Answer: 49929 years ago
Step-by-step explanation:
Radiocarbon dating is a method that provides objective age estimates for carbon-based materials that originated from living organisms
To calculate the time, we will use exponential formula
R% = e^ -kt
Where t = number of years
0.25/100 = e^- 0.00012t
Log both sides with natural logarithm
Ln0.0025 = lne^-0.00012t
-5.9915 = -0.00012t
t = 5.9915/0.00012
t = 49928.9 years
Approximately t = 49929 years
The whale died approximately 49,929 years ago.
To determine how long ago the whale died, we use the fact that its vertebrae contain roughly 0.25% as much carbon-14 as they originally did when the whale was alive. This suggests the carbon-14 has decayed, following its known decay rate.
The carbon-14 decay formula is:
N(t) = N0 × [tex]e^{-kt}[/tex]
where:
N(t) is the remaining quantity of carbon-14.N0 is the initial quantity of carbon-14.k is the decay constant (given as 0.00012).t is the time in years.Given that N(t)/N0 = 0.0025, we solve for t:
1. Divide both sides by N0:
0.0025 = [tex]e^{(-0.00012 * t)}[/tex]
2. Take the natural logarithm of both sides:
ln(0.0025) = -0.00012 × t
3. Solve for t:
t = ln(0.0025) / -0.00012
t = −5.991464547/−0.00012
Calculating this, we get:
t ≈ 49928.87 ≈ 49,929 years
Therefore, the whale died approximately 49,929 years ago.
A number cube with the numbers 1 through 6 is rolled. Find the probability of rolling a number different from 9.
Probability of rolling a number different from 9 is 1.
Given,
Cube with numbered 1 to 6.
Now,
Numbers on cube: 1, 2 , 3 , 4 , 5 ,6 .
Then, the sample space is
S= {1, 2, 3, 4, 5, 6}
The probability of rolling a number different from 9,
Since we don't have 9 in the sample space, then the probability of rolling a number different from 9 will be the have 1,2,3,4,5 and 6 as the outcome
Then,
P(rolling number different from 9) = 6 / 6 = 1
P(rolling number different from 9) = 1.
Know more about probability,
https://brainly.com/question/31828911
#SPJ6
F(x)=4x+3x g(x)=2x-5 find (f-g)(x)
Find the missing length
Answer:
9 yd
Step-by-step explanation:
15 yd - 6 yd = 9 yd
Please mark my answer as brainiest
Answer:
9 yd
Step-by-step explanation:
The top has a length of 15 yd
The bottom has a length of 6 +x
15 = 6+x
Subtract 6 from each side
15-6 = 6-6+x
9 = x
9 yds in the missing length
There are 12 white shirts, 8 blue shirts, and 6 red shirts on a rack. Which colors have a ratio of 3:4?
Answer:
8:12 or blue to white
I hope this helps! If it does, please mark brainliest UwU
What is the volume of a sphere with a radius of 4.5 inches?
Use 3.14 for .
Answer:
V≈381.7in³
Step-by-step explanation:
V=4/3πr³
=4/3•π•4.5³
≈381.70351in³
The volume of a sphere with a radius of 4.5 inches, calculated using the volume formula V = 4/3 * π * r^3, comes out to approximately 381.51 cubic inches.
Explanation:The volume of a sphere can be calculated using the formula for volume, V = 4/3 * π * r^3, where V denotes the volume, π is approximately 3.14, and r is the radius of the sphere. In this case, the radius (r) of the sphere is 4.5 inches. Plugging these values into our formula gives:
V = 4/3 * 3.14 * (4.5)^3
When you perform the calculations, you'll find the volume of the sphere to be approximately 381.51 cubic inches.
Learn more about Volume of Sphere here:https://brainly.com/question/32048555
#SPJ2
Rewrite the function to determine whether it represents exponential growth or exponential decay. Identify the percent rate of change. Round numbers to the nearest hundredth, if necessary. y=(1.06)8t In the form y=a(1+r)t, the function is y≈ . To the nearest percent, the rate of change is a %.
Answer:
y ≈1*(1+0.59)^t. The rate of change is = 59%
Step-by-step explanation:
We have t mulitplied by 8 in the expression of y. We can write that power with a power of powers, using the property
[tex]a^{bc} = (a^b)^c = (a^c)^b[/tex]
Therefore,
[tex]a^{8t} = (a^8)^t[/tex]
If we replace a with 1.06, we obtain
[tex] y = 1.06^{8t} = (1.06^8)^t \approx 1.59^t = 1*(1+0.59)^t[/tex]
Thus, y ≈1*(1+0.59)^t. The rate of change is ln(1.59) * 1.59^t. After 1 unit of time t, the rate of change is 0.59*100 = 59%
The given function represents exponential growth with a rate of change of 6%. The function already fits the form y = a(1 + r)^t with a = 1 and r = 0.06.
Explanation:To rewrite the function y = (1.06)^8t in the form y = a(1 + r)^t, we can identify a as the initial amount and r as the rate of change. In this case, the initial amount a is implied to be 1 (since it is not explicitly multiplied by the base), and the base 1.06 represents the growth factor. Seeing as the base is greater than 1, this function represents exponential growth.
The percent rate of change can be found by subtracting 1 from the base and then converting it to a percentage. Therefore, the rate r is 1.06 - 1, which equals 0.06 or 6% when expressed as a percentage. Thus, the function in the requested form is y = (1 + 0.06)^8t, or simplifying the exponent, y = (1.06)^8t.
To the nearest percent, the rate of change is 6%.
Find the value of x
we apply alternate angles approach to solve questions like this
7. It takes ounces of honey to make one apple pie. Betty baked 4 apple
pies. She also baked 4 pecan pies. Each pecan pie takes 4.4 ounces of
honey. How much honey did Betty use to bake the apple and pecan
pies?
ir
Answer:
17.6 ounces to make the pecan pies. I dont know how much honey she used to make the apple pie so if you could pls say I could edit the answer :)
Step-by-step explanation:
Betty used a total amount of honey equal to 4 times the ounces of honey needed for one apple pie plus 17.6 ounces of honey for the pecan pies. The exact total amount of honey used cannot be determined without knowing the amount of honey (x) used in an apple pie.
Explanation:The question is asking how much honey Betty used to bake apple and pecan pies. First we need to determine the amount of honey required per pie and then add the total amounts for each type of pie. Let's say it takes x ounces of honey to make one apple pie. Since Betty baked 4 apple pies, she would use 4x ounces of honey for the apple pies. For the pecan pies, each requires 4.4 ounces of honey, so for 4 pecan pies she would use 4 × 4.4 ounces which equals 17.6 ounces of honey.
To find the total honey used, add the honey used for apple pies and pecan pies: 4x + 17.6 ounces. Without the specific amount of honey for the apple pies (x), we cannot calculate the exact total amount of honey used.
The perimeter of a rectangular field is 368 yards. If the width of the field is 87 yards, what is it’s length
Answer: The length of the rectangle would be 97 yards.
Step-by-step explanation:
87 multiplied by 2 would be 174.
Subtract 174 from 368 to get 194.
194 divided by two equals 97.
To check,
97 plus 97 equals 194.
87 plus 87 equals 174.
174 plus 194 equals 368, the perimeter.
What is 87.5% of 8?
Answer:
7
Step-by-step explanation:
Convert 87.5% to a decimal.
87.5%/100%=.875
Multiply it with 8 to get 7
.875*8=7
Answer:
7
Step-by-step explanation:
h(x) = -5x2 + 10x + 15
What is the height of the stone at the time it is thrown?
Answer:
The height of the stone at the time it is thrown is 15.
Step-by-step explanation:
You have a quadratic function of the form h (x) = ax² + bx + c. In this case it is h (x) = -5x²+10x+15, where a =-5, b =10, c =15, x is the time and h (x) is the height of the stone after being thrown.
The moment the stone is thrown is instant zero. So if x = 0, h (0) is calculated:
h(0)= -5*0² +10*0 +15
h(0)= 0 + 0 + 15
h(0)= 15
The height of the stone at the time it is thrown is 15.
Express this number in standard form.
9.647 x 10^7= ?
Answer: 9647
Step-by-step explanation:
Answer:
9647000
Step-by-step explanation:
Hi I was wondering if I could get help on this please
Answer:
B
Step-by-step explanation:
The equation of line is y=-1/2 x+3 as it takes the form of y=mx+c
From this, the graph having gradient of -1/2 then the line will run from left to right. This eliminates options A and D
The pictures are not clear but we must ensure where the line crosses y intercept, the value of y should be 3 hence the only graph having these properties is option B.
A land surveyor was measuring the distances from various pA land surveyor was measuring the distances from various points on a plot of land. Her measuring tool broke before the last leg measure was determined. Right triangle A B C. Side A C is x, side A B is 12 feet, and hypotenuse B C is 37 feet. The unknown length can be found using the Pythagorean theorem. The theorem states that the of the squares of the legs is the square of the hypotenuse. The missing length is feet.oints on a plot of land. Her measuring tool broke before the last leg measure was determined. Right triangle A B C. Side A C is x, side A B is 12 feet, and hypotenuse B C is 37 feet. The unknown length can be found using the Pythagorean theorem. The theorem states that the of the squares of the legs is the square of the hypotenuse. The missing length is feet.
This is sorta late, but here's the answer for the people who are going to be searching it up in the future:
The first one is sum
The second one is equal to
The third one is 35
Good luck, guys!!
Answer:
sum
equal to
35
Step-by-step explanation:
The theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse.
The missing length is 35 feet.
Please someone answer urgent will give thanks and mark brainliest
What are the solutions of x2+10x+16=0
Which is the graph of r = 4 sin theta
Answer:
the second one
Step-by-step explanation:
Option (b) represents the graph of r = 4 sin θ.
What is polar curve?"A polar curve is a shape constructed using the polar coordinate system."
We have been given a function r = 4 sin θ .
We need to determine the graph for given function.
We know, r = a sin θ is a circle where “a” is the diameter of the circle that has its bottom-most edge at the pole (origin).
This means, r = 4 sin θ is a circle that has bottom-most edge at the origin (0, 0).
In the graph (b), a circle has bottom-most edge at the pole.
Therefore, the correct graph is option (b)
Learn more about polar graphs here:
https://brainly.com/question/19392344
#SPJ2
Can 9,15,20 be a right triangle
With one mighty swipe of his sword, the knight cut off the flying dragon's head. If the dragon's head weighed 56.7 kg, how much force was used by the head to fall to the ground?
Answer:
The force used to fall by the head is
556.3N
Step-by-step explanation:
Given the the dragon's head has a mass m=56.7kg
Let us assume the acceleration due to gravity of the dragon's head is
9.81m/s^2
We know that the force
F=m*g
Substituting our data into the expression we have
F= 56.7*9.81
F= 556.2N
how can you use measures of the center to describe a data set
Measures of the center, such as mode, median, and mean, provide a summary of typical values in a data set.
Explanation:The measures of the center, "such as the mode, median, and mean", provide a summary of the typical values in a data set. The mode is the most frequent value, the median is the middle value, and the mean is the arithmetic average. These measures help describe the central tendency of the data, giving insight into what is considered a typical response or value.
Learn more about Describing data sets using measures of the center here:https://brainly.com/question/31467397
#SPJ12
Volume of a hemisphere when radius is 2.5?
Answer:
that is the solution to the question
A bacterium in a petri dish multiplies by a factor of 31 every day. On day O,
there is 1 bacterium; on day 1, there are 31 bacteria; on day 2, there are
bacteria; on day 3, there are
bacteria, and so on.
What logarithmic equation can be used to find the number of days it takes for
a colony of 1 bacteria to develop?
Answer:
Step-by-step explanation:
Given that,
The bacterial increase a factor of 31 every day ,
Day 0 = 1 bacterium = 31^0
Day 1 = 31 bacterial = 31¹
Day 2 = 31× 31 bacterial = 31²
Day 3 = 31 × 31 × 31 bacterial = 31³
And so on,
Then, nth day will have
Day n = 31ⁿ bacterial
So, when will the bacterial be 1,000,000,000
Then,
31ⁿ = 1,000,000,000
Take the Natural logarithmic to base 31 of both sides
Log_31 (31)ⁿ = Log_31 (1,000,000,000)
n•Log_31 (31) = Log_31 (1,000,000,000)
Then, log_a (a) = 1
n = Log_31 (1,000,000,000)
Check attachment for better view
Then,
The correct answer is A
Consider ΔABC, where ∠C = 90° and ∠A + ∠B = 90°. Click on the statements that are true about the relationships of the angles Angles A and B are complementary angles. If sin A ≈ 0.766, then sin B ≈ 0.766. If sin A ≈ 0.766, then cos B ≈ 0.766. If cos B ≈ 0.766, then the sin A ≈ 0.766,
Answer: Angles A and B are complementary angles
If Sin A ≈ 0.766 then Cos B ≈ 0.766.
If Cos B ≈ 0.766 then Sin A ≈ 0.766
Step-by-step explanation: In any given right angled triangle, one angle measures 90 degrees while the addition of the other two angles equals to 90 degrees. Hence if angle C is given as 90 degrees, then angles A and B added together equals 90 degrees (complementary angles equal 90 degrees).
Also, Sin A cannot be the same value as Sin B, since angle A and angle B are not equal in measurement. However, being complementary, the Sin of angle A equals the Cos of angle B.
If Sin A ≈ 0.766, then angle A ≈ 50 degrees
That makes angle B equal to 40 degrees. The Cos of B ≈ 0.766
Therefore if Sin A ≈ 0.766, then Cos B ≈ 0.766
If Cos B ≈ 0.766 then Sin A ≈ 0.766 are both correct
What is s
1 /2 s + 38 = 1642
Step-by-step explanation:
1/2s+38=1642
0.5s=1642-38
s=1604/0.5
s=3208
You play a game that involves rolling a die. You can roll as many times as you want, but if you roll a six your score is zero and your turn is over. You attempt to devise a good strategy by simulating several plays to see what might happen. On what roll do you expect to get a six for the first time?
Answer:
6
Step-by-step explanation:
P(6) = ⅙
Expected no. of trials for first 6:
1 ÷ (1/6) = 6
here is a right cone. what is the one shape of cross section we could create by slicing the cone parallel to its base
When a right cone is sliced parallel to its base, the resulting cross section is always a circle.
Explanation:If a cone is sliced parallel to its base, the shape that results is a circle. This is an aspect of conic sections, which are the curved shapes created when a plane intersects a cone. Other than circles, other possible shapes that we can obtain from slicing a cone include ellipses, parabolas, and hyperbolas, depending on the angles and location of the slice made. However, when the cut is parallel to the base, a circle is always formed. This is due to the consistent radius from the cone's axis to its slant height along the same parallel plane.
Learn more about Cones here:
https://brainly.com/question/10670510
#SPJ12
70 divided by the ratio 3:2
Answer:
42 : 28
Step-by-step explanation:
Sum the parts of the ratio , 3 + 2 = 5
Divide 70 by 5 to find the value of one part of the ratio
70 ÷ 5 = 14 ← value of 1 part of ratio, thus
3 parts = 3 × 14 = 42
2 parts = 2 × 14 = 28
70 divided in the ratio 3 : 2 is 42 : 28
What is the surface area of the triangular pyramid shown?round to the nearest tenth.
Answer:
57.6 cm/mm/m/in/ft squared
Step-by-step explanation:
You will need to answer the each triangle separately which you have to use the formula 1/2*b*h
5.2*1/2(6) = 15.6
4*1/2(6) = 12
5*1/2(6) = 15*2 (2 sides)
total = 57.6 cm/mm/m/in/ft squared
hope this helps
Briana is looking at the nutrition information on a bag of popcorn. According to the label, a single serving is 1/6 of the bag. How many servings are there in 4 bags?
Answer:
There are 2/3 of the content as servings in 4 bags
Step-by-step explanation:
In this question, we are asked to calculate the amount of servings in 4 bags
From the question, we can see that the amount of servings in a single bag is 1/6 of the bag.
Now the number of servings in 4 bags will be mathematically equal to ; 1/6 + 1/6 + 1/6 + 1/6 = 4 * 1/6 = 4/6 = 2/3
This means that in 4 bags, 2/3 of the total content is the servings
What can you tell about the mean of each
distribution?
) The difference between the mean cost to treat dogs at A New Leash on Life
Animal Clinic and the mean cost to treat cats at A New Leash on Life Animal
Clinic is about 19 times the MAD. This is a moderate difference.
The difference between the mean cost to treat dogs at A New Leash on Life
Animal Clinic and the mean cost to treat cats at A New Leash on Life Animal
Clinic is about 10 times the MAD. This is a moderate difference.
The difference between the mean cost to treat dogs A New Leash on Life
Animal Clinic and the mean cost to treat cats at A New Leash on Life Animal
Clinic is about 10 times the MAD. This is a large difference.
» The difference between the mean cost to treat dogs at A New Leash on Life
Animal Clinic and the mean cost to treat cats at A New Leash on Life Animal
Clinic is about 19 times the MAD. This is a large difference.
Answer: The difference between the mean cost to treat dogs at A New Leash on Life
Animal Clinic and the mean cost to treat cats at A New Leash on Life Animal
Clinic is about 10 times the MAD This is a large difference.
Step-by-step explanation:
I GOT THIS RIGHT! THIS IS THE ANSWER
The differences in mean costs to treat dogs and cats compared to the MAD at A New Leash on Life Animal Clinic suggest different levels of variability in the data. A 19 times difference labeled as 'moderate' implies high variability, while if labeled as 'large', the implication is that the variability is lower.
Explanation:The question relates to the comparison of the mean costs to treat dogs and cats at A New Leash on Life Animal Clinic, using the Mean Absolute Deviation (MAD) as a measure of variability. When we say that the difference between the mean cost to treat dogs and cats is about 19 times the MAD, and that this is a moderate difference, it suggests that the variability within each of the distributions is quite high, making a 19-fold difference in means seem less extreme. Conversely, the same difference being described as a large difference implies that the variability (MAD) is comparatively lower, hence a difference of the same scale appears more substantial relative to the spread of the data. This provides insight into the differences in treatment costs and the consistency of those costs within each group of animals.