14.375 grams of the radioactive isotope will be left after 3 half-lives.
The initial mass of the isotope = 115 gm
after each half-life, the amount of the isotope is reduced to half
therefore,
after the first half-life, the mass of the isotope will become = 115/2
= 57.5 gram
now after the second half live, the mass will again be reduced to half of the previous mass = 57.5/2
= 28.75 gram
similarly, after the third half-life, the mass will be half of the previous mass = 28.75/ 2
= 14.375 gram
OR
simply we can write that
weight after 3 half-lives will be = 115/ 2³
= 115 / 8
= 14.375 grams.
So the mass after 3 half-lives is 14.375 grams.
A risky form of a chemical element that releases radiation as it breaks down and will become extra stable. Radioisotopes may additionally arise in nature or be made in a laboratory. In medication, they may be used in imaging exams and in treatment. additionally known as a radionuclide.
Atoms of equal detail with extraordinary numbers of neutrons are known as isotopes. Many elements have one or extra isotopes which might be radioactive. Their nuclei are risky, so they destroy down, decay, and emit radiation.
whilst utilized in cautiously controlled clinical programs, radioactive isotopes are safe and no longer almost as frightening as we first imagined. The radiation from those isotopes has a quick half of lifestyles and handiest give off low stages of radiation. Radioactive isotopes are not constantly risky, though. a few most effective ones supply tiny amounts of radiation. There are radioactive isotopes in nature all around us. maximum of them cause us very little damage.
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(1 point) college officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. how many randomly selected student
Probability Theory
P (K) =[tex]\frac{n (K) }{n (S)}[/tex]
P(K) : probability of selected K
n (K) : number of occurence of K
n (S) : number of all occurence
In question is not contain information about the number of students who curry a gun, knife, or other weapon and the number of all students. so, we can desribe that :
n (A) : the number of occurence of students who curry a gun
n (B) : the number of occurence of students who curry a knife
n (C) : the number of occurence of students who curry other weapon
and the number of all students is n ( A U B U C) -> union of sets
how many randomly selected student? in question, there is no specific about the student. so, we can answer with :
1) probability of students who curry a gun
P (A) = [tex]\frac{n (A) }{n (AUBUC)}[/tex]
2) probability of students who curry a knife
P (B) = [tex]\frac{n (B) }{n (AUBUC)}[/tex]
3) probability of students who curry other weapon
P (C) = [tex]\frac{n (C) }{n (AUBUC)}[/tex]
and if question want to estimate with percentage, we can multiply with 100%. example :
1) percentage of probability of students who curry a gun
P (A) = [tex]\frac{n (A) }{n (AUBUC)}[/tex] x 100%
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In the space provided below, solve the equation 4x² 768 = 0 for x algebraically. Write your answer in simplest radical form. Show all work.
Answer:
Step-by-step explanation:-b± √b²-4ac. X =
suppose that among the 6000 students at a high school, 1500 are taking honors courses and 1800 prefer watching basketball to watching football. if taking honors courses and preferring basketball are independent, how many students are taking both honors courses and prefer basketball to football?
Students taking both honors courses and prefer basketball to football is 450.
Total number of students at a high school = 6000
Number of students who has taken honors courses = 1500
Number of students who prefer watching basketball to football = 1800
Let event of taking honors courses be A
and event of preferring watching basketball be B
P(A) = 1500 / 6000 = 0.25
P(B) = 1800 / 6000 = 0.3
If both the event of taking honors courses and preferring watching basketball is independent then
By using property of independent events ,
P(A∩B) = P(A) . P(B)
= (0.25)(0.3) = 0.075
Number of students taking both honors courses and prefer basketball to football = 0.075 × 6000
= 450 Students
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Mr. Fitch needs to get a loan to replace the air-conditioning system in his home.
The cost of the replacement, including installation, is $4,348.00.
He can apply for a 5-year loan or a 3-year loan.
Both loans involve simple interest with an annual interest rate of 6.5%.
If Mr. Fitch applies for the 5-year loan, how much more will he pay in interest than with the 3-year loan?
If Mr. Fitch applies for the 5-year loan, the amount he will pay in interest with the 3-year loan is: $565.24.
How to find the interest amount?First step is to find the cost of replacement left
Cost of replacement = $4,348 x 6.5%
Cost of replacement =$282.62
Second step is to calculate the amount of 5-year loan
Loan = $282.62 x 5
Loan = $1413.1
Third step is to calculate the amount of the 3-years loan
Loan = $282.62 x 3
Loan = $847.86
Now let find the amount he will pay in interest with the 3-year loan
Amount = $1,413.1- $847.86
Amount =$565.24
Therefore the interest amount is $565.24.
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What is the range of the given function?
Responses
y≤3y is less than or equal to 3 - no response given
y≤0y is less than or equal to 0 - no response given
−6≤y≤3−6≤y≤3 - no response given
R (all real numbers)
The range of the given function, using it's concept, is given by the following option.
y≤3: y is less than or equal to 3.
How to obtain the range of a function?The range of a function is the set that is composed by all the output values on a function.
Om the graph of a function, we have that:
The input values are given by the x-axis, that is, by the horizontal axis.The output values are given by the y-axis, that is, by the vertical axis.Hence from the graph, the range of the function is given by the values of y of the function.
From the graph of the function given at the end of the answer, the function assumes values of 3 and greater, hence the first option is the correct option giving the range of the function.
Missing InformationThe function is given by the image presented at the end of the answer.
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4(y-4)=8
ANSWER WITH EXPLINATION PLEASE
Answer:
y=6
Step-by-step explanation:
4(y-4)=8
4×y-16=8
4×y=8+16
4×y=24
y=6
4(6-4)=8
4×2=8
Find two positive integers whose sum is 16 and the sum of squares is minimum.
x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.
According to the question,
The two numbers are positive and the sum of the two numbers is 16 and the sum of the squares of the two numbers is the minimum.
Now to solve the question we will consider,
x and y are the two numbers, such that x > 0 and y > 0
Sum of the numbers : x + y = 16
Sum of squares of the numbers: S = x²+ y²
x + y = 16 y = (16 - x)
Assume, S = x² + y²
S = x² + (16 - x)²
Now we will differentiate with respect to x
dS/dx = 2x+ 2(16-x)(-1)
2x-2(16-x)=0
2x-32+2x=0
4x-32=0
4x=32
x=32/4
x=8
As x > 0, x = 8
d²S/dx² = d/dx [2x+ 2(16-x)(-1)]
d²S/dx² = d/dx (2x) - 2 d/dx (16-x)
d²S/dx² = 2 - 2[0-1]
d²S/dx² = 4
Now when x=8
d²S/dx² = 4 ≥0
Therefore, the function S = sum of the squares of the two numbers is minimum at x = 8.
y = 16-8 = 8
Therefore, x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.
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a research team believes that a recently discovered treatment will have an effect on the dependent variable. they randomly selects a sample of 12 people, and with their permission, provides them a treatment. they then evaluate the evidence regarding whether their treatment had an effect. here's the data: the mean for their sample is 99. the mean for the population is 102, with a standard deviation of 11. assume a normal distribution for the individual scores. the research team sets their alpha level to .05. . calculate the z test, and decide whether the research team should: 0 - retain the null hypothesis 1 - reject the null hypothesis.
Using the z test the value of z is -0.9404 and the value of z the research team should 0 - retain the null hypothesis.
In the given question,
They randomly selects a sample of 12 people, and with their permission, provides them a treatment.
So n = 12
The mean for their sample is 99.
x = 99
The mean for the population is 102.
μ=102
A standard deviation of 11.
σ = 11
Test statistic z:
z = (x-μ)/σ /√n
Now putting the value
z = 99-102/11/√12
z=-3/11/3.45
z=-3/3.19
z= -0.9404
Test statistic z = -0.9404
From the value of z the research team should 0 - retain the null hypothesis.
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I need help with this, I "apparently get it wrong"
Answer:
Step-by-step explanation:
Which one adds up to 14 is the question? There are dots on the dice which correspond to numbers. The dots are saying that they are numbers. And if you get to 14 with the dices, you pick it.
Distribute and then Combine Like Terms: 5(3x + 4) + 7x
Answer:
22x + 20
Step-by-step explanation:
Distribute:= (5)(3x) + (5)(4) + 7x
= 15x + 20 + 7x
Combine Like Terms:= 15x + 20 + 7x
= (15x + 7x) + (20)
= 22x + 20
Answer:
22x +20
Step-by-step explanation:
5(3x + 4) + 7x
5 x 3x + 5 x 4 +7x
15x + 5 x 4 + 7x
15x + 20 + 7x
22x + 20
The volume of this prism is 378 cm*.
What is the length of x?
27 cm*
Answer:14
Step-by-step explanation:All you have to do is Divide 378 by 27 to get x
Hope This Helps!
The length of a rectangle is four more than triple the width. If the perimeter is 160 inches, find the dimensions.
The length and the width of the rectangle are 61 inches and 19 inches, respectively
How to determine the dimensions of the rectangle?The mathematical statement from the question is given as
Length of a rectangle is four more than triple its width.
Mathematically, this can be represented as
Length = 3Width + 4
The perimeter is given as
Perimeter = 160 meters
The perimeter is calculated as
Perimeter = 2 x (Length + Width)
So, we have
2 x (3Width + 4 + Width) = 160
Divide by 2
3Width + 4 + Width = 80
This gives
4Width= 76
Divide by 4
Width = 19
Recall that
Length = 3Width + 4
So, we have
Length = 3 * 19 + 4
Evaluate
Length = 61
Hence, the dimensions are 61 inches by 19 inches
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What is a, the starting term, for the function: f(x) = 300(1.16)^x?
The starting term of the function f(x) = 300 (1.16)^x is 300
What is an exponential function?This is a type of function that are of 3 main parts
the starting or initial valuebase function the exponentsConsidering the given problem, f(x) = 300(1.16)^x
the starting = 300
the base = 1.16
the exponents = x
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.
The base is what determines exponential growth or decay
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the sat math scores of 1,000 future engineers and physicists are recorded. what will be the relationship between the mean and median of the collected data? think about if you would expect the distribution of sat math scores to be a normal distribution, skewed right distribution, or skewed left distribution.
The relationship between the mean and median of the collected data is that the mean will be smaller than the median.
Since the SAT Math scores for these students will be mostly high scores, the distribution will be skewed to the left. Thus, the few low scores (outliers) will make the mean smaller than the median.
Outliers that do not change the mean have an impact just on the mean. As a result, the mean is frequently lower than that of the median when the distribution of data is skewed to the left. The mean is frequently higher than the median when the distribution is tilted toward the right. We anticipate that the mean and median in symmetrical distribution will be about identical in value. This is a crucial link between the connection here between mean and median as well as the distribution's form. Nevertheless, it isn't applicable to all sets of data. Collections of data sets are where exceptions happen much more frequently.
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a spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. (a) how fast is the radius of the balloon changing at the instant the radius is 50 centimeters?
0.015 the radius of the balloon changing at the instant the radius is 50cm
given that
a spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute
radius = 50 centimeters
now we need to find the volume of the balloon
Let V = volume of the balloon at time t
r = radius of the balloon at time t
V = (4/3)πr3
Given: dV/dt = 500
Find: dr/dt when r = 50
dV/dt = (4/3)(3πr^2)(dr/dt)
500 = 4π(50)^2(dr/dt)
dr/dt = 1/(20π)
dr/dt = 0.015 cm/min
0.015 the radius of the balloon changing at the instant the radius is 50cm
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Two trains are traveling at constant speeds on different tracks. Trains Train A is traveling 12.5 meters per second. What speed is Train B traveling? meters per second.
Train B is traveling faster because it traveled 100 meters in four seconds.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
We have to determine which train is moving faster based on the image.
We can tell by looking at the train speeds.
As per the formula,
distance/time = speed
Train A travels 12.5 metres in one second = 12.5/1 = 12.5 metres per second
Train B travels 100 meters in four seconds, hence its speed is 100/4 = 25 meters per second.
This is because it traveled 100 meters in four seconds, whereas train A covered 12.5 meters in one second.
Hence, train B is traveling faster.
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The question seems to be incomplete the correct question has been in attached file
f(x) = x
f(x) = 3
f(x) = 5-x
f(x) = 3-x
Domain
x=2
2
0≤x<2
3
f(x) = 1
f(x) = 2
Function Equation
Given f(x)=2−∣x−5∣
Domain of f(x) is defined for all real values of x.
Since, ∣x−5∣≥0⟹−∣x−5∣≤0
⟹2−∣x−5∣≤2⟹f(x)≤2
Hence, range of f(x) is (−∞,2].
What is the maximum or minimum value of the function what is the range y=-2x^2+32x-12.
The maximum or minimum value of the function y = -2x² + 32x - 12 is (8, 116) and the range of the function y = -2x² + 32x - 12 lies in the interval
(−∞ ,116).
Given, the function is y = -2x2 + 32x - 12
According to the question we have to extract the maximum or minimum value of the function.
The maximum or minimum of a function which is a quadractic function occurs at the point x = -b/2a.
If a is negative, then the maximum value of the function is f(-b/2a).
If a is positive, then the minimum value of the function is f(-b/2a).
According to this, we can derive the general equation as
fmax(x) =ax²+bx+c occurs at x = -b/2a.
From the given equation, comparing we get
a = -2, b = 32, c = -12
Substitute the value of a and b in in the general equation and we get
x = -32/2(-2)
x = -32/-4
x = 8
Put x = 8 in the given general equation,
y = -2(8)² + 32(8) - 12
y = -2(64) + 256 - 12
y = -128 + 256 - 12
y = 256 - 140
y = 116
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Tony planned to spend $100 for food this week. On Monday he spent $22 and on Thursday he spent $52. How much money dose he have left for the week
Answer:$26
Step-by-step explanation:
52+22=74
100-74=26
A dog kennel charges $40 for each night the dog stays in the kennel. Each day includes a 2 hour play time and
1 hour etiquette training. The kennel also charges a $10 bathing fee for a bath before the dog returns home.
Think of the linear function that demonstrates the cost of putting a dog in the kennel (c) in terms of the number
of nights (n)
Answer:
c=40n+10
Step-by-step explanation:
They charge 40$ per night from which we get 40n
The extra 10$ is from the bathing fee
The rest of the information they give us isn't useful in this case because they didn't ask us the cost per hour
Janet buys 4 bags of potatoes.
The first bag has 8 potatoes in it.
The second bag has 6 potatoes in it.
The third bag has 10 potatoes in it.
She has not yet counted the number of potatoes in the fourth bag.
To represent the total number of potatoes she has, Janet writes (8+6+10)
+x, where x is the number of potatoes in the fourth bag. Which expression
also represents the total number of potatoes Janet has?
2(4+3+5+x)
O 25+1+B)4x
O (8+6)(10+x)
O (8+6)+(10+x)
Answer:
(8+6)+(10+x)Step-by-step explanation:
2(4+3+5+x) Not valid since x represents the total number of potatoes in the fourth bag. The expression expands to (8+6+10 + 2x), not just x.25+1+B)4x Not valid as written, the expression has a new, undefined variable, B. Plus the 25+1 are not related to the actual inforamation. (8+6)(10+x) Not valid since there is no logic in multiplying the two expressions.(8+6)+(10+x) Valid: The expression can also be writte as 8+6+10+x, which matches the potatoe count in the four bags.Francesca has 2615 comic books.
She wants to put them into groups of 8.
How many comic books would be left over
after putting them into groups?
Answer: 7 comic books would be left after putting them into groups of 8.
Step-by-step explanation: There will be 326 groups of comic books. 326 x 8 = 2,608 which means that there will be 7 comic books left after putting them all into groups of 8.
3. What equation matches the graph below?
Answer:
B, or y - 1 = 1/2(x + 2)
Step-by-step explanation:
when you solve B, you get y = 1/2x + 2, which is the equation being shown on the graph.
True or false: The numerical coefficient of 14xy4z5 is 4.
Answer:
False
Step-by-step explanation:
The numerical coefficient is 14, not 4.
Answer:
it's False
Step-by-step explanation:
Trust me IT worth it
Savio leaves his home 9.00 to drive to a work appointment. He drives a distance of 40miles.
Savio thinks he drives at an average speed of 60 miles per hour.
If Savio is correct what time will he arrive at his appointment
Answer:
9:40
Step-by-step explanation:
Distance = rate x time
Let t = time
40 = 60t Divide both sides by 60
[tex]\frac{40}{60}[/tex] = t An hour would be 60 minutes so the number of minutes out of the total would be 40.
Doughnuts are sold in bags and cartons.
A bag holds 4 doughnuts and a carton holds 10 doughnu*
Tom buys B
bags of doughnuts and C cartons of doughnuts.
He buys a total of T doughnuts.
Write down a formula for T in
terms of B and C.
Answer:
Step-by-step explanation:
Answer:
b= c + t (the amount bought)
Step-by-step explanation:
I need help please!!!
The slope of the line that passes through (9, 1) and (-8, 2) is -1/17
How to find the slope?If we have a linear equation or a segment that passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by the formula:
slope = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that the two points are (9, 1) and (-8, 2), using the above formula we can find the slope to be:
slope = (2 - 1)/(-8 - 9)
slope = 1/-17 = -1/17
That is the slope of the line or segment that passes through the given points.
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Justin wants to find the volume of a rectangular box. He starts by placing a layer of cubes in the bottom of the box (as shown).
Each cube has a length, width, and height of `1/2` inches. He continues placing cubes in the box until it is full. What is the volume of the box?
The volume of the given rectangular box is given by 225 cubic inches.
We know that the volume of the rectangular box with length L and width W and height H is given by,
V = LWH
So given the length of rectangular box is = 12 1/2 inches = 25/2 inches
The width of rectangular box is = 4 1/2 inches = 9/2 inches
The height of box is = 4 inches
So the volume of the rectangular box = (25/2)*(9/2)*4 = 25*9 = 225 cubic inches.
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Sketch and Solve. A rectangular page is 2 inches longer than it is wide. If the diagonal of the pag is 52 inches, what is the perimeter of the page
The Perimeter of the Rectangle is 144cm;
What is the Perimeter of a Rectangle?
The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in meters, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.
A rectangle has four 90° angles.
The lengths of a rectangle's diagonals are equal. Rectangle perimeter is calculated using the formula perimeter of a rectangle = 2(l + w), where l is the rectangle's length and w is its width.
According to the question
Let the length of the rectangle be x cm;
So, The breadth of the rectangle will be: (x+2) cm;
And, we have the diagonal = 52 cm;
So,
we can use the Pythagoras triangle to find the value of x cm;
⇒[tex]x^{2} + (x+2)^{2} = (52)^{2}[/tex]
⇒[tex]2x^{2} +4+4x = 2704;\\[/tex]
⇒[tex]2x^{2} +4x = 2700[/tex]
⇒[tex]2x^{2} +4x - 2700 =0;[/tex]
By solving the above equation, we get:
x = 35 cm;
So, the length of the rectangle = is 35 cm;
Breadth of the rectangle = 37 cm;
and
Perimeter of the Rectangle = 2(35 + 37) cm;
The perimeter of the Rectangle = = 144 cm;
Hence,
The perimeter of the Rectangle = = 144 cm;
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A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122. 5 grams per apple. Calculate and interpret a 95% confidence interval for the mean weight per apple.
The average apple weight's 95% confidence interval is (119.14, 125.86).
According to one manufacturer, an apple weighs 120 grams on average with a 12-gram standard variation. According to statistics generated from a sample of 49 apples randomly selected from a shipment, the average weight per apple was 122. 5 grams.
Let,
n = 49
x = 122.5
σ = 12
To figure up and analyze a 95% confidence interval for the average apple weight;
The formula for a 95% confidence interval is
(x ± 1.96*σ√n)
(122.5 ± 1.96*12/√49)
(119.14, 125.86)
Consequently, a 95% confidence interval for the average apple weight is (119.14, 125.86).
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