represented as (s, t) = (-7/15 - 2k, k), where k is an integer.
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The Powerball lottery works as follows
A. There is a bowl of 69 white balls. Five are randomly chosen without replacement. For purpose of being the winner , order does not count.
B. A second bowl contains 29 red balls. One red ball is chosen randomly. That red ball is called the power ball .
C. The winner of the grand prize will chosen correctly all five of the white balls and the one correct red ball .
ale correct red ball.
Use the factional (I) bused formula to find the likelihood of being the winner of the Powerball lottery
The probability of choosing all five white balls correctly from a bowl of 69 white balls and the probability of choosing the correct red ball from a bowl of 29 red balls is \({}^{69}C_5/29\) .
The probability of choosing all five white balls correctly can be calculated using the formula for combinations, where the order does not matter and the balls are chosen without replacement. The probability is given by:
P(Choosing all 5 white balls correctly) = (Number of ways to choose 5 white balls correctly) / (Total number of possible combinations)
The number of ways to choose 5 white balls correctly is 1, as there is only one correct combination.
The total number of possible combinations can be calculated using the formula for combinations, where we choose 5 balls out of 69. It is given by:
Total number of combinations = \({}^{69}C_5\)
Next, we need to calculate the probability of choosing the correct red ball from a bowl of 29 red balls. Since there is only one correct red ball, the probability is 1/29.
Finally, to find the likelihood of being the winner of the Powerball lottery, we multiply the probability of choosing all five white balls correctly by the probability of choosing the correct red ball:
Likelihood = P(Choosing all 5 white balls correctly) * P(Choosing correct red ball)
=\({}^{69}C_5 \times 1/29\\\)
This gives us the probability of being the winner of the Powerball lottery.
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Reduce each expression to a polynomial
((y-b)^(2))/(y-b+1)+(y-b)/(y-b+1)
The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.
In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:
((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)
Now, we can combine the two terms in the equation by finding a common denominator:
(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)
Next, we can combine the terms in the numerator by factoring out (y-b):
[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)
Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:
(y-b)(y-b+1)/(y-b+1) = y-b
Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1) after being simplified, is equivalent to the polynomial y-b.
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A floor is covered with 50 square-foot tiles.
All the tiles are purple except for those listed in the table. If
you toss
a quarter onto the floor at random, what is the probability that it
will land on a purple tile?
Thus, the probability that a quarter will land on a purple tile is 80%.
The total area of the floor is covered with 50 square-foot tiles. However, some of these tiles are not purple. We are not given the exact number of non-purple tiles, but we are provided with a table that lists some of them.
To find the probability that a quarter will land on a purple tile, we need to first determine the total area of the purple tiles.
If we assume that all the non-purple tiles are the same size as the purple tiles, then we can calculate the total area of the non-purple tiles using the information in the table.
The table lists five tiles that are not purple, and each of these tiles has an area of 2 square feet.
Therefore, the total area of the non-purple tiles is 5 x 2 = 10 square feet.
Subtracting the area of the non-purple tiles from the total area of the floor, we get the area of the purple tiles:
50 - 10 = 40 square feet
Therefore, the probability that a quarter will land on a purple tile is:
Area of purple tiles / Total area of floor = 40 / 50 = 0.8 or 80%
In other words, if you toss a quarter onto this floor at random, there is an 80% chance that it will land on a purple tile.
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