Answer:
an = -3 · an - 1 where a1 = -1.
Step-by-step explanation:
The first term a1 = -1 and the common ratio is -3 so ecah term is formed form the previous one by multiplying by -3.
Find the value of x. Round to the nearest degree. Explain step by step
the half life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial amount . The half-life of the radioactive gas radon is approximately 3.8 days. The initial amount of radon used in an experiment is 75 grams. if N represents the number of grams of radon remaining t days after the start of the experiment,
a. Write an equation that gives N in terms of t.
b. How much gas radon approximately remains after 3.8 days?
c. approximately when will the amount of radon remaining be 10 grams?
Using an exponential function, it is found that:
a) [tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
b) 37.5 grams of the gas remains after 3.8 days.
c) The amount remaining will be of 10 grams after approximately 11 days.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.Item a:
We start with 75 grams, and then work with a half-life of 3.8 days, hence the amount after t daus is given by:
[tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
Item b:
This is N when t = 3.8, hence:
[tex]N(t) = 75(0.5)^{\frac{3.8}{3.8}} = 37.5[/tex]
37.5 grams of the gas remains after 3.8 days.
Item c:
This is t for which N(t) = 10, hence:
[tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
[tex]10 = 75(0.5)^{\frac{t}{3.8}}[/tex]
[tex](0.5)^{\frac{t}{3.8}} = \frac{10}{75}[/tex]
[tex]\log{(0.5)^{\frac{t}{3.8}}} = \log{\frac{10}{75}}[/tex]
[tex]\frac{t}{3.8}\log{0.5} = \log{\frac{10}{75}}[/tex]
[tex]t = 3.8\frac{\log{\frac{10}{75}}}{\log{0.5}}[/tex]
[tex]t \approx 11[/tex]
The amount remaining will be of 10 grams after approximately 11 days.
More can be learned about exponential functions at https://brainly.com/question/25537936
A triangle has two sides of length 1 and 8. What is the smallest possible whole-number length for the third side?
Answer:
8
Step-by-step explanation:
For the smallest possible length, this has to be one of the shorter sides. Let the length of this side be x.
So, by the triangle inequality theorem, 1+x>8, which means x>7.
So, the smallest possible whole number length is 8.
Choose the appropriate table for the differential equation dy/dx=x+1/x
Answer: 1.
x |0|0.5|2
dy/dx |2|5 |undefined
2.
x |0 |0.5| 2
dy/dx |undefined|5 | 2
3.
x | 0 |0.5|2
dy/dx|undefined |4 |2
Step-by-step explanation:
Understanding Distance Units
х
Stephen Kiprotich, the 2012 Olympic marathon winner,
completed the 26.219 miles in 128 minutes. What was
his speed in kilometers per minute? ?
What steps should you take to solve this problem?
Answer:
divide
Step-by-step explanation:
divide 26.216 and 128 to get ur anser
Eva is solving the equation 4(x+3/2)=8 She says, “I can subtract 3/2 from each side to get 4x=13/2 and then divide by 4 to get x=13/8."
Answer:
Wrong
Step-by-step explanation:
Eva must subtract 4*3/2=6 from each side to get 4x=2, the divide by 4 to get x=1/2
Another way:
First, divide both sides with 4 to get x+3/2=2. Then subtract 3/2 from each side and we will have x= 2-3/2= 1/2
what percent of 32 is 5.6
Answer:
17.5 %
Step-by-step explanation:
5.6 is 17.5 percent of 32
Joey has 23 cards in his baseball card collection. Monica has 24 cards in her collection. How many times more cards does Monica have than Joe?
Answer:
Monica has 1 more card than Joey
Step-by-step explanation:
its simple math
At Frome International train station, 35% of trains were late in a week.
In that week there were 440 trains.
Calculate how many trains were on time.
Answer: Two rational numbers between 1/3 and 1/5 are 4/15 and 7/39.
Step-by-step explanation:
Jill wants to have ride at least 144 miles on her bike. Her riding speed is 9 miles per hour. Which inequality(s) represents how many h hours she needs to ride?
Hey there!
Let's make an equation
=> 9h = 144
{ Make h the subject of formula}
=> 9h = 144
=> 9h/9 = 144/9
=> h = 144/9
=> h = 16
Find the area of the figure. Use 3.14 for π.
Total Area:- Area of square + area of Semicircle
Total area :- (L×B)+ (½× πr²)
Total area:- (12×12)+(½×π6²)
Total area:- 144+(½× 113)
Total area:- 144+ 56.5
Total area :- 200.5
Please help to solve this question
Answer:
Step-by-step explanation:
Please help will give brainlest! locks in 30 min!
Answer:
1
Step-by-step explanation:
[tex] \tan( \frac{5\pi}{4} ) \times \frac{\pi}{180} = 1.19[/tex]
The question wants in radian, not in degrees since using the unit circle. Hope this helps
Answer:
a) 1
Step-by-step explanation:
Tan 5pi/4: 1
Tan (-5pi/4): -1
Tan 5pi/4 in degrees: tan (225°)
Find the Area of the shaded part.
To find the area of the shaded part we have to subtract the rectangle area from the triangle area :
[tex]s = \frac{1}{2} \times (8x + 2)(6x) - (x)(3x + 1) \\ [/tex]
[tex]s = \frac{1}{2} \times (48 {x}^{2} + 12x) - (3 {x}^{2} + x) \\ [/tex]
[tex]s = \frac{48}{2} {x}^{2} + \frac{12}{2} x - 3 {x}^{2} - x \\ [/tex]
[tex]s = 24 {x}^{2} + 6x - 3 {x}^{2} - x[/tex]
[tex]s = 24 {x}^{2} - 3 {x}^{2} + 6x - x[/tex]
[tex]s = 21 {x}^{2} + 5x[/tex]
And we're done
Have a great day ♡
Can you reflect an angle over the line y = -x? Explain.
O No, there is not a way to map the vertex of the preimage angle to the vertex of the image angle.
Yes, only angles can be reflected over diagonal lines.
O No, you cannot reflect angles over diagonal lines.
O Yes, you can reflect angles, or any object, in the coordinate plane over any line in the plane.
Answer: Yes, only angles can be reflected over diagonal lines.
Step-by-step explanation:
see photo
B^2-6b+9 b=2 evaluate the expression
Answer:
the answer is 5 :)
Step-by-step explanation:
B^2-6b+9 b=2
2^2-6(2)+9
8-6(2)+9
8-12+9
-4 + 9
=5
A circular pizza that is 17 inches in diameter is cut into 6 equal slices. What is the area of one of the slices?
The area of one slice is in?
Answer:
51
Step-by-step explanation:
17x6=51
WHO IS GOOD AT MATH AND CAN HELP ME WITH 20 QUESTIONS
The rectangular prisms shown are packed with unit cubes. Match the rectangular prisms that have the same volume.
Answer:
Step-by-step explanation:
In order to find which prisms have the same, we use the formula:
A = L x W x H (Area = Length x Width x Height)
So, count the individual squares on each side, multiply them, and that is the area. Then, find which ones are the same:
Cube 1: A = 4 x 4 x 3 = 48
Cube 2: A = 6 x 4 x 2 = 48
Cube 3: A = 4 x 3 x 3 = 36
Cube 4: A = 8 x 2 x 2 = 32
Cube 5: A = 4 x 2 x 4 = 32
Cube 6: A = 6 x 2 x 3 = 36
So, Cube 1 and Cube 2 are the same with 48.
Cube 3 and Cube 6 are the same with 36.
Cube 4 and Cube 5 are the same with 32.
:)
Answer: 1 and 2, 4 and 5, and 3 and 6.
Step-by-step explanation: To find the volume of a rectangular prism, you multiply the length, width, and height to get the volume. The volumes for each cube is in the order of top left and continue until the bottom right.
48 cubic units.48 cubic units.36 cubic units.32 cubic units.32 cubic units.36 cubic units.From there, you can match them, and then your answer is complete.
Let me know if this is right! :)
One number is 32 more than another. Their product is −256.
Answer:
ok so this is a system of equations
x+32=y
x*y=-256
so lets just make y x+32
x^2+32=-256
-32
x^2=-288
find root
this can't be solved since negitive numbers don't have roots
Hope This Helps!!!
Find the range of:
8, 14, 6, 12, 11,9
The steps below show the incomplete solution to find the value of x for the equation 8x − 3x − 1 = −2 + 16:
Step 1: 8x − 3x − 1 = −2 + 16
Step 2: 8x − 3x − 1 = 14
Step 3: 5x − 1 = 14
Which of these is most likely the next step?
5x = 14
5x = 10
5x = 13
5x = 15
Answer:
5x=15. I hope it can help you a lots. thanks.
Step-by-step explanation:
5x=14+1
5×=14.
solve each system.
(x-1)^2 - (x+2)^2 = 9y
(y-3)^2 - (y+2)^2 = 5x
Answer:
Step-by-step explanation:
y=−2x + 1 over 3
x intercept (1,0)
y-intercept(s): (0,1/2)
hope this helps, you didnt give an exact thing to solve about them.
In an amusement park ride, a rider suspended by cables swings back and forth from a tower. The maximum speed v (in meters per second) of the rider can be approximated by v=2gh, where h is the height (in meters) at the top of each swing and g is the acceleration due to gravity (g≈9.8 m/sec^2). Determine the height at the top of the swing of a rider whose maximum speed is 15 meters per second. Round your answer to the nearest tenth.
According to the equation for the maximum speed, it is found that the height at the top of the swing of the rider is of 0.8 m.
What is the equation for the maximum speed?As stated in the problem, it is given by:
v = 2gh.
In which:
v is the maximum speed.g is the gravity.h is the height.In this problem, the parameters are g = 9.8, v = 15. Hence we can solve for h to find the height.
v = 2gh
2 x 9.8h = 15
19.6h = 15
h = 15/19.6
h = 0.8.
The height at the top of the swing of the rider is of 0.8 m.
More can be learned about functions at https://brainly.com/question/25537936
Can someone please help me out with this question?
Answer:
A. x=6, y=3
Find the point where the two lines intersect and find the x and y coordinates where they intersect.
Find of 14. 3/7
A. 3
B. 5
C. 6
D. 2
Answer:
C. 6.
Step-by-step explanation:
3/7 of 14
= 3*14/7= 42/7
= 6.
Which model best fits the data shown in the scatterplot?
A. y=-0.7x+1.9
B. y = 0.7x+1.9
C. y=-0.7x-3.8
D. y=1.9x-07
Answer:
A. y = -0.7x + 1.9
Step-by-step explanation:
The y-intercept is roughly +2 as you can see from the scatterplot therefore ⇒ Not option C or D [both of which are negative]The slope is slanted from top left to right bottom [meaning the slope is negative] ⇒ Not BThe correct option is AThe human resources manager at a company records the length, in hours, of one shift at work, X. He creates the probability distribution below. What is the probability that a worker chosen at random works at least 8 hours? A probability distribution has the number of hours on the x-axis and the probability on the y-axis. The probability of 6 hours is 0. 02; 7 hours is 0. 11; 8 hours is 0. 61; 9 hours is 0. 15; 10 hours is 0. 9. 0. 62 0. 78 0. 84 0. 96.
The probability that a worker chosen at random works at least 8 hours is Option C: 0.84 approx.
How to evaluate the probability of a random variable getting at least some fixed value?Suppose the random variable in consideration be X, and it is discrete.
Then, the probability of X attaining at least 'a' is written as:
[tex]P(X \geq a)[/tex]
It is evaluated as:
[tex]P(X \geq a) = \sum_{\forall \: x_i \geq a} P(X = x_i)[/tex]
The probability distribution of X is:
x f(x) = P(X = x)
6 0.02
7 0.11
8 0.61
9 0.15
10 0.09
Worker working at least 8 hours means X attaining at least 8 as its values.
Thus, probability of a worker chosen at random working 8 hours is
P(X ≥ 8) = P(X = 8) + P(X = 9) +P(X = 10) = 0.85 ≈ 0.84 approx.
By the way, this probability distribution seems incorrect because sum of probabilities doesn't equal to 1.
The probability that a worker chosen at random works at least 8 hours is Option C: 0.84 approx.
Learn more about probability distributions here:
https://brainly.com/question/14882721
Find the equation of a line that passes through the point (1,-4) and has a gradient of 2. Leave your answer in the form y = m x + c
Answer:
Step-by-step explanation:
(1,-4) m=2
first find c
-4=2×1+c
c=-6
y=2x+-6
write an absolute value equation in the format lx-bl=c (where b is a number and c could be both a number or expression) with one solution x=-3
6
It costs 35p per minute to hire a powerful computer. How much will it cost to hire the
computer from 07:40 to 08:15?
Answer:
1225p
Step-by-step explanation:
1 minute = 35p
07:40 to 08:15 : 35 minute
=> 35 minute *35p=1225p