The 715 cm² area of the disc and the ±5 cm² error tolerance, gives;
a) x = √(715/π) cm
b) The range for the radius is; [√(710/π) cm, √(720/π) cm]
c)
f(x) = π•x²
L = 715 cm²
E = 5 cm
d = √(5/π) cm
How can the variables in the [tex] \epsilon / \delta [/tex] definition of limits be found?Area of the circular metal disk = 715 cm²
a) Required; The disk radius
Let A represent the area of the disk and let x represent the radius, we have;
A = π•x²
Therefore;
x = √(A/π)
Which gives;
x = √(715/π) cm
b) Allowed area error tolerance = ± 5 cm²
The allowed range of values for the area is therefore;
710 ≤ A ≤ 720Which gives;
√(710/π) ≤ x ≤ √(720/π)
c) From the [tex] \epsilon / \delta [/tex] definition of limits, we have;
[tex] \lim\limits_{x → √(715/π)} f(x) = 715 [/tex]
Which gives;
f(x) = A = π•x²
L = 715
|f(x) - L| < E = 5 cm
|x - √(715/π)| < d = √(5/π)
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Evaluate the function f(x)= |x+4|−5 for
Answer:
f(-1) = |-1+4| - 5 = -2
f(0) = |0+4| -5 = -1
f(2) = |2+4| -5 = 1
Figure ABCD is a kite. What is the length of line segment AD? 8 units O 14 units 22 units 36 units
Length of line segment AD = 22 units .
Given : ABCD is a kite
AB and BC are congruent
AD and CD are congruent
AB = 14 units
CD = 22 units
To find : length of line segment AD
When 2 sides of a triangle are congruent , they are equal in measure ie. their magnitude is equal .
Since , AB and BC are congruent
⇒ AB = BC = 14 units
Similarly , CD = AD = 22 units
Therefore , length of line segment AD = 22 units .
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Answer: c on edge
Step-by-step explanation:
Use the Angle Addition Postulate to find the measure of the unknown angle
Answer:
Hey there!
Step-by-step explanation:
This is ur answer....
61 + 42 = 103ABC = 103Hope it helps!
Brainliest pls!
Follow me!
through: (3, 4), perp. to x = 0
Standard form
Answer: y=4
Step-by-step explanation:
If the line is perpendicular to the y - axis and goes through the point (3,4) then it's just y=4
-2x(-3)=
(-3x4)÷(-8)=
(-2x(-3))x(-4)=
Answer:
61,5-24Step-by-step explanation:
[tex]1. \: \: - 2 \times - 3 = \\ = 6[/tex]
[tex]2. \: \: ( - 3 \times 4) \div ( - 8) = \\ = ( - 12) \div ( - 8)\\ = ( - 6 )\div ( - 4) \\ = ( - 3 )\div ( - 2 )\\ = 1.5[/tex]
[tex]3. \: \: ( - 2) \times ( - 3) \times ( - 4) = \\ = 6 \times ( - 4) \\ = - 24[/tex]
Yasmin is the youngest of three siblings who ages are consecutive integers. If the sum of their ages is 57, find Yasmin's age. 17 18 19 20
Answer: 18
Step-by-step explanation:
18
If Yasmin is the youngest of three siblings who ages are consecutive integers then Yasmin's age is 18, option B is correct.
Let's assume Yasmin's age is represented by the variable "Y".
Yasmin is the youngest, so her age is the smallest integer among the three siblings' ages.
Since their ages are consecutive integers, we can represent the ages of the three siblings as Y, Y+1, and Y+2.
According to the given information, the sum of their ages is 57.
So we can write the equation:
Y + (Y+1) + (Y+2) = 57
Now, let's solve for Y:
3Y + 3 = 57
Subtract 3 from both sides:
3Y = 54
Divide both sides by 3:
Y = 18
So, Yasmin's age (Y) is 18 years old. Option B is correct.
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a number divided by 3 and then subtracted by 4 is the same as -10
Answer:
-18
Step-by-step explanation:
x=???
First, we know that the number we are looking for is divisible by 3. So lets list so numbers that are divisible by 3:
all (+,-) 6,9,12,15,18,........
Second, since we know the answer has to be in the double digits from the list we can have only 3 possibles answers.
12÷3=4
4-4=0
-12÷3=-4
-4-4=-8
So 12 nor -12 cant be the answer
18÷3=6
6-4=2
-18÷3=-6
-6-4=-10
So, the answer to the problem is -18÷3-4=-10
Find the difference of 6.761 x 1012 and 4.1 x 1012. 2.661 x 100 6.351 x 100 2.661 x 1012 6.351 x 1012
The difference between 6.761 x [tex]10^{12}[/tex] and 4.1 x [tex]10^{12}[/tex] is 2.661x [tex]10^{12}[/tex].
What is subtraction?Minuend and subtrahend are the terminology used in subtraction, while difference refers to the result. The minuend is the first number; it's the number you take things from, and it has to be bigger than the other numbers. The number being subtracted is known as the subtractend, and it must be the lower number.
Given that 6.761 x [tex]10^{12}[/tex], 4.1 x [tex]10^{12}[/tex]
We need to find the subtraction value of these expressions
Now 6.761 x [tex]10^{12}[/tex] [tex]-[/tex] 4.1 x [tex]10^{12}[/tex]
= 2.661x [tex]10^{12}[/tex]
Therefore, the difference between 6.761 x [tex]10^{12}[/tex] and 4.1 x [tex]10^{12}[/tex] is 2.661x [tex]10^{12}[/tex].
Hence, option (c) is correct.
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Complete question
Find the difference of 6.761 x 10 ^12 and 4.1 x 10 ^12.
(a) 2.661 x 10 ^0
(b) 6.351 x 10 ^0
(c) 2.661 x 10 ^12
(d) 6.351 x 10 ^12
Long division 1,755 divided by 27
Answer:
65
Step-by-step explanation:
Please do this algebra 2 for me. Please please. You can dm in insta what you want if u solve it just to do this please
Answer:
1231938-481881388111The perimeter of a rectangle is 180 meters. If the length of the rectangle is 20 meters more than the width, what are the dimensions of the rectangle?
Aunt Anne has a container of 24 cookies. The container has 2 oatmeal raisin cookies, and the rest are chocolate chip cookies. If Cyrus reaches in and takes a cookie without looking, is the probability of choosing a chocolate chip cookie impossible, unlikely, likely, or certain? Express the probability as a number between 0 and 1.
Answer:
Likely
11/12 aka 0.916666666667 aka 91.67%
Step-by-step explanation:
24 - 2 = 22
22/24
11/12
Likely means more than 50% but not 100% in this case.
The kinetic energy k of an object varies jointly with its mass m and its velocity v. The formula to kinetic energy is K = 1/2mv^2. Rearrange the formula to write the mass m in terms of K and v, where v is not equal to 0.
(I will rate brainliest if only right)
The mass m in terms of K and v is expressed as m= 2K/v^2
Subject of formulaThe subject of formula is a way of representing a variable in terms of other variables.
Given the equation below;
K = 1/2mv^2
Make m the subject of the formula
2K = mv^2
Divide both sides by v^22K/v^2 = mv^2/v^2
2K/v^2 = m
Swap
m= 2K/v^2
Hence the mass m in terms of K and v is expressed as m= 2K/v^2
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If 8 people consisting of 4 couples are randomly arranged in a row, find the probability that no person is next to their partner.
The Probability that no person is next to their partner is 104/105.
Probability of an event E represented by P(E) can be defined as (The number of favorable outcomes )/(Total number of outcomes).
Permutations is defined as arrangement of elements/objects in a particular way.
According to the question ,
8 people can be arranged in 8! ways = 40320ways
First let us find the probability that person is next to their partner.
4 couples can be arranged in 4! ways
and the couple itself can be arranged in 2! ways
Since there are 4 couples ,
Number of arrangement = [tex]4!(2!)^{4}[/tex]
=24x16
=384 ways
Probability that person is next to their partner = [tex]\frac{384}{40320} =\frac{1}{105}[/tex]
and the probability that no person is next to their partner is [tex]1-\frac{1}{105} =\frac{104}{105}[/tex].
Therefore , the probability that no person is next to their partner is [tex]\frac{104}{105}[/tex].
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A mother wants to invest $15,000.00 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $900.00, how much money was invested in the CD account?
The total interest earned after one year is $900.00.
How much money was invested in the CD account? $
(Round to the nearest cent, if necessary.)
From the analysis of the above math, the amount she invested in the CD account is 5,000. See the analysis below.
What is the analysis showing the above answer?Let A be the amount invested in the CD.
Let B be the amount invested in the savings bond.
A + B = 15, 000
.04A + .07B = 900
Multiply the first equation by -.04 and add it to the second equation to get rid of the A term.
-.04A-.04B = -600 add this equation to the second equation.
.03B = 300 multiplying by 100. 3B = 30,000
dividing by 3 on both sides: B = 10,000. So A = 5,000
So she invested 5,000 in the CD account
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Which is the correct way to write 602,200,000,000,000,000,000,000 in scientific notation? 6022 times. 1019 6022 times. 1020 6.022 times. 1022 6.022 times. 1023
The correct way to write 602,200,000,000,000,000,000,000 in scientific notation is 6.022 [tex]*[/tex] [tex]$$10^{23[/tex].
What is meant by scientific notation?Scientific notation is a method of expressing numbers that are either too large or too small to be written in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.
The proper scientific notation format is [tex]a*10^b[/tex], where an is a number or decimal number with an absolute value greater than or equal to one and less than ten, or 1 |a| 10. b is the power of ten required for scientific notation to be mathematically equivalent to the original number.
In the scientific notation, the number is written as a multiplication of a number from 1 to 9 and 10 raised to the adequate power.
602,200,000,000,000,000,000,000
= 6.202 [tex]*[/tex] 100,000,000,000,000,000,000,000.
Since 10 = [tex]10^1[/tex]; 100 = [tex]$$10^2[/tex]; 1,000 = [tex]$$10^3[/tex], etc. then
100,000,000,000,000,000,000,000 = [tex]$$10^{23[/tex].
602,200,000,000,000,000,000,000
= 6.202 [tex]*[/tex] 100,000,000,000,000,000,000,000 = 6.022 [tex]*[/tex] [tex]$$10^{23[/tex].
The correct way to write 602,200,000,000,000,000,000,000 in scientific notation is 6.022 [tex]*[/tex] [tex]$$10^{23[/tex].
Therefore, the correct answer is option d) 6.022 [tex]*[/tex] [tex]$$10^{23[/tex].
The complete question is:
Which is the correct way to write 602,200,000,000,000,000,000,000 in scientific notation?
a) 6022 [tex]*[/tex] [tex]$$10^{19[/tex]
b) 6022 [tex]*[/tex] [tex]$$10^{20[/tex]
c) 6.022 [tex]*[/tex] [tex]$$10^{22[/tex]
d) 6.022 [tex]*[/tex] [tex]$$10^{23[/tex]
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Answer: D
Explanation: 6.022 x 10^23
a rectangular piece of metal is 5in longer than it is wide, squares of 1in long are cut from the four corners and the flaps are folded upward to form an open box. if the volume of the box is 456in^(3) , what were the original demensions of the piece of metal?
The original dimensions (length and width) of this rectangular piece of metal are 19.81 inches and 14.81 inches respectively.
How to calculate the volume of a rectangular prism?Mathematically, the volume of a rectangular prism can be calculated by using this formula:
Volume = L × W × H
Where:
L represents the length of a rectangular prism.H represents the height of a rectangular prism.W represents the width of a rectangular prism.Given the following data:
Length, L = W + 5
Since squares of 1 in long are cut from the four corners, the length and width are reduced by 2 in. Also, the height of the box would be 1 inches.
Therefore, the volume of this rectangular box is given by:
456 = (L - 2) × (W - 2) × 2
456 = (W + 5 - 2) × (W - 2) × 2
456 = (W + 3) × (W - 2) × 2
228 = (W² - 2W + 3W - 6)
228 = W² + W - 6
W² + W - 6 - 228 = 0
W² + W - 234 = 0
Next, we would solve the quadratic equation by using the quadratic formula:
[tex]W = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\W = \frac{-1\; \pm \;\sqrt{1^2 - 4(1)(-234)}}{2 \times 1}\\\\W = \frac{-1\; \pm \;\sqrt{1 + 936}}{2}\\\\W = \frac{-1\; \pm \;\sqrt{937}}{2}[/tex]
Width, W = 14.81 or -15.81
Since the width cannot be negative, the value of W is equal to 14.81 inches.
For the length, we have:
Length, L = W + 5
Length, L = 14.81 + 5
Length, L = 19.81 inches.
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The population of pine bluff is 654 and is increasing at the rate of 7 per year
If the population of pine bluff is 654 and is increasing at the rate of 7 per year, then the equation will be y=654+7x and the population after 3 years will be 675.
Given that the population of pine bluff is 654 and is increasing at the rate of 7 per year.
We are required to find the equation which shows the population and the population after 3 years.
Equation is basically the relationship between two or more variables that are expressed in equal to form and can be solved to find the value of variables. It may be linear equation, quadratic equation, cubic equation and many more depending on the power of the variables that are present in the equation.
Suppose the number of years be x.
The equation which shows the population after x months be:
y=654+7x
To find the population after 3 years, we can use x=3 in the equation.
y=654+7*3
y=654+21
y=675
Hence if the population of pine bluff is 654 and is increasing at the rate of 7 per year, then the equation will be y=654+7x and the population after 3 years will be 675.
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distance between points -10,6 and 2, -3
Answer:
15 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 10, 6 ) and (x₂, y₂ ) = (2, - 3 )
d = [tex]\sqrt{(2-(-10))^2+(-3-6)^2}[/tex]
= [tex]\sqrt{(2+10)^2+(-9)^2}[/tex]
= [tex]\sqrt{12^2+81}[/tex]
= [tex]\sqrt{144+81}[/tex]
= [tex]\sqrt{225}[/tex]
= 15 units
two friends Natasha and Trisha shared a sum of money in the ratio 5:3 respectively. if Trishia share is $ 120 calculate the total amount of money shared
The money shared by Natasha and Trisha is $160.
What is defined as the term ratio?A ratio is a measure of 2 or more numbers which indicates their relative sizes. A ratio compares two amount by dividing them, with the dividend or number divided referred to as the antecedent and thus the divisor or number divided referred to as the consequent.Let the amount paid by the Natasha is 'x'
And the amount Paid by Trisha is 'y';
Their amounts are in the ratio of 5:3
Thus, x/y = 5/3
Trisha shares a amount of $120.
y = $12.
Then, put y = 120 in the ratio.
x/y = 5/3
x = 5y/3
x = (5×12)/3
x = 5×4
x = 40 (amount shared by Natasha)
Total amount = Natash's share + Trisha's share
Total amount = 40 + 120
Total amount = 160
Thus, the total amount of money shared is $160.
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Some Math i can’t helppp
Annually The amount after 10 years = $ 7247.295
quarterly compound after 10 years = $7393.5
Continuously interest =$7,419
Given:
P = the principal amount
r = rate of interest
t = time in years
n = number of times the amount is compounding.
Principal = $4500
time= 10 year
Rate = 5%
To find: The amount after 10 years.
The principal amount is, P = $4500
The rate of interest is, r = 5% =5/100 = 0.05.
The time in years is, t = 10.
Using the quarterly compound interest formula:
A = P (1 + r / 4)4 t
A= 4500(1+.05/4)40
A= 4500(4.05/4)40
A= 4500(1.643)
Answer: The amount after 10 years = $7393.5
Using the Annually compound interest formula:
A = P (1 + r / 100) t
A= 4500(1+5/100)10
A= 4500(105/100)10
Answer: The amount after 10 years = $ 7247.295
Using the Continuously compound interest formula:
e stands for Napier’s number, which is approximately 2.7183
[tex]A=Pex^{rt} \\A=4500(e)^{.5} \\A= 4500(2.71)^{.5}[/tex]
A= $2,919
Answer: The amount after 10 years = $4500+$2,919=$7,419
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CAN SOMEONE HELP ME ASAP PLEASE I WOULD REALLY APPRECIATE!!!
Answer:
See explanation
Step-by-step explanation:
a. f(x)=|x|
b. |x|==> -|x| ==> f(x) has been flipped over the y-axis.
-|x| ==> -2|x| ==> Then, f(x) doubled by 2, scale factor of 2
-2|x| ==> -2|x|-3 ==> Finally, f(x) became g(x) when it translated 3 units down
c. Use the transformations in part b to graph
Is √35 rational or irrational
Answer:
Irrational
Step-by-step explanation:
It can not be square rooted, the closest squared number to 35 is 36. The square root of 36 is 6 as 6x6= 3.
Therefore it is irrational.
Answer:
see below
Step-by-step explanation:
sqrt35 is irrational since by the definition of rational: able to be expressed as a whole number or a fraction.
sqrt35 is approximatly 5.91607978. which is not able to be a whole number or a fraction
thus sqrt35 is irrational
How Do I Order These From Least To Greatest Value?
Answer:
Step-by-step explanation:
-2.2*3.4=-7.48
4.2/-6=-0.7
-18/5+3/10=-3.3
-11/4-19/6=-5.91
draw a real number line, sign these on the line, you can see the order
10. How many times smaller
is 0.98 than 9.8?
David has 10 yd. Of material that he wiil cut into 15in. Thick mats. How many mats can David make?
Step-by-step explanation:
10 yards is equal to 360 inches. If you divided 360 inches by 15 inches, the answer will be 24. So the answer is 24 mats.
is five less than a number an equation or expressions
it hard to tell what you are saying, but if we know what the other number is, then expression.
What are
the domain and the range of the graph?
4. Liness and t are parallel. Find the value of x.
Answer: The value of X = 50°
Step-by-step explanation:
from diagram:
40° = 40°(vertically opposite angles)
40° + 90° + opposite side of X = 180 °(exterior angle property)
130° + opposite side of X = 180°(linear pair property)
opposite side of X = 180° - 130°
= 50°
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Please help 11 points add 11/3 + (-5/6) using the number line. select the location on the number line. select the location on the number number line to plot the sum.
The value of 11/3 + (-5/6) using the number line is 17/6.
Number line:
The number line is a visual representation of numbers on a straight line.
In a number line, Zero (0) is considered to be the origin of a number line. The numbers to the left of 0 are negative numbers and the numbers to the right of 0 are all positive numbers.
Given,
Here we have to add the values 11/3 + (-5/6) by using the number line.
To solve this one,
First we have to convert the fractions into decimals,
So, the decimal equivalent of
11/3 = 3.6
-5/6 = -0.8
So, the addition of these two is
=> (11/3) + (-5/6)
=> 3.6 + (-0.8)
=> 2.8
The fraction of the number is
=> 2.8 = 17/6.
This can be expressed in the following number line.
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