Let [tex]A(t)[/tex] = amount of salt (in pounds) in the tank at time [tex]t[/tex] (in minutes). Then [tex]A(0) = 11[/tex].
Salt flows in at a rate
[tex]\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}[/tex]
and flows out at a rate
[tex]\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}[/tex]
where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.
Then the net rate of salt flow is given by the differential equation
[tex]\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}[/tex]
which I'll solve with the integrating factor method.
[tex]\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95[/tex]
[tex]-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}[/tex]
[tex]\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}[/tex]
Integrate both sides. By the fundamental theorem of calculus,
[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}} [/tex]
[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right) [/tex]
[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}[/tex]
[tex]\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}[/tex]
[tex]\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}[/tex]
After 1 hour = 60 minutes, the tank will contain
[tex]A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131[/tex]
pounds of salt.
What is the perimeter of the given triangle?
10 units
16 units
17.2 units
19.2 units
Answer:
17.2 units
Step-by-step explanation:
You would use the Pythagorean Theorem to solve. The height (a) is 4 units. The base (b) is 6 units.
4^2 + 6^2 = sqrt(52)
This would mean that the hypotenuse is 7.211102550927979 units or 7.2 units (the square root of 4^2 + 6^2).
Now you would need to just add all three sides.
6 + 4 + 7.2 = 17.2 units
Hope that helps! Please mark me brainliest!
The appropriate test for a comparison a group of 10 dogs and group of 10 cats is:_____.
The appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.
In this question,
The independent samples t test (also called the unpaired samples t test) is the most common form of the T test. It helps you to compare the means of two sets of data.
The Independent samples t test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.
The independent sample t-test is a useful statistical method of hypothesis testing when an organization wants to determine whether there is a statistical difference between two categories, groups, or items and, furthermore, if there is a statistical difference, whether that difference is significant.
From the definition, the independent sample t-test is the appropriate test for a comparison a group of 10 dogs and group of 10 cats.
Hence we can conclude that the appropriate test for a comparison a group of 10 dogs and group of 10 cats is called independent sample t-test.
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A father and his son decide to sum their age. The sum is equal to sixty years. Six years ago, the age of the father was five times the age of the son. Six years from now the son’s age will be?
Answer:
20
Step-by-step explanation:
To solve this you have to make a system of equations.
Since the father and son's age sum up to 60, the first equation will be:
f + s = 60
Secondly, since the father's age is 5 times the age of the son 6 years ago the equation will be:
6 - (5s) = f
Now, you have to solve the first equation to let it equal to s
f + s = 60
f = 60 - s
Plug in
6 - 5s = 60 - s
+s +s
6 - 4s = 60
-6 -6
---------------------
-4s = 54
----- -----
-4 -4
s ≅ 14
14 + 6 = 20
Answer:
20.
Step-by-step explanation:
x = father's age and y = son's age,
x + y = 60
x - 6 = 5(y - 6)
x - 5y = -24
Subtract this from first equation:
6y = 84
y = 14
So the son's age is 14.
Six years time son will be 20.
Verify the identity. sin() tan() = cos() use a reciprocal identity to rewrite the expression in terms of sine and cosine, and then simplify. sin
The identity Sin(α)/Tan(α) = Cos(α) is valid
Trigonometry is study of triangles. All trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. Three major of them are as follows :-
Sine Function:
sin(θ) = Opposite / Hypotenuse
Cosine Function:
cos(θ) = Adjacent / Hypotenuse
Tangent Function:
tan(θ) = Opposite / Adjacent
Lets prove this identity by proceeding with the LHS
= Sin(α)/Tan(α)
= Sin(α)/ (Sin(α)/Cos(α)) (Tan(α) = Sin(α)/Cos(α))
= Sin(α)xCos(α) / Sin(α)
= Cos(α)
Hence verified
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Profit is the difference between revenue and cost. the revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 30x – 130. the cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. the variable x represents the number of skateboards sold.
Profit function in terms of x = 33x + 390.
What is a profit in business?
In its simplest form, it's the amount left after subtracting your total expenses from your total revenue. The money remaining, your profits, can either be kept in the business and re-invested to finance future growth, or distributed as a draw or dividends to stakeholders.Given that revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial
[tex]2x^{3} + 30x - 130[/tex]
The cost, in dollars, of producing the skateboards can be modeled by
[tex]2x^{3} -3x - 520[/tex]
Profit function = Revenue - cost
= [tex]2x^{3} + 30x - 130 - ( 2x^{3} - 3x - 520)[/tex]
= 33x + 390
Therefore, profit function in terms of x = 33x + 390
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Susan drove 4 hours. Her average speed was 60 mph. Finish the chart below to give her an average speed of 60 mph.
║hour ║ speed║
______________
║1st ║ 65 ║
║2nd ║ 70 ║
║3rd ║ ____ ║
║4th ║ 55 ║
Answer:
Its 50
Step-by-step explanation:
60 times 4 it gives you 240.
Now minus all the numbers on the table like this
240 - 55 - 70 - 65 which equals to 50
240 would be the miles
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 20, 16, 21, 16, 22, 16, 15
Answer:
2.57
Step-by-step explanation:
The mean absolute deviation is the mean of the absolute values of the differences from the mean.
ApplicationThe mean of the dataset is the sum of values, divided by their number:
mean = (20 +16 +21 +16 +22 +16 +15)/7 = 126/7 = 18
The absolute values of the differences from 18 will have an average of ...
mean(|differences|) = (2 +2 +3 +2 +4 +2 +3)/7 = 18/7
mad(data) ≈ 2.57
__
Additional comment
Some calculators have the mad( ) function built-in. See the second attachment, for example.
If "a", "b" and "c" vectors are in cyclic order then:
If a, b and c vectors are in cyclic order , the scalar product is equals to zero which makes Option C to be correct.
What are scaler and vector quantities?A vector can be regarded as quantities that posses both magnitude and a direction this is the opposite to scalar quantity which posses just the magnitude without any direction.
Geometrically, the vector can be described as the line segment, having its length as the magnitude with the arrow over it showing direction.
The scalar product can be gotten with the multiplication of the magnitudes of vectors .
Hence, If a, b and c vectors are in cyclic order , the scalar product is equals to zero .
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CHECK THE COMPLETE QUESTION IN THE ATTACHMENT
y = 3x + 15
3x + 3y = 9
Answer:
[tex]\Large\boxed{x=-3}[/tex][tex]\Large\boxed{y=6}[/tex]
Step-by-step explanation:
Given the system of equations
[tex]1)~y=3x+15[/tex]
[tex]2)~3x+3y=9[/tex]
Divide 3 on both sides of the 2) equation
[tex]3x+3y=9[/tex]
[tex]3x\div3+3y\div3=9\div3[/tex]
[tex]x+y=3[/tex]
Current system
[tex]1)~y=3x+15[/tex]
[tex]2)~x+y=3[/tex]
Substitute 1) equation into the 2) equation
[tex]x+(3x+15)=3[/tex]
Combine like terms
[tex]x+3x+15=3[/tex]
[tex]4x+15=3[/tex]
Subtract 15 on both sides
[tex]4x+15-15=3-15[/tex]
[tex]4x=-12[/tex]
Divide 4 on both sides
[tex]4x\div4=-12\div4[/tex]
[tex]\Large\boxed{x=-3}[/tex]
Substitute the x value into one of the equations to find the y value
[tex]y=3x+15[/tex]
[tex]y=3(-3)+15[/tex]
[tex]y=-9+15[/tex]
[tex]\Large\boxed{y=6}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Point R divides PQin the ratio 1:3. If the x-coordinate of Ris -1 and the x-coordinate of Pis -3, what is the x-coordinate of Q?
Since Point R divides PQ in the ratio 1:3. the x-coordinate of Q is 3
The question has to do with line division
What is line division?This is the division of a line into a given ratio.
How to find the coordinate of Q?
Since Point R divides PQ in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is -3.
Let
x₁ = coordinate of P = -3, x₂ = coordinate of R = -3 and x₃= coordinate of Q.Since R divides PQ in the ratio, 1:3, we have that
PR/RQ = 1/3
(x₂ - x₁)/(x₃ - x₂) = 1/3
Substituting the values of the variables into the equation, we have
(x₂ - x₁)/(x₃ - x₂) = 1/3
(-1 - (-3))/(x₃ - (-3)) = 1/3
(-1 + 3)/(x₃ + 3) = 1/3
2/(x₃ + 3) = 1/3
x₃ + 3 = 2 × 3
x₃ + 3 = 6
x₃ = 6 - 3
x₃ = 3
So, the x-coordinate of Q is 3
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Potenciación audita amigos
Answer: 4096.
Step-by-step explanation:
[tex](8^3)^8\div(8^4)^5=\\8^{3*8}\div8^{4*5}=\\8^{24}\div8^{20}=\\8^{24-20}=\\8^4=\\4096.[/tex]
find the missing numbers in the following equivalent fractions: [tex]\frac{?}{5} =\frac{8}{10} =\frac{16}{?} =\frac{?}{40}[/tex]
A pencil at a stationery store costs $1, and a pen costs $1.50. stella spent $21 at the store. she bought a total of 18 items. which system of equations can be used to find the number of pencils (x) and pens (y) she bought? x 18y = 21 x = 1.5y 18x y = 21 x = 1.5y x 1.5y = 21 x y = 18 1.5x y = 21 x = 18y
Equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18
The correct option is C.
What is liner equation?One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.
According to the given information:Let x stand for the number of pencils Stella purchased, and y for the number of pens Stella purchased.
Since Stella purchased a total of 18 things, the quantity of pencils and pens purchased must equal 18 or one of the following:
x + y = 18
We also know she spent $21, that a pencil costs $1, and that a pen costs $1.50. Therefore,
1x + 1.5y = 21
Thus, the set of equations that may be utilized to determine the quantity of pencils (x) and pens (y) that she purchased is as follows:
X+1.5Y = 21, and X+Y = 18
equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18
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PLEASE HELP!!!!!! I CAN’T UNDERSTAND!!!! How to do this one
The coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84
What is binomial expansion?Binomial expansion is the expansion of two term expressions such as (a + b)ⁿ where n is a rational number.
What is Pascal's triangle?Pascal's triangle is atriangle used in determining the coefficients of a binomial expansion.
What is the coefficient of t²s⁵ in the expansion of (2t + s)⁷?
The general term for the expansion (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ.
So, each term is ⁿCₓaˣbⁿ⁻ˣ.
Comparing (a + b)ⁿ with (2t + s)⁷,
a = 2t, b = s and n = 7.So, its general term is ⁿCₓ(2t)ˣsⁿ⁻ˣ = ⁷Cₓ(2t)ˣsⁿ⁻ˣ
= ⁷Cₓ(2)ˣtˣsⁿ⁻ˣ
So, the coefficient term is ⁷Cₓ(2)ˣ
Now for the term t²s⁵, x = 2.
So, the coeficient term is ⁷Cₓ(2)ˣ = ⁷C₂(2)²
= 7!/2!(7 - 2)! × 4
= 7!/2!5! × 4
= 7 × 6 × 5!/(2! × 5!) × 4
= 7 × 6/2 × 4
= 7 × 3 × 4
= 84
So, the coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84
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Pls solve this with step by step.
Step-by-step explanation:
-x+5+6x-7x-14
6x-8x+5-14
-2x-9
If the infinite curve y = e^−2x, x ≥ 0, is rotated about the x-axis. Find the area of the resulting surface.
The area of the resulting surface of this infinite curve is π units.
In this question,
The infinite curve is y = e^−2x, x ≥ 0.
The curve is rotated about x-axis.
Since x ≥ 0, the limits will be 0 to ∞.
Then the area of the resulting surface is,
[tex]A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )[/tex]
Now substitute,
u = -2x
⇒ du = -2dx
⇒ dx = [tex]-\frac{1}{2} du[/tex]
Then,
[tex]\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du[/tex]
Now substitute u and du, we get
⇒ [tex]-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx[/tex]
⇒ [tex]-\frac{-2}{2} \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex](1) \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex]\int\limits {e^{-2x} } \, dx[/tex]
Thus the area of the resulting surface is
[tex]A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx[/tex]
⇒ [tex]A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0[/tex]
⇒ [tex]A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\[/tex]
⇒ [tex]A= -\pi [0-1} \,]\\[/tex]
⇒ [tex]A= \pi[/tex]
Hence we can conclude that the area of the resulting surface is π units.
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Identify tanX as a fraction and as a decimal rounded to the nearest hundredth.
The figure shows right triangle X Y Z with right angle Y. The length of leg Z Y is equal to 7 point 2 units. The length of leg Y X is equal to 6 point 4 units. The length of hypotenuse X Z is equal to 9 point 6 units.
The value of tan(X) in fraction is 7.2/6.4 and in decimal is 1.13
How to determine the tangent trigonometry ratio?The complete question is added as an attachment
From the question, the given parameters are as follows:
Hypotenuse = XZ
Hypotenuse XZ = 9.6
Leg ZY = 7.2
Leg YX = 6.4
The tangent of X is then calculated as:
tan(X) = ZY/YX
Substitute the known values in the above equation
tan(X) = 7.2/6.4
Evaluate the above quotient
tan(X) = 1.125
Approximate the above result
tan(X) = 1.13
Hence, the value of tan(X) in fraction is 7.2/6.4 and in decimal is 1.13
So, the complete parameters are:
Hypotenuse = XZ
Hypotenuse XZ = 9.6
Leg ZY = 7.2
Leg YX = 6.4
tan(X) = 7.2/6.4
tan(X) = 1.13
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Pls help
On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
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Researchers surveyed recent graduates of two different universities about their income. the following two-way table displays data for the sample of graduates who responded to the survey. how many graduates in the sample had an income of \$40\text{,}000$40,000dollar sign, 40, start text, comma, end text, 000 and over?
Universities A had an income under $20,000 25% graduates.
What is a two-way table?A two way table is a way to display frequencies or relative frequencies for two categorical variables. One category is represented by rows and a second category is represented by columns.
Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.
A had an income under $40,000 25% graduates.
We have to add 30 45 together and get 75 because those are the students that have income under $40,000 dollars in both Universities
Then u convert have to convert it to a percentage and get 25%.
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The above question is not complete:
Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.
How many graduates from University A had an income under $40,000?
________graduates.
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The answer is 25%
its what khan says :>
Can anyone help me with this?
Putting the question into an online calculator gives me 4 Rad x. but what are the steps to solve it?
Simplify the following expression:
(x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6
Show all work to recive full credit.
The simplified expression of (x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6 is x^(12) y^(10/9) z^(-1/3)
How to simplify the expression?The algebraic statement is given as:
(x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6
Rewrite the algebraic statement as:
[(x^0 y^2/3 z^-2y)^2/3]/[(x^2 z^1/2)^-6]
Evaluate the like factors
[(x^0 y^(2/3+1) z^-2)^2/3]/[(x^2 z^1/2)^-6]
Evaluate the sum
[(x^0 y^5/3 z^-2)^2/3]/[(x^2 z^1/2)^-6]
Expand the exponents
[(x^(0*2/3) y^(5/3 * 2/3)z^(-2*2/3)]/[(x^(2*-6) z^(1/2*-6)]
Evaluate the products
[(x^0 y^(10/9) z^(-4/3)]/[(x^(-12) z^(-3)]
Apply the quotient law of indices
x^(0+12) y^(10/9) z^(-4/3+3)
Evaluate the sum of exponents
x^(12) y^(10/9) z^(-1/3)
Hence, the simplified expression of (x^0 y^2/3 z^-2y^)^2/3 divided by (x^2 z^1/2)^-6 is x^(12) y^(10/9) z^(-1/3)
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How do you construct a frequency distribution table using sturge’s approximation
The steps to use to construct a frequency distribution table using sturge’s approximation is as below.
How to construct a frequency distribution table?The steps to construct a frequency distribution table using Sturge's approximation are as follows;
Step 1: Find the range of the data: This is simply finding the difference between the largest and the smallest values.
Step 2; Take a decision on the approximate number of classes in which the given data are to be grouped. The formula for this is;
K = 1 + 3.322logN
where;
K= Number of classes
logN = Logarithm of the total number of observations.
Step 3; Determine the approximate class interval size: This is obtained by dividing the range of data by the number of classes and is denoted by h class interval size
Step 4; Locate the starting point: The lower class limit should take care of the smallest value in the raw data.
Step 5; Identify the remaining class boundaries: When you have gotten the lowest class boundary, then you can add the class interval size to the lower class boundary to get the upper class boundary.
Step 6; Distribute the data into respective classes:
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Which inequality written in vertex form represents the graphed region?
Answer:
C
Step-by-step explanation:
The inequalities y < 4 (x-1)² - 16 written in vertex form represents the graph region.
Option C is the correct answer.
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
We have,
Inequalities where we need to find the coordinates and see which inequalities represent the graph.
y < 4 (x- 1)² - 11 ____(1)
y < -4 (x-1)² - 11 _____(2)
y < 4 (x-1)² - 16 ______(3)
From (1),
y = 4 (x- 1)² - 11
x = 0, y = 4 x 1 - 11 = 4 - 11 = -7
From (2),
y = -4 (x-1)² - 11
y = -4 x 1 - 11 = -4 - 11 = -15
From (3),
y = 4 (x-1)² - 16
x = 0, y = 4 x 1 - 16 = 4 - 16 = -12
We see that,
y < 4 (x-1)² - 16 gives us the coordinates (0, -12) on the graph.
Similarly,
x = 1, y = 4 x 0 - 16 = 0 -16 = -16
x = 1, y = 4 x 1 - 16 = 4 - 16 = -12
(1, -16) and (2, -12) coordinates are on the graph.
Thus,
The inequalities y < 4 (x-1)² - 16 written in vertex form represents the graph region.
Option C is the correct answer.
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which is equivalent to (-2x^3y^5)^2
Answer:
[tex]4x^{6} y^{10}[/tex] A.
Point P is on line segment \overline{OQ}
OQ
. Given PQ=x+7,PQ=x+7, OP=4x-10,OP=4x−10, and OQ=4x,OQ=4x, determine the numerical length of \overline{OQ}.
OQ
.
Answer:
Step-by-step explanation:
4x - 10 + x + 7 = 4x
5x - 3 = 4x
-3 = -x
x = 3
4(3) - 10 = 12 - 10 = 2
3 + 7 = 10
10+2 = 12
4(3)= 12
An engineer is designing an arch-shaped gate for the entrance to an amusement park. the gate must be 80 feet wide and 25 feet tall. what will be the equation of the parabolic shape of the gate? a. x2 = -16(y − 25) b. (x − 16)2 = -4(y − 25) c. x2 = -64(y − 25) d. (x − 25)2 = -16(y − 16) e. x2 = -40(y − 25)
The equation of the parabolic shape of the gate is:
(x - 40)² = -64(y - 25)
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
The vertex is at the middle of the parabola, that is, a width of 80/2 = 40 meters and a height of 25 meters, hence h = 40, k = 25, and the equation is:
y = a(x - h)² + k
y = a(x - 40)² + 25
When x = 0, y = 0(start of the arc), hence the leading coefficient is found as follows:
0 = 1600a + 25
a = -25/1600
a = -1/64.
Hence the equation is:
y = -1/64(x - 40)² + 25
(x - 40)² = -64(y - 25)
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Two health clubs offer different pricing plans for their members. Both health clubs charge a one-time sign-up fee and a monthly membership fee. The equation y=60x+30
y=60x+30 represents what Health Club B charges. Health Club A charges a $50 sign-up fee and $27 per month.
Answer is Healthclub A costs $33 less in monthly fees than Healthclub B
The number next to the “x” is your rate.
So Healthclub A charges $33 less than B
A charges 27 monthly fee
B charges 60 monthly fee
60-27=33
Given a polynomial function f(x) = 2x2 7x 6 and an exponential function g(x) = 2x 5, what key features do f(x) and g(x) have in common?
f(x) = 2x² + 7x + 6 and g(x) = 2^x + 5 have -
Equal y-intercept at (0,6)Same end behavior as x approaches positive infinityHow to determine the common features of the polynomial equations?
The equation of the functions are given as:
f(x) = 2x² + 7x + 6 &
g(x) = 2^x + 5
Next, we plot the graph of both functions (see attachment)
From the graph, we have the following highlights
The y-intercept of both functions is (0,6)Both functions approach positive infinity as x approaches positive infinityTo learn more about polynomial functions from given link
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Paul teaches math to five classes in sixth grade. he wants to measure the variation in the performances of students of each class. which measures will help him?
The measures of variation that can be used by Paul are interquartile range and mean absolute deviation.
What are the measures of variation?
The interquartile range is the difference between the third quartile and the first quartile.
Third quartile = 3/4(n + 1)
First quartile = 1/4 x (n + 1)
The mean absolute deviation is the average of the distance of a data set from its mean.
Mean absolute deviation = ∑ l x - m(x) l
Mean, median and mode are measures of tendency. They are used to measure the number at the center of a dataset.
Here are the options:
Mean absolute deviation
mean
interquartile range
median
mode
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mean absolute deviation
mean
median
interquartile range
mode
hey can you help me with this one ?
Answer:
[tex]a = 8[/tex] or [tex]a = -\frac{14}{3}[/tex]
Step-by-step explanation:
[tex]13(a+4)+24(a+5) = 3(a^{2} +9a+20)[/tex]
[tex]3a^{2} -10a-112=0[/tex]
[tex](3a+14)(a-8)=0[/tex]
[tex]a = 8[/tex] or [tex]a = -\frac{14}{3}[/tex]
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13}{a + 5} + \cfrac{24}{a + 4} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13(a + 4) + 24(a + 5)}{(a + 5)(a + 4)} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{13a + 52+ 24a + 120}{a {}^{2} + 5a + 4a + 20} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ 37a + 172}{a {}^{2} +9a + 20} = 3[/tex]
[tex]\qquad \sf \dashrightarrow \: 3( {a }^{2} + 9a + 20) = 37a + 172[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} + 27a + 60 = 37a + 172[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} + 27a - 37a + 60 - 172 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} - 10a - 112= 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 {a}^{2} - 24a + 14a - 112 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: 3a(a - 8) + 14(a - 8) = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: (a - 8) + (3a + 14) = 0[/tex]
So, required values of " a " are :
[tex]\qquad \sf \dashrightarrow \: a = 8 \: \: \: or \: \: \: a = - \cfrac{ 14}{3} [/tex]
A research wants to examine the grams of fat in milk. They separate the milk into the groups: Whole Milk, 2% Fat, and Low Fat. Then randomly select cartons from each of the groups to measure grams of fat. This is an example of ____________ sampling.
if there was a random selection of cartons from each of the groups to measure grams of fat. This is an example of stratified sampling
What is stratified sampling?Stratified sampling can be defined as a method of sampling that involves division of a population into smaller groups or items, these are called strata.
This groups or strata are then arranged or organized based on the shared characteristics or attributes of the members in the group of the given population.
Stratification is the process of classifying the population into groups.
Features of stratified sampling are;
It is a precise metric It provides for a better representation of the overall populationIt can be time-consuming, and potentially expensiveFrom the information given, we can see that it is an example of stratified sampling.
Thus, if there was a random selection of cartons from each of the groups to measure grams of fat. This is an example of stratified sampling
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