1. Bob's accounting profit is $25,000.
2. Bob's economic loss is $25,000.
3. The implicit cost in this example is the teacher's salary of $50,000 Bob could have got, working as a teacher.
What are explicit and implicit costs?Explicit cost refers to the accounting cost that a business incurs.
Explicit cost is different from implicit cost because implicit cost involves an opportunity cost.
What are accounting profit and economic profit?Accounting profit is the difference between total revenue and explicit cost.
Economic profit is the difference between accounting profit and opportunity cost or the cost of forgone alternatives.
Salary as a teacher = $50,000
Explicit restaurant cost = $500,000
Revenue = $525,000
Accounting profit = $25,000 ($525,000 - $500,000)
Economic loss = -$25,000 ($525,000 - $500,000 - $50,000)
Thus, whereas Bob makes an accounting profit of $25,000, he actually incurs an economic loss of $25,000 by forgoing his teacher's salary.
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an automated weight monitor can detect underfilled cans of beverages with probability 0.98. what is the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled can?
The probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].
What is probability?
Probability is defined as the possibility of an event to occur.
An automated weight monitor can detect underfilled cans of beverages with probability [tex]0.98[/tex]
Thus probability of success will be [tex]p=0.98[/tex]
So probability of failure [tex]q=1-p=1-0.98=0.02[/tex]
To find the first wrong detection happening on the tenth trial the first nine trials must be success followed by failure in the tenth trial.
Thus, required probability [tex]=p^9q^1=(0.98)^9(0.02)=0.01667496[/tex]
Hence the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].
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[3] How many solutions does the system of equations have? y = 5x - 6 y = 5x + 2
The system of equations has no solution when solving with elimination or substitution
so No solution is the answer
checking
y = 5x -6 ------(1)
y =5x +2------(2)
5x +2 = 5x-6
5x -5x = -6 -2
0 =-8
hence there is no solution since all variables are eliminated
A laptop computer originally priced at $1,700 now sells for $1,800. What is the percent of increase?%.The percent of increase is(Type an integer or decimal rounded to one decimal place as needed.)
EXPLANATION:
We are given the original price of a laptop computer at $1,700.
Now the price has been increased to $1,800.
Note that there is a $100 increase over the original price.
For us to calculate the percent increase we shall use the ratio of the increase over the original price and calculate as a percentage.
[tex]\begin{gathered} Original\text{ price}=1700 \\ Increase=100 \\ Percent=x \end{gathered}[/tex]We can now set up the following equation;
[tex]\frac{100}{1700}=\frac{x}{100}[/tex]We now cross multiply;
[tex]\frac{100\times100}{1700}=x[/tex][tex]\frac{10000}{1700}=x[/tex][tex]x=5.8823...[/tex]Rounded to one decimal place, the percent increase is;
ANSWER:
[tex]Increase=5.9\%[/tex]Comparing and Scaling Rates: Investigation 2.3 Homework 1. Keeley buys songs from a music website. She buys 35 songs for $26.25. What is the price per song? a. Complete the table. b. Lucius and Javier discuss how to write an equation relating price and number of songs. Lucius writes the equation n = 0.75C. Javier writes the equation C = 0.75n. Do you agree with Lucius or with Javier? Use the information from parts (a) to explain. 2. For each situation, find a unit rate and write an equation relating the two quantities. a. 3 dozen apples for $4.50 b. 30 bottles of water for $4.80 c. 24 ounces of mozzarella cheese for $2.88 Number of Songs, n 35 50 1 70 Cost, C $26.25 $3 $15
0.75
37.50
cost
dozen
= 4.50/3 = $1.50 / dozen
cost/bottles
2 3. Which of these items is the better buy? a. an 8-pack of glue sticks for $3.99 or 1 glue stick for $.54 b. a 12-pack of tape for $2.50 or 1 roll of tape for $.19 c. a 100-pack of pencils for $4.88 or 1 pencil for $.05 d. a 50-pack of paper clips for $.89 or a 25-pack of paper clips for $.45.
Answer:
Use the information from parts a
Step-by-step explanation:
Justin works in a department store selling clothing. He makes a guaranteed salary of $450 per week, but is paid a commision on top of his base salary equal to 30% of his total sales for the week. How much would Justin make in a week in which he made $2425 in sales? How much would Justin make in a week if he made x dollars in
We can convert that 30% into a decimal, as: 0.3 (That's 30/100)
Now, we can multiply this 0.3 by any quantity that we want to calculate 30% from.
For example, let's take Justin's commission:
[tex]2425\cdot0.3=727.5[/tex]Adding this to his base salary,
[tex]450+727.5=1177.5[/tex]We can conclude that Justin's paycheck for the week would be $1,117.5
Similarly, the expression for Justin's paycheck in a week were he made x dollars in sales is:
[tex]0.3x+450[/tex]shelly sews a square blanket that has an area of 144 square feet. it has 36 square blocks, each the same size. what is the approximate length of each side of a block? (1 point)
The side of the square of each block = 2 feet
Given,
Shelly sews a square blanket that has an area of 144 square feet.
and, it has 36 square blocks, each the same size.
To find the approximate length of each side of a block
Now, According to the question:
36 square blocks of same size. We need to find the area of each square block. so we divide = area / square blocks
= 144/ 36
= 4
The area of each square = 4 square feet
We know that
Area of square = side ^2
Side ^2 = 4
side = [tex]\sqrt{4}[/tex]
Side = 2
Hence, The side of the square of each block = 2 feet
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suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 15 days and a standard deviation of 5 days. let x be the number of days for a randomly selected trial. round all answers to 4 decimal places where possible. a. what is the distribution of x? x ~ n( , ) b. if one of the trials is randomly chosen, find the probability that it lasted at least 12 days. c. if one of the trials is randomly chosen, find the probability that it lasted between 17 and 22 days. d. 72% of all of these types of trials are completed within how many days? (please enter a whole number)
a. the distribution of X ~ N(15,5)
b. the probability that it lasted at least 12 days = 0·72575
c. the probability that it lasted between 17 and 22 days = 0.30567
d. 72% of all of these types of trials are completed within 13 days
(a)
The x follow normal distribution with mean standard deviation
X ~ N(15,5)
(b)
probability at least 12 days.
P(X≥12) = 1 - P(X ≤12)
= 1 - P((X - μ)/б ≤ (12-15)/5 ]]
= 1 - P[Z < -0.6]
= 1 - 0·27425
= 0·72575
(c)
Probability at least between 16 & 21 days
P(16 < x < 21) = p( (16-15)/5 < (X - μ)/б - (21-15)/5]
= p (0.2 < Z < 1.2 )
= p[Z < 1.2] - P[Z < 0.2]
= 0.8849 - 0.5792
= 0.30567
(d)
standard normal table z is 0.65
p (Z < 0.65) = 0.74215
using Z score formula
X = Z x б + μ
X = 0.65 x 5 + 15
X = 13
Explain probability ?This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.
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please help thank you
Answer:
%25 of customers ordered ice tea.
Step-by-step explanation:
To find percentage = Part/Whole x 100
35/140 x 100 = 0.25 x 100 = %25
f(x) = 2x³ - 4x + 6
f(3) =
Graph the cubic using its end behaviour and a few selected points.
The leading coefficient test requires one variable only
Select the correct answer.
Consider this function.
f(x) = 2x -2
Which graph represents the inverse of function f?
A. The first graph (Y)
B. The second graph (W)
C.The third graph (X)
D. The last graph (Z)
Answer:
option
Step-by-step explanation:
THE THIRD GRAPH(X)
The store at which Andy usually shops is having a sale. Roast beef cost four dollars a pound and shrimp cost $10 a pound. Write an equation to describe different possible combinations of roast beef and shrimp that he can buy for $96.
The equation to describe different possible combinations of roast beef and shrimp that he can buy for $96 is 4b + 10s = 96.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let roast beef = b
Let shrimp = s
Total cost = 96
Therefore the equation will be:
(4 × b) + (10 × s) = 96
4b + 10s = 96
This illustrates the equation.
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Tell whether the given situation is an example of Direct Variation or Inverse Variation. Write DV if it is a Direct Variation and IV for Inverse Variation. (NEED THE ANSWER ASAP)7. The height of a person and his weight
Given,
The statement is "The height of a person and his weight".
Required/
Identify the statement is inverse or direct variation.
As the height of the person increase then its their weight is also increased.
Similarly,
The height of the person decrease then its their weight is also decreased.
Hence, it is direct variation.
joanne graphed a linear funtion with a slope of -4 passing through 0,-2 nick graphed the function y=-2x - 4
Answer:
Explanation:
The slope-intercept form of the equation of a line can be written as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
So if Joanne graphed a linear function with a slope(m) of -4 passing through (0, -2), let's go ahead and determine the y-intercept of the line as shown below;
[tex]\begin{gathered} -2=-4(0)+b \\ -2=b \\ b=-2 \end{gathered}[/tex]Therefore, the equation of line will be y = -4x - 2 as graphed below;
Given Nick's function as y = -2x - 4, combining both graphs, we'll have the below;
The red line is Joanne's line while the blue line is Nick's line.
We can see from the above graph of both lines that Joanne's line intersects the y-axis above Nick's line's
x^2+5x−21=0
complete the square
The solutions to the quadratic equation using completing the square method are x = -(√109)/2 - 5/2 and x = (√109)/2 -5/2.
What is the solution to the quadratic equation?
Given the quadratic equation in the question;
x² + 5x - 21 = 0x = ?To solve using completing the square method, first add 21 to both sides
x² + 5x - 21 = 0
x² + 5x - 21 + 21 = 0 + 21
x² + 5x = 21
Next, create a trinomial square on the left side of the equation, determine the value that is equal to the square of half of b which is 5.
( b/2 )² = ( 5/2 )²
Now, add ( 5/2 )² to both sides of the equation
x² + 5x + ( 5/2 )² = 21 + ( 5/2 )²
Simplify
x² + 5x + 25/4 = 21 + 25/4
Add 21 and 25/4
x² + 5x + 25/4 = 109/4
Factor the perfect trinomial.
x² + 5x + 25/4 = 109/4
( x + 5/2 )² = 109/4
Solve for x by taking the square root of both sides.
x + 5/2 = ±√( 109/4 )
x = -5/2 ±√( 109/4 )
x = ±(√109)/2 -5/2
x = -(√109)/2 - 5/2, (√109)/2 -5/2
Therefore, the solutions to are x = -(√109)/2 - 5/2 and x = (√109)/2 -5/2.
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How many solutions does this equation have?
-7k 2k= -9k
no solution
one solution
infinitely many solutions
Submit
Answer:
1 answer
Step-by-step explanation:
when the terms are collected
[tex]4k = 0[/tex]
[tex]k = 0[/tex]
4x5y² how would I solve this
multiply the numbers
Answer is 20y2
Trigonometry question
Given the following function, choose the graph with the two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees.
1. sin0 = -2/3
2. sec0 = 2/1
3. tan0 = 4/5
4. csc0 = -3/2
5. cos0 = -3/5
Graph 1 contains the two angles in the domain 0 ≤ θ ≤ 360º that have cosine given by cos(θ) = -3/5.
Where is the cosine of angle negative?The sine and the cosine of an angle are represented in the unit circle, in which:
The x-axis is composed by the cosine of the angle.The y-axis is composed by the sine of the angle.Hence the cosine of the angle is negative when the x-axis is negative, which happens in these following quadrants:
Second quadrant.Third quadrant.The only equation that can be solved in the context of this problem is:
cos(θ) = -3/5.
The solution is composed by two angles, one in the second quadrant and one in the third quadrant, hence Graph 1 shows the correct solution.
The exact angles are found applying the inverse cosine function as follows:
θ = arccos(-3/5) = 126.9º = 233.1º.
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An acorn fell from a branch 20 feet high and landed on a branch 7 feet high. How long did it
take the acorn to fall?
It will take 1.62 seconds for an acron to fall on the branch of 7 feet high.
What is defined as the speed of object?The definition of speed is the rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity.For the given question,
An acorn fell from a branch 20 feet high.
An acorn landed on a branch 7 feet high.
The total distance travelled by and acron is 20 - 7 = 13 feet.
Let the final velocity of an acron is 'v'.
The initial velocity of an acron 'u' is zero.
Using third equation of straight line.
v² = u² + 2gsu = 0g = 9.8 /sec²s = 13 feetPut the values.
v² = 2×9.8×13
v = 15.96 ft/sec
Put the value in first equation of straight line.
v = u + gt
15.96 = 0 + 9.8×t
t = 15.96/9.8
t = 1.62 seconds.
Thus, it will take 1.62 seconds for an acron to fall on the branch of 7 feet high.
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100 POINTS Which statement about this figure is true?
It has no rotational symmetry.
It has rotational symmetry with an angle of rotation of 90°.
It has reflectional symmetry with four lines of symmetry.
It has point symmetry
before you answer, just know it does have rotational symmetry, just not 90° so A and B are out. i'm just stumped about C and D
Answer:
It has reflectional symmetry with four lines of symmetry.
Step-by-step explanation:
======================================================
Explanation:
Choice A is false since it does have rotational symmetry. See choice B.
Choice B is close, but the "90 degrees" needs to be "45 degrees". Each 45 degree rotation of the figure has the "before" and "after" be the same.
Choice C is one of the answers. There's a vertical line of symmetry, and a horizontal one as well. Then there are two diagonal lines of symmetry. Each goes through the center. A line of symmetry is a mirror line to allow us to reflect one half over this line to get the other half.
Choice D is another answer. It has point symmetry since we can pick any point on the figure and reflect it over the center point, to land on a corresponding image point on the opposite side of the figure. For example, the northern most point reflects over the center to land on the southern most point.
Your bus is traveling 60 km/hr on a class trip to a museum that is 90
kilometers from your school. How long will it take to get there?
OA. 1.5 hours
O
B. 2.0 hours
O
O
C. 0.5 hour
D. 1.0 hour
Answer:
nothing but B2. 0 hours
The bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.
Speed can be thought of as the rate at which an object covers distance.
i.e.
Speed = distance traveled/time taken
After arranging the equation we get,
Time taken = Distance traveled/Average speed
Here distance traveled by bus = 90 km
The average speed of the bus = 60 km/hr
So total time taken = 90/60 = 1.5 hours
So the bus will take 1.5 hours to cover 90 kilometers at an average speed of 60 km/hr.
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At basketball practice you made 21 out of 80 shots.
Which choice is closest to the percentage of shots you made?
Answer: 26.25% basketball practice
Step-by-step explanation: At basketball practice I made 21 out of 80 shots.
Therefore the percentage of shots I made is = 21/80×100%
=26.25%
Solve the equation. -5x + 1 = 31 x=
we get that:
[tex]\begin{gathered} -5x+1=31\rightarrow-5x=31-1=30 \\ x=-\frac{30}{5}=-6 \end{gathered}[/tex]so the answer is x=-6
simplify the expression then write a rule for the pattern (√t)²
The expression of (√t)² is t.
What are square and square roots?A number can be squared, but it can also be divided into its square root. The value we get from multiplying a number by itself yields its square value, whereas the value we get from finding a number that, when squared, yields the original value of the number yields its square root value. In the event that 'a' is the square root of 'b,' then a a = b. Any number has two square roots, one with a positive value and the other with a negative value, because any number's square is always a positive number. As an illustration, the square root of 4 has the values 2 and -2. A number's power 1/2 value is represented by a number's square root. In other words.
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in addition to the facts in the diagram which other statements are necessary to prove that? ABC is congruent to? EFG by the ASA criterion
Triangle ABC and the triangle EFG are congruent by the first and third statement.
What is the congruent diagram?
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
In the given example triangle ABC and triangle EFG having one same side of length 2.
By the ASA (Angle side angle) criteria, we want two angles are same then the triangles are congruent.
When "m ∠ B and m ∠ F" and "m ∠ A and m ∠ E" are same then the triangles are congruent.
Therefore, the first option is correct.
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Leo wants to buy two pairs of shoes. He found the shoes at two different stores at different prices and discounts. Store X is offering 10% off the price of the shoes. Store Y is offering $6 off the price of the shoes. For each shoe price listed in the table, indicate which store offers the lowest discounted price. Select the correct answer in each row.
The correct option regarding the discounts is given as follows:
Store Z has the best sale price of $28.
How to calculate the discount?The discount can be a percentage or an amount off, and the calculations are explained as follows:
Percentage: the original price is multiplied by the subtraction of one and the equivalent decimal of the discount.Amount off: the equivalent amount is given by the original amount subtracted by the amount off. ($6 off, the amount is subtracted by $6).Considering the discount plans and the original price of $35, the discounted prices in this problem are as follows:
Store X: 0.85 x 35 = $29.75.Store Y: 35 - 5 = $30.Store Z: 4/5 x 35 = 0.8 x 35 = $28.Hence the correct statement is given as follows:
Store Z has the best sale price of $28.
Missing information
The complete problem is:
Leo wants to buy some shoes. He found the shoes at three different stores for a price of $35. The stores are each having a sale:
Store X is offering 15% off the price of the shoes.Store Y is offering $5 off the price of the shoes.Store Z is offering a ⅕ discount off the price of the shoes.Which statement about the sale price of these shoes is true?
Store X has the best sale price of $20.Store Z has the best sale price of $28.Store Y has the best sale price of $30.More can be learned about discounts at https://brainly.com/question/7459025
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10. Which of the following is equivalent to thisexpression?72.7-4Tutor
To answer this question we need to remember that:
[tex]a^ma^n=a^{m+n}[/tex]then:
[tex]\begin{gathered} 7^2\cdot7^{-4}=7^{2-4} \\ =7^{-2} \end{gathered}[/tex]now we need to remember that:
[tex]a^{-n}=\frac{1}{a^n}[/tex]hence:
[tex]7^{-2}=\frac{1}{7^2}[/tex]Therefore:
[tex]7^{-4}\cdot7^2=\frac{1}{7^2}[/tex]and the asnwer is A.
2x + 3y = 13
Step 2 of 2: Determine the missing coordinate in the ordered pair (?, 3/2) so that it will satisfy the given equation
Answer:
[tex]\frac{17}{4}[/tex]
Step-by-step explanation:
Replace y with 3/2 and solve for x
2x + 3(3/2) = 13
2x + 9/2 = 13 Subtract 9/2 from both sides
2x = [tex]\frac{13}{1}[/tex] - [tex]\frac{9}{2}[/tex]
2x = [tex]\frac{26}{2}[/tex] - [tex]\frac{9}{2}[/tex]
2x = [tex]\frac{17}{2}[/tex] Divide both sides by 2
x = [tex]\frac{17}{2}[/tex] ÷ [tex]\frac{2}{1}[/tex]
x = [tex]\frac{17}{2}[/tex] x [tex]\frac{1}{2}[/tex]
x = [tex]\frac{17}{4}[/tex] o r4 [tex]\frac{1}{4}[/tex] or 4.25
Need an explanation why it’s 46.4
The perimeter of the triangle is 46.4 and the length of a triangle's boundary taken as a whole is referred to as its perimeter.
What is the perimeter of a triangle?The length of a triangle's boundary taken as a whole is referred to as its perimeter.A triangle is a polygon with three sides, and depending on the size of the sides and angles, there are various varieties of triangles.Any 2D shape's perimeter is determined by the total distance encircling it.Since perimeter indicates how long a shape's perimeter is, it is given in linear units.Calculate the perimeter of a triangle:
Perimeter of a triangle = a +b + c
a = 2 *9 = 18b = 2 * 7 = 14c = 2 * 7.2 = 14 .4a +b + c = 18 +14 +14.4 = 46.4Therefore, the triangle's perimeter is 46.4, and the whole length of a triangle's boundary is referred to as the triangle's perimeter.
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Dwayne puts $200.00 into an account to use for school expenses. The account earns 9% interest, compounded quarterly. How much will be in the account after 4 years? nt 1 Use the formula A = P 1 + where A is the balance (final amount), P is the principal (starting n 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.
Solution
For this case we can use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
P= 200
r= 0.09
n = 4
t= 4
And solving we got:
[tex]A=200(1+\frac{0.09}{4})^{4\cdot4}=285.52[/tex]
Write answer in scientific notation
(1.94 × 10³) (8 × 10")
Scientific notation the
