Part (a)
The length is supposed to be 22.2 cm, but it could be 0.3 cm less
So 22.2 - 0.3 = 21.9 cm is the smallest value for the length. This is the lower bound of the length.
The upper bound is 22.2 + 0.3 = 22.5 cm as it is the largest the length can get.
-------------
Use this for the width as well
The width is supposed to be 12 cm, but it could be as small as 12-0.3 = 11.7 cm and as large as 12+0.3 = 12.3 cm
-------------
Answers:smallest length = 21.9 cmlargest length = 22.5 cmsmallest width = 11.7 cmlargest width = 12.3 cm============================================
Part (b)
Use the smallest length and width to get the smallest possible area
smallest area = (smallest width)*(smallest length) = 11.7*21.9 = 256.23
-------------
Repeat the same idea but for the largest length and width to get the largest possible area
largest area = (largest width)*(largest length) = 12.3*22.5 = 276.75
-------------
Answers:smallest area = 256.23 square cmlargest area = 276.75 square cmIf cot^(4)x − cot^(2)x = 1, then the value of cos^(4)x + cos^(2)x is
Answer:
1
Step-by-step explanation:
[tex]cot^4x-cot^2x=1\\cot^4x=1+cot^2x\\cot^4x=cosec^2x\\ cos^4xsin^2x=sin^4x\\cos^4x=\frac{sin^4x}{sin^2x}\\cos^4x=sin^2x[/tex]------- (1)
Putting the value of [tex]cos^4x[/tex] in the equation:
[tex]cos^4x+cos^2x\\sin ^2x +cos^2x\\1[/tex] (Using the identity [tex]cos^2x +sin^2x=1)[/tex]
A stopwatch measures time to the hundredth of a second. Which of the following quantities is not possible using this measurement tool?
Answer:
A. 10.125 minutes
Step-by-step explanation:
A stopwatch measures time to the hundredth of a second. Which of the following quantities is not possible using this measurement tool?
A. 10.125 minutes
B. 10.125 seconds
C. 10.12 seconds
D. 10.1 seconds
The stopwatch measures time to the hundredth of a second.
Option A. Measures the time to thousandth of a minutes
Option B. Measures time to thousandth of a second
Option C measures time to hundredth of a second
Option C measures time to tenth of a second.
Option A. 10.125 minutes is the quantity which is not possible using the stopwatch because it is in MINUTES.
Option B 10.125 seconds can be rounded up to 10.13 seconds (hundredth of seconds).
Emergency help will mark brainliest answer
Answer:
Step-by-step explanation:
Use the formula
[tex]A(t)=P(1+r)^t[/tex] where P is the initial investment, r is the interest rate in decimal form, and t is the time in years. Filling in what we are given:
[tex]A(t)=5000(1+.05)^6[/tex] and simplifying a bit:
[tex]A(t)=5000(1.05)^6[/tex] and a bit more:
A(t) = 5000(1.340095641) so
A(t) = 6700.48
Each student of a class contributed as many 5 rupees as the numbers of the students in the class.Find the number of the students in the class if the total collection was RS 10125.
And=2025 students gave 10125 rs
just divide it by 5hope it helps...pls mark me brainliest
ux=x+y/k, solve for x
Answer:
x = y/( ku-1)
Step-by-step explanation:
Here in this question, we are asked to solve for x.
we have;
Ux = x+ u/ k
cross multiply;
k * Ux = x + y
kUx = x + y
kUx- x = y
x(KU-1) = y
x = y/( ku-1)
(2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i)
Answer:
50+50iStep-by-step explanation:
Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.
Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)
On expansion
(3 - i)(3 + i)
= 9+3i-3i-i²
= 9-(-1)
= 9+1
(3 - i)(3 + i) = 10
For the expression (2 + i)(1 - i), we have;
(2 + i)(1 - i)
= 2-2i+i-i²
= 2-i+1
= 3-i
Multiplying 3-i with the last expression (1 + 2i)
(2 + i)(1 - i)(1 + 2i)
= (3-i)(1+2i)
= 3+6i-i-2i²
= 3+5i-2(-1)
= 3+5i+2
= 5+5i
Finally, [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]
= 10(5+5i)
= 50+50i
Hence, (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i
Graph the relation shown in the table. Is the relation a function? Why or why not?
Answer:
Not a function fails the vertical line test
Step-by-step explanation:
This is not a function. The value of x = -1 goes to two different values of y
This would fail the vertical line test
Answer:
the first one
Step-by-step explanation:
use the vertical line test. the horizontal line would intersect at two points.
HAI HELP ME ASAP PLEASE
Answer:
Y/X = 2/3 x^2 + 16/3
Y= 2/3 x^3 + 16/3 x
Just replace y with y/X and X with x^2
Suppose you roll a fair six-sided die 25 times. What is the probability that you roll 5 or more 6’s on that die?
A. 0.3883
B. 0.5937
C. 0.5
D. 0.4063
Answer:
D. P(5+ 6's) = 0.4063
Step-by-step explanation:
Binomial distribution.
For the distribution to be applicable, the experiment must
1. Have a know and constant number of trials
2. Probability of success of each trial remains constant (and known if available)
3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.
4. Independence between trials.
Let
n = number of trials = 25
p = probability of success of each trial = 1 / 6
x = number of successes (0 ≤ x ≤ n) = 5
C(n,x) = number of combinations of picking x identical objects out of n
Applying binomial distribution
P(x,n) = probability of x successes in an experiment of n trials.
= C(n,x) * p^x * (1-p)^(n-x)
For n = 25 trials with probability of success (roll a 6) = 1/6
and x = 5,6,7,8,...25
It is easier to calculate the complement by
P(5+ 6's) = 1 - P(<5 6's)
= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )
1- (
P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961
P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051
P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532
P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883
P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171
)
= 1 - 0.59373
= 0.40626
= 0.4063 (to 4th decimal place)
550
Х
X =
degrees
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Answer:
35⁰
Step-by-step explanation:
180-90-55=35⁰
there is a right angle
The angle sum property of a triangle:
The total measure of the three angles of a triangle is 180°
[tex]\rm\large\rightarrow \: \: x \: + \: 55 \degree \: + \: 90 \degree \: = \: 180 \degree[/tex]
[tex]\rm\large\rightarrow \: \: x \: + \: 145 \degree \: = \: 180 \degree[/tex]
[tex]\rm\large\rightarrow \: \: x \: = \: 180 \degree \: - \: \: 145 \degree [/tex]
[tex]\rm\large\rightarrow \: \: x \: = \: 35 \degree[/tex]
How to do this question plz answer me step by step plzz plz
Answer:
194.25meters
Step-by-step explanation:
The distance around the running track is calculated as:
Perimeter of the first semi circle + Perimeter of the second circle +50m + 50m
Semi circle has a length or diameter of = 30m
r = 30/2 = 15m
Perimeter of a circle = 2πr
Hence for a semi circle = 2πr/2 = πr
Perimeter of the first semi circle = π × 15
= 47.123889804m
Perimeter of the second semi circle is the same hence,
π × 15 = 47.123889804m
The distance around the running track
= 47.123889804m + 47.123889804m + 50m + 50m
= 194.24777961m
Approximately= 194.25meters.
the sum of 5 times a number and 8 is equal to 9
Answer:
The unknown number is [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Let's make the unknown number x.
The sum of 5 TIMES a number (x) & 8 is 9.
Let's write it mathematically.
5x + 8 =9
We are trying to find the unknown number, so let's remove all the numbers from the left side to find x. Minus 8.
5x=1
5x is basically 5 times x, so to find x, we need to divide and from there we can remove 5.
x= [tex]\frac{1}{5}[/tex]
if 4 is a root of x^2- kx+12=0 , then the value of k and the other roots are what?
Answer:
k=7
Other root=3
Step-by-step explanation:
If x=4 is a root of the given equation, then it satisfies the given equation.
4^2-k(4)+12=0
We can solve this equation for k.
16-4k+12=0
28-4k=0
28=4k
28/4=k
7=k
So the equation is x^2-7x+12=0
Factor form is (x-3)(x-4)=0 since-3(-4)=12 and -3+-4=-7.
This implies x=3 and x=4 are roots.
Due to employee safety negligence at a nuclear waste facility, 2000 tons of a radioactive element is spilled into the nearby pond. The half-life of the radioactive element is 36 days. In order to be declared safe for swimming, based on its size and the amount of water, there must be less than 100 tons of the material found in the pond. How long, to the nearest day, until it is safe to swim again?
How long, to the nearest day, until it is safe to swim again will be 156 days
Let x represent number of day until it is safe to swim again
First step
=2000 *1/2^x
100=2000 *0.5^x
0.05=0.5^x
Second step
Log 0.05=xLog 0.5
Log 0.05/L0g 0.5=x
x=36 days* Log 0.05/L0g 0.5
x=36 days*43.22
x=156 days
Inconclusion How long, to the nearest day, until it is safe to swim again will be 156 days
Learn more about radioactive element here:
https://brainly.com/question/13812761
How is the product of a complex number and a real number represented on the coordinate plane?
Answer:
A complex number bein scaled by a real number would NOT produce any "rotation" ... "C" should be the answer.
Step-by-step explanation:
Which Property of real numbers does this equation show? 4 x 1 = 4
Answer:
This is multiplicative identity in which 4✖️1=4
Step-by-step explanation:
Hope it will help you:)
She walks to her school at a distance of 800m from her house in 55 seconds. On reaching, she finds that the school is closed and comes back by car with her friend and reaches home in 25 seconds. Find her average speed in m/s
Answer:
per second she was walking 14.54m roughly and driving is 32m per second therefore the average is 23.27m/s
Step-by-step explanation:
divide both sides by 55 to get one.
divide both sides by 25 to get one
THEN
to find the average you simply add them and divide by two which is 46.54 which divided by two is roughly 23.27.
Graph y=2x+4………………………………
Answer:
Step-by-step explanation:
If the ratio of two supplementary angles is 10 to 47, calculate the measure of the larger of the two angles.
Answer:
a) 148.52
Step-by-step explanation:
If sum of two angles is 180, then they are supplementary
Ratio = 10 : 47
Smaller angle = 10x
Larger angle = 47x
10x + 47x = 180
57x = 180
Divide both sides by 57
x = 180/57
x = 3.16
Larger angle = 47x = 47 * 3.16 = 148.52
(04.01 LC) The science club surveyed 50 students about the number of science courses in which they were enrolled and the time it took them to complete their homework. Classify the random variables from the survey. (2 points) Select one: a. Number of science courses, continuous; time to complete homework, continuous b. Number of science courses, continuous; time to complete homework, discrete c. Number of science courses, discrete; time to complete homework, continuous d. Number of science courses, discrete; time to complete homework, discrete e. Unable to determine from information given
Answer:
The correct option is;
c. Number of science courses, discrete; time to complete homework, continuous
Step-by-step explanation:
There are two types of random variables, discrete random variables and continuous random variables
Discrete random variables are variables that are always re-presentable by a finite countable number, such that discrete random variables can be taken as a count of items count
Therefore, as the number of science courses are fixed and such that a specific number can be ascribed to the courses at any time (except there are changes), is a discrete random variable
A continuous random variable is one whose possible values are infinite and are generally measurements of values of such as weight, height, time, and amount
Therefore, the time to complete the homework is a continuous random variable.
(01.02 HC)Morris is showing his work in simplifying (−6.7 + 4.3) − 1.2. Step 1: (4.3 − 6.7) − 1.2 Step 2: 4.3 − (6.7 + 1.2) Step 3: 4.3 − (7.9) Step 4: −3.6
Answer:
Option (C)
Step-by-step explanation:
This question is incomplete; here is the complete question.
Morris is showing his work in simplifying,
(-6.7 + 4.3) - 1.2
Step 1: (4.3 - 6.7) - 1.2
Step 2: 4.3 - (6.7 + 1.2)
Step 3: 4.3 - 7.9
Step 4: -3.6
Which statement is true ?
A). Step 1, Morris used the commutative property.
B). Step 2, Morris used the distributive property.
C). Step 3, Morris used the associative property.
D). Step 4, Morris's answer is incorrect.
In associative property,
a + (b + c) = (a + b) + c
By this property,
(-6.7 + 4.3) - 1.2
Step 1, (-6.7 + 4.3) - 1.2 = (4.3 - 6.7) - 1.2
Step 2, (4.3 - 6.7) - 1.2 = 4.3 - (6.7 + 1.2) [Use of associative property]
Step 3, 4.3 - 7.9
Step 4, -3.6
Show that the equations x^2-7x+6=0 and y^2-14y+40=0 form a rectangle.Also find the joint equations of diagonals.
Answer:
1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The joint equations of diagonals are;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Step-by-step explanation:
The equations are;
x² - 7·x + 6 = 0......................(1)
y² - 14·y + 40 = 0.................(2)
Factorizing equation (1) and equation (2) , we get
x² - 7·x + 6 = (x - 6)·(x - 1) = 0
Which are vertical lines at points x = 6 and x = 1
For equation (2) , we get
y² - 14·y + 40 = (y - 10)·(y - 4) = 0
Which are horizontal lines at point y = 4 and y = 10
The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The points of intersection of the equations are;
(1, 4), (1, 10), (6, 4), and (6, 10)
The end point of the diagonals are;
(1, 10), (6, 4) and (1, 4), (6, 10)
The slope of the diagonals are;
(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5
The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)
y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5
5·y = 56 - 6·x
The other diagonal is therefore;
y - 4 = 6/5×(x - 1)
y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5
5·y = 6·x + 14.
The joint equations of diagonals are therefore;
5·y = 56 - 6·x and 5·y = 6·x + 14.
) What should be subtracted from -5/3 to get 5/6?
Answer:
[tex]-\frac{5}{2}[/tex]
Step-by-step explanation:
Step 1: Put this into an equation
[tex]-\frac{5}{3} - x = \frac{5}{6}[/tex]
Step 2: Solve for x
[tex]-x = \frac{5}{6} + \frac{5}{3}[/tex]
[tex]-x = \frac{5}{2}[/tex]
[tex]x =- \frac{5}{2}[/tex]
Therefore you need to subtract [tex]-\frac{5}{2}[/tex] from [tex]-\frac{5}{3}[/tex] to get [tex]\frac{5}{6}[/tex]
Answer:i don’t know
Step-by-step explanation:I’m sorry dude I have no idea I tried doing it in the browser and I could not find an answer sorry
Complete the statement with always, sometimes, or never. Explain your reasoning.
An altitude is _____ the same line segment as an angle bisector.
Step-by-step explanation:
it's ur answers I hope it's helpful
The difference of two trinomials is x2 − 10x + 2. If one of the trinomials is 3x2 − 11x − 4, then which expression could be the other trinomial? 2x2 − x − 2 2x2 + x + 6 4x2 + 21x + 6 4x2 − 21x – 2
Answer:
[tex]4x^2-21x-2[/tex]
Step-by-step explanation:
Given that:
Difference of two trinomials is [tex]x^2 - 10x + 2[/tex]
One of the two trinomials is [tex]3x^2 - 11x - 4[/tex]
To find:
The other trinomial = ?
Four options are:
[tex]2x2 - x - 2 \\2x2 + x + 6 \\4x2 + 21x + 6\\ 4x2 - 21x - 2[/tex]
Solution:
Let the two trinomials be A and B.
Given A - B = [tex]x^2 - 10x + 2[/tex]
B = [tex]3x^2 - 11x - 4[/tex]
We have to find the other trinomial A.
A - B = [tex]x^2 - 10x + 2[/tex]
A - ([tex]3x^2 - 11x - 4[/tex]) = [tex]x^2 - 10x + 2[/tex]
[tex]\Rightarrow[/tex] A = [tex]x^2 - 10x + 2[/tex] + ([tex]3x^2 - 11x - 4[/tex])
[tex]\Rightarrow[/tex] A = [tex]4x^2-21x-2[/tex]
So, the correct answer is [tex]4x^2-21x-2[/tex].
Which is most applicable when continuous inspection is used? I-chart, P-chart, c-chart C-bar chart
There are various charts which represents mathematical and statistical data with graphical representation.
The correct answer for the given question is ,
I - Chart
Since this chart is used to present data for continuous inspection.
The charts are used for representation of inspected data in to structure way which helps understand the changes easily.
I chart is usually used when there is continuous inspection for the data. This type of chart used to monitor the process when measuring data at regular intervals.
Learn more at https://brainly.com/question/24366019
What is the volume of the following rectangular prism?
Answer:
1/10 units ^3
Step-by-step explanation:
The formula for the volume is given by
V = Bh where B is the area of the base and h is the height
V = 3/20 units ^2 * 2/3 units
= 3/20 * 2/3
= 1/10 units ^3
Multiply. Write your answer in scientific notation
Answer:
3×3×10^5×10^2
9×10^5-2
9×10³
The time required to drive a fixed distance varies inversely as the speed. It takes 2 hr at a speed of 200 km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 80 km/h?
Answer:
5 hours
Step-by-step explanation:
From the question, we are told that:
Time required to drive a fixed distance varies inversely as the Speed
T ∝ 1/S
k = proportionality constant hence,
T =k × 1/S
T = k/S
Step 1
Find k
It takes 2 hr at a speed of 200 km/h to drive a fixed distance
T = 2 hours, S = 200km/h
T = k/S
2 = k / 200
k = 2 × 200
k = 400
Step 2
How long will it take to drive the same distance at a speed of 80 km/h?
S = 80km/h
T = k/S
k = 400
T = 400/80
T = 5
Therefore, it takes 5 hours to drive the same distance at a speed of 80km/hr
Simplify x + 6.2 + 8.5.
6.2x + 8.5
x + 14.7
14.7x
Answer:
x + 14.7
Step-by-step explanation:
x + 6.2 + 8.5.
Combine like terms
x + 14.7