Step-by-step explanation:
[tex]here \: is \: your \: solution : - \\ \\ GIVEN \: \: -:- \\ \\ = > \: area \: of \: circle \: = 616 \: m {}^{2} \\ \\ \ = > pi = 22 \div 7 \\ \\ = > we \: need \: to \: find \: radius \: \\ \\ = > area \: of \: circle \: = \pi \: r {}^{2} \\ \\ = > \: \pi \: r {}^{2} = 616 \: m {}^{2} \\ \\ = > \: r {}^{2} \times (22 \div 7) = 616 \\ \\ = > \: r {}^{2} =( 616 \times 7) \div 22 \\ \\ = > \: r { }^{2} = 4312 \div 22 \\ \\ = > r {}^{2} = 196 \\ \\ = > \: r = \sqrt{196} \\ \\ = > \: r = 14 \: \: \: (ANSWER✓✓✓) \\ \\ HOPE \: IT \: HELPS \: YOU \: (◕ᴗ◕✿)[/tex]
The mass, m grams, of a radioactive substance, present at time t days after first being observed, is given by the formula m=24e^-0.02t. Find
(i) the value of m when t=30.
(ii) the value of t when the mass is half of its value at t=0.
(iii) the rate at which the mass is decreasing when t=50.
Answer:
(i) The value of m when t = 30 is 13.2
(ii) The value of t when the mass is half of its value at t=0 is 34.7
(iii) The rate of the mass when t=50 is -0.18
Step-by-step explanation:
(i) The m value when t = 30 is:
[tex] m = 24e^{-0.02t} = 24e^{-0.02*30} = 13.2 [/tex]
Then, the value of m when t = 30 is 13.2
(ii) The value of the mass when t=0 is:
[tex] m_{0} = 24e^{-0.02t} = 24e^{-0.02*0} = 24 [/tex]
Now, the value of t is:
[tex] ln(\frac{m_{0}/2}{24}) = -0.02t [/tex]
[tex] t = -\frac{ln(\frac{24}{2*24})}{0.02} = 34.7 [/tex]
Hence, the value of t when the mass is half of its value at t=0 is 34.7
(iii) Finally, the rate at which the mass is decreasing when t=50 is:
[tex] \frac{dm}{dt} = \frac{d}{dt}(24e^{-0.02t}) = 24(e^{-0.02t})*(-0.02) = -0.48* (e^{-0.02*50}) = -0.18 [/tex]
Therefore, the rate of the mass when t=50 is -0.18.
I hope it helps you!
Marcella incarica Dora di aiutarla a suddividere 35 perle tra le sue tre figlie. Alla figlia maggiore vuole regalare la metà, alla mediana la terza parte e alla minore la nona parte. Inoltre Marcella vuole dare una perla a Dora come ricompensa. Quante perle riceverà ciascuna figlia?
Answer:
La hija mayor recibirá 17.5 perlas, la hija del medio recibirá 11.66 perlas, y la hija menor recibirá 3.88 perlas.
Step-by-step explanation:
Dado que Marcella le pide a Dora que la ayude a dividir 35 perlas entre sus tres hijas, y quiere darle la mitad a la hija mayor, la tercera parte a la del medio y la novena a la menor y, además, Marcella quiere darle una perla a Dora como recompensa, para determinar cuántas perlas recibirá cada hija se debe realizar el siguiente cálculo:
35 / 2 = Mayor = 17.5 perlas
35 / 3 = Medio = 11.66 perlas
35 / 9 = Menor = 3.88 perlas
Así, la hija mayor recibirá 17.5 perlas, la hija del medio recibirá 11.66 perlas, y la hija menor recibirá 3.88 perlas.
Part 1- Make sure to show all work. Write both the (i) recursive formula and the (ii) explicit formula for the sequences
A) {-23,-15,-7,1,...}.
B) {5, 5.25, 5.50, 5.75,...}
Part 2- Calculate the 15th term in each of the above sequences, Use the Recursive method for one sequence and the Explicit formula for the other sequence. (make sure to label your work & show each step).
Answer:
A) The sequence is {-23, -15, -7, 1,...}
The common difference of the sequence above, d = 8
The first term, a = -23
The number of terms, n = 15
The recursive formula is, aₙ = aₙ₋₁ + d
Using the recursive method gives;
a₅ = a₍₅₋₁₎ + d
Where;
a₍₅₋₁₎ = 1
Therefore, a₅ = 1 + 8 = 9, a₆ = 9 + 8 = 17, a₇ = 17 + 8 = 25, a₈ = 25 + 8 = 33, a₉ = 33 + 8 = 41, a₁₀ = 41 + 8 = 49, a₁₁ = 49 + 8 = 57, a₁₂ = 57 + 8 = 65 a₁₃ = 65 + 8 = 73, a₁₄ = 73 + 8 = 81, a₁₅ = 81 + 8 = 89
The 15th term of the sequence, {-23, -15, -7, 1,...}, a₁₅ = 89
We check by using explicit formula to get, aₙ = a + (n - 1)·d
Therefore
a₁₅ = -23 + (15 - 1)×8 = 89
B) The given sequence is B) {5 5.25, 5.50, 5.75,...}
The common difference, d = 0.25
The first term, a = 5
The required number of terms, n = 15
Using the recursive method gives;
a₅ = a₍₅₋₁₎ + d
Where;
a₍₅₋₁₎ = a₄ = 5.75
Therefore, a₅ = 5.75 + 0.25 = 6
a₆ = 6 + 0.25 = 6.25, a₇ = 6.25 + 0.25 = 6.5, a₈ = 6.5 + 0.25 = 6.75, a₉ = 6.75 + 0.25 = 7, a₁₀ = 7 + 0.25 = 7.25, a₁₁ = 7.25 + 0.25 = 7.5, a₁₂ = 7.5 + 0.25 = 7.75, a₁₃ = 7.75 + 0.25 = 8, a₁₄ = 8 + 0.25 = 8.25, a₁₅ = 8.25 + 0.25 = 8.5
The 15th term, of the sequence, {5 5.25, 5.50, 5.75,...}, a₁₅ = 8.5
We check by explicit formula to get, aₙ = a + (n - 1)·d
Therefore
a₁₅ = 5 + (15 - 1)×0.25 = 8.5
Step-by-step explanation:
please help so I can watch Coop and Cami ask the world
Step-by-step explanation:
Simple interest=principal x rate x time÷100
amount borrowed=$500
I=$500x7x6÷100
I=$210
therefore you will pay
amount borrowed+interest
$500+$210
$710
hope this is helpful
Help pls it’s the last day of summer school
Rectangle PQRS is rotated 90° clockwise about the origin.
On a coordinate plane, rectangle P Q R S has points (negative 3, negative 1), (negative 1, negative 1), (negative 1, negative 4), (negative 3, negative 4).
What are the coordinates of R’?
R’(4,–1)
R’(–4,1)
R’(1,4)
R’(–1,–4)
Answer:
R' (-4 , 1)
Step-by-step explanation:
Rotation of 90°
(Clockwise)
(x, y) ----> (y, -x) (take opposite of x, then switch the x and y)
Rotation of 90°
(CounterClockwise)
(x, y)------>(-y, x)
Rotation of 180°
(Both Clockwise and Counterclockwise)
(x, y) ----->(-x, -y)
Rotation of 270°
(Clockwise)
(x, y) ----->(-y, x)
Rotation of 270°
(CounterClockwise)
(x, y)------>(y, -x)
Answer:
The answer is: R'(-4,1).
Step-by-step explanation:
If the 90 degree angle is clockwise, the new figure will be in quadrant 2 (or in the section directly above the pre-image). Therefore, (x,y) maps to (y,-x), which will give us (-4,1).
PLEASE HURRY!! NEED IT ASAP!! WILL MAKE BRAINLIEST
Question 1 of 10
Which choice is equivalent to the expression below when y > or equal to 0?
Answer:
I think B
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
[tex]\sqrt{y^3} +\sqrt{9y^3} -3y\sqrt{y} \\=\sqrt{y^2 *y} +\sqrt{9*y^2*y} -3y\sqrt{y} \\=y\sqrt{y} +3y\sqrt{y} -3y\sqrt{y} \\=y\sqrt{y}[/tex]
To the nearest square metre, calculate the curved surface area of the half pipe if it is 9m long? (With a radius of 2.5m)
Answer:
70.686 [tex]m^{2}[/tex]
Step-by-step explanation:
A=2πrh (area of cylinder without top or bottom)
A = 2[tex]\pi[/tex](2.5)(9)
A = 141.372
divide by two for half of pipe.
A = 70.686
someone help me please with this algebra homework
Answer:
the 4th option
Step-by-step explanation:
the 4th one
Answer:
D. 2.99x + 12.99y = 43.92
Step-by-step explanation:
1 pair of socks costs $2.99
x pairs of socks cost 2.99x
1 blouse costs $12.99
y blouses cost 12.99y
The total cost is the sum of the two costs
2.99x + 12.99y
We are told the total cost is $43.92
2.99x + 12.99y = 43.92
Answer: D. 2.99x + 12.99y = 43.92
a trio and a quartet got together and played a song how many musicians were there?
Answer:
7
Step-by-step explanation:
trio meaning 3 quartet (quart) 4
If f(x) = k where k is a constant, and the
points (6, 1) and (8, 1) lie on the graph of y
= f(x), what is the value of f(0)?
Answer:
f(0) = 1Step-by-step explanation:
Since f(x) = k, is constant the value of k is same for any x.
From the given points we see:
f(6) = 1 and f(8) = 1It means k = 1 and the function is:
y = f(x) = 1The value of f(0) = 1
A bag contains 6 black tiles, 5 white tiles, and 4 blue tiles. Event A is defined as drawing a white tile from the bag on the first draw, and event B is defined as drawing a black tile on the second draw. If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in simplest form? A. 4/45 B. 1/7 C. 4/15 D. 5/14
Answer:
5/14
Step-by-step explanation:
There are 15 tiles in total
5 white| 6 black | 4 blue
event A results in the subject pulling a white tile and not replacing it
5-1= 4
so the first answer should be 4/15
event B results in the subject pulling another tile, a black one and not replacing it.
6-1= 5
given this answer, there is one less tile in the total, since we removed another tile.
So our answer would be-
5/14 or D
1. In a board game, you must roll two 6-sided number cubes. You can only start the game if you roll a 3 on at least one of the number cubes.
(a) Make a list of all the different possible outcomes when two number cubes are rolled.
(b) What fraction of the possible outcomes is favorable?
(c) Suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? Explain. Answer:
Answer:
34
Step-by-step explanation:
You should not expect more than 34 times to be favorable, because favorable outcomes are about 28% of outcomes, and 28% of 100 is 28, which is less than 34.
6/21 outcomes will be favorable.
Here is a list of all possible :
1 - 1
1 - 2
1 - 3
1 - 4
1 - 5
1 - 6
2 - 2
2 - 3
2 - 4
2 - 5
2 - 6
3 - 3
3 - 4
3 - 5
3 - 6
4 - 4
4 - 5
4 - 6
5 - 5
5 - 6outcomes29 out of every 100 outcomes will likely
6 - 6
One or two of the underlined outcomes have a three. The total number of outcomes is 21, and six of them include 3's. Therefore, when we multiply 6/21 by .286, we get 28.6%. be favorable.
Hope this helps! : )
write a function rule for the following data
what is the answer to this?
Answer:
any number
Step-by-step explanation:
It is because all real numbers are solutions to this
Answer:
x = infinite solutions
Step-by-step explanation:
[tex]\frac{2}{3}(6x+ 3) = 4x + 2\\\\\frac{12}{3}x + \frac{2 \times 3}{3} = 4x + 2\\\\4x + 2 = 4x + 2 \\\\Which\ is \ true \ for \ all \ values \ of \ x.[/tex]
what is the slope of the line shown below (6, 6) (1, -4)
Answer:
2
Step-by-step explanation:
if you're looking at the table and you heard of rise/run, your rise is -10 if you go down from (6,6) and -5 if you go left to reach (1,-4). That will give you -10/-5 which gives you a positive 2. it would be the same if you went up 10 from (1,-4) and then 5 right to reach (6,6).
Determine the measure of ZA.
45.6°
57.7°
55.2°
32.3°
Step-by-step explanation:
Cos A = 40^2 + 25^2- 34^2 ÷ (2×40×25)
= 200+625-1156 ÷ (2000)
= 1069 ÷2000
Cos A = 0.5345
A= cos inverse 0.5345
A = 57.7
Answer:
57.7
Step-by-step explanation:
took the test
If (2,1) is the midpoint of the line segment ST and the coordinates of S are (5,4), find the coordinates of T.
Answer:
Step-by-step explanation:
The formula to find the midpoint of a segment is
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex] and we have the midpoint and we also have a coordinate of (5, 4). Let's let x₁ = 5 and y₁ = 4. Filling in what we have:
[tex](2,1)=(\frac{5+x_1}{2},\frac{4+y_2}{2})[/tex] and we'll deal with the x terms first. The x coordinate of the midpoint is 2, so:
[tex]2=\frac{5+x_2}{2}[/tex] and multiply both sides by 2 to get rid of the denominator to get:
4 = 5 + x₂ so
x₂ = -1. Going on to the y coordinate. The y coordinate of the midpoint is 1, so:
[tex]1=\frac{4+y_2}{2}[/tex] and again multiply both sides by 2 to get rid of the denominator to get:
2 = 4 + y₂ so
y₂ = -2
The coordinates of T are (-1, -2)
Help and explain !!!!( Solve using the substitute method )
Answer:
x=13
y= -9
(13, -9)
Step-by-step explanation:
If we are solving using the substitution method, we can take the first equation and set it to y so y=4-x.
Then, we can take that equation and plug it into the bottom one so
3x+4(4-x)=3
Simplify:
3x+16-4x=3
-x=-13
x=13
We can then plug 13 into any of the two given equations (I am just going to plug it into the top one)
So, 13+y=4 which y= -9
Input value for the function machine that gives an output value of 3.
Answer:
x = –1
Step-by-step explanation:
From the question given above, the following data were obtained:
y = √(–2x + 7)
y = 3
x =?
The value of x can be obtained as follow:
y = √(–2x + 7)
3 = √(–2x + 7)
Take the square of both side
3² = –2x + 7
9 = –2x + 7
Collect like terms
9 – 7 = –2x
2 = –2x
Divide both side by –2
x = 2 / –2
x = –1
Last question of this. Please help.
Answer:
26 hours
Step-by-step explanation:
Add all of them up and get 26
Out of the 30 days in June, you run 13 days and swim 6 days. You lift weights 7 days
and ride a bike 4 days. If you make a pie chart to show this data, how many degrees
of the circle should represent swimming?
9514 1404 393
Answer:
72°
Step-by-step explanation:
In a properly constructed pie chart, the proportion of the circle devoted to each section is the same as the proportion of that section to the the whole.
(6 swim days)/(30 days) = (swim pie angle)/(360°)
Multiply by 360° to find ...
swim pie angle = (360°)(6/30) = 72°
72° of the circle should represent swimming.
Leonardo is solving the equation 4 (x minus one-fifth) = 2 and two-thirds. His work is shown. Where is his error?
Answer:
Step 3
Step-by-step explanation:
Leonardo is solving the equation 4 (x minus one-fifth) = 2 and two-thirds. His work is shown. Where is his error?
Given :
4(x - 1/5) = 2 2/3
Open the bracket
4x - 4/5 = 2 2/3
Add 4/5 to both sides
4x - 4/5 + 4/5 = 8/3 + 4/5
Lcm of 3 and 5 = 15
4x = (40 + 12) / 15
4x = 40/15 + 12/15
4x = 52/15
Multiply by 1/4
4x * 1/4 = 52/15 * 1/4
x = 52 / 60
x = 13 / 15
Hence, the error is in step 3
15/5 * 3 = 12
Rather ; Leonardo wrote 16
Find the measure of the indicated side
Answer: X = 8
Step-by-step explanation:
Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12
Answer:
C
Step-by-step explanation:
use Pythagorean theorem
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
c is the longest side
if [tex]a^{2}[/tex] + [tex]b^{2}[/tex] > [tex]c^{2}[/tex] then it's acute (greater than)
if [tex]a^{2}[/tex] + [tex]b^{2}[/tex] < [tex]c^{2}[/tex] then it's obtuse (less than)
if they are equal, then its a right triangle
[tex]6^{2}[/tex] + [tex]10^{2}[/tex] = [tex]12^{2}[/tex]
36 + 100 = 144
136 = 144
136 < 144 obtuse
The correct classification for this triangle is:
obtuse, because 6² + 10² < 12²
Option C is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
To determine the classification of a triangle based on its side lengths, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have a triangle with side lengths of 6 cm, 10 cm, and 12 cm. Checking the sum of the lengths of each pair of sides, we have:
6 + 10 = 16 > 12
6 + 12 = 18 > 10
10 + 12 = 22 > 6
Since all three pairs satisfy the triangle inequality theorem, the given side lengths do form a valid triangle.
Next, we can use the law of cosines to determine the measure of the largest angle in the triangle, which will allow us to classify it.
The law of cosines states that, for a triangle with side lengths a, b, and c, and the angle opposite c denoted as C, we have:
[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]
In this case, the side lengths are a = 6 cm, b = 10 cm, and c = 12 cm. Substituting these values into the formula and solving for cos(C), we get:
cos(C) = (6² + 10² - 12²) / (2 x 6 x 10)
cos(C) = -1/5
Since the cosine function is negative for angles between 90 and 180 degrees, we know that angle C is obtuse.
Therefore,
The correct classification for this triangle is:
obtuse, because 6² + 10² < 12²
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ7
Don't squeeze. Fiver shoppers buy Charmain toilet paper. One charmin out of 10 in this batch is defective-its unsqueezable. You want to save every one from this catastrophe, so you stop them at the door and ask to squeeze their charmin. After squeezing 5 rolls, what is the possibility that you have located 1 or more defective charmins? Hint start off with the chance that you squeezed no defective rolls.
Answer:
The probability of finding aleast one or more defective charmins = 0.40951
Step-by-step explanation:
The probability of not finding a defective charmin = 1
probability of finding defective charmain = 1-0.1 =0.9
The probability of not finding all five defective item =
Then,
probability of not finding all five defective item=0.59049
Thus,
The probability of finding atleast one or more defective chairmins = 1-0.59049
Therefore,
The probability of finding atleast one or more defective chairmins =0.40951
Fiona rolls a fair dice 144 times.
How many times would Fiona expect to roll an even number?
There are 3 even numbers out of 6 total numbers.
Rolling an even number would be 3/6 = 1/2
She would expect half the rolls should be even.
144/2 = 72
The answer is 72 times.
The price of a laptop was first increased by 10% and then the new price was decreased by 20%. The final price was what percent of the initial price.
Answer:
88%
Step-by-step explanation:
to initial price (100%) was increased by 10% (resulting in 110% of the initial price).
then these 110% were decreased by 20%.
so, the final price is actually 80% of 110% of the initial price
20/100 = 1/5
80/100 = 4/5
so, the customer pays only 4/5 of the 110% price.
110 × 4/5 = 22 × 4 = 88%
so, the final price was 88% of the initial price
Someone please tell me what the cube root of x to the power of 3 is?
Answer:
x
Step-by-step explanation:
The cube root of x to the power of 3 is
( [tex]\sqrt[3]{x}[/tex] )³ = ( [tex]x^{\frac{1}{3} }[/tex] )³ = x
or
[tex]\sqrt[3]{x^3}[/tex] = x
Which should equal 105° to prove that f I g?
abcd
Answer:
Step-by-step explanation:
sorry bout the poor drawing but it should be legible
