Answer: The required function formula is,
S(t) = 2 - 0.25 t
Step-by-step explanation:
Here, the initial thickness of the ice sheet = 2 meters,
After 3 weeks, the thickness of ice sheet = 1.25 meters
Total changes in the thickness in 3 weeks = 2 - 1.25 = 0.75 meters,
⇒ Total changes in the thickness in 1 weeks = 0.75/3 = 0.25 meters,
Since, the ice is melting with the constant rate.
⇒ The rate of ice decreasing = 0.25 meters per week.
⇒ Total changes in t weeks = 0.25 t meters
The new thickness of ice after t weeks = Initial thickness - Total changes in t weeks.
⇒ S(t) = 2 - 0.25 t
Which is the required function's formula.
The function's formula for the ice sheet's thickness as a function of time is S(t) = -0.25t + 2.
Explanation:To write the function's formula, we can use the slope-intercept form of a linear equation, which is given by the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope represents the rate at which the ice thickness decreases over time. From the given information, we know that the thickness decreases by 0.75 meters over 3 weeks. Therefore, the slope is -0.75/3 = -0.25 meters per week.
Since the ice thickness is 2 meters in the beginning, the initial point on the graph is (0, 2). Using the slope-intercept form, we can write the formula for the ice sheet's thickness as a function of time as:
S(t) = -0.25t + 2
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Mindy is training to run a marathon. She runs 4 miles each day. Write an equation that would represent the number of miles m, she runs on a given day, d.
What number goes in the missing space?
This is a question from my homework "Rosina finds a pair of shorts on the sale rack for $12.50. This price reflects a discount of 60%. What is the original price of the shorts? What is the amount of the discount?"
Please help me with this!
I have no idea how to do this equation, please help
Find a quadratic function associated with vertex (h, k) = (2, 1) and point (x, y) = (6, 7) that the parabola passes through.
To find the quadratic function with vertex (2, 1) that passes through (6, 7), use the vertex form of a quadratic equation and solve for 'a' using the given point. The resulting function is y = ([tex]\frac{3 }{ 8}[/tex])(x - 2)² + 1.
To find a quadratic function associated with the vertex (h, k) = (2, 1) and a point (x, y) = (6, 7) that the parabola passes through, we need to use the vertex form of a quadratic equation:
y = a(x - h)² + k
Since we know the vertex (h, k), we can substitute h=2 and k=1 into the equation, which gives us:
y = a(x - 2)² + 1
We also know that the parabola passes through the point (6,7), so we can substitute x=6 and y=7 into the equation to find the value of 'a':
7 = a(6 - 2)² + 1
7 = a(4)² + 1
6 = 16a
[tex]a = \frac{6 }{ 16} = \frac{3 }{ 8}[/tex]
Now, substituting the value of 'a' into the vertex form, we get the quadratic function:
y = ([tex]\frac{3 }{ 8}[/tex])(x - 2)² + 1
At what rate must $287.50 be compounded annually for it to grow to $572.86 in 8 years?
You are a builder and need to submit an estimate to a customer for remodeling a bathroom. Your project costs are $451.75 for labor, $332.52 for materials and $289.12 for subcontracting for plumbing. Round these amounts to whole numbers to estimate the cost of the total project.
An elephant can run mile in 36 seconds. Which of the following correctly shows this rate as miles per hour? = 25 miles per hour = 144 miles per hour = 25 miles per hour = 144 miles per hour
Find a generating function for the number of integer solutions of 2x+3y+7z=r
If p(a) = 0.50, p(b) = 0.60, and p(a intersection
b.= 0.30, what is the p(a union b)? enter your answer as a decimal rounded to two places.
The probability is 0.80.
To find the probability of the union of two events, calculate the sum of their individual probabilities and subtract the probability of their intersection.
The probability of the union of events A and B (P(A ∪ B)) can be calculated using the formula:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Given P(A) = 0.50, P(B) = 0.60, and P(A ∩ B) = 0.30, substitute these values into the formula to find P(A ∪ B) = 0.50 + 0.60 - 0.30 = 0.80
what expression must the center cell of the table below contain so that the sums of each row, each column, and each diagonal are equivalent?
x 8x -3x
-2x ? 6x
7x -4x 3x
The missing value in the center cell (y) should be 2x to achieve equivalent sums in each row, column, and diagonal.
To achieve equivalent sums in each row, column, and diagonal, we need to determine the missing value in the center cell. Let's denote the missing value as "y."
The table is as follows:
x 8x -3x
-2x y 6x
7x -4x 3x
Now, let's consider the sum along each row, column, and diagonal:
Rows:
x + 8x - 3x = 6x (1st row)
-2x + y + 6x = 4x + y (2nd row)
7x - 4x + 3x = 6x (3rd row)
Columns:
x - 2x + 7x = 6x (1st column)
8x + y - 4x = 4x + y (2nd column)
-3x + 6x + 3x = 6x (3rd column)
Diagonals:
x + y + 3x = 4x + y (from top-left to bottom-right)
-3x + y + 7x = 4x + y (from top-right to bottom-left)
To ensure equivalent sums, the expression for "y" in the center cell should be such that 4x + y = 6x. Solving for "y," we find y = 2x.
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Find r for the geometric series with s5 = 484, a1 = 4, a5 = 324
A scatter plot is shown below:
Which two ordered pairs can be joined to draw most accurately the line of best fit on this scatter plot?
(4, 9.5) and (10, 5.5)
(5, 0) and (10, 10)
(0, 6) and (5, 0)
(0, 9.5) and (10, 1.5)
Answer:
(0, 9.5) and (10, 1.5)
Step-by-step explanation:
as we can see the closest points that assimilate the scatter plot, these is the answer.
How do i solve a Real world problem that involves finding the product of a fraction and a mixed number?
Combine the like terms to create an equivalent expression. 12p + p
Answer: The equivalent expression of the given terms is 13 p
Step-by-step explanation:
Like terms are defined as the terms which have same variable. Mathematical operation are applied on these terms.
Unlike terms are defined as the terms which do not have same variable. Mathematical operation are not applied on these terms.
For Example: [tex]x^2+2x+5x^2+7[/tex]
In the above expression, [tex]x^2\text{ and }5x^2[/tex] are the like terms because they have same variable which is '[tex]x^2[/tex]'
In the given expression: 12 p + p
Both the terms are like terms, and thus the operation can be applied.
Hence, the equivalent expression of the given terms is 13 p
1 2 3 4 5 6 7 8 9 10 The two conditional relative frequency tables below show the results of a survey asking students whether they are taking a foreign language or not. Table B: Frequency of Foreign-Language Studies by Row Which table could be used to answer the question "Assuming a student is taking a foreign language, what is the probability the student is also in high school?” Table A, because the given condition is that the student is in high school. Table A, because the given condition is that the student is taking a foreign language. Table B, because the given condition is that the student is in high school. Table B, because the given condition is that the student is taking a foreign language.
Answer:
B. Table A, because the given condition is that the student is taking a foreign language.
Step-by-step explanation:
ED 2020
David was looking at his limousine bill and saw that the total number of miles he has ridden in the car was tracked, as shown below: Month Miles 5 580 6 695 7 810 8 925 The function representing David's miles per month is f(m) = 115m + 5. What does the 115 represent?
The number of additional miles each month.
In the decimal value 4256, the weight of the numeral 2 is ________.
Answer: 200
Explanation:
Numeral system is a system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems.
For example:
2356:-
We start from left
6 = 6*10⁰ = 6*1 = 6
5 = 5*10¹ = 5*10 = 50
3 = 3*10² = 3*100 = 300
2 = 2*10³ = 2*1000 = 2000
Similarly,
Given number is 4256
6 = 6*10⁰ = 6*1 = 6
5 = 5*10¹ = 5*10 = 50
2 = 2*10² = 2*100 = 200
what is the best definition for marginal cost?
Marginal cost is the additional cost incurred when producing one extra unit of a good or service.
Marginal Cost: Marginal cost is the change in total cost that occurs when the quantity produced is increased by one unit. It represents the cost of producing one more unit of a good, encompassing all additional costs required for that extra unit.
Example: If producing one more car necessitates building an additional factory, the marginal cost includes all costs associated with setting up the new factory.
Marginal cost is the additional cost of producing one more unit of a good or service.
To calculate marginal cost, you divide the change in total cost by the change in the quantity produced. Mathematically, it can be expressed as:
Marginal Cost = (Change in Total Cost) / (Change in Quantity)
This concept is crucial in economics and business for decision-making purposes. It helps firms determine the cost-effectiveness of increasing or decreasing production levels.
For instance, if a company is considering expanding its production, understanding the marginal cost allows it to assess whether the additional revenue from selling more units will outweigh the additional costs incurred.
It is also used to make pricing decisions and optimize resource allocation. In summary, marginal cost provides insight into how production decisions impact overall costs and profitability.
Find the general solution of x'1 = 3x1 - x2 + et, x'2 = x1.
Final answer:
To find the general solution of the given system of differential equations, first, solve the second equation for x1 in terms of x2. Then substitute x1 into the first equation and simplify to isolate x'2. Next, solve the second equation for x2 in terms of x1 and substitute x2 into the first equation. Simplify and rearrange to isolate x'1. Finally, solve the resulting differential equations to find the general solution.
Explanation:
To find the general solution of the given system of differential equations:
x'1 = 3x1 - x2 + et, x'2 = x1
Step 1: Solve the second equation for x1 in terms of x2:
x1 = x'2
Step 2: Substitute x1 into the first equation:
x'1 = 3(x'2) - x2 + et
Step 3: Simplify and rearrange the equation to isolate x'2:
x'2 = (x'1 + x2 - et)/3
Step 4: Solve the second equation for x2 in terms of x1:
x2 = x'1 - 3x'2 + et
Step 5: Substitute x2 into the first equation:
x'1 = 3x1 - (x'1 - 3x'2 + et) + et
Step 6: Simplify and rearrange the equation to isolate x'1:
x'1 = (3x'2 + x'1 - 2et)/3
Now we have two differential equations for x'1 and x'2 in terms of each other. These can be solved using standard methods to find the general solution.
An urn contains eight blue balls and seven yellow balls. if six balls are selected randomly without being replaced, what is the probability that of the balls selected, two of them will be blue and four of them will be yellow
Miguel ordered a rectangular print for his bedroom. The print is 78 feet wide and 135 feet long.
What is the area of the print?
Here is the sample space for three tosses of a coin.
{HHH, HHT, HTH, HTT, THH, THT, TTH, THT}
Calculate the probability that this compound event will yield a result of 2 heads and 1 tail (in any order)
A. 0.125
B. 0.25
C. 0.333
D. 0.375
The probability that the compound event of tossing a coin 3 times will yield a result of 2 heads and 1 tail (in any order) is option D. 0.375.
Given that:
A coin is tossed three times.
The sample space is given as:
{HHH, HHT, HTH, HTT, THH, THT, TTH, THT}
Now, it is required to find the probability of getting 2 heads and 1 tail in any order.
Total number of outcomes = number of elements in the sample space
= 8
Outcomes that yield two heads and one tail = {HHT, HTH, THH}
Number of outcomes that yield two heads and one tail = 3
So, the probability is
[tex]P(\text{2 heads and 1 tail})=\frac{3}{8}\\[/tex]
So, P = 0.375
Hence, the correct option is D.
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Determine whether the lines l1 and l2 are parallel, coincident, skew, or intersecting. if they intersect, find the point of intersection: ℓ1:x1(t)=1−6t,y1(t)=2+9t,z1(t)=−3t ℓ2:x2(u)=2+2u,y2(u)=3−3u,z2(u)=u
To determine whether the lines are parallel, coincident, skew, or intersecting, we first analyze the direction vectors of both lines obtained from the parametric equations. The lines are not parallel or coincident as they're not proportional. They could be intersecting or skew, which we can confirm by finding a potential point of intersection.
Explanation:To determine the relationship between lines ℓ1 and ℓ2, we should analyze the direction vectors of both lines. The coefficients of t or u in the parametric equations for the lines refer to the direction vectors. For ℓ1, the direction vector is (-6, 9, -3). For ℓ2, it's (2, -3, 1).
Lines are parallel if their direction vectors are proportional, and intersect if they pass through a common point and their direction vectors are not proportional. Lines are coincedent if all corresponding points are identical, while skew lines are nonintersecting, nonparallel lines.
Given the direction vectors, we can see they are not proportional. Hence, ℓ1 and ℓ2 are neither parallel nor coincident. They might be intersecting or skew. To distinguish between these two, we need to try to find a point of intersection by equating ℓ1 and ℓ2 and solving for t and u. If a solution exists, the lines intersect at that specific point; if no solution exists, the lines are skew.
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We have enough material to build a fence around a station that has a perimeter of 180 feet. The width of the rectangular space must be 30 1/4 feet. What must the length be?
A purse contains 5-cent coins and 10-cent coins worth a total of $1.05. If the 5-cent coins were replaced with 10-cent coins and the 10-cent coins were replaced with 5-cent coins, the coins would be worth a total of $2.15. How many coins are in the purse? HELP PLEASE WITH WORK
Answer:
The other person should be correct
Step-by-step explanation:
If a one dollar bill is 0.0001 meters thick, how many meters tall would a stack of 4 trillion one dollar bills be?
Answer:
[tex]4*10^{8}\text{ meters}=400,000,000\text{ meters}[/tex].
Step-by-step explanation:
We have been given that a one dollar bill is 0.0001 meters thick. We are asked to find the height of a stack of 4 trillion one dollar bills.
We know that [tex]\text{1 trillion}=10^{12}[/tex]. To find the thickness of a stack of 4 trillion one dollar bills we will multiply 0.0001 by 4 trillion.
Let us convert 0.0001 into scientific notation as:
[tex]0.0001=1\times 10^{-4}[/tex]
[tex]\text{The height of 4 trillion one dollar bills}=4*10^{12}\times 1\times 10^{-4}\text{ meters}[/tex]
Using exponent property [tex]a^b\times a^c=a^{b+c}[/tex] we will get,
[tex]\text{The height of 4 trillion one dollar bills}=4*10^{12-4}\text{ meters}[/tex]
[tex]\text{The height of 4 trillion one dollar bills}=4*10^{8}\text{ meters}=400,000,000\text{ meters}[/tex]
Therefore, the stack of 4 trillion one dollar bills would be [tex]4*10^{8}\text{ meters}=400,000,000\text{ meters}[/tex].
Annie's cafe borrows $6100 at 6% for 290 days. Find the total amount that must be repaid after 290 days. (Use a 365 day year.)
The total amount that must be repaid after 290 days is $6330.67.
Explanation:To find the total amount that must be repaid after 290 days, we can use the formula:
Amount = Principal + Interest
Principal is the amount borrowed, which is $6100. Interest is calculated using the formula:
Interest = Principal * Rate * Time
Since the loan is for 290 days, we need to convert it to years by dividing by 365:
Time = 290/365 = 0.7945 years
Plugging in the values, the interest is:
Interest = 6100 * 0.06 * 0.7945 = $230.67
Adding the principal and interest together, the total amount to be repaid is:
Total Amount = Principal + Interest = $6100 + $230.67 = $6330.67
q
the set of points (-3,4), (-1,1), (-3.-2), and (-5,1) identifies the vertices of a quadrilateral. which is the most specific describtion to tell which figure the points form?