Answer:
5249 years
Step-by-step explanation:
Half-Life of Carbon-14 is approximately 5730 years.
When we want to determine the age of a fossil using carbon dating, we use the formula:
[tex]t=\dfrac{\ln(N/N_0)}{-0.693} \cdot t_{1/2}[/tex]
Where:
[tex]t_{1/2}[/tex] is the half-life of the isotope carbon 14, t = age of the fossil (or the date of death) and ln() is the natural logarithm functionIn this case:
N(t)=100
[tex]N_o=53\\t_{1/2}\approx 5730$ years[/tex]
Therefore, the age of the mummy
[tex]t=\dfrac{\ln(53/100)}{-0.693} \cdot 5730\\=5249.43$ years\\t \approx 5249$ years[/tex]
Answer:
the answer is 6349 :)
Step-by-step explanation:
Someone put the correct answer in the comments so I figured I would put it here so you wouldn't miss it :) (It is correct I have tested it)
Suppose we know that a confidence interval for a population proportion is (0.572,0.662), with a sample proportion of p′=0.617. What is the margin of error?
Explanation:
The sample proportion 0.617 is at the exact midpoint of the interval from 0.572 to 0.662
We can confirm this by applying the midpoint formula.
The distance from the center (0.617) to either endpoint will be the margin of error. In other words, it is half the width of the confidence interval
L = lower boundary of confidence interval = 0.572
C = center of confidence interval = 0.617
U = upper boundary of confidence interval = 0.662
We have three methods to find the confidence interval
margin of error = U - C = 0.662-0.617 = 0.045margin of error = C - L = 0.617 - 0.572 = 0.045margin of error = (width)/2 = (U-L)/2 = (0.662-0.572)/2 = 0.045Each yielding the same result of 0.045
With the third method, you don't need to know the center of the confidence interval.
You want to install a 1 1 yd wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the walk? Use 3.14 for pi π.
Complete Question:
You want to install a 1 yd wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the walk? Use 3.14 for pi π.
Answer:
75.36 square yard
Step-by-step explanation:
From the question,
The diameter of this circular pool inside is 23 yd.
This means that the radius = Diameter/2 = 23yd/2 = 11.5 yd.
The formula for the area of a circle =
A = πr²
A = π(11.5)²
A =3.14 × 11.5²
A = 415.265 yd²
This is the Area of the inner circle.
We were told in the question also that he wants to install a walk of 1 yard
Hence, the radius of outer circle =
radius of inner circle +length of the walk
11.5yard + 1 yard
= 12.5 yard
A = πr²
A = 3.14 × (12.5)²
A = 490.625yd²
Area of the walk = Area of the Outer circle - Area of the inner circle
= (490.625 - 415.265)yd = 75.36 yd²
Therefore, the area of the walk is 75.36 square yards.
WHO ELSE HATES MATH LIKE ME!? OR ALGEBRA I SHOULD SAY! UGH!!! :( I NEED A PERSONAL STUDY BUDDY TO HELP ME GET THROUGH THESE TOUGH ?'S :( Brian works in a lab, and fills an empty cylindrical flask with 200 cubic centimeters of liquid. The flask has a radius of 3 cm and a height 12 cm. What percent of the volume of the flask is not filled with liquid? (Use π=3.14 . WHAT IS THE answer rounded to the nearest whole percent.)
Answer:
The answer is 41%.
Step-by-step explanation:
First, you have to find the total volume of the cylindrical flask using the formula. Then, you have to substitute the following values into the formula :
[tex]v = \pi \times {r}^{2} \times h[/tex]
[tex]let \: \pi = 3.14 \\ let \: r = 3 \\ let \: h = 12[/tex]
[tex]v = 3.14 \times {3}^{2} \times 12[/tex]
[tex]v = 3.14 \times 108[/tex]
[tex]v = 339.12 {cm}^{3} [/tex]
Next, given that 200cm³ of liquid is poured into the cylinder. So in order to find the volume of flask that is not filled by liquid, you have to subtract :
[tex]v = 339.12 - 200 = 139.12 {cm}^{3} [/tex]
Lastly, you have to find the percentage :
[tex] \frac{139.12}{339.12} \times 100 = 41\% \: (near. \: whole \: number)[/tex]
look at the figure below:
Answer: A) ΔABD ≡ ΔECD
Step-by-step explanation:
Match up the letters of the congruent sides.
AD = ED and BD = CD
A D B D → ABD
E D C D → ECD
This can be written in any order as long as the letters are matched properly. A & E, D & D, B & C
ADB or BDA or ...
EDC CDE
The only correct option provided is option A.
Answer:
Answer is option 1)
Answer is given below with explanations.
Step-by-step explanation:
[tex]triangle \: ABD \: and \: triangle \:ECD \: are \: congruent \\ length \: of \: BD \: = \: length \: of \: CD \\ \: and \: also \\ length \: of \: AD = length \: of \: ED \\ angle \: BDA \: = \: angle \: CDE \\ by \: \: side \: - angle - side \: postulate \\ triangle \: ABD \: and \: triangle \:ECD \: are \: congruent.[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
8 sump pumps working at the same rate drain a flooded basement in 6
1/4 hours. How long would it take 4 pumps to drain the same amount
from the basement?
Answer:
12 1/2
Explanation:
6 1/4 ÷ 2
= 25/4 × 2/2
= 25 × 2 ÷ 2
= 12 1/2
Form three equations starting with x=1/2
Answer:
Step-by-step explanation:
x - 1/2 =0
2x = 1
4x = 2
Answer:
x + 3 = 7/2
100x = 50
16/x = 24
Step-by-step explanation:
The value of x is 1/2 in the three equations.
Solve 6 + 5 √ 2 4 9 − 2 x = 7
[tex]
6+5\sqrt{249}-2x=7 \\
-2x=7-6-5\sqrt{249} \\
-2x\approx-77.9 \\
x\approx\frac{-77.9}{2}\approx38.95
[/tex]
Hope this helps.
A restaurant offers a special pizza with any 4 toppings. If the restaurant has 15 topping from which to choose, how many different special pizzas
are possible.
Answer: 1,365 possible special pizzas
Step-by-step explanation:
For the first topping, there are 15 possibilities, for the second topping, there are 14 possibilities, for the third topping, there are 13 possibilities, and for the fourth topping, there are 12 possibilities. This is how you find the number of possible ways.
15 * 14 * 13 * 12 = 32,760
Now, you need to divide that by the number of toppings you are allowed to add each time you add a topping.
4 * 3 * 2 * 1 = 24
32,760 / 24 = 1,365
There are 1,365 possible special pizzas
Using the combination principle, the number of special pizzas from which to choose from is 1365
Total number of toppings to choose from = 15 Number of topping on a special pizza = 4Using Combination :
nCr = [(n! ÷ (n - r)! r!)]
15C4 = [(15! ÷ (15 - 4)! 4!)]
15C4 = [(15! ÷ 11!4!)]
15C4 = (15 × 14 × 13 × 12) ÷ (4 × 3 × 2 × 1)
15C4 = 32760 / 24
15C4 = 1365
Therefore, 1365 different special pizzas can be made.
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10.
AA'B'C' is a dilation image of AABC. Which is the correct description of the dilation?
12
of a
А)
6
B' =B
С
Answer:
Option (2)
Step-by-step explanation:
In the figure attached,
ΔA'B'C' is a dilation image of ΔABC or both the triangle are similar.
Therefore, by the property of similarity of two similar triangles, corresponding sides these similar triangles will be proportional.
Scale factor = [tex]\frac{\text{Side of image triangle}}{\text{Side of the pre-image}}[/tex]
= [tex]\frac{\text{B'A'}}{\text{B'A}}[/tex]
= [tex]\frac{\text{(B'A+AA')}}{\text{B'A}}[/tex]
= [tex]\frac{(6+12)}{6}[/tex]
= 3
Therefore, scale factor is 3 when center of dilation is B.
Option (2) will be the answer.
A division problem is shown below. 4 and one-third divided by 5 and StartFraction 1 over 6 EndFraction The reciprocal of a fraction must be found to solve the problem. What is the reciprocal fraction that is required?
Answer:
6/5
Step-by-step explanation:
you have to flip the numerator and denominator. If it is 5/6 then it would be 6/5.
The reciprocal fraction that is required will be 31/26.
What is a fraction?A fraction is a numerical number that is represented in the numerator and denominator form.
We have Two mixed fractions, the First fraction = 4(1/3) and the Second fraction = 5(1/6).
Now,First, convert mixed fractions into simple fractions,i.e.First fraction = 4(1/3) = 13/3And,Second fraction = 5(1/6) = 31/6
Now, According to the question,
Divide First fraction by Second fraction;i.e.= (13/3) / (31/6)Now simplify,= ( 13 × 6) / (31 × 3)
Now, We get,= 26/31
So, the reciprocal fraction = 31/26.
Hence we can say that the reciprocal fraction that is required will be 31/26.
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A population has a known standard deviation of 1.27 and a sample space contains 85 values find the margin of error needed to create a 99% confidence interval estimate of the mean of the population
Answer:
The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]\sigma = 1.27, n = 85[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 2.575*\frac{1.27}{\sqrt{85}}[/tex]
[tex]M = 0.3547[/tex]
The margin of error needed to create a 99% confidence interval estimate of the mean of the population is of 0.3547
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. Andrew asked seven of his friends how many cousins they had. The results are listed below. Find the mean number of cousins. 15 12 5 14 4 4 6
Answer:
8.57Step-by-step explanation:
Mean is defined as the ratio of the total sum of all the given datas to the total number of data present. It is expressed mathematically as;
[tex]\overline x = \frac{ \sum Xi}{N}[/tex] where;
[tex]\overline x = mean\\Xi= individual \ data\\N = total\ amount\ of \ data[/tex]
Given N = 7
[tex]\overline x = \frac{15+12+5+14+4+4+6}{7}[/tex]
[tex]\overline x= \frac{60}{7} \\\overline x = 8.57[/tex]
The mean number of cousins is 8.57
If 1 card is drawn at random from a standard 52-card deck, what is the probability that the card drawn is a king?
Answer:
1/13 chance or roughly 7.7% chance.
Step-by-step explanation:
There are 4 Kings in a standard 52-card deck. If one King was to be pulled out, you'd get a probability of 4/52 chance of pulling a king. Simplified, 4/52 is 1/13 chance.
Please answer this correctly
Answer:
75%
Step-by-step explanation:
There are 6 numbers that fit the rule, 1, 2, 3, 4, 6, 8. Since there are a total of 8 numbers, there is a 6/8 chance picking one or 75% chance.
Answer:
50%
Step-by-step explanation:
so the original fraction is 4/8 or 1/2 so it is 50%.
a solution to the inequality n ÷ 4 – 125 > 300
Answer:
n > 1700
Step-by-step explanation:
n ÷ 4 – 125 > 300
Add 125 to both sides.
n ÷ 4 > 425
Multiply both sides by 4.
n > 1700
Answer:
n > 1700
Step-by-step explanation:
n ÷ 4 - 125 > 300
Add 125 to both parts.
n ÷ 4 > 300 + 125
n ÷ 4 > 425
Multiply both sides with 4.
n > 425 × 4
n > 1700
A toy falls from a window 80 feet above the ground. How long does it take the toy to hit the ground?
Answer:
2.24 s
Step-by-step explanation:
Given:
Δy = 80 ft
v₀ = 0 ft/s
a = 32 ft/s²
Find: t
Δy = v₀ t + ½ at²
80 ft = (0 ft/s) t + ½ (32 ft/s²) t²
t = 2.24 s
HELP PRAGYA! (x+6)(x-9)
Answer:
x^2-3x-54
Step-by-step explanation:
Once again FOIL is the way to go!
First, Outside, Inside, Last
x^2-3x-54
Answer:
[tex]x^2-3x-54[/tex]
Step-by-step explanation:
=> (x+6)(x-9)
USING FOIL
=> [tex]x^2-9x+6x-54[/tex]
=> [tex]x^2-3x-54[/tex]
Shopping at discount clothing stores can save you a lot of money. Felicia recently bought a jacket
at a discount store for $20 that would normally cost $60 at a retail store. What percent discount
off the retail price did Felicia get the jacket for?
Answer:
33.33%
Step-by-step explanation:
use a proportion
20/60 =10/30=1/3=33.333%
hope this helped!
(+3
+(+2)
help me with directed numbers pls
Answer:
5
Step-by-step explanation:
(+3 + (+2))
Remove the brackets.
3 + (+2)
3 + 2
Add the numbers.
= 5
Answer:
+5 or 5
Step-by-step explanation:
(+3)+(+2)
=> According to the rule, ( + )( + ) = ( + )
So,
=> +3+2
=> +5
HELP PLS!!! ITS DUE ASAP AND I NEED HELP ITS THE LAST QUESTION
Answer:
See below.
Step-by-step explanation:
Recall the volume of a sphere: [tex]V=\frac{4}{3}\pi r^3[/tex]
We know that the diameter is 14, so the radius is 7.
Plug it into the equation:
[tex]V=\frac{4}{3}(3.14)(7^3)\approx 1436.03cm^3[/tex]
There is 278 calories for 100g of kiri cheese, each portion of kiri cheese has 46 calories. how many kiri portions do I need to equal 50g?
Answer:
Two Portions!!!
Step-by-step explanation:
Please answer this question fast in two muintues
Answer:
W
Step-by-step explanation:
W is the vertex, you can see the letter above the angle
Answer:
W
Step-by-step explanation:
The vertex is where the 2 rays meet, or the corner of the angle
The vertex is W
11. If AD = 8 centimeters, what is BD?
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
what is the Expected value of the probability distribution also called?
Answer:
The expected value is also known as the expectation, mathematical expectation, mean, average, or first moment.
What is the volume of this aquarium?
Answer:
2,973 in^3
Step-by-step explanation:
3000- large section
27- smaller center cut-out
Answer:
2973 in³
Step-by-step explanation:
volume of cuboid - volume of cube
20*15*10 - 3³
3000 - 27
= 2973
The volume of the aquarium is 2973 in³.
Buchtal, a manufacturer of ceramic tiles, reports on average 2.3 job-related accidents per year. Accident categories include trip, fall, struck by equipment, transportation, and handling. The number of accidents is approximately Poisson. Please upload your work for all of the parts at the end. a) What is the probability that more than one accident occurs per year? Include at least 3 decimal places in your answer. Submit Answer Tries 0/5 b) Suppose that 5 years are randomly selected. What is the expected number of accidents in this time period? Submit Answer Tries 0/5 c) What is the standard deviation of the number of accidents in 5 years? Submit Answer Tries 0/5 d) What is the probability that exactly 8 accidents occur in 5 years? Include at least 3 decimal places in your answer. If you get an error on your calculator, please use an online source like Wolfram Alpha to calculate the number. Submit Answer Tries 0/5
Answereippcb.jrc.ec.europa.eu
Step-by-step explanation:
this I the wed go on it and you will get your answer
How to calculate a circumference of a circle?
Answer:
πd or 2πr
Step-by-step explanation:
To calculate the circumference of a circle, multiply the diameter of the circle by pi or multiply 2 times the radius times pi.
Hope that helps.
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Write down the formula for finding the circumference of a circle using the diameter. The formula is simply this: C = πd. In this equation, "C" represents the circumference of the circle, and "d" represents its diameter. That is to say, you can find the circumference of a circle just by multiplying the diameter by pi. Plugging π into your calculator will give you its numerical value, which is a closer approximation of 3.14 or 22/7.
` OR `
Plug the given value of the diameter into the formula and solve.[2]
Example problem: You have a circle tub with a diameter of 8 feet, and you want to build a white fence that creates a 6-foot wide space around the tub. To find the circumference of the fence that has to be created, you should first find the diameter of the tub and the fence which will be 8 feet + 6 feet + 6 feet, which will account for the entire diameter of the tub and fence. The diameter is 8 + 6 + 6, or 20 feet. Now plug it into the formula, plug π into your calculator for its numerical value, and solve for the circumference:
C = πd
C = π x 20
C = 62.8 feet
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●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Find the first, fourth, and eighth terms of the sequence A(n)=-3 X 2^n-1
1; –216; –279,936
–6; –48; –768
–12; –96; –1,536
–3; –24; –384
Answer:
The answer is
3, 24, 384Step-by-step explanation:
Usng the formula
[tex]A(n) = 3(2) ^{n - 1} [/tex]
Where n is the number of terms
For the first term
[tex]A(1) = 3(2)^{1 - 1} \\ = 3(2) ^{0} \\ = 3(1) \\ \\ = 3[/tex]
For the fourth term
[tex]A(4) = 3(2)^{4 - 1} \\ = 3 ({2})^{3} \\ = 3 \times 8 \\ \\ = 24[/tex]
For the eighth term
[tex]A(8) = 3 ({2})^{8 - 1} \\ = 3 ({2})^{7} \\ = 3(128) \\ \\ = 384[/tex]
Hope this helps you
Answer: –3; –24; –384
Step-by-step explanation:
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.y=-6x+6 y=-3x-3
Hey there! :)
Answer:
Has one solution.
(Graphed below)
Step-by-step explanation:
***The equations are graphed below, but this can also be solved algebraically.***
Set each equation equal to each other:
-6x + 6 = -3x - 3
Add 6x to both sides:
6 = 3x - 3
Add 3 to both sides:
9 = 3x
x = 3.
Plug in the value of x into an equation to solve for y:
y = -6(3) + 6
y = -18 + 6
y = -12.
The system of equations only has ONE solution at (3, -12).
On the graph, as well, the point of intersection is at (3, -12). This is the solution.
Two dice are rolled. What is the probability that the sum of the numbers rolled is either 6 or 9? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answer:
1/4
Step-by-step explanation:
There are 36 possible combinations. Of those 36, the ones that add up to either 6 or 9 are:
1+5, 2+4, 3+3, 4+2, 5+1, 3+6, 4+5, 5+4, 6+3
There are 9 combinations that add up to either 6 or 9. So the probability is 9/36, or 1/4.
The probability that the sum of the numbers rolled is either 6 or 9 is [tex]\frac{1}{4}[/tex] . In rounded to the nearest millionth, the probability is 0.25.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
Possible outcomes are
1+5, 2+4, 3+3, 4+2, 5+1, 3+6, 4+5, 5+4, 6+3.
The number of possible outcomes is 9.
Each dice has 6 possible outcomes.
Total number of outcomes = 6 × 6 =36
The probability is the ratio of total number of outcomes to possible outcomes.
The probability is 9/ 36 = 1/4 = 0.25
Hence, required probability is 1/4 or 0.25.
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