a) The maximum area of such a rectangle is 50 square units. b) The maximum area of such a rectangle is 36.
What is Quadratic and Linear equation ?When graphed, a linear equation results in a straight line. Since each value of x results in just one value of y, this relationship is referred to as being one-to-one. When a quadratic equation is graphed, the result is a parabola that extends uphill or downward in the y direction, starting at a single point known as the vertex. Because there are two values for x for every value of y (aside from the y-value at the vertex point), the relationship between x and y is not one-to-one.
a) The given equation is 2y + 4x =40
Let the coordinates of the top right corner be (x,y).
Then, y = (40 -4x)/2
The area of the rectangle is given by A =xy
A= x x (40 -4x)/2
A = 20x-2x²
We have to find the maximum area of the rectangle.
Differentiate the expression for Area A with respect to x to get the slope of the curve
A’ = 20-4x
At the maximum area, A’=0
Therefore, 20 -4x =0
4x =20
X=5
Substituting x=5 in the equation of the line 2y + 4x =40
2y +20 =40
2y = 20
Y =20
Therefore, the coordinates of the top right corner of the rectangle are (5,10).
The maximum area of the rectangle is given by A = xy = 5 x 10 =50 sq.units
b) The maximum area of such a rectangle can be found by using the formula: A = lw,
where l is the length of the rectangle
w is the width of the rectangle
Since the base of the rectangle is on the x-axis and the upper left corner is on the line y=2x+6, the length of the rectangle is equal to the distance between y=2x+6 and the x-axis, which is 6. The width of the rectangle is equal to the distance between y=-2x+6 and the x-axis, which is also 6. Thus, the maximum area of such a rectangle is 36 square units.
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Magic number puzzle. Help asap
Answer:
Step-by-step explanation:
1. 0
2. 3
3. 18
4. 33
5. 48
6. 198
recursively define the set of binary strings with more 0s than 1s.
0>1,If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y.
What do binary strings mean?A series of bytes make up a binary string. A binary string is used to store non-traditional data, including images, as opposed to a character string, which typically holds text data. The quantity of bytes in a binary string determines its length. The CCSID for a binary string is 65535.Binary refers to this system of 1s and 0s. Because of the way they are made, computers only speak in binary. A computer is nothing more than a sizable number of switches. On those curiously engraved boards inside the computer, there are millions of microscopic electronic switches.If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y. A procedure P is defined recursively if its action, P(x), is defined in terms of another action, P(y), where x>y.Explanation:
0>1.
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use the following probability distribution to answer questions 1 and 2. x -15 -10 -5 0 5 10 15 p( x
The Value of probability for the distribution is 0.24 and -0.29
Probability distribution is a statistical function that describes all the possible values and probabilities for a random variable within a given range
F(x) = P(X ≤ x) = P(a < X ≤ b) = f(b) - f(a)
The Probability Distribution is given
(1) By looking at the table ,
Value P(x = 0 ) at x =0 is 0.24
Hence , P(x=0) = 0.24
Option b is correct
(2) P(-10 ≤x ≤ 15) = P(x = 15) - P(x = -10)
By using the table ,
=> 0.05 - 0.34
=> -0.29
Option c is correct.
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You have a sample of 12 measurements, with a sum of the squares of the deviations from the mean of 42. What is the standard deviation?.
The sample standard deviation of the 14 measurements is 3.93
The standard deviation = √(variance)
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean
N = number of variables
For 12 variables,
N = 12
σ = 4.25
xbar = 38
Σ(x - xbar)² = sum of the square of all deviations; let it be equal to D
4.25 = √[Σ(x - xbar)²/12]
4.25 =√(D/12)
4.25² = D/12
D = 216.75.
For 14 measurements,
N = 14
The mean is going to still be 38, because the two new measurements are each 38.
xbar = 38
And the new additions to the sum of deviations, will be (38 - 38)² twice, that is, 0.
Standard deviation for 14 measurements
Standard deviation = σ = √[Σ(x - xbar)²/N]
σ = √(216.75/14) = 3.93
Therefore, the standard deviation is 3.93
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Disclaimer
The question given by you is incomplete, the solution provided is of a similar question, the question is
A sample of 12 measurements has a mean of 38 and a sample standard deviation of 4.25. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 38 each. The sample standard deviation of the 14 measurements is:
Part 1: Parallel & Skew Lines & Planes
1.) Name a segment skew to line AB.
2.) Name a segment parallel to line AD.
3.) Name a plane parallel to plane DCH.
4.) Name a plane that is NOT parallel to plane EFG.
1. The skew segment to line AB is of: GF.
2. The parallel segment to line AD is of: EH.
3. The plane parallel to plane DCH is of: ABF.
4. The plane that is not parallel to plane EFG is of: EFB.
What are the skew/parallel lines and planes in this problem?Skew lines are lines that share these two features:
The lines are not parallel.The lines are not intersecting.Hence the skew line to line AB is of:
Line GF.
Parallel lines are planes are defined as lines or planes that never intersect as they have the same orientation and inclination, hence:
Line EH is parallel to line AB.Plane ABF is parallel to plane DCH.Plane EFB is not parallel to plane EFG, as they have the common vertices E and F.More can be learned about skew lines at brainly.com/question/2603508
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2.3
0.6
Each number is the sum of the two numbers below it.
0.8
0.2
0.6
0.9
1.5
Answer:
Explanation vvvvvv
Step-by-step explanation:
2.3
0.8+1.5 = 2.3
Also.. for 0.6, do you also find the sum or could you find the difference?
0.8-0.2 = 0.6
I will answer in comments if this isn't right.
15 POINTS,RELATION OF A FUNCION(pic provided)
The relation that represents a function is option 1 which is in the image attached below.
What is a Function?If a graph of a relation represents a function, every set of x-values that is plotted on the graph will each correspond to exactly one y-value, which implies that a function cannot have an x-value that has two corresponding y-values that are plotted against it.
In the image given, the first graph shows a relation whereby every x-value has only one possible y-value it corresponds to.
The other graphs have at least an x-value that has more than 2 corresponding y-values, therefore, the first graph is a relation that represents a function and it is given in the attachment below
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in a technique called _____, the programmer simulates each program outcome or result and displays a message to indicate whether or not the program executed successfully.
In a technique called stub testing, the programmer simulates each program outcome or result and displays a message to indicate whether or not the program executed successfully.
What is stub testing?Test stubs are programs that imitate the behaviors of software components that a module undergoing tests rely on in advanced polymorphism computer science. Test stubs react to calls with pre-programmed prefabricated responses; they typically don't respond at all to calls that aren't part of the test. A stub is a brief piece of code used in testing to replace another component. Using a stub has the advantage of returning consistent results, which makes the test easier to write. And tests can be performed even if the other components are not yet operational.
The programmer simulates each program outcome or result and displays a message to show whether or not the program executed successfully. This process is known as stub testing.
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help meeeee please i do not understand this
Answer:
10.4 g/cm³
Step-by-step explanation:
Find the volume with formula, l x b x h
Then the formula gram / volume to find density.
1. Tyler was driving to the grocery store. As he was turning into the parking lot he was rear-ended by Harold. Tyler's head hit the steering wheel and he was taken to the hospital by ambulance. Harold failed to pay his insurance premium for several months and his policy was canceled. What type of automobile insurance coverage(s) is needed in this situation?
The type of automobile insurance coverage that is needed in this problem is of:
Liability coverage.
What are the types of car insurance coverage?The types of car insurance coverage are listed as follows:
Liability coverage.Uninsured and underinsured motorist coverage.Comprehensive coverage.Collision coverage.Personal Injury coverage.In this problem, the situation is that Harold caused a collision that resulted in injuries to Tyler, who has to pay the ambulance/hospital bill.
This means that Harold is liable to the injuries caused to Tyler, meaning that he needs liability coverage to help pay the hospital/ambulance bill, as collision coverage and personal injury coverages are for the victim and not for the person that caused an accident.
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what is the equation in slope intercept form of the line that passes through the point (-0.5,7) and is parallel to the graph of y=-8x-2 please help
Answer:
y = -8x + 3
Step-by-step explanation:
Pre-SolvingWe are given that a line passes through the point (-0.5,7), and is parallel to y = -8x - 2
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name.
Parallel lines have the same slopes.
Therefore, we can start by finding the slope of y = -8x - 2.
It is also written in slope-intercept form. -8 is where m (slope) should be; therefore, the slope of the line is -8.
SolvingWe can plug in -8 for m in y=mx+b.
y = -8x + b
Now we need to find b.
As the equation passes through the point (-0.5,7), we can use its values to help solve for b.
Substitute -0.5 as x and 7 as y.
7 = -8(-0.5) + b
Multiply
7 = 4 + b
Subtract 4 from both sides
3 = b
Substitute 3 as b in the equation.
y = -8x + 3
Topic: parallel and perpendicular lines
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[tex]3({\frac{7}{5} x+4)-2(\frac{3}{2} -\frac{5}{4}x)[/tex]
Answer: -1.34328358
Step-by-step-explanation;
3(7/5x + 4) - 2(3/2-5/4x) = 0
3·(7/5·x + 4) - 2·(3/2-5/4·x) = 0
134x = -180
x = -180/134 = -1.34328358
Marco has 2 peices of rope that are each 8 yards long.how many feet of rope does m arco have
Answer:
48 feet
Step-by-step explanation:
Marco has 2 pieces of rope that are each 8 yards long.
2 x 8 = 16 yards.
Marco has a total of 16 yards of rope.
Note that for converting yard to feet, that: 1 yard = 3 feet.
Marco, in this case, has 16 yards. Multiply 16 yards with 3 feet to obtain your answer:
16 yards x (3 feet/1 yard) = 48 feet/16 yards.
Marco has 48 feet worth of rope.
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what is 10 to the 10th power rounded to the nearest 10th?
Answer:
10,000,000,000
Step-by-step explanation:
[tex]10^{10}[/tex]= 10,000,000,000
rounded to the nearest 10th = 10,000,000,000
. If g = -4 and h = -5 find the value of
a) 4gh
b) g²h
c) 5h - g²
Answer:
a) 80
b) -80
c) -41
Step-by-step explanation:
For g = -4 and h = -5, you want the values of ...
4ghg²h5h -g²To evaluate these expressions, put the value of the variable where the variable is, and do the arithmetic. A calculator can help.
a) 4gh= 4(-4)(-5) = 80
b) g²h= (-4)²(-5) = -80
c) 5h -g²= 5(-5) -(-4)² = -25 -16 = -41
find the distance between the two points rounding to the nearest tenth (if necessary). (5,5) (-1,-3)
The distance between the two points (5,5) and(-1,-3) is 10 from the distance formula.
Given that,
The points area (5,5) and (-1,-3)
We have to find the distance between the two points.
We know that,
What is distance formula?The distance between two points is the length of the line segment spanning those two points on the plane.
d=√((x₂ - x₁)² + (y₂ - y₁)²) is a common formula to calculate the distance between two points.
Any two points on an x-y plane or coordinate plane can have their separation between them determined using this equation.
We get,
(5,5) and (-1,-3)
Distance= [tex]\sqrt{(-1-5)^{2}+(-3-5)^{2} }[/tex]
Distance= √(-6)²+((-8)²
Distance= √36+64
Distance= √100
Distance =10
Therefore, The distance between the two points (5,5) and(-1,-3) is 10 from the distance formula.
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what is the future value of $800 one year from today if the interest rate is 7 percent?
Answer:
800(1+7/100)
800(1.7)
1360
Step-by-step explanation:
formula isp(1+r/100)power t
The exponential or the future value with interest is A = $ 856
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the future value be represented as A
To calculate the future value of $800 after one year with an interest rate of 7%, we can use the formula for simple interest:
The future value = present value x (1 + (interest rate x time))
So , the exponential equation is
x ( t ) = x₀ × ( 1 + r )ⁿ
Plugging in the values we have:
The future value = $800 * (1 + (0.07 * 1))
The future value = $800 * 1.07
The future value = $856
Hence , the future value of $800 one year from today with a 7% interest rate would be $ 856
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whats the percent? ............
Answer: 32%
Step-by-step explanation: add up the total and divide 16 by the total number of all people surveyed
Find f(6) if f(x)=x²÷3+x.
4
10
18
Answer:Answer:
The value of f(6) is, 18
Step-by-step explanation:
Given the function:
.....[1]
We have to find the value of.
Put x = 6 in [1] we have;
⇒
⇒
Simplify:
Therefore, the value of f(6) is, 18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
we fill in where x is and make it 6
And I will use pemdas
f(6)=6^2÷3+6
f(6)=36÷3+6
f(6)=12+6
f(6)=18
Hopes this helps please mark brainliest
I'm a bit stuck, please can anyone help me?
8x-12 = 6x + 2
Answer:
x = 7
Step-by-step explanation:
8x - 6x = 2 + 12
2x = 14
2/2 x = 14/2
x = 7
A company that makes haircare products had 2,000 people try a new shampoo. Of the 2,000 people, 12 had a mild allergic reaction. What percent of the people had a mild
allergic reaction?
The percent of the people had a mild that has an allergic reaction is 0.6%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Given that the company that makes haircare products had 2,000 people try a new shampoo. Of the 2,000 people, 12 had a mild allergic reaction.
It should be noted the percentage will be:
= Allergic people / Total people × 100
= 12/2000 × 100
= 0.6%
The percentage is 0.6%.
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3k/2 - k+3/3=8- k+2/4
answer is 6
pls help and explain
Answer:
3k/2 - k+3/3=8- k+2/4
(3k/2)x3 - (k+3/3)x2=(8)x4 - k+2/4
9k-2k-6/6 = 32-k-2/4
7k-6/6 = 30-k/4
(7k-6)x4 = (30-k)x6
28k - 24 = 180 - 6k
34k = 204
k = 204/34
k=6
Step-by-step explanation:
First, you multiply both sides by the numbers there to both the numerator and denominator, to get the same denominator. Then, simplify the answers in the second step. Next, cross multiply by multiplying the numerator of the left side to the denominator of the right side; and multiplying the numerator of the right side of the denominator of the left side. When you reach the fifth step, move -6k to the left side it will turn to +6k and add with 28k to get 34k. Move -24 to the right side it will turn +24 and add with 180 to get 204. Lastly, divide 204 by 34 to get k = 6.
observations 1 2 3 4 5 6 num. of defects 10 18 13 15 9 12the number of runs above and below the sample median is:
The median element of a dataset is the middle element of the dataset.
There are 3 runs above and below the sample median
What is the median of a data set ?
The median of a data set is the value that falls in the middle, indicating that 50% of the data points have values that are lower or equal to the median and 50% of the data points have values that are higher or equal to the median. When working with a small data collection, you must first count the number of data points (n) and organize them in ascending order.
The information is given as:
Observations 1 2 3 4 5 6
Defects 10 18 13 15 9 12
In ascending order, the information is represented as:
Defects 9 10 12 13 15 18
Observations 5 1 6 3 4 2
The total number of observations is:
n=5+1+6+3+4+2 = 21
The median element is calculated as:
Median = (n+1)/2 th
Substitute 21 for n
Median = (21+1)/2 th
Median = 11th
The 11th element is 12.
So, the median is:
median = 12
Considering the given information;
Observations 1 2 3 4 5 6
Defects 10 18 13 15 9 12
The defects greater than the median (i.e. 12) are above (A) the median, while the defects less than the median are below (B)
So, we have:
Observations 1 2 3 4 5 6
Defects 10 18 13 15 9 12
Status B A A A B -
Next, we take a count of the number of times the status changes, i.e. from B to A, from A to B, from A or B to -
The count is 3.
Hence, there are 3 runs above and below the sample median
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three less than the product of nine and number is eight as a word equation
Answer:9x-3=8
Step-by-step explanation:
3 less means minus 3 from a number
product of 9 and a number is 9 times x
9x-3=8
is eight means = sign
M+ 1/5 < -1 2/3 help me
The solution to the inequality is M < -28/15.
What is inequality?The relation between two unequal expressions is defined as inequality.
The given inequality is M + 1/5 < -1 (2/3).
Solve the inequality as follows:
M + 1/5 < -1 (2/3)
M < -5/3 -1/5
M < (-25-3)/15
M < -28/15
Hence, the solution to the inequality is M < -28/15.
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Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.
The number of terms in the Arithmetic Progression is 20 if the sum is 990.
How to find the number of terms in an Arithmetic Progression?We should know that Arithmetic Progression is a type of sequence in which the difference between consecutive terms are derived from the addition or subtraction of a common tern known as the common difference (d).
The given parameters are
Sum of the Arithmetic Progression (n)=990
Common difference (d) =5
The common difference is derived as follows:
5*0+2=2
5*1+2=7
5*2+2=12
5*3+2=17
d=7-2=12-7=17-12=5
The formed AP is 2,7,12,17,.....
Using the formula
[tex]S_{n} =[/tex]n/2[{2a+(n-1)d}
Where:
a=first term n=number of termsd=common differenceSn=sum of termApplying the formula
990=[tex]\frac{n}{2}[/tex][2*2(n-1)5]
1980=n[4+5n-5]
1980=4n+5n²-5n
Rearrange the equation
5n²-n-190=0
Solving the equation
[tex]n=\frac{-b \frac{+}{-}\sqrt{b^{2}-4ac } }{2a}[/tex]
Where
a=5
b=-1
c=-1980
Applying the formula
n=[tex]\frac{1+199}{10} or \frac{1-199}{10} \\[/tex]
200/10 or -198/10
n=20 or n=-19.8
Taking the positive value of n=20
There the number of terms in the AP is 20
In conclusion, the number of terms in the Arithmetic Progression is 20 if the sum is 990.
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what is the slope of line g
to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 1 } \implies \text{\LARGE - 3}[/tex]
SOLVE ALL THREE OF THE QUESTIONS BY SUBSITITUON AND SHOW YOUR WORK. I will mark you brain list PLEASEERE
Answer: The correct answers are:
8) x=5/2 and y=0
9) An infinite number of solutions
10) x=1/4 and y=-1/2
Step-by-step explanation:
QUESTION 8:
Rewrite equations
y+3y=0
2x-5=-y
2x+y=5
Solve for y
y+3y=0
4y=0
y=0
Substitute 0 for y in 2x+y=5
2x+0=5
2x=5
Divide both sides by 2
x=5/2
x=5/2 and y=0
QUESTION 9:
Rewrite equations
3x-y=5
y=3x-5
Linear equation
a1/a2 = b1/b2 = c1/c2
3/-3 = -1/1 = -5/5
-1 = -1 = -1
Answer: An infinite number of solutions
QUESTION 10:
Rewrite equations
2x+y=0
4x-2y=2
Substitute and Simplify
2(2x-y)=2⋅1
2x-y=1
Solve for y
2x+y=0
y=-2x
Substitute y=-2x in 2x-y=1
2x-1(-2x)=1
2x+2x=1
4x=1
x=1/4
Substitut3 1/4 for x:
y=-2x
y=-2(1/4)
y=-1/2
x=1/4 and y=-1/2
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If the rate of inflation is 2.8% per year, the future price p (t) (in dollars) of a certain item can be modeled by the following exponential function, where it is the
number of years from today.
p(t) = 800 (1.028)
Find the current price of the item and the price 10 years from today.
Round your answers to the nearest dollar as necessary.
Current price:
Price 10 years from today: $
Para calcular la tasa de inflación, debemos seguir una serie de pasos.
Para ello, hemos propuesto un ejemplo en el que, paso a paso, calcularemos para un caso real la tasa de inflación.
Imaginemos que hacemos un listado de las compras realizadas en un año determinado, el cual tomamos como base. Esta compra incluye, a la hora de elaborar un listado, una serie de productos, todos ellos con sus respectivos precios. Productos que, en este caso, son barras de pan, cafés, servicios de taxi y un pantalón de vestir.
En primer lugar, lo que debemos hacer es calcular el gasto de cada producto, para ello, multiplicando las cantidades de cada producto o servicio adquiridas, por el precio que se pagó por cada una de ellas, así como por los servicios.
En este caso, sería lo siguiente:
Barras de pan: 1,50€ x 150 = 225€.
Cafés: 2,40€ x 100 = 240 €.
Taxi: 5€ x 40 = 200€.
Pantalón: 120€.
espero haberte ayudado
Make x the subject of the formula y= (xw/t) +p
Answer: The correct answer is x=(-pt+ty)/w
Step-by-step explanation:
Solve the equation for x:
y=xw/t+p
Step 1: Multiply both sides by t:
ty=pt+wx
Step 2: Flip the equation:
pt+wx=ty
Step 3: Add -pt to both sides:
pt+wx+−pt=ty+−pt
wx=−pt+ty
Step 4: Divide both sides by w.
wx/w=(−pt+ty)/w
x=(−pt+ty)/w
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Answer:
[tex]\huge\boxed{\sf x=\frac{ty-tp}{w} }[/tex]
Step-by-step explanation:
Given equation:[tex]\displaystyle y=\frac{xw}{t} +p\\\\Subtract \ p \ to \ both \ sides\\\\y-p=\frac{xw}{t} \\\\Multiply \ t \ to \ both \ sides\\\\t(y-p)=xw\\\\ty-tp=xw\\\\Divide \ w \ to \ both \ sides\\\\\frac{ty-tp}{w} =x\\\\x=\frac{ty-tp}{w} \\\\\rule[225]{225}{2}[/tex]
