Answer:
Function: A=1.5(1+0.114)^1000
Step-by-step explanation:
1.5 is the initial amount and 0.114 in the rate and the 1000 is the time
In carbon dating, the Carbon-14 concentration decays exponentially, and can be described by a formula involving its initial concentration and decay rate. To find a fossil's age with a concentration of 0.3 ppt, we use this decay formula, solve for t (time in millennia), and calculate the fossil's age.
Explanation:To determine the Carbon-14 concentration as a function of time and the age of a fossil with a concentration of 0.3 ppt, we will use the formula of exponential decay based on the half-life concept in carbon dating.
The formula for the carbon-14 concentration as a function of time (t, in millennia) is:
C(t) = C_0 × (1 - 0.114)^t
Where:
C(t) is the Carbon-14 concentration at time t,C_0 is the initial Carbon-14 concentration (1.5 ppt), and0.114 is the rate of decay per millennium (11.4%).To find the age of a fossil with a measured concentration of 0.3 ppt, we solve for t in the above equation with C(t) set to 0.3 ppt:
0.3 = 1.5 × (1 - 0.114)^t
Dividing both sides by 1.5 and taking the natural logarithm:
t = ln(0.3/1.5) / ln(1 - 0.114)
Solving this gives us the age of the fossil in millennia.
Data shows the probability of dying feom cardiovascular disease is 0.45 and that the probability from dying ofncancer is .22. What is the probability of dying from some other cause?
Answer:
0.33
Step-by-step explanation:
because 0.45 plus 0.22 is 0.67 which means the other probability is 0.33.
The probability of dying from some other cause will be 0.33. Probability always lies between 0 and 1.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
The given data in the problem is;
P(A) is the probability of dying from cardiovascular disease = 0.45
P(B) is the probability of dying from cancer = 22
P is the probability of dying from some other cause =?
The probability of dying from some other cause will be found as;
[tex]\rm P =1- P(A)+P(B) \\\\ \rm P =1- 0.45+0.22 \\\\ \rm P =0.33[/tex]
Hence the probability of dying from some other cause will be 0.33.
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Evaluate 2a + 4b
if a = 10 and b = 6
Answer:
44
Step-by-step explanation:
Answer:44
Step-by-step explanation:
2(10)+4(6)
20+24
=44
The decay rate, k , for a particular radioactive element is 2.5%, where time is measured in years. Find the half life of the element. (Round to one decimal place)
Given a decay rate of 2.5% per year for a radioactive element, the half-life of this element, calculated using first-order kinetics, would be approximately 27.7 years.
Explanation:The question seeks to find the half-life of a radioactive element given a decay rate of 2.5% per year. To solve this, we need to utilize the concept of first-order kinetics which is used to model radioactive decay.
First, we express the decay rate as a decimal, thus 2.5% is 0.025. To find the half-life or T1/2, we can make use of the formula T1/2 = ln(2) / k, where k is the decay constant or rate.
By inserting the values into this formula, it would be T1/2 = ln(2) / 0.025 which gives us approximately 27.7 years (rounded to one decimal place) as the half-life of the given radioactive element.
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The half-life is 27.7 years.
Half-life is the time required for half of the radioactive atoms to decay in a sample. In this case, the decay rate k = 2.5% is equivalent to 0.025 in decimal form.
By using the formula t1/2 = ln(2) / k, we can calculate the half-life.
Plugging in k = 0.025,
t1/2 = ln(2) / 0.025
= 27.7 years.
Therefore, the half-life of the element is approximately 27.7 years.
Complete Question:
The decay rate, k, for a particular radioactive element is 2.5%, where time is measured in years. Find the half-life of the element.
The half-life is ___ years. (Round to one decimal place as needed.)
The data shown has a least-squares regression line of y=3.2x−6.4.
Use the drop-down menus to complete the statements and identify the residual of the data point (8,19.2).
Point (8,19.2) is ___ the least-squares regression line.
A. on
B. below
C. above
The value of the least-squares regression line at x=8 is ___.
A. -6.4
B. 0
C. 12
D. 19.2
E. 25.6
So, the residual of the data point (8,19.2) is ____.
A. -19.2
B. -12
C. 0
D. 12
E. 19.2
Answer:
1) B. on, 2) D. 19.2, 3) C. 0
Step-by-step explanation:
1) The value of y according to the regression line is:
[tex]y = 3.2\cdot (8) - 6.4[/tex]
[tex]y = 19.2[/tex]
Hence, the point (8,19.2) is on the least-squares regression line.
2) The value of y according to the regression line is 19.2.
3) The residual is the difference between the value from the regression line and the real value. In this case, the residual value is 0.
Final answer:
The data point (8,19.2) lies on the least-squares regression line. The value of the least-squares regression line at x=8 is 19.2. Hence, the residual of the data point (8,19.2) is 0.
Explanation:
The data point (8,19.2) is on the least-squares regression line since when we substitute x=8 into the equation y=3.2x−6.4, we get y=3.2(8)−6.4 which simplifies to y=25.6−6.4, yielding y=19.2, which is exactly the y-value of the given data point.
The value of the least-squares regression line at x=8 is therefore 19.2 which corresponds to option D.
Since the observed y-value is exactly predicted by the regression line at this x-value, the residual for the data point (8,19.2) is 0, which represents the difference between the observed y-value and the value predicted by the regression formula. Therefore, option C is correct for the residual.
Which is a factor of x2 + 8x – 48? (x – 6) (x + 4) (x – 16) (x + 12)
Answer:
(x+12)
Step-by-step explanation:
The middle number is 8 and the last number is -48.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 8
Multiply together to get -48
Can you think of the two numbers?
Try -4 and 12:
-4+12 = 8
-4*12 = -48
Fill in the blanks in
(x+_)(x+_)
with -4 and 12 to get...
(x-4)(x+12)
But, since (x-4) isn't an option, the answer would be (x+12)
Answer:
(x + 12)
Step-by-step explanation: It's D on edg
A person is walking downhill at a constant speed. Which graph best represents the distance the person walks over time.
Answer:
Step-by-step explanation:
What is the base area of a cylinder with a volume of 150 cubic cm and a height of 10 cm?
Final answer:
The base area of a cylinder with a volume of 150 cubic cm and a height of 10 cm is 15 square centimeters, obtained by dividing the volume by the height.
Explanation:
To find the base area of a cylinder with a known volume and height, we can use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius of the base, and h is the height. Since the volume (V) is 150 cubic cm and the height (h) is 10 cm, we can rearrange the formula to solve for the base area (A): A = V/h.
By substituting the given values into our rearranged formula, we get: A = 150 cm³ / 10 cm = 15 cm². Thus, the base area of the cylinder is 15 square centimeters.
PLEASE HELP ME I DONT UNDERSTAND
Answer:
Picture #1: x=16 ; y=10
Picture #2: x=21 ; y=15
Picture #3: x=18
Step-by-step explanation:
Picture #1:
(8x-14)* and (5x+34)* are Alternate Exterior Angle so they are congruent. And (8x-14)* and (5y+16)* are supplementary so they equal 180*.
Picture #2:
(6x+7)* and (3x-16)* are supplementary so they equal 180*. And (6x+7)* and (11y-32)* are Vertical Angles so they are congruent.
Picture #3:
(7x-6)* and (4x-7)* are supplementary so they equal 180*.
If hannah uses 300 ounces for 3 people how much will she use for 9 people
Answer:
she will use 900 ounces for 9 people
Step-by-step explanation:
Answer:
900 ounces
Step-by-step explanation:
you would take 300 and divide it by 3 because thats how many people were listed, then you would get 100 per person as a unit rate. Multiply 100 by 9 and you have your answer!
3. Find the mean and the median of this data set: 9,6,5, 3, 28, 6, 4, 7.
Answer:
Mean= 8.5
Median= 6
Step-by-step explanation:
3,4,5,6,6,7,9,28
Median= Middle (If two middle number, add and divide by 2)
Mean= (3+4+5+6+6+7+9+28) ÷8
If you could only plot 5 points to graph y=sinx, which points would you choose? How would you connect these points? Please explain
If you could only plot 5 points to graph y = cosx, which points would you choose? How would you connect these points? Please explain this too!
Answer:
For both graph I would choose the following points: 0°, 90°, 180°, 270° and 360°. I would connect the points (in both cases) with an smooth arc.
Step-by-step explanation:
x sin(x) cos(x)
0° 0 1
90° 1 0
180° 0 -1
270° -1 0
360° 0 1
Rechel is paid $11 for every hour at her dog walking job she is also get tip.she earned a total of $73 for 6 hours of work.how much was her tip?
Answer:
So you would think 6 hours= 11$ so 6x11=66 now 73-66= 7 so her tip was 7 dollars
please mark me brainliest
Step-by-step explanation:
Answer:
1.16
Step-by-step explanation:
she earned 66 dollers the hour then she got and extra 1.16 for tip the hour and 7 dollers of tip the whole 6 hours
please mark brainliest
Fractions is equipment to 3/8
Answer:
Step-by-step explanation:
It is eqivilent to 37.5
I think you meant to say "equivalent" instead of "equipment"
To find equivalent fractions to 3/8, you would multiply top and bottom by the same number.
If we multiply the top and bottom by 5 for instance, then
3*5 = 15
8*5 = 40
So 3/8 is equivalent to 15/40
--------------
Another example: multiply top and bottom by 9
3*9 = 27
8*9 = 72
This means 3/8 is equivalent to 27/72
-------------
Now let's say you were asked if 15/40 was equivalent to 3/8
To check this, you would assume they are equal, then cross multiply like so
15/40 = 3/8
15*8 = 40*3 ... cross multiply
120 = 120
Since we end up with the same thing on both sides, we have confirmed that 15/40 = 3/8 is a true equation.
What is the greatest common factor of 72
and 18?
Answer: 2, and 33
Step-by-step explanation:
Answer:
the greatest common factor is 18
help and explain pls
Answer:
108 cm^2
Step-by-step explanation:
which expression is equivalent to -2/5(x + 0.8) + 1/50
Answer:
-0.4x - 0.30 or [tex]-\frac{2x}{5} - \frac{3}{10}[/tex]
Step-by-step explanation:
Change all the fractions to decimals.
-2/5 = -0.4 Distribute that over x and 0.8 1/50 = 0.02
you get -0.4x -0.32 + 0.02
Change all the decimals to fractions.
0.8 is 8/10 so -2/5 times 8/10 is -16/50
-2x/5 - 16/50 + 1/50 add or subtract the fractions to get -15/50 Then reduce (÷5)
-2x/5 - 3/10
What is the volume (V) and surface area (SA) of a rectangular prism that is 11 ft long, 8 ft wide, and 4 ft tall?Immersive Reader
5 + 4 – (10/2 – 8 × 3) × 4
Answer:85
Step-by-step explanation:
Use PEMDAS (Parentheses Expinents Multiplication Divison Addition Subtraction) in that order to solve in the correct order
Answer:
85
Step-by-step explanation:
first you have to reduce the factor with 2, them multiply the numbers.
Calculate the difference (when there is a "-" in front of an expression in parenthesis, change the sign of each term of the expression)
Multiply the numbers
Calculate the sum of the positive numbers
now, solution: 85
Which sequence represents an arithmetic sequence?
A −5, −7, −10, −14, −19, …
B 1.5, −1.5, 1.5, −1.5, …
C 4.1, 5.1, 6.2, 7.2, …
D −1.5, −1, −0.5, 0, …
Answer:
D
Step-by-step explanation:
We know that an arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is always constant.
−5, −7, −10, −14, −19, …
Here difference between -5 and -7 is -2
But difference between -10 and -7 is -3
⇒ Difference is not constant.
Therefore, this sequence does not represents an arithmetic sequence.
1.5, −1.5, 1.5, −1.5, …
Here difference between 1.5 and -1.5 is 3
But difference between -1.5 and 1.5 is 3
⇒ Difference is not constant.
Therefore, this sequence does not represents an arithmetic sequence.
4.1, 5.1, 6.2, 7.2, …
Here difference between 4.1 and 5.1 is 1
But difference between 6.2 and 5.1 is 1.1
⇒ Difference is not constant.
Therefore, this sequence does not represents an arithmetic sequence.
−1.5, −1, −0.5, 0, …
Here difference between -1.5 and -1 is 0.5
But difference between -1 and -0.5 is 0.5
⇒ Difference is constant.
Therefore, this sequence represents an arithmetic sequence.
plz mark brainliest
Answer:
D.−1.5, −1, −0.5, 0, …
Step-by-step explanation:
Latoya earns $25.05 for 3 hours of tutoring. How much money does latoya earn each hour?
Answer:
$8.35 per hour
Step-by-step explanation:
Take the dollars and divide by the hours to determine the dollars per hour
25.05/3
$8.35 per hour
Each bacterium in a petri dish splits into 2 bacteria after one day. The function b(d) = 600 • 24 models
the number of bacteria, b, in the petri dish after d days.
Part A)
What is the initial number of bacteria in the petri dish?
Part B)
How many bacteria will be in the petri dish after 5 days?
Answer:
(a)Initial Number of Bacteria=600
(b)[tex]\text{Number of bacteria after 5 days}=19200[/tex]
Step-by-step explanation:
Given an initial number [tex]b_0[/tex] of bacteria in a petri dish, and each bacteria splits into 2 bacteria after one day.
The function [tex]b(d) = 600 \cdot 2^d[/tex] models the number of bacteria, b after d days.
Part A
Given [tex]b(d) = 600 \cdot 2^d[/tex]
When d=0,
The initial number of bacteria in the petri dish,
[tex]b_0=b(0) = 600 \cdot 2^0=600[/tex]
Part B
After 5 days, when d=5
[tex]b(5) = 600 \cdot 2^5=600 \cdot 32\\\text{Number of bacteria after 5 days}=19200[/tex]
Find the area of the shaded sector below. Use 3.14 for
Answer:
816.4
Step-by-step explanation:
i multiplied 65,4 and 3.14 to get 816.4
To plot the point (3,4) on a scatter plot, which of the following steps should you follow? move three places vertically and four places horizontally move three places horizontally and four places vertically move three places vertically and three places horizontally move four places horizontally and four places vertically
Answer:
You should move 3 places horizontally, and 4 places vertically.
Step-by-step explanation:
Final answer:
To plot the point (3,4) on a scatter plot, you should follow:
Move three places horizontally and four places vertically.Explanation:
To plot the point (3,4) on a scatter plot, you should follow these steps:
First, move three places horizontally from the origin along the x-axis; this represents the x-coordinate of the point. Next, from that position, move four places vertically along the y-axis; this represents the y-coordinate of the point.
By doing this, you will have plotted the point (3,4) correctly on the scatter plot.
This process is based on the convention that the first number in the ordered pair (x,y) corresponds to the horizontal (x-axis) movement while the second number corresponds to the vertical (y-axis) movement.
Therefore, plotting a point on a scatter plot or any Cartesian plane involves finding the x-coordinate on the x-axis and then finding the y-coordinate on the y-axis and marking the point where these two meet.
Can y’all help me please
Answer: fourths
Step-by-step explanation:
Mona is hang gliding \dfrac{5}{4}
4
5
start fraction, 5, divided by, 4, end fraction kilometers above sea level. Directly below her, she sees a whale 0.20.20, point, 2 kilometers below sea level.
Which of the following expressions represents the distance between Mona and the whale?
Choose 1 answer:
Answer:
A
Step-by-step explanation:
i promise it's A.
Mona is hang gliding 1.25 kilometers above sea level and a whale is 0.2 kilometers below sea level. The total distance between them is the sum of both distances, which is 1.45 kilometers.
Explanation:The distance between Mona and the whale is given by the sum of 2 distances. One is Mona's altitude above sea level (5/4=1.25 kilometers) and the other is the whale's depth below sea level (0.2 kilometers). Both values should be added because both distances are defined with respect to the sea level, and their signs indicate direction rather than distance. Therefore, the expression that represents the distance between Mona and the whale is 1.25 km+0.2 km = 1.45 km, where 1.25 km is the distance Mona is gliding above the sea level and 0.2 km is the distance the whale is under the sea level.
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The expression y? - 10y + 24 has a factor of y-4. What is another factor of y? - 10y + 24?!
y-20
y-14
y-8
y-6
Answer:
y=6
Step-by-step explanation:
y² - 10y + 24
factor: y - 4
24 / -4 = -6
y - 6 is the other factor.
(y-4)(y-6) ⇒ y(y-6) -4(y-6) = y² - 6y -4y + 24 ⇒ y² - 10y + 24
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The other factor of the expression y² - 10y + 24, other than y - 4, is y - 6. The expression can be factored as (y - 4)(y - 6).
Explanation:The given expression is y² - 10y + 24. You have given that one factor is (y - 4). To find the other factor of the equation, we can divide the whole equation by (y - 4). By doing this, we find out that the other factor is (y - 6).
So, the expression y² - 10y + 24 can be factored as (y - 4)(y - 6).
This concludes that other than (y - 4), the other factor of the expression y² - 10y + 24 is (y - 6).
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Factor the trinomial 3x2 + 16x + 21
Answer:
(3x+7)(x+3)
Step-by-step explanation:
Factors 3x^2+16x+21
3x^2+16x+21
=(3x+7)(x+3)
Answer:
[tex]3 {x}^{2} + 16x + 21 \\ 3 {x}^{2} + 9x + 7x + 21 \\ 3x(x + 3) + 7(x + 3) \\ = (3x + 7)(x + 3)[/tex]
Given the diagram below, what is m_D?
1080
108
Answer:
The correct Awnser is Awnser choice C. (Or third one)
Answer:c)72
Step-by-step explanation:u got it right on ape
Rotation maps point K24,-15 to K-15,-24 whats the rotation?
Answer:
90 degree CW
Step-by-step explanation:
Since the point is at (24, -15) and was rotated to (-15, -24):
x, y --> y, -x
This is a 90 degree rotation clockwise
Simplify -3(2x-7) + 5(4x-8).
Answer:
14x-19
Step-by-step explanation: Now can someone answer my question look at my page