Answer:
sqrt(67)
Step-by-step explanation:
sqrt(23×3-2)
sqrt(69-2)
sqrt(67)
Step-by-step explanation:
√{23×3-2}=√{69-2}=√67 is your answer
Work out the size of angle A.
A
11 cm
9 cm
38°
B
С
The function N(t) = 100e^−0.023t models the number of grams in a sample of cesium-137 that remain after t years. On which interval is the sample's average rate of decay the fastest?
Options:
A. [1,10] B. [10,20] C. [15,25] D. [1,30]
Answer:
A. [1,10]
Step-by-step explanation:
Given
[tex]N(t) = 100e^{-0.023t}[/tex]
Required
Interval with the fastest rate of decay
The rate of change over [a,b] is calculated as:
[tex]Rate = \frac{N(b) - N(a)}{b - a}[/tex]
So, we have:
A. [1,10]
[tex]Rate = \frac{N(10)-N(1)}{10 - 1}[/tex]
[tex]Rate = \frac{N(10)-N(1)}{9}[/tex]
Calculate N(10) and N(1)
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{79.45-97.73}{9} = \frac{-18.28}{9} = -2.03[/tex]
B. [10,20]
[tex]Rate = \frac{N(20)-N(10)}{20 - 10}[/tex]
[tex]Rate = \frac{N(20)-N(10)}{10}[/tex]
Calculate N(20) and N(10)
[tex]N(20) = 100e^{-0.023*20} = 100e^{-0.46} = 63.13[/tex]
[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]
So:
[tex]Rate = \frac{63.13 - 79.45}{10} = \frac{-16.32}{10} = -1.632[/tex]
C. [15,25]
[tex]Rate = \frac{N(25)-N(15)}{25 - 15}[/tex]
[tex]Rate = \frac{N(25)-N(15)}{20}[/tex]
Calculate N(25) and N(15)
[tex]N(25) = 100e^{-0.023*25} = 100e^{-0.575} = 56.27[/tex]
[tex]N(15) = 100e^{-0.023*15} = 100e^{-0.345} = 70.82[/tex]
So:
[tex]Rate = \frac{56.27 - 70.82}{10} = \frac{-14.55}{10} = -1.455[/tex]
D. [1,30]
[tex]Rate = \frac{N(30)-N(1)}{30 - 1}[/tex]
[tex]Rate = \frac{N(30)-N(1)}{29}[/tex]
Calculate N(30) and N(1)
[tex]N(30) = 100e^{-0.023*30} = 100e^{-0.69} = 50.16[/tex]
[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]
So:
[tex]Rate = \frac{50.16 - 97.73}{29} = \frac{-47.57}{29} = -1.64[/tex]
By comparing the values of the calculated rates,
-2.03 is the smallest, in other words; the fastest rate
Hence, the interval [1,10] has the fastest rate of decay
The required average rate of change is the fastest on [tex][1,10][/tex].
The average rate of change :The formula for the average rate of change on the interval [tex][a,b][/tex] is,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{b-a}[/tex]
Now, applying the given function into the above function is,
Now, [tex]a=1,b=10[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{10-1} =-2.03[/tex]
Now, [tex]a=10,b=20[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{20-10} =-1.6325[/tex]
Now, [tex]a=15,b=25[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{25-15} =-1.455[/tex]
Now, [tex]a=1,b=30[/tex] then,
[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{30-1} =-1.64[/tex]
So the average rate of change is fastest on [tex][1,10][/tex]
Learn more about the topic of the average rate of change:
https://brainly.com/question/20884505
What is the answer to the problem 4x + 6x
Answer:
10x lmboooo
Step-by-step explanation:
combine like terms
Answer:
10x.
Why? Well because 4 + 6 = 10. And since they both are x values the sum is 10x.
Step-by-step explanation:
Hope that this helps! :)
Have great rest of your day/night!
What is the product of 5.2 x 10^4 and 1.3 x 10^-2?
a. 6.76×10^8
b. 6.76×10^2
c. 6.76×10^-2
d. 6.76×10^-8
Answer:
B is the answer.
6.76×10^2
Brandon just bought a new coffee table. The length of the coffee table is 5 more than 3 times the width. If the perimeter of the coffee table top is 58 inches, what is the length and width of the coffee table?
Answer:
The length is 23 inches and the width is 6 inches.
Step-by-step explanation:
The perimeter for a rectangular shape is represented as:
P = 2L + 2W, where L represents length and W represents width
We can represent the length as:
L = 3W + 5
Substituting this into the perimeter function, we get:
P = 2 (3W + 5) + 2W
Substituting 58 for P, we get:
58 = 2 (3W + 5) + 2W
58 = 6W + 10 + 2W
58 = 8W + 10
58 - 10 = 8W + 10 - 10
48 = 8W
48 / 8 = 8W / 8
6 = W
With 6 being the established value for the width, we can substitute this back into the equation for length:
L = 3W + 5
L = 3(6) + 5
L = 18 + 5
L = 23
To check our work, we can substitute both the width and length into the perimeter equation:
P = 2L + 2W
58 = 2(23) + 2(6)
58 = 46 + 12
58 = 58
Therefore, length is 23 inches and the width is 6 inches.
There are two bags containing only purple and yellow marbles. Bag A has yellow marbles and purple marbles. Bag B has yellow marbles and purple marbles. A marble is randomly chosen from each bag. List these events from least likely to most likely. Event : choosing a purple marble from Bag B. Event : choosing a yellow or purple marble from Bag A. Event : choosing a red marble from Bag B. Event : choosing a yellow marble from Bag A.
Charles inherited $500,000 from his grandfather. He decides to invest the money into a fund that has 4% annual interest. If the interest is compounded continuously, what is the total amount that is compounded annually?
Answer:
this is answer$10,000$1o,5oo ok
Help will mark brainliest no links it trolls. Thx
Answer:
the answer to this question is 22ft
Student A starts with $100 in the bank and makes $5 a day. Student B starts with $50 and makes $7 a day. Assuming the students save their money, when will they have the same amount of money ?
Answer:
No. They will not have the same amount of money.
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.875/100
r = 0.03875 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 10,000.00(1 + 0.03875/12)(12)(7.5)
A = 10,000.00(1 + 0.003229167)(90)
A = $13,366.37
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 3.875% per year compounded 12 times per year over 7.5 years is $13,366.37. Therefore, they cannnot save the same amount.
5x-4<4(1+x) what is the answer and how do you do it
Answer:
Step-by-step explanation:
5x-4<4(1+x)
5x-4<4+4x
5x-4x<4+4
x<8
Find an expression for the area of the rectangle. Write your answer in standard form.
Answer:
B. 8x² + 18x - 5
Step-by-step explanation:
(2x + 5)(4x - 1)
Use the distributive property to multiply 2x + 5 by 4x - 1.
8x² - 2x + 5(4x) + 5(-1)
8x² - 2x + 20x - 5
Combine 20x and -2x to get 18x.
8x² + 18x - 5
The expression for the area of the rectangle is 8x² + 18x - 5, which is B.
Make “a” the subject of the following formula
y + az = z
Write the equation of the line shown in the graph below
Can someone please help both of these
Answer:
4x/3-2
-x/2 +5
this are the answers
esme takes the bus to university 40 times during a term to relative frequency of the bus being late is 0.3
how many times is the bus late ?
Answer:
I Don't know....
Step-by-step explanation:
sry.....
Answer: 12
Step-by-step explanation:
So.
40 multiplied by 0.3 is 12
Enter the equation of the circle with the given center and radius.
Center: (9, 0)
radius: √5
Answer:
(x - 9)² + y² = (√5)² = 5
Step-by-step explanation:
Start with the standard equation of a circle with center at (h, k) and radius r:
(x - h)^2 + (y - y)^2 = r^2
Now substitute 0 for k, 9 for h and √5 for r:
(x - 9)² + (y - 0)² = (√5)², which simplifies to:
(x - 9)² + y² = (√5)² = 5
Greg rented a truck for one day. There was a base fee of $15.95, and there was an additional charge of 85 cents for each mile driven Grey had to pay $159.57
when he returned the truck For how many miles dhe drive the truck
Answer:
168.964706 miles
Step-by-step explanation:
Turn the info into a equation: 159.57 = .85x + 15.95
Solve for x (miles)
159.57 = .85x + 15.95
143.62 = .85x
x = 168.964706
Marissa's work to find the missing
length of the triangle is shown.
Explain Melissa's error.
24 units
az + b2 = c2
102 + 242 = c2
100 + 576 = C2
676 = C2
V676 = 0
338 = C
10 units
Step-by-step explanation:
She has done one mistake at last that under root 676 is not equal to 338, rather it is equal to 26.
Hope it helps ^_^
Johnny Rockefeller had a bad credit rating and went to a local cash center. He took out a $100.00 loan payable in two weeks for
$109.00. What is the percent of interest paid on this loan? (Do not round intermediate calculations. Round your answer to the
nearest whole percent.)
Percentage of interest paid
HELP!!!
Answer:
[tex]33 {5 = > { <}^{2} }^{2} }^{2} }^{?} [/tex]
Sally has a car that accelerates at 5 m/s^2. If the car has a mass of 1000 kg, how much force does the car produce?
F=______
m=______
a=______
Answer:
You have to use the equation F=ma.
F: the force an object has (in this case the unknown)
M: the mass an object has (in this case 1000kg)
A: the acceleration an object has (in this case 5m/s^2)
when you plug in everything you should get F=5000N
Answer:
The answer is 5000 N (Newtons).
Explanation:
F=M*A
F=1000 kilograms * 5 m/s squared
F=5000 Newtons
The American antelope (pronghorn) and the wildebeest are among the fastest mammals on the planet,
particularly at running long distances. The maximum recorded speed for the antelope is 88.5 km/h, which it
can sustain for nearly one kilometer.
On the other hand, the distance, d, in kilometers that the wildebeest can run in t hours is given by the equation
d=80.5t
Assuming both animals are running at constant speeds, which animal can run faster?
Choose 1 answer:
The American antelope
B
The wildebeest
They can run at the same speed.
Answer:
The Wildebeest
Step-by-step explanation:
I’m guessing
Answer:
Correct answer is a
Step-by-step explanation:
If a coin and a is die is rolled at same time how many outcomes are possible? Please help me
Answer:
Answer:
12
Step-by-step explanation:
a coin has two possibilities: Head and Tales
a die has six possibilities: 1, 2, 3, 4, 5, 6
2x6=12
can guys help me please
Answer:
there is 243.84 cm in 8 feet
round to the nearest hundredths =3266.53
please help me. i will give give brainlist. and i will give 5 stars. links will be reported. please follow the directions on the page.
Answer: Graph is not possible here, but i can say plotting point
for first equation (0,3) (2,4) (4,10)
for second equation ( 0,-3) ( 2,-4) (4,-10) plot yourself
Step-by-step explanation:
Can you please help me
nvm there is the right answer
Are the ratios 4:18 and 2:9 equivalent?
yes
no
Answer:
yes
Step-by-step explanation:
Step-by-step explanation:
Two ratios are given to us and we need to tell whether they are equivalent or not . Firstly let us say we have two ratios q:p and r:s . Here p & q are co-primes and r & s are also co-primes. Then the two ratios will be equal if and only if
q = rp = s .Theefore , the Ratios are ,
[tex]\begin{cases}\tt 4 : 18 \\\tt 2:9 \end{cases}[/tex]
Here we see that the ratio 2:9 is in simplest form that is HCF of 2 & 9 is 1 . But here 4:18 is not in simplest form . HCF of 4 & 18 is not 1 it's 2 .On dividing numerator and denominator by 2 , we have ,
[tex]\tt= \dfrac{4}{18}\\\\ = \tt \dfrac{4 \div 2}{18\div 2}\\\\ = \boxed{\orange{\tt \dfrac{2}{9}}}[/tex]
Therefore since the Ratios are equal in the simplest form . Therefore the Ratios are equal.
Giving brainliest for the correct answer
Answer:
72 is the surface area
SA=2lw+2lh+2hw
l=6
w=3
h=2
Which point is located at -8.65?
Answer: point b
Step-by-step explanation:
eatch mark on the line is 0.1, b is right behind the 8.6 mark in the middle making it 8.65
Answer:
The answer is point b.
Step-by-step explanation:
1) (-13 ) + (-5) =
6) (+5 ) x ( +4 ) =
2) (+17) + (-9 ) =
7) ( +3 ) x ( 6 ) =
3) (-9)-(-5) =
8) ( 8 ) x ( -7 ) =
4) (+9) - (-12 ) =
9) (-14 ) = (+2) =
5) (-10) - (-10 ) =
10) (-16) = ( 8 ) =
PLEASE HELP!!!!! Due to 20 mins!!!! i'll give points
Answer:
1)-18
2)8
3)-4
4)21
5)0
6)20
7)18
8)-56
Step-by-step explanation:
f(x) = 3x - 5 for x < -5
f(x) = 5 for 5 < x < 4 4
f(x) = -2x + 5 for 4 < x
piecewise function
the principal likes to keep the ratio of students to teachers at 24:1 if he has hired 32 teachers then how many students are expected to enroll
Answer:
768 students are expected to enroll
Step-by-step explanation:
24 : 1
? : 32
24 times 32 = 768