We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.
How to find the volume?To find the dimensions of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is:
V = l x w x h
where V is the volume, l is the length, w is the width, and h is the height.
We know that the volume of the box of tissues is 288 cubic inches. We want to find the length, width, and height.
We can start by listing all the factors of 288:
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
We can see that some of these factors are repeated, so we can pair them up to find the dimensions of the rectangular prism.
For example, we can pair 2 and 144, since 2 x 144 = 288. This means that the length of the rectangular prism could be 144 inches and the width could be 2 inches.
We can also pair 3 and 96, since 3 x 96 = 288. This means that the length of the rectangular prism could be 96 inches and the width could be 3 inches.
We can continue pairing the factors until we find all the possible combinations. Once we have all the possible combinations, we can choose the one that makes the most sense based on the context of the problem (in this case, the dimensions of a box of tissues).
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Evie rolls a fair number cube with faces labeled 1 through 6. She selects a marble from a bag were 3 are green and 1 is red. Select which point on the number line correctly represents the probability she
will land on an even number and then selects a green marble
The point on the number line that represents the probability of rolling an even number and selecting a green marble is 3/8, which is between 0.3 and 0.4 on the number line.
Will she land on an even number and then selects agreen marble?
The probability of rolling an even number is 3/6, which can be simplified to 1/2, because there are three even numbers (2, 4, and 6) out of six possible outcomes.
The probability of selecting a green marble from the bag is 3/4, because there are three green marbles out of four total marbles in the bag.
To calculate the probability of both events happening together (rolling an even number and selecting a green marble), you multiply the probabilities of each event:
P(even number and green marble) = P(even number) x P(green marble)
P(even number and green marble) = (1/2) x (3/4)
P(even number and green marble) = 3/8
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If you roll a number cube 96 times, how many times would you expect to roll a three or a six?
a. 36
b. 32
c. 34
d. 38
ANSWER FAST (show work please)
The calculated number of times you would expect to roll a three or a six is 32 times
How many times would you expect to roll a three or a six?From the question, we have the following parameters that can be used in our computation:
Cube = 96
In a cube, we have the following probability equation
P(3 or 6) = 1/6 + 1/6
When the sum is evaluated, we have
P(3 or 6) = 2/6
So, when the die is rolled 96 times, we have
Expected value = 2/6 * 96
Evaluate the products
Expected value = 32
Hence, the expected number of times is 32
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Calculate the change in entropy of the system when 10. 0 g of ice at −10. 0 °C is converted into water vapour at 115. 0 °C and at a constant pressure of 1 bar. The molar constant-pressure heat capacities are: Cp,m(H2O(s)) = 37. 6 J K−1 mol−1; Cp,m(H2O(l)) = 75. 3 J K−1 mol−1; and Cp,m(H2O(g)) = 33. 6 J K−1 mol−1. The standard enthalpy of vaporization of H2O(l) is 40. 7 kJ mol−1, and the standard enthalpy of fusion of H2O(l) is 6. 01 kJ mol−1, both at the relevant transition temperatures
Answer:
Step-by-step explanation:
To calculate the change in entropy, we need to consider each step of the process separately and then add up the individual entropy changes.
Step 1: Heating ice from -10.0°C to 0°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of ice, Cp is the molar constant-pressure heat capacity of ice, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 37.6 J/K/mol * 10.0°C = 20.8 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the temperature in Kelvin.
ΔS = 20.8 J / 263.15 K = 0.079 J/K
Step 2: Melting ice at 0°C
The heat required for this step can be calculated using the formula:
q = n * ΔHfus
where n is the number of moles of ice and ΔHfus is the standard enthalpy of fusion of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 6.01 kJ/mol = 3.33 kJ = 3330 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the melting point of water in Kelvin (273.15 K).
ΔS = 3330 J / 273.15 K = 12.2 J/K
Step 3: Heating water from 0°C to 100°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of water (which is equal to the mass of ice that melted), Cp is the molar constant-pressure heat capacity of water, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 75.3 J/K/mol * 100.0°C = 415.9 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the average temperature during the heating process (which is 50°C).
ΔS = 415.9 J / 323.15 K = 1.29 J/K
Step 4: Vaporizing water at 100°C
The heat required for this step can be calculated using the formula:
q = n * ΔHvap
where n is the number of moles of water and ΔHvap is the standard enthalpy of vaporization of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 40.7 kJ/mol = 22.6 kJ = 22600 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the boiling point of water in Kelvin (373.15 K).
ΔS = 22600 J / 373.15 K = 60.5 J/K
Step 5: Heating steam from 100°C to 115°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of steam (which is equal to the mass of ice that melted and the mass of water that vaporized), Cp is the molar constant-pressure heat
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Pls help, I need to pass geometry. Guess I'm failing <3
A chicken and a roaster, on the same straight line, are heading towards the chicken coop which is halfway between them. The chicken is at A(-2,4) and the roasted is at B(4,-4)
Please answer a & b with an explanation :)
The x-coordinate of the chicken coop is 1, which means that the chicken coop is located at the point (1, 0).
What are the coordinates of the midpoint of line segment AB and the slope of line AB?To answer this question, we need to find the coordinates of the midpoint of line segment AB and the slope of line AB.
a) To find the midpoint of line segment AB, we use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.
Substituting the values, we get:
Midpoint = ((-2 + 4)/2, (4 - 4)/2)
Midpoint = (1, 0)
Therefore, the midpoint of line segment AB is (1, 0).
b) To find the slope of line AB, we use the slope formula:
Slope = (y2 - y1)/(x2 - x1)
Substituting the values, we get:
Slope = (-4 - 4)/(4 - (-2))
Slope = (-8)/(6)
Slope = -4/3
Therefore, the slope of line AB is -4/3.
Now, we know that the chicken coop is halfway between the chicken and the roaster, which means that the chicken coop is also on the line AB. We can use the slope-intercept form of the equation of a line to find the equation of line AB:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
Substituting the values of slope and midpoint, we get:
y = (-4/3)x + (4/3)
Therefore, the equation of line AB is y = (-4/3)x + (4/3).
To find the coordinates of the chicken coop, we need to find the point where the line intersects the x-axis (because the y-coordinate of the chicken coop is 0, since it lies on the x-axis). To do this, we set y = 0 in the equation of line AB:
0 = (-4/3)x + (4/3)
4/3 = (4/3)x
x = 1
Therefore, the x-coordinate of the chicken coop is 1, which means that the chicken coop is located at the point (1, 0).
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The distance between the chicken at A(-2,4) and the roasted is at B(4,-4).
How chicken and roasted of points?To determine the chicken of the line that contains points A(-2,4) and B(4,-4), we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the coordinates, we get:
slope = (-4 - 4) / (4 - (-2)) = -8 / 6 = -4 / 3
So the slope of the line is -4/3.
To find the equation of the line, we can use the point-slope form:
y - y1 = m(x - x1)
Substituting one of the points and the slope, we get:
y - 4 = (-4/3)(x - (-2))
Simplifying, we get:
y = (-4/3)x + 4/3
Therefore, the equation of the line that contains points A(-2,4) and B(4,-4) is y = (-4/3)x + 4/3.
To find the distance between the chicken and the roaster, we can use the distance formula:
d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
Substituting the coordinates, we get:
d = sqrt[(4 - (-2))^2 + (-4 - 4)^2] = sqrt[6^2 + (-8)^2] = sqrt[100] = 10
Therefore, the distance between the chicken and the roaster is 10 units.
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You earn $130.00 for each subscription of magazines you sell plus a salary of $90.00 per week. How many subscriptions of magazines do you need to sell in order to make at least $1000.00 each week?
You decide to make and sell bracelets. The cost of your materials is $84.00. You charge $3.50 for each bracelet. Write a function that represents the profit p for selling b bracelets.
The function that represents the profit p for selling b bracelets is p = 3.5b - 84
Write a function that represents the profit p for selling b bracelets.From the question, we have the following parameters that can be used in our computation:
The cost of your materials is $84.00. You charge $3.50 for each bracelet.This means that
Cost of b brackets = 3.5b
So, we have
Profit = Cost of b brackets - Cost price
substitute the known values in the above equation, so, we have the following representation
p = 3.5b - 84
Hence, the function that represents the profit p for selling b bracelets is p = 3.5b - 84
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x > -1 but drawn on a graph for inequality due tmr !!!
The graph of the inequality is on the image at the end.
How to graph an inequality?Here we have an inequality on one variable which is:
x > -1
This is the set of all the numbers larger than -1.
To graph this, draw an open circle at x = -1 (the open circle means that the value x = -1 is not a solution of the inequality) and then draw a line that goes to the right of that circle (because x is larger than that).
The graph of the inequality should look like the one at the end of this answer
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please help with the question for it will give you 15 points!
1. The next two term for the sequence using Geometric Progression is 8 and 16
2. The next two terms for the sequence using arithmetic progression is 7 and 11
What is sequence?A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.
Using Geometric Progression, the common ratio is 2/1 = 2
therefore the next two terms will be
4× 2 = 8 and 8× 2 = 16
Using Arithmetic progression , the common difference will be increasing by 1 per number of term, i.e r+1
for the fourth term ,common difference = 2+1 = 3
fourth term = 4+3 = 7
for the fifth term , common difference = 3+1 = 4
fifth term = 7+4 = 11
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I need help solving ration expressions
The simplified form of the given expression is (x-7)/3x.
The given expression is (2x²-8x-42)/6x² ÷ (x²-9)/(x²-3x)
Here, (x²-4x-21)/3x² ÷ (x-3)(x+3)/x(x-3)
= (x²-4x-21)/3x² ÷ (x+3)/x
= (x²-4x-21)/3x² × x/(x+3)
= (x²-4x-21)/3x × 1/(x+3)
= (x²-4x-21)/3x(x+3)
= (x²-7x+3x-21)/3x(x+3)
= [x(x-7)+3(x-7)]/3x(x+3)
= (x-7)(x+3)/3x(x+3)
= (x-7)/3x
Therefore, the simplified form of the given expression is (x-7)/3x.
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A piece of wire of length 50 is out, and the resulting two pieces are formed to make a corde and a square. Where should the wre be cut to day minance and provimine the continet water who? (e) To minimize the combined area, the wire should be cut so that a length of 25.964 used for the circle and a longen er 3.04 es lo quem (Round to the nearest thousandth as needed) (1) To maximize the combined uros, there should be cut so that a length of used for the circle and we canned tere dere (Round to the nearest thousandth as needed) Evaluate the following limit. Use Thôpitals Rule when it is convenient and applicable Iim cox How should the given timt be evaluated? Select the correct choice below and, if necessary, in the answer box to complete your choice A. U topitals Rule more than once to rewrite the imtin ta final fomas tim 9. Multiply the expension by a una traction to obtain im (1) OG UTHopitals Rule exactly once to rewrite the imit im OD. Vse direction Evaluate the limit imetype an exact answer
To minimize the combined area of a circle and a square made from a wire of length 50, you should cut the wire so that 25.964 units are used for the circle (as the circumference) and 24.036 units are used for the square (as the perimeter).
To maximize the combined areas, the optimal cutting point cannot be determined due to the lack of information provided in the question. For the limit evaluation, it's not clear which limit should be evaluated, as the question has some typos and irrelevant parts. If you can provide the correct limit expression, I will be happy to help you evaluate it using the appropriate method, such as Hsopital's Rule or other techniques.
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At a craft shop, a painter decided to paint a welcome sign to take home. An image of the sign is shown. A five-sided figure with a flat top labeled 5 and one-half feet. A height labeled 4 feet. The length of the entire image is 9 ft. There is a point coming out of the right side of the image that is created by two line segments. What is the area of the sign? 19 square feet 22 square feet 29 square feet 36 square feet Question 2(Multiple Choice Worth 2 points) (Volume of Rectangular Prisms MC) A family is building a sandbox for their yard that is shaped like a rectangular prism. They would like for the box to have a volume of 43,972.5 in3. If they already have the length measured at 71.5 inches and the width at 60 inches, what is the height needed to reach the desired volume? 5.25 inches 10.25 inches 131.5 inches 283.5 inches Question 3(Multiple Choice Worth 2 points) (Perimeter and Area on the Coordinate Plane MC) An office manager needs to cover the front face of a rectangular box with a label for shipping. The vertices of the face are (–8, 4), (4, 4), (–8, –2), and (4, –2). What is the area, in square inches, of the label needed to cover the face of the box? 18 in2 36 in2 60 in2 72 in2 Question 4(Multiple Choice Worth 2 points) (Perimeter and Area on the Coordinate Plane MC) The vertices of a rectangle are plotted in the image shown. A graph with the x-axis and y-axis labeled and starting at negative 8, with tick marks every one unit up to positive 8. There are four points plotted at negative 2, 6, then 3, 6, then negative 2, negative 3, and at 3, negative 3. What is the perimeter of the rectangle created by the points? 14 units 19 units 28 units 45 units Question 5(Multiple Choice Worth 2 points) (Volume of Rectangular Prisms MC) What is the volume of a rectangular prism with a length of fourteen and one-fifth yards, a width of 7 yards, and a height of 8 yards? seven hundred ninety-five and one-fifth yd3 seven hundred thirty-nine and one-fifth yd3 four hundred fifty-two and four
The area of the sign can be calculated by finding the area of the trapezoid shape. The formula for the area of a trapezoid is A = (1/2) * (base1 + base2) * height. In this case, the bases are 5.5 feet (half of 11 feet, which is the flat top of the five-sided figure) and 9 feet (the entire length of the image), and the height is 4 feet. Plugging these values into the formula, we get:
A = (1/2) * (5.5 + 9) * 4
A = (1/2) * 14.5 * 4
A = 7.25 * 4
A = 29
So, the area of the sign is 29 square feet.
The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the length is given as 71.5 inches, the width is given as 60 inches, and the volume is given as 43,972.5 in^3. We can solve for the height by dividing the volume by the product of the length and width:
Height = Volume / (Length * Width)
Height = 43,972.5 / (71.5 * 60)
Height ≈ 10.25 inches
So, the height needed to reach the desired volume is approximately 10.25 inches.
The area of the rectangular box face can be calculated by finding the length of the sides of the rectangle using the given coordinates, and then using the formula for the area of a rectangle, which is A = length * width. In this case, the length is the difference between the x-coordinates of the two points on the x-axis (4 - (-8) = 12) and the width is the difference between the y-coordinates of the two points on the y-axis (4 - (-2) = 6). Plugging these values into the formula, we get:
A = 12 * 6
A = 72
So, the area of the label needed to cover the face of the box is 72 square inches.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, we can use the given coordinates of the four points to find the lengths of the sides. The length is the difference between the x-coordinates of the two points on the x-axis (3 - (-2) = 5) and the width is the difference between the y-coordinates of the two points on the y-axis (6 - (-3) = 9). Since the opposite sides of a rectangle have equal lengths, the perimeter is twice the sum of the length and width:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (5 + 9)
Perimeter = 2 * 14
Perimeter = 28
So, the perimeter of the rectangle created by the points is 28 units.
The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the length is given as 14.2 yards (14 and one-fifth yards), the width is given as 7 yards, and the height is given as 8 yards. Plugging these values into the formula, we get:
Volume = Length * Width * Height
Volume = 14.2 * 7 * 8
Volume ≈ 795.2
So, the volume of the rectangular prism is approximately 795.2 cubic yards. Answer: seven hundred ninety-five and one-fifth yd3
Manuel the trainer has two solo workout plans that he offers his clients: plan a and plan b. each client does either one or the other (not both). on monday there were 3 clients who did plan a and 8 who did plan b. manuel trained his monday clients for a total of 7 hours and his tuesday clients for a total of 6 hours. how long does each workout plans last?
Plan a lasts 1/5 of an hour (or 12 minutes) and plan b lasts 29/5 hours (or 5 hours and 48 minutes).
Let's denote the length of plan a by 'a' and the length of plan b by 'b' (measured in hours).
From the problem, we know that:
- On Monday, 3 clients did plan a and 8 clients did plan b. Therefore, the total time spent on plan a on Monday was 3a and the total time spent on plan b on Monday was 8b.
- On Tuesday, we don't know how many clients did each plan, but we do know that the total time spent on both plans was 6 hours.
Putting these together, we can create a system of two equations:
3a + 8b = 7 (total time spent on Monday)
a + b = 6 (total time spent on Tuesday)
We can solve this system by using substitution. Rearranging the second equation, we get:
b = 6 - a
Substituting this expression for b into the first equation, we get:
3a + 8(6 - a) = 7
Simplifying and solving for a, we get: a = 1/5
Substituting this value back into the expression for b, we get:
b = 6 - a = 29/5
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Solve the equation
Complete using the provide data and solve
Answer:
VM = 20
Step-by-step explanation:
Basic proportionality theorem or Thale's theorem:
If a line is drawn parallel to one side of a triangle to intersect the other sides in two side in distinct points, the other two sides are divided in the same ratio.
VN = VT - NT
= 49 - 14
= 35
[tex]\sf \dfrac{VM}{MU} = \dfrac{VN}{NT}\\\\\\\dfrac{VM}{8}=\dfrac{35}{14}\\\\\\\dfrac{VM}{8}=\dfrac{5}{2} \\\\\\VM = \dfrac{5}{2}*8\\\\VM=5*4\\\\\boxed{\bf VM = 20}[/tex]
I need to find the expense and percent of the budget monthly total and annual expenses please help
The job in Lubbock is better as he would have more savings
The job in Lubbock has a lower income but also lower expenses and more savings
What is a Financial Goal?A financial goal is a specific and measurable objective that an individual or organization sets for themselves to achieve with their finances. It could be anything from saving for a down payment on a house, paying off debt, building an emergency fund, or planning for retirement.
The annual expenses in Austin is $36,000
The annual expenses in Lubbock is $30,000
The job in Lubbock is better and more viable and economical
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I tried to do it but it gave me 6.
Answer:
(c) 12.5
Step-by-step explanation:
You want the unknown leg of a right triangle with one leg 10 and hypotenuse 16.
Sanity checkThe triangle inequality tells you the unknown leg of the triangle will have a length between the difference of the two known legs, and the longest leg of the triangle.
Since this is a right triangle, its longest leg is the hypotenuse. The unknown side cannot be longer than that, so must be less than 16.
The difference of the given lengths is ...
16 -10 = 6
so the missing leg must be longer than 6.
Only one answer choice is between 6 and 16: 12.5.
The missing leg length is 12.5 units.
__
Additional comment
If you want to figure the length, you can use the Pythagorean theorem:
c² = a² +b²
16² = 10² +b²
b² = 256 -100 = 156
b = √156 ≈ 12.49 ≈ 12.5
The length of the unknown leg is 12.5 units.
The function C(x) = 25x2 - 98x shows the cost of printing magazines (in dollars) per day at a printing press. What is the rate of change of cost when the number of magazines printed per day is 17?
A. 327$/print
B. 552$/print
C. 752$/print
D. 227$/print
The rate of change of cost when the number of magazines printed per day is 17 is 752 dollars per print. The correct option is C.
The function C(x) = 25x² - 98x represents the cost of printing magazines per day at a printing press. To find the rate of change of cost when 17 magazines are printed per day, we need to calculate the derivative of the function with respect to x (the number of magazines printed), which represents the rate of change at a given point.
The derivative of C(x) with respect to x can be found using the power rule for differentiation. For a function of the form f(x) = [tex]ax^n[/tex], its derivative is f'(x) = [tex]n*ax^{(n-1)[/tex].
Applying the power rule to our function, we get:
C'(x) = 2(25x) - 98 = 50x - 98.
Now, we need to evaluate C'(x) when x = 17 (the number of magazines printed per day):
C'(17) = 50(17) - 98 = 850 - 98 = 752.
Therefore, the rate of change of cost when the number of magazines printed per day is 17 is 752 dollars per print. So, the correct answer is: C. 752$/print.
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Watch help video
Express tan J as a fraction in simplest terms.
4
√55
H
The value of the tangent of J, tan J = 6.2/4
How to determine the valueTo determine the value, we need to find the opposite side of the angle J.
Using the Pythagorean theorem, we have that;
(√55)² = 4² + j²
Find the square of the values, we get;
55 = 16+ j²
collect the like terms, we have;
j² = 55 - 16
subtract the values
j² = 39
Find the square root of both sides
j = 6. 2
Then, using the tangent identity, we have;
tan J = opposite/adjacent
Opposite = 6. 2
Adjacent = 4
Substitute the values
tan J = 6.2/4
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5) If the price charged for a bolt is p cents, then x thousand bolts will be sold in a certain hardware store, where p = 82 - x 26 . How many bolts must be sold to maximize revenue?
To maximize the revenue, we need to find the maximum value of the revenue function.
The revenue function, R(x), is given by the product of the price per bolt (p) and the number of bolts sold (x thousand), which is R(x) = p * x.
Given the price function p = 82 - 26x,
we can substitute this into the revenue function:
R(x) = (82 - 26x) * x
Now, we need to find the maximum value of R(x). We'll do this by taking the derivative of R(x) with respect to x and setting it to zero:
R'(x) = d/dx[(82 - 26x) * x] R'(x) = 82 - 52x
Now, we set R'(x) = 0 and solve for x: 0 = 82 - 52x 52x = 82 x = 82 / 52 x ≈ 1.58
So, approximately 1.58 thousand (or 1580) bolts must be sold to maximize revenue in the hardware store.
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Mrs vilakazi is a retired consumer studies educator .she owns a small business of selling different types of cakes including scones.the cost price for ingredients plus water and electricity is r0,53 per scone .she sells scones at r2 ,00 each . calculate the profit mrs vilakazi will make if she bakes 204 scones and sells 171.
Mrs. Vilakazi will make a profit of r233,88 if she bakes 204 scones and sells 171.
The profit is the difference between the total revenue and the total cost.
The total cost is the cost per scone multiplied by the number of scones baked:
total cost = r0,53/scone × 204 scones = r108,12
The total revenue is the selling price per scone multiplied by the number of scones sold:
total revenue = r2,00/scone × 171 scones = r342,00
Therefore, the profit is:
profit = total revenue - total cost
profit = r342,00 - r108,12
profit = r233,88
Mrs. Vilakazi will make a profit of r233,88 if she bakes 204 scones and sells 171.
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The function f(x) = 1. 25x2 models the packaging costs, in cents, for a box shaped like a rectangular prism. The side lengths are 2x in. , 2x in. , and 0. 5x in. What are reasonable domain and range values for this function, if the longest side length of the box can be no greater than 20 in. ? Write the answers in interval notation
The range of the function f(x) is Range: [0, 125] In interval notation, this can be written as [0, 125] if the longest side length of the box can be no greater than 20 in.
The function f(x) = 1.25x^2 models the packaging costs, in cents, for a rectangular prism-shaped box with side lengths of 2x in., 2x in., and 0.5x in.
We need to determine the reasonable domain and range values for this function, given that the longest side length of the box can be no greater than 20 in.
Since the longest side length is 20 in., we know that:
2x ≤ 20
x ≤ 10
Therefore, the domain of the function f(x) is all real numbers less than or equal to 10, or: Domain: [-∞, 10]
To find the range of the function, we need to examine the behavior of the function as x varies. Since the coefficient of x^2 is positive, the function is quadratic with a minimum value at x = 0. Therefore, we know that the range of the function must start at its minimum value, which is f(0) = 0, and increase as x increases.
To determine the upper limit of the range, we can evaluate f(x) when x = 10 (the maximum value of x allowed):
f(10) = 1.25(10)^2 = 125
Therefore, the range of the function f(x) is:
Range: [0, 125]
In interval notation, this can be written as [0, 125].
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The height of the storage space is 6 feet. The length is 2 times the width. The volume of the storage is 48 cubic feet. What is the width and length of the storage space
Step-by-step explanation:
Let's use the formula for the volume of a rectangular prism, which is:
V = lwh
where V is the volume, l is the length, w is the width, and h is the height.
We are given that the height is 6 feet, and the volume is 48 cubic feet. Therefore, we can solve for the product of the length and width:
lw = V / h = 48 / 6 = 8
We are also given that the length is twice the width, so we can substitute 2w for l:
(2w)w = 8
Simplifying this equation, we get:
2w^2 = 8
Dividing both sides by 2, we get:
w^2 = 4
Taking the square root of both sides, we get:
w = 2
Therefore, the width of the storage space is 2 feet. Since the length is twice the width, the length is:
l = 2w = 2(2) = 4
So the length of the storage space is 4 feet.
(2^-1/2) / (2^1/2)
How to flip negative exponents
The value of the expression is 2
What are index forms?Index forms are described as those forms that are used to represent numbers that are too large or small in more convenient forms.
They are also described as numbers that are raised to a variable or an exponents.
Other names for index forms are scientific notations and standard forms.
One of the rules of index forms is that the exponents are added when the have the same and are being multiplied.
From the information given, we have that;
(2^-1/2) / (2^1/2)
subtract the exponents
2^-1/2-1/2
subtract the values
2^ -1
Then, we have;
2
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Helppppppppppppppppp
Square oabc is drawn on a centimetre grid.o is (0,0) a is(3,0) b is(3,3) c is (0,3)write down how many invariants points there are on the perimeter of the square when oabc is translated by the vector (1 3)
There are 4 invariant points on the perimeter of the square when oabc is translated by the vector (1 3).
To find the invariant points on the perimeter of the square when oabc is translated by the vector (1 3), we need to apply this translation to each vertex of the square and see which ones remain on the square.
If we add the vector (1 3) to each vertex, we get:
o + (1 3) = (1 3)
a + (1 3) = (4 3)
b + (1 3) = (4 6)
c + (1 3) = (1 6)
Now we need to check which of these points are still on the square. We can see that points (1 3) and (4 3) are on two adjacent sides of the square, and points (1 6) and (4 6) are on the other two adjacent sides.
Therefore, there are 4 invariant points on the perimeter of the square when oabc is translated by the vector (1 3). These invariant points are the points where the sides of the original square intersect with the sides of the translated square.
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Find the sum of the series: 5 2 (K _2k) k=4 5 2 (K2-2k) = k=4
To find the sum of the series given, we need to evaluate the expression for each value of k from 4 to 5 and then add the results together. The expression is 2(K²- 2K). Let's calculate the sum:
For k = 4:
2(4² - 2*4) = 2(16 - 8) = 2(8) = 16
For k = 5:
2(5² - 2*5) = 2(25 - 10) = 2(15) = 30
Now, we add the results together:
Sum = 16 + 30 = 46
So, the sum of the series is 46.
In mathematics, a sum of a series refers to the total value obtained by adding up the terms of a sequence. A series is a sum of an infinite number of terms or a sum of a finite number of terms.
For example, the sum of the series 1 + 2 + 3 + 4 + 5 is:
1 + 2 + 3 + 4 + 5 = 15
The sum of the series can be found using different methods depending on the type of series. For example, if the series is an arithmetic series, which means each term is obtained by adding a constant difference to the previous term, we can use the formula:
Sn = n/2 [2a + (n - 1)d]
Where Sn is the sum of the first n terms of the series, a is the first term, d is the common difference, and n is the number of terms in the series.
If the series is a geometric series, which means each term is obtained by multiplying the previous term by a constant ratio, we can use the formula:
Sn = a(1 - r^n) / (1 - r)
Where Sn is the sum of the first n terms of the series, a is the first term, r is the common ratio, and n is the number of terms in the series.
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a barber has scheduled two appointments, one at 5 pm and the other at 5:30 pm. the amount of time that appointments last are independent exponential random variables with mean 45 minutes. assuming that both customers are on time, find the expected amount of time that the 5:30 appointment spends at the barber shop.
The expected amount of time that the 5:30 appointment spends at the barber shop is, E[W] = 45 + 45/e.
Given that, the barber has scheduled two appointments, one at
5 pm and the other at 5:30 pm.
Since the amount of time that appointments last are independent exponential random variables with mean 45 minutes.
Let W be the time the 2nd person has to wait in chamber Let X be the time the barber takes checking 1st person X-exp(45)
The distribution is,
W= X-45 if X >45
otherwise.
Expected time 2nd person spends in barber chamber
= E (W)+45
[ 45 is the mean time barber takes checking 2nd person]
[tex]E(W) = \int\limits^{\infinity }_0 {WP(X=45+W)} \, dw\\ \\\\=\int {W.1/45e^{\frac{-45+w}{45} } \, dw\\\\[/tex]
[tex]=e^{-1} \int\frac{W}{45} e^{\frac{-w}{45} } dw\\=\frac{45}{e}[/tex]
The expected amount of time that the 5:30 appointment spends at the barber's office is,
[tex]E[W]=45+\frac{45}{e}[/tex].
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A cuboid has a volume of 1815 cm³. Each side of the cuboid is a whole number of centimetres and each side is longer than 1 cm. Find all the possible dimensions of the cuboid
There are 4 possible sets of dimensions for the cuboid with a volume of 1815 cm³.
How to solve for the dimensionsFirst, find the prime factors of 1815:
1815 = 3 × 5 × 11 × 11
Now, we need to find all possible combinations of these factors into three whole numbers. Each combination of three numbers, when multiplied, should give 1815. We can do this by finding the different ways the prime factors can be distributed among the three dimensions:
3 × 5 × (11 × 11) = 15 × 121 (height × width × length)
3 × 11 × (5 × 11) = 33 × 55
5 × 11 × (3 × 11) = 55 × 33
11 × 11 × (3 × 5) = 121 × 15
We have found 4 different sets of dimensions for the cuboid:
15 × 121 × 1
33 × 55 × 1
55 × 33 × 1
121 × 15 × 1
There are 4 possible sets of dimensions for the cuboid with a volume of 1815 cm³.
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Complete the following statement. Use the integers that are closest to the number in the
middle.
44
The closest integers to 44 are 43 and 45.
How to find the integers closest to 44?To complete the statement using the integers closest to the number in the middle, we need to determine the middle number in a sequence or set of numbers. However, the given prompt only provides the number "44" without any context or additional information.
If we assume that the number "44" is part of a sequence or set, we would need more information to determine the middle number and complete the statement accurately.
Without additional context or information, it is not possible to provide a specific answer or complete the statement. Please provide more details or clarify the question to assist further.
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The length of human hair is proportional to the number of months it has grown.
a. what is the hair length in centimeters after 6 months? round your answer to the nearest hundredth.
the hair length is about blank
centimeters.
question 2
b. how long does it take hair to grow 8 inches?
it takes blank
months.
question 3
c. use a different method than the one in part (b) to find how long it takes hair to grow 20 inches.
it takes blank
months.
human hair to grow 20 inches, considering the length of hair is proportional to the number of months it has grown.
First, let's establish the proportionality constant, which is the average rate at which human hair grows. On average, human hair grows approximately 0.5 inches per month.
Now, let's find out how many months it takes for hair to grow 20 inches. We can set up a proportion equation as follows:
Length of hair (in inches) / Number of months = Proportionality constant
Let "x" be the number of months it takes for hair to grow 20 inches. We can write the equation as:
20 inches / x months = 0.5 inches/month
To solve for x, we can multiply both sides by x months, which gives us:
20 inches = 0.5 inches/month * x months
Now, we can divide both sides by 0.5 inches/month:
x months = 20 inches / 0.5 inches/month
x months = 40 months
So, it takes 40 months for human hair to grow 20 inches, considering the length of hair is proportional to the number of months it has grown.
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The slant height if the cone is 26 cm. what is the volume of a cone having a radius of 10 cm and a slant height of 26 cm.
Therefore, the volume of the cone is approximately 800π cubic centimeters, or approximately 2512.44 cubic centimeters when rounded to two decimal places.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object or a substance. The volume of a solid object can be determined by measuring its dimensions, such as its length, width, and height, and applying an appropriate mathematical formula depending on its shape.
Here,
The volume of a cone can be calculated using the formula:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is a constant equal to approximately 3.14. In this case, we are given the radius of the cone as 10 cm and the slant height as 26 cm. We can use the Pythagorean theorem to find the height of the cone:
h² = (slant height)² - (radius)²
h² = 26² - 10²
h² = 576
h = √576
h = 24
Now that we have the height of the cone, we can use the formula for the volume of a cone:
V = (1/3)πr²h
V = (1/3)π(10²)(24)
V = (1/3)π(100)(24)
V = (1/3)(2400π)
V = 800π
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Answer:
Volumeof a cone=2,723.8095238095
Step-by-step explanation:
Slant height = 26cm
radius = 10cm
volume of a cone = ‽
The volume of cone =
[tex]v = \frac{1}{3} \pi {r}^{2} h[/tex]
[tex]v = \frac{1}{3} \times \frac{22}{7} \times 10 \times 10 \times 26 \\ \frac{1}{3} \times \frac{22}{7} \times 100 \times 26 \\ = \frac{22}{21} \times 2600 \\ = \frac{57200}{21} \\ = 2,723.8095238095cm[/tex]