It would take the three of them about 6 hours to paint the four rooms.
How to solve an equation?Let t represent the time that it would take all three of them to paint one room.
It would take Amy 6 hours to carpet one of the rooms; it would take Beth 4 hours to carpet one room; and it would take Cassandra 8 hours to carpet one room.
Therefore:
(1/6 + 1/4 + 1/8)t = 1
(2/3)t = 1
t = 1.5 hours
It would take all of them 1.5 hours each to paint one room.
For 4 rooms:
Total time = 1.5 hours * 4 = 6 hours
It would take the three of them about 6 hours to paint the four rooms.
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HELP. I'm really struggling on this one. My calculus teacher claimed this to be the easiest math problem ever but I still can't understand. Is anyone smart enough to figure this one out. Whats 1 + 1?
Answer:
The answer to 1 + 1 is 2.
Very complicated problem, please mark brainliest!
Answer:
1+1 = 2
Or, 1=2-1
1=1
we know value of one is one
so,
1+1=11
By how much percent will the area of circle will increase if the diameter increases by 40%?
The area of the circle will decrease by 51% if the diameter increases by 40%. Then the new diameter will be 1.4 times the original diameter.
Let's assume the original diameter is d and the original area of the circle is A.
Then, the new diameter will be 1.4d and the new area of the circle can be calculated as follows:
New area = pi * (New diameter/2)²= pi * (1.4d/2)² = pi * (0.7d)² = 0.49 * pi * d²
Therefore, the new area is 0.49 times the original area.
To calculate the percentage increase in area, we can use the following formula:
Percentage increase = (New value - Old value) / Old value * 100%
In this case, the old value is the original area A and the new value is the new area, which is 0.49*A. Therefore,
Percentage increase = (0.49A - A) / A * 100%
= -0.51A / A * 100%
= -51%
Therefore, the area of the circle will decrease by 51% if the diameter increases by 40%.
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Construct a triangle PQR such that PQ=8cm, PR=5cm and QR=6cm. Construct a circle which will pass through P, Q and R. What is the special name given to this circle?
Construct a triangle PQR with sides PQ=8cm, PR=5cm, and QR=6cm, then draw a circle passing through P, Q, and R. This circle is called the circumcircle of triangle PQR.
We draw a line segment PQ = 8 cm long. From point P, we draw a line segment PR = 5 cm long at an angle of 60 degrees to PQ. Then, we draw a line segment QR = 6 cm long joining points Q and R to complete the triangle. Next, we use a compass to draw a circle passing through points P, Q, and R. This circle is called the circumcircle or circumscribed circle of the triangle, which is the unique circle that passes through all three vertices of the triangle. The circumcircle has a special property that its center is equidistant from the three vertices of the triangle.
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Evaluate the impact which the 16Days of Activism campaign has had on Gender Based Violence in South Africa (High order)
Answer:
Evaluating the impact of the 16 Days of Activism campaign on Gender Based Violence (GBV) in South Africa requires a high-order analysis that considers various factors and perspectives. The campaign, which runs annually from November 25th (International Day for the Elimination of Violence against Women) to December 10th (International Human Rights Day), aims to raise awareness and mobilize action to prevent and respond to GBV.
The impact of the 16 Days of Activism campaign on GBV in South Africa can be evaluated through different lenses, including quantitative data, policy and legal changes, societal attitudes, and lived experiences of survivors.
Quantitatively, South Africa has one of the highest rates of GBV in the world, with statistics showing that one in five women in the country is a survivor of GBV. While there has been a slight decrease in the incidence of GBV in recent years, the numbers remain alarmingly high. It is difficult to attribute the reduction to the 16 Days of Activism campaign alone, as there are several other factors at play.
However, the campaign has contributed to policy and legal changes aimed at addressing GBV in South Africa. For instance, the Domestic Violence Act was amended in 2018 to include broader definitions of domestic violence and harsher penalties for perpetrators. In addition, the government has established various institutions and initiatives, such as the National Council Against Gender-Based Violence and the GBV Command Centre, to respond to GBV and provide support to survivors.
The 16 Days of Activism campaign has also had an impact on societal attitudes towards GBV in South Africa. Through awareness-raising activities, community dialogues, and media campaigns, the campaign has helped to break the silence and stigma around GBV, and encouraged more people to speak out and seek help. However, entrenched patriarchal norms and gender inequalities continue to fuel GBV in the country, and changing these attitudes requires sustained efforts beyond the 16 Days of Activism campaign.
Lastly, the impact of the 16 Days of Activism campaign on GBV in South Africa can be evaluated through the lived experiences of survivors. While the campaign has provided a platform for survivors to share their stories and advocate for change, many still face significant barriers in accessing justice and support. This includes systemic issues such as under-resourced police and healthcare systems, as well as cultural and social norms that blame and stigmatize survivors.
In conclusion, while the 16 Days of Activism campaign has had some impact on GBV in South Africa, it is clear that much more needs to be done to effectively address the root causes of this pervasive issue. The campaign serves as an important reminder of the urgent need for sustained and collaborative efforts from all sectors of society to prevent and respond to GBV.
Step-by-step explanation:
what is the angle of x when the other is 51
Answer:
I'm sorry, your question is not clear. Please provide more information or context so I can better understand what you are asking.
Step-by-step explanation:
a1. Give an example of a nonzero vector that has a component of zero.
2. Explain why a vector cannot have a component greater than its own magnitude.
3. If the vectors A and B are perpendicular, what is the component of A along the direction of B? What is the component of B along the direction of A?
The both vectors' components are independent of each other, and they do not interfere with each other.
1. A nonzero vector that has a component of zero is a vector with one of its component set to zero. An example of such a vector is a two-dimensional vector (x,0). For instance, a vector of (5,0) has a component of zero in the y-axis.
2. A vector cannot have a component greater than its own magnitude because the magnitude is the total length of the vector, which represents its total strength. The components of the vector are directional pieces that define the vector. Thus, if the component is more significant than the total length, it means the vector's direction has been multiplied in that component, and the vector's magnitude cannot handle the force. Therefore, the component cannot be more significant than the vector's magnitude.
3. If the vectors A and B are perpendicular, the component of A along the direction of B is zero, and the component of B along the direction of A is zero. When two vectors are perpendicular, it means they meet at a 90-degree angle, and their dot product is zero, implying that the product of the magnitude of one vector and the magnitude of the other vector multiplied by the cosine of the angle between them is zero. Therefore, both vectors' components are independent of each other, and they do not interfere with each other.
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NEED THIS ANSWERED ASAP!!
The line of site to the horizon would be tangent to the Earth’s surface. What kind of angle is formed between the radius of the Earth and the line of site?
Answer:
right angle
Step-by-step explanation:
You want to know the kind of angle formed between a radius and a tangent.
TangentA tangent to a circle is always perpendicular to the radius at the point of tangency.
The angle is a right angle.
Point C is 3/4 of the way from point A(-4,-2) to point B(8, 6). What are the coordinates of C?
The coordinates of point C are: C = (2 + (3/2) * √(13), 2 + (3/2) *√ ((13))
How to find coordinates of point?
To find the coordinates of point C, we can use the midpoint formula, which gives the coordinates of the midpoint of a line segment. We know that point C is 3/4 of the way from point A to point B, so it is closer to B than to A. Therefore, we can find the coordinates of C by finding the midpoint of the line segment AB and then moving 3/4 of the distance from the midpoint to B.
The midpoint of AB can be found by averaging the x-coordinates and the y-coordinates of A and B, respectively:
Midpoint M = ((-4 + 8)/2 , (-2 + 6)/2) = (2, 2)
Now, we need to find the distance from M to B and move 3/4 of that distance in the direction of B. We can use the distance formula to find the distance between two points:
distance MB = √((8 - 2)² + (6 - 2)²) = √(36 + 16) = √(52)
So, the distance from M to C is 3/4 of √(52), which is:
distance MC = (3/4) * √(52) = (3/4) * 2 * √(13) = (3/2) * √(13)
To move in the direction of B, we need to add the x-component and y-component of the distance MC to the x-coordinate and y-coordinate of M, respectively:
x-coordinate of C = 2 + (3/2) * √(13)
y-coordinate of C = 2 + (3/2) * √(13)
Therefore, the coordinates of point C are:
C = (2 + (3/2) * √(13), 2 + (3/2) * √(13))
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A rectangular plate of sides a and b is subjected to a force that is perpendicular to the plate. The plate is located on the xy-plane as shown. The pressure, p, at point (x, y) on the plate is proportional to the square of the distance of that point from the origin. (a) Find a formula for the pressure at point (x, y). Use k as the constant of proportionality. Use a lower case k. P(x,y) = (b) If pressure is force per unit area, set up the integral needed to find the total force on the plate. (c) Evaluate the integral in part (b). Your answer will be in terms of a, b, and k. Use all lower case letters.
In calculus, integration is the process of finding the integral of a function. The integral is a mathematical concept that represents the area under a curve or the net accumulation of a quantity over a given interval.
(a) The pressure, p, at point (x, y) on the plate is proportional to the square of the distance of that point from the origin, so we have:
p(x,y) = k(x^2 + y^2)
where k is the constant of proportionality.
(b) To find the total force on the plate, we need to integrate the pressure over the entire surface of the plate. The surface area of the plate is given by A = ab, so the total force on the plate is:
F = ∬p(x,y) dA
where the double integral is taken over the surface of the plate.
(c) We can evaluate the integral by expressing the pressure as a function of either x or y and integrating it over the other variable. Since the pressure is symmetric in x and y, we can integrate over an either variable. Let's integrate over x first:
F = ∫[0,b] ∫[0, a] k(x^2 + y^2) dx dy
= k ∫[0,b] (a^3/3 + ab^2/2) dy
= kab^2/2 + k(a^3/3) ∫[0,b] dy
= kab^2/2 + k(a^3/3) b
= (kab^2/2 + ka^3b/3)
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The table contains data on the number of people visiting a historical landmark over a period of one week.
Which type of function best models the relationship between the day and the number of visitors?
A. A quadratic function with a negative value of a.
B. A quadratic function with a positive value of a.
C. A square root function.
D. A linear function with a positive slope.
Hence , it is to be quadratic function where a has to be less than zero or
A quadratic function with a negative value of a.
Given that ,
The table contains data on the number of people visiting a historical landmark over a period of one week.
We have to find,
The relationship between the day and the number of visitors.
According to the question,
y = a√x +b
And where x = no. of days = 1
y = no. of visitors = 45
45 = a √1 + b
45 = a + b
And When x = 2 and y = 86
86 = a √2 +b
Solving the equation for the values of a and b.
From equation 1
45 - a = b
Put the value of b in equation 2
⇒ 86 = + 45 - a
⇒ 86 - 45 = a √2 - a
⇒ 41 = a (√2 - 1 )
⇒ a = [tex]\frac{41}{\sqrt{2}- 1 }[/tex]
⇒ a = 41/0.41
⇒ a = 100
Put the value of a = 100
45 = 100 + b
45 - 100 = b
b = -55
Now,
The required equation is y = 100 -55.
When x = 4
y = 100√2 - 55
⇒ y = 100(1.4) - 55
⇒ y = 140 - 55
⇒ y = 85
And,
when x = 5
y = 100√5 - 55
⇒ y = 223.5 - 55
⇒ y = 168.60
⇒ y = 168 ( approx. )
Therefore, 168 ≠ 158
Since the function rises less and less in later stage , it can not be a first order function.
So, it is to be quadratic function where a has to be less than zero.
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Each of these measures is rounded to nearest whole: a=5cm and b=3cm Calculate the upper bound of a +b
The upper bound of a + b can be found by adding the upper bounds of a and b.
For a = 5cm, the nearest whole number is 5. The upper bound would be the midpoint between 5 and 6, which is 5.5.
For b = 3cm, the nearest whole number is 3. The upper bound would be the midpoint between 3 and 4, which is 3.5.
So the upper bound of a + b is:
5.5 + 3.5 = 9
Therefore, the upper bound of a + b is 9cm.
HELP PLS ILL GIVE U POINTS
Answer:
i think 16 im not sure
Step-by-step explanation:
Mrs. Perez's class donated 99 different products for the food drive. One-ninth of it was vegetables,2/3 pasta,
and 2/9 was soup. How much of each product did they donate?
Simplifying Mrs. Perez's class donated 11 units of vegetables, 66 units of pasta, and 22 units of soup.
What does the term "simplify expression" mean?The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible
vegetables = (1/9) x 99
Simplifying this expression, we get:
vegetables = 11
So the class donated 11 units of vegetables.
Next, we can figure out how much of the donation was pasta. We know that 2/3 of the donation was pasta, so we can set up the equation:
pasta = (2/3) x 99
Simplifying 66 units homemade pasta, 22 units of soup, and 11 units of veggies were all provided by Mrs. Perez's students.
Which expression should I simplify?
A math difficulty is simply solved by simplifying the expression. When you simplify a phrase, your goal is essentially to make it as simple as you can. There shouldn't be any more multiplication, dividing, adding, or removing to be done at the conclusion.
veggies = 1/9 times 99
When we condense this statement, we get:
eleven vegetables
Hence, the class gave away 11 units of produce.We can then determine what proportion of the contribution was pasta. Given that we know that pasta made up 2/3 of the donation, we can construct the following equation:
spaghetti equals (2/3) x 99
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Im a trapezoid measuring 8cm, 10cm, 16 cm and 10cm on its sides. What is my Perimeter? 1-5 po lhat
Answer:
See Below.
Step-by-step explanation:
To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.
In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.
Perimeter = 8 cm + 10 cm + 16 cm + 10 cm
Perimeter = 44 cm
Therefore, the perimeter of the trapezoid is 44 cm.
17. The sum of the interior angles of a pentagon is6x + 6y. Find y in term of x
Answer:
We know that, the sum of interior angles of an n-sided polygon is (n−2)×180⁰
For a pentagon, n=5
so,
[tex] \implies \rm \: 6x + 6y = (n - 2)180[/tex]
[tex] \implies \rm \: 6(x + y) = (5 - 2)180[/tex]
[tex] \implies \rm \: 6(x + y )= 3 \times 180[/tex]
[tex] \implies \rm \: (x + y) = \dfrac{3 \times 180}{6} [/tex]
[tex] \implies \rm \: (x + y) = \dfrac{ 3 \times \cancel{180} \: \:30}{ \cancel6} [/tex]
[tex] \rm \implies \: x + y = 90[/tex]
[tex] \underline{\boxed{\implies \rm \: y= 90 - x}}[/tex]
Pentagon FormulasThere are many formulas related to a pentagon. A few basic ones are given below.
Diagonals of a pentagon: = n × (n − 3) ÷ 2 = 5 × (5 − 3) ÷ 2 = 5Sum of interior angles of a pentagon: = 180° × (n − 2) = 180° × (5 − 2) = 540°Each exterior angle of a regular pentagon: = 360° ÷ n = 360° ÷ 5 = 72°Each interior angle of regular pentagon: = 540° ÷ n = 540° ÷ 5 = 108°Area of a regular Pentagon = 1/2 × Perimeter × ApothemPerimeter of Pentagon = (side 1 + side 2 +side 3 + side 4 + side 5)The cost of a gallon of gas is $3.50. What is the maximum number of of gallons you can buy for $20?
Answer:
5 gallons
Step-by-step explanation:
20÷3.50=5.714...
so the answer is 5 gallons
11. How much time will it take for ₹5000
5618 at 6% per annum
annually?
to become
compounded
Answer:
2.31 Years
Step-by-step explanation:
To calculate the time it will take for ₹5000 to grow to ₹5618 with a 6% annual interest rate when compounded annually, we can use the following formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (₹5618)
P = the principal amount (₹5000)
r = the annual interest rate (6% or 0.06)
n = the number of times the interest is compounded per year (1, since it's compounded annually)
t = the time period in years
Plugging in the values, we get:
5618 = 5000(1 + 0.06/1)^(1t)
Simplifying:
1.1236 = 1.06^t
Taking the natural logarithm of both sides:
ln(1.1236) = ln(1.06^t)
Using the power rule of logarithms:
ln(1.1236) = t ln(1.06)
Solving for t:
t = ln(1.1236) / ln(1.06)
t ≈ 2.31 years
Therefore, it will take approximately 2.31 years for ₹5000 to grow to ₹5618 at a 6% annual interest rate when compounded annually.
. A circular fence is being used to surround a dog house. How much fencing is needed to build the fence?
45.53 ,fencing is needed to build the fence.
What is area?A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition polyhedra of arc length for one-dimensional curves and the definition of surface area for (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double much simpler mathematical concepts than the definition of surface area integration and is based on techniques used in infinitesimal calculus.sought a general definition of surface area.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
2*3.14*14.5/2
45.53ft
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Patty para sus maquetas representadas en las figuras 1 y 2 planea colocar árboles en los puntos rojos que están separados una distancia de 5 cm uno de otro ¿cuanto miden los lados de cada maqueta ?¿Cuántos árboles colocará en cada una por favor ayuda
The total length of the rope in feet required by Patty to make a ladder is equal to 17.5 feet.
length of each piece of rope = 18 inches
Convert the length of the pieces of rope into feet.
One foot is equal to 12 inches
⇒ 18 inches = 18/12 feet
⇒ 18 inches = 1.5 feet.
Since Patty needs five of these pieces of rope.
The total length of rope needed for the steps is equal to,
5 x 1.5 = 7.5 feet
Patty also needs two pieces of rope that are each 5 feet long for the sides of the ladder.
Total length of rope needed for the ladder is,
2 x 5 = 10 feet
Add up the total length of all the pieces of rope required for the ladder,
7.5 + 10 = 17.5 feet
Therefore, Patty needs 17.5 feet of rope to make the ladder.
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The given question is incomplete, I answer the question in general according to my knowledge:
Patty is building a rope ladder for a tree house. She needs two 5-foot pieces of rope for the sides of the ladder. She needs 5 pieces of rope, each 18 inches long, for the steps. How many feet of rope does Patty need to make the ladder?
PLEASE HELP NOW!!! What would be the experimental probability of drawing a white marble?
Ryan asks 80 people to choose a marble, note the color, and replace the marble in Brianna's bag. Of all random marble selections in this experiment, 34 red, 18 white, 9 black, and 19 green marbles are selected. How does the theoretical probability compare with the experimental probability of drawing a white marble? Lesson 9-3
Answer: 18/80 for theoretical and then 18/80=.225 = 22.5% for experimental
Step-by-step explanation: theoretical: theres 18 white marbles, and then add up 34 + 18+9+19 to get 80. to get theoretical its number of favorable outcomes over total size of sample space, therefore 18 over 80
Experimental: divide 18/80 to get .225 then move decimal over by 2 to get 22.5%
The function h is defined by the following rule.
h(x) = 4x-2
Complete the function table.
-3
0
2
4
5
X
h(x)
0
0
0
Answer:
h(-3) = -14
h(0) = -2
h(2) = 6
h(4) = 14
h(5) = 18
Step-by-step explanation:
h(x) = 4x - 2
x=-3
h(-3) = 4(-3) - 2
h(-3) = -12 - 2
h(-3) = -14
x=0
h(0) = 4(0) - 2
h(0) = 0 - 2
h(0) = -2
x=2
h(2) = 4(2) - 2
h(2) = 8 - 2
h(2) = 6
x=4
h(4) = 4(4) - 2
h(4) = 16 - 2
h(4) = 14
x=5
h(5) = 4(5) - 2
h(5) = 20 - 2
h(5) = 18
enlarge triangle by scale factor 3 using the blue dot as the centre of enlargement
The new enlarged triangle has vertices at P4, P5, and P6, and is three times larger than the original triangle, with the blue dot as its center of enlargement.
What is a triangle?
A triangle is a geometric shape that consists of three straight sides and three angles. It is one of the most basic and fundamental shapes in geometry, and it is formed when three non-collinear points are connected by straight lines.
To enlarge a triangle by a scale factor of 3 using the blue dot as the center of enlargement, follow these steps:
Draw a line connecting the blue dot and each vertex of the triangle.
Mark a point on each line that is 3 times the distance from the blue dot as the corresponding vertex of the original triangle.
Connect the points on each line to form the new enlarged triangle.
Here is a step-by-step visual guide:
1. Draw lines connecting the blue dot to each vertex of the original triangle.
B
/\
/ \
/ \
P1 / \ P2
/ \
/ \
/____________\
A P3 C
2. Mark a point on each line that is 3 times the distance from the blue dot as the corresponding vertex of the original triangle.
B
/\
/ \
/ \
P1 / \ P2
/ \
/ P4 \
/____________\
A P3 C
Note that P4 is located 3 times the distance from the blue dot to vertex A along the line connecting them. Similarly, P5 and P6 are located 3 times the distance from the blue dot to vertices B and C respectively along their respective lines.
3. Connect the points on each line to form the new enlarged triangle.
P5
/\
/ \
/ \
P1 / \ P2
/ \
/ P4 \
/____________\
P3 P6 P7
Therefore, the new enlarged triangle has vertices at P4, P5, and P6, and is three times larger than the original triangle, with the blue dot as its center of enlargement.
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find the length of a cube with a volume of 8/729in3
Step-by-step explanation:
Volume of a cube = s x s x s (all of the sides are the same length)
s^3 = 8 / 729
s = 2 / 9 in
Can someone give me the answer please and the other one
Answer:
58 degrees
Step-by-step explanation:
51+27=58 degrees
second one is 56 degrees
132-76=56 degrees
Sippy brought home 2 tortoise as pets. She collected money to build a comfortable home for them. She had a total of Rs. 8200 in the form of Rs. 100, Rs. 500 and Rs. 2000 currency notes.
Rs. 500 notes were half of Rs. 100 notes. Rs. 2000 were one-third of Rs. 500 notes.
i) Write and solve the linear equation to find the number of notes of each denominations.
ii) Calculate the value of money obtained from Rs. 100 notes.
Find the volume of the washer. Round to the nearest whole millimeter
The volume of the washer as per the given dimensions is calculated to be 7,854 mm³.
In order to calculate the volume of the washer, we are required to subtract the volume of the hole in the center from the volume of the solid cylinder with the outer radius. The volume of the solid cylinder with the outer radius can be calculated using the formula:
V1 = πr1²h (Here, r1 is the outer radius and h is the thickness)
Substituting the given values, we have:
V1 = π(30mm)²(5mm) = 14,137.17 mm³
The volume of the hole in the center can be calculated using the same formula, but with the inner radius,
V2 = πr2²h (Here r2 is the inner radius and h is the thickness)
Substituting the given values, we have:
V2 = π(20mm)²(5mm) = 6,283.19 mm³
Therefore, the volume of the washer is:
V = V1 - V2 = 14,137.17 mm³ - 6,283.19 mm³ = 7,853.98 mm³
Therefore, on rounding the obtained result to the nearest whole millimeter, the final volume is calculated to be 7,854 mm³.
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The complete question is :
What is the volume of a washer with an outer radius of 30 mm, an inner radius of 20 mm, and a thickness of 5 mm? (Round your answer to the nearest whole millimeter)
can someone please explain?
It would make it easier for the cafe to adjust prices if necessary, as they would only need to modify the cost per ounce for each size.
What is cost?Cost is the amount of money or resources required to purchase or produce something. It can be the total expenditure on a product, service, or activity. It can also refer to the amount of money or resources consumed in order to maintain or achieve something. Cost can also be the value of a resource lost or sacrificed in order to obtain something.
To make the price of smoothies a function of the size, the sign should be modified to include the following additional information:
8 ounce $2.29/ounce
12 ounce $2.79/ounce
12 ounce. $3.09/ounce
16 ounce $3.69/ounce
20 ounce $4.09/ounce
22 ounce
( Bonus size). $4.09/ounce
This change would make the price of smoothies a function of the size, as each smoothie size would then have its own associated cost per ounce. This would make it easier for customers to compare the cost of different sizes and make an informed decision. Furthermore, it would make it easier for the cafe to adjust prices if necessary, as they would only need to modify the cost per ounce for each size.
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Suppose that a phone originally sold for $800 loses 3/5 of its value each year after it is released. After 2 years, how much is the phone worth?A. $800B. $1333C. $128D. $288
The phone is worth $128 after 2 years, which is option C.
What is exponential decay ?
Exponential decay is a decrease in a quantity over time where the rate of decay is proportional to the current value. In this case, the value of the phone decreases by 3/5 each year after it is released. This means that the value after one year is 2/5 of the original value, and the value after two years is (2/5) times (2/5) of the original value. Exponential decay is a common phenomenon in many areas of science and mathematics, including radioactive decay, population growth and decay, and financial investments.
Calculating the worth of the phone :
The phone is not worth the same amount after 2 years, as it loses 3/5 of its value each year. We need to calculate its worth after 2 years.
Let's use the formula for exponential decay: [tex]A = A_0(1 - r)^t[/tex], where A is the final amount, [tex]A_0[/tex] is the initial amount, r is the decay rate, and t is the time elapsed.
In this case, the initial amount is $800, the decay rate is 3/5, and the time elapsed is 2 years. Substituting these values into the formula, we get:
[tex]A = 800(1 - 3/5)^2[/tex]
[tex]A = 800(2/5)^2[/tex]
[tex]A = 800(4/25)[/tex]
[tex]A = 128[/tex]
Therefore, the phone is worth $128 after 2 years, which is option C.
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Qual o resultado do problema 3528÷98?
Answer:
36
Step-by-step explanation:
2. Oil is leaking from an uncapped well and polluting a lake. Ten days after the leak is discovered, environmental engineers measure the amount of oil in the water to be 200 gallons with a current inflow rate of 30 gallons per day. The leak is slowing so that on the tenth day, the inflow rate is decreasing by 5 gallons/day each day. Suppose Q(t) is the amount of oil (in gallons) t days after the leak is discovered. (a) Find the second degree Taylor polynomial for Q(t) centered at t=10. (b) Use your answer in the previous part to estimate the amount of oil in the lake at t=12
As a result, 210 gallons of oil are thought to have been present in the lake at time 12 (t=12).
what is polynomial ?A polynomial is a mathematical equation that only uses addition, subtraction, multiplication, and non-negative integer exponents and is made up of variables and coefficients. To put it another way, a polynomial is an algebraic expression made up of terms that are sums, products, and/or products of variables and coefficients. The leading coefficient is the coefficient of the term with the highest degree, while the degree of a polynomial is the maximum power of the variable in the expression.
given
(a) We need to determine Q(10), Q'(10), and Q" in order to determine the second degree Taylor polynomial for Q(t) with a center at t=10 (10).
As we are aware, Q(10) = 200. (given in the problem statement).
We must take the derivative of Q(t) with respect to t in order to determine Q'(10):
Q'(t) = -5t + 250
Q'(10) = -5(10) + 250 = 200
We must take the derivative of Q'(t) with respect to t in order to determine Q"(10):
Q''(t) = -5
Q''(10) = -5
The second degree Taylor polynomial can now be calculated using the following formula: P2(t) = Q(10) + Q'(10)(t-10) + (1/2)Q"(10)(t-10)2.
With the numbers we discovered, we can calculate P2(t) as 200 + 200(t-10) + (1/2)(-5)(t-10)2.
[tex]P2(t) = 200 + 200(t-10) - (5/2)(t-10)^2[/tex]
(b) We must assess the second degree Taylor polynomial at t=12 in order to determine how much oil is in the lake at that time.
P2(12) = 210 gallons because P2(12) = 200 + 200(12-10) - (5/2)(12-10)2. (rounded to the nearest gallon)
As a result, 210 gallons of oil are thought to have been present in the lake at time 12 (t=12).
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