Answer:
A) A = 200w - w²
B) w = 100 yards
C) Max Area = 10000 sq.yards
Step-by-step explanation:
We are told that Robert has available 400 yards of fencing.
A) we want to find the expression of the area in terms of the width "w".
Since width is "w", and perimeter is 400,if we assume that length is l, then we have;
2(l + w) = 400
Divide both sides by 2 gives;
l + w = 200
l = 200 - w
Thus, Area of rectangle can be written as;
A = w(200 - w)
A = 200w - w²
B) To find the value of w for which the area is largest, we will differentiate the expression for the area and equate to zero.
Thus;
dA/dw = 200 - 2w
Equating to zero;
200 - 2w = 0
2w = 200
w = 200/2
w = 100 yards
C) Maximum area will occur at w = 100.
Thus;
A_max = 200(100) - 100(100)
A_max = 10000 sq.yards
a) Does the Range Rule of Thumb estimate more often underestimate or overestimate the actual standard deviation?
The Range Rule of Thumb is a simple method to estimate the standard deviation based on the range of a dataset.
It states that approximately 68% of the data lies within one standard deviation of the mean, and about 95% of the data falls within two standard deviations of the mean.
In terms of underestimating or overestimating the actual standard deviation, the Range Rule of Thumb tends to underestimate the true standard deviation. This is because the rule assumes a uniform distribution of data within each standard deviation, which is not always the case in real-world datasets. In reality, data distributions can be skewed or have outliers, which the Range Rule of Thumb does not consider.
As a result, relying solely on the Range Rule of Thumb for estimating the standard deviation may lead to inaccuracies, especially in datasets with non-uniform distributions or significant outliers. More robust methods, such as the sample variance and standard deviation formulas, are preferred for accurate estimation.
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Simplify the following expression.
Be sure to follow the correct oder of operations.
23.3 + 5.4 x 15.75
Answer:
108.35
Step-by-step explanation:
Order of Operations: PEMDAS
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction.
First, multiply 5.4 with 15.75:
5.4 x 15.75 = 85.05
Next, add:
85.05 + 23.3 = 108.35
108.35 is your answer.
~
Answer:
108.35Step-by-step explanation:
[tex]23.3+5.4\cdot \:15.75\\\\\mathrm{Multiply\:the\:numbers:}\:5.4\cdot \:15.75=85.05\\=23.3+85.05\\\\\mathrm{Add\:the\:numbers:}\\:23.3+85.05=108.35[/tex]
...............................
Answer:
Where's the question that you want to be solved?
What’s an equivalent expression to 3/5 - 13/5
Answer:
-2
Step-by-step explanation:
A proposed design for a habitable Mars colony is a hemispherical
biodome used to maintain a breathable atmosphere for the colonists.
Estimate the radius of the biodome if it is required to contain 5.5
billion cubic feet of air.
Answer:
r = 1.37 billion feet
Step-by-step explanation:
It is given that,
A proposed design for a habitable Mars colony is a hemispherical biodome used to maintain a breathable atmosphere for the colonists.
The volume of biodome is 5.5 billion cubic feet of air.
It is in the shape of a hemisphere. The volume of a hemisphere is given by :
[tex]V=\dfrac{2}{3}\pi r^3[/tex], r = radius
V = 5.5 billion cubic feet
[tex]r^3=\dfrac{3V}{2\pi}\\\\r^3=\dfrac{3\times 5.5}{2\times 3.14}\\\\r=(\dfrac{3\times 5.5}{2\times 3.14})^{1/3}\\\\r=1.37\ \text{billion feet}[/tex]
So, the radius of the biodome is 1.37 billion feet.
The radius of the biodome if it is required to contain 5.5 billion cubic feet of air is 1.38 billion feet and this can be determined by using the formula of the volume of the hemisphere.
Given :
A proposed design for a habitable Mars colony is a hemispherical biodome used to maintain a breathable atmosphere for the colonists.Volume of the biodome is 5.5 billion cubic feet.The following steps can be used in order to determine the radius of the biodome:
Step 1 - The formula of the volume of the hemisphere can be used in order to determine the radius of the biodome.
Step 2 - Formula of the volume of the hemisphere is given by:
[tex]\rm V =\dfrac{2}{3}\pi r^3[/tex]
where r is the radius of the hemisphere.
Step 3 - Now, substitute the value of V in the above formula in order to determine the value of 'r'.
[tex]\rm 5.5=\dfrac{2}{3}\pi r^3[/tex]
Step 4 - Simplify the above expression.
[tex]r^3=\dfrac{5.5\times 3}{2\pi}[/tex]
[tex]r = \sqrt[3]{\dfrac{16.5}{2\pi}}[/tex]
r = 1.38 billion feet
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In randomized, double-blind clinical trials of a new vaccine, were randomly divided into two groups. Subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. After the second dose, of subjects in the experimental group (group 1) experienced as a side effect. After the second dose, of of the subjects in the control group (group 2) experienced as a side effect. Does the evidence suggest that a higher proportion of subjects in group 1 experienced as a side effect than subjects in group 2 at the level of significance?
Answer: YES.
the evidence supports this claim.
Step-by-step explanation:
We have that from the complete information,
H0: p1 = p2
Ha : p1 > p2
N1 = 654, P1 = 103/654
N2 = 615, P2 = 52/615
First we have to check the states of typicality that is if n1p1 and n1*(1-p1) and n2*p2 and n2*(1-p2) all are more prominent than equivalent to 5 or not
N1*p1 = 103
N1*(1-p1) = 551
N2*p2 = 52
N2*(1-p2) = 563
All the conditions are met so we can utilize standard typical z table to direct the test
Test measurements z = (P1-P2)/standard mistake
Standard blunder = √{p*(1-p)}*√{(1/n1)+(1/n2)}
P = pooled extent = [(p1*n1)+(p2*n2)]/[n1+n2]
After replacement
Test measurements z = 3.97
From z table, P(Z>3.97) = 0.000036
Thus, P-Value = 0.000036
As the got P-Value is not exactly the given noteworthiness 0.01
We reject the invalid speculation
Thus, we have enough proof to help the claim.that a higher extent of subjects in bunch 1 experienced drowsiness.
cheers I hope this helped !!
Help me please thank you
Answer: 55°
Step-by-step explanation: y and x are supplementary and equal 180°. Triangles also equal 180° so subtract the two angles you know and x is 125°. 180 - 125 = 55°
Answer:
y = 55°
Sum of the interior angles of a triangle = 180°
Therefore, x + 25°+30° = 180°
or, x + 55° = 180°
or, x = 180°-55°
or, x = 125°
Now, x + y = 180° ( straight angles)
125°+y = 180°
y= 55°
How can i get the number 4 using 6 number 3's?
you can use addition, subtraction, multiplication, division and ( )
Answer:
(3+3)÷3+(3+3)÷3
=6÷3+ 6÷3
=2+2
=4
is correct answer
hope it helped you:)
Use any method to determine whether the series converges or diverges. Give reasons for your answer. sin Choose the correct answer below
A) The series converges because, by the Alternating Series lest, un sin _are nonincreasing for n25 sin
B) The series diverges because, by the Limit Comparison lest, is constant and lim n-70o diverges n 5 Vin O C.
C) The series diverges because, by the Integral Test,sin dx is divergent -- 0 D.
D) The series converges because, by the Ratio Test, lim sin n-oo
Answer:
hello the series to your question is missing attached below in the solution is the missing series
Answer : The series diverges because, by the Limit Comparison lest, is constant and lim n-70o diverges n 5 Vin O C. ( B )
Step-by-step explanation:
Attached below is the detailed solution of the question and the series is divergent because p = 1/5 < 1
Simplify. Please Someone answer ASAP!!
7
х
3
х
Answer:
[tex]x^{4}[/tex]
Step-by-step explanation:
18.2x^3 + 4x^2 + 2x
A. This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.
B. This polynomial could be factored by using the difference of squares method, perfect squares method, or grouping.
C. This polynomial could be factored only by using the perfect squares method.
D. This polynomial could be factored by using grouping or the perfect squares methods.
E. This polynomial could be factored only by using the difference of squares method.
F. This polynomial cannot be factored by any of the methods used in this lesson.
Answer:
A. This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.
Step-by-step explanation:
2x^3 + 4x^2 + 2x
First factor out the GCF
2x ( x^2 + 2x +1)
Then factor the inside by either using grouping or recognizing that this is a perfect square a^2 + 2ab + b^2 = ( a+b) ^2
2x ( x^2 + 2 * x * 1 + 1^2)
2x ( x+1) ^2
Answer:
A. This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method.
Step-by-step explanation:
2x^3+4x^2+2x
factor common term 2x
= 2x (x² + 2x + 1)
then factor x² + 2x + 1 to (x + 1)(x + 1)
= 2x (x + 1)(x + 1)
refining the equation
= 2x (x + 1)²
explain how you got the answer
Answer:
[tex]\huge\boxed{Center = (3,3),Radius = 2\sqrt{15} }[/tex]
Step-by-step explanation:
Given equation is
[tex]x^2 + y^2 -6x-6y -42 = 0[/tex]
Adding 42 to both sides
[tex]x^2 + y^2 -6x-6y = 42\\[/tex]
Completing squares
[tex]x^2 -6x+y^2 -6x = 42\\(x)^2 - 2(x)(3) +y^2 - 2(y)(3) = 42[/tex]
Adding (3)² => 9 and (3)² => 9 to both sides
[tex](x-3)^2+(y-3)^2 = 42+9+9\\(x-3)^2 + (y-3)^2 = 60\\(x-3)^2 (y-3)^2 = (2{\sqrt{15})^2}[/tex]
Comparing it with [tex](x-h)^2+(y-k)^2 = r^2[/tex] where Center = (h,k) and Radius = r
We get:
Center = (3,3)
Radius = [tex]2\sqrt{15}[/tex]
What is the scale factor & the length of x & y?
Answer:
see explanation
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, thus
scale factor = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex] , then
x = [tex]\frac{2}{3}[/tex] × 9 = 2 × 3 = 6
y = [tex]\frac{2}{3}[/tex] × 7 = [tex]\frac{14}{3}[/tex]
Given the diagram above, m∠Z is:
Answer:
120 deg
Step-by-step explanation:
The sum of the measures of the interior angles of a quadrilateral is 360 deg.
2t + 2t + t + t = 360
6t = 360
t = 60
m<Z = 2t = 2(60) = 120
Answer: 120 deg
For data at the interval level you cannot calculate meaningful differences between data entries.
a. True
b. False
Answer: A. FALSE
Step-by-step explanation: The interval scale presents a measurement level for representing numerical variables in an ordered and fixed manner. Measurement are represented on the scale at equal intervals with each difference between consecutive intervals being the same. With this attribute, data represented on an interval scale gives meaningful difference between the data entries also allowing the US to know the size of the interval. Interval scales allows us to make subtraction and addition on data it's data. Examples of data represented on interval scale include, Temperature, ph and other numeric data with arbitrary zero levels
63,416,831 to the nearest ten thousand help p
Which figure represents an undefined term?
Answer:
The last figure, line XY.
Step-by-step explanation:
The 4th figure represents a line.
A line is an undefined term in Geometry.
Graph the exponential function.
f(x)= -(5/2)^x
Answer:
see below
Step-by-step explanation:
Your spreadsheet or graphing calculator can do this for you.
__
If you want to do it by hand, pick a few values for x, compute the corresponding values of f(x), plot those points, and draw a smooth curve through them. You know the horizontal asymptote is y=0, and the whole graph is in the 3rd and 4th quadrants, since the exponential function has been reflected over the x-axis by the leading minus sign.
Simplify the equation 4x+3y=45
Answer: y = -4/3x + 15
3y = 45 - 4x (subtract 4x from both sides)
y = -4/3x + 15 (divide both sides by 3)
Answer:
10.5=x
Step-by-step explanation:
subtract 3y from both sides the divide by 4x which gives you the answer 10.5=x
Please answer? help me!
Reposting
Answer:
151 degrees
Step-by-step explanation:
the angle alternate to 50 degrees is also 50 degrees
now, we have 2 angles inside our triangle, we can use the angle sum property to find the third one, which is forming a linear pair with the angle 'x'
so, 29 + x = 180 (linear pair)
hence, x = 151 degrees
Steven Kellogg, a machine operator, works at an hourly rate of $10.60 and
earns time and a half if he works any overtime. Given this, last week he
worked 37 hours plus 8 hours overtime. What is his straight-time pay? What
is his overtime pay? What is his total pay?
Answer:
[tex]Straight\ Time\ Pay = \$392.2[/tex]
[tex]Overtime\ Pay = \$42.4[/tex]
[tex]Total = \$434.6[/tex]
Step-by-step explanation:
Given
Hourly Rate = $10.60
Overtime = half hourly rate
Hours worked = 37 hours
Overtime = 8 hours
Calculating the Straight Time Pay
[tex]Straight\ Time\ Pay = Hourly\ Rate * Hours\ Worked[/tex]
[tex]Straight\ Time\ Pay = 37 * \$10.60[/tex]
[tex]Straight\ Time\ Pay = \$392.2[/tex]
Calculating the Overtime Pay
[tex]Overtime\ Pay = Overtime\ Rate * Overtime\ Hours[/tex]
Since, overtime rate is half of hourly rate; we have
[tex]Overtime\ Pay = \frac{\$10.6}{2} * 8[/tex]
[tex]Overtime\ Pay = \$5.3 * 8[/tex]
[tex]Overtime\ Pay = \$42.4[/tex]
Calculating Total Pay
This is calculated by adding results in (i) and (ii)
[tex]Total = Straight\ Time + Overtime[/tex]
[tex]Total = \$392.2 + \$42.4[/tex]
[tex]Total = \$434.6[/tex]
Use the unit circle to find tan 30
Answer:
√3/3
Step-by-step explanation:
Memorize your unit circle.
30° is π/6 rad
tan(π/6) = √3/3
In a different plan for area codes, the first digit could be any number from 2 through 5, the second digit was either 2, 3, 4, or 5, and the third digit could be any number except 4, 5, or 8. With this plan, how many different area codes are possible?
Answer:
Step-by-step explanation:
First digit 2,3,4,5 = 4 different digits.
Second digit 2,3,4,5 = 4 different digits.
Third digit = 1,2,3,6,7,9 = 6 different digits.
Total number of possibilities = 4*4*6 = 96
Question Find the product of your age and the number of pets you have.
I am 9 years old and I have 2 pets
Answer:
18
Step-by-step explanation:
What you would do is becouse is says Product.
product mean the result of multiplication
so all you would do is just multiply 9 by 2 and your answer would be 18.
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The product of your age and the number of pets you have is 18.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given that you are 9 years old, also, you have two pets. Therefore, the product of your age and the number of pets you have is,
Product = your age x Number of pets you have
= 9 x 2
= 18
Hence, the product of your age and the number of pets you have is 18.
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How is team performance calculated in SAFE?
Answer:
By strengthening key elements of their safety and health programs, they also can improve their overall organizational performance. In addition to the social benefits, employers that use leading indicators to find and fix hazards can realize direct savings to their bottom line.
Question 4
Select all of the set to which the number belongs.
0
Natura Numharc
Answer:
0 is a:
Rational Number
Integer
Whole Number
Step-by-step explanation:
Answer:
0 is a:
Rational Number
Integer
Whole Number
Step-by-step explanation:
Find the average rate of change for the given function from x = 1 to x = 2
Answer:
2
Step-by-step explanation:
Average Rate of Change: [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Step 1: Define variables
f(b) = 5
f(a) = 3
b = 2
a = 1
Step 2: Plug into formula
(5 - 3)/(2 - 1)
2/1
2
1732.2097 has
significant figures.
Answer:
1732.2097 has 8 significant figures.
Step-by-step explanation:
Every non-zero digit is considered a significant number. Also, in some exceptional cases, zero can also be considered a significant figure if it is in the middle of two non-zero digits.
Just like in the number given, 1732.2097. We have 7 non-zero digits which certainly would be considered to be significant figures. Zero is between two significant figures, 2 and 9, therefore, it would also be referred to as a significant figure.
Therefore, the number, 1732.2097, has 8 significant figures.
ASAP What is the volume of a sphere, to the nearest cubic inch, if the radius equals 3 inches? Use π = 3.14. A. 101 in³ B. 210 in³ C. not given D. 96 in³
Answer: C. not given
Step-by-step explanation:
formula for volume of sphere: V=(4/3)πr³
V=(4/3)πr³
V=(4/3)(3.14)(3)³
V=(4/3)(3.14)(27)
V=113 in³
Answer:
C. Not given
V≈ 113 in³
Step-by-step explanation:
The volume of a sphere can be found using the following formula.
[tex]V= \frac{4}{3} \pi r^3[/tex]
We know the radius is 3 inches and we are using 3.14 for pi. Therefore, we can substitute [tex]3 in[/tex] in for [tex]r[/tex] and [tex]3.14[/tex] in for [tex]\pi[/tex]
[tex]V= \frac{4}{3} *3.14* (3 in)^3[/tex]
Evaluate the exponent first.
(3 in)³= 3 in * 3 in * 3 in = 9 in² * 3 in = 27 in³
[tex]V= \frac{4}{3} *3.14* 27 in^3[/tex]
Multiply 3.14 and 27 in³
[tex]V= \frac{4}{3} * 84.78 in^3[/tex]
Multiply 4/3 and 84.78 in³
[tex]V= 113.04 in^3[/tex]
Round to the nearest cubic inch. The 0 in the tenth place tells us to leave the 113 as is.
[tex]V= \approx 113 in^3[/tex]
Since 113 cubic inches is not an answer choice given, the correct answer is C. not given
A segment in the complex plane has a midpoint at -1 + 7i. If one endpoint of the segment is at 3 + 8i, what is the other endpoint?
The other endpoint
Answer: -5 , 6i
Answer: mark me brainliest please!!
1. -3+(-1)i
2. -7.5+2.5i
3. -5+6i
4. -7+1i
Step-by-step explanation:
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