The possible change in volume that results from the error in measuring the radius is 32. 06 millimeters
How to determine the volume of the sphereIt is important to note that the formula for volume of a sphere is expressed by;
Volume = 4/3 πr³
Given that;
r is the radius of the sphereπ has the value 3.14Based on the information given, we have the measure of the radius to be 5 mm, with a possible measurement error of 0.1 mm
The original value of radius = 5mm
Radius after the measurement error = 5 + 0. 1 = 5. 01mm
Let's substitute the values into the formula
Volume = 4/ 3 (3.14)(5)³
We then expand the bracket
Volume = 4/ 3 (392.5)
Volume = 523. 3 cubic millimeters
For radius of the measurement error = 5.01mm
Volume = 4/ 3 (3.14)(5.1)³
Then, expand the bracket
Volume = 4/3 (416.52)
Volume = 555. 4 cubic millimeters
Change in volume = 555. 4 - 523. 3 = 32. 06 cubic millimeters
Hence, the change in volume is given as 32. 06 cubic millimeters
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the length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 7 cm/s. when the length is 11 cm and the width is 9 cm, how fast is the area of the rectangle increasing (in cm2/s)?
The area of the rectangle is increasing at a rate of 122cm²/s if the length of the rectangle is 11 cm and the width is 9 cm.
The area of a rectangle can be described as the product of the length and width of that rectangle, therefore;
Area = L × W
Here L represents length and W represents the width
Now by differentiating using the product rule;
dA/dt = (dL/dt)(W) + (dW/dt)(L)
As the length is 11 cm and the width is 9 cm and the length is increasing at a rate of 5 cm/s and its width is increasing at a rate of 7 cm/s; substituting these values in the equation;
dA/dt = (5)(9) + (7)(11)
dA/dt = 45 + 77
dA/dt = 122
Hence, the area of the rectangle is increasing at the rate of 122cm²/s.
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Please help me I really need help. ILYSM THANK YOU :)
How many pounds of apples will he get if he goes to David’s orchard?
The pounds of apples that he get if he goes to David’s orchard is 20 pounds.
How to calculate the pounds of apples?Let the assumed amount with him be $40.
It should be noted that for David's orchard, the first ten pounds are $2 per round and each additional round is $1 per pound.
Therefore, the expression to illustrate this will be:
($2 × 10) + ($1 × r)
where r = additional pounds
Therefore,
($2 × 10) + ($1 × r) = $40
20 + r = 40
r = 40 - 20
r = 20
He will get 20 pounds.
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if w=20 compute the value of
12w^12 over 60w^10
Answer: 80
Step-by-step explanation:
12(20)^12
/
60(20)^10
= 80
In a city, the people use
approximately 4,140,000,000
pounds of burgers in a year.
Write this number in scientific
notation.
Answer: [tex]4.14 \times 10^9[/tex]
Explanation:
Place the decimal point between the first two digits to get 4.14
Now ask yourself: How many places must we move the decimal point to go from 4.14 back to 4,140,000,000?
The answer is 9 places to the right.
This means we'll have 9 as the exponent over the 10
[tex]4,140,000,000 = 4.14 \times 10^9[/tex]
Graph the linear equation, 64 Points!!!
The graph for the three selected points can be found in the photos section. Good luck!
I need help with this pls
Answer:
B
Step-by-step explanation:
The given fraction means to divide -3/8 by -7/54.
You are dividing a fraction, -3/8, by another fraction, -7/54.
To divide a fraction by a fraction, multiply the first fraction by the reciprocal of the second fraction.
-3/8 / -7/54 = -3/8 • (-54/7)
Answer: B
Hello!
Let's solve:
[tex]\text{Write down the function}\\\dfrac{-\dfrac{3}{8} }{-\dfrac{7}{54} } \\\\\\\text{When dividing by a fraction, flip the fraction over and multiply it to the numberator}\\-\dfrac{3}{8} *-\dfrac{54}{7}[/tex]
Thus an equivalent multiplication expression is choice (B)
Hope that helps!
A
∠A and
∠
B
∠B are supplementary angles. If
m
∠
A
=
(
4
x
−
16
)
∘
m∠A=(4x−16)
∘
and
m
∠
B
=
(
x
+
1
)
∘
m∠B=(x+1)
∘
, then find the measure of
∠
B
∠B.
Answer:
a
Step-by-step explanation:
what in the hell type of question is that need more easy work not alien work, But just put (B/)
5
8
of the staff are male. 5
12
of the staff works part time at
the aquarium. What fraction of the staff is female?
The fractions of the staffs that are female if the total fraction of staff is 5/12 is 5/24.
Difference between fractionsFractions are expressed as a ratio of two integers. Given the following parameters;
Fraction of staffs that works in the aquarium = 5/12
Fractions of staffs that are male = 5/8
Determine the fraction of female staffs
Fraction of female staffs = 5/8 - 5/12
Fraction of female staffs = 30-20/48
Fraction of female staffs = 10/48
Fraction of female staffs = 5/24
Hence the fraction of the staff is female is 5/24.
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a patient is known to have contracted a rare disease which comes in two forms, represented by the values of a binary random variable d ∈ {0,1}. symptoms of the disease are represented by the binary random variables sk ∈{0,1}, and knowledge of the disease is summarized by the belief network:
According to a societal viewpoint, sickness and treatment characteristics that the general public values highly should be taken into account within value frameworks.
The study's goal was to better understand how the general public values characteristics other than health benefits and costs associated with the healthcare system, as well as how they value characteristics that are often associated with rare genetic disorders like Duchenne muscular dystrophy (DMD). The general population placed a high value on attributes including disease severity, impact on life expectancy and HRQoL, and treatment accessibility. These results add to the mounting data that emphasizes the usefulness of broadening value assessments to incorporate characteristics seen as significant from a societal standpoint.
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Find m/BCD if m and m
Answer: 180
Step-by-step explanation:
1) Add the two angles together
160 + 20 = 180
180
You can tell this because a 180-degree line is flat, just like in this picture.
Some one help pls!!! Solve p = kwm for k
Fill in the blanks below with the correct units. (a) Boris's bed is about 7 long. (b) Ivanna's 5 year old cat weighs about 9 . (c) Today, Kira drank a total of 7 of water.
(a) Boris's bed is about 7 inches long
(b) Ivanna's 5 year old cat weighs about 9 kg.
(c) Today, Kira drank a total of 7 liters of water.
What are Units of Measurement?Units of measurement give standards so that the numbers from our measurements refer to the same thing.
Measurement is to find a number that shows the amount of something. A measurement unit is a standard quantity used to express a physical quantity.
(a) Boris's bed is about 7 inches long
The inch is a commonly used customary unit of length
(b) Ivanna's 5 year old cat weighs about 9 kg.
Kilogram is a unit of measurement used to measure much heavier objects.
(c) Today, Kira drank a total of 7 liters of water.
A liter is a metric unit of volume primarily used to measure liquids. .
Hence inches, Kilograms and liters are the units for respective blanks of a, b and c.
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The principal would like to assemble a committee of 5 students from the 15-memberstudent council. How many different committees can be chosen?
SOLUTION
The question involves combination since it only deals with the selection without arrangement.
Hence the formula to use is
[tex]^nC_r=\frac{n!}{(n-r)!r}[/tex]For this question, we have
[tex]\begin{gathered} n=15,r=5 \\ ^nC_r=\frac{n!}{(n-r)!r} \\ \text{becomes } \\ ^{15}C_5=\frac{15!}{(15-5)!5!} \end{gathered}[/tex]Simplifying the last expression we obtained
[tex]\begin{gathered} ^{15}C_5=\frac{15!}{10!5!} \\ =\frac{15\times14\times13\times12\times11\times10!}{10!\times5!} \\ =3003 \end{gathered}[/tex]Therefore,
The number of committees to be chosen is 3003
find the circumference and area if its 56 cm
If the diameter of the circle is 56cm² then the circumference of the circle is 176cm and the area of the circle is 2464cm².
How do you determine a circle's area?A circle's area is equal to pi times the radius squared (A = πr). Discover how to apply this formula to determine a circle's area given its diameter.
Area of Circumference: What Does It Mean?The length of a circle's outline is referred to as its circumference, while the length of a form with straight sides is referred to as its perimeter. Circle circumference equals 2πr.
The circle has a 56 cm diameter, determine its circumference and area.Diameter of the circle =56cm
Radius of circle =56/2 =28cm
Therefore,
Circumference of circle
=2πr
=2*22/7*28
=176 cm²
Also,
Area of circle
=πr
=(22/7)*28*28
=2464cm²
Hence the circumference of the circle is 176cm² and the area of the circle is 2464 cm².
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Note: The question is incomplete in the portal. Here is the total question,
Question: Find the circumference and area of the circle if its diameter is 56 cm.
Dakota Lane purchased a car stereo for
$279.99. If he made a 35% down pay-
ment, how much did he finance?
A $189.99
C
$181.99
1
B $244.99
D $98.99
What can -85 be classified as like a Rational, Whole or a Integer number?
Answer:
-85 is rational and an integer, though an integer is the most specific
Step-by-step explanation:
Whole numbers do not include negative numbers
:]
Low flow showerheads use 2 1/2 gallons of water per minute. If family members shower a total of 2 1/3 hours per week, how much water does the family use for showers each week? Write an expression that represents the problem. Then solve the problem
The expression that represents the situation is (5/2)x = y and the family uses 350 gallons of water for each week.
First, we convert the given fractions into improper fractions as follows;
2 1/2 = 5/2
2 1/3 = 7/3
As the showerhead uses 5/2 gallons of water per minute an expression for this situation can be given as;
(5/2)x = y
Here x is the amount of time in minutes and y represents the gallons of water used by the family each week
As the family uses the showerhead for 7/3 hours per week, we first convert the hours into minutes as follows;
(7/3) × 60 = 140 minutes
Now substituting this value in the equation (5/2)x = y;
(5/2)x = y
(5/2)140 = y
y = 350 gallons
Therefore, 350 gallons of water is used by the family per week.
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Help!! Me! Please
(You don’t have to answer all)
1. Which kind of model do you think best represents the profit for each business?
2. Find a function that models the profit you can expect, based on your projections, for each business. You can round your values to the nearest thousandth, as needed.
Answer:
Please see below for answers and explanation and attachments
Step-by-step explanation:
These models are best figured out using regression analysis which is a rather complicated computation but luckily there are calculators that can solve
1. The best way to approach this problem is to plot the values and see whether the model is a linear equation or a higher degree equation.
For all three cases it appears that the equations are not linear which would have suggested a model of the form y = mx + b where y = profit in $, x = hours, m is the slope (rate of increase in profit) and b a constant, the y-intercept
For example if you look at the data for the dog walker table, the increase in $ for every additional hour of service is not constant eliminating a linear model. For the first hour, the increase is $7, the second hour it is $11, the third it is $27
So i assumed a quadratic model of the form y = ax² + bx + c where y = profit in $ and x is the number of hours of service for all three businesses
There are plenty of online calculators out there which can rapidly compute the quadratic regression model parameters fitting the data and provide a level of goodness of fit of the equation through a statistic known as the correlation coefficient, r
I entered the data for all 3 rows and came up with the following results
In all the equations, y represents the profit in $ and x the hours
I have also attached screenshots of the computation results which should be self explanatory
Dog Walker
Equation:
y = 1.05357x² + 8.3964x - 6.7
Correlation Coefficient r:
0.9913546 (pretty high goodness of fit)
House Sitter
Equation:
[tex]y = 1.482x^2 + 1.396x + 9.3[/tex]
Correlation Coefficient r:
0.99556069
Lawn Care
Equation:
y = -5.875x² + 30.582143x + 116.9
Coefficient of Correlation r:
0.9794537681
The attached screenshots will provide all necessary info.
I hope that helps ya out :)
What is the equation of the line that passes through the point (5,−5) and has a slope of 1/5
Answer:
y= 1/5x -6
Step-by-step explanation:
Use point-slope form (could be wrong name): y-y1= slope(x-x1)
Substitute in the numbers: y-(-5)= 1/5(x-5)
Distribute: y+5= 1/5x-1
Solve for final answer: y= 1/5x -6
PS write 1/5 as [tex]\frac{1}{5}[/tex]
The table represents a quadratic function. Write an equation of the function in standard form
-4-2 02
f(x) -3 0 10
X
https://tex.z-dn.net/?f=y%3D%5Cboxed%7B-%5Cdfrac%7B1%7D%7B4%7D%7D%5Cleft(x-%5Cboxed%7B-2%7D%5C%3A%5Cright)%5E2%2B%5Cboxed%7B4%7D
Determine the rate of change on the graphs below
Answer:
a. 3
b. -3/2
c. 4/3
d. -5/3
e. 0
f. undefined
Step-by-step explanation:
PLS HELPP I WILL MARK BRAINLIEST
The halves of triangle CAD are congruent, because sides CB and BA are congruent, they share the center side, and both are right triangles. So, CD = AD, or:
5x + 1 = 4x + 4
5x + 1 - 1 = 4x + 4 - 1
5x = 4x + 3
5x - 4x = 4x + 3 - 4x
x = 3
AD = 4x + 4
= 4(3) + 4
= 12 + 4
= 16
AD = 16
[tex]\huge \boxed{\sf 16} \\\\\\\displaystyle \sf Both\ right\ triangles\ are\ a\ reflection\ of\ each\ other.\\ Thus,\ they\ are\ equal\ in\ size.\\\\5x+1=4x+4\\5x-4x=4-1\\x=3 \\\\Substituting\ x=3\\\\4(3)+4=12+4=16[/tex]
2(w + 2) - 5w simplify
Answer: -3w + 4
Step-by-step explanation:
2(w+2) - 5w
2w + 4 - 5w
-3w + 4
15. Write an equation that goes through point (-6, 8) and has a y-intercept of -4.
Answer:
y = -2x - 4
Step-by-step explanation:
First, substitute the known values into the slope-intercept form, y = mx + b, where m represents the slope of the line and b represents the y-coordinate of the point of intersection of the line and the y-intercept. We are given that the graph has a y-intercept of -4, so substitute -4 for b. The graph contains the point (-6, 8), so substitute -6 for x and 8 for y.
8 = -6m - 4
12 = -6m
m = -2
Finally, substitute -2 for m and -4 for b to write the equation of the line in the form, y = mx + b.
y = -2x - 4
Express 9 as a fraction of 27.
Give your answer in its simplest form.
Answer:
[tex]\frac{9}{27}[/tex] =[tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex] = [tex]3[/tex]
Hope this will help you
what does the point (1,18) represent
The point (1, 18), in the proportional relationship, means 18 cookies will require 1 cup of flour.
How to Interpret a Proportional Relationship Graph?In a proportional relationship graph that models the relationship between two variables, x and y, a point on the graph means the value of x that will give a corresponding value of y. It is expressed as, (x, y).
(x, y) means the quantity of x that will give a corresponding quantity of y considering the proportional relationship between variables x and y.
Thus, the graph shows a proportional relationship between the number of cups of flour (y) that was used to make different numbers of cookies.
Thus, the point (1, 18) means that for 18 cookies to be made, 1 cup of flour is to be used.
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Suma:
1) 21+(-45)-67-100+234=
2)76-43+222-21-78-44+99-345=
Answer:
1. 43
2. -123
a bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green wooden balls. a ball is selected from the bag and kept. you then draw a second ball and keep it also. what is the probability of selecting one white ball and one blue ball? round your answer to four decimal places.
Answer:0.096
here this is your answer
Determine if 0.18750.1875 is rational or irrational and give a reason for your answer.
Need this answer ASAP
Step-by-step explanation:
All decimals which either terminate or have a repeating pattern after some point are also rational numbers. The number 0.2 is a rational number because it can be re-written as 1/5 . The number 0. 33333… is a rational number because it can be re-written as 1/3 .
find the lcm:- x⁴+x³-x²-x, x⁴-x and 4x²-4.
The LCM of both the factors x⁴+x³-x²-x, x⁴-x and 4x²-4 is discovered to be x(x+1)²(x-1).
Explain LCM.The LCM of any two numbers is the value that is evenly divisible by the two given numbers. Least Common Multiple is an abbreviation for Least Common Multiples. It's also known as the Least Common Divisor (LCD).
What exactly is an LCM example?The smallest integer that is a multiple of two or more numbers is known as the LCM. For instance, the LCM of 4 and 6 is 12, and the LCM of 10 and 15 is 30.
The two given expressions are:
x⁴+x³-x²-x, x⁴-x and 4x²-4
Let us simplify both these factors.
x⁴+x³-x²-x = x(x³ + x² -x -1)
= x(x+1)(x+1)(x-1)
= x(x+1)²(x-1)
4x²- 4 = 2²(x+1)(x-1)
Multiplying each factor with the highest power,
4x²- 4 = 2²x(x+1)²(x-1)
= 4x(x+1)²(x-1)
Thus x(x+1)²(x-1) is the least common factor of both factors.
As a result, it is discovered that the LCM of x⁴+x³-x²-x, x⁴-x and 4x²-4. is x(x+1)²(x-1).
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