Answer:
To put the equation in standard form, we need to get all the terms with variables on one side of the equation and all the constants on the other side. We can start by moving the 4/3 to the right side of the equation:
Y - 2/3 = 4/3(x + 2)
Y = 4/3(x + 2) + 2/3
Next, we can distribute the 4/3 on the right side of the equation to get:
Y = (4/3)x + (4/3)2 + 2/3
Y = (4/3)x + (8/3) + 2/3
Finally, we can combine like terms to get:
Y = (4/3)x + (10/3)
This is the standard form of the equation.
Answer -3y+4x=-10
Step-by-step explanation:
A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?
The final temperature is calculated to be 41.8 degrees Celcius if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa
The final temperature can be calculated by using the combined gas law as follows;
[tex]\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }[/tex]
Here [tex]P_{1}[/tex] and [tex]P_{2}[/tex] represent the initial and final pressure respectively,
[tex]V_{1}[/tex] and [tex]V_{2}[/tex] represent the initial and final volume respectively
[tex]T_{1}[/tex] and [tex]T_{2}[/tex] represent the initial and final temperature respectively
Converting [tex]T_{1}[/tex] to kelvin as follows;
[tex]T_{1}[/tex] = 27 degrees Celcius = 27 + 273 = 300 K
Now the final temperature can be determined by substituting the values in this equation of the combined gas law as follows;
(0.50×10^5)(1.25) / 300 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]
208.333333333 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]
208.333333333 ([tex]T_{2}[/tex]) = (0.82×10^5)(0.80)
[tex]T_{2}[/tex] = (0.82×10^5)(0.80) ÷ 208.333333333
[tex]T_{2}[/tex] = 314.8 K
Converting K to degree Celcius as follows;
[tex]T_{2}[/tex] = 314.8 - 273 = 41.8 degree Celcius
Hence 41.8 degrees Celcius is calculated to be the final temperature.
Although a part of your question is incorrect, you might be referring to this question:
A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m^3. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?
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Thinking and Reasoning Choose Efficient Methods What are two different ways to simplify the expression 4(3x + 7x + 5) so that it equals 40x - 20? Explain.
A carpenter used 29 ft of molding in three pieces to trim a garage door. If the
long piece was 1 ft longer than twice the length of each shorter piece, then
how long was each piece?
Answer:
Let's call the length of the long piece x, and the length of each shorter piece y. We can set up the following equation to represent the problem:
x + 2y = 29
Since the long piece is 1 ft longer than twice the length of each shorter piece, we can write this equation as:
x = 2y + 1
Substituting this expression for x in the first equation, we get:
2y + 1 + 2y = 29
Combining like terms on both sides, we get:
4y + 1 = 29
Subtracting 1 from both sides, we get:
4y = 28
Dividing both sides by 4, we get:
y = 7
Substituting this value for y in the expression for x, we get:
x = 2(7) + 1 = 14 + 1 = 15
Thus, the length of the long piece is 15 ft, and the length of each shorter piece is 7 ft.
Frames-for-All sells framed pictures to hotels and other corporations across the country. Last year, the company sold a total of 720,460 pictures. This year, they sold 972,621 picyures. What is the percent of increase in yearly sales?
The percent of increase in yearly sales is 35%.
What is a percentage increase?A percentage increase means the eventual increase in the quantity in percent form. The percentage increase formula is use to compare growth in a quantity from the initial value to its final value over a period of time.
The formula for getting a percentage increase is "[(Final Value - Initial Value)/Initial Value] × 100"
Initial value = 720,460 pictures
Final value = 972,621 pictures.
The percentage increase:
= [(972,621 - 720,460] / 720,460} * 100
= 0.35 * 100
= 35%
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2x + 4
6x - 3y = -12
Is this no solution or infinite
How do you write 82 in scientific notation?
How you write it is...
m x 10n
a survey found that 78% of the men questioned preferred computer-assisted instruction to lecture and 68% of the women preferred computer-assisted instruction to lecture. there were 100 randomly selected individuals in each sample. find the 95% confidence interval for the difference of the two proportions.
The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.
Given that,
In a survey, it was discovered that 68% of women and 78% of men preferred computer-assisted education to lectures, respectively. Each sample contained 100 people that were chosen at random.
We have to calculate the 95% confidence range for the difference between the two proportions.
We know that,
The 95% confidence interval for difference between two population proportions is given as follows :
[tex]((\bar p_{1} -\bar p_{2})[/tex]±[tex]Z_{0.05/2}\sqrt{\frac{PQ}{n_{1} } +\frac{PQ}{n_{2} }} })[/tex]
Here,
p₁ is 0.78
p₂ is 0.68
n₁ is 100
n₂ is 100
Z is 1.96
P is 0.73
Q is 0.27
So,
((0.78-0.68)±[tex]1.96\sqrt{\frac{(0.73)(0.27)}{100 } +\frac{(0.73)(0.27)}{100 }} })[/tex]
(0.10±0.122)
(0.10-0.122,0.10+0.122)
(-0.022,0.222)
Therefore, The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.
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the graphs of these two equations intersect in how many points? \begin{align*} x^2 y^2
The graphs of these two equations intersect in 4 points.
What is an example of a hyperbola?
A hyperbola is a collection of points in a plane whose separations from two fixed points, known as its foci (plural of focus), differ by an amount that is always the same.
Using the figure as an example, a hyperbola with foci at (-3,0) and The point at illustrates its constant distance as being 4. (-3,-2.5).
x²+y²=25
it is a circle with radius=5
x²-y²=3
it is a hyperbola.
x²-y²=3
so, they intersect in four points.
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The complete question is -
The graphs of these two equations intersect in how many points?
x^2+y^2=25
x^2-y^2=3
I am too tired to think, please help my daughter finish her homework
Answer: 3(p-5) + 2s
Step-by-step explanation:
Let p represent the henna powder, we know that she has a discount of $5 dollar for every henna powder, and she will buy 3.
So the equation is 3(p-5), plus the two bottles, we get the equation
3(p-5) + 2s
pls help tyyy!!!!!
.
Answer: Those both would be 21 with work ....
suppose that an experimenter studies the lifespan of members of a colony of bacteria. let t be the lifespan of a randomly chosen member of the colony. suppose the lifespan of the bacteria has an exponential distribution with expected value 100 minutes. if we choose 5 members of the colony, what is the probability that at least one of them lives more than 87 minutes?
The probability that at least one of them lives more than 87 minutes is 0.87.
Probability
In statistics, the possible way of happening a particular event is called probability.
Given,
Suppose that an experimenter studies the lifespan of members of a colony of bacteria. let t be the lifespan of a randomly chosen member of the colony. suppose the lifespan of the bacteria has an exponential distribution with expected value 100 minutes.
Here we need to find if we choose 5 members of the colony, then what is the probability that at least one of them lives more than 87 minutes.
Here we know that,
Total number of members = 5
Life span = 87 minutes
Expected value = 100 minutes
So, the probability is calculated as,
=> 87 /100
=> 0.87
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HELP MEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!
find formula for growth of city
y intercept of 300,000 because the function starts here
the slope is 1.08 because it grows by 8 percent each year
population at x year = 300,000(1.08)^x
you can better understand why the x is in the exponent by this example
in one year, it grows 8 percent
300,000 * 1.08 = 324,000
the next year, that previous year grows 8 percent
324,000 * 1.08 = 349,920
300,000 * 1.08 * 1.08 =349,920
300,000 * 1.08^2 = 349,920
in 2 years it grows to that
just do it to the 14th power now
300,000 * 1.08^14 = 881,158
hope this helps :)
if you got any questions just comment
Graph f(x) = √√x+2 over the domain -2 ≤x≤7.
The graph of the function square root of the square root of x + 2 in the given domain is given by the image shown at the end of the answer.
How to graph the function?The function for this problem is defined as follows:
f(x) = √√x+2
The double square root means that in reality, we have the fourth root of the function, hence the function is then defined as follows:
f(x) = fourth root(x + 2).
The fourth root function is defined for values of x for which the inner term is zero and greater, hence:
x + 2 >= 0
x >= -2.
Then the graph is made over a domain that goes until x = 7, and is given by the image presented at the end of the answer.
(the domain is chosen because it is the domain given by the problem).
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a simple random sample of 100 8th graders at a large suburban middle school indicated that 82% of them are involved with some type of after school activity. find the 95% confidence interval that estimates the proportion of them that are involved in an after school activity. a) [0.745, 0.895] b) [0.745, 0.695] c) [0.795, 0.800] d) [0.645, 0.845] e) [0.665, 0.895] f) none of the above
The 95% confidence interval that estimates proportion of 8th graders that are involved in an after school activity (0.745, 0.895) , the correct option is (a) .
In the question ,
it is given that ,
simple random sample of 100 8th graders is taken ,
that means ,
n = 100 ,
also given that , 82% of them are involved with some type of after school activity.
means ; p = 0.82 .
the level of significance (α) = 100 - 95 = 5% = 0.05 .
the critical value= [tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.025}[/tex] = 1.959964 ......from the Z table .
the lower limit of the 99% confidence interval is = p - [tex]Z_{\alpha /2}[/tex]*SE
and the upper limit for the 99% confidence interval is= p + [tex]Z_{\alpha /2}[/tex]*SE .
the standard error is √(p(1-p)/n
= √(0.82(1 - 0.82)/100
= 0.0384
So , the lower limit is ⇒ 0.82 - 1.959964*0.0384
On simplification ,
we get ,
lower limit is = 0.7447006 ≈ 0.745 .
the upper limit is = p + [tex]Z_{\alpha /2}[/tex]*SE
= 0.82 + 1.959964*0.0384
On Simplification ,
we get ,
upper limit is = 0.8952994 ≈ 0.895 .
Therefore , the confidence interval is (0.745, 0.895) .
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A small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time period. Explain how you got it.
The rate of change in the profit for the five months earned by the given small business is $2750.
How to calculate the rate of change?The rate of change explains the relationship between two quantities.
Consider two quantities such profit and time in a small business.
Then, the rate of change in the profit is calculated by the ratio of change in the profit for the particular period to the time. I.e.,
rate of change in the profit = (change in the profit)/time
or
r = (p2 - p1)/(t2 - t1)
Where p1 is the profit gained at time t1 and p2 is the profit gained at time t2.
Calculation:Given that, a small business earns a profit of $6500 in January (the first month of the year) and $17,500 in May (the fifth month of the year).
So, here p1 = $6500; p2 = $17,500; t1 = 1; and t2 = 5
Then, the rate of change in the profit for this period is
r = (17,500 - 6500)/(5 - 1)
= 11000/4
= 2750
Therefore, the rate of change in the profit for the five months is $2750.
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Bill had 15 coins in his pocket, some quarters and the rest, dimes. If he had
$3.30 in his pocket, how many were quarters and how many were dimes?
Answer:
Step-by-step explanation:
So bill haves 12 quarters and 3 dimes
A certain quadratic function has x-intercepts at 2 and 3. What is the x-coordinate of its vertex?
Answer: [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
The vertex is halfway between the [tex]x[/tex]-intercepts.
So, the answer is [tex]\frac{2+3}{2}=\frac{5}{2}[/tex].
Twenty-Five Decreased By One Fifth Of A Number Is Eighteen. Find The Number.
The equation of the given condition is written as 25 - (1/5)x = 18. And the solution of the equation will be 35.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.
Twenty-Five Decreased By One-Fifth Of A Number Is Eighteen.
Let the number be 'x'. Then the equation is given as,
25 - (1/5)x = 18
Simplify the equation, then the value of the variable 'x' is calculated as,
25 - (1/5)x = 18
(1/5)x = 25 - 18
(1/5)x = 7
x = 7 (5)
x = 35
The equation of the given condition is written as 25 - (1/5)x = 18. And the solution of the equation will be 35.
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Determine the measure of the indicated angle 53 106 127 307
Answer: 127
Step-by-step explanation: It must add up to 180 degrees
Interior consecutive = congruent
Corresponding = 180
How do you calculate (1+i)/(1−i)?
Answer:
i
Step-by-step explanation:
1. Multiply the Numerator and the Denominator by the Complex Conjugate of the Denominator:
[tex]\frac{1+i}{1-i}*\frac{1+i}{1+i}=\frac{1+2i+i^{2}}{1-i^{2}}[/tex]
Remember that i² = -1:
[tex]\frac{1+2i+i^{2}}{1-i^{2}}=\frac{2i}{2}[/tex]
2. Simplify
if f(x) = , what is f(7.6)? 3 3.5 3.8 4
The solution of the given greatest integer function is found as 3.5.
Explain the term greatest integer function?The largest integer function is one that yields an integer that is closest to the specified real value. Additionally known as the step function. The closest integer is used to round off the input using the biggest integer function.We have to compute;
f(x) = 1/2[x]
Given what we have; f(7.6).
Enter x = 7.6 in the function provided;
f(7.6) = 1/2[7.6]
As ,the value (7.6) --> 7.0 (greatest integer function)
f(7.6) = 7/2
f(7.6) = 7/2
f(7.6) = 3.5
Thus, the solution of the given greatest integer function is found as 3.5.
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The correct question is-
If f(x) = 1/2[x], what is f(7.6)?
3
3.5
3.8
4
find the relative maxima and relative minima, if any, of the function. (if an answer does not exist, enter dne.) g(x)
The relative maxima and minima of the function g(x) are at the point (-4, 22) at the local maxima and at point (4,-124) at the local minima.
Given:
Function g(x) = x^3 - 48x + 4
Take the derivative and set it equal to zero
3x^2 - 48 = 0
x^2 = 48/3 = 16
x = sqr16 = ±4
At x=+4, y = (4)^3 -48(4) + 4 = 64 -192+4 = -124
Point (4,-124) is a local or relative minimum
At x-4 y=(-4)^3 -48(-4)+4 = -64 + 192 + 4 = 122
The point (-4, 22) is a local or relative maximum
Refer to this complete question:
Find the relative maxima and minima, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x3 − 48x + 4 relative maximum (x, y) = relative minimum (x, y) =?
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In the expansion of (2a + 4b), which of the following are possible variable terms? Explain your reasoning.
a²b³; a8; a5b³; ab8; a³b5; a7b; a6b5; b8
The possible variable terms for the given expression are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression is (2a+4b)⁸.
The expansion is
(2a+4b)⁸=256a⁸+4096a⁷b+2867a⁶b²+114688a⁵b³+286720a⁴b⁴+458752a³b⁵+458752a²b⁶+262144ab⁷+65536b⁸
Hence, in the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.
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Which statement describes the graph f(x)=4x^7+40x^6+100x^5?
Answer:
Step-by-step explanation:
Graph crosses the x-axis at x = 0 and has zeros at {-5, -5}.Step-by-step explanation: Note that f(x) factors as follows: f(x) = 4x^5 (x^2 + 10x + 25) …
Can a triangle be formed with side lengths 4, 8, 11? Explain. No, because 11 − 8 < 4 Yes, because 11 − 4 < 8 No, because 4 + 8 > 11 Yes, because 4 + 8 > 11
A triangle can be formed with side lengths 4, 8, 11. Yes, because 4 + 8 > 11
How to illustrate the triangle?According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the remaining side.
If the sum of any two sides is greater than the sum of the third, then the difference of any two sides is less than the sum of the third. The sum of any two sides must be greater than the sum of the third. The longest side in a triangle is the side opposite a larger angle.
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please help memeemeemee
Answer:
6
Step-by-step explanation:
it is a8=a1 +(n-1)x d
41=-1+ 7xd
42/7=d
d=6
Answer: 6
Step-by-step explanation:
[tex]a_1=-1\ \ \ \ \ \ \ \ a_8=41\ \ \ \ \ \ \ \ d=?\\\\\boxed{a_n=a_1+d(n-1)}\\\\Hence,\\\\a_8=-1+d(8-1)\\\\41=-1+7d\\\\41+1=-1+7d+1\\\\42=7d\\\\[/tex]
Divide both parts of the equation by 7:
6=d
Thus, d=6
the area of the rectangle is given by the polynomial function a(x)=6x^2 10x. if the width of the rectangle is 2x, what is the length?
Using the area of the rectangle, we know that the length of the given rectangle is x + 9.
What is the area?The area is described as the amount of space occupied by a flat (2-D) surface or shape of an object.
Take a marker pen and attract a square on a bit of paper. It is a 2-D figure.
The space the shape occupies on the article is called its Area. Consider your square as being composed of smaller unit squares.
So, we have the area of the rectangle as:
A(x)=2x^2+18x
Area formula: Area = length * width
So, the length of the rectangle will be:
Area = length * width
2x^2+18x = length * 2x
Length = (2x^2 + 18x) / 2x
With the help of long division:
2x√2x² + 18x
Length = x + 9
Therefore, using the area of the rectangle, we know that the length of the given rectangle is x + 9.
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Correct question:
The area of the rectangle is given by the polynomial function A(x)=2x^2+18x. If the width of the rectangle is 2x what is the length?
the function models the height of a ball dropped from 40 feet in the air. what was the speed of the ball when it was traveling the fastest (instantaneous rate of change)? round all answers to three decimal places.
Therefore ,the speed at height 40 feet in the air = 16*40=640 feet/sec
Function is what?A mathematical function from one set X to another gives each element of X exactly one element of the other. The sets X and Y, respectively, represent the function's domain and codomain.
Here,
the given function is
f(t)=−8[tex]t^{2}[/tex]+25
Therefore, the speed of the ball can be calculated by using derivative of f(t)
f(t)=−8[tex]t^{2}[/tex]+25
Differentiating f(t) w.r.t t
=> d(f(t)/dt=-8*2t
=> d(f(t)/dt=-16t
Therefore the speed at height 40 feet in the air = 16*40=640 feet/sec
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determine if a-1 c = c a–1 given
CA ⁻¹ is undefined because there are more columns in A ⁻¹ than there are rows in C.
What is matrix?A matrix is a numerical arrangement that is divided into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements. A matrix is a rectangular array of integers divided into rows and columns. Matrix A, for example, contains two rows and three columns. A matrix is a rectangular organization of a collection of integers into a defined number of rows and columns. When the elements are arranged in a matrix horizontally, it forms the rows of a matrix. When the elements are arranged in a matrix vertically, it forms the columns of a matrix.
CA⁻¹ is undefined because A⁻¹ contains more columns than rows in C.
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what is the hypotenuse?
Answer:
20
Step-by-step explanation:
h=hypotenuse. s1=side 1. s2=side 2
h^2 = (s1)^2 + (s2)^2 ==> hypotenuse formula
h^2 = 12^2 + 16^2 => plug in known values
h^2 = 144 + 256
h^2 = 400 ==> simplify
[tex]\sqrt{h^2 = 400}[/tex] ==> take the square root on both sides to remove the power
[tex]\sqrt{h^2}[/tex] = [tex]\sqrt{400}[/tex]
h = 20
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