Percentage profit on a chocolate bar is 150%
What is percentage profit?Profit percentage is a top-level and the most common tool to measure the profitability of a business. It measures the ability of the firm to convert sales into profits. i.e., 20% means the firm has generated a net profit of $20 for every $100 sale.
%profit = (selling price - cost price)/cost price × 100
%profit =( 1.50-0.6)/0.6 × 100
%profit = 0.9/0.6 × 100
= 1.5 × 100
= 150 %
therefore the percentage profit on a chocolate bar is 150%
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in a class, there are 4 freshman boys, 6 freshman girls, and 6 sophomore boys. how many sophomore girls must be present if sex and class are to be independent when a student is selected at random?
We need 9 sophomore girls to make sex and class independent when a student is selected at random.
No. of freshman boys (fb) = 4
No. of freshman girls (fg) = 6
No. of sophomore boys (sb) = 6
Let, the no. of sophomore girls = sg
The total number of students in the class T = fb + fg + sb +sg
T = 4+6+6+sg
T = 16 + sg
The probability of selecting a girl is P(G) = (fg + sg) / T
= (6+sg)/(16+sg)
The probability of selecting a sophomore is P(S) = (sb + sg)/T
= (6+sg)/(16+sg)
As the events are independent, the probability of selecting a sophomore girl is P(sg) = P(G)*P(S)
sg/(16+sg) = (6+sg)*(6+sg)/(16+sg)(16+sg)
sg(16+sg) = (6+sg)(6+sg)
16sg + [tex]sg^{2}[/tex] = 36 + 6sg + 6sg + [tex]sg^{2}[/tex]
4sg = 36
sg = 9
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The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose intensity is 8000 units at a distance of 2 miles. What will the intensity be at a distance of 12 miles? Round your answer to the nearest unit.
a.
205 units
b.
222 units
c.
248 units
d.
186 units
Please select the best answer from the choices provided
A
B
C
D
Answer is B
B, 222 units, is the correct answer.
pins each cost £1.10
1000 pins are sold
35% of the pins are donated to charity
the rest are sold: 60% are sold for £3
40% are sold are sold £5 for 2
work out the percentage profit the company should make
The profit is £1,370. Then the percentage profit of the company will be 124.54%.
What is a profit?A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running, or creating anything.
The profit is given as,
Profit = Selling price - Cost price
The number of pins left after the donation to charity is given as,
⇒ (1 - 0.35) x 1,000
⇒ 0.65 x 1,000
⇒ 650 pins
The selling price when 60% are sold for £3 and 40% are sold for £5 is given as,
Selling price = 0.60 x 650 x £3 + 0.40 x 650 x £5
Selling price = £1,170 + £1,300
Selling price = £2,470
The cost price is given as,
Cost price = £1.10 x 1,000
Cost price = £1,100
The profit is given as,
P = £2,470 - £1,100
P = £1,370
Then the percent of profit is given as,
P = [(£1,370) / £1,100] x 100
P = 124.54%
The profit is £1,370. Then the percentage profit of the company will be 124.54%.
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two cards are selected at random from a deck of 52. what is the probability that one is a spade and the other is a king
The probability that one card is a spade and the other is a king when two cards are drawn at random from a deck of 52 cards is 0.0196.
To calculate the probability that one card is a spade and the other is a king when two cards are drawn at random from a deck of 52 cards, we need to first determine the total number of possible outcomes, which is the number of ways to select two cards from a deck of 52. This can be calculated using the formula for combinations, which is:
nCr = n! / r!(n-r)!
where n is the total number of objects (52 cards in this case), r is the number of objects to be selected (2 cards), and ! denotes the factorial operation.
So, the total number of possible outcomes is:
52C2 = 52! / 2!(52-2)! = 1326
Next, we need to determine the number of favorable outcomes, which is the number of ways to select one spade and one king from the deck. Since there are 13 spades and 4 kings in a deck, there are 13 x 4 = 52 ways to select one spade and one king.
However, we need to divide this number by 2 to avoid double counting the two possible orders (king-spade or spade-king), which gives us 26 favorable outcomes.
P = favorable outcomes / total outcomes = 26 / 1326 = 0.0196 or about 1.96%
So, there is a very low probability of selecting one spade and one king when two cards are drawn at random from a deck of 52 cards.
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What is the radius of a cylinder with a volume of 950 inches to the third power in a height of 10 inches
Answer:
Step-by-step explanation:
Given the volume of a cylinder, V = πr^2h, where r is the radius, h is the height, and π is Pi, we can find the radius by rearranging the equation and solving for r.
V = πr^2h, so r^2 = V / (πh)
Taking the square root of both sides, we have:
r = √(V / (πh))
Substituting the given values:
r = √(950 / (π * 10))
Since Pi is approximately equal to 3.14, we can calculate the approximate value of r:
r = √(950 / (3.14 * 10))
r ≈ 7.46
Therefore, the radius of the cylinder with a volume of 950 cubic inches and a height of 10 inches is approximately 7.46 inches.
7. Evaluate the function for x = 2, then evaluate the function for x = 7.
h(x) = −4x + 61 (SHOW YOUR WORK)
The solution of the expression at x = 2 is 53 and at x = 7 is 33.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that the expression is h(x) = −4x + 61. The value of the expression at x = 2 and x = -7 will be calculated as:-
At x = 2,
h(x) = −4x + 61
h(2) = -4 x 2 + 61
h(2) = -8 + 61
h(2) = 53
At x =7
h(x) = −4x + 61
h(2) = -4 x 7 + 61
h(2) = -28 + 61
h(2) = 33
Therefore, the values are 53 and 33.
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Evaluate the trigonometric function of the quadrant angle. (If an answer is undefined, enter UNDEFINED.)
Question: csc (3/2)
The value of csc(3π/2) is -1.
What is a trigonometric function?
Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Numerous trigonometric identities and formulas indicate the relationship between the functions and aid in determining the triangle's angles.
The given trigonometry function is csc(3π/2)
Assume that y = csc(3π/2)
Break the angle:
y = csc(π + π/2)
Applying the formula csc(π + θ) = -csc θ:
y = - csc(π/2)
y = -1 [since csc(π/2) = 1]
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doughnuts are sold in bags and cartons
a bag holds 4 doughnuts and a carton holds 10 doughnuts
Answer:
Step-by-step explanation:
14 doughnuts in total
as a rule of thumb, altitude corrections of less than 100 feet should be corrected by using
As a rule of thumb, altitude corrections of less than 100 feet for determining the pressure at a given altitude should be corrected using the standard pressure-altitude correction tables.
These tables provide the correction factor for the difference between the actual and standard atmospheric pressure at a given altitude. The correction factor can then be applied to the standard pressure value to obtain the actual pressure value at that altitude. Note that the standard atmospheric pressure is defined as 29.92 inches of mercury (in Hg) at sea level. The pressure decreases with increasing altitude in the lower atmosphere. The pressure-altitude correction tables provide a convenient and accurate way of determining the atmospheric pressure at different altitudes.
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DUE FRIDAY NEED HELP NOW!!!
Let P, Q, R, and S be the midpoints of sides AB, BC, CD, and DA, respectively. Use a ruler to locate these points as precisely as you can, and join them to form a new quadrilateral PQRS. What do you notice about the quadrilateral PQRS?
ABCD is a rectangle, and P, Q, R, and S are mid points of the sides AB, BC, CD, and DA, respectively. show that the quadrilateral PQRS is a rhombus
Solve for x questions in picture
Answer:
x = 4
Step-by-step explanation:
Move the x to the left-hand side and change its sign
2x - x = 9 - 5
x = 9 - 5
Answer:
x=4
Step-by-step explanation:
Subtract 1x from both sides
Subtract 5 from both sides to isolate the variable
x=4
Find the integral : [tex]\frac{x+1}{x(1+x.e^x)}[/tex]
The value of the equation [tex]\frac{x+1}{x(1+x.e^x)}dx[/tex] after taking the integral is [tex]ln ( \frac{x.e^x}{x.e^x+1} ) + c[/tex].
What is meant by the integral of an equation?
Calculating areas, volumes, and their extensions require the use of integrals, which are the continuous equivalent of sums. One of calculus' two fundamental operations is integration, which involves computing integrals. The other essential operation is differentiation. The area under the graph of a function for some interval can be expressed numerically as the integral (definite integral), or a new function can be created whose derivative is the original function (indefinite integral).
Given equation [tex]\frac{x+1}{x(1+x.e^x)}dx[/tex]
Multiply and divide the equation by eˣ
The equation becomes [tex]\frac{e^x(x+1)}{e^xx(1+x.e^x)}dx[/tex]
Now substitute eˣx = a
Differentiating both sides
[eˣ + xeˣ]dx = da
eˣ[1+x]dx = da
Substituting the above in the equation
[tex]\frac{e^x(x+1)}{e^xx(1+x.e^x)}dx = \frac{da}{a(1+a)}[/tex]
Now add and subtract a in the numerator
[tex]\frac{1 da}{a(1+a)} = \frac{a-a+1}{a(1+a)} da = \frac{a+1-a}{a(1+a)} da = \frac{1}{a} da - \frac{1}{a+1} da[/tex]
Now taking integral
[tex]\int \frac{1}{a} da -\int \frac{1}{a+1} da = ln(a) - ln(a+1) + c = ln ( \frac{a}{a+1} ) + c[/tex]
Now substituting back the value of a = eˣx
Therefore the value of the equation after taking the integral is [tex]ln ( \frac{x.e^x}{x.e^x+1} ) + c[/tex].
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Frank in going to plant b vegetables in one garden and 2b+1 vegetables seeds in a another how many seed is frank going to plant
Answer: Frank is going to plant "b" vegetables in one garden and "2b + 1" vegetables in another garden. So, the total number of seeds he is going to plant is b + (2b + 1) = 3b + 1.
Step-by-step explanation:
need help with this asap please!!
Answer:
A van can carry 18 students; a bus can carry 41 students.
Step-by-step explanation:
Let v = capacity of van.
Let b = capacity of bus.
School A:
3v + 12b = 546
School B:
13v + 6b = 480
Our system of equation is:
3v + 12b = 546
13v + 6b = 480
3v + 12b = 546
+ -26v - 12b = -960
-----------------------------
-23v = -414
v = 18
3v + 12b = 546
3(18) + 12b = 546
54 + 12b = 546
12b = 492
b = 41
Answer: A van can carry 18 students; a bus can carry 41 students.
pls help i don’t understand
Solve for n: 4^n+3 x 16^n - 8^3n
The expression 4^n+3 x 16^n - 8^3n cannot be solved for n
How to determine the solution of nfrom the question, we have the following parameters that can be used in our computation:
4^n+3 x 16^n - 8^3n
The question implies that we solve for n
This in other words mean that we determine the solution for n
The given parameter is an expression (not an equation or an inequality)
To solve for a variable, the given parameter must be an equation or an inequality
Hence, the value of n cannot be determined or it has infinite many solutions
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at a fixed operating setting, the pressure in a line downstream of a reciprocating compressos os known to maintain a mean value of 12.0 bar with a standard deviation of 1.0 bar based on its history. what is the probability that the line presure will exceed 13.0 bar during any measurement
The probability that the line pressure will surpass 13.0 bars during any measurement is P [Z > 13] = 0,1587, or 15.87%.
If the line pressure exceeds 13.0 bars, there is a chance that:
P [ Z > 13 ] = 1 - P [ Z ≤ 13]
P [Z 13] will be located in the z table when z (score) =
Z (score) equals (Z - 0) /
Z = (13 - 12)/1 (score).
the z-table, we then discover
P [ Z ≤ 13] = 0,8413
Finally . P [ Z > 13 ] = 1 - P [ Z ≤ 13]
P [ Z > 13 ] = 1 - 0,8413
P [Z > 13] = 0,1587, which is equal to 15,87%.One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprovable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it.
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Are both correct? EXPLAIN your reasoning.
We can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.
What are equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, and others.
Equation: A declaration that two expressions with variables or integers are equal.
In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
So, as we have the equation:
12x + 3 = 3(5x + 9)
Now, as we can see, Sadio took out 3 as common from LHS and RHS and solved the equation.
Which gave her the value of x as -8.
Amir, on the other hand, did not take out anything as common and directly multiply 3 with other terms in the brackets to solve the equation.
He also got -8 as the value of x.
Hence, we can conclude that yes both the ways of solving the equation is correct which is done by Sadio and Amir.
Therefore, we can draw the conclusion that Sadio and Amir's methods for solving the equation are both valid.
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the original price of shoe is 80$. They are on sale 25% off. The sales tax is 6.25%. How much will you pay for the shoes?
Answer: The total amount paid for shoes = $63.75
Step-by-step explanation:
The original price of the shoes = $ 80
Sale Discount = 25 %
So, the discount offered = 25 % of 80 = 20
So, the Discounted Price = Marked price - discount
= $ 80 -$ 20 = $ 60
Now, we need to calculate the sale tax of 6.25 % on $ 60.
Also, we know that Sales Tax = Sales Tax rate x Sale Price
= $ 60 x 0.0625 = $ 3.75
Total Cost = Sale Price + Sales Tax
= $ 60 + $ 3.75 = $63.75
Hence, the total amount paid for shoes = $63.75 included sales tax
What is the answer? The answer choices were 45, 40, and 50.
Solve the following system equation, showing your work in the space
provided.
y = 5x + 3
-2x-4y= 10
Step-by-step explanation:
the first equation is already (without any transformation) expressing y in terms of x.
we can use that identity in the second equation :
-2x - 4(5x + 3) = 10
-2x - 20x - 12 = 10
-22x = 22
x = -22/22 = -1
and then we use the first equation to solve for y :
y = 5×-1 + 3 = -5 + 3 = -2
so,
x = -1
y = -2
Please help me
the town's population has increased for 80000 to 9000 in the past 10 years . what was the present % increase
The percent increase of the population in the past 10 years is 12.5%.
What is the percent increase of the population?Percent increase is simply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.
It is expressed as;
C = ((x₂ - x₁) / x₁)100%
Where x₁ is initial value and x₂ is new value
Given that;
Initial population x₁ = 8000New population x₂ = 9000Percentage increase C = ?Plug in the given values into the above equation and simplify.
C = ((x₂ - x₁) / x₁) × 100%
C = (( 9000 - 8000 ) / 8000) × 100%
C = ( 1000 / 8000) × 100%
C = 0.125 × 100%
C = 12.5%
Therefore, the percent increase is 12.5.
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Solve four-ninths plus five-eighteenths equals blank.
how many times larger is a centigram than a milligram
A centigram is 100 times larger than miligram as evident through comparison of the two values.
We know that centi can be represented as 1/100 and milli will be represented as 1/1000. Now, the magnitudes representing each of these will be in relation to gram. So, further calculating the times with which centigram is larger than miligram.
For this, the expression to be used is -
Value = centigram/milligram
Keep the values in formula to find the comparison
Value = 1/100 ÷ 1/1000
Rewriting the expression
Value = 1000/100
Performing division on Right Hand Side of the equation
Value = 100
So, we see that centigram is 100 times larger than miligram.
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With the information given, can you prove
that this quadrilateral is a parallelogram?
Yes
No
We can see here that with the information given, one can prove that this quadrilateral is a parallelogram. Thus, it is yes>
What is a quadrilateral?A polygon with four sides and four vertices (corners) is called a quadrilateral. Its internal angles add up to 360 degrees.
Squares, rectangles, parallelograms, trapezoids, and rhombuses are all examples of quadrilaterals.
We can see that looking at the quadrilateral, we can deduce that it is parallelogram. This is because the opposites sides are equal. Also, their opposite angles are equal.
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if you need 8 coins in 1 box and there are 240 coins how many boxes will you be able to fill
Hunter, Trace, and Jacob were adding up their ages. The total was 49, If Hunter is 3 years older than Trace, and Jacob is twice Hunter's age. What are the ages of the three boys?
Answer:
Step-by-step explanation:
Let's say Trace's age is "x".
Then, Hunter's age would be (x+3)
And Jacob's will be 2*(x+3)
The Total of three ages would be
x+(x+3)+2*(x+3)=49
4x+9=49
4x=40
x=10
So Trace is 10 years old
Hunter is 13 years old
Jacob is 26 years old.
-4x+4y=-4 & 4x-24y=-16
Answer:
Hello if you are solving for x the for the equation -4x+4y=-4
your answer is x=y+1
Step-by-step explanation:
4y -4x= -4
subtract 4y from both sides
-4x = -4y- 4
divide both sides by -4
x= y+1
I HOPE THIS HELPS!
Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms. 8d-2-4d^3
For the polynomial "8d⁻² - 4d³" , the standard form is "-4d³ + 8d⁻²" , the degree is "3" and the leading coefficient is "-4" and the number of terms is "2" .
The polynomial is ⇒ 8d⁻² - 4d³.
To write the polynomial in standard form, we first rearrange the terms by putting the terms with the highest degree first ;
So , the standard form is ⇒ -4d³ + 8d⁻² ;
The degree of the polynomial is 3, because it is the highest power of the variable "d" in the polynomial "-4d³ + 8d⁻²" .
The leading coefficient of the polynomial is "-4" , because it is the coefficient of the term with the highest degree.
The polynomial has 2 terms, so it is a binomial.
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The given question is incomplete , the complete question is
Write the polynomial " 8d⁻² - 4d³ " in standard form. Identify the degree and leading coefficient of the polynomial. Then classify the polynomial by the number of terms.
zach keeps his pet chameleon pinky in a terrarium with the dimensions shown below. there's sand in the bottom of the terrarium that reaches a height of 8 88 centimeters. zach gets a new terrarium for pinky that is larger. the base of the new terrarium is 25 2525 by 64 6464 centimeters. zach moved the existing sand to the new terrarium. how deep will the sand be in the new terrarium?
If Zach moved the existing sand from the old terrarium into the new terrarium , then the sand in the new terrarium will be 5cm deep .
The dimensions of the old terrarium is = 20 by 50 cm ;
The dimensions of the new terrarium is = 25 by 64 cm ;
So , amount of sand that Zach has is = Volume of sand in the old terrarium, that is ( Area of base of the old terrarium) × (height of sand) ;
Volume of Sand = 20 × 50 × 8 = 8000 cm³ ;
When Zach moves the sand to the new terrarium, volume of sand will be same, so we can write the equation ;
⇒ 20 × 50 × 8 = 25 × 64 × h ;
where h is = height of sand in new terrarium.
Now solving for h, we get ;
⇒ h = (20 × 50 × 8 cm)/(25 × 64 )
⇒h = 8000/1600 ;
⇒ h = 5 cm ;
Therefore, the sand will be 5 centimeters deep in the new terrarium.
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The given question is incomplete , the complete question is
Zach keeps his pet chameleon pinky in a terrarium with the dimensions 20 by 50 cm . there's sand in the bottom of the terrarium that reaches a height of 8 88 centimeters.
Zach gets a new terrarium for pinky that is larger. the base of the new terrarium is 25 by 64 centimeters. Zach moved the existing sand to the new terrarium. how deep will the sand be in the new terrarium ?
