The possible change in volume (in mm3) resulting from the error in measuring the radius is 32. 06 mm³
How to determine the volumeThe formula for volume of a sphere is expressed by;
Volume = 4/3 πr³
Where;
r is the radius of the spherepi takes the value 3.14From the information given, we have that the measured radius is 5 mm, with a possible measurement error of 0.1 mm
Then, radius a = 5mm
Radius b = 5 + 0. 1 = 5. 01mm
Now, substitute the values into the formula
Volume, v = 4/ 3 (3.14)(5)³
expand the bracket
Volume, v = 4/ 3 (392.5)
Volume, v = 523. 3 mm³
For radius of 5.01mm
Volume = 4/ 3 (3.14)(5.1)³
expand the bracket
Volume = 4/3 (416.52)
Volume = 555. 4 mm³
The change in volume = 555. 4 - 523. 3 = 32. 06 mm³
Hence, the change in volume is 32. 06 mm³
Learn more about volume here:
https://brainly.com/question/1972490
#SPJ1
In Foundations of Art, students are cutting circular paper plates into sectors. If the diameter of the plate is 22 cm, determine the central anglenecessary to create a sector with an area of 220 cm². Round to nearest thousandth if necessary.
STEP 1
Interpret question to make sense geometrically.
We have circular shapes, thus, we are dealing with circles and these circles have their area, however, we seek the angle with which when used to cut the circle will give us an area of 220 sq cm.
Note that this is a fraction of the total area of the circle.
This will be illustrated diagrammatically below
Area of a sector is given as:
[tex]\begin{gathered} \frac{\theta}{360}\times\pi(\frac{d^2}{4}) \\ \text{The question requires us to get the angle }\theta\text{ after equationg the expression to 220 sq cm} \end{gathered}[/tex]STEP 2
Find unknown
[tex]\begin{gathered} \text{Making }\theta\text{ the subject of the formulae gives} \\ \theta=\frac{220\times360\times4}{\pi\times22^2}=208.348^o \end{gathered}[/tex]The ci
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
The solution of the equation ( x - 7 ) × 2 = 36 is x = 25
The equation is
( x - 7 ) × 2 = 36
To solve this equation we have to rearrange the terms and do the arithmetic operations
The arithmetic operation is a branch of mathematics. The basic arithmetic operations are addition, subtraction, division and multiplication.
Move the 2 to the right hand side of the equation
x - 7 = 36 / 2
Divide the term
x - 7 = 18
Move the 7 to the right hand side of the equation
x = 18 + 7
Add the term
x = 25
Hence, the solution of the equation ( x - 7 ) × 2 = 36 is x = 25
Learn more about arithmetic operation here
brainly.com/question/13585407
#SPJ1
a rectangle is x units long and y units wide what is it area what its perimeter
Pls help if able to send a picture of answer and work
Joan walked 20 brown dogs.
As per the question, the 40% of total number of dogs are brown. So, finding 40% of the number 50 will give us the number of brown dogs.
Number of brown dogs = 50×40%
Converting Percentage to fraction
Number of brown dogs = 50×40/100
Cancelling zero as it is common
Number of brown dogs = 5×4
Performing multiplication to find the number of brown dogs
Number of brown dogs = 20
Thus, out of 50 dogs, Joan walked 20 brown dogs.
Learn more about Percentage -
https://brainly.com/question/24304697
#SPJ1
If p (x) is a polynomial of degree 3 with p(0) = p(1) = p(-1) = 0 and p(2) = 6, then
a show that p(-x) = -p (x).
b find the interval in which p(x) is less than zero.
Answer:
p(x) is a function, and a polynomial of degree 3, then
By remainder theorem and factor theorem,
p(0) = p(1) = p (-1) = 0 if and only if
x = 0, 1, -1 are zeroes if and only if
p(x) = k(x - 0)(x - 1)(x + 1) = k(x)(x^2 - 1) = k(x^3 - x) = kx^3 - kx
p(2) = k(2)^3 - k(2) = 6
8k - 2k = 6
6k = 6
k = 1
Thus p(x) = x(x - 1)(x + 1) = x(x^2 - 1) = x^3 - x
p(-x) = (-x)^3 - (-x) = x^3 + x
-p(x) = -(x^3 - x) = -x^3 + x
As you can see, p(x) does not equal to -p(x), unless x = 0, 1, -1,
because p(0) = -p(0) = 0, p(-1) = - p(1) = 0, p(1) = -p(-1) = 0
p(x) = x(x - 1)(x + 1)
If x < -1, then x < 0, x - 1 < 0, x + 1 < 0
That means p(x) < 0
If -1 < x < 0, then x < 0, -2 < x - 1 < -1 < 0, 0 < x + 1 < 1
That means p(x) > 0
If 0 < x < 1, then x > 0, -1 < x - 1 < 0, 0 < 1 < x + 1 < 2
That means p(x) < 0
If x > 1, then x > 0, x - 1 > 0, x + 1 > 2 > 0
That means p(x) > 0
Thus p(x) < 0 if x < -1 or 0 < x < 1
What is transitive property/
Diego bought some raisins and walnuts to make trailmix. Raisins cost $4 a pound and walnuts cost $8 apound.Diego spent $24 on both ingredients. Diego bought atotal of 5 pounds of raisins and walnuts combined.There are two constraints represented here (COST &WEIGHT).Write an equation for each constraint. This shouldcreate a system of linear equations.Let x = pounds of raisinsy = pounds of walnuts
Let x = pounds of raisins
Let y = pounds of walnuts
The first linear equation for the system is representing COST
[tex]\text{ \$4x + \$8y = \$24}[/tex]The second linear equation for the system is representing WEIGHT
[tex]x\text{ + y = 5}[/tex]Hence the two-equation for each constraint are
[tex]\begin{gathered} \text{\$4x + \$8y = \$24} \\ x\text{ + y = 5} \\ \end{gathered}[/tex]Multiply 3.7x and 6x.
09.7x
09.7x²
O 22.2x
22.2x²
HELP ASAP
The product of 3.7x x 6x = (3.7 x 6) x (x x x) = 22.2x².
In mathematics, a product is the outcome of multiplication or an expression that specifies the factors to be multiplied.The outcome of multiplying two or more numbers is known as the product of those numbers, and the numbers that are multiplied are referred to as the factors.What is Multiplication?For whole numbers, multiplication can be used as counting objects arranged in a rectangle or as calculating the area of a rectangle whose sides have a certain length. Because of the commutative principle, a rectangle's area is independent of which side is measured first.A new kind of measurement is the sum of two measures. For instance, the area of a rectangle can be calculated by multiplying the lengths of its two sides. An analysis of this product's dimensions is performed.One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication.Multiply in mathematics refers to the continual addition of sets of identical sizes.To learn more about Multiplication, refer to:
https://brainly.com/question/24327297
#SPJ13
10 Please help I’ll give brainly
Answer:
11) 7d + 28 and 7(d+4)
12) y^2 + 3y and y(y+3)
Step-by-step explanation:
ANSWER FOR BRAINLIST HELP PLOT THE POINTS BTW
Answer:
Plot the point (6, 2). From there, move 3 units up and then 4 units to the left. You will be at (2, 5). Plot that point, and then draw a line through (6, 2) and (2, 5).
Sadie stands on a platform that is 15 ft. above the pool surface. The pool has a depth of 12 ft.
a. What value can be used to represent the water's surface?
27 ft. can be used to represent the water's surface if the platform is 15 ft. above the pool surface and the pool has a depth of 12 ft.
As Sadie stands on a platform that is 15 ft. above the pool surface. The pool has a depth of 12 ft. then, and the total height of the water surface is, the total hight,
The total height = distance between pool surface to platform + the depth of the pool
∵ The total height = 15 ft. + 12 ft.= 27 ft.
To know more about height and distance visit,
https://brainly.com/question/15939509?referrer=searchResults
#SPJ9
How do u distributive property to find the product 27x34=27x(30+4)
The distributive property for the product of 27x34 will give a value of 918.
What is distributive property?It should be noted that distributive property simply means that one can distribute the contents of the parentheses into the other so that one can get the answer.
The distributive property is illustrated as:
a × (b + c) = a×b + a×c
In this case, using distributive property to find the product 27x34 will be:
=27x(30+4)
= 27 × 30 + 27 × 4
= 810 + 108
= 918
Learn more about distributive property on:
brainly.com/question/4077386
#SPJ1
Write an equation in standard form for the line that passes through the given points
(7,0) and (0, -4)
Answer:
y = 0.57143x - 4
Step-by-step explanation:
NEED HELP ASAP - 100 Points (Algebra 2 - Complex Numbers)
Every complex number has the form a+bi with a and b as real numbers. Is it possible to create a complex number in which b=0? If so, create two examples to show your hypothesis is true. If not, explain why it is not possible.
Your response must be at least 50 words.
It is not possible to create a complex number in which b = 0, as it would be equivalent to a real number.
Complex numbersThe general format of a complex number is given as follows:
z = a + bi.
The meaning of the parameters a and b are given as follows:
a is the real component of the number.b is the imaginary component of the number.If the coefficient b has a value of zero, then the complex number is written as follows:
z = a + 0i.
z = a.
Which is equivalent to a real number, that is, the number would have only a real component, hence it is not possible to find an imaginary number with b = 0.
Basically, any real number can be represented as a complex number with imaginary part 0, but then the number would not be complex.
More can be learned about complex numbers at https://brainly.com/question/10662770
#SPJ1
How can you use a number line to represent the subtraction between two integers?
Answer:
down below
Step-by-step explanation:
You can use a number line to show the subtraction between two integers by plotting the first night number and then move backwards, (left) however many spaces you are subtracting by. It is a visual representation of subtraction.
Hope this helps! :)
a printer cartridge with 3 2/3 millilters of ink will print off 2/4 of a box of paper. How many millilters of ink will it take to print an entire box
When given a sample set with a variance of n (a number), how would you estimate the range?
Simply subtract the lowest value from the highest value in the data set to determine the range.
Find the biggest observed value of a variable (the maximum) and subtract the smallest observed value to determine the range (the minimum). The data points between the distribution's two extremes are not taken into account by the range; just these two values are.
Because of its sensitivity to extreme values, it is frequently employed as a supplement to other measures of dispersion rather than as the single measure.
To help find the quartiles for bigger data sets, you can utilise the cumulative relative frequency distribution or, even better, the fundamental statistics algorithms found in spreadsheets or statistical applications that provide results more quickly.
To know more about sample variance refer to the given link:
https://brainly.com/question/28213657?referrer=searchResults
#SPJ1
The time required to load a truck is exponentially distributed with a mean of 15 minutes. What is the probability that a truck will be loaded in 20 minutes or more? enter your answer as a decimal not as a percent and round your answer to 3 decimal places.
Using the exponential distribution, there is a 0.263 probability that a truck will be loaded in 20 minutes or more.
Exponential distributionThe exponential probability distribution, with mean m, is described by the following probability mass function:
[tex]f(x) = \mu e^{-\mu x}[/tex]
[tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
The integral has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
Hence the probability of finding a value higher than x is given by:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In the context of this problem, the mean and the decay parameter are given, respectively, by:
[tex]m = 15, \mu = \frac{1}{15} = 0.0667[/tex]
Hence the probability that a truck will be loaded in 20 minutes or more is:
[tex]P(X > 20) = e^{-0.0667 \times 20} = 0.263[/tex]
More can be learned about the exponential distribution at https://brainly.com/question/16371214
#SPJ1
Write as a monomial in standard form.
The expression will be written in monomial standard form as -64x⁶a³.
A monomial may be defined as an expression which consists of only one term. If we are to write an expression in monomial standard form, then we will have to form an expression consisting of numbers and variable along with their powers. The variable containing the maximum power will be written first and so on. In the question we have to write monomial standard form of third power of (-4ax³). This can be written as
(-4ax³)³ and on further expanding
-64a³x⁶, but in standard from we write the variable having maximum power first, so we rearrange the terms, and we get
-64x⁶a³ which is the required answer.
Learn more about Standard form at:
brainly.com/question/11859115
#SPJ1
Can someone help me answer the top one?
When the spacecraft launched, it was 254 miles away from the Earth and its distance away from the Earth is increasing at a rate of 270 miles per hour.
How do we interpret the linear equation?The equation that represents the distance of the space craft is known as a linear equation. A linear equation is an equation that has only one variable that is raised to the power of one.
A linear equation increases or decreases at a constant rate. When drawn on a graph, a linear equation is a straight curve that slopes either upward or downward.
A linear equation usually has this form y = mx + b
Where:
m = slope b = interceptD = 254 + 270t
Where:
254 = intercept = initial distance from the Earth270 = slope = change in the speed of the spacecraft per hourTo learn more about linear functions, please check: https://brainly.com/question/26434260
#SPJ1
what value of makes the equation true 7+3(x - 1)=5x+-2(x+1)
An equation is a collection of variables and constants with the value of x which will make the equation 7+3(x - 1)=5x+-2(x+1) to be true is 1/2.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given equation,
7+3(x - 1)=5x+-2(x+1)
7 + 3x - 3 = 5x + 2x + 2
3x + 4 = 7x + 2
7x + 2 = 3x + 4
7x - 3x = 4 - 2
4x = 2
x = 1/2
Hence "The value of x which will make the equation 7+3(x - 1)=5x+-2(x+1) to be true is 1/2".
For more about the equation,
brainly.com/question/10413253
#SPJ1
when a cold drink is taken from a refrigerator, its temperature is 5°c. after 25 minutes in a 20°c room its temperature has increased to 10°c. (round your answers to two decimal places.) (a) what is the temperature of the drink after 55 minutes? °c (b) when will its temperature be 13°c? min
use the cross multiplication method :)
Darlene has 634 gallons of gasoline. Every time she mows her lawn, she uses 38 gallon. How many times can she mow her lawn before she needs more gas?
Answer: 16 times
Step-by-step explanation:
So in this situation, an equation helps!
634 = 38x
Where 634 is the number of gallons of gas she has; 38x is how much she needs to mow her lawn each time.
Now simply divide!
If we round we get x= 16.68 however this is not the correct answer because you can't mow 68/100 of a lawn! So even though 0.68 is greater than 0.5, we would round down to 16.
what is the domain of f?
Answer:
x ∈ {-8, 0, 2, 4, 7}Step-by-step explanation:
The domain is the set of x-coordinates.
The domain of the function f(x) is:
x ∈ {-8, 0, 2, 4, 7}Find the Area of the irregular polygon
Answer: 242 square ft
Step-by-step explanation:
Divide the polygon into 2 pieces so you have 2 rectangles. Then find the area of both rectangles.
Subject: Trigonometry, Evaluation of Functions
Hi, I only need help matching the graphs to the questions :) Brainly only allows me to attach 5/10 of the graphs, if the ones i've attached aren't the answer i posted a similar question before this one with the rest of the graph choices. Sorry!!
1. Find <0 if cos0 = 4/7 and sin0 is negative.
2. Find <0 if sec0 = -13/5 and tan0 is negative.
3. Find <0 is sin0 = 7/10 and cot0 is positive.
4. Find <0 if tan0 = 3/4 and sin0 is negative.
(i) cosФ = 4/7 and sinФ is negative → It lies in the 4th quadrant 304.8° and the suitable graph is not provided here.
(ii) secФ = -13/5 and tanФ is negative → It lies in the IInd quadrant 112.6° and the suitable graph is J.
(iii) sinФ = 7/10 and cotФ is positive → It lies in Ist quadrant =44.4° and the suitable graph is I.
(iv) tan0 = 3/4 and sin0 is negative → It lies in the IIIrd quadrant 216.9° and the suitable graph is not provided here.
What is quadrant?
The point is in the first quadrant if both x and y were positive. If both x and y are negative, the point will reside in the second quadrant. In the third quadrant, if either x and y are negatives, the point is located. The point is situated in the fourth quadrant if both x and y are positive.(i) cosФ = 4/7 and sinФ is negative
Ф=cos^(-1)(4/7)= 55.2°
It lies in 4th quadrant (360-55.2)°=304.8°
A suitable graph is not provided here.
(ii) secФ = -13/5 and tanФ is negative.
Ф=sec^(-1)(-13/5)=67.4°
It lies in IInd quadrant (180-67.4°)=112.6°
A suitable graph is J.
(iii) sinФ = 7/10 and cotФ is positive.
Ф=sin^(-1)(7/10)=44.4°
It lies in Ist quadrant =44.4°
A suitable graph is I.
(iv) tan0 = 3/4 and sin0 is negative.
Ф=tan^(-1)(3/4)=36.9°
It lies in IIIrd quadrant (180+36.9)=216.9°
A suitable graph is not provided here.
To learn more about quadrants visit:
https://brainly.com/question/28471977
#SPJ1
Evaluate 5(x - 1) - 2 when x = 3.
OA. 8
OB. 0
O C. 12
OD. -4
The value of f(3) for the given expression is 8.
What is evaluation of an expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression. The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Given, the expression is 5(x - 1) - 2
Let y = f(x) = 5(x - 1) - 2 = 5x - 5 - 2 = 5x - 7
Therefore, f(3) using the equation above is: f(3) = 5(3) - 7 = 8
Thus, the value of f(3) or y at x = 3 for the given expression is 8.
To learn more about this, tap on the link below:
https://brainly.com/question/4344214
#SPJ9
Your distance from lightning varies directly with
the time it takes you to hear thunder. If you
hear thunder 10 seconds after you see lightning,
you are about 2 miles from the lightning.
Estimate how many seconds it would take for
the thunder to travel a distance of 5 miles.?
The time taken by thunder to travel a distance of 5 miles is 25 seconds.
Which is the direct variation?A direct variation, as well known as a direct proportion, is a relationship that exists between two variables.Your distance from lightning differs directly with duration it takes you to hear thunder. If you hear thunder 10 seconds upon seeing lightning, you are approximately 2 miles away.Let d denote the distance and t the time.
Distance varies linearly with time, implying that distance is proportional to time.
Distance ∝ Time
d ∝ t
When the proportionality symbol is removed;
d = kt or k = d/t
Where k is the constant of proportionality.
In the equation, d = 2 and t = 10 are substituted.
k = 2/10 = 1/5
Therefore,
The following is a direct variation formula for the correlation between time and distance: d = (1/5)t
Now, for the distance of 5 miles, the time taken by the thunder is-
5 = (1/5)t
t = 5 × 5
t = 25 seconds.
Thus, the time taken by thunder to travel a distance of 5 miles is 25 seconds.
To know more about the direct variation, here
https://brainly.com/question/6499629
#SPJ13
THERE IS 5 QUESTIONS I NEED TO GET DONE IN TOTAL, BUT IT WONT LET ME PUT MANY PICS IN ONE QUESTION SO PLS GO TO MY ACC AND VIEW THE OTHER ONES!!I NEED THIS BY **TODAY**
(TY WHOEVER COMPLETES THESE <3333 )
Answer:
A. yes the y-intercept is 2
B. the graph is a straight line
C. The Slope of the Line is 1/2
D. The line Does Not pass through the origin
Step-by-step explanation:
A. the y-intercept is when x=0... y=([tex]\frac{-1}{2}[/tex]*0)+2
B. It is a straight line because x is raised to the 1st power and not another number
C. Although the slope of the equation is [tex]\frac{-1}{2}[/tex]... the slope is still 1/2
D. The line Does Not pass through the origin
origin= (0,0)
x=0 --> y=([tex]\frac{-1}{2}[/tex]*0)+2=
y=0---> 0=([tex]\frac{-1}{2}[/tex]*x)+2
[tex]\frac{-x}{2}[/tex]=2---> x=-4
Answer:
The first two statements are true.
Click "The y-intercept of the line is 2" and "The graph is a straight line"
Step-by-step explanation:
The most important thing to know for this question is the equation of a line, y=mx+c, where m is the slope of the line and c is the y-intercept (where the lines crosses the y-axis).
Our formula is y= - [tex]\frac{1}{2}[/tex]x+2, which means the y-intercept is 2. Therefore, the first statement is true.
The equation follows the general equation for a straight line, so the second statement is true.
Our formula is y= - [tex]\frac{1}{2}[/tex]x+2, which means the slope is - [tex]\frac{1}{2}[/tex], not [tex]\frac{1}{2}[/tex]. Therefore, the third statement is not true.
For a line to pass through the origin (0,0), it's y-intercept must be 0, but we already know the y-intercept here is 2. Therefore, the fourth statement is not true.
To see if the line passes through (0, -2), we must sub these values into the equation and see if it makes sense
y= - [tex]\frac{1}{2}[/tex]x+2?
-2=- [tex]\frac{1}{2}[/tex](0)+2?
-2 = 2? This is not true, so the last statement is also not true.
A number, m, rounded to 1 d.p. is 48.2 Another number, n, rounded to 1 d.p. is 6.7 What are the lower and upper bounds of m - n?
The corresponding values of the lower and upper bounds of m - n are 41.41 and 41.59.
What are the values of the lower and upper bounds of m - n?
Upper and lower bounds are the possible maximum and minimum values of a number before it was rounded.
The upper and lower bounds can be expressed using the error interval
The lowest value of m is 48.15
The highest value of m is 48.24
The lowest value of n is 6.65
The highest value of n is 6.74
Therefore, lower bound of m - n = 48.15 - 6.74 = 41.41
Also, the upper bound of m - n = 48.24 - 6.65 = 41.59
So values of the lower and upper bounds of m - n are 41.41 and 41.59 respectively.
Learn more about lower and upper bounds on:
https://brainly.com/question/28154881
#SPJ1