Final answer:
To calculate the percent uncertainty in the volume of a spherical beach ball when the radius is uncertain, you multiply the square of the radius by four (surface area), by the uncertainty in the radius, and then compare this value to the total volume. The percent uncertainty is found to be approximately 2.62%.
Explanation:
To determine the percent uncertainty in the volume of a spherical beach ball with a radius of 2.86 1 0.09 meters, one must first calculate the volume's uncertainty, then relate this to the total volume, and finally convert this relationship into a percentage.
The formula for the volume of a sphere is [tex]V = (4/3)\pi(r^3)[/tex]. Since volume is proportional to the cube of the radius, any uncertainty in the radius dramatically affects the volume uncertainty. Using a function for the volume V(r) and applying the approximation for small changes in r, we have:
[tex]V = (4/3)\pi(r^2))(r)[/tex]
For a radius of 2.86 meters and an uncertainty of 0.09 meters, the uncertainty V in volume is 170 [tex]cm^3[/tex]. The volume is approximately V = [tex](4/3)(3.14)(2.86^3)[/tex] = 6538 [tex]cm^3[/tex]. Therefore, the volume expressed with its uncertainty is [tex]6500 \pm170[/tex] [tex]cm^3,[/tex] rounded to avoid false precision.
To find the percent uncertainty:
Convert the uncertainty to the same units as the ball's volume if needed (here both are in cm^3).
Divide the uncertainty by the volume: (170/6500) x 100%.
The percent uncertainty is approximately 2.62%.
(02.05 MC)
Two similar triangles are shown on the coordinate grid:
Which set of transformations has been performed on triangle ABC to form triangle A'B'C'?
Dilation by a scale factor of 4 followed by reflection about the x-axis
Dilation by a scale factor of 2 followed by reflection about the x-axis
Dilation by a scale factor of 4 followed by reflection about the y-axis
Dilation by a scale factor of 2 followed by reflection about the y-axis
Answer:
Dilation by a scale factor of 2 followed by reflection about the x-axis
Step-by-step explanation:
To answer it and view it properly let's do it by parts.
1) A closer look at the Triangle ABC shows us the coordinate points A(-2,-1) B(0,0) and C(1,-3).
2) Reflection across the x-axis gives us this triangle: A'(-2,1) B'(0,0) and C'(1,3). Notice that all y-coordinates have an opposite sign. This is a natural characteristic of a Reflection: an opposed sign of one Coordinate.
3) Finally, To Dilate a Triangle is to transform it so that it gets bigger than its original size.
If we compare the triangle with points A''(-4,2) B"(0,0) and C"(2,6) to A'(-2,1) B'(0,0) C'(1,3). Each coordinate is multiplied by 2.
Dilation by a scale factor of 2 followed by reflection about the x-axis
Write an equation in point-slope form for the line through the given point with the given slope. (8, –3); m = -1/4
To write the equation in point-slope form, plug in the given values of the point and slope into the formula and simplify.
Explanation:To write an equation in point-slope form for a line, we use the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, the given point is (8, -3) and the slope is -1/4. Plugging in these values into the formula, we get:
y - (-3) = (-1/4)(x - 8)
Simplifying the equation, we have:
y + 3 = (-1/4)x + 2
Therefore, the equation in point-slope form for the line through the point (8, -3) with slope -1/4 is y + 3 = (-1/4)x + 2.
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The population of a local species of flies can be found using an infinite geometric series where a1 = 940 and the common ratio is one fifth. write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.
A. Sigma notation
The formula for finding the nth value of the geometric series is given as:
an = a1 * r^n
Where,
an = nth value of the series
a1 = 1st value in the geometric series = 940
r = common ratio = 1/5
n = nth order
The sigma notation for the sum of this infinite geometric series is therefore,
(see attached photo)
B. Sum of the infinite geometric series
The formula for calculating the sum of an infinite geometric series is given as:
S = a1 / (1 – r)
Substituting the given values:
S = 940 / (1 – 1/5)
S = 1,175
Mr. Smith brings home 7 animals for his 7 children. Each child will adopt a pet to be her or his own. There are 4 different cats (a Siamese, a Persian, a Calico, and a Minx), 2 different dogs (a Poodle and a Golden Retriever), and a goldfish. Anna and Betty refuse to take care of the goldfish, and Charlie and Danny insist on having cats. The other 3 kids are easier to please -- they'll take anything. In how many ways can Mr. Smith give the children pets?
Given the constraints, the total number of ways Mr. Smith can distribute pets to his children is calculated as 216 ways. This involves the concept of combinations and permutations from combinatorics in mathematics.
Explanation:The problem posed is a typical combinatorics or probability question found in mathematics. Given the constraints, the number of ways Mr. Smith can distribute pets is calculated as follows:
Let's first assign pets to Charlie and Danny. They insist on having cats, but are not particular about which one. As there are 4 cats, there are *4 choose 2* ways to select two cats for them, which is 6. Anna and Betty refuse to take care of the goldfish, so they can either get the remaining two cats or one of the two dogs. This can be done in *4 choose 2* ways, or 6 ways. The remaining three children can accept any of the three remaining pets. Therefore, there are *3!* (3-factorial) ways to distribute the remaining pets. The factorial function (represented by !) means multiply all positive integers from the number to 1. Therefore, 3! = 3x2x1 = 6.
Since these scenarios are independent, we multiply these results. Hence, the total number of ways Mr. Smith can distribute pets to his children is 6 x 6 x 6 = 216.
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Considering the preferences of each child, there are 2160 different possible ways Mr. Smith can distribute the 7 pets to his 7 children.
Explanation:The question posed is a classic problem of combinatorics. We have Anna, Betty, Charlie, Danny, and three other unnamed children who will be receiving pets. Anna and Betty do not want the goldfish, and Charlie and Danny want only cats. Therefore, options for Anna and Betty include the 4 cats and 2 dogs (6 choices total). For each choice Anna makes, Betty has one less choice (5). We can multiply these together, which will give us 30 possible assignments for Anna and Betty. For Charlie and Danny, who just want cats, there are 4 available. Charlie can have one of 4, then Danny can have one of the remaining 3, yielding 12 possibilities.
With Anna, Betty, Charlie, and Danny assigned pets, there are 3 children and 3 pets (2 dogs and 1 goldfish) remaining. Three children can be given 3 pets in 3! = 3*2*1 = 6 ways.
Finally, multiplying these together gives us 30 * 12 * 6 = 2160 possible ways Mr. Smith can distribute the pets among his children.
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find the area of the kite
The diagonals are 3 cms long each. The area of the kite in the given figure is 9 [tex]cm^2[/tex].
Mathematically, a quadrilateral with two pairs of adjacent sides that are congruent (have equal length) is termed a "kite". Note that not all quadrilaterals with congruent adjacent sides are kites. Kites have numerous applications in geometry, including the study of polygons, symmetry, and angles. They can be used to solve geometric problems and to analyze relationships between sides, angles, and diagonals within the quadrilateral.
Given that the length of the diagonals = 3 cm.
It is known that
Area of a quadrilateral with equal diagonals = product of the diagonals.
Area = 3 [tex]\times[/tex] 3.
Area = 9 [tex]cm^2[/tex].
The area of the kite is 9 [tex]cm^2[/tex].
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I need help with number 17
Traveling at 55 miles per hour how many minutes rounded to the nearest whole number does it take to drive 310 miles
Find the slope of the line that contains the points named c (3,8),d (-2,5)
[tex]\bf c(\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad d(\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-8}{-2-3}\implies \cfrac{-3}{-5}\implies \cfrac{3}{5}[/tex]
Answer:
3/5
Step-by-step explanation:
To find the slope, we use the formula
m = (y2-y1)/(x2-x1)
= (5-8)/(-2-3)
= -3/-5
=3/5
The slope is 3/5
Find the slope and y-intercept of the line. y = 7/4x – 10
represent each of the fractions below both with a diagram and with words. A.2/3. B.1 1/8. C.6/9.
Given the Arithmetic sequence A1,A2,A3,A4 A1,A2,A3,A4 45, 58, 71, 84 What is the value of A43 A43 ?
Solve x2 + 8x − 3 = 0 using the completing-the-square method
(02.01 LC)
Line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A prime B prime. What is the length of A prime B prime?
A. 1 unit
B.2 units
C. 3 units
D. 5 units
Answer:
The correct option is C.
Step-by-step explanation:
It is given that line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A'B'.
Translation is a rigid transformation. It means the shape and size of preimage and image are same. In other words we can say that the preimage and image are congruent.
Corresponding sides of congruent figures are congruent.
[tex]AB\cong A'B'[/tex]
[tex]AB=A'B'[/tex] (Definition of concurrent segment)
[tex]3=A'B'[/tex] (AB=3 units)
The length of A'B' is 3 units. Therefore the correct option is C.
Need some help on geometry practice problems!
Probability help please? In a certain instant lottery game, the chances of a win are stated as "1 in 19." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. (round to three decimal places) I am confused and need a step by step instructions. Please help
Final answer:
To convert the chances of a '1 in 19' win into a probability value, you divide 1 by 19 to get 0.05263 and then round to 0.053. Therefore, the lottery win probability is 0.053.
Explanation:
To express the likelihood of a win in a lottery game as a probability value between 0 and 1, when the chances of a win are stated as "1 in 19", you follow these steps:
Understand that "1 in 19" means there is one chance to win for every 19 trials, so the total number of possible outcomes is 19 (18 losses + 1 win).
Express the chance to win as a fraction with the number of wins (1) over the total number of potential outcomes (19).
Convert the fraction into a decimal by dividing the numerator (1) by the denominator (19), which gives you approximately 0.05263.
Round the result to three decimal places, as requested, which gives you a probability value of 0.053.
Therefore, the probability of winning the lottery game is 0.053.
Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.
Write the sum using summation notation, assuming the suggested pattern continues. -8 - 3 + 2 + 7 + ... + 67
The correct answer is [tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex]
The sum using summation notation, assuming the suggested pattern continues, can be written as:
[tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex]
[tex]-8 - 3 + 2 + 7 + \ldots + 67 = \sum_{n=1}^{20} (-8 + 5(n-1))[/tex]
Explanation:
- The pattern appears to be an arithmetic progression with a common difference of 5.
- The first term is -8, and the common difference is 5.
- The nth term of an arithmetic progression can be expressed as [tex]a_n = a_1 + (n-1)d[/tex], where [tex]a_1[/tex] is the first term, and [tex]d[/tex] is the common difference.
- Substituting [tex]a_1 = -8[/tex] and [tex]d = 5[/tex], we get [tex]a_n = -8 + 5(n-1)[/tex].
- The sum of the first 20 terms of this arithmetic progression can be represented using the summation notation, with the index [tex]n[/tex] ranging from 1 to 20.
Therefore, the sum using summation notation is [tex]\sum_{n=1}^{20} (-8 + 5(n-1))[/tex].
Complete question:
Write the sum using summation notation, assuming the suggested pattern continues.
-8 - 3 + 2 + 7 + ... + 67
summation of the quantity negative eight plus five n from n equals zero to fifteen
summation of negative forty times n from n equals zero to infinity
summation of negative forty times n from n equals zero to fifteen
summation of the quantity negative eight plus five n from n equals zero to infinity
The number of chips of different colors in vicky's bag is shown below: 5 blue chips 11 pink chips 9 white chips vicky takes out a chip from the bag randomly without looking. she replaces the chip and then takes out another chip from the bag. what is the probability that vicky takes out a blue chip in both draws? 5 over 25 multiplied by 5 over 25 equals 25 over 625 5 over 25 plus 5 over 25 equals 10 over 25 5 over 25 multiplied by 4 over 24 equals 20 over 600 5 over 25 plus 4 over 24 equals 220 over 600
The probability that Vicky takes out a blue chip in both draws is 5/25 x 5/25 = 25/625.
What is the probability that vicky takes out a blue chip in both draws?
Probability determines how likely it is that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
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Solve x2 + 2 = 6 by graphing the related function.
Answer:
[tex]x=-2,x=2[/tex]
Step-by-step explanation:
we have
[tex]x^{2}+2=6[/tex]
we know that
The solution of the function is equivalent to solve the following system of equations
[tex]y=x^{2}+2[/tex] ------> equation A
[tex]y=6[/tex] ------> equation B
The x-coordinate of the intersection point both graphs is the solution of the given function
Using a graphing tool
see the attached figure
The intersection points are [tex](-2,6)[/tex] and [tex](2,6)[/tex]
therefore
The solution of the given function are
[tex]x=-2,x=2[/tex]
WILL GIVE BRAINLIEST!! PPLEASE HELP!!
The graph of which function does not contain the point (0, 1)?
A.
y=(3/4)^x
B.
y=-2^x
C.
y=3^x
D.
y=(1/2)^x
Evaluate the expression below when y = -3.
2y + 7
-4y − 10
i need help#awnser
replace y with -3
2y + 7 becomes 2(-3) + 7 = -6 +7 =1
-4(-3)-10 = 12-10 = 2
What is the solution to the system of linear equations graphed below?
A. (0,3)
B. (0,-2)
C. (-2,-2 1/2)
D. (-2 1/2, -2)
The solution to the system of linear equations graphed is (-2.5, -2). So, the correct answer is option D.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The ordered pair that is a solution to both equations is the system's solution. We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found.
In the given graph, the intersection point is (-2.5, -2).
Therefore, option D is the correct answer.
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The following data show the height, in inches, of 11 different plants in a garden: 9 4 10 9 5 2 22 10 3 3 5 After removing the outlier, what does the mean absolute deviation of this data set represent?
Segment JG is the same as segment GJ
A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions?
Find all complex solutions of x^2+5x-5=0.
(If there is more than one solution, separate them with commas.)
The complex solutions of x^2+5x-5=0 are (-5 + √45)/(2) and (-5 - √45)/(2).
Explanation:To find the complex solutions of x2+5x-5=0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Substituting the values a=1, b=5, and c=-5 into the formula, we get:
x = (-5 ± √(5^2 - 4(1)(-5)))/(2(1))
Simplifying further,
x = (-5 ± √(25 + 20))/(2)
x = (-5 ± √(45))/(2)
Since the square root of 45 cannot be simplified, we can write the solutions as:
x = (-5 ± √45)/(2)
Therefore, the complex solutions to the equation x2+5x-5=0 are:
x = (-5 + √45)/(2), (-5 - √45)/(2)
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What is the mean salary of a salesperson at the company
Can you guys help me with 3-8 please thank you <3
Tammy wants to raise $175 for a school fundraiser. She has raised $120 so far. How much does she need to reach her goal?
What is the solution of x=2+\sqrt(x-2)
x = 2
x = 3
x = 2 or x = 3
no solution
Answer:
The solution is x = 2 or x = 3
Step-by-step explanation:
we have to find the solution of the equation
[tex] x=2+\sqrt{(x-2)}[/tex]
[tex]x=2+\sqrt{(x-2)}\\ \\x-2=\sqrt{x-2}\\\\\text{Squaring on both sides }\\\\(x-2)^2=x-2\\\\x^2+4-4x=x-2\\\\x^2-5x+6=0\\\\x^2-2x-3x+6=0\\\\x(x-2)-3(x-2)=0\\\\(x-2)(x-3)=0\\\\x=2\text{ or }x=3[/tex]
Hence, correct option is x = 2 or x = 3
Answer:
C) x = 2 or x = 3
Step-by-step explanation:
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