Step-by-step explanation:
No,
if the sprinkler covers a distance of 12 m meaning the 12 m is the diameter...then to find the area that it covers we use the formula for the circle since it's circular
A=πr2
A=3.142*36
A=113.112 cm3
At the bookstore, best-sellers are normally $19.95 each. During the store-wide 20% off sale, how much would it cost you, before tax, to buy two best-sellers?
F. $3.99
G. $7.98
H. $15 96
J. $31.92
K. $39.90
Step-by-step explanation:
20% off means you pay 80 % of the original price for two books
80% * ( 2 x 19.95 ) = .8 ( 39.90) = $ 31.92
a researcher wishes to study railroad accidents. he wishes to select 3 railroads from 10 class i railroads, 2 railroads from 6 class ii railroads, and 1 railroad from 5 class iii railroads. how many different possibilities are there for his study?
There are, 6300 different possibilities for the researcher’s study.
How do we calculate the different possibilities?Total number of class I railroads = 10Number of class I railroads selected = 3Total number of class II railroads = 6Number of class II railroads selected = 2Total number of class III railroads = 5Number of class III railroads selected = 1Number of different possibilities for selecting 3 class I railroads from 10 class I railroads = 10C3 = (10 x 9 x 8)/(3 x 2 x 1) = 120
Number of different possibilities for selecting 2 class II railroads from 6 class II railroads = 6C2 = (6 x 5)/(2 x 1) = 15Number of different possibilities for selecting 1 class III railroad from 5 class III railroads = 5C1 = 5Total number of different possibilities for selecting 3 class I railroads from 10 class I railroads, 2 class II railroads from 6 class II railroads, and 1 class III railroad from 5 class III railroads = 10C3 x 6C2 x 5C1= 120 x 15 x 5= 6300Therefore, there are 6300 different possibilities for the researcher’s study.
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HELP ASAP!!
A kite is flying 10 feet off the ground. It’s line is pulled out in casts a 9 foot shadow, find the length of the line if necessary round to the nearest 10th.
Answer:
We can use similar triangles to solve this problem. Let's call the length of the kite's line "x". Then, we can set up a proportion:
(length of kite) / (length of shadow) = (height of kite) / (length of shadow)
x / 9 = 10 / 9
To solve for x, we can cross-multiply and simplify:
x = 90 / 9
x = 10
Therefore, the length of the kite's line is 10 feet.
Step-by-step explanation:
A and B are independent.
If P(A) = 1/2 and P(An B) = 6/15
Find the slope-intercept form of the line with the slope m= 1/7 which passes through the point (-1, 4).
Answer:
y = 1/7x + 29/7
Step-by-step explanation:
Slope intercept form is y = mx + b
m = the slope
b = y-intercept
m = 1/7
Y-intercept is located at (0, 29/7)
So, the equation is y = 1/7x + 29/7
Determine the total amount of money that was utilized on fuel in June 2022
Therefore, the total amount of money utilized on fuel in June 2022 is R11 095,60.
What is percent?Percent is a way of expressing a quantity as a fraction of 100. It is denoted by the symbol %, which means "per hundred". Percentages are often used to represent proportions or ratios in various fields, including finance, science, and statistics. For example, an interest rate of 5% means that for every hundred dollars borrowed or invested, five dollars of interest will be charged or earned.
Here,
(a) To calculate the total distance covered by the water tanker in March 2022, we need to find the distance travelled per day and multiply it by the number of days in March.
Distance travelled per day = 2 × 18 = 36 km (since it's a return trip)
Number of weekdays in March = 31 - 4 (Saturdays) = 27
Total distance covered = distance per day × number of weekdays
= 36 km/day × 27 days
= 972 km
(b) To determine the quantity of fuel utilized by the water tanker in March 2022, we need to divide the total distance covered by the average fuel consumption rate.
Fuel consumption rate = 5 km/ℓ
Total distance covered = 972 km
Fuel utilized = total distance covered / fuel consumption rate
= 972 km / 5 km/ℓ
= 194.4 ℓ
(c) To determine the total amount of money utilized on fuel for the water tanker in March 2022, we need to multiply the fuel quantity by the fuel price.
Fuel price in March 2022 = R16,28/ℓ
Fuel utilized = 194.4 ℓ
Total cost of fuel = fuel price × fuel quantity
= R16,28/ℓ × 194.4 ℓ
= R3 163,39
Therefore, the total amount of money utilized on fuel for the water tanker in March 2022 is R3 163,39.
(d) To determine the total amount of money utilized on fuel in June 2022, we need to repeat the above calculation using the June fuel price.
Fuel price in June 2022 = R24,14/ℓ
Fuel capacity = 460 ℓ
Total cost of fuel = fuel price × fuel capacity
= R24,14/ℓ × 460 ℓ
= R11 095,60
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Complete question:
Records of the number of water tankers that were supplied to the construction site appear in the calender on ANNEXURE A. The water source is at a distance of about 18 km (return trip) from the construction site. The water tanker has a fuel capacity of 460 litres.. The rate of fuel consumption of the Mercedes water tanker averages 5 km/ℓ. The prices of fuel per litre in March and June 2022 appear below. JUNE 2022 FUEL PRICES \begin{tabular}{|l|l|} \hline DIESEL & COST \\ \hline 50ppm & R24,14 \\ \hline \end{tabular} Source: 4.1 (a) Calculate the total distance that the water tanker has covered in March (2) 2022. (b) Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022. (c) Determine the total amount of money that was utilized on fuel for the water tanker in March 2022. (2) 4.2 Determine the total amount of money that was utilized on fuel in June 2022.
Are the following statements equivalent? a>b and there is the number c ,so that a=b+c
No, the statements are not equivalent as the statement "a > b" simply means that "a" is greater than "b" and there exists a number "c" such that when added to "b", it equals "a". This does not necessarily mean that "a" is greater than "b".
The statements "a>b" and "there is the number c, so that a=b+c" are not equivalent. The statement "a>b" simply means that "a" is greater than "b," while the statement "there is the number c, so that a=b+c" means that "a" can be expressed as the sum of "b" and another number "c."
These statements are not equivalent because even if "a" is greater than "b," it may not be possible to express "a" as the sum of "b" and another number "c."
Additionally, even if "a" can be expressed as the sum of "b" and another number "c," it may not necessarily be true that "a" is greater than "b."
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Solve for x and graph the solution on the number line below
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
A cylindrical tank is one-fifth full of oil. The cylinder has a base radius of 80 cm. The height of the cylinder is 200 cm. 1 litre 1000 cm3 How many litres of oil are in the tank? Round your answer to the nearest litre
The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).
The volume of any cylinder can be calculated using the formula,
V = πr²h
(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)
As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:
Volume of oil = (1/5) x Total Volume
Substituting the given values, we have:
Total Volume = π(80cm)²(200cm) = 4,031,240 cm³
Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³
Converting cm³ to litres, we have:
1 litre = 1000 cm³
Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres
Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.
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three traffic lights on a street span 120 yards. if the second traffic light is 85 yards away from the first, how far in yards is the third traffic light from the seccond
The distance between the third traffic light from the second traffic light is 35 yards.
What is the distance?Three traffic lights on a street span 120 yards.
If the second traffic light is 85 yards away from the first.
Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.
This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.
Thus, the distance between the third traffic light from the second traffic light is 35 yards.
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A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places Part 1 of2 (a) Find P(5) P(5)- Part 2 of2 (b) Find P(More than 3) P(More than 3)
(a) n = 10, p = 1/4, and x = 5. Using the formula of binomial probability function,P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)
(b) P(More than 3) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)≈ 0.2784 (rounded to three decimal places)
Here n = 10, p = 1/4, and x = 5.Using the formula of binomial probability function,P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)
Find P(More than 3)For this, we need to calculate P(4), P(5), P(6),...,P(10) and add them.Using the formula of binomial probability function,P(4) = 10C4 * (1/4)^4 * (3/4)^6 = 0.2503 (rounded to three decimal places)P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)P(6) = 10C6 * (1/4)^6 * (3/4)^4≈ 0.0014 (rounded to three decimal places)P(7) = 10C7 * (1/4)^7 * (3/4)^3≈ 0.0001 (rounded to three decimal places)P(8) = 10C8 * (1/4)^8 * (3/4)^2≈ 0.0000 (rounded to three decimal places)P(9) = 10C9 * (1/4)^9 * (3/4)^1≈ 0.0000 (rounded to three decimal places)P(10) = 10C10 * (1/4)^10 * (3/4)^0≈ 0.0000 (rounded to three decimal places)P(More than 3) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)≈ 0.2784 (rounded to three decimal places)
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Pls answer my question it will be amazing if you do just pls.
The equation to show the relationship between x and y is y = 0.08x, where y is the amount of sales tax in dollars for the item and x is the cost of the item in dollars before tax.
What is tax?Tax is a compulsory financial charge or some other type of levy imposed upon a taxpayer by a governmental organization in order to fund various public expenditures. A failure to pay, along with evasion of or resistance to taxation, is punishable by law. Taxes consist of direct or indirect taxes and may be paid in money or as its labour equivalent. Most countries have a tax system in place to pay for public, common or agreed national needs and government functions. Some levy a flat percentage rate of taxation on personal annual income, but most scale taxes based on annual income amounts.
This equation reflects the fact that the amount of sales tax for an item is 8% of its cost before tax.
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Sales tax: The equation to show the relationship between x and y is x + y = C,
What is equation?An equation is a mathematical statement that expresses two mathematical expressions to be equal. It usually consists of two numbers, variables, or a combination of the two. An equation may be used to calculate a desired result, or to determine the relationship between two variables. Equations can also be used to test whether a statement is true or false. Most equations are written in the form of "a = b," where a and b are two numbers or variables.
where C is the cost of the item plus the sales tax. This equation can be explained mathematically as follows: the cost of the item (x) is added to the amount of sales tax (y) to give the total cost of the item with tax (C).
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the ratio of students who ade the honor roll to the total number of stoudents is 1:50. if there are 500 students in total how many made the honor roll?
If there are 500 students in total, the number of students who made the honor roll is 10 students, given that the ratio of students who made the honor roll to the total number of students is 1:50.
The number of students who made the honor roll can be found using proportions. Here's how to do it:
Let X be the number of students who made the honor roll.
The proportion can be set up using the given ratio as follows:
1:50 = X:500
Cross-multiplying this equation and solving for X gives:
50X = 500
X = 10
Therefore, 10 students made the honor roll.
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On January 1,1999 , the average price of gasoline was $1.19 per gallon. If the price of gasoline increased by 0.3% per month, which equation models the future cost of gasoline? y=1.19(1.003)^(x) y=1.19(x)^(1.03) y=1.19(1.03)^(x)
Answer:
first one
Step-by-step explanation:
The equation that models the future cost of gasoline is y=1.19(1.003)^(x), where "y" represents the future cost of gasoline per gallon and "x" represents the number of months since January 1, 1999.
In this equation, the initial cost of gasoline is $1.19 per gallon, and the cost increases by 0.3% per month, which is represented by the factor of (1.003)^(x).
Using this equation, you can calculate the future cost of gasoline for any number of months after January 1, 1999. For example, if you want to calculate the cost of gasoline 24 months after January 1, 1999, you can plug in x=24 and calculate y as follows:
y = 1.19(1.003)^(24)
y = 1.19(1.08357)
y = 1.288 per gallon
Therefore, the predicted cost of gasoline 24 months after January 1, 1999 is $1.288 per gallon.
Austin has a dimes and y nickels, having at most 28 coins worth a minimum of $2
combined. At least 18 of the coins are dimes and no more than 6 of the coins are
nickels. Solve this system of inequalities graphically and determine one possible
solution.
The solution of system of inequalities solved graphically is (18,6).
What is system of linear inequalities?A group of two or more linear inequalities are graphed together on a coordinate plane to discover the solution that concurrently satisfies all the inequalities. This is known as a system of linear inequalities. The location where all the half-planes overlap is where the system is solved. Each inequality defines a half-plane on the coordinate plane. Every point in this area, which is referred to as the feasible region, fulfils all of the system's inequalities. To identify the optimum solution for an optimization problem given a set of constraints, systems of linear inequalities are frequently utilised.
Let us suppose the number of dimes = a.
Let us suppose the number of nickels = y.
According to the problem we have the following conditions:
a + y ≤ 28 (at most 28 coins)
0.10a + 0.05y ≥ 2 (worth at least $2)
a ≥ 18 (at least 18 dimes)
y ≤ 6 (no more than 6 nickels)
Using different values of a and y plot the points.
The solution of this system of inequality is any point that lies in the feasible region.
One such point is (18, 6).
Hence, the solution of system of inequalities solved graphically is (18,6).
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At a basketball game, an air cannon launches T-shirts into the crowd. The function y=−18x2+4x
represents the path of a T-shirt. The function 3y=2x−14
represents the height of the bleachers. In both functions, y
represents vertical height (in feet) and x
represents horizontal distance (in feet). At what height does the T-shirt land in the bleachers?
The height that the T-short lands on the bleachers is x = 0.65.
What is quadratic formula?The quadratic equation may be solved by adding and subtracting the same number within the parenthesis to get a perfect square trinomial, which is how the quadratic formula is obtained. A version of the equation that can be solved using the square root function is the result of this method.
Given that it can be used to solve any quadratic equation regardless of the values of the variables a, b, and c, the quadratic formula is an effective tool for solving quadratic equations.
The equation of the path of T-shirt is y = -18x² + 4x and that of the height of bleachers is 3y=2x−14 or y = 2/3x - 14/3
To find the height of the T-shirt landing we find the intersection of the two equations as follows:
-18x² + 4x = (2x - 14)/3
-54x² + 12x = 2x - 14
54x² - 10x - 14 = 0
27x² - 5x - 7 = 0
Using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Substitute the values;
x = (-(-5) ± √((-5)² - 4(27)(-7))) / 2(27)
x = (5 ± √(925)) / 54
x = (5 ± 5√37) / 54
x = (5 + 5√37) / 54 = 0.65 and
x = (5 - 5√37) / 54 = -0.47
Hence, the height that the T-short lands on the bleachers is x = 0.65.
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What is the y-intercept of the line with the equation y = 4 x + 2?
a. -2
b. 4
c. 2
d. -1/2
Answer:
C. 2-----------------------------------
The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.
To find the y-intercept, substitute 0 for x in the equation y = 4x + 2:
y = 4*0 + 2 y = 2The y-intercept is 2 and matching choice is C.
Answer:
2
Step-by-step explanation:
We need to find out the y intercept of the given equation which is y = 4x + 2 .
y intercept is a point where the graph of the equation cuts the y axis. So at y intercept x coordinate will be 0 , so plug in x = 0 , in the given equation as ;
y = 4x + 2
y = 4(0) + 2
y = 0 + 2
y = 2
Therefore the y intercept of the line is 2 . ( option C )
A grocer has two kinds of candies, one selling for 90 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
? pounds of 40 − cent candies, ? pounds of candies that cost $1.40 per pound
Using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
So, we have:
x + y = 100 .........A
40 × x + 140 y = 85 × 100
40 x + 140 y = 8500 ........B
Solving (A) and (B) as follows:
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
(40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
0 + 100 y = 4500
y = 4500/100
Hence, the price per unit of grocery is $1.40 = y = 45 pounds.
Now, put the value of y in equation (A) as follows:
x + y = 100
x = 100 - y
x = 100 - 45
x = 55 pounds
The number of groceries at the 40-cent price is x = 55 pounds.
Therefore, using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
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Correct question:
A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
Solve for x,
using the tangent lines.
X
42°
x = [?]
can someone pls help explain how they got the answer? i’m having a hard time understanding, ty :)
Answer:
138°
Step-by-step explanation:
You want the measure of the angle at two tangents when they intercept an arc of 42°.
Supplementary anglesThe short answer is that the exterior angle x is the supplement of the measure of the arc:
x = 180° -42°
x = 138°
Exterior angleAn exterior angle where secants meet is half the difference of the arcs of the circle they intercept. Here, the secants have been located so the corresponding chord length between the near and far circle intercept points have degenerated to zero. That is, they are tangents.
The angle relation still holds:
x = (long arc - short arc)/2 = ((360° -42°) -42°)/2 = (360° -2·42°)/2
x = 180° -42° = 138°
QuadrilateralThe tangents, together with their associated radii form a quadrilateral. The angles at the tangents are 90°, and the total of all angles is 360°. This gives us the relation ...
x + 90° +42° +90° = 360°
x +42° = 180° . . . . . . . . . . . . . subtract 180°
x = 180° -42° = 138°
(We solved this with an extra step, so you could see the same "supplementary angles" relationship between x and 42°.)
4-77 Is the relationship shown in the 28+
graph at right below proportional? If
241
so, find the unit rate. If not, explain
why not.
The graph is/is not proportional
because
Unit rate:
Cost ($)
20
16-
12+
8
2 3 4 5
Number of Books
Purchased
Answer:
Step-by-step explanation:
A graph is proportional if the relationship between the two variables represented on the axes is constant, meaning that if one variable increases, the other variable also increases by the same factor. In other words, the graph forms a straight line that passes through the origin.
To find the unit rate, you need to look for the constant of proportionality, which is the ratio between the two variables represented on the graph. In this case, the variables are the number of books purchased and the cost in dollars.
If the graph is proportional, then the unit rate is the constant of proportionality, which is the cost per book. You can find the unit rate by dividing the total cost by the number of books purchased. For example, if the total cost for 4 books is $16, then the unit rate would be $4 per book.
If the graph is not proportional, then there is no constant of proportionality, and the unit rate cannot be calculated. The relationship between the two variables may be nonlinear, meaning that the rate of change between the variables is not constant.
A sector subtends an angle of 42° at the centre of a circle of radius 2.8 cm. Calculate the perimeter of the sector.
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ r=2.8 \end{cases}\implies s=\cfrac{(42)\pi (2.8)}{180}\implies s=\cfrac{49\pi }{75}\implies s\approx 2.05 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Perimeter of the sector} }{2.8~~ + ~~2.8~~ + ~~2.05} ~~ \approx ~~ \text{\LARGE 7.65}[/tex]
let's recall that the sector's perimeter includes the arc plust the radii.
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
w = 28 miles
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides.
The sum of the lengths of the sides is w + 28 + 28.
The perimeter is 84.
w + 28 + 28 must equal 84.
w + 28 + 28 = 84
Now we solve for w.
Add 28 and 28.
w + 56 = 84
Subtract 56 from both sides.
w = 28
Answer: w = 28 miles
Which of the following statements is about CD and CE is true? A. CD is longer than CE B. CE is longer than CD C. CD and CE are the same length D. CE is 5 units long
From the given graph, CE is longer than CD.
What is the distance between two coordinates?The length of the line segment bridging two locations in a plane is known as the distance between the points. d=√((x₂ - x₁)²+ (y₂ - y₁)²) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
Coordinates of E(8,6)
Coordinates of C(6,1)
Coordinates of D(3,-3)
x=8, y=6
x=6, y=1
x=3, y=-3
Distance CE=√{(8-6)² +(6-1)²} = √29
Distance CD=√{(6-3)² +(1+3)²}= √25=5
Therefore, CE is longer than CD.
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What is 6/11 as a decimal rounded to 3 decimal places?
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
X
The surface area of the triangular prism is 2016 [tex]feet ^2[/tex], we get to the answer by adding area of all faces in this prism.
What is surface area ?
Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.
To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.
First, let's find the area of the triangular base.
Area of triangle = (1/2) x base x height
Area of triangle = (1/2) x 18 x 24
Area of triangle = 216 [tex]feet ^2[/tex]
Next, let's find the area of each rectangular face.
Area of rectangle = length x width
Area of rectangle 1 = 24 x 22 = 528 [tex]feet ^2[/tex]
Area of rectangle 2 = 18 x 22 = 396 [tex]feet ^2[/tex]
Area of rectangle 3 = 22 x 30 = 660 [tex]feet ^2[/tex]
Now, we can add up the areas of all three faces to get the total surface area of the prism:
Surface area = area of rectangle (1+2+3) + 2 x area of triangle
Surface area = 528 + 396 + 660 + 2(216)
Surface area = 2016 [tex]feet ^2[/tex]
Therefore, the surface area of the triangular prism is 2016 [tex]feet ^2[/tex].
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
The second figure.
Step-by-step explanation:
The first figure's perimeter is:
70 in + 42 in + 56 in = 168 inches.
And the second figure's perimeter is:
42 in + 33 in + 33 in + 64 in = 172 inches.
Therefore, Figure 1 < Figure 2.
What is the number of normal subgroups of order 7 in a group of order 14?
In this particular question, we are being asked to find the number of normal subgroups of order 7 in a group of order 14. Before we begin, let's try to understand the different types of subgroups.Subgroups can be of two types: Proper Subgroups and Improper SubgroupsProper Subgroups are defined as subgroups which have more than one element and not equal to the entire group. Improper Subgroups are the subgroups which contain every element of the group.To determine the number of normal subgroups of order 7 in a group of order 14,
we need to use the following formula: `n_p = n/H`, where `n` represents the total number of subgroups of the group, `p` is the order of the subgroup we are looking for, and `H` is the normalizer of the subgroup in question.Using this formula, we can find that the order of the group is 14, and since 7 is a prime number, any subgroup of order 7 will be cyclic. Now, let's look at the different subgroups of the group of order 14:As 7 is a prime number and 7 divides 14, there will be one unique subgroup of order 7, and it will be cyclic.Since the group of order 14 is not a cyclic group, there are no other subgroups of order 7 besides the cyclic subgroup. Thus, the number of normal subgroups of order 7 in a group of order 14 is 1.
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Angela compro un terreno rectangular que tiene un perimetro de
10x - 28a
Si el ancho del terreno es 2x - 4a
¿Cual es la expresión que muestra la medida del largo del terreno?
The expression that shows the measurement of the length of the land is L = 3x - 10a.
Let L be the length of the rectangular plot.
We know that the perimeter of a rectangle is given by the sum of the lengths of all its sides. In this case, the perimeter is 10x - 28a, so we can write:
Perimeter = 2L + 2W
10x - 28a = 2L + 2(2x - 4a)
10x - 28a = 2L + 4x - 8a
2L = 6x - 20a
L = 3x - 10a
In other words, the length of the land is equal to three times the width minus ten times the value of 'a'.
To explain this equation in a little more detail, we can say that the length of the rectangular plot is dependent on both the width of the land and the value of 'a'.
The expression tells us that as the value of 'a' increases, the length of the land decreases, and as the width of the land increases, the length of the land also increases. This equation is useful because it allows us to calculate the length of the land without having to measure it directly, as long as we know the value of 'a' and the width of the land.
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a normal distribution of exam scores has a standard deviation of 8. a score that is 12 points above the mean would have a z-score of: a score that is 20 points below the mean would have a z-score of:
The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.
What is the z-score?The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.
z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.
z = {x-μ}/{σ} = {-20-0}/{8} = −2.5
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.
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ramona owns a small coffee shop, where she works full-time. her total revenue last year was $200,000, and her rent was $5,000 per month. she pays her one employee $3,000 per month, and the cost of ingredients averages $1,000 per month. ramona could earn $55,000 per year as the manager of a competing coffee shop nearby. her economic profit last year was were....
a. $18,000
b. $37,000
c. $55,000
d. $66,000
e. $92,000
Ramona's economic profit last year was $92,000 - $55,000 = $37,000. Therefore, the correct option is b. $37,000.
Ramona owns a small coffee shop, where she works full-time. Her total revenue last year was $200,000, and her rent was $5,000 per month. She pays her one employee $3,000 per month, and the cost of ingredients averages $1,000 per month. Ramona could earn $55,000 per year as the manager of a competing coffee shop nearby. Her economic profit last year was $37,000.An economic profit can be calculated by subtracting total costs from total revenue. Given that Ramona's total revenue is $200,000, her total cost is $5,000 + $3,000 + $1,000 = $9,000 per month. Multiplying this by 12 gives us her total cost for the year: $9,000 x 12 = $108,000. Ramona's economic profit last year was therefore $200,000 - $108,000 = $92,000. However, this figure doesn't take into account the opportunity cost of Ramona earning $55,000 as the manager of a competing coffee shop nearby. This needs to be subtracted from Ramona's economic profit.
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