Answer:
The integrating factor, u(t), for the initial value problem t* dy/dt+3y=8t with y(1)=8 is u(t) = e^(3t). The solution to this equation is y(t) = 8e^(-3t)+2te^(-3t).
Step-by-step explanation:
The integrating factor, u(t), for the given initial value problem t(dy/dt)+4y=3t with y(1)=8 is u(t) = e^(4∫t dt) = e^(2t^2).
Using this integrating factor, the solution to the initial value problem is y(t) = (3/8)te^(2t^2)+Ce^(-2t^2), where C is a constant of integration. Since y(1)=8, we can solve for C and find that C=-7/4. Therefore, the solution to the initial value problem is y(t) = (3/8)te^(2t^2)-7/4e^(-2t^2).
We are asked the solve the following differential equation, [tex]t\frac{dy}{dt}+3y=8t[/tex]. This is an ordinary, linear, first-order DE. We need it in the form [tex]\frac{dy}{dt}+P(t)y=Q(t)[/tex], where [tex]\mu(t)=e^{\int\ {P(t)} \, dt }[/tex], which is the integrating factor.
[tex]\Longrightarrow t\frac{dy}{dt}+3y=8t[/tex], multiply everything by t.
[tex]\Longrightarrow \frac{dy}{dt}+(\frac{3}{t} )y=8[/tex]
We now have the correct form for solving a linear, first-order DE.
Find [tex]\mu(t)[/tex].
[tex]\Longrightarrow \mu(t)=e^{\int\ {P(t)} \, dt } \Longrightarrow \mu(t)=e^{\int\ {\frac{3}{t} } \, dt }[/tex]
[tex]\Longrightarrow \mu(t)=e^{3\int\ {\frac{1}{t} } \, dt }\Longrightarrow \mu(t)=e^{3ln|t|} \Longrightarrow \mu(t)=e^{ln(t^3)}[/tex]
[tex]\Longrightarrow \mu(t)=t^3[/tex]
Now multiply the entire DE by [tex]\mu(t)[/tex].
[tex]\Longrightarrow t^3[\frac{dy}{dt}+(\frac{3}{t} )y=8][/tex]
[tex]\Longrightarrow (t^3)\frac{dy}{dt}+(t^3)(\frac{3}{t} )y=(t^3)8[/tex]
[tex]\Longrightarrow (t^3)\frac{dy}{dt}+(3t^2)y=(t^3)8[/tex]
Verify that the L.H.S is a product rule of [tex]t^3y[/tex].
Product rule: [tex]\frac{d}{dx}[f(x)g(x)]=f(x)g'(x)+f'(x)g(x)[/tex]
[tex]\frac{d}{dt}[t^3y]=(t^3)(\frac{dy}{dt} )+(3t^2)(y)[/tex]
It is the product rule, so we can move forward by integrating both sides of the DE.
[tex]\Longrightarrow \int\ {[t^3y]'} \, =\int\ {8t^3} \, dt[/tex]
[tex]\Longrightarrow t^3y=2t^4+C[/tex]
Now using the initial condition to find the arbitrary constant, C.
[tex]t^3y=2t^4+C ;y(1)=8[/tex]
[tex]\Longrightarrow (1)^3(8)=2(1)^4+C[/tex]
[tex]\Longrightarrow 8=2+C[/tex]
[tex]\Longrightarrow 6=C \Longrightarrow C=6[/tex]
Now we have, [tex]t^3y=2t^4+6[/tex], solve for y.
[tex]\Longrightarrow t^3y=2t^4+6[/tex]
[tex]\Longrightarrow y=2\frac{t^4}{t^3} +\frac{6}{t^3}[/tex]
[tex]\Longrightarrow y=2t +6t^{-3}[/tex]
Thus the given differential equation with the initial condition is solved, [tex]y=2t +6t^{-3}[/tex].
the following associations can be described by generalized linear models. for each one, identify the response variable and the explanatory variables select a probability distribution for the response and write down the linear component
In each case, the response variable, the explanatory variables, and the probability distribution is specified.
Before answering this question, let's us understand the Generalized linear models
Generalized linear models (GLMs) are used to model a response variable that has a non-normal distribution by linking the mean of the response variable to a linear combination of explanatory variables through a link function.
The Identification of cases are given below:
a) Response variable: number of trips per week to the supermarket for a household
Explanatory variables: number of people in the household, household income, distance to the supermarket
Probability distribution: Poisson
Justification: The response variable "number of trips per week" is count data and can be modeled using a Poisson distribution.
Linear component: log(μ) = β0 + β1 * number of people in the household + β2 * household income + β3 * distance to the supermarket
b) Response variable: person's weight
Explanatory variables: age, sex, height, mean daily food intake, mean daily energy expenditure
Probability distribution: Gaussian (Normal)
Justification: The response variable "person's weight" is continuous and approximately normally distributed.
Linear component: μ = β0 + β1 * age + β2 * sex + β3 * height + β4 * mean daily food intake + β5 * mean daily energy expenditure
c) Response variable: proportion of mice infected after exposure to bacteria
Explanatory variables: exposure level
Probability distribution: Binomial
Justification: The response variable "proportion of mice infected" is binary (yes/no) and can be modeled using a binomial distribution.
Linear component: logit(p) = log(p/(1-p)) = β0 + β1 * exposure level
The linear component represents the relationship between the mean of the response variable and the explanatory variables.
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____ The given question is incomplete, the complete question is given below:-
The following associations can be described by generalized linear models. For each one, identify the response variable and the explanatory variables, select a probability distribution for the response (justifying your choice) and write down the linear component.
a. The association between the number of trips per week to the supermarket for a household and the number of people in the household, the household income and the distance to the supermarket.
b. The effect of age, sex, height, mean daily food intake and mean daily energy expenditure on a person’s weight.
c. The proportions of laboratory mice that became infected after exposure to bacteria when five different exposure levels are used and 20 mice are exposed at each level.
Como se hace este problema? X+4x=235
Respuesta:
x = 47
Explicación paso a paso:
Necesitamos resolver x en este problema.
[tex]x+4x=235[/tex]
Combinar los términos x juntos
[tex]5x=235[/tex]
Divide 5 en ambos lados
[tex]x=47[/tex]
Nuestra respuesta es 47
Find an ordered pair (x,y) that is a solution to the equation
Answer:
(3, -7)
Step-by-step explanation:
If you choose 3 as one of your x-coordinates, you simply need to solve for y to get -7 as your y-coordinate:
[tex]3x+y=2\\3(3)+y=2\\9+y=2\\y=-7[/tex]
Please help due tonight!!!!!!
Answer: -4,9 I AM PRETTY SURE FROM ALL OF MY RESEARCH SIORRY IF I AM WRONG I WISH YOU GOODLUCK
Step-by-step explanation:
pls help
Given right triangle ABCABC with altitude \overline{BD}
BD
drawn to hypotenuse \overline{AC}
AC
. If AD=7AD=7 and DC=5,DC=5, what is the length of \overline{BD}
BD
in simplest radical form?
The given assertion states that the length of BD in its simplest radical version is 7/√2.
In arithmetic, what is a triangle?A triangle is indeed a 3-sided shape that is occasionally (though not frequently) referred to as the trigon. There are three edges and three angles in every triangle, some of which could be the same.
Since BD is an altitude of the right triangle ABC, we can use the Pythagorean Theorem to find the length of BD. First, let's determine the size of AC:
AC² = AD * DC = 7 * 5 = 35
When we square the two edges, we obtain:
AC = √35
Now, we can use the fact that BD is an altitude to write:
BD = (AC * AD) / hypotenuse
where hypotenuse is the length of BC.
Using the Pythagorean Theorem, we can find the length of BC:
BC² = AC² + AB²
Since triangle ABC is a right triangle, we have AB = BC, so we can write:
BC² = AC² + BC²
Simplifying, we get:
BC² / AC² = 2
When we square the two edges, we obtain:
BC / AC = √2
Multiplying both sides by AC, we get:
BC = AC * √2 = √35 * √2 = √70
Now, we can substitute the values of AC, AD, and BC into the formula for BD:
BD = (AC * AD) / BC = (√35 * 7) / √70 = 7 / √2
Therefore, the length of BD in simplest radical form is 7 / √2.
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The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 40 in, find its area.
Answer:
Step-by-step explanation:
Let, width = x
length = x+4
perimeter, 2(x+4+x) = 40
4x+8 = 40
4x = 32
x = 8
so, (x+4) = 8+4 = 12
so, the area would be,
= 12 * 8 = 96 in²
What is the area, in square feet, of the
isosceles trapezoid below?
8 ft
6.2 ft
15.4 ft
Answer:
86.4 ft^2
Step-by-step explanation:
Finally, you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V says: At least three of us are knights. W says: At most three of us are knights. X says: Exactly five of us are knights. Y says: Exactly two of us are knights. Z says: Exactly one of us is a knight. Which are knights? (Select all that apply.) U V w MX OY Z Which are knaves? (Select all that apply.) U V w MX Z X
In this type of puzzle, "knight" means that the speaker is telling the truth, and "knave" means that the speaker is lying.
Let's start by analyzing the first two statements:
U says: None of us is a knight.
V says: At least three of us are knights.
If U is a knight, then his statement is false, meaning that at least one of the six is a knight, which contradicts V's statement that at least three of them are knights. Therefore, U must be a knave.
Next, let's look at the statement of W:
W says: At most three of us are knights.
If W is a knight, then his statement is true, meaning that there are three or fewer knights among the six. Since U is a knave, this would mean that at most two of the remaining five are knights, which contradicts V's statement that at least three of them are knights. Therefore, W must be a knave.
Continuing in this way:
X says: Exactly five of us are knights.
If X is a knight, then his statement is false, meaning that exactly five of them are not knights. But since U is a knave, this means that U is a knight, which is a contradiction. Therefore, X must be a knave.
Y says: Exactly two of us are knights.
If Y is a knight, then his statement is true, meaning that exactly two of them are knights. Since U is a knave, this means that exactly two of the remaining five are knights, which means that W, X, Y, Z are knaves. This is consistent with all of the statements so far, so Y must be a knight.
Z says: Exactly one of us is a knight.
If Z is a knight, then his statement is true, meaning that exactly one of them is a knight. Since Y is a knight, this means that Y is the only knight, and U, V, W, X, Z are all knaves. This is consistent with all of the statements so far, so Z must be a knight.
Therefore, the knights are Y and Z, and the knaves are U, V, W, X.
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Is the ordered pair (4,1) a solution of the system of linear equations:
-x + y = -3
x + 3y = 6
a. yes
b. no
The ordered pair (4, 1) is not a solution to the system,
- x + y = - 3 and x + 3y = 6.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
Given, A system of linear equations - x + y = - 3 and x + 3y = 6.
An ordered pair must satisfy both equations simultaneously.
For, - x + y = - 3
- 4 + 1 = - 3.
- 3 = - 3 (satisfied).
For, x + 3y = 6.
4 + 3(1) = 6.
4 + 3 = 6.
But, 7 ≠ 6.
Therefore, the ordered pair is not a solution.
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Carly has 2.85 pounds of cat food she uses 0.19 pound of cat food to feed one cats. How many cats can Carly feed
Answer:
To find the number of cats Carly can feed, divide the total weight of cat food by the weight of cat food used per cat.
2.85 lbs ÷ 0.19 lbs/cat = 15 cats
Therefore, Carly can feed 15 cats.
would someone be able to help me out with this problem? thank you so much if u can! been stuck on it for 20 minutes now
Answer:
Form W-2 is completed by an employer and contains important information that you need to complete your tax return. It reports your total wages for the year and the amount of federal, state, and other taxes withheld from your paycheck.
Form 1040 is used by U.S. taxpayers to file an annual income tax return.
Head of household offers wider tax brackets, a bigger standard deduction and faster eligibility for other write-offs.
Step-by-step explanation:
Kirsty counts the number of peas in a sample of pea pods. Number of pods Number of peas in a pod 4 5 6 7 8 c) 2 10 18 14 6 What was the mean number of peas in a pod?
The number of pea is 6. By using formulas of mean, median and mode.
What is a mean?A dataset's mean (also known as the arithmetic mean, which differs from the geometric mean) is calculated by dividing the sum of all values by the total number of values. It is frequently referred to as the "average" and is the most widely used measure of central tendency.
Taking pea counts into account,
A pod of peas contains 4, 5, 6, 7 or 8 peas.
Number of pods: 2, 10, 18, 6, and 14
The mode is the number that corresponds to the highest frequency.
The frequency of each number in the list is 1.
Mode is not possible with the information provided.
The middle value, after sorting the numbers in ascending or descending order, is the median if all of the numbers are odd.
The median of the given numbers is.
Replace the values in the formula to get the mean value.
Mean = 4+5+6+7+8/5 = 30/5 = 6
Consequently, based on the quantity of peas provided, the values of the following measure are as follows:
It is impossible to use Peas in a Pod mode.
The median number of peas in a pod is 6.
the typical quantity of peas is 6.
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translate then solve:five times the difference of twice and number and three decreased by the sum of the number and 8 equals 13
Answer: x = 4
Step-by-step explanation:
Translating the problem into mathematical terms:
Let's call the number x. Then the problem can be written as:
5 * (2x - 3) - (x + 8) = 13
Expanding the left side of the equation:
5 * 2x - 5 * 3 - x - 8 = 13
Simplifying the left side of the equation:
10x - 23 - x - 8 = 13
Combining like terms:
9x - 31 = 13
Adding 31 to both sides of the equation:
9x = 44
Dividing both sides of the equation by 9:
x = 4.88888...
Since x has to be a whole number, we round down to the nearest whole number:
x = 4
Therefore, the number that satisfies the equation is 4.
sin(pi/3-a) if cos(a)=-0.6 and pi < a < 3pi/2
The exact values of two trigonometric functions are listed below:
- 2√2 / 3 and ± √6 / 3
How to determine the exact values of the trigonometric functions?In this problem we have the exact values of two trigonometric functions, and of which we need to determine the exact value of a set of trigonometric functions of more complexity, each of which can be found by understanding the nature of the trigonometric functions and trigonometric formulas.
Since sin(π/3-a) if cos(a)=-0.6 and π < a < 3π/2
Then, by the fundamental formula:
cos α = - √(1 - sin² α)
cos α = - √[1 - (1 / 3)²]
cos α = - √(8 / 9)
cos α = - 2√2 / 3
sin (π/3-a):
sin (π/3-a) = ± √[(1 - cos a) / 2]
sin (π/3-a) = ± √[[1 - (0.6)] / 2]
sin (π/3-a) = ± √6 / 3
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Use the range rule of thumb to estimate the standard deviations.
HW Score: 17.71%, 1.95 of 11 points
Points: 0.67 of 1
The 155 heights of males from a data set of body measurements vary from a low of 150.0 cm to a high of 191.1 cm. Use the range rule of thumb to estimate the standard deviations and compare
the result to the standard deviation of 10.84 cm calculated using the 155 heights. What does the result suggest about the accuracy of estimates of s found using the range rule of thumb? Assume the
estimate is accurate if it is within 1.4 cm.
Answer: The range rule of thumb is used to estimate the standard deviation by taking the range of the data and dividing it by 4:
s = (max - min) / 4
In this case, the range is 191.1 cm - 150.0 cm = 41.1 cm.
s = 41.1 cm / 4 = 10.275 cm
This estimate of the standard deviation is 10.275 cm, which is close to the actual standard deviation of 10.84 cm. Since the difference between the two is less than 1.4 cm, we can say that the estimate is accurate.
SOS. Please help with this……i Really need it!
The equation for the table is r = -3s + 15,
when s = 0, r = 15 and when s = 9, r = -12
the formula for Δr in terms of Δs is Δr = -3Δs.
What is a linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Both linear equations with one variable and those with two variables exist.
Given value of r is varying at a constant rate with respect to s,
given table for r and s
s(independent quantity) r(dependent quantity)
1 12
3 6
9 ?
12 -21
since both quantities vary at a constant rate so it is the condition of a linear equation,
y = mx + c
where m is the slope or the rate of change,
let s₁ = 1, s₂ = 3 and r₁ = 12, r₂ = 6
coordinates for graphs (1, 12) and (3, 6)
the equation is a form of s and r is
r = ms + c (because s is independent and r is dependent)
A: formula for Δr in terms of Δs is
Δr = mΔs
m = Δr/Δs = (6 - 12)/(3 - 1)
m = -3
Δr = -3Δs
the equation will be,
r = -3s + c
when s = 1 r = 12
12 = -3(1) + c
c = 15
the formula for r in terms of s is,
r = -6s + 15
B: the value of r when s = 0
r = -3(0) + 15
r = 15
and when s = 9
r = -3(9) + 15
r = -12
C: true and false;
i. The graph that represents s in terms of r is linear: True
ii. r is proportional to s: False, no r is not proportional to s because the relation between r and s has a constant
iii. Δr is proportional to Δs: True because the relation is Δr = -3Δs.
iv. The graph of r in terms of s is a straight line that passes through the origin (0, 0): False, because when s = 0 r = 15, so the graph does not pass from the origin.
Hence equation for r and s is: r = -3s + 15
when s = 9, r = -12 and when s = 0, r = 15
and Δr = -3Δs.
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Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 31 psi (pounds per square inch.) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning?
If the car’s average tire pressure is on target, the probability that the TPMS will trigger a warning is 0.0000.
What is a distribution?The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.
Given:
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure.
Suppose the target tire pressure of a certain car is 31 psi (pounds per square inch.)
Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.
Target pressure = 31 psi
So, 26% of 31,
31 x 0.26 = 8.06
TPMS warns at below (31 - 8.06) = 22.94
Let X be tire pressure.
µ = 31, σ = 2
P(X < 22.94)
= P(x-µ / σ < (22.94 - 31) / 2)
= P(Z < -4.03)
= 0.0000 {from the z-score table}
Hence, the probability is zero.
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Pablo's is a popular Mexican restaurant, known especially for its homemade salsa. During dinner last night at Pablo's, 7 tables of people ordered chips and salsa for every 2 tables that did not. Pick the diagram that models the ratio in the story. A total of 108 tables of people dined at Pablo's last night. How many of the tables ordered chips and salsa?
Answer: Let X be the number of tables that ordered chips and salsa. Then, 7X tables did not order chips and salsa. So, X + 7X = 108, which simplifies to 8X = 108. Dividing both sides by 8, we have X = 13.5.
Since X must be a whole number, we round down to get X = 13 tables ordered chips and salsa.
Step-by-step explanation:
The scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 15. What test score is 1.2 standard deviations above the mean?
87 is the test score is 1.2 standard deviations above the mean.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that scores on a standardized test are normally distributed with a mean of 105 and standard deviation of 15.
We need to find the test score is 1.2 standard deviations above the mean
1.2 standard deviations is 1.2×15 =18
So 105-18=87
87 is the score that is 1.2 standard deviations from the mean.
Hence, 87 is the test score is 1.2 standard deviations above the mean.
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Sorry I cant do this for much points, But i need help asap pleaseeee!
The perimeter of the figure is given by the sum of the perimeter of rectangle and a semicircle P = 20.28
What is the Perimeter of a Rectangle?The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P of rectangle = 2 ( Length + Width )
Given data ,
Let the perimeter of the figure be represented as P
Let the width of the rectangle W = 4
So , the radius of the circle = 4 / 2 = 2
Now , the length of the rectangle = 5
And , the perimeter of the figure = 5 + 5 + 4 + ( perimeter of semicircle )
where the perimeter of semicircle = πr
On simplifying , we get
The perimeter of the figure P = 14 + 2π
The perimeter of the figure P = 14 + 6.28
The perimeter of the figure P = 20.28
Hence , the perimeter of the figure is 20.28
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The team chooses another site on the bank of the river, point A, and determines that the distance AB is 45 feet. They then move to another site, C, that is collinear with A and X. They measure to find that AC is 20 feet.
The team then moves from C to D, which is on a path parallel to Point D is also collinear with X and B. They measure CD to be 63 feet and measure BD to be 27 feet.
Based on this, what is the distance between X and B?
The distance between X and B is 67.5 feet for the given triangle.
What are Similar Triangles?Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.
As per the given figure, we have two similar triangles, as below:
ΔXAB and ΔXCD are similar,
So AB/CD = BX/DX
45/63 = BX/(BX+BD)
45/63 = BX/(BX+27)
45(BX+27) = 63BX
63BX - 45BX = 1215
18BX = 1215
BX = 67.5
Thus, the distance between X and B is 67.5 feet.
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Write each rate as a unit rate. $ 46 for 5 toys.
Answer:
$9.20 per toy or $9.20/1
Step-by-step explanation:
$46/5 hours=9.2
13. ABCD is
a. Congruent
b. Similar
c. Neither
to A'B'C'D'.
2 wholes 4 by 5 minus 4 wholes 1 by 3
Maria kept a log of the number of miles she jogged each time she went for a run as she trained for an upcoming marathon. She displayed the logged runs in the histogram below.
A histogram titled Maria's Monthly Jogging has miles run on the x-axis and number of runs on the y-axis. 1 to 1.99 miles is 2 runs; 2 to 2.99 miles is 5 runs; 3 to 3.99 miles is 5 runs; 4 to 4.99 miles is 3 runs; 5 to 5.99 miles is 4 runs; 6 to 6.99 miles is 7 runs; 7 to 7.99 miles is 4 runs.
What is the range of the number of miles Maria jogged?
0 to 7
0 to 7.99
1 to 7.99
1 to 8
Answer:
1 to 7.99 miles
Step-by-step explanation:
According to the given histogram, Maria logged runs for 1 to 7.99 miles, and the number of runs for each mile range is also given. Therefore, the range of the number of miles Maria jogged is 1 to 7.99 miles.
Note that the histogram shows that there were no recorded runs for exactly 8 miles, so the range does not include 8.
The Wilson family's back yard is a rectangular plot that has a length of 100 feet and a width of 80 feet. The family planted a garden with a length and width of 60 feet. The family planted a lawn in the remaining area of the back yard, as shown.What is the area, in square feet, of the lawn in the Wilson family's back yard?
The area of the lawn in the Wilson family's back yard is 4400 square feet.
The Wilson family's back yard is a rectangular plot that has a length of 100 feet and a width of 80 feet.
Let us assume that A₁ be the area of the reactangular plot.
Using the formula for the area of rectangle,
A₁ = 100 × 80
A₁ = 8000 sq. ft.
The family planted a garden with a length and width of 60 feet.
This means, the shape of the garden must be square.
Using the formula for the area of square,
A₂ = 60 × 60
A₂ = 3600 sq. ft.
The family planted a lawn in the remaining area of the back yard, as shown.
Let us assume that A represents the area of the lawn in the Wilson family's back yard.
A = A₁ - A₂
A = 8000 - 3600
A = 4400 sq. ft.
Therefore, the required area is: 4400 sq.ft.
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The slope line below is:
Answer: 4/3
Step-by-step explanation:
Look at the points (0,-4) (3,0)
Formula: y2-y1/x2-x1
Substitute: 0-(-4)/3-0 = 4/3
Please make me brainliest, I would also add you as friend if you make me brainliest!
Let's consider what the question asks for:
--> slope of line
The slope of the line is calculated by:
[tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
--> where:
[tex](x_1,y_1)-- > \text{any one point on the line}\\\\(x_2,y_2)-- > \text{another point on the line}[/tex]
Let's find our points
[tex](x_1,y_1)-- > (3,0)\\\\(x_2,y_2)-- > (0,-4)[/tex]
Let's plug these points into our equation:
[tex]\text{Slope}=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{-4-0}{0-3}=\dfrac{-4}{-3} =\dfrac{4}{3}[/tex]
Answer: 4/3
Write a problem about a real-life situation involving temperature or money. The situation should include a number and its opposite that results in an answer of zero
Therefore , The negative linear equation result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.
A linear equation is precisely what?A straightforward regression graph is created using the equation y=mx+b. The y-intercept is m, and the slope is B. Despite the fact that the line before it contains independent parts, it is repeatedly alluded to as a "mathematical formula combining many factors." Only two factors are present in bivariate linear equations. There are no known solutions to application issues concerning linear equations. Y=mx+b.
Here,
Let H be the number of hot coffee drinks sold yesterday, and I be the number of iced coffee drinks sold yesterday. We know that:
H + I = 100 (since a total of 100 cups were sold)
We also know that the average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00. Therefore, the total revenue from hot coffee drinks is:
3.50H
And the total revenue from iced coffee drinks is:
2.00I
To find the difference in revenue between the hot and iced coffee drinks sold yesterday, we need to subtract the revenue from iced coffee drinks from the revenue from hot coffee drinks:
3.50H - 2.00I
We want this expression to equal zero, so we can set it equal to zero and solve for H:
3.50H - 2.00I = 0
3.50H = 2.00I
H = (2/3.50)I
H ≈ 0.57I
Since H + I = 100, we can substitute 0.57I for H in the equation:
0.57I + I = 100
1.57I = 100
I ≈ 63.7
Rounding to the nearest whole number, we get:
I = 64
Therefore, H = 100 - I = 36
So the difference in revenue between the hot and iced coffee drinks sold yesterday is:
3.50H - 2.00I = 3.50(36) - 2.00(64) = $72 - $128 = -$56
The negative result indicates that the coffee shop made $56 less from hot coffee drinks than from iced coffee drinks yesterday.
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The complete question is "Write a problem about a real-life situation involving temperature or money. The situation should include a number and its opposite that results in an answer of zero
A local coffee shop sells iced and hot coffee drinks. Yesterday, the shop sold a total of 100 cups of coffee. The average price of a hot coffee drink was $3.50 and the average price of an iced coffee drink was $2.00.
What is the difference in revenue between the hot and iced coffee drinks sold yesterday?"
find the largest possible value of $k$ for which $3^{11}$ is expressible as the sum of $k$ consecutive positive integers.
The largest possible value of [tex]$k$[/tex] is [tex]$k=3^{11}$[/tex].
Largest Sum of Consecutive IntegersLet [tex]$a_1, a_2, \ldots, a_k$[/tex] be the [tex]$k$[/tex] consecutive positive integers, such that [tex]$a_1 + a_2 + \ldots + a_k = 3^{11}$[/tex]. The average of these [tex]$k$[/tex] numbers is [tex]$\frac{a_1 + a_k}{2} = \frac{3^{11}}{k}$[/tex], which is an integer if and only if [tex]$k$[/tex] divides [tex]$3^{11}$[/tex].
The largest divisor of [tex]$3^{11}$[/tex] is [tex]$3^{11}$[/tex] itself, so the largest possible value of [tex]$k$[/tex] is [tex]$k=3^{11}$[/tex].
However, [tex]$k$[/tex] must also be an integer greater than 0, so the largest possible value of [tex]$k$[/tex] for which [tex]$3^{11}$[/tex] is expressible as the sum of [tex]$k$[/tex] consecutive positive integers is [tex]$3^{11} - 1 = 177147$[/tex].
This problem is about finding the largest number of consecutive positive integers whose sum is equal to a given number. In this case, the given number is [tex]$3^{11}$[/tex].
By using the formula for the sum of consecutive integers, the average of the numbers is calculated, and the requirement for this average to be an integer is used to find the largest possible value of [tex]$k$[/tex], which represents the number of consecutive positive integers. The solution shows that the largest possible value of [tex]$k$[/tex] is [tex]$177147$[/tex].
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kylie has 1/3 of a cake she divides it equally 8 how much does she have left
Answer:
1/24
Explanation:
1 1 8
- ÷ 8 This translates to: - ÷ -
3 3 1
1 1
- = -
3x8 24
Hope this helps!