The area of square is increasing with the rate of 144 cm/s2.
What is rate of expansion of solid ?For physics, The term "thermal expansion" refers to a material's change in length, width, height, or volume when its temperature is raised or lowered. Solids exhibit particularly noticeable thermal expansion due to their closely packed atoms. There are numerous uses for thermal expansion of solids in daily life.
A solid's atoms vibrate more quickly around their fixed positions when it is heated. As a result, there is little relative growth in the size of solids during heating. In order to prevent buckling when exposed to heat from the sun, metal train tracks feature tiny gaps.
CalculationL = length of a side
A = L2
dA/dt = 2L dL/dt
dL/dt = 8 cm/s
A = 81 cm2 ⇒ L = √A = √81 cm = 9 cm
dA/dt = 2(9cm)(8 cm/s) = 144 cm/s2
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Sorry guys one last question
Matthew wants his run today to take no more than 90 minutes. He already has run 30 minutes at a pace of 10 minutes per mile. Part A) Write an inequality that Matt could solve to find out how many more miles he can run if he keeps his current pace. Show or explain the reasoning you used to determine your answer.
The inequality that Matt could solve to find out how many more miles he can run if he keeps his current pace is less than 6 miles.
How to express the inequality?It should be noted an inequality is used to show the expressions that are not equal.
In this case, Matthew wants his run today to take no more than 90 minutes and he already has run 30 minutes at a pace of 10 minutes per mile.
Therefore, the appropriate inequality will be;
Let miles = m
m <= 90/10 - 30/10
m <= 9 - 3
m <= 6
He has about 6 miles more.
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just help me please. it might be easy but I kinda forgot what goes into where. Please help me out tho!!
The matching of the mathematical terms to the equations, and expressions is as follows;
Area of a circle → π•r²
Percent equation → P = %dec × w
Percent proportion → [tex] \displaystyle{ \frac{p}{w} = \frac{\%}{100} }[/tex]
Circumference → π × d
Pi → π
Base equation → y = k•x
Constant of proportionality → [tex] \frac{y}{x} [/tex]
% increase → [tex] \frac{Amount \: increase}{Original \: amount} [/tex]
%decrease →[tex] \frac{Amount \: decrease}{Original \: amount} [/tex]
Interest Earned → P×r×t
What is an expression in mathematics?An expression in mathematics consists of mathematical symbols and variables joined together operators in the proper manner
Area of a circleThe area of a circle is π × r²
Where;
r = The radius of the circle
Percent equationA percent equation equation is one of the sides of the equation consists of a percentage
Percent proportion;A percent proportion express a proportion as a percentage
Circumference;The circumference of a circle is the distance round the circle, which is given by the product of Pi and the radius of the circle
Pi.The symbol Pi is π
Base EquationThe base equation is one written in simple form
Constant of proportionalityThe constant of is the constant ratio between variables that are proportional
%increaseThis is the ratio of the increase to the original amount expressed as a percentage
%decreaseThe ratio of the decrease to the original amount expressed as a percentage
Interest EarnedThis is the amount added to an investment sum or amount and it is given by the product of the principal, P, rate, r and time, t
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k(x) = 2x²-x-1 find the roots
Answer:
x = -1/2 , 1
Step-by-step explanation:
Find the slope of the line passing through each of the following pairs of points and draw the graph of the line. (-4, 3), (2,3)
Answer: The slope is 0.
Step-by-step explanation:
We will use the slope formula to find the slope of the line going through these two points.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{3-3}{2--4}=\frac{0}{2+4} =0[/tex]
The slope of this line is 0.
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exapnd and simplify (3x+4)(2x+3)
Caroline’s cell phone plan costs $32 per month. Create a table that shows the sum of the amounts that Caroline will pay for her cell phone plan over the next 4 months. Can y'all please help me
Answer:
Month:
1 = 32$
2 = 64$
3 = 96$
4 = 128$
Step-by-step explanation:
A lead sphere of diameter 6cm is melted down and cast into balls 5mm in diameter. How many of the
smaller balls are there?
Total Smaller balls measuring 5mm diameter will be 12.
What is a Sphere?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the specified point represents its center.
1 cm = 10mm
6 cm = 60mm
Ball diameter is 5 mm.
diameter of the lead sphere divided by the number of balls
= 60mm/ 5mm
= 12 balls
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A solar panel covers the hood of a truck. The area is 0.8 the width of the panel is 1.6 meters, what is the length of the panel
The length of the panel is 0.5 meter.
What is the area of rectangle?To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Given that,
Area of the panel = 0.8 [tex]m^{2}[/tex]
width of the panel = 1.6 meter
Here, solar panel is in the form of rectangle.
Area of rectangle = length× width
0.8 = 1.6 × length
length = [tex]\frac{0.8}{1.6}[/tex]
length = 0.5 meter
Hence, The length of the panel is 0.5 meter.
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The simplest form of 7x²-5x(x+2)
Answer:
factored form: [tex]2x(x-5)[/tex], standard form: [tex]2x^2-10x[/tex]
Step-by-step explanation:
so we're given the expression: [tex]7x^2 - 5x(x+2)[/tex]
In this case we want to use the distributive property, which essentially states that: [tex]a(b+c)=ab+ac[/tex]
So we can use this to rewrite:
[tex]-5x(x+2)=(-5x)(x)+(-5x)(2)[/tex]
which simplifies to
[tex]-5x^2-10x[/tex]
this just simplifies the last part of our expression, so using this instead of what we originally had gives us
[tex]7x^2-5x^2-10x[/tex]
Since the 7x^2 and the -5x^2 have the same variable, we can subtract their coefficients.
Another way to think of it is
[tex]7x^2-5x^2\implies x^2(7-5)[/tex]
so in a way we're "factoring" out the x^2, which means we can simply subtract the coefficients for this reason.
This of course gives us 2, by we're multiplying by x^2 so we get
[tex]2x^2-10x[/tex]
Now if you want you can factor out a 2x, to get
[tex]2x(x-5)[/tex]
Question 1 (2 points)
(02.04)
For the function f(x) = -2(x + 3)2 - 1, identify the vertex, domain, and range.
Answer:
Vertex: (-3,-1)
Domain : (negative inf. , inf.)
Range: (negative inf. , 1]
A baseball Dimond is a square with sides of 90 feet. What is the shortest distance, to the nearest tenth of a foot, between first base and third base?
Using the pythagorean theorem we get that:
[tex]\begin{gathered} d^2=(90ft)^2+(90ft)^2=2(90ft)^2 \\ d=\sqrt[]{2}(90ft)=127.3ft \end{gathered}[/tex]Note: the shortest distance between two points in a plane is a stright line, that is why we calculated d.
A rental company charges $80 a day and 40 cents a mile for renting a truck. Michael rents a truck for 4 days, and his bill comes to $460. How many miles did he drive?
The most appropriate choice for distance will be given by-
Michael drove [tex]350[/tex] miles
What is Distance?
The length of the path an object takes without taking into account the direction of motion of the object is known as distance.
If [tex]s[/tex] is the speed of the object and [tex]t[/tex] is the time, then
Distance = [tex]s \times t[/tex]
Here,
Amount of money charged by a rental company for one day = $[tex]80[/tex]
Amount of money charged by a rental company for four days = $[tex](80 \times 4)[/tex]
= $320
Total bill charged by the rental company = $[tex]460[/tex]
Remaining bill = $[tex](460 - 320)[/tex]
= $[tex]140[/tex]
Amount of money charged by a rental company for one mile = [tex]40[/tex] cents
= $[tex]0.40[/tex]
Number of miles driven by Michael = [tex]\frac{140}{0.40}[/tex]
= [tex]350[/tex] miles
Michael drove [tex]350[/tex] miles
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solutions to 2-variable equations 4x-1=3y+5
Factor completely. 2x^2-9x-5
Answer:
(2x+1)(x-5)
Step-by-step explanation:
factorsed by grouping them
roots are -1/2 and 5
A company has been forced to reduce its number of employees. today the company has33% fewer employees than it did a year ago. if there are currently 335 employees, how many employees did the company have a year ago?
The employees that the company had a year ago is 500.
How many employees were there last year?Percentage is the rate expressed as a number out of 100. Percentage is used to measure the frequency of a dataset. The sign that represents percentages is %.
The employees last year would be greater than the employees this year. The equation that can be used to represent employees last year is:
Employees this year = employees last year x (1 - percentage decrease)
335 = employees last year x (1 - 0.33)
335 = employees last year x 0.67
employees last year = 335 / 0.67
employees last year = 500
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What is the mean of the normal distribution shown below?
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
Explain about the normal distribution ?A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.
The median, mode, and means are the same. At its centre, or the mean, the curve is symmetric. To the left of centre, precisely half of the values are located, and to the right, exactly half. The curve has a total area under it of one.
The answer for normal distribution is 4
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Please please please help me it's due at 10:00 P.M today
Answer: 20x
Step-by-step explanation:
Answer:
20x
Step-by-step explanation:
just trust me because you have to mulitply
Suppose you want to convert kilometers to miles. Which unit should be in the
numerator of the conversion factor? Which unit should be in the denominator?
Explain your reasoning.
Answer:
see below
Step-by-step explanation:
km * miles/km
see how the 'km' then 'cancels out' and you are left with 'miles' the underlined shows the units of the conversion factor
a shipment of 22-inch pipes contains a pipe that is exactly 21.78 inches. What is the percent error, rounded to the nearest percent.
Please explain what you did step by the step. Thank you!
The percent error of the shipment pipes is 1.01%
Percent error:
Percent error is defined as a difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.
It can be calculated using the formula,
PE = (|Estimated value-Actual value|/ Actual value) × 100
Given,
A shipment of 22-inch pipes contains a pipe that is exactly 21.78 inches.
Here we need to find the percent error of the shipment.
According to the percent error formula,
Here we have the values of the shipment are
Estimated value = 22
Actual value = 21.78
So, now we have to apply the values on the formula, then we get,
PE = (|22 - 21.78/21.78|) x 100
When we simplify it, then we get,
PE = 0.0101 x 100
PE = 1.01%
Therefore, the percent error in the shipment is 1.01%.
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according to flightstats.com, american airlines flights from dallas to chicago are on time % of the time. suppose flights are randomly selected, and the number of on-time flights is recorded. (a) explain why this is a binomial experiment. (b) determine the values of n and p. (c) find and interpret the probability that exactly flights are on time. (d) find and interpret the probability that fewer than flights are on time. (e) find and interpret the probability that at least flights are on time. (f) find and interpret the probability that between and flights, inclusive, are on time.
According to the flight on certain routes, the experiment is a binomial experiment and this will be determined by observing that Flights on a certain route are on-time 80% of the time and 10 flights are randomly selected and the number of on-time flights is recorded.
(a) This is a binomial experiment since there are only two possible outcomes for each data that is a flight is either on time (p = 80% = 0.8) or late (q = 1 - p = 1 - 0.8 = 0.2).
(b) Using the formula:
P(a out of n) = (nCa)(pᵃ)(qⁿ⁻ᵃ), where n = 10 flights, a = the number of flights that arrive on time:
P(7/10) = (10C7)(0.8)⁷ (0.2)³= 0.2013
Therefore, 0.2013 chance is there that exactly 7 of 10 flights will arrive on time.
(c) Fewer than 7 flights are on time means that we must add up the probabilities for P(0/10) up to P(6/10).
P(0/10) + P(1/10) + ... + P(6/10) = 0.1209
This means that 0.1209 chance that less than 7 flights will be on time.
(d) The probability that at least 7 flights are on time is the exact opposite of part (c), where less than 7 flights are on time. So instead of calculating each formula from scratch, we can simply subtract the answer in part (c) from 1.
1 - 0.1209 = 0.8791.
So there is a 0.8791 chance that at least 7 flights arrive on time.
(e) For this, we must add up P(5/10) + P(6/10) + P(7/10), which gives us
0.0264 + 0.0881 + 0.2013 = 0.3158, so the probability that between 5 to 7 flights arrive on time is 0.3158.
According to the flight on certain routes, the experiment is a binomial experiment
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DISCLAIMER: The question provided is incomplete as some data are missing. The above answer is solved as per a relevant question
According to an airline, flights on a certain route are on time 80 % of the time. suppose 10 flights are randomly selected and the number of on-time flights is recorded. (a) explain why this is a binomial experiment. (b) find and interpret the probability that exactly 7 flights are on time. (c) find and interpret the probability that fewer than 7 flights are on time. (d) find and interpret the probability that at least 7 flights are on time. (e) find and interpret the probability that between 5 and 7 flights, inclusive, are on time.
45x12=________
15x10=________
35x15=________
43X14=________
Answer:45 x 12 = 450
15 x 10 = 150
35 x 15 = 525
43 x 14 = 602
Step-by-step explanation:
Each packet of washing powder
Answer:
What happened to each packet of washing powder
please finish the question so i can answer xD
if i infer right then each packet of washing powder was washed up in the washing machine! :)
what 5+5+5+7= what is it
Add 5 x 3 + 7
5 x 3 + 7
15 + 7
22
Answer:
Alternatively, you may use addition to solve
Step-by-step explanation:
5+5 = 10 and 5+7 = 12, and we know that 10+10 = 20
Just add the number 2 from the number 12 to 20, and you have the same answer
what is 2.41x2.5 please help me out on this one
Answer:
6.025
Step-by-step explanation:
hope this helps:)
Answer:6.025
Step-by-step explanation:use calculator
You borrowed $1,690 for 5 1/2 years a at 5.7% compounded semi annually. What total will you pay back?
Answer: You would pay $2,302 back.
Step-by-step explanation:
Compound interest occurs when the interest is reinvested rather than paying it out. When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
consider the function rpresented by 9x + 3y = 12 with x as the independant variable. How can this function be writte using function notation? f(y) = - 1/3y + 4/3, f(x) = -3x + 4, f(x) = - 1/3 x + 4/3 f(y), = - 3y + 4
The slope-intercept form of a function f(x) = mx + c therefore,f(x) = -3x + 4 is the correct notation of the function 9x + 3y = 12 so option (B) is correct.
What is a function?The function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given function,
9x + 3y = 12
Subtract 9x both sides,
9x - 9x + 3y = 12 - 9x
3y = 12 - 9x
Divide by 3 into both sides,
y = 12/3 - 9x/3
y = -3x + 4
Since,y = f(x)
f(x) = -3x + 4 .Here -3 is the slope while 4 is the y-intercept.
Hence "The slope-intercept form of a function f(x) = mx + c therefore,f(x) = -3x + 4 is the correct notation of the function 9x + 3y = 12".
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help, i’ll give 20 points and thanks, and 5 stars
Answer: 8.75
Step-by-step explanation:
(0, 20) and (40, 370) any two coordinate points can be chosen
(370 - 20) / (40 - 0)
= 35/4 or 8.75
find the slope 35 points
When we want to find the slope of a line,
We find two points and connect them to form a right triangle.
We then divide the increase in the [tex]y[/tex]-axis by the increase in the [tex]x[/tex]-axis to find the slope.
Since the line is tilted to the right, the slope is positive.
The answer must be 3.Anya earns $150 less than three times Rick's monthly salary. If Rick's salary is represented by x which expression represents Anya's salary
A x-3- $150
B 3(x+$150)
C 3(x-$150)
D 3x-$150
E 3x+$150
Answer:
d
Step-by-step explanation:
3 multiplied by ricks salary minus 150