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.)
Which sale gives the greatest percent discount? 1) Take 25% off, 2) original price reduced by 30%, 3) on sale at 60% of the original price, 4) it depends on the original price.
The greatest percent discount is the option where the item is on sale at 60% of the original price. This is because you are paying the smallest percentage (60%) of the original price compared to the other options, representing the largest discount.
Explanation:The question is pertaining to discounts and how to determine which option gives the greatest percent discount. Finding the greatest percent discount involves comparing the different percentage decreases from the original price. We can ignore any impact of sales tax for this particular comparison.
Here are the discounts rephrased in terms of how much of the original price you would pay:
25% off - You pay 75% of the original price.Original price reduced by 30% - You pay 70% of the original price.On sale at 60% of the original price - You pay 60% of the original price.Now, comparing these percentages (75%, 70%, and 60%), the smallest percentage represents the largest discount. Therefore, option 3, where the item is on sale at 60% of the original price, represents the greatest discount as you're paying the smallest percentage of the original price. The original price does not impact which discount is greater since we are comparing percentages, not absolute values, which means the answer does not depend on the original price.
Final answer:
Comparing percent discounts shows that being on sale at 60% of the original price (Option 3) is effectively a 40% discount, which is the greatest discount among the given options.
Explanation:
The question asks about comparing different percent discounts to determine which one is the greatest. To compare the discounts, we consider a hypothetical original price and apply each discount to see which reduced price is the lowest.
Option 1: 25% off means the sale price is 75% of the original price.
Option 2: A reduction of 30% means the sale price is 70% of the original price.
Option 3: On sale at 60% of the original price means the sale price is exactly that, 60% of the original price.
Option 4: The sale that offers the greatest percent discount does not depend on the original price because percentages are relative, not absolute values.
Considering these options, Option 3, being on sale at 60% of the original price, is equivalent to a 40% discount, which offers the greatest percent discount.
True or false order matter in ratio
Answer:
true
Step-by-step explanation:
Order matters because if you switch it around it means a totally diffrent thing for example 1:2= 1/2 and 2:1 = 2/1. you see it really does matter.
What is the volume (in cubic units) of a cone with a radius
of 3 units and a height of 16 units? Assume that pie = 3.14
and round your answer to the nearest tenth when
necessary.
Answer:
150.72
Step-by-step explanation:
Used calculator
3. A numbers is subtracted from seven. When the result is divided by
three, the quotient is two. What is the number?
Answer:
so a number s (s) is subtracted from seven (7 take away s or 7-s) when the result (7-s) is divided by 3 [(7-s)/3] the quotient is 2 (=2)
(7-s)/3=2
multiply both sdis by 3
7-s itmes 3/3=2 times 3
7-s=6
subtract 7 from both sdies
-s=-1
multily -1
s=1
7-x=y
y/3=2
y=6
7-x=6
-x= -1
x=1
What is the surface area of the prism in square inches?
Sin.
3 in
14 in.
8 in
60 square inches
168 square inches
276 square inches
304 square inches
Answer:
The answer is B.276.
Step-by-step explanation:
Got it right on Edge 2020 :)
Have a great day!!!! :)
Five times two fifths
Answer:=2
Step-by-step explanation:
Determine the solution by using substitution. Write your answer as a point below (x,y).
Answer:
x is 1 and y is negative 2. (1, -2).
Step-by-step explanation:
Hope this helps!
ANSWER
X=1 and y=-1
Hopefully this is the correct answer
What is the equation of a circle with center (8,1) and radius 6?
A. (x - 3)2 + (y - 1)2 = 6
B. (x - 3)2 + (y - 1)2 = 36
C. (X + 8)2 + (y + 1)2 = 36
D. (X + 8)2 + (y + 1)2 = 6
Answer:
(x - 8)² + (y - 1)² = 36
None of the above
Step-by-step explanation:
Equation of a circle:
(x - h)² + (y - k)² = r²
(x - 8)² + (y - 1)² = 6²
(x - 8)² + (y - 1)² = 36
what is x+4x+6x= simplify with work
Answer:
11x
Step-by-step explanation:
You can add all the coefficients together:
1+4+6 = 11
Answer:
11x.
Step-by-step explanation:
Combine like terms, they are alike because they share the same variable. Add x with 4x which is 5x, or you could do this. x+ x+x+x+x= 5x. 5x means you have 5 x's. Then combine 5x with 6x which is 11x. Hope this helps!
URGENT! What is the Range of the function y= 7cos(9x) ?
Answer:
-7 ≤ f(x) ≤7
Why:
The set of values of the dependent variable for which the function is good.
Due: Thursday at 11:00 PM
6
.
At the beginning of class, Mrs. Smith asked each of her 25 students to write his/her name on an index card and place
it in a closed container. Mrs. Smith draws a card in the morning and replaces it and repeats the process at the end of
the day. What is the probability that the same student will have his/her name drawn both times in the same day?
Answer: 1/25
Step-by-step explanation:
A storage shed in the shape of a cube has a height of 12 ft. There are 16 identical cube-shaped boxes in the shed. The edge of each box is 2.5 ft. How much space is left in the shed?
There are____ cubic feet left in the shed.
Answer:
576
Step-by-step explanation:
Answer:
1478ft³
Step-by-step explanation:
12x12x12=1728 ft³
16(2.5x2.5x2.5)= 250ft³
1728-250=1478ft³
There are 1478ft³ left in the shed
The mean percent of childhood asthma prevalence in 43 cities is 2.23%. A random sample of 31 of these cities is selected. What is the probability that the
mean childhood asthma prevalence for the sample is greater than 2.6%? Interpret this probability. Assume that o = 1.24%.
The probability is
(Round to four decimal places as needed.)
Given Information:
Mean percent of childhood asthma = μ = 2.23%
Sample size = n = 31
Standard deviation = σ = 1.24%
Required Information:
P(X > 2.6) = ?
Answer:
P(X > 2.6) = 0.0475 = 4.75%
Step-by-step explanation:
Let X is the random variable that represents percent of childhood asthma prevalence.
We want to find out the probability that the mean childhood asthma prevalence for the sample is greater than 2.6%
[tex]P(X > 2.6) = 1 - P(X < 2.6)\\\\P(X > 2.6) = 1 - P(Z < \frac{x - \mu}{\frac{\sigma}{\sqrt{n} } } )\\\\P(X > 2.6) = 1 - P(Z < \frac{2.6 - 2.23}{\frac{1.24}{\sqrt{31} } } )\\\\P(X > 2.6) = 1 - P(Z < \frac{2.6 - 2.23}{0.222} )\\\\P(X > 2.6) = 1 - P(Z < \frac{0.37}{0.222} )\\\\P(X > 2.6) = 1 - P(Z < 1.67)\\[/tex]
The z-score corresponding to 1.67 is 0.9525
P(X > 2.6) = 1 - 0.9525
P(X > 2.6) = 0.0475
P(X > 2.6) = 4.75%
Therefore, there is 4.75% probability that the mean childhood asthma prevalence for the sample is greater than 2.6%
How to use z-table?
Step 1:
In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 1.6)
Step 2:
Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 1.67 then go for 0.07 column)
Step 3:
Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.
Using the normal distribution and the central limit theorem, it is found that that there is a:
0.0485 = 4.85% probability that the mean childhood asthma prevalence for the sample is greater than 2.6%. The interpretation is that when many samples of 31 are chosen, around 4.85% of them will have an asthma prevalence greater than 2.6%.
---------------------------------
When the distribution is normal, the z-score formula is used, with [tex]\mu[/tex] as the mean and [tex]\sigma[/tex] as the standard deviation.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. Each z-score has a p-value associated with it.This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X. For a sample of n observations, by the Central Limit Theorem, the standard deviation is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]---------------------------------
Mean of 2.23% means that [tex]\mu = 2.23[/tex]Standard deviation of 1.24% means that [tex]\sigma = 1.24[/tex]Sample of 31 means that [tex]n = 31, s = \frac{1.24}{\sqrt{31}} = 0.2227[/tex]---------------------------------
The probability of a sample mean above 2.6% is 1 subtracted by the p-value of Z when X = 2.6. Thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2.6 - 2.23}{0.2227}[/tex]
[tex]Z = 1.66[/tex]
[tex]Z = 1.66[/tex] has a p-value of 0.9515.
1 - 0.9515 = 0.0485.
0.0485 = 4.85% probability that the mean childhood asthma prevalence for the sample is greater than 2.6%. The interpretation is that when many samples of 31 are chosen, around 4.85% of them will have an asthma prevalence greater than 2.6%.
A similar problem is given at https://brainly.com/question/22934264
A rock climber climbs at a rate of 720 feet per hour. Write and solve an equation to find the number of minutes m it takes for the rock climber to climb 288 feet.
Answer:
The equation is y=12x. It takes 24 minutes for the rock climber to get to 288 feet.
Step-by-step explanation:
Since we know there are 60 minutes in an hour, we can divide 720 by 60. This gives us 12. Therefore, for every minute, the rock climber gets 12 feet higher. Assuming y is the height in feet, and x is the time in minutes, we can create the equation y=12x. Now, to find how long it takes to get to 288 feet, we will substitute y with 288.
288=12x
288/12 = 12x/12
24 = x
Now, we have time in minutes that it takes to get to 288 feet.
Hope this helps!
The equation is y=12x.
It takes 24 minutes for the rock climber to get to 288 feet.
The calculation is as follows:
here we know that
One hour = 60 minutes
so, by dividing 720 from 60 we get 12
here we assume the time in minutes be x
So, the equation is
y = 12x
288=12x
288/12 = 12x/12
24 = x
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4
A farmer ties 4 bags on his mule. If the
mule can carry up to 200 lb and each
bag weighs 30 lb, how many more bags
can the mule carry?
Answer:
the mule can carry 2 more bags
Step-by-step explanation:
Q4) Kiarah collects data throughout the basketball season and uses these 1 point
data to determine the probabilities of different teams playing in the league
championship game. The probabilities for her four favorite teams playing in
the championship game are shown below. Which of these teams is least
likely to play in the championship game?*
• Tigers: P =
• Redbirds: P =
• Bulldogs: P =
•Titans: P =
a. Tigers
B. Redbirds
C. Bulldogs
D. Titans
Answer:
C. Bulldogs
Step-by-step explanation:
In this question, we want to compare several numbers with different denominators and find out which number is the least. To compare this number, we have to change the denominator into the same number by finding the least common multiple (LCM) of the 4 numbers. The factor of each number will be:
3= 3 ^1
5= 5^1
8= 2 * 2 * 2 = 2^3
2= 2^1
We can find the LCM by multiplying a higher exponent of each prime number. The LCM will be:3^1 * 5^1 * 2^3 = 120
Each number will be:
Tiger= 2/3 * 40/40= 80/120
Redbird = 4/5 * 24/24= 96/120
Bulldogs = 3/8 * 15/15 = 45/120
Titans = 1/2 * 60/60 = 60/120
As you can see, the team with the lowest chance to play is Bulldogs = 45/120
Answer:
bulldogs (i think)
Step-by-step explanation:
Please answer ASAP! Can someone help? 25 points! Please show your work!
A diameter of a circle has endpoints P(-10, -2) and Q(4, 6).
a. Find the center of the circle.
b. Find the radius. If your answer is not an integer, express it in radical form.
c. Write an equation for the circle
you and a friend play a game twice. what is the probability that you win both games? P(win) = 1/2
Answer:
1/4
Step-by-step explanation: 1/2*2=1/4
The probability of winning two games in a row, with each win having a 1/2 chance, is 1/4 or 25 percent, calculated by multiplying the individual probabilities for each game using the product rule.
The probability that you win a game is given as 1/2, and since the games are independent, the probability of winning both games in a row is found by multiplying the probabilities of each individual game. Using the product rule, P(win game 1 and game 2) = P(win game 1) × P(win game 2).
Since P(win) = 1/2 for each game, we simply calculate:
P(win both games) = (1/2) × (1/2) = 1/4.
Therefore, the probability of winning both games is 1/4 or 25 percent.
If A represents the number of pencils in a pack, which expression represents 6 packs of pencils?
A +6
A-6
Ax6
A6
Answer:
Ax6
Step-by-step explanation:
For example, If you had 2 pencils in a pack and there were 6 packs of pencils. You would do 6 times 2 to find out how many pencils you have in total. In other words, you do A times 6.
Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 71^\circ$, $\angle STU = 36^\circ$, and $\angle TUS = 73^\circ$, then what is $\angle NZM + \angle NPM$ in degrees?
Answer:
<NPM + <NZM = 146°
Step-by-step explanation:
Given:
In triangle STU: M, N and P are the midpoints of the line TU, US and ST respectively.
Line UZ is the altitude of the triangle STU
<TSU =71°, <TSU = 36°, <TUS = 73°
From the diagram:
N is the midpoint of line SU and M is the mid point of line UT.
∴ Line NM is parallel to line ST
P is the mid point of line ST and M is the mid point of line UT
∴Line PM is parallel to line SU
N is the mid point of line SU and P is the mid point of line ST
∴Line NP is parallel to line UT
Δ SPN = Δ STU = 36°
<SPN + <NPM + <MPT (Sum of angles in a triangle = 180°)
<UST = <MPT = 71°
36° + <NPM + 71° = 180°
<NPM + 107° = 180°
<NPM= 180°-107°
<NPM= 73°
In ΔSNZ, line SN = line NZ
∴ side SN = side NZ
< NSZ = <NZS = 71°
<MTZ = <MZT = 36°
<NZS + <NZM <MZT = 180° (Sum of angles in a triangle = 180°)
71° + <NZM + 36° = 180°
107° + <NZM = 180°
<NZM = 180° - 107°
<NZM = 73°
<NPM + <NZM =73° + 73°
<NPM + <NZM = 146°
Help me asap ok thanks
Answer: total profit = $418
======================================================
Work Shown:
June
Income = (4 lawns)*($27 per lawn) = $108
Expenses = ($32 for gas)+($12 for trim line) = $44
Profit = income - expenses = 108-44 = $64
----------------------------
July
Income = (12 lawns)*($20 per lawn) = $240
Expenses = ($89 for gas)+($29 for blade sharpening) = $118
Profit = income - expenses = 240 - 89 = $151
----------------------------
August
Income = (16 lawns)*($20 per lawn) = $320
Expenses = ($101 for gas)+($16 for oil) = $117
Profit = income - expenses = 320-117 = $203
----------------------------
Total profit = (june profit)+(july profit)+(august profit)
Total profit = (64) + (151) + (203)
Total profit = $418
If the final result was negative, then we would call this a loss. However, we have a positive value, so we go with a profit.
What is the area of the shaded region?
Given:
Radius of in circle (r) = 2 cm
Radius of out circle (R) = 4 cm
To find:
The area of the shaded region.
Solution:
The value of π = 3.14
Area of in circle = πr²
= 3.14 × 2²
Area of in circle = 12.56 cm²
Area of out circle = πR²
= 3.14 × 4²
Area of out circle = 50.24 cm²
Area of the shaded region = Area of out circle - Area of in circle
= 50.24 - 12.56
= 37.68 cm²
The area of the shaded region is 37.68 cm².
2. Ms. Bever has one roll of toilet paper with 500 sheets. How many days will the roll of toilet
paper last if she uses 5 sheets of toilet paper every time she uses the washroom. One the
average day, Ms. Bever uses the washroom 6 times. How many days will she have toilet paper
for?
Answer: 30 days
Step-by-step explanation: 5 x 6 = 30 and she has 500 sheets it would take her about 30 days
Ms. Bever uses 30 sheets of toilet paper per day. A roll of 500 sheets would last her approximately 16.67 days, which means it will last for 16 full days.
Ms. Bever uses 30 sheets of toilet paper per day since she uses the washroom 6 times and uses 5 sheets each time (5 sheets * 6 uses = 30 sheets per day).
To find out how many days a roll will last, we will calculate the number of total sheets divided by the sheets used per day. So, with a roll of 500 sheets, the calculation is 500 sheets / 30 sheets per day = approximately 16.67 days.
Since Ms. Bever cannot use two-thirds of a sheet, the toilet paper will last for 16 full days, with some extra sheets left over which aren't sufficient for another full day of use.
Solve the problem.
2) There are 5 roads leading from Charleston to Mattoon, 6 roads leading from Mattoon to Toledo,
and 3 roads leading from Toledo to Greenup. How many ways are there to get from Charleston to
Greenup?
A) 180
B) 14
C) 90
D) 30
Answer:
There will be 90 ways to reach Greenup from Charleston.
Step-by-step explanation:
Option C: 90 is correct.
Let's name all the ways and try to visualize the roads.
C = Charleston
M = Mattoon
T = Toledo
G = Greenup
Task = Charleston to Greenup. How many different ways to reach?
1 1
2 2 1
C 3 M 3 T 2 G
4 4 3
5 5
6
So, Refer to this above diagram.
If we Start from C then go to 1 and then go to M and then go to 1 and then go to T and then go to 1 and then go G.
If you notice, in this single possibility we have 3 ways: C to 1 to M, M to 1 to T, T to 1 to G.
It means we will have: 5 x 6 x 3 = 90 number of ways to reach greenup from Charleston.
The total number of ways to get from Charleston to Greenup is option C) 90.
To determine this, multiply the number of roads for each section:
Charleston to Mattoon: 5 roadsMattoon to Toledo: 6 roadsToledo to Greenup: 3 roadsThen, multiply the numbers of roads for all the sections: [tex]5 * 6 * 3 = 90[/tex].
PLEASE HELP ASAP!!!!!!!
A.) If two lines are parallel, then the same-side interior angles formed are congruent.
B.) If two lines are parallel, then the corresponding angles formed are congruent.
C.) Vertical angles are congruent.
D.) If two lines are parallel, then the alternate interior angles formed are congruent.
Answer: D
Step-by-step explanation:
The reason that justifies Step 2 in the proof is Vertical angles are congruent.
Therefore, the correct answer is C. Vertical angles are congruent.
Vertical angles are angles that are opposite each other when two lines intersect.
They are always congruent, regardless of whether the lines are parallel or not.
In the given diagram, angles ∠NQT and ∠SQR are vertical angles. Therefore, they are congruent, and Step 2 of the proof is justified.
The other answer choices are not correct:
A: Same-side interior angles are only congruent when the lines are parallel.
B: Corresponding angles are only congruent when the lines are parallel.
D: Alternate interior angles are only congruent when the lines are parallel.
Therefore, the correct answer is C. Vertical angles are congruent.
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ANother math question -_-
Answer:
point c is the correct answer
Step-by-step explanation:
A factory produces weighted balls to use for exercise by filling spherical rubber shells of different sizes with the sand like material. The materials density is 1.5 grams per centimeter. Assuming the shell weighs 10 grams, what should the balls radius so, when full, it weighs 1 kilogram(or 1000 grams)?
Answer:
r=5.4
As mentioned above, the actual \goldE{\text{total quantity}}total quantitystart color #a75a05, start text, t, o, t, a, l, space, q, u, a, n, t, i, t, y, end text, end color #a75a05 is 1000-10=\goldE{990}1000−10=9901000, minus, 10, equals, start color #a75a05, 990, end color #a75a05 grams, since we are trying to find the volume of the air within the shell.
Let's denote the ball's radius as rrr. Then, the \maroonD{\text{volume}}volumestart color #ca337c, start text, v, o, l, u, m, e, end text, end color #ca337c is \maroonD{\dfrac43\pi r^3}
3
4
πr
3
start color #ca337c, start fraction, 4, divided by, 3, end fraction, pi, r, cubed, end color #ca337c.
Now we can plug \blueE{\text{density}=1.5}density=1.5start color #0c7f99, start text, d, e, n, s, i, t, y, end text, equals, 1, point, 5, end color #0c7f99, \goldE{\text{total quantity}=990}total quantity=990start color #a75a05, start text, t, o, t, a, l, space, q, u, a, n, t, i, t, y, end text, equals, 990, end color #a75a05, and \maroonD{\text{volume}=\dfrac43\pi r^3}volume=
3
4
πr
3
start color #ca337c, start text, v, o, l, u, m, e, end text, equals, start fraction, 4, divided by, 3, end fraction, pi, r, cubed, end color #ca337c in the equation.
Kaden makes 2 cups of salsa for a party. The 6 guests share the salsa equally. Write a fraction that shows how much each guest eats.
Answer:
1/6
Step-by-step explanation:
if it's split equally between 6 people then each gets 1/6
Final answer:
Each guest at the party would get ⅓ cup of salsa.
Explanation:
Kaden makes 2 cups of salsa for a party and the 6 guests share the salsa equally. To determine how much each guest eats, we divide the total amount of salsa by the number of guests. We perform the following calculation:
Total amount of salsa: 2 cupsNumber of guests: 6We divide the total cups of salsa, which is 2, by the number of guests, which is 6:
2 cups ÷ 6 guests = ⅓ cup per guest
Therefore, the fraction that shows how much each guest eats is ⅓ cup.
Gabriel makes a model of a pyramid with the dimensions shown. A square pyramid. The square base has side lengths of 12 inches. The triangular sides have a height of 11 inches. Gabriel wants to paint the model. How much paint will he need? The area of the square base is in.2. The area of each triangular face is in.2. Gabriel will need in.2 of paint.
Answer:
The area of the square base is 114 in. 2
The area of each triangular face is 66 in. 2
Gabriel will need 408 in. 2 of paint
What is the measure of Angle M R N? Triangle M R N. Angle N is 98 degrees. Side N M extends to form exterior angle with a measure of 109 degrees.
Answer: Angle MRN equals 11 degrees (11°)
Step-by-step explanation: Please see the picture attached for details.
The triangle MRN has been drawn such that angle N as shown equals 98 degrees. Then line NM has been extended and the exterior formed there is 109 degrees. That means angle M can be calculated as follows
Angle M = 180 - 109 {Angles on a straight line equals 180}
Angle M = 71
Now we have two angles given as angle N which is 98 degrees and angle M which is 71 degrees.
Angle MRN can now be calculated as follows;
∠ MRN = 180 - (71 + 98) {Sum of angles in a triangle equals 180}
∠ MRN = 180 - 169
∠ MRN = 11
Therefore angle MRN measures 11 degrees.
Answer:16
Step-by-step explanation:Take 98 and subtract it from 109