The City Housing Authority has received 75 applications from qualified applicants for ten low-income apartments. Five of the apartments are on the north side of town, and five are on the south side. If the apartments are to be assigned by means of a lottery, find the following probabilities. (a) A specific qualified applicant will be selected for one of these apartments. (Round your answer to three decimal places.) (b) Two specific qualified applicants will be selected for apartments on the same side of town. (Round your answer to five decimal places.)
Do the side lengths of 5, 6, and 8 form a Pythagorean triple?
Yes
No
Find three real numbers x, y, and z whose sum is 6 and the sum of whose squares is as small as possible. g
The numbers that fit the conditions of the question are x = 2, y = 2, and z = 2. This sums to 6 and minimizes the sum of their squares (12).
Explanation:The subject of this problem involves real numbers and their sums and squares. The intention is to find three real numbers (x, y, and z) such that their sum equals 6, and the sum of their squares is minimized. By symmetry, it is preferable if these three numbers are equal. Therefore, x = y = z = 6/3 = 2 is the optimal solution.
So the three real numbers are x = 2, y = 2, and z = 2, which sum to 6 and the sum of their squares is as small as possible (12).
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A class has 6 boys and 15 girls
What is the ratio of the boys to girls
In a kitchen there are four containers that can hold different quantities of water as shown in the figure below
1-(x-2) liters
2- x liters
3- (x+2)liters
4- (x+4) liters
How many liters of water can the four containers hold in all
X^4+4
2x+4
X^2+2x
4x+4
Find f. (use c for the constant of the first antiderivative and d for the constant of the second antiderivative.) f ''(x) = 12x + sin x
A publishing company is going to have 24000 books printed. There are between 3 and 4 books out of every 3000 printed that will have a printing error. At this rate, which number could be the number of books that will have a printing error in the 24000
Given:
24,000 books
Between 3 and 4 books will have a printing error in every 3000 printed books
Find: in the 24000 books, the total number of books that will have a printing error
Solution:
Based from the given, we need to know how many sets of 3000 we
have in the 24000 books so:
24000 / 3000 = 8
Now, in each set of 3000 we have between 3 and 4 errors and we have 8 sets of 3000 books:
minimum errors 3 * 8 = 24
maximum errors 4 * 8 = 32
Therefore, at this rate, the number of books that will have a printing error in the 24000
will be between 24 and 32 or 24 < E < 32.
In 24,000 books, the number of printing errors could be between 24 and 32. This is calculated based on an error rate of 3 to 4 errors per 3,000 books.
To determine the number of printing errors in 24,000 books, we need to understand the error rate. The problem states that there are between 3 and 4 books with errors per 3,000 printed books.
First, find the range of error rates per 3,000 books:
Minimum errors: 3 errors per 3,000 booksMaximum errors: 4 errors per 3,000 booksNext, scale this up to 24,000 books:
Minimum errors: (3 errors/3,000 books) x 24,000 books = 24 errorsMaximum errors: (4 errors/3,000 books) x 24,000 books = 32 errorsTherefore, the number of books with printing errors in 24,000 books will be between 24 and 32.
Kim scored the least number of points. Claire scored five more points than Kim. Sam scored twice as many points as Kim. Together the three students scored 85 points. How many points did each student score?
A test consists of 20 problems and students are told to answer any 10 of these questions. In how many different ways can they choose the 10 questions?
Answer: The required number of ways is 184756.
Step-by-step explanation: Given that a test consists of 20 problems and students are told to answer any 10 of these questions.
We are to find the number of different ways in which the students choose 10 questions.
We know that
the number of ways in which r things can be chosen from n different things is given by
[tex]N=^nC_r.[/tex]
Therefore, the number of ways in which students chose 10 questions from 20 different questions is given by
[tex]N\\\\=^{20}C_r\\\\\\=\dfrac{20!}{10!(20-10)!}\\\\\\=\dfrac{20\times19\times18\times17\times16\times15\times14\times13\times12\times11\times10!}{10!\times 10\times9\times8\times7\times6\times5\times4\times3\times2\times1}\\\\\\=184756.[/tex]
Thus, the required number of ways is 184756.
An item is regularly priced at
$80
. It is now priced at a discount of
85%
off the regular price. What is the price now?
85% = 0.85
1-0.85 = 0.15
80 x 0.15 = 12
the price now is $12
On which number line do the points represent negative seven and one over two and +1?
Answer:
d
Step-by-step explanation:
You received 1⁄3 pound of candy from your grandmother, 1⁄2 pound of candy from your sister, but your best friend ate 1⁄5 pound of candy. How much candy do you have left?
The total amount of candy left after adding the candy received from the grandmother and the sister, and subtracting the candy eaten by the friend, is approximately 0.63 pounds.
Explanation:First, we add up the amounts of candy you received. You started with 1/3 pound from your grandmother and received an additional 1/2 pound from your sister, for a total of 5/6 pound of candy. However, because your friend ate some, we subtract 1/5 pound from this total. To do this, we need to convert all fractions to have a common denominator, which is 30 in this case. Therefore, 5/6 becomes 25/30, and 1/5 becomes 6/30. Subtraction gives us (25-6)/30 = 19/30 or approximately 0.63 pounds of candy left.
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Write the quadratic function in the form f (x)= a ( x - h) ^2 + k . Then, give the vertex of its graph. f (x) = -3x ^2 + 18x - 25
Writing in the form specified:f (x) = _______________
Vertex: (_, _)
Which transformations could be preformed to show that ABC is similar A"B"C"?
Assume that two fair dice are rolled. First compute P(F) and then P(F|E). Explain why one would expect the probability of F to change as it did when we added the condition that E had occurred.
F: the total is two
E: an even
total shows on the dice
Compute P(F).
P(F)equals=
nothing
(Simplify your answer.)
In the process of calculating probabilities of events on a pair of dice, we found P(F), the probability of rolling a total of two, to be 1/36. P(E), the probability of rolling an even total, to be 1/2. However, when determining P(F|E), the probability of rolling a two given we've rolled an even total, the probability changes to 1/18 due to the reduced sample space.
Explanation:The concepts involved in this question are related to probability, specifically the principles governing dice rolls. In this particular scenario, the events are rolling two dice and getting a total of two (Event F), and rolling an even total on the dice (Event E).
In this specific scenario, event F (the total is two) can only occur in one way - when both dice show 1. Since there are 36 potential outcomes when two dice are rolled (6 possibilities for the first die and 6 for the second), the probability of event F, P(F), is 1/36.
Event E (an even total) can occur in 18 ways (2,4,6 for the first die and 1,3,5 for the second or 1,3,5 for the first die and 2,4,6 for the second). So, P(E) = 18/36 = 1/2. However, when considering P(F|E) (the probability of event F given that event E has occurred), you need to adjust your consideration of 'total possibilities' based only on event E. Since P(E) = 1/2, your total possibilities now become 18. From these 18, only one will result in a total of two. Therefore, P(F|E) = 1/18.
Of course, there's different perspectives to consider how adding the condition that E had occurred would change the probability of event F. Essentially, by narrowing down the potential outcomes to only those that involve event E, you're working with a reduced sample space. This in turn affects the likelihood of event F occurring, hence the alteration in probability.
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Which set of coordinates, when paired with (-3, -2) and (-5, -2), result in a square?
find the slope of each line 5x-y=-7
You arrive in your history class today only to discover there is a pop quiz! You haven't studied and you aren't at all prepared. Fortunately, the quiz is multiple choice. Each question has five answer choices. You happen to have a die in your pocket. For each question you roll the die and answer A if the die shows 1, B if the die shows 2, etc, leaving the question blank if the die shows a six. For each question you are given one point if you answer it correctly and lose 1/4 point if you answer it incorrectly. You aren't penalized if you leave it blank, you just don't earn a point. What is the expected value for points earned on each question? Enter your answer as a decimal, rounded to two decimal places if necessary
Sam took his family to the zoo. An adult's ticket is two times the cost of a child's ticket. The total cost for two adults' tickets and three children's tickets was $28. How much do the tickets cost? A. Child's ticket = $5.60, adult's ticket = $11.20 B. Child's ticket = $2, adult's ticket = $4 C. Child's ticket = $4, adult's ticket = $8 D. Child's ticket = $7, adult's ticket = $14 \
The larger of two numbers is eight more than three times the smaller number.The sum of the two numbers is forty-eight.Find the two numbers.
The Rectangles are similar. Find the value of the variable (Picture Included)
A copy machine makes 28 copies per minute. How long does it take to make 154 copies?
Find the sum of the series. 1 + z/5 + z^2/25 + z^3.125
An aquarium 7 m long, 1 m wide, and 1 m deep is full of water. find the work needed to pump half of the water out of the aquarium. (use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.) show how to approximate the required work by a riemann sum. (let x be the height in meters below the top of the tank. enter xi* as xi.) lim n → ∞ n i = 1 δx express the work as an integral. 0 dx evaluate the integral. j
Final answer:
The work needed to pump out half the water from the given aquarium is 17,150 Joules. This is determined by applying physical principles to calculate the mass of the water, the effect of gravity, and using an integral to find the total work done against gravity.
Explanation:
The student is asking about the work required to pump half of the water out of an aquarium with dimensions 7 m long, 1 m wide, and 1 m deep using physics concepts involving work, force, and Riemann sums. To approach this problem, we must consider the work done against gravity to move the water from its initial position to the top of the aquarium. The density of water (ρ) is 1000 kg/m³, and the acceleration due to gravity (g) is 9.8 m/s².
First, calculate the volume of water to be pumped out, which is half the aquarium volume: V = ½ × 7 m × 1 m × 1 m = 3.5 m³. Convert this volume to mass using the density of water, m = ρV = 1000 kg/m³ × 3.5 m³ = 3500 kg.
The work done to pump out half the water can be calculated using the concept of the center of mass of the water being lifted, which is at a height h/2 from the top of the water when the tank is half full, where h is the depth of the tank. Therefore, the work is W = mgh/2 = 3500 kg × 9.8 m/s² × 0.5 m = 17150 J.
To approximate the required work using a Riemann sum, consider the small amount of work to lift a thin layer of water δx from a depth x to the top of the tank, dW = ρgAdx(x), where A is the area of the tank's surface. We set up the integral ∫ W = ρgA ∫ xdx from 0 to h/2, and find the limit as the number of partitions goes to infinity. The integration gives us the same work W = 17150 J.
A cube is packed with decorative pebbles. If the cube has a side length of 6 inches, and each pebble weighs on average 0.5 lb per cubic inch, what is the total weight of the pebbles in the cube?
Answer: 108 lbs.
Step-by-step explanation:
Given : A cube is packed with decorative pebbles. If the cube has a side length of 6 inches.
Volume of cube = [tex](side)^3[/tex]
i.e. Volume of cube = [tex](6)^3=216\text{ cubic inches}[/tex]
Since , each pebble weighs on average 0.5 lb per cubic inch.
Then, the total weight of the pebbles in the cube will be
= 0.5 x Volume of cube
= [tex]0.5\times216=108\text{ lb}[/tex]
Hence, the total weight of the pebbles in the cube =108 lbs.
Crestwood Paint Supply had a beginning inventory of 10 cans of paint at $25.00 per can. They purchased 20 cans during the month at $30.00 per can. They had an ending inventory valued at $500. How much paint in dollars was used for the month? A. $250 B. $1,350 C. $850 D. $350
the most efficient first step in the process to factor the trinomial 4x^3-20x^2+24x
A. Factor out -1
B. Factor out 4
C. Factor out 4x
D. Factor out (x-3)
BC is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?
A savings bank invests $58,800 in municipal bonds and earns 12% per year on the investment. How much money is earned per year?
1. Compare the strengths and weaknesses of the horizontal and vertical methods for adding and subtracting polynomials. Include common errors to watch out for when using each of these methods.
2. Explain why you cannot use algebra tiles to model the multiplication of a linear polynomial by a quadratic polynomial.
As an added challenge, develop a model similar to algebra tiles that will allow you to show this multiplication. Describe an example of your model for the product (x + 1)(x2 + 2x + 2).
3. Imagine that you are teaching a new student how to multiply polynomials. Explain how multiplying polynomials is similar to multiplying integers. Then describe the key differences between the two.
4. If you multiply a binomial by a binomial, how many terms are in the product (before combining like terms)? What about multiplying a monomial by a trinomial? Two trinomials?
Write a statement about how many terms you will get when you multiply a polynomial with m terms by a polynomial with n terms. Give an explanation to support your statement.
Answer:
1.To add and subtract polynomials, the horizontal technique of deleting parenthesis, collecting like terms, and simplifying is the simplest. When there are negative terms, it gets more difficult since one must ensure that the term remains negative when gathering comparable terms. The vertical approach of building up a box and adding vertically takes longer to set up, but once completed, there is a clear depiction of where all of the similar terms are.
2.Because the product of a linear factor and a quadratic factor is a cubic product, algebra tiles cannot be used to simulate the multiplication of a linear polynomial by a quadratic polynomial.
3.Distribute the first polynomial's terms to the second polynomial's terms. When multiplying two terms together, remember to multiply the coefficients (numbers) and add the exponents. However, with Integers, you multiply two integers with opposite signs.
4.Before combining like terms, there will be four terms. When a monomial is multiplied by a trinomial, the result is six. There will be nine terms in two trinomials.
Step-by-step explanation: