Answer:
a) Function A(x) = (60*x - 1/2*x²)
b)Side length x = 60 m the other side y = 30 m
c) A (max) = 1800 m²
Step-by-step explanation:
Area of rectangular garden with length " x " and wide "y"
A = x*y
Perimeter of rectangular area ( only three sides 2*y and 1*x)
P(r) = 2*y + x
P(r) = 120 = 2*y + x
y = ( 120 - x ) /2
Area of the garden as function of x is
A(x) = [( 120 - x ) /2]*x ⇒ A(x) = (60*x - 1/2*x²)
Taking derivatives on both sides of the equation:
A´(x) = 60 - x
A´(x) = 0 60 - x = 0
x = 60 m
Then
y = ( 120 - x ) / 2 ⇒ y = (120 - 60 )/2
y = 30 m
A(max) = 30 * 60
A(max) = 1800 m²
The side length (x) is 30 m each
The maximum area is 1800 m².
He has 120 meters for fencing . He use it to form 3 sides of a rectangular garden.
Therefore,
let
the side parallel to the house = y
the sides perpendicular to the house = x (2 sides)
Therefore,
perimeter = 2x + y
120 = 2x + y
y = 120 - 2x
area = x(120 - 2x)
area = 120x - 2x²
area = -2x² + 120x
The leading coefficient is less than zero, therefore, the parabola is facing downward. The maximum area is at (h, k).
where
h = - b / 2a
a = -2
b = 120
h = - 120 / 2 × -2
h = 120 / 4 = 30
The sides perpendicular to the building = 30 meter
The side parallel to the building = 120 - 2(30) = 60 meters
The maximum area = 60 × 30 = 1800 m²
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what is x in 2x + 5x
Answer:
in this question is hard to identify the value of x when it is not equated to a number so hey you'll just have to add to get 7 x
The radius of a circle is 10 m. Find its area in terms of 7.
Answer:
[tex]\pi \: r{2} \\ = \frac{22}{7} \times 10 {}^{2} \\ = 3.14 \times 100 \\ = 314[/tex]
I think the Answer is 314.....
Thank you ☺️
I’LL MARK BRAINLEST! :)
Find the measure of the missing angle
Suppose a carpenter's ruler was marked in thirty-seconds. What would be the fraction and its decimal equivalent for the mark on the ruler between 29/32 and 30/32?
Answer:
the fraction and its decimal equivalent for the mark on the ruler
= 59/64 = 0.921875
Step-by-step explanation:
Given that;
A CARPENTER 's ruler is marked in thirty seconds
mark on the ruler between 29/32 and 30/32 is the average of the values
we know that average is the summation of all terms divided by the number of appearance of terms
so
= (29/32 + 30/32) / 2
= ((29 + 30) / 32) / 2
= (59 / 32) / 2
= 59 / 64
= 0.921875
therefore the fraction and its decimal equivalent for the mark on the ruler = 59/64 = 0.921875
A nurse has an annual income of $52,175. The income tax the nurse must pay is 9%. What is the amount of income tax in dollars and cents that the nurse must pay?
Answer:
The amount of income tax in dollars and cents is $4,695.75
Step-by-step explanation:
To find the amount of income tax that should be paid, we simply use the percentage said to be for the income tax
Mathematically;
income tax = 9% of 52,175
= 9/100 * 52175
= $4695.75
The income tax to be paid on the income is $52,175
Answer:4695.75
Step-by-step explanation:
Well if u made 52175 a whole then put 9 as a percentage you would cross multiply 52175 with 9 then divided with the whole percentage (100)
will give u brainliest if i get it write hurry!!!
Answer:
c trust me
and well i just did that 20 mins ago
Answer:
C for sure hope you get it
the product of 9 and the sum of a number z and 4
g Nationwide, a certain disease occurs only a small proportion of people (.000215). A certain town has 74,000 residents. Use the Poisson approximation. c) Determine the probability that the town has 30 or fewer residents with the illness.
Answer:
The probability that the town has 30 or fewer residents with the illness = 0.00052.
Step-by-step explanation:
So, we have the following set of data or information or parameters given from the question above and they are; the number of people living in that particular society/community/town = 74,000 residents and the proportion of people that the diseases affected = .000215.
The first step to do is to determine the expected number of people with disease. Thus, the expected number of people with disease = 74,000 × .000215 = 15.91.
Hence, the probability that the town has 30 or fewer residents with the illness = 1.23 × 10^-7 × 15.91^30/ 2.65253 × 10^-32 = 0.00052.
Note the formula used in the calculating the probability that the town has 30 or fewer residents with the illness = e^-λ × λ^x/ x!
At a bake sale there were 72 raisin cookies sold. If the ratio of raisin cookies sold to oatmeal cookies sold was 9 : 1, what is the combined amount of raisin and oatmeal cookies sold?
Answer:
80
Step-by-step explanation:
72/9 is 8
9x8 is 72
so 1x8 is 8
72 plus 8 is 80
Consider the function and its inverse.
and
When comparing the functions using the equations, which conclusion can be made?
f(x) = x^2 +4 and f^-1 (x) = square root of x-4
The domain of f(x) is restricted to x ≥ 0, and the domain of f–1(x) is restricted to x ≥ 0.
The domain of f(x) is restricted to x ≥ 0, and the domain of f–1(x) is restricted to x ≤ 0.
The domain of f(x) is restricted to x ≤ 0, and the domain of f–1(x) is restricted to x ≥ 4.
The domain of f(x) is restricted to x ≤ 0, and the domain of f–1(x) is restricted to x ≤ 4.
Answer:
The domain of [tex]f(x)[/tex] is restricted to [tex]x\leq 0[/tex], and the domain of [tex]f^{-1}(x)[/tex] is restricted to [tex]x\geq 4[/tex].
Step-by-step explanation:
From Function Theory we know that domain of a function is the set of values such that an image exist. Let [tex]f(x) = x^{2}+4[/tex] and [tex]f^{-1}(x) = \sqrt{x-4}[/tex] the function and its inverse, respectively.
At first glance we notice that function is a second order polynomial and every polinomial is a continuous function and therefore, there exists an image for every element of domain.
But domain of its inverse is restricted to every value of x so that [tex]x-4 \geq 0[/tex], which means that [tex]x\geq 4[/tex].
Finally, we concluded that following answer offers the best approximation to our result:
The domain of [tex]f(x)[/tex] is restricted to [tex]x\leq 0[/tex], and the domain of [tex]f^{-1}(x)[/tex] is restricted to [tex]x\geq 4[/tex].
Answer:
C. The domain of f(x) is restricted to x ≤ 0, and the domain of f–1(x) is restricted to x ≥ 4.
Step-by-step explanation:
Which two options describe the standard deviation?
The variance square
The extreme distance from the mean expected from the data points
The square root of the variance.
The average distance from the mean expected of the data.
Answer:
The square root of the variance.
The average distance from the mean expected of the data.
Step-by-step explanation:
Standard deviation is a measure of dispersal. It determines the average distance from the mean expected of the data.
Variance is also related to the standard deviationIt is the square root of the variance. The dispersion or variation of a set of values away from the mean is the standard deviation.
Standard deviation = [tex]\sqrt{variance}[/tex]
What is the first step when solving the equation 3(3x-5x)+2=-8
Answer:
Collect the like terms
Step-by-step explanation:
(3x-5x)
3x (-2x) + 2 = -8
The function h(x)=1/x^2+1 is the result of the composition f(g(x)). If g(x) = x^2+1,what is f(x)? A f(x)=1/square root x B f(x)=1/x C f(x)= 1/x+1 D f(x)=1/x^2+1
Answer:
Option B is correct
Step-by-step explanation:
Given: [tex]h(x)=\frac{1}{x^2+1}[/tex] is the result of the composition [tex]f(g(x))[/tex].
Also, [tex]g(x)=x^2+1[/tex]
To find: [tex]f(x)[/tex]
Solution:
Take [tex]f(x)=\frac{1}{x}[/tex]
Now check whether [tex]h(x)[/tex] is equal to [tex]f(g(x))[/tex] or not.
First find [tex]f(g(x))[/tex]
[tex]f(g(x))=f(x^2+1)=\frac{1}{x^2+1}[/tex]
Also, [tex]h(x)=\frac{1}{x^2+1}[/tex]
Therefore,
[tex]h(x)=f(g(x))[/tex]
So,
Option B is correct
Answer: B. f(x)=1/x
Step-by-step explanation:
Edge
On Monday, Mr. Sanchez started reading a 225-page biography. He plans to read 15 pages each day until he finishes the book. Write an explicit function to represent the number of pages he has left to read depending on the day number; Monday is day number 1, Tuesday is day number 2, and so on. Find f(5) and interpret its meaning in this situation.
Answer:
Step-by-step explanation:
answen
Step-by-step explanationCan y’all help me ...
Answer:
b=4
Step-by-step explanation:
1. Write equation out
•3b-6+b-2=180
2. Combine like terms
•4b-8=180
3. Add the 8 to both sides
•4b-8=180
+8. +8
4b=188
4. Divide by 4
•4b=188
÷4. ÷4
b=47
Hi i need help on letters:
L,A,E,R,T,C,I,S,F,G,H,D,N,and O
Im giving 14 points if u answer all of them!!;)
Answer:
Step-by-step explanation:
E = 10:15 C = 4:5 F = 1:10 D = 1:2 R = 1:3 I = 30: 80 G = 16:48 N = 20: 40
A = 2:1 T = 6:10 S= 9:12 H = 9 O = 1: 11
(wouldve explained them but im in class :)
Points H, G and F are collinear. Point G is between Hand G. Solve for x. HG = x, GF = 1, HF = 10 *
Answer:
x = 11
Step-by-step explanation:
It is given that,
Points H, G and F are collinear. Point G is between H and G.
It means,
HG = GH + HG
We have, HG = x, GH = 1, HG = 10
Putting all the values, we get:
x = 1 +10
x = 11
It is very clear that the value of x is 11.
Which of the following are like terms
Answer:
i would say a but i could be wrong
Step-by-step explanation:
For each of the following variables, determine whether the variable is categorical or numerical. If the variable is numerical, determine whether the variable is discrete or continuous. a. Amount of time spent shopping for clothing in the past week b. Preferred brand of shoes c. Number of deliveries received at the household per week d. Most likely time period during which shopping for clothing takes place (weekday, weeknight, or weekend) a. Amount of time spent shopping for clothing in the past week is what kind of variable? categorical continuous numerical discrete numerical b. Preferred brand of shoes is what kind of variable? categorical discrete numerical continuous numerical c. Number of deliveries received at the household per week is what kind of variable? continuous numerical discrete numerical categorical d. Most likely time period during which shopping for clothing takes place is what kind of variable? continuous numerical discrete numerical categorical
Answer:
a. Amount of time spent shopping for clothing in the past week = CONTINUOUS NUMERICAL
b. Preferred brand of shoes = CATEGORICAL
c. Number of deliveries received at the household per week = DISCRETE NUMERICAL
d. Most likely time period during which shopping for clothing takes place (weekday, weeknight, or weekend) = CATEGORICAL
Step-by-step explanation:
Determine whether variable is Categorical or Numerical (Discrete or continuous) :
Categorical variables are used in grouping data values into a defined set of classes or distinct groups. Numerical variables are those usually represented with numbers and this posses numerical meaning. Numerical variables can either be discrete when the values in the dataset are finite or continuous, when values aren't finite and usually uncountable.
a. Amount of time spent shopping for clothing in the past week = CONTINUOUS NUMERICAL
b. Preferred brand of shoes = CATEGORICAL
c. Number of deliveries received at the household per week = DISCRETE NUMERICAL
d. Most likely time period during which shopping for clothing takes place (weekday, weeknight, or weekend) = CATEGORICAL
Categorical Variables : b) Preferred shoe brand; & d) Likely period of shopping
Numerical Continuous Variable : a) Amount of shopping time ; & Numerical Discrete Variable : c) Number of deliveries
Numerical Variables, as the name denotes - can be expressed in numbers. Like : Number of variable x.
Discrete Variables are only in real values : like 1,2,3 etc. Continuous Variables can take values between these real values also : like 1.4 , 1.5 , 2.8 etc. Example : Number of People is discrete, Height & Weight can be continuous.Categorical Variables, as the name denotes - cant be expressed n numbers but rather in categories. Like : A person being man, woman or other gender.
A] Amount of time spent shopping for clothing in the past week : Numerical & Continuous, can be in decimal values like 2.8 , 4.5 hours etc
B] Preferred brand of shoes : Categorical Variable, will be amongst the brand names like Pima, Nuke etc
C] Number of deliveries received at the household per week : Numerical & Discrete , can be only in non decimal whole values - like 4 , 5 , 10 etc
D] Most likely time period during which shopping for clothing takes place : Categorical Variable, will be amongst the mentioned period of weeks or days - like weekday, weeknight, or weekend
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please help!!!!!!!!!!
Answer:
Is B
3x+3
____
4x
Step-by-step explanation:
I think is B
During game play, Juan threw 2 darts onto the board.
Determine the likelihood of the scores Juan could get
with his two throws.
4 or greater:
Answer:
likely, impossible, unlikely
Step-by-step explanation:
Answer:likely
Impossible
Unlikely
Step-by-step explanation:
In a recent election Corrine Brown received 13,436 more votes than Bill Randall. If the total number of votes was 119,444 find the number of votes for each candidate.
Answer:
53151 for Bill Randall
66565 for Corrine Brown
Step-by-step explanation:
X + X+13414 = 119716
2x + 13414 = 119716
2x = 106302
x=53151
119716 - 53151 = 66565
A stick is broken into two pieces, at a uniformly random breakpoint. Find the CDF and average of the length of the longer piece.
Answer:
Step-by-step explanation:
See attachment
g÷2+ 19 > 15
what is g?
Answer: g > -8
Step-by-step explanation:
sadmep
help and ill give u brainly And points ASAp
Solve the formula for f2
f =
f1f2/
f1 + f2
Answer:
The answer is "[tex]\bold{ F2 = \frac{F F1}{(F1-F)}}[/tex]"
Step-by-step explanation:
Given:
[tex]\bold{F = \frac{F1 F2}{(F1 + F2)}}\\\\[/tex]
Cross multiplication:
[tex]\to F (F1 + F2) = F1 F2\\\\\to F F1 + F F2 = F1 F2\\\\\to F F1 = F1 F2 - F F2 \\\\\to F F1 = F2 (F1 - F) \\\\\to F2 = \frac{F F1}{(F1-F)}[/tex]
Use 4's to create problems that will equal 1-12. Remember to use the correct order of operations to solve your problems: Parentheses, Exponents, Multiply or Divide, Add or Subtract.
Answer and Step-by-step explanation:
Solution:
Order of operations:
1- Parentheses
2- Exponent
3- Multiply
4- Divide
5- Subtract
By using these operations we can find out the solution of 4’s to create problems that will equal to 1 – 12.
1 = 44 / 44 or (4+4) / (4+4)
2= 4/4 + 4/4
3 = (4+4+4) /4
4 = 4 x (4 – 4) +4
5 = (4 x 4 + 4)/ 4
6 = 4 x .4 + 4.4
7 = 44 / 4 – 4
8 = 4 + 4.4 - .4
9 = 4/4 +4 +4
10 = 44 / 4.4
11= 4 / .4 + 4/4
12 = (44 + 4) / 4
What are the similarities and differences between translations, reflections, and rotations? Describe a real-world transformation? Give examples of two different transformations.
Answer:
There are four main types of transformations: translation, rotation, reflection and dilation.Translation moves the object without rotating it or changing its size. Reflection flips the object about a line of reflection. Rotation rotates a figure about a fixed point. Dilation changes the size of a figure without changing its essential shape.When you reflect a point across the x-axis, the x-coordinate remains the same,but the y-coordinate is transformed into its opposite. a negative angle of rotation turns the figure in a clockwise direction.Transformation can be done in a number of ways, including reflection, rotation, and translation. ~When you reflect a point across the x-axis, the x-coordinate remains the same,but the y-coordinate is transformed into its opposite. a negative angle of rotation turns the figure in a clockwise direction.
Step-by-step explanation:
Transformation simply means changing the size and location of shapes, lines and points in the coordinate geometry
The similarities
Translations, reflections, and rotations are all rigid transformations
This means that, they do not change the side lengths and angle measure of the shape they transform.
The differences
Translation: can only change the position of shapes without rotating or flipping the shape.
Rotation: This means that a shape is to be turned around a center at a particular degree
Reflection: This simply means that, a shape is mirrored over a line
Real-world transformation
A scenario is when the blades of a fan rotates when the fan is powered on
Examples
Reflection
MirrorLeaves of a bookRotation
Fan rotationWheels of vehicleTranslation
Movement Changing positionsRead more about transformations at:
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F = ma
(a) Solve this equation for a.
(b) Let the force be units and the mass be m = 10 units. What is the acceleration, a?
(c) Let the force be F = 25 units and the acceleration be a = 5 units. What is the mass, m?
Let
F--------> represent the force
m--------> represent the mass
a-------> represent the acceleration
we know that
The formula that relates three quantities: Force (F), mass (m), and acceleration (a) is equal to
Part a) Solve this equation for a
Divide both sides by the mass
therefore
the answer part a) is equal to
Part b) Let the force be 25 units and the mass be m = 10 units. What is the acceleration, a?
we know that
the formula of acceleration is equal to
in this problem
we have
Substitute the values n the formula
therefore
the answer part b( is equal to
Part c) Let the force be F = 25 units and the acceleration be a = 5 units. What is the mass, m?
we know that
Solve for m
Divide both sides by the acceleration
in this problem
we have
Substitute the values n the formula
therefore
the answer Part c) is