To solve this, we can use the z statistic. The formula for z score is given as:
z = (x – u) / s
where x is the actual cost = 4000, u is the mean cost = 5000, and s is the standard deviation = 2000
Solving for z:
z = (4000 – 5000) / 2000
z = - 0.5
Therefore the piano cost is only 0.5 standard deviations below the average cost.
One number is 2 more than another. The difference between their squares is 32. What are the numbers
The two numbers are 7 and 9, which are determined by setting up an algebraic equation based on the information that one number is 2 more than the other and the difference between their squares is 32.
Explanation:The question involves finding two numbers where one number is 2 more than another and the difference between their squares is 32. To solve this problem, we denote the first number as ‘x’. Therefore, the second number will be '‘x+2’, as it is given to be 2 more than the first number. Next, we set up an equation based on the provided information that the difference between their squares is 32: ‘(x+2)² - x² = 32’.
Expanding the squared terms, we get ‘x² + 4x + 4 - x² = 32’. After simplifying the equation by canceling out ‘x²’ from both sides and subtracting 4 from both sides, we get ‘4x = 28’. Dividing both sides by 4 gives us ‘x = 7’. Thus, the first number is 7, and the second number is 7 + 2, which is 9.
The two numbers in question are 7 and 9, and they meet the criteria given in the problem statement.
In a gambling game, a woman is paid $3 if she draws a jack or a queen and $5 if she draws a king or an ace from an ordinary deck of 52 playing cards. if she draws any other card, she loses. how much should she pay to play if the game is fair?
The amount that the woman should pay to play the game is $1.23. Computed using the expected return and the probability of an event.
What is the probability of an event?The probability of an event is the ratio of the number of favorable outcomes to the event, to the total number of possible outcomes in the experiment.
How to solve the question?In the question, we are given that in a gambling game, a woman is paid $3 if she draws a jack or a queen and $5 if she draws a king or an ace from an ordinary deck of 52 playing cards. If she draws any other card, she loses.
We are asked the amount the woman should pay to play the game if it is fair.
The amount that the woman should pay to play the game is her expected return from the game.
Her expected return can be shown as E(X), where X represents all possible returns, which is calculated as:
E(X) = ∑ x.P(x), where P(x) is the probability of x.
The values of x can be:
3 when she draws a jack or a queen,
5 when she draws a king or an ace, and
0 when she draws any other card.
The probabilities of drawing a:-
The total number of possible outcomes remains constant throughout as 52.
Jack or a queen:
Number of favorable outcomes = 8 {4 jacks + 4 queens}.
Thus, the probability = 8/52 = 2/13.
King or an ace:
Number of favorable outcomes = 8 {4 kings + 4 ace}.
Thus, the probability = 8/52 = 2/13.
Any other card:
Number of favorable outcomes = 36 {All remaining cards, that is, 52 - 8 - 8 = 36}.
Thus, the probability = 36/52 = 9/13.
Thus, the expected return:
E(X) = ∑ x.P(x),
or, E(X) = 0.(9/13) + 3.(2/13) + 5(2/13),
or, E(X) = 0 + 6/13 + 10/13,
or, E(X) = 16/13 = 1.23.
Thus, the amount that the woman should pay to play the game is $1.23. Computed using the expected return and the probability of an event.
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Find the limit. lim θ→0 cos(4θ) − 1 / sin(7θ)
Can't figure this out. Any help is appreciated!
The limit of the given expression is undefined.
Explanation:To find the limit of lim θ→0 cos(4θ) - 1 / sin(7θ), we can simplify the expression first. Using the identity cos(2θ) = 2cos²θ - 1, we can rewrite the numerator as 2(cos²(2θ) - 1). The denominator, sin(7θ), can be rewritten as sin(2θ + 5θ). By applying the sum-to-product identities, we get sin(2θ)cos(5θ) + cos(2θ)sin(5θ), or cos(5θ)sin(2θ) + cos(2θ)sin(5θ).
Now, if we multiply both numerator and denominator by 1/sin(2θ)cos(5θ), we can simplify the expression further:
lim θ→0 (2cos²(2θ) - 1) / (cos(5θ)sin(2θ) + cos(2θ)sin(5θ)) = lim θ→0 (2cos(2θ) - 1/sin(2θ)) / (cos(5θ) + cos(2θ)tan(5θ)).
Now, we can substitute θ = 0 into the expression. Since cos(0) = 1 and sin(0) = 0, the denominator becomes cos(5(0)) + cos(2(0))tan(5(0)) = cos(0) + cos(0)tan(0) = 1 + 1(0) = 1. Thus, the limit is:
lim θ→0 (2cos(2θ) - 1/sin(2θ)) / (cos(5θ) + cos(2θ)tan(5θ)) = (2cos(2(0)) - 1/sin(2(0))) / 1 = (2cos(0) - 1/0) / 1 = (2(1) - 1/0) / 1 = (2 - 1/0) / 1 = 1/0 = undefined.Learn more about Limits here:https://brainly.com/question/8533149
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Terms that have the same variables raised to the same powers are called ___ terms.
Like terms are terms with the same variables raised to the same powers, allowing them to be combined by addition or subtraction.
Explanation:Terms that have the same variables raised to the same powers are called like terms.
In mathematics, particularly algebra, like terms are terms that contain the same variables to the same power, which allows them to be combined through addition or subtraction. An example of like terms would be 3x2y and 7x2y. Both contain the variable x raised to the second power, and y raised to the first power, thus they can be combined to form 10x2y.
Terms that have the same variables raised to the same powers are called "like" terms. In algebraic expressions, like terms are essential for simplifying and combining expressions efficiently. The concept is rooted in the understanding that terms with identical variable factors, such as x^2 or y, can be grouped together. This simplification aids in solving equations, factoring, and performing various algebraic operations.
Identifying and combining like terms streamline mathematical processes, providing a clearer and more concise representation of expressions. Ultimately, the recognition of like terms is a fundamental aspect of algebraic manipulation, contributing to the coherence and simplicity of mathematical expressions.
Final answer:
Terms that have identical variables raised to the same powers are called like terms. They can be added or subtracted as they represent the same quantities of variables to the same exponent powers.
Explanation:
Terms that have the same variables raised to the same powers are called like terms.
Like terms can be combined (added or subtracted) because they represent the same types of quantities raised to the same power. For example, in the expression 3x2 + 5x2, both terms are like terms because they both involve the variable x raised to the second power, which means that these two terms can be added together to get 8x2.
Raising a number to an exponent, such as squaring (raising to the second power) or cubing (raising to the third power), is a way to express repeated multiplication of the number by itself. For instance, the expression 52 = 5 x 5 = 25 shows that 5 is being squared, and the result is 25.
The population of rabbits in a national forest is modeled by the formula P= 12,000 + 1000 (t+1) where t is the number of years from the present. How many rabbits are now in the forest?
The current population of rabbits in the forest can be found by substituting t = 0 into the given formula P = 12,000 + 1000(t+1).
Explanation:To find the number of rabbits currently in the forest, we can substitute the value of t = 0 into the given formula. The formula P = 12,000 + 1000(t+1) represents the population of rabbits in the forest at any given year, where t is the number of years from the present. Since we want to find the current population, we substitute t = 0:
P = 12,000 + 1000(0+1)
P = 12,000 + 1000(1)
P = 12,000 + 1000
P = 13,000
Therefore, there are currently 13,000 rabbits in the forest.
The volume(capacity) in cubic inches of a reach-in refrigerator that measures 24 inches by 26 inches by 70 inches is_____cubic inches.
Please show work
The manager at a movie theater keeps track of the number of evening tickets and matinee tickets sold each day and the total money received. On Friday, a total of 63 tickets were sold, and the money collected was $742. If evening tickets are sold for $14 and matinee tickets are sold for $10, how many evening tickets and matinee tickets were sold?
A florist has 54 red roses and 36 white roses. If the florist creates the greatest number of identical bouquets possible with a combination of red and white roses without any roses leftover, how many red roses are in each bouquet?
PLEASE ANSWER THIS ASAP!!!!!!!!!!
54-36 =18
they can make 18 bouquets
54/18 =3
36/18 =2
18 bouquets with 3 red and 2 white roses each
Answer:
3
GCF of 54 and 36 = 18
so, 18 bouquets
then,
54 red roses ÷ 18 = 3 red roses in each bouquet
Suppose that in a population of 1000 there are 300 defective items and 700 items that are not defective. if you are selecting two items at random from this population, what is the probability they will both be defective?
The sum of three consecutive numbers is 57. What is the largest of these numbers?
57 / 3 =19
18 + 19 +20 = 57
largest number is 20
Answer:
20
Step-by-step explanation:
Solve for x
2+8-x=-24
The length of the shadow on flat ground of a man who is 6 feet tall and is standing up straight is 8 feet. The distance between the top of his head and the top of his head in the shadow is ___ feet.
20 POINTS
Determine the prime fractorization of 364
The measure of the largest angle of a triangle is 80º more than the measure of the smallest angle, and the measure of the remaining angle is 10º more than the measure of the smallest angle. Find the measure of each angle.
Assume f(x) = g(x). Which of the following two functions may be used to represent the function 3x = x – 4?
A null hypothesis can only be rejected at the 5% significance level if and only if:
The total cost for office expenses to run the organic strawberry farm varies directly with the number of months it is used. Which equation represents this scenario?
https://coststudyfiles.ucdavis.edu//uploads/cs_public/c5/a1/c5a181af-8e1b-474a-9509-443c3cb223ed/strawberry2ndyrcc2011.pdf
pages 15-16
Answer:
There are so many little things that go into organic farming and each of them adds additional costs.
Some of these additional costs are listed in the article located here.
Use the data table at the end of the document to answer the questions.
Which cost category in the table shows an example of direct variation?
Weed-Hand
The total cost for office expenses to run the organic strawberry farm varies directly with the number of months it is used. Which equation represents this scenario?
y = 63x
What would be the total cost for office expenses for 24 months?
$1,512.00
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what is the final amount of $70.00 that is put into a savings account with 16% interest rate for 25 years, if the interest is comounded 4 times per year?
The number that appears more frequently than any other in a set of numbers is the ________.
The lateral area of the right regular triangular prism is 18cm2. find the total surface area. give your answer in decimal form rounded to 2 decimal places
What is an estimate of the solution. If the equation 6n + 3 = 2? Use a table.
380 students increase 5% what is the new amount of students
Each car on the Steel Force train has 3 rows with 2 seats in each row. How many seats are on the train?
Reggie Jackson hit five home runs in the 1977 World Series, which lasted six games. By contrast, Lou Gehrig hot four homeruns in the 1982 World Series, a four-game series. On the average, which baseball player hit fewer home runs per game?
Reggie Jackson hit 5 home runs in 6 games sos he hit 5/6 = 0.833 home runs per game
lou gehrig hit 4 home runs in 4 games so he hit 4/4 = 1 home run per game
0.833 is less than 1 so Reggie Jackson hit fewer home runs per game
A system of equations has infinitely many solutions. If 2y-4x=6 is one of the equations, which could be the other equation?
Answer:
Equation is [tex]-8x+4y-12=0[/tex]
Step-by-step explanation:
An equation is a mathematical statement that two things are equal .
A system of equations is a set of two or more equations consisting of same unknowns.
Two equations [tex]a_1x+b_1y+c_1=0\,,\,a_2x+b_2y+c_2=0[/tex] have unique solution if [tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}[/tex]
infinite solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
no solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
Here, given: [tex]-4x+2y=6[/tex]
We can write this equation as [tex]-4x+2y-6=0[/tex]
Take another equation as [tex]-8x+4y-12=0[/tex]
Here, [tex]a_1=-4\,,\,a_2=-8\,,\,b_1=2\,,\,b_2=4\,,\,c_1=-6\,,\,c_2=-12[/tex]
[tex]\frac{a_1}{a_2}=\frac{-4}{-8}=\frac{1}{2}\\\frac{b_1}{b_2}=\frac{2}{4}=\frac{1}{2}\\\frac{c_1}{c_2}=\frac{-6}{-12}=\frac{1}{2}[/tex]
such that [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
Find last year’s salary if after. 2% pay rate, this year’s salary is $35,700
My friend sets out walking at a speed of 3 miles per hour. I set out behind her 5 minutes later at 4 miles per hour. For how many minutes will my friend have been walking when I catch up to her?
Please please help. The table list the heights of four trees, Sycamore 15 and 2/3, Oak 14 and 3/4, Maple 15 and 3/4, Birch 15.72. Study the table above select all true statements. A. The oak tree is the shortest. B. The birch tree is the tallest. C. Two of the trees are the same height. D. The sycamore tree is taller than the maple tree.
An investment firm recommends that a client invest in bonds rated AAA, A, and B. The average yield on AAA bonds is 4 %, on A bonds 6 %, and on B bonds 11 %. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond under the following conditions?
A. The total investment is $26,000 , and the investor wants an annual return of $1,620 on the three investments.
B. The values in part A are changed to $38,000 and $2,360 , respectively
A. The client should invest $(?) in AAA bonds, $(?)in A bonds, and $(?)in B bonds.
Final answer:
To meet the client's investment goals with an investment return of $1,620 on a total of $26,000, the client should invest $8,000 in AAA bonds, $14,000 in A bonds, and $4,000 in B bonds. This is derived from setting up and solving a system of linear equations based on the conditions provided.
Explanation:
Part A: Investment Calculations
To solve for the amount to invest in each type of bond, we can set up a system of equations based on the given conditions. Let x be the amount invested in AAA bonds, y be the amount invested in A bonds, and z be the amount invested in B bonds. We are told that the client wants to invest twice as much in AAA bonds as in B bonds, which gives us the equation x = 2z. The total investment is $26,000, so we have x + y + z = $26,000. The desired annual return is $1,620, and this gives us another equation based on the yields: 0.04x + 0.06y + 0.11z = $1,620.
By solving this system of equations, we can find the amounts to invest in each bond.
From x = 2z, we can substitute for x in the other equations.
The total investment equation becomes 2z + y + z = $26,000, simplifying to 3z + y = $26,000.
The return equation becomes 0.08z + 0.06y + 0.11z = $1,620, simplifying to 0.19z + 0.06y = $1,620.
We can now solve these two new equations for y and z, and then find x using x = 2z.
After solving, we get:
z (B bonds) = $4,000
x (AAA bonds) = 2z = $8,000
y (A bonds) = $26,000 - x - z = $14,000
Part B: Investment Calculations with Updated Values
The process for part B is similar, but with the updated total investment of $38,000 and a desired return of $2,360. The equations are adjusted accordingly, and after solving, we would get the new investment amounts for AAA, A, and B bonds.
The client should invest $8,000 in AAA bonds, $14,000 in A bonds, and $4,000 in B bonds for the conditions in part A.
How can you use rates to compare the cost of two boxes of cereal that are different sizes