Answer:
Selling price of an item is $256.50 (A).
Step-by-step explanation:
Given : WE have given an item listed at $400 subject to a discounted series of $25%, 10%, and 5% .
To find : Find the selling price of an item.
Formula used : Selling price = marked price - discount.
Solution : We have an item listed at = $400.
Discount percentage = $25% , $10% , $5.
Discount 1 = $400 ×[tex]\frac{25}{100}[/tex] = $100.
Selling price = $400-100 = $300.
Discount 2 = $300 ×[tex]\frac{10}{100}[/tex] = $30.
Selling price = $300-30 = $270.
Discount 3 = $270 ×[tex]\frac{5}{100}[/tex] = $13.50.
Final selling price = $270-13.50 = $256.50.
Therefore, Selling price of an item is $256.50 (A).
Derive the equation of the parabola with a focus at (−2, 4) and a directrix of y = 6. Put the equation in standard form.
Answer: f(x) = -1/4x² -x + 4
Find all solutions in the interval [0, 2π). 7 tan^3x - 21 tan x = 0
To solve this problem, the first thing we can do is to take out 7 tan (x) from the whole equation, this results in simplification:
7 * tan (x) * (tan (x)^2 - 3) = 0
Therefore the initial roots are taken from:
tan (x) = 0
Calculating for x:
x = 0, pi
The other roots can be taken from:
(tan (x)^2 - 3) = 0
Calculating for x:
tan (x)^2 = 3
tan (x) = ± sqrt (3)
x = pi/3 , 2pi/3 , 4pi/3 , 5pi/3
Therefore the solutions are:
0 , pi, pi/3 , 2pi/3 , 4pi/3 , 5pi/3
an article with a net weight of 10 lb (pounds) is packaged in a box that weighs 1/2 lb. If 20 of these boxed articles are put into a freight container 15 lb, what is the gross weight?
Final answer:
The gross weight of the freight container with 20 boxed articles inside is 225 lb, calculated by adding the total weight of all the boxed articles (210 lb) to the weight of the container (15 lb).
Explanation:
To calculate the gross weight of the freight container with the packaged articles inside, we need to add the weight of the articles, the boxes, and the container itself.
First, we calculate the weight of one boxed article. Since the net weight of the article is 10 lb and the box weighs 0.5 lb, the total weight for one boxed article is 10 lb + 0.5 lb = 10.5 lb.
Next, we multiply the weight of one boxed article by the number of articles to find the total weight of all the boxed articles. For 20 articles, this is 20 imes 10.5 lb = 210 lb.
Finally, we add the weight of the freight container. The container weighs 15 lb, so the gross weight of the container with the articles is 210 lb + 15 lb = 225 lb.
Therefore, the gross weight of the freight container with 20 boxed articles inside is 225 lb.
Let log p/n=6 and log m/n=8 what is the relationship between p and m?
Given the logarithmic equations, it can be deduced that m is 100 times greater than p, assuming n>0 which is not zero to avoid division by zero and it is positive as logarithm is undefined for negative numbers.
Explanation:The question asks to find the relationship between p and m given two log equations. Using the rule of logarithms The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers (also known as the quotient rule), we can work out the relationship.
Given that log p/n = 6, it can be rearranged in exponential form: p = 106*n. And log m/n = 8 can be rewritten as m = 108*n.
Therefore, the relationship between p and m is that m is 100 times p, assuming n>0.
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There are 20 students on the school's student council. A special homecoming dance committee is to be formed by randomly selecting 7 students from student council. How many possible committees can be formed?
Final answer:
Using the combinations formula, there can be 77,520 different committees formed by selecting 7 students from a student council of 20 students.
Explanation:
To determine the number of possible committees that can be formed by selecting 7 students from a group of 20 students, we will use the combinations formula since the order of selection does not matter. This is a classic example of a combinatorial problem where we are choosing a subgroup from a larger group without regard to the order in which they are chosen.
The formula for combinations is as follows:
C(n, k) = n! / (k! * (n - k)!)
Where:
n is the total number of items,
k is the number of items to choose,
! indicates factorial, which means the product of all positive integers up to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
Applying this formula to our problem:
C(20, 7) = 20! / (7! * (20 - 7)!) = 20! / (7! * 13!) = (20 x 19 x 18 x 17 x 16 x 15 x 14) / (7 x 6 x 5 x 4 x 3 x 2 x 1)
After simplifying the factorial expressions and canceling out common factors, we find the number of possible committees that can be formed.
Therefore, there are 77520 possible committees that can be formed from a student council of 20 students by selecting 7.
Marijuana contains _____________ more carcinogens than cigarettes.
a. 20–30%
b. 40–60%
c. 50–70%
d. 60–80%
The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. find the length of the median of the trapezoid.
Final answer:
The length of the median of the trapezoid with perpendicular diagonals of lengths 8 and 10 is 9 units. This is calculated using properties of the median and the Pythagorean theorem.
Explanation:
The question you've asked regarding the median of a trapezoid with perpendicular diagonals of lengths 8 and 10 can be resolved by recognizing a property of the median in a trapezoid. The median (also known as the mid-segment) of a trapezoid is parallel to the bases and its length is equal to the average of the lengths of the bases. Since the diagonals are perpendicular, they would form right triangles with the two bases and the median line, dividing the trapezoid into four right triangles.
Let's denote the lengths of the bases as a and b, and the median as m. We know the diagonals intersect at their midpoints, thus splitting each into segments of lengths 4 and 5. Now we can form two right triangles sharing the median as a common side. Applying the Pythagorean theorem, we get two equations: m² + 4² = a² for the first right triangle and m² + 5² = b² for the second right triangle.
Since the median is the average of the bases, we have m = (a + b) / 2. Using the equations above, after some algebraic manipulations, we find that a² - b² = 16. With more manipulation, eventually, we find that (a - b)(a + b) = 16, and, since m is the average, 2m = a + b. Hence, we derive that 2m - b = (a - b), which simplifies to give us m = 9. This gives us the length of the median of the trapezoid as 9 units.
Marla swims twice a week. her equipment cost her $32.85 and she has a membership to the pool for $35 plus #3.50 per visit. she can walk to the pool, so transportation is free. how much will swimming cost her for the year?
Find the angular size of a circular object with a 3-inch diameter viewed from a distance of 4 yards.
Final answer:
To determine the angular size of an object with a diameter of 3 inches from 4 yards away, one can use the formula θ = d / D to calculate θ in radians, which is then converted to degrees, resulting in an angular size of approximately 1.19°.
Explanation:
To find the angular size of a circular object with a 3-inch diameter viewed from a distance of 4 yards, one can use the following formula for angular size θ (in radians): θ = d / D, where d is the diameter of the object and D is the distance to the object.
First, we convert the diameter and the distance to the same units. There are 36 inches in a yard, so 4 yards is 144 inches:
Diameter (d): 3 inchesDistance (D): 4 yards = 144 inchesThen, we calculate the angular size in radians:
θ = d / D = 3 inches / 144 inches = 0.0208333...
This can be converted to degrees by multiplying with 180/π:
θ(in degrees) = 0.0208333... * (180/π) = 1.19° (approximately).
Thus, the angular size of the object is approximately 1.19° when viewed from a distance of 4 yards.
Prove that a set with n elements has 2n subsets.
The number of electrons in the shell equals 2n² and in each subshell is 2(2l + 1), derived from the quantum mechanical principles and the Pauli exclusion principle governing electron arrangement in atoms.
Explanation:To prove that the number of electrons in the shell equals 2n² and that the number in each subshell is 2(2l + 1), we need to use the quantum mechanical principles that govern the arrangement of electrons in an atom. According to the quantum model, each electron in an atom is described by four quantum numbers: n, l, mi, and ms. The principal quantum number n represents the shell level, the angular momentum quantum number l describes the subshell (with values ranging from 0 to n-1), the magnetic quantum number mi describes the orientation of the subshell (ranging from -l to +l), and the spin quantum number ms indicates the electron's spin (which can be +1/2 or -1/2).
Each shell level n can have subshell values from 0 to n-1. For each value of l, there are 2l+1 possible values for mi, and for each mi, there can be two electrons (one with spin up and one with spin down, according to the Pauli exclusion principle). Therefore, the maximum number of electrons in any subshell is 2(2l+1). Summing over all values of l will give the total number of electrons in a shell, which is 2n². This follows from considering all possible orientations and spin states for each value of l within a shell. For the n=2 shell as an example, there are l=0 and l=1 subshells. The s subshell (l=0) can hold 2 electrons, and the p subshell (l=1) can hold 6 electrons, for a total of 2(2^2) = 8 electrons in the n=2 shell. Using similar calculations for other values of n will confirm the general formula.
The application of the Pauli exclusion principle ensures that no two electrons can have the same set of all four quantum numbers, which fundamentally limits the number of possible electrons in a subshell and a shell.
Are the functions f(x) = (x^2-1)/(x-1) and g(x)= x+1 equal for all x?
PLS HELP ILL GIVE BRAINLIEST TO WHO EVER ATTEMPTS THIS: The function H(t) = −16t2 + 112t + 24 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 5 + 3.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 4 through 7 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points) Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
The point P(12, 16) is on the terminal side of θ. Evaluate tan θ.
Answer:
tan(θ)=4/3
Step-by-step explanation:
Since opposite leg of the reference triangle equals 16 and the adjacent leg equals 12, tan(θ)=16/12 simplified to tan(θ)=4/3.
help plzzzzzzzz this is hard
Answer:
A is correct!
Step-by-step explanation:
Pedro has created the function f(x)= 4x-3/2 to represent the number of assingments he has completed where x represents the number of weeks in the course Person discovers that using the inverse function to solve for x=30, he can predict when he will have 30 assignments completed explain to Pedro how to accomplish this using complete sentences
Rachel has $100 in her savings account and deposits an additional $25 per week. joanna has $350 in her account and is saving $5 per week. after how many weeks will the two girls have the same amount of money?
Solve :
3x − 6 = 2x − 1
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?
Answer:
An expression can be used to find the value of y when x is 2 is,
y=8x ; Value of y = 16 when x = 2
Step-by-step explanation:
Direct variation states:
If y varies directly as x
⇒[tex]y \propto x[/tex]
then the equation is in the form of:
[tex]y = kx[/tex] where, k is the constant of variation.
As per the statement:
If y varies directly as x, and y is 48 when x is 6.
⇒[tex]y = kx[/tex]
y = 48 when x = 6
Substitute the given values in [1] and solve for k we have;
[tex]48= 6k[/tex]
Divide both sides by 6 we have;
8 = k
or
k = 8
Then, an equation we have;
y =8x ....[2]
We have to find value of y when x is 2.
Substitute the value of x = 2 in [2] we have;
[tex]y = 8(2) = 16[/tex]
Therefore, an expression can be used to find the value of y when x is 2 is,
y=8x and Value of y = 16 when x = 2
Given the function f (x) = 10x + 4, find each of the following. f(8), f(-4), f (0)
f(8)=?
f(-4)=?
f(0)=?
An increase in the money supply that causes money to lose its purchasing power and prices to rise is known as______________
Answer: An increase in the money supply that causes money to lose its purchasing power and prices to rise is known as Inflation.
Inflation means an increase in the money supply that causes money to lose its purchasing power and prices to rise.
As in case of inflation situation, prices get rise because of increase in the money supply to reduce the purchasing power of the individual or firms.
Measures to rectify the inflation :
1) Fiscal expenditure
2) Revenue expenditure
3) Reduction in deficit financing
Hence, Inflation is the correct answer.
The length of a rectangle is 11 ft less than three times the width, and the area of the rectangle is 70 ft2 . find the dimensions of the rectangle.
The width and length of the rectangle is 7ft and 10 feet respectively.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, The length of a rectangle is 11 ft less than three times the width has an area of 70ft².
Assuming the width of the rectangle to be x ft, therefore the length of the rectangle is (3x - 11) ft.
We know the Area of a rectangle (A) = length×width.
∴ x.(3x - 11) = 70.
3x² - 11x = 70.
3x² - 11x - 70 = 0.
3x² - 21x + 10x - 70 = 0.
3x(x - 7) + 10(x - 7) = 0.
(x - 7)(3x + 10) = 0.
x - 7 = 0 Or 3x + 10 = 0.
x = 7 Or x = - 10/3.
A negative value of x is inadmissible here as length cannot be negative.
So, the width of the rectangle is 7 ft and the length of the rectangle is
10 ft.
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Alexandra Romar has a previous balance at Porter Pharmacy of $68.42. She had payments and credits of $18.25. The monthly finance charge is 1.85% of the unpaid balance. After the finance charge was calculated, she made $34.00 in new purchases. What is her new balance?
Answer:
Her new balance is $85.10.
Step-by-step explanation:
Alexandra Romar has a previous balance at Porter Pharmacy = $68.42
She had payments and credits = $18.25
Now the unpaid balance = 68.42 - 18.25 = $50.17
The monthly finance charge on unpaid balance = 1.85% × 50.17
= [tex]\frac{1.85}{100}[/tex] × 50.17
= 0.928145 ≈ $0.93
So the balance with finance charge = 50.17 + 0.93 = 51.10
She made a new purchase = $34.00
Her new balance = 51.10 + 34.00 = $85.10
Her new balance is $85.10.
In attachment, help please 1 QUESTION, BRAINLIEST GETS 20 PTS
Answer:
Above is the right answer he got here first so give him brainiest
Find all the real square roots of 0.0004.
A. 0.00632 and -0.00632
B. 0.06325 and -0.06325
C. 0.0002 and -0.0002
D. 0.02 and -0.02
Pick the geometric term that matches the real-word object: a lip-gloss tube.
Answer: Cylinder.
Step-by-step explanation: Lip-gloss tubes may have different shapes, but the usual form of a lip-gloss tube is, as the name says, a tube.
This means that it has a circular base and a circular top, and a given height that connects the base and the top, the geometrical shape that has this shape is called a cylinder.
Rectangle 800 feet long and 700 feet wide. if fencing costs $13 per yard, what will it cost to place fencing around the playground
Three different circles and one line intersect each other.What is the largest possible number of intersection points
The largest possible number of intersection points between three different circles and one line is 12. This is calculated by considering that a line can intersect each circle at two points and each pair of circles can intersect at two points.
Calculating the Maximum Number of Intersection Points
To determine the largest possible number of intersection points between three different circles and one line, we can analyze the intersections one circle can have with a line and with another circle. A line can intersect a circle at most at two points - where it enters and exits the circle. Therefore, one line can intersect three circles at a maximum of 2 points per circle, totaling 6 points for the line intersections.
As for circle to circle intersections, each pair of circles can intersect at most at two points. With three circles, we can form three distinct pairs (Circle 1 with Circle 2, Circle 1 with Circle 3, and Circle 2 with Circle 3). Each pair can contribute up to 2 points of intersection, which gives us 6 points for the circle intersections.
Combining both types of intersections, we have a total possible number of intersections of 6 (from the line) + 6 (from the circles) = 12. Therefore, the maximum number of intersection points is 12.
I already answered this but I just want to make sure if I did it right
In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
c. If PX = 20, find PQ
Because C is the centroid, therefore:
Segments PZ = ZR; RY = YQ; QX = XP
A.
If CY = 10, then
PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answer: PC = 20 PY = 30
B.
If QC = 10, then
ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answer: ZC = 5 ZQ = 15
C.
If PX = 20
Because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer: PQ = 40
If a line has a slope of 2 and contains the point (-2, 1), what is its equation in point-slope form?